al hossan cs3 - alhosn university j. of engineering & applied sciences 4 (2) ... n. m hassan, r....

A bi-annual, refereed journal published byALHOSN University - Abu Dhabi - UAE

Volume 4 Number 2 May 2012

ChairmanProf. Abdulla Ismail

EditorProf. Abdul Rahim Sabouni

Associate EditorProf. Raymond Tennant

MembersDr. Abdellatif QamhaiehDr. Dr. George MarkouDr. Mama ChachaDr. Marko Savic

Managing EditorDr. Al Haj Salim Mustafa

Address:P.O. Box : 38772Abu Dhabi - UAETel. : +971 2 4070700Fax : +971 2 4070799E-mail : [email protected] : www.alhosnu.ae

ISSN 2076-8516

AHU J. of Engineering & Applied Sciences 4 (2) 2012© 2012 ALHOSN University

CONTENTS

ARTICLES

MODELING OF ROCKS UNDER DIRECT SHEAR LOADINGBY USING DISCRETE ELEMENT METHOD 5A.K. Alzo’ubi.

CURRENT STATE OF CONTAMINATION OF DOLPHINS FROMTHE FRENCH MEDITERRANEAN COASTAL ENVIRONMENT(2007-2009) IN PCBs AND DDTs 21Emmanuel Wafo,Véronique Risoul, Thérèse Schembri, Mama Chacha,Véronique Lagadec, Frank Dhermain, Henri Portugal

CHLORINATED PESTICIDES IN THE BODIES OF DOLPHINS OF THEFRENCH MEDITERRANEAN COASTAL ENVIRONMENT 35Emmanuel Wafo, Mama Chacha, Véronique Risoul, Thérèse Schembri,

MODELING OF REINFORCED CONCRETE STRUCTURES WITH3D DETAILED FINITE ELEMENT MODELS 47George Markou, Manolis Papadrakakis

A DEVELOPED MICROPLANE MATERIAL MODEL FOR NONLINEARFINITE ELEMENT ANALYSIS WITH EMPHASIS ON CONFINEDREINFORCED CONCRETE COLUMNS 65Omar Al-Farouk Salem Al-Damluji , Ihsan A.S. al-Shaarbaf, Wamidh Ajil Jassim

SETTING MAXIMUM AND MINIMUM SPEED LIMITS FORFREEWAY SAFETY IMPROVEMENT. 93N. M Hassan, R. A. Kady

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MODELING OF ROCKS UNDER DIRECT SHEAR LOADING BY USING DISCRETE ELEMENT METHOD

A.K. Alzo’ubi.Department of Civil Engineering, CECS, Abu Dhabi University, P.O.Box 1790, Al Ain, UAE

Email: [email protected]

ABSTRACT: The geometrical properties are of great concern in characterizing a rock mass. The blocks in a rock mass are formed by flaws with different patterns formed in nature under different geological circumstances. One of the block tessellation models is the Voronoi tessellation, which can be utilized in the discrete element method and used to create realistic rock mass simulation this approach is called UDEC-DM. The UDEC-DM approach has been implemented to model experimental direct shear tests and the results were in good agreement. The effect of degree of persistency of joints inside a direct shear sample was modeled numerically and compared to the behaviour of intact rock. Both closed and opened joints models showed a good agreement with the laboratory results.

KEYWORDS: Numerical Analysis, Tensile Failure, Discrete Element, and Direct Shear

1. INTRODUCTION

Many numerical analysis approaches have been developed in the geotechnical engineering domain, for example: limit equilibrium, discontinuum, continuum, and hybrid methods. Stead et al. [1] presented many of these methods and their disadvantages and advantages; in particular the use of hybrid tech-niques such as the modeling approach presented in this paper is promising and can handle fracturing of rock masses. Cundall [2] proposed the discrete element numerical modeling method to allow for the finite displace-ment and rotations of discrete deformable or rigid blocks, as well as for complete detachment. In the discrete element method, a rock mass is represented as discrete blocks, and discontinuities are treated as interfaces between bodies. The contact displacements and forces at the interfaces are calculated by tracing the movements of the blocks. Applied loads or forces to a block system can cause disturbances that propagate and result in movements. The propagation speed in this dynamic process depends on the physical properties of the blocks and the contacts [3]. The behaviour of the solid material and the dis-continuities must be considered. A time-stepping algorithm must be used to represent the dynamic behaviour, and within a time-step, the velocities and accelerations are assumed to be constant. The time-step is small enough to prevent the propagation of disturbances between one block and its neighbors. This explicit time marching solution scheme is identical to that used by the explicit finite difference method for continuum analysis. The time-step restriction applies to both blocks and contacts as follows. For deformable blocks, the size of the zone is used, and the stiffness of the system includes contributions from both the intact rock modulus and the stiffness at the contacts. For rigid blocks, the block mass and interface stiffness between blocks define the time-step limitation. The discrete element method calculation step alternates between application of a force displacement law at the contacts and application of Newton’s second law at all blocks. Local and global damping is necessary to keep the model under control. This logic is used by the Universal Distinct Element Code (UDEC) [3].


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In UDEC, a rock joint is represented numerically as a contact surface formed between two block edges. In general, to detect and identify a contact, for each pair of blocks that touch (or is separated by a small enough gap), data elements are created to represent the point contacts. The adjacent blocks can touch along a common edge segment or at discrete points where a corner meets an edge or another corner (Itasca, [3]). Thus, the number of contact points is increased as a function of the blocks, thereby in in-creasing the cycle time. A number of different constitutive models can be applied to the contacts and the solids, such as the Mohr Coulomb failure criterion, which is one of the most acceptable failure criterion in rock mechanics (Figure 1).

Figure 1: Mohr-Coulomb surface in principal space

Pierce et al. [4] introduced a synthetic rock mass model to simulate jointed rocks that contain joints; this model is also capable of modeling discrete fractures and rupturing inside the rock mass. In their model rounded shaped particles were used which is rarely the case of rock masses.

2. DAMAGE MODEL

The progressive failure of geo-materials is a gradual and time-dependent failure process at localized areas, followed by the redistribution of the stresses in the slope. These new stresses build up and cause the propagation of the failure. If this fracturing continues, a rupture surface connecting all the failed parts will form. Many factors can cause progressive failure, such as the time-dependent degradation of the strength parameters, increasing pore pressures, and/or thermal stresses. In addition, the presence of non-persistent joints and the heterogeneity of the rock mass might cause tensile stresses inside the rock mass and also the initiation and propagation of cracks that might lead to failure. Figure 2 presents a conceptual diagram of the tensile stresses resulting from the compression forces in a block assembly. Cho et al. [5] showed that the development of the through-going rupture surface through intact material is preceded by tensile fracturing.

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Figure 2: Block assembly subjected to compression forces and the resulting tensile stresses at the bond (Modified from Potyondy and Cundall, [6]

To simulate the rock failure processes by using discrete element modeling, a polygonal block compo-nent is added to the usual capability of UDEC [3] to model discrete fractures by using the Voronoi tes-sellation generator command, which creates randomly sized polygonal blocks. The Voronoi tessellation creates random points within the specified region. Points are also distributed uniformly along each edge. The position of interior points may be relaxed by iteration to create more uniform block distribution. The line segments forming the Voronoi polygons are then generated by constructing perpendicular bisectors of all triangles which share a common side.

Figure 3: Illustration of the polygonal structure used to simulate blocky intact rock using 100 itera-tions to generate the flaws.

The randomly sized polygons are analogous to the flaws in the intact rock that can represent grain-boundary flaws or larger-scale internal flaws (Figure 3). The size, seed and number of iterations can be varied to generate randomly sized blocks. For example decreasing the number of iterations to generate the blocks in Figure 3 will result in less uniform blocks. These flaws are defined such that they have intact rock properties and do not contribute additional jointing to the joint system of the rock mass. It should be noted that the term “Damage” is used to describe fracturing of flaws and joint, not plasticity damage.


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Lorig and Cundall [7] introduced the Voronoi tessellation to model a concrete member as assemblage of blocks bonded at common boundaries. Failure is simulated by progressive breakage of bonds, Lorig and Cundall’s [7] simulation showed the ability to visualize deformed shape and crack development with displacement. Watson et al. [8] used the Voronoi joint to simulate material flow toward dam reservoir in the Checkerboard Creek rock slope, British Columbia, Canada.

Alzo’ubi et al. [9] used this approach to model rock slopes that include persistent and non-persis-tent smooth rock joints. This polygonal block model will be referred to as the UDEC damage model (UDEC-DM) in this paper. This polygonal block pattern provides a unique method for simulating ten-sile and/or shear fracturing through intact rock. As they add a new degree of freedom in the model that allows for development of non-directional rupture surface or localized fracturing [7], [10]. Cohesion, friction, and tensile strength can be assigned to the boundaries of these polygonal blocks such that the strength is the same as that of intact rock. Local variation in strength and stiffness can also be applied if required, to simulate any anisotropy in the rock mass such as rocks in sedimentary rocks susceptible to toppling [11].

While the polygonal flaw structure shown in Figure 3 may represent the flaws found in crystalline rocks, these discontinuities are not commonly observed in sedimentary rocks. For sedimentary rocks, the main set of joints should be generated first and then the flaws generated next inside the major bedding units this would simulate the anisotropic rock masses. This approach produces polygonal shapes that are more representative of the cross-cutting joints observed in sedimentary rock than other shapes. Hence, in the UDEC-DM, the user has control over the creation of the internal flaws to match the geological condi-tions of the rock mass being analyzed.

The blocks created in this approach assigned the elastic, isotropic model of material behaviour. This model exhibits linear stress-strain behaviour with reversible deformations upon unloading. In this mod-el, the relation of stress to strain in increments is expressed by Hookes law. The blocks can be attached together by specifying the friction, cohesion, and tensile bond strength. The boundaries of the blocks were assigned a Mohr-Coloumb criterion that allows slippage and irreversible deformation. The values assigned to these strengths influence the strength of the synthetic rock and the nature of cracking and failure. Once the shear stresses exceed the strength, the shear strength is set to its residual value as long as blocks stay in contact, which is a function of compressive normal stress and the friction angle at the contact. However, once a tensile bond fails the tensile strength of the contact is set to zero.

This flaw pattern provides an extra degree of freedom that is useful to simulate the fracturing of the rock masses through intact material. Thus, failure is not restricted to the joints but, rather, can be developed simultaneously and/or progressively in both intact and joint segments. The random shape of the blocks generated in the modeling approach can allow tensile stresses to arise and produce tensile fracturing throughout the intact material.

This approach is not based on a fracture mechanics approach where fracture propagation is controlled by the fracture toughness and the stress intensity factor at the crack tip. Instead a failure approach is adopted in the UDEC-DM where fracturing occurs when the stress level exceeds the strength in any flaw inside the model. In the present study, the Mohr-Coulomb criterion with a tensile cutoff is used, and the flaws may fail either in shear or in tension.

A.K. ALZO’UBI.

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3. FLAW PATTERNS IN ROCK

In addition to the geomechanical properties of rock mass flaws, the geometrical properties are of great concern in characterizing a rock mass. The blocks in a rock mass are formed by flaws with different patterns formed in nature under different geological circumstances. Understanding the origin of a rock mass would help to have a general idea about the pattern of those flaws. For example, in sedimentary rocks, flaws are generally three perpendicular sets with different degree of persistency. In plutonic rocks, these flaws have an irregular shape that intersect each other at different angles.

Dershowitz and Einstein [12] pointed out that two main approaches have been used to describe the as-semblage of geometric flaw characteristics in a rock mass: the disaggregate characterization in which each flaw is described separately, for example, through spacing distribution, and the aggregate charac-terization in which the interdependence of the flaw characteristics is captured through the formulation of flaw system models. The models can represent real flaw geometries and, as a result, can represent the rock mass geometry. Examples of these flaw model systems are the orthogonal system, which consists of three sets of orthogonal flaws, and the mosaic block tessellation models. According to Ambarcumjan [13] the mosaic tessellation randomly subdivides of the plane into non-overlapping convex polygons. The block shapes can vary and be irregular, and the flaws are the faces of those blocks. Dershowitz and Einstein [12] stated:

Since jointing in Mosaic Block Tessellation models is defined by the faces of a process of non-overlapping blocks completely containing the rock mass, they are appropriate for joint systems which are actually the result of a process of block formation in a rock mass. One example of such a joint system is jointing in columnar Basalts. (p. 26).

One of the mosaic block tessellation models is the Voronoi tessellation, which can be utilized in the discrete element modeling approach and used to create realistic rock mass simulation. Dearman [14] discussed the types of blocks formed in natural rock masses. He stated that flaws’ patterns and the difference in spacing and degree of persistency within each flaw set determined the shape of the resulting blocks. For example, these blocks can be described in three dimensions as polyhedral, cubic, etc. (see Figure 4). These examples are few of many patterns that can be encountered in natural rock formations.

4. FAILURE CRITERION OF THE FLAWS

In UDEC, the numerical contacts are of two types: corner-to-corner contacts and edge-to-corner con-tacts. However, in rocks, edge-to-edge contact is important because it corresponds to the case of a rock joint closed along its entire length. A physical edge-to-edge contact corresponds to a domain with ex-actly two numerical contacts. The joint is assumed to extend between the two contacts and to be divided in half, with each half-length supporting its own contact stress. Incremental normal and shear displace-ments are calculated for each point contact and associated length [3].

In the normal direction, the stress-displacement relation is assumed to be linear and controlled by the constant normal stiffness such that


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Figure 4: Rock mass block shape, the numbers refers to various flaw sets(modified from Dearman, [14])

where is the effective normal stress increment, and is the normal displacement increment. There is also a limiting tensile strength, T, for the joint in the normal direction. If the tensile strength is exceeded

, then . In the shear direction, the response is governed by constant shear stiffness. The shear stress, , is controlled by a cohesive (c) and frictional strength according to the Coulomb slip model (Itasca, [3]), such that

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where is the elastic component of the incremental shear displacement, and is the total incremen-tal shear displacement (Itasca, [3]).

The basic joint model used in UDEC that captures several of the features in the normal and shear di-rection is the Coulomb slip model with tension cutoff. The Coulomb slip model is an elastic-perfect plastic model (Figure 5). Notice that in Figure 5, should be drawn in space not shear-normal stress space and this diagram is only for demonstration purpose. The Coulomb model can also be used to approximate a displacement-weakening behaviour by setting the joint cohesion, friction, and tensile strength to reduced values whenever either the tensile or shear strength is exceeded.

Figure 5: Coulomb-slip model used to simulate the flaws behavior

Lajtai [15] stated that at low normal stress the rock mass strength is totally controlled by the tensile strength (Equation 6). The tensile stresses cause nonlinearity in the failure envelope in the Mohr-Cou-lomb space. Moreover, Cho et al. [5] found that the formation of the shear zone was preceded by tensile fracturing aligned with the major principal stress direction. In addition, in rock slopes, the majority of the back-calculated cohesion is mostly apparent cohesion due to asperities and interlocking but not true cohesion.

Moreover, Skempton [16] showed that the long term (decades long) stability of slopes in stiff overcon-solidated clay was a function of the loss of cohesion with time. In soils, cohesion is a function of Van de Vaals’ bonding forces which are influenced by environmental factors such as water content. In many rocks, the cohesive forces are dominated by ionic and covalent bonds, which are not readily susceptible to environmental factors. However, these bonds are weaker in tension than in shear. Hence, if tensile stresses exist, these bonds may break at relatively low stress magnitudes.

Aydin and Basu [17] showed, using Brazilian tensile tests that the tensile strength of a rock is extremely sensitive to the degree of weathering. They found that the tensile strength could decrease by an order of magnitude depending on the extent of weathering, and that the stiffness of the rock decreased as the tensile strength decreased. In other words, weathering may be a significant factor in controlling the


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behaviour of rock slopes, if the stability of the slope is controlled by the tensile strength. Hence, in this study, the tensile strength of the flaws was decreased gradually to study the effect of tensile strength degradation on rock slopes, while, cohesion and friction angle were kept constant. Figure 5 presents the modeling procedure used in this paper.

where is the tensile strength, and is the normal stress.

The normal stiffness of the flaws is calculated from Equation 7. At the beginning of each simulation, the shear stiffness is assumed to be equal to the normal stiffness, and then the response of the model is examined. Next, a trial-and-error procedure is adopted to match the deformation of the numerical model with the actual measured deformation, if any. If the measured deformation is not available, the shear stiffness is changed to match the expected behaviour of the model.

According to Itasca [3], up to ten times the normal stiffness calculated from Equation 7 can be assigned to the flaws. If the joint stiffnesses are greater than 10 times the equivalent stiffness, the solution time of the model will be longer than for the case in which the ratio is limited to ten, without a significant change in the behaviour of the model:

where = normal stiffness, is the bulk modulus, is the shear modulus, and is the smallest width of an adjoining zone in the normal direction (see Figure 6).

Figure 6: Definition of zone dimension used in stiffness calculation, Equation 7.

Small scale flaws can be very stiff i.e., relative to the size of the model, as the flaws can represent grain-boundary flaws or larger scale internal flaws which have a very small aperture and justify the relatively high normal and shear stiffness used in some models.

A.K. ALZO’UBI.

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5. DAMAGE MODEL ON DIRECT SHEAR TESTS

Lajtai [18] conducted a series of tests using plaster of Paris to simulate intact rock blocks. The blocks, containing rectangular voids to represent the discontinuous nature of the joints, were subjected to direct shear stress at various normal stresses. Lajtai argued that for non-continuous joints, the minor principal stress in the rock bridge is tensile even if the all around stresses are compressive, and that these tensile stresses are responsible for forming the fractures in the rock bridges. Lajtai concluded that at low nor-mal stress, tensile fracturing in the rock bridge was the dominant mode of failure, but that as the normal stress increased, the failure mode progressively became dominated by shear mechanisms.

Based on his finding, Lajtai suggested that the failure of rock containing intact rock bridges between joints could be represented by a nonlinear envelope whose nonlinearity occurred because of the non-uniform mobilization of friction [19]. At low normal stress, the tensile strength controlled the failure while at high normal stress; the frictional strength dominated the failure process. The properties of the plaster of Paris used by Lajtai [18] were as follows: unconfined compressive strength of 4.1 MPa, a friction angle of 37°, tensile strength of 1.1 MPa, and an estimated cohesion of less than twice the tensile strength. The Mohr-Coulomb failure criterion with tension cutoff was used to control the flaws’ behaviour in this modeling approach.

To model the direct shear test, the cohesion, the friction angle and the tensile strength needed to be known prior to conducting the analysis. However, the tensile strength and the friction angle were known while the cohesion was unknown, so the UDEC-DM was utilized to back-calculate the cohesion strength. A two-to-one model was prepared with an edge length of 7 mm, which is the same edge used in the direct shear model. The model was subjected to a constant displacement rate to induce stresses until failure was achieved. The axial stress and vertical strain were monitored by using Fish functions. A trial-and-error study was conducted to match the unconfined compressive strength of 4.1 MPa by varying the cohesion of the flaws while keeping the tensile strength and friction angle constant, Table 1 shows the flaws’ properties used in the unconfined compressive strength model. Figure 7(a) shows the stress-strain curve resulting from this test. The failed sample is shown in Figure 7(b).

a) Stress-strain response b) Model of intact rock after failure

Figure 7: The unconfined compressive strength of plaster of Paris


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Figure 8: Effect of cohesion strength on the uniaxial strength

Figure 8 shows the variation of the cohesion with the unconfined compressive strength, at cohesion of 1.2 MPa the unconfined compressive strength was approximately equal to the UCS of the laboratory sample. The UDEC-DM model was used to simulate Lajtai’s direct shear experiments (Figure 9). The tensile strength of the plaster of Paris was approximately 1.1 MPa, and the friction angle was 37°, these values assigned to the flaws in the model.

The plaster of Paris Young’s modulus can range between 2-10 GPa (Vekinis et al., [20]). In this model, the blocks had a Young’s modulus of 4.5 GPa. The UDEC-DM model was calibrated to these properties such that the uniaxial compressive strength was captured as mentioned above (Table 1). In these simula-tions, the flaw size in the plaster of Paris was very small, i.e., sub-mm scale. However, in the UDEC-DM model, the length of the polygonal block was limited to 7.0 mm.

ited to 7.0 mm.

Figure 9: The UDEC-DM model used to simulate Lajtai’s direct shear experimental results

Different block lengths were evaluated ranging from 5 mm to 11 mm, and the length used in this study (7 mm) provided a reasonable compromise between accuracy and simulation time. A total of 23 UDEC-DM models were carried out, Figure 10 compares the UDEC-DM model results with those obtained by

A.K. ALZO’UBI.

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Lajtai. These results suggest that this approach is capable of capturing the behaviour of discontinuous rock joints subjected to direct shear and automatically captures the nonlinear failure envelope com-monly observed in rock testing. Lajtai [17] also presented a direct shear test results from samples with closed joints.

Table 1: Comparison between Lajtai’s plaster of Paris model properties and those used in the UDEC-DM

Properties UDEC-DM Lajtai

Friction angle(°) 37 37

ót(MPa) 1.1 1.1

C(MPa) 1.2 < 2

Normal Stiffness (GPa/m) 40

Shear Stiffness (GPa/m) 20

Joint aperture (mm) 0.1

Figure 10: Comparison of UDEC-DM model results with the results from direct shear testson plaster of Paris and open joints (data from Lajtai, [18])

The direct shear experiment was also modeled numerically by using the UDEC-DM in the same man-ner for the model with the open joints and the same properties shown in Table 1. A close agreement was achieved between the experimental results and the numerical simulation (see Figure 11). Notice that the direct shear tests were performed under a limited range of normal stress. More data points are needed to explain the small discrepancy between the results in Figure 11; however, the trend of the data is in good agreement. In addition, while the actual friction of the joint is unknown the joints in the numerical model were assigned a friction angle of 30°.


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6. THE EFFECT OF DISCONTINUITY PERSISTENCE

The effect of discontinuity persistence has been investigated by using numerical modeling of the direct shear test. The degree of persistence (k) is equal to the ratio between the total lengths of the joint seg-ments to the total length of the model in the direction of shearing. Five models with k = 0, 0.25, 0.5, 0.7 and 1.0 were simulated. Joints were inserted at each side of the model (see Figure 13). A friction angle of 30° was used for both the flaws and the joint segments. The flaws ware assigned a tensile strength of 1.0 MPa, while the tensile strength and the cohesion for the joint segments were equal to zero. Table 1 shows the properties used in this model with a friction angle of 30° for the intact rock and the joints to allow shear failure at low (k). The normal and shear stiffness of the joints were the same as the flaws in table 1.

Figure 11: Comparison of UDEC-DM model results with the results from direct shear testson plaster of Paris and closed joints [18]

Figure 12: Non-persistent joints direct shear model

Normal stress was applied, and the model was subjected to shear displacement from left to right (see Figure 12). The shear stresses were monitored along the forced shear plane. For each model, the normal stress was varied between 0.3 to 2.4 MPa. Figure 13 shows the failure envelope for the five models. As the length of the joints increased, the rock became weaker in the shear, and the shear strength decreased

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as a sign of the progressive failure effect due to the presence of the joints. As the normal stress increased the rock mass dilation will be inhibited, in nature the rock mass, the intact material will be sheared off and will not contribute to the total rock mass strength under relatively high normal stress (compared to the UCS) and sliding will occur on the basic friction angle. Moreover, at high value of k (greater than 0.7), the contribution of the intact rock to total strength will be less compared to the contribution at low values of k as shown in Figure 13.

Figure 13: Failure envelope of non-persistence joint direct shear model

If k>0, i.e., if the rock is jointed, the strength of the rock is controlled by both the joints and the intact material. At k=1.0, the strength was totally controlled by the basic friction angle of the rock (30°). As the normal stress increased, the shear strength decreased to the ultimate strength at a normal stress lower for high k than for low k. As the normal stress approached or exceeded the unconfined compressive strength of the rock material, the degree of discontinuity had no effect as the strength of the rock was controlled by the friction angle of the crushed material (the basic friction angle). In order to clarify this point, the shear strength of the jointed models was normalized to the intact material strength derived from the UDEC-DM direct shear model. The results are plotted against the normal stress in Figure 14.

As this figure shows, the difference between the normalized strength and the frictional strength de-creased as the normal stress increased, and eventually at high normal stress, the strength of the partially jointed rock (k<1) became equal to the ultimate strength derived from the basic friction angle. These results support the importance of the joints in rock mass analysis, especially in low-stress environments such as those involving slope stability problems. To build a complete geological model for a rock mass, the planes of weakness must be included to contribute to the rock mass’s total strength. This modeling approach can explicitly model the joints and allow fractures to initiate and propagate and cause coales-cence between the pre-fractured joints. The existence of joints inside the rock mass will introduce weak-ness planes and reduce the shear strength of the intact rock. The direct shear model using the UDEC-DM provides insights into the effect of the planes of weakness on the rock mass strength envelope and the progressive failure.


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Figure 14: Normalized shear strength of jointed rock to the strength of the intact material

7. EFFECT OF TENSILE STRENGTH IN THE DIRECT SHEAR TEST

The model shown in Figure 12 represents a direct shear test model. If k =0, the direct shear for the intact material is obtained. The advantage of this damage model is that it provides heterogeneity and inter-locking inside the rock mass, and the failure path is not predetermined; i.e., the failure can follow any arbitrary path, and the material can also fail in different mechanisms.

To examine the ability of the UDEC-DM to capture the tensile strength in the direct shear model, two models with a friction angle of 30° and tensile strengths of 0.5 MPa and 1.0 MPa were numerically simulated. Nonlinear failure envelopes were obtained by using this modeling approach. Figure 15 shows the failure envelope for both cases. These results indicate that the UDEC-DM captured the nonlinear-ity in the failure envelope predicted in the experiments and also captured the tensile strength effect as shown in Figure 15. The normal and shear stiffness and the cohesion of the flaws used in this model are shown in Table 1.

Figure 15: Failure envelope and the tensile strength effect on direct shear discrete element damage model simulation

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8. SCALE EFFECT IN UDEC-DM

The effect of edge length scale effect on the UDEC-DM was studied by four models with edge lengths of 0.5, 0.7, 0.9, and 1.1 cm long. The models were similar to the one shown in Figure 12 with no joint seg-ments. The size of the models was kept constant throughout the modeling process. The joint normal and shear stiffness were varied according to Equation 1.7. The models were tested under direct shear load-ing; a range of normal stress was applied to the model and shearing started. The peak shear stress was monitored and plotted against the applied normal load in Mohr-Coulomb space, (see Figure 16). The results in this direct shear simulation showed that within the range of the edge lengths used in this study, the scale effect was minimal, and the failure envelopes for the four models were reasonably close.

Figure 16: Direct shear results for different edge lengths

9. CONCLUSIONS Direct shear test was successfully modeled. The discrete element formulation in UDEC was used to create a damage model (UDEC-DM) that can simulate a jointed rock mass and accommodate both continuous and discontinuous joints. The intact rock between the joints are assigned internal flaws and the flaw properties can be adjusted to simulate a rock mass that varies from a strong brittle rock mass to a very weak one. The UDEC-DM showed close agreement with experimental results conducted on plaster of Paris. Numerical modeling was also used to model direct shear tests of discontinuous open and closed joints. The resulting failure envelopes were nonlinear and were found to be in good agreement with experimental results.

10. ACKNOWLEDGMENTS

I would like to thank Dr. Derek Martin and Dr. David Cruden for their advice during this research.

11. REFER ENCES

[1] Stead, D., Eberhardt, E., Coggan, J., and Benko, B., (2001). “Advanced numerical techniques in rock slope stability analysis-application and limitations.” In Landslide-Causes, Impacts and countermea-sures, pp. 615-624. Davos, Switzerland.

[2] Cundall, P. A., (1971). “A computer model for simulating progressive large scale movements in blocky rock systems”. In Proceedings of the Symposium of the International Society of Rock Mechanics, ISRM, pp. 129–136. ISRM, Nancy, France.

[3] Itasca, (2004). “UDEC Universal Distinct Element Code, Version 4.0.” Itasca Consulting Group,Inc., Minneapolis.


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[4] Pierce, M., Mas Ivars, D., Cundall, P.A. & Potyondy, D.O. (2007). “A synthetic rock mass model for jointed rock.” In Rock Mechanics, Meeting Society’s Challenges and demands, edited by E. Eberhardt, D. Stead, and T. Morrison, vol. 1, pp. 341-349. Vancouver, B.C.

[5] Cho, N., Martin, C., and Sego, D., (2008). “Development of a shear zone in brittle rock sub-jected to direct shear”. International Journal of Rock Mechanics & Mining Sciences, doi:10.1016/j.ijrmms.2008.01.019.

[6] Potyondy, D. and Cundall, P., (2004). “A bonded particle model for rock”. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstract, 41: 1329–1364.

[7] Lorig, L. J. and Cundall, P. A., (1987). “Modeling of reinforced concrete using the Distinct Element Method”. In Fracture of Concrete and Rock, edited by S. B. Shah and S. E. Swartz, pp. 276–287. SEM-RILEM international Conference, Springer Verlag New York Inc., Houston, Texas, USA.

[8] Watson, A., Martin, C., Moore, D., Thomas, W., and Loren, J., (2006). “Integration of geology, moni-toring and modelling to assess rockslide risk”. Rock and Soil Engineering, Felsbau, 3: 50–58

[9] Alzo’ubi, A., Martin, C., and Cruden, D., (2007). “A discrete element damage model for rock slopes”. In Rock Mechanics, Meeting Society’s Challenges and demands, edited by E. Eberhardt, D. Stead, and T. Morrison, vol. 1, pp. 503–510. Vancouver, B.C.

[10] Lorig, L.J., Watson, A., Martin, C.D., Moore, D.P. (2009). “Rockslide run-out prediction from distinct element analysis.” Geomechanics and Geoengineering 4(1): 17-25. doi:10.1080/ 17486020902767321.

[11] Alzo’ubi, A, Martin, C.D., Cruden, D.M. (2010). “Influence of tensile strength on toppling failure in centrifuge tests.” International Journal of Rock Mechanics and Mining Sciences 47(1): 974-982.

[12] Dershowitz, W. and Einstein, H., (1988). “Characterizing rock joint geometry with joint system models”. Rock Mechanics and Rock Engineering, 21: 21–51.[13] Ambarcumjan, R. V., (1974). “Convex polygons and random tessellations”. In Stochastic Geom-etry, edited by E. Harding and D. Kendall, pp. 176–191. Wiley, New York.

[14] Dearman, W. R., (1991). “Engineering Geological Mapping”. Butter worth Heinemann Ltd., Oxford.

[15] Lajtai, E., (1969b). “Shear strength of weakness planes in rock”. International Journal of Rock Mechanics and Mining Science, 6: 499–515.

[16] Skempton, A., (1964). “Longterm stability of clay slopes”. Geotechnique, 14: 75–101.

[17] Aydin, A. and Basu, A., (2006). “The use of Brazilian test as a quantitative measure of rock weath-ering”. Rock Mechanics and Rock Engineering, 39(1): 77–85.

[18] Lajtai, E., (1969c). “Strength of discontinuous rocks in direct shear”. Geotechnique, 6: 499–515.

[19] Hajiabdolmajid, V., Kaiser, P., and Martin, C., (2003). “Mobilized strength components in brittle failure of rock”. Geotechnique, 53: 327–336.

[20] Vekinis, G., Ashby, M. F., and Beaumont, P. W. R., (1993). “Plaster of Paris as a model material for brittle porous solids”. Journal of Material Science, 28: 3221–7.

A.K. ALZO’UBI.

21

CURRENT STATE OF CONTAMINATION OF DOLPHINS FROM THE FRENCH MEDITERRANEAN COASTAL

ENVIRONMENT (2007-2009) IN PCBs AND DDTs

Emmanuel Wafo1,4*, Véronique Risoul1, Thérèse Schembri1, Mama Chacha2, Véronique Lagadec1,

Frank Dhermain3, Henri Portugal4

1Laboratoire d’Hydrologie et Molysmologie Aquatique, Faculté de Pharmacie Marseille, France2Faculty of Engineering and Appl. Sci., ALHOSN University, P.O. Box 39772 Abu Dhabi, UAE

3Groupe d’Etude des Cétacés de Méditerranée, Clinique Vétérinaire du Redon, Marseille, France4Laboratoire de Chimie Analytique, UMR INRA 1260, Faculté de Pharmacie Marseille, France

ABSTRACT: Organochlorinated compounds, including PolyChloroBiphenyles, Dichloro-DiphenylTrichloroethan and metabolites were determinated in Stenella coeruleoalba (n=37) stranded on the French Mediterranean coasts from 2007 until 2009. Studies were carried out on lung, muscle, kidney, liver, and blubber. The sought-after compounds were all detected to variable levels in each tissue and organ. In general, total PCBs were the most abundant, followed by total DDTs. The concentration (in ng/g of lipid weight) in blubber of Stenella coeruleoalba, varied from 2,052 to 158,992 for PCBs and from 1,120 to 45,779 for DDTs. The ratios DDE/tDDTs were higher than 80% in almost all samples. The overall results of this work, compared to previous studies concerning the Mediterranean Sea, confirmed the tendency to a decrease of the contamination by organic compounds for the cetaceans in the Western Mediterranean Sea.

KEYWORDS: Polychlorinated Biphenyls, Organochlorides Striped Dolphins (Stenella Coeruleoalba), Bottlenose Dolphins (Tursiops Truncatus), Mediterranean Sea.

1. INTRODUCTION

The Polychlorinated Biphenyls (PCBs) are synthetic organic compounds produced since the 1920s. They are used in many industrial sectors such as electricity and plastics and rubber productions. These are good hydraulic fluids. The incorporation of PCBs into the chemical mixtures improves their physico-chemical resistance. The presence of these compounds in the environment finds its origin in various sources such as:

• the discharges of equipment containing them or having contained them

• accidental pollution

The aquifers and river systems are the main vehicles for the dissemination of these products. In addition, the wind currents may contribute, with the food chains in the dispersion of these products.These pollutants are considered responsible for the alteration of calcium metabolism and therefore, are dangerous to wildlife and more particularly, the marine fauna (oysters, mussels, fish, etc...). The chemical stability of these molecules, their capacity of concentration in organisms and the uncertainties on their chronic effects led the French authorities, on the recommendation of the scientific community, to regulate the use of these products starting in 1975. Since then, the succeeding regulations have led to the prohibition of manufacture, marketing and acquisition of PCBs and devices having contained PCBs since 1986 [1]. This regulation has gradually extended to the entire European community.

* Corresponding Author: E-mail: [email protected]


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After rejection to the environment, PCBs are strongly accumulated by living organisms [2-5]. Thus, organisms at the top of the food chain such as cetaceans can be considered as actual indicators of the level of contamination of their natural environment. Since the early seventies, numerous stud-ies have indicated strong levels of PCB and pesticides in tissues and organs of cetaceans in the Mediterranean and in the other seas of the globe. The organo-chlorinated compounds, combined with the degradation of the habitat of these marine mammals, are widely suspected to contribute to their stranding. It follows a continued decline in their populations [6, 7]. Since then, they have been protected and most of the data found in the literature refer to biopsies or to cetaceans unfortunately trapped in fishing nets.

In this work, we report the levels of contamination by PCBs, DDT in cetaceans stranded along the French Mediterranean coast between 2007 and 2009. Our specimens included 37 blue and white dolphins (Stenella coeruleoalba) and two bottlenose dolphins (Tursiops truncatus). The analyses were carried out on the blubber, the liver, the muscle, the kidney, and the lung of the cetaceans.

2. MATERIALS AND METHODS

2.1. Sampling and Storage

The 39 specimens (37 Stenella coeruleoalba and two Tursiops truncatus) of our study were found dead, along the Mediterranean coast (Fig. 1) between 2007 and 2009. The collection of tissues and organs was performed by the French Mediterranean Cetacean Study Group (GECEM). Mammals were measured beforehand and weighed when it was possible. After dissection, the tissues and organs were delicately sampled and wrapped in aluminum foil and placed in an ice bath and subsequently frozen to –20°C. Before analysis, the tissues and organs were lyophilized, pulverized and homogenized, and stored in little airtight vials at 4°C.

2.2. Age Estimate

The age of cetaceans is usually, fairly difficult to determine. Moreover, some samples were severely deteriorated. In general, the age of the dolphins has been determined from the dentition. We selected to classify the individuals into two groups, following their sexual maturity that could be assessed from the size of individuals [6, 8]:

young cetaceans, with size smaller than 120 cm •

adult cetaceans, with size greater than 120 cm•

Overall, there were 37 Stenella coeruleoalba (19 males, 13 females and five young dolphins) and two Tursiops truncatus (two males). The size and sexual maturity of these individuals as well as the date and place of stranding are included in Table 1.

E WAFO, V RISOUL, T SCHEMBRI, M CHACHA, V LAGADEC, F DHERMAIN, H PORTUGAL

23

Figure 1: Map showing principal sampling locations

2.3. Chemicals analysis

C ommercial standard solutions were used for calibration and, in the case of PCB, a sample of DP6 (a commercial mixture equivalent to Arochlor 1260) was used for comparison of the proportions of the congeners in the different organs. The total amount of DDT (tDDTs) was calculated as the sum of the amounts of pp’-DDT, pp’-DDD, and pp’-DDE. The PCB congeners 118 (CB118), 138 (CB138), 153 (CB153) and 180 (CB120) were the major constituents of the reference DP6, and represented 41% of the total amount of PCBs. The total amount of PCBs (tPCBs) was estimated as tPCBs = (CB118 + CB138 + CB153 + CB180) × 100 / 41 [9, 10].

Results in the blubber were expressed in ng/g lipid weight (ng/g lw); while, in all other tissues and organs, they were expressed in ng/g dried weight (ng/g dw). Since the concentrations of chlorinated hydrocarbons in most samples were above 1ng/g, decimals were omitted from tables.

2.4. Extraction and Quantitative Analysis

A bout 1g of freeze-dried sample was extracted with hexane in the thimbles of a soxhlet apparatus for at least 16 hours. The final solution was concentrated to 3 mL; from which 1mL was taken to determine the content of lipid: it introduced in an initially tarred container and deposited into a desiccator and after drying to constant weight, the lipid content is determined by gravimetry. The second part was twice purified with concentrated sulfuric acid, according to the procedures described by Murphy [11], and the resulting extract was concentrated to 1mL. Then the extract underwent liquid chromatography on a column containing silica gel and alumina following the procedures described by Wafo et al. [12]. All the analyses were performed in our laboratory (COFRAC accreditation n°1-1234 since 2001). The laboratory participates regularly to inter-laboratory comparison exercises and data from our laboratory were in good agreement with those of reference materials.

CURRENT STATE OF CONTAMINATION OF DOLPHINS FROM THE FRENCH MEDITERRANEAN

24

Table 1: Code and characteristics of the studied dolphins; lipid content and concentrations (ng/g lw) of organo-chlorine compounds in the blubber of the studied dolphins (stenella coeruleoalba; “17” and “54”: tursiops truncates — M = male, F = female, na = not analyzed).

2.5. Quality Control

Fo r this study, we used as certified material, an IAEA/UNEP inter-comparison sample of Tuna homogenate (IAEA-435), which was distributed to world-wide laboratories in October 2004 [13]. In each batch, a blank and a certified material were systematically introduced in order to validate the results. For quality assurance and quality control, 7 IUPAC congeners (28, 52, 101, 118, 138, 153, and 180) were analyzed as well as the pesticides. The results obtained for the reference materials were used to plot control charts and to decide upon acceptance or rejection of the data produced for each sample batch. Rejected batches were reanalyzed. Ten replicas of IAEA 435 were conducted on the same day, in order to determine the average recovery for each PCB congener and each pesticide: results for the


25

PCB congeners varied from 89.1 to 92.7% and for pesticides from 84.8 and 101.2%. The detection limit ranges from 1.10-2 for PCB congeners to 0.2 ng.g-1 for pesticides taking into consideration the lowest calibration level of a particular analyte, and the amount sample extracted.

3. RESULTS AND DISCUSSION

3.1. PCBs and DDTs in the Blubber

We chose to treat the blubber separately in order to facilitate the interpretation and to allow an easy comparison with other authors. Results concerning total PCB (tPCBs), total DDT (tDDTs) in the blub-ber are presented in Table 1. Regardless of the gender and age, these results show a clear predominance of total PCB on the total DDT. The levels of total PCB and total DDT varied respectively from 2,052 to 158,992 ng/g lw (average 57,336 ± 46,232 ng/g lw) and from 1,822 to 55,360 ng/g lw (average 15,995 ± 13,268 ng/g lw).

Considering the sex and the sexual maturity (Figure 2), the average concentrations of tPCBs and tDDTs for young dolphins were 77,198 ± 57,395 ng.g-1 lw and 24,003 ± 22,407 ng.g-1 lw respectively. The average levels of tPCBs and tDDTs, for males, were 57,724 ± 41,900 ng.g-1 lw and 14,387 ± 7,403 ng.g-1 lw respectively. For females, they were 45,315 ± 45,689 ng.g-1 lw and 13,789 ± 13621 ng.g-1 lw respectively. So, from all the results, two main observations emerged:

The levels for both tPCBs and tDDTs were higher for young dolphins than for adult ones.1.

Among adults, males seemed more contaminated with tPCBs than females; by contrast, no 2. significant difference appeared in levels of tDDTs between males and females (significance level p < 0.05).

These observations are in agreement with those of several studies, [14-16], which have showed similar accumulation mechanisms. The accumulation of organic compounds begins during the fetal life. At this stage, levels of contaminants in the fetus organs can reach those of the maternal organs. In the newborn dolphins, these levels increase steadily during the phase of feeding through the breast milk. Then, contaminants continue to accumulate throughout life, except for the females who eliminate organic contaminants during gestation and nursing because the organic compounds are transferred to their baby [17, 18].

Previous works have shown that this transfer may be important: Stockin et al. [19] have indicated ratios of approximately 5.7 % transferred from the mother to the fetus for the tDDTs and 4.3 % for the tPCBs (calculated from 45 congeners of PCBs). These authors have also indicated that this transfer of contaminants, via the placenta, might lead to an “imbalance” of the levels between the mother and the fetus.

Regardless of the gender and age, the results showed a clear predominance of the level of tPCBs on the level of tDDTs in the bubbler of the studied dolphins (Figure 2). This could reflect the aging of DDTs in relation to the PCBs in the natural environment. Indeed, the use of DDT has been banned in the Mediterranean basin since the late 1970s. During the same period, the use of PCB has been spreading, and even augmented. It is only in 1986 that the manufacturing and marketing of products or equipment containing PCB has been strictly forbidden in France. However, existing stockpiles are still substantial, and visibly continue to contaminate the environment. Borrell and Aguilar [20, 21] have reported that, between 1987 and 2002, the tDDTs has decreased by a factor of 23. During the same period, the tPCBs has decreased by a factor of 6 only. Previous results may confirm these observations:


26

On the one hand, the analyses of samples taken downstream of the sewage plant of Marseilles • (France) in 2004, has shown tPCBs contents above 1200 ng/L (Wafo, Pers. Comm.). Moreover, in February 2006, water samples from the Rhône have been analyzed: they contained 256 ng.L-1 of tPCBs (Wafo, Pers. Comm.) and had a PCB congener profile similar to that of Dp6, evidence that these compounds, newly arrived in the environment.On the other hand, in sediment samples from Cortiou (Marseilles - France) that we have analyzed • in 2002, we have measured tDDTs levels of 254 ng.g-1 dw [22]. These levels can also sometimes be found in the water body by effect of rocking action. The degradation of DDTs can be facilitated in the zone of bioturbation that constitute the 10-12 first centimetres of the sediments. All these data confirm the ubiquity of these compounds which, added to their chemical stability lead to their per-sistence in the environment.

Figure 2: Average concentration (tPCBs and tDDTs) in blubber foryoung, male and female stenellas coeruleoalba

The tursiops truncatus (code 17 and 54 in Table 1) were more contaminated in their blubber than the stenellas. The average concentrations in PCBs and total DDT were 206,536 and 27,450 ng/g lw in the blubber respectively. The ratios DDE/tDDT were relatively low (73 %) compared to the stenella. These high concentrations in the blubber were probably in connection with their habitat. In principle, the tur-siops truncatus is a coastal species and is facing higher levels of pollution. In the blubbers of tursiops truncatus collected at “southeastern US estuarine”, Fair et al. [23] have reported the levels of PCBs ranging from 1,510 to 255,000 ng/g lw, and 14,900 to 86,800 ng/g lw for DDTs.

3.2. Distribution of Organochlorinated Compounds in the Other Tissues, and Organs

Considering all the studied organs, the analyzed samples showed heterogeneous contents for each compound. This heterogeneity might be mainly linked to the “personal history” of each dolphin. Thus, interpretation of data was based on the average values. Figure 3 shows the average distribution of tPCBs and tDDTs in the various organs, for the young dolphins, the males and the females respectively. The average levels of tPCBs and tDDTs, in the organs, decreased in the order: liver > kidney Muscle > lung. Overall, these values were lower than those obtained in the blubber. These observations were consistent with the various studies on the Mediterranean Stenella [13, 24-26] from diverse geographic origins: Italy, Spain and France.


27

The almost constant distribution of the tPCBs levels in the organs of each subject was explained by the highly lipophilic nature of these compounds. As we have shown, the ultimate accumulation took place in blubber; nevertheless, during their progression in the organism, the contaminants distributed in the different tissues and organs. The affinity between organic compounds and organs might be correlated to the lipid content. Furthermore, depending on the organs, there might be an accumulation through mobilization of residues previously accumulated or on the contrary, of decontamination processes via the metabolism. The distribution of the contamination between the organs is therefore linked to complex mechanisms difficult to characterize.

0

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Figure 3: Average concentration (tPCBs and tDDTs) in organs other than blubber foryoung, male and female Stenellas coeruleoalba

The dolphin contamination by the DDTs naturally followed the same mechanism as the contamination by the PCBs. The DDTs levels were however much lower than the PCBs concentrations: 9-fold, 4-fold and 3-fold decrease in young dolphins, males and females respectively.In the two tursiops truncatus, the average concentrations in tPCBs and tDDTs were respectively:

15,032 and 2,588 ng/g dw in the liver •

6,981 and 3,663 ng/g dw in the kidne• y


28

The average concentrations in tDDTs in the liver and the kidney were therefore, of the same order of magnitude as those of the stenellas. The ratios tPCB/tDDT showed, as with the stenellas, the predominance of PCBs over the DDTs. The ratios DDE/tDDT reached 90% in the liver and the kidney.

3.3. Profile of the Congeners

Figures 4A and 4B represent the variation of the congener composition of PCBs in the various organs for males and females respectively, as compared with the DP6. In DP6, the congeners with 5, 6, and 7 atoms of chlorine represented 20%; 41% and 27% of tPCBs respectively. The molecules having 3, 4, and 8 atoms of chlorine constituted only small proportions: 0.2%; 1% and 11% of tPCBs, respectively.

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Figure 4: Composition of PCB in relation with chlorine number in different s organs:(A) females; (B) males.

The profiles appeared broadly similar in all organs and similar to the profile of the DP6. However, some substantial differences could be found. The proportion of octochlorinated compounds was in general much lower for all the organs relatively to that of the DP6. This difference was even more pronounced for the liver (especially for females) and for the blubber (especially for males). In parallel, the proportion of hexachlorinated compounds was dominant for the whole organs in comparison with that of the DP6. For the other “classes” of congeners, variable differences according to organs appeared: especially, a relatively high proportion of the heptachlorinated compounds was found in the male livers.


29

Moreover, the proportion of hexachlorinated congeners (41% in the technical mixture DP6) varied, depending on the tissues and organs, from 39 to 48% among the males, and from 41 to 48% among the females. At the same time, the proportion of octochlorinated compounds (11% in the technical mixture DP6) varied from 3 to 8% in the various tissues and organs, letting to suspect that the “dechlorination” of the most chlorinated compounds took place. Therefore, despite the apparent similarity of the profile of PCBs in the various samples, variations happened in the relative proportions of congeners in comparison with the distribution in initial industrial mixtures. However, it was impossible to assert if these variations were caused by the compound metabolism within the organism or if dechlorinations took place in the natural environment before absorption of PCBs by the dolphins.

3.4. Distribution of DDT and its Metabolites

Figure 5, shows the average proportions of DDT, DDD and DDE in all the tissues and organs of the studied Stenella coeruleoalba. DDE was always the major component in the different organs. DDD and DDT were in much lower proportions. In fact, DDE has been shown to be the ultimate stage of degradation of DDT, and this stable derivative has been considered as less toxic than DDT. One may consider that the ratios DDE/tDDTs represent the state of degradation of the DDTs; i.e. the “aging” of the contamination by these compounds: higher is the ratio; older is the pollution by the DDT. Figure 6 shows that these ratios were relatively stable from one organ to another for the same dolphin, and from one specimen to another. They varied from 78 to 96 % regardless of the organ considered and independently of the size and the sex of the dolphin. Similar results were obtained for the tursiops truncates.

0%

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Figure 5: Average relative proportions of DDT, DDD and DDE in all the tissues andorgans studied for stenellas coeruleoalba

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30

I n living organisms, most of the detoxification pathways (leading to the DDE from the DDT and DDD) generally are taking place in the liver. In the present study, we would have expected the ratios DDE/tDDTs to be lower in the liver than the other organs. However, homogeneous distributions of the DDT, DDE and DDD were measured in all the studied organs. Thus, the bulk of the degradation of DDT into DDE must have been initiated in the natural environment, even before this compound could penetrate the organism of the dolphins. These results are in agreement with most of the studies on the cetaceans in the Mediterranean Sea [20]. In particular, Marsili et al. [27] have shown that in the tissues and organs of the dolphins collected along the Italian coastline, DDE represented 80% of tDDTs. This proportion differed with results obtained for cetaceans from the Indo-Pacific coasts where DDE represented 68% of tDDTs: in this region of the world, restrictions concerning the use of DDT were less drastic or the restriction of use was later than in Europe [28, 29].

The ratios DDE/tDDTs close to 100% clearly means that DDTs were present in the natural environment of the Mediterranean Sea for a long period of time and were not widespread any more. These results are in agreement with the prohibitions of the use of these compounds, particularly in France and in the Mediterranean pool since the 1970s.

3.5. Correlation between the Organs

I n order improve distribution analyses of the organochlorinated contaminants in the different organs of dolphins, the level of tPCBs in the blubber, the lung, the muscle, and the kidney were plotted vs. the level of tPCBs in the liver, for males, on the one hand, and for females, on the other hand. The same correlations were plotted for the level of tDDTs. Each correlation took into account all the dolphins for which both organs considered to have been analyzed (Figure 7).

I n the case of the muscle, no significant correlation between organs could be highlighted. For tPCBs, positive correlations could be calculated between:

the liver and the blubber (R• 2: 0.88 to 0.70 for male and female respectively)

the liver and the kidney (R• 2: 0.86 to 0.59 for male and female respectively)

the liver and the lung (R• 2: 0.52 to 0.81 for male and female respectively)

For tPCBs, positive correlations could be determined only for:

the liver and the kidney, for male (R• 2: 0.86)

the liver and the lung (R• 2: 0.62 to 0.19 for male and female respectively)

The calculated correlations showed that tPCBs contents in the liver were about:

3 times lower than in the blubber•

3 times higher than in the kidney•

3 times higher than in the lungs of the females and 6 times higher than in the lungs of the males•

tDDTs contents in the liver were about:

3 times higher than in the lung•

2 times higher than in the kidney (only for male)•

Thus, we confirmed the previous results on the distribution of organochlorinated compounds according to organs.


31

DDT- females

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Figure 7: Correlation between the organs and tissues studied, for the concentrations of

tPCBs and tDDTs

3.6. General Trend of the Contamination

Th e ethological conditions vary from one marine environment to another. So, dolphins could be classified both by kind and by geographical areas. Figure 8 presents a comparison between the present results and results obtained previously by other authors for Stenella coeruleoalba from the Mediterranean Sea.

Alzieu and Duguy [6] have shown relatively low levels of tPCBs and tDDTs as compared with other studies which have been published between 1993 and 1996. However, taking into account the improvement of the analytical techniques for detection and determination of organochlorined compounds since the 1980s, the data of Alzieu and Duguy are hardly comparable to more recent results (since 1990) and are presented here only for information.

The study of Borrell [30] has concerned the region of Gibraltar where important exchanges between the Mediterranean Sea, and the Atlantic Ocean has been taking place. It has shown lower values for tDDTs and tPCBs than the other studies carried out in the «inner» Mediterranean Sea. Except the study mentioned previously, variable but relatively high levels had always reported concerning the different areas of the Mediterranean Sea in the 1990s (150-450 μg.g-1 lw for the tDDTs and 150-800 μg.g-1 lw for the tPCBs). For the most recent works, since 2000s, a net tendency to a decrease has been detected for both tDDTs and tPCBs.

So , the overall results of this work, compared to previous studies concerning the Mediterranean Sea, seems to confirm the tendency to a decrease of the contamination by organics compounds for the cetaceans in the Western Mediterranean Sea.


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Figure 8: Temporal trends in concentrations of tPCBs and tDDTs in blubber of cetaceanfrom Mediterranean Sea between 1979- 2010

4. CONCLUSION

In general, levels of organic compounds in the organs of dolphins are rather heterogeneous and may vary significantly from one individual to another. This heterogeneity may be in relationship with the nutritional conditions of the animals, their state of health, but also with the state of preservation of the tissues. For the interpretation of results, we have chosen the average values bearing in mind that standard deviations are often high.

PCBs and DDT were found in significant proportions regardless of sex and age. A substantial analysis of the juvenile and adult stenellas coeruleoalba has shown that the young males were more contaminated with PCBs, as compared to males and to females. The same observation could be made with DDT; however, without any significant level differences between the adult males and the adult females.

The blubber was in general the tissue the most contaminated with average values in tPCBs of 70 μg/g (with peaks above 250 μg/g of PCB), and in tDDTs of 17μg/g (with specific values up to 45μg/g). Contamination of the liver was generally low, followed by that of the kidney, the muscle, and the lung.

The two tursiops truncatus showed levels twice as high for both PCB and DDT as compared to stenellas coeruleoalba. Given the available information and the present results, it is difficult to link the causes of death of stranded dolphins and the PCBs levels in different tissues. However, the high levels that were found are likely to have contributed significantly to their deaths. The comparison of our results to those of previous studies on the Mediterranean Sea dolphins confirmed the tendency to a contamination decrease of the dolphins by the organo-chlorinated compounds. These results are certainly to be put in perspective with the ban of these compounds in the Mediterranean basin in 1970 and 1980 for the DDT and the PCB respectively.

5. REFERENCES

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[2] Nakata, H., Kannan, K., Jing, L., Thomas, N., Tanabe, S., Giesy, J.P. (1998). “Accumulation pattern of organochlorine pesticides and polychlorinated biphenyls in southern sea otters (Enhydra lutris nereis) found stranded along coastal California, USA.” Environmental Pollution 103, 45-53.

[3] Tanabe, S., Iwata, H., Tatsukawa, R. (1994a). “Global contamination by persistent organochlorines and their ecotoxicological impact on marine mammals.” Sci Total Environ 154, 163-177.

[4] Tanabe, S., Sung, J.K., Choi, D.Y., Bara, N., Kiyota, M., Yoshida, K., Tatsukawa, R. (1994b). “Per-sistent organochlorine residues in nothern fur seal from the pacific coast of Japon since 1971.” Environ Pollut 85, 305-314.

[5] Poster, X, Simmonds, M. (1992). Proceedings of the Mediterranean Striped Dolphins Mortality International Workshop, Greanpeace International Mediterranean Sea projet, Palma de Mallorca, Spain, 4-5, 190.

[6] Alzieu, c., Duguy r. (1979). “Teneurs en composés organochlorés chez les cétacées et les pinipèdes fréquantant les côtes françaises.” Océanologica acta 2 (1), 107-120.

[7] Borrell, A., Cantos, G., Pastor, T., Aguilar, A. (2001). “Organochlorine in common dolphins from the Atlantic and Mediterranean waters of Spain.” Environ Pollut 114, 265-274.

[8] Cardellicchio, N., Decataldo, A., DI Leo, A., Giandomenico, S. (2002). “Trace elements in organs and tissues of striped dolphins from the Mediterranean Sea.” Chemosphere 49, 85-90.

[9] Monod, J.L., Arnaud, P.M., Arnoux, A. (1995). “PCB Congeners in the Marine Biota of Saint Paul and Amsterdam Islands.” Southern Indian Ocean Mar Pollut Bull 30(4), 272-274.

[10] Perez, T., Wafo, E., Fourt, M., Vacelet, J. (2003). “Marine Sponge as Biomonitor of Polychlorobi-phenyl contamination: Concentration and Fate of 24 Congeners.” Environ Sci Technol 37, 2152-2158.

[11] Murphy, P.G. (1972). “Sulfuric acid for the cleanup of animal tissues for analysis of acid-stable chlorinated hydrocarbon residues.” J Ass Off Anal Chem 55, 1360-1362.

[12] Wafo, E., Sarrazin, L., Diana, C., Dhermain, F., Schembri, Th., Lagadec,V., Pecchia, M., Rebouil-lon, P. (2005). “Accumulation and distribution of organochlorines (PCBs and DDTs) in various organs of Stenella coeruleoalba and a Tursiops truncatus from Mediterranean littoral environment.” Sciences of the Total Environment 348, 115-127.

[13] Villeneuve, J.P., de Mora, S.J., Cattini, C. (2006). “World-wide and Regional Intercomparison for the determination of organochlorine compounds and petroleum hydrocarbons in Tuna homogenate IAEA-435.” Marine Environment Laboratory, 4 Quai Antoine Ier, MC-98000 Monaco.

[14] Tanabe, S., Loganathan, B.G., Subramanian, A.N., Tatsukawa, R. (1987). “Organochlorine residues in short-finned pilot whales. Possible use as tracers of biological parameters.” Mar Pollut Bull 18, 561-563.

[15] Aguilar, A., Borrell, A. (1994). “Reproductive transfert and variation of body load of organochlo-rine polluants with age in fin whales.” Arch Environ Contam Toxicol 27, 546-554.

[16] Borrell, A., Bloch, D., Desportes, G. (1995). “Age trends and reproductives transfert of organochlo-rine compounds in long-finned pilot whales from the Faroe Islands.” Environtal Pollution 88, 283-292.


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[17] Tanabe, S., Murayama K., Tatsukawa, R., Miyazaki N. (1982). “Transplacental transfer of PCBs and chlorinated hydrocarbon pesticides from the pregnant striped dolphin (Stenella coeruleoalba) to her fetus.” Agr Biol Chem 46, 1249-1254.

[18] Alzieu, C., Duguy, R. (1982). “Babin P. Pathologie des Delphinidae: contamination fœtale et néo-natale par les PCB. Lésions cutanées ulcératives.” Rev Tr Inst Pêch mar 46 (2), 157-166.

[19] Stockin, K.A., Law, R.J., Roe, W.D., Meynier, L., Martinez, E., Duignan, P.J., Bridgen, P., Jones, B. (2010). “PCBs and organochlorines pesticides in Hectors’s (Cephalorhynchus hectiri hectori) and Maui’s (Cephalorhynchus hectiri hectori Maui’s) dolphins.” Marine Pollution Bulletin 60, 834-842

[20] Borrell, A., Aguilar, A. (1987). “Variation in DDE percentage correlated with total DDT burden in the blubber of fin and sea whales.” Mar. Pollut. Bull 18(2), 70-74.

[21] Borrell, A., Aguilar, A. (2007). “Organochlorine concentrations declined during 1987 – 2002 in western Mediterranean bottlenose dolphins, a coastal top predator.” Chemosphere 66, 347-352.

[22] Wafo, E., Sarrazin, L., Diana, C., Schembri, Th., Lagadec,V., Monod, J.L. (2006). “Polychlorinated biphenyls and DDT residues distribution in sediments of Cortiou.” Marine Pollution Bulletin 52, 104-120

[23] Fair, P.A., Adams, J., Mitchum, G., Hulsey, TH.C., Reif, J.S., Houde, M., Muir, D., Wirth, E., Wetzel, D., Zolman, E., Mcfee, W., Bossart, G.D. (2010). “Contaminant blubber burdens in Atlantic bottlenose dolphins (Tursiops truncatus) from two southeastern US estuarine areas: concentrations and patterns of PCBs, pesticides, PBDEs, and PAHs.” Sciences of the Total Environment 408, 1577-1597.

[24] Marsili, L., Forcardi, S. (1997). “Chlorinated Hydrocarbon (HCB, DDTs, and PCBs) Levels in Cetaceans Stranded Along the Italian Coast: an Overview.” Environ Monitoring and Assessment 45, 129-180.

[25] Marsili, L. (2000). “Lipophilic contaminants in marine mammals: review of the results of ten years’ work at the Department of Environmental Biology, Siena University (Italy).” Int J Environ pollut 13 (1-6), 416-452.

[26] Aguilar A., Borrell A. (1990). “Patterns of lipid content and stratification in the blubber of fin whales (Balaenoptera physalus).” J. Mammals 71(4), 544-554.

[27] Marsili, L., Forcardi, S., Cuna, D., Leonzio, C., Casini, L., Bortolotto, A., Stanzani, L. (1992). “Chlorinated Hydrocarbons and heavy Metals in tissues of Striped Dolphins (Stenella coeruleoalba), Stranded Along the Apulian and Sicilian Coasts (summer 1991).” Eur. Res. Cetaceans 6, 234-237.

[28] Fossi, C., Marsili, L., Neri, G., Natoli, A., Politi, E., Panigada, S. (2003). “The use of a non-lethal tool for evaluating toxicological hazard of organochlorine contaminants in Mediterranean cetaceans: new data 10 years after the first paper published in MPB.” Marine Pollution Bulletin 46(8), 972-982.

[29] Jefferson Th. A. (2006). “Population biology of the Indo-Pacific Humpacked dolphin in Hong Kong waters.: Wildlife Monographs 14, 1-65.

[30] Borrell A. (1993). “PCB and DDTs in Blubber of Cetaceans from the North-Eastern North Atlan-tic.” Mar Pollut Bull 26 (3), 146-151.


35

CHLORINATED PESTICIDES IN THE BODIES OF DOLPHINS OF THE FRENCH MEDITERRANEAN COASTAL

ENVIRONMENT

Emmanuel Wafo1*, Mama Chacha2, Véronique Risoul3, Thérèse Schembri3,Frank Dhermain4, Henri Portugal1

1Laboratoire de Chimie Analytique, UMR INRA 1260, Faculté de Pharmacie Marseille, France2Faculty of Engineering and Appl. Sci., ALHOSN University, P.O. Box 39772 Abu Dhabi, UAE3Laboratoire d’Hydrologie et Molysmologie Aquatique. Faculté de Pharmacie Marseille, France

4Groupe d’Etude des Cétacés de Méditerranée, Clinique Vétérinaire du Redon, Marseille, France

ABSTRACT: The concentrations of organochlorinated pesticides, including lindane, heptachlor, aldrin, heptachlor-epoxide, endosulfan I, dieldrin, and endrin were determined in striped dolphins(Stenella coeruleoalba; n = 26), and bottlenose dolphins (Tursiops truncates; n = 2), stranded on the French Mediterranean coasts. Studies were carried out on the lung, the muscle, the kidney, the liver, and the blubber. The concentrations of all the analyzed compounds were detected to variable levels in each tissue and organ. In the blubber, dieldrin was generally the most abundant compound (215.3 ± 290.3 ng g-1 lw), followed by Endrin (207.7 ± 217.5 ng.g-1 lw); heptachlor-epoxid (106,6 ± 107.1 ng.g-1 lw); endosulfan I (46,6 ± 32.8 ng g-1 lw); lindane (16,6 ± 12.1 ng/g lw); Aldrin (11,9 ± 8.4 ng.g-1 lw) and heptachlor (6,7 ± 4.2 ng.g-1 lw). The values found in this study were comparable to those previously obtained by other authors in the nineties.

KEYWORDS: Organochlorine pesticides, organs, striped dolphins, bottlenose dolphins, Mediterranean Sea.

1. INTRODUCTION

Contamination pattern of any marine environment contains a wide variety of compounds, non-biodegradable substances being the most dangerous. Organochlorine pesticides are of great concern because of the high distribution of their residues in the aquatic ecosystem and of their toxic and carcinogenic properties [1].

Due to their toxicity, their persistence [2–5], their hydrophobic nature and their low solubility in water, the chlorinated pesticides are adsorbed on the particulate matters and finally in sediments. The chlorinated pesticides enter the environment through human activities and various other pathways till atmospheric and fluvial transport. In particular, they enter in the marine environment from the urban waste, the deposits of the waste cleaning plants, the agricultural cultivations as well as rinsing of the soils through flows.MacKay et al. [4] reported that the half-life of pesticides could range approximately from 8 months to 6 years depending on the compounds.

Despite their hydrophobicity, the immense volume of water in the oceans is capable of dissolving a significant quantity of pesticide. Moreover, industrial or accidental discharges can be transported and

* Corresponding Author: E-mail: [email protected]


36

dispersed into oceans by rivers. After release in the natural environment, the pesticides are strongly accumulated by organisms, which succeed one another in the food chain [6–8]. Organisms being at the top of the food chain (such as cetaceans) store large quantities of these pollutants [7, 9]. Thus, cetaceans can be considered as actual bio-indicators of the level of contamination of their natural environment.

The organochlorinated compounds, combined with the degradation of the habitat of these marine mammals are widely suspected to contribute to their stranding and continued decline of their populations [10, 11]. Since the early seventies, cetaceans have been protected and most of the data found in the literature refer to biopsies or to cetaceans stranded on beaches or unfortunately trapped in fishing nets. These studies have indicated high levels of pesticides in tissues and organs of cetaceans from the Mediterranean Sea [9, 12–16] and also, from other seas of the globe [6–8, 17– 19].

In this work, we report levels of pesticides: lindane, heptachlor, aldrin, heptachlor-epoxide, endosulfan I, dieldrin, and endrin in some cetaceans stranded on the French Mediterranean coasts between 2007 and 2009. The evaluations were achieved on the blubber, the liver, the muscle, the kidney, and the lung of the cetaceans. The samples were represented by 26 striped dolphins (Stenella coeruleoalba), and 2 bottlenose dolphins (Tursiops truncatus).

One of the objectives of this study was to assess the current status of the dolphins’ contamination by organochlorinated compounds, in the French Mediterranean coastline region. We also examined the repartition of the contamination in the different organs and compared the levels of contamination according to age and sex.

2. MATERIALS AND METHODS

2.1. Sampling and storage

The twenty six specimens of Stenella coeruleoalba and the two Tursiops truncatus (code 17 and 54), (Table 1) studied in this work, were found stranded, along the French Mediterranean coast (Figure 1) between 2007 and 2009.

The collection of tissues and organs was performed by the French Mediterranean Cetacean Study Group (GECEM), represented by Dr. Franck Dhermain [20]. Mammals were measured beforehand and possibly weighed. After dissection, the tissues and organs were delicately sampled and wrapped in aluminum foil and placed in an ice bath and then frozen at –20°C. Before analysis, the tissues and organs were lyophilized, pulverized, homogenized, and stored in little airtight vials at 4°C.The collection of the samples started before the beginning of this study, so all the organs of all the dolphins had not been sampled. The samples were analyzed for the following compounds: lindane (HCH), heptachlor, aldrin, Heptachlor-epoxide, endosulfan I, dieldrin, and endrin. Results in the blubber were expressed in ng.g-1 lipid weight (ng.g-1 lw); while, in all other tissues and organs, they were expressed in ng.g-1 dried weight (ng.g-1 dw).

E WAFO, M CHACHA, V RISOUL, T SCHEMBRI, F DHERMAIN, H PORTUGAL

37

Figure 1: Map showing principal sampling locations

2.2. Extraction and Quantitative Analysis

T he used glassware must be cleaned with an appropriate detergent, then dried at 200°C for at least 24 hours, and rinsed at least twice with the solvent (hexan), before use. Whatman cellulose thimbles (22-80 mm, no.350211, Schleicher and Schuell) used for extraction of samples were pre-extracted for 12 h in a soxhlet apparatus with hexane Pestipur (Pestipur 99%, SDS, Peypin, France), in order to remove any organochlorine contamination. About 1g of freeze-dried sample was extracted with hexane in the thimbles of a soxhlet apparatus for at least 16 hours. The resulting solution was concentrated to 3 mL; from which 1 mL was taken to determine the content of lipid. The second part was twice purified with concentrated sulfuric acid, according to the procedures described by Murphy [21], and the resulting extract was concentrated to 1mL. Then the extract underwent liquid chromatography on a column containing silica gel and alumina following the procedures described by Wafo et al. [22]. Analyses were performed with a HP 6890 series gas chromatograph equipped with a 63Ni electron capture detector (ECD) at 300°C and an automatic injector on-column, HP 6890 series. The column used was a DB5 J & W (60 m × 0.32 i.d. × 0.25 μm). The carrier gas was helium. The temperature of injection was 60°C and was programmed to increase up to 250° C at 100°C/min. The column temperature was 60°C and programmed to increase first up to 160°C (10°C/min) and then up 280°C at 2°C/min. The variation in the response of the ECD detector was corrected by a daily calibration with a standard solution of pesticides.

CHLORINATED PESTICIDES IN THE BODIES OF DOLPHINS OF THE FRENCH MEDITERRANEAN

38

Octochloronaphtalen (OCN) is used as internal standard. The sample response was matched to that of the standard solution by dilution or concentration of the sample.

Table 1: Code and characteristics of the studied dolphins; lipid content and concentrations (ng.g-1 lw) of organochlorinated compounds in the blubber of the studied dolphins (Stenellas coeruleoalba; “17” and “54”: Tursiops truncates – M = Male, F = Female)

2.3. Lipid determination

On e milliliter of the aliquoted extraction residue was introduced in an initially tarred container and deposited into a desiccator. After drying to constant weight, the lipid content was determined by gravimetry.

2.4. Quality control

Al l the analyses were performed in our laboratory, which owns a COFRAC accreditation n°1-1234 since 2001. The laboratory has been participating regularly to interlaboratory comparison exercises and data from our laboratory have been in good agreement with those of reference materials.

For this study, we used, as certified material, an IAEA/UNEP intercomparison sample of Tuna homogenate (IAEA-435), which was distributed to world-wide laboratories in October 2004 (Villeneuve et al 2006 [23]). In each batch, a blank and a certified material were systematically introduced in order to validate the results. For quality insurance and quality control, all the pesticides were analyzed as


39

detailed previously. The results obtained for the reference materials were used to plot control charts and to decide upon acceptance or rejection of the data produced for each sample batch. Rejected batches were reanalyzed. Ten replications of IAEA 435 were conducted on the same day, in order to determine the average recovery for each pesticide: results varied from 84.8 and 101.2%. The detection limit was to 0.1 ng.g-1 for pesticides taking into consideration the lowest calibration level of a particular analyte, and the amount sample extracted.

3. RESULTS AND DISCUSSION

Tw enty six cetaceans have been studied in this work: 26 Stenella coeruleoalba and 2 Tursiops truncatus. Since the dolphins’ teeth were not sampled by the GECEM, the sexual was determined according to the data of Alzieu & Duguy [10] and Cardellicchio et al. [24]. The population of Stenella coeruleoalba included 13 males, 8 females and 5 young dolphins. The 2 Tursiops truncates consisted of 1 male and 1 young dolphin. The size and sexual maturity of these individuals as well as the date and place of stranding are presented in Table 1. For each specimen, all the organs could not be sampled and thus, could not be analyzed in this study. As organochlorines are very lipophilic compounds, they are mainly accumulated in the blubber. We chose to study this tissue separately from the other organs to facilitate the interpretation and to allow an easier comparison with results from other works.

3.1. Pesticides in the blubber of Stenella coeruleoalba

Co ncentrations of pesticides measured in blubbers of stenella are always detected but are very low in some cases (Table 2). The average concentrations vary from one organism to another. Heptachlor-epoxide, dieldrin, and endrin have average concentrations higher than 70 ng.g-1 lw for all organisms (youngs, males and females). These values were relatively low as compared to those reported in the literature. Borrell & Aguilar [25], in a study on Mediterranean dolphins have reported levels for dieldrin superior to 1,500 ng.g-1. On the other hand, levels of dieldrin ranging from 256 to 1,420 ng.g-1 have been reported for dolphins in India [26], and levels ranging from 2,214 to 4,100 ng.g-1 were published for dolphins originating from Australia [27].

The endosulfan levels ranged between 4.6 and 134.2 ng.g-1 lw with an average level under 60 ng.g-1 lw. The levels of aldrin, heptachlor and lindane were in general low in all organisms. They varied from 1.5 to 60.1 ng.g-1 lw, for an average level under 25 ng.g-1 lw. The coefficient of distribution octanol-water (log Kow) of dieldrin is in the order of 3.6-6.2 [28] and was equivalent to the coefficients of tetra-polychlorinated biphenyls [4]. Dieldrin is a metabolite of aldrin [29]. In the same sample, dieldrin, unless exception has been often in high proportion compared with aldrin, reflecting certainly the presence of this compound in the medium for a long period of time. Nevertheless, in organisms, due to microbiological activities, dieldrin may in turn be transformed into aldrin [30]. By contrast, we have measured contents in endrin varying from 6 to 1,526 ng/g, in the blubber. These values were relatively high compared to the former pesticides and were comparable to those obtained by Hensen [31]: 582 to 1,101 ng.g-1.coeruleoalba

Th e present data reflect the persistent nature of the organic compounds in the environment. Some of them, like lindane or dieldrin are particularly toxic for many aquatic species from the early stages of the life. In the marine organisms these refractory compounds, associated with many other toxic compounds can lead to the suppression of immune defense [32], modulate reproduction [33], and may even generate tumors [34]. In synergy with other chlorinated compounds such as polychlorinated biphenyls, they are suspected to contribute to the stranding of dolphins.


40

An analysis of the relationship of the levels in males/females and young/females showed that:

The ratios of adult male (M) to female (F), R(M/F)

1 for aldrin and heptachlor. For all the other compounds, R

(M/F) < 1, which is to say that in the blubber, adult females seem to accumulate prefer-

entially some compounds as compared to others.

The ratios young (Y) to female adult (F), R(Y/F)

1 for heptachlor, aldrin, heptachlor-epoxid, endo-sulfan. For the other compounds (lindane, dieldrin, endrin), the females seem to collect them more than the young dolphins and the adult males.

However, additional studies with higher sampling are required to validate the present results.

Table 2: Mean concentration, Standard Deviation (S.D.) and number of individual (n) for young,male and female Stenella

Young Male Female Range Mean S.D. n Range Mean S.D n Range Mean S.D n

Lindan 7.0 - 19.6 14.1 5.2 5 5.1-23.3 13.5 5.0 13 3.2- 60.1 22.3 19.6 8 Heptachlor 2.8 - 11.1 6.6 3.7 5 1.9-17.1 6.8 4.6 13 1.7-12.7 5.9 3.7 8

Aldrin 3.2 - 31.3 16.2 10.1 5 1.5-29.7 10.9 7.8 13 3.2-31.0 10.9 8.7 8 Hept.-epoxide 14.0 - 226.1 177.1 159.6 5 21.3-100.8 56.8 60.0 13 4.8-416.5 74.1 116.8 8 Endosulfan I 4.6 - 134,2 55.5 52.2 5 12.9-72.9 38.5 21.4 13 11.8-102.7 56.1 36.3 7

Dieldrin 17.6 - 756.0 232.1 303.7 5 4.8-537.6 178.1 196.7 13 9.3-1254.8 356.6 464.7 8 Endrin 10.7 - 553.7 174.8 219.9 5 30.4-644.2 193.2 181.5 13 6.1-763.1 336.3 382.9 8

3.2. Pesticides in the blubber of Tursiops truncatus

In principle, the Tursiops truncatus is a coastal species and thus is more confronted to strong pollution than Stenella Coerroleoalba, wich is a pelagic dolphin.The comparison of results of other pesticides between the Tursiops truncatus (Table 1, n° 17 and 54), and Stenella coeruleoalba showed no significant difference of accumulation between the two species. Kajiwara et al. [35] and Leonel et al. [36] have reported similar results in other species of cetaceans.

In the Tursiops truncatus, Fair et al. [26] have obtained levels of 1,230 to 1,650 ng.g-1 lw in dieldrin. These contents have been similar to those obtained by Borrell & Aguillar [25], in the dolphins of the Mediterranean Sea. Nevertheless, this comparison must be tempered, because the determination has been performed in two specimens of Tursiops truncatus only. Moreover, the juvenile was a premature runt, which was never suckled, and never caught preys, which is not the case of the specimens of Stenella coeruleoalba.

3.3. Pesticides in different organs of Stenella coeruleoalba

We quantified each of the pesticides listed above in most of our samples of striped dolphins. The average concentrations for each compound in the different tissues and organs are included in Table 3 in young, male and female dolphins respectively. Few significant differences appeared between juveniles and adults for the total contents of pesticides in the various organs. However, the young dolphins already contained relatively important levels of organochlorinated pesticides.


41

Table 3: Mean concentration, Standard Deviation (S.D.) and number of individual (n)for pesticides in organs other than blubber, for young, male and female Stenella coeruleoalba.

In all the tissues and organs, for young dolphins and adult, the overall average contents varied approximately in the same way as in the blubber: dieldrin and endrin were the predominant compounds with some exceptions (for instance, a very low level of dieldrin in the lung of young dolphins). The levels of heptachlor and aldrin were the lowest in most of the samples. The levels of lindane, heptachlor-epoxide and endosulfan I, were in general between the two previous groups.

We established the ratios of concentration between male (M) and female (F) R(M/F)

, then between young (Y) dolphins and females R

(Y/F) and finally between young and male R

(Y/M); the aim being to understand

the behavior of pesticides in the different organs. Results are presented in Figure 2.

The ratios of concentrations between the males and the females R(M/F)

, with a few exceptions, were higher than or equal to 1, which showed, the tendency of a strong accumulation of organochlorinated compounds in males compared to females. The ratios of concentrations between the young dolphins and the females R

(Y/F) demonstrated globally the same trends, and it confirmed the strong contamination of

young dolphins in comparison to adult females. Exceptions could be noted for the Endosulfan in the liver and the muscle, the dieldrin in the lung and the kidney and the Endrin in the lung and the liver. These disparities remained unexplained. But in the marine environment, the kinetics of exposure to pollutants is variable from one organism to another and also depends on physic-chemical factors.


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Ratios of concentrations between young dolphins and the males, R(Y/M)

, seemed broadly to indicate that young ones would be more contaminated than the adults, but the trends are less sharp.

Figure 2: Average ratios of concentration of pesticides in different tissues and organs between male and female (M/F), young and female (Y/F) and young and male (Y/M) for Stenellas coeruleoalba.

4. CONCLUSION

In g eneral, levels of organic compounds in the organs of dolphins have been found rather heterogeneous and might vary significantly from one individual to another. This heterogeneity could be linked to the conditions of nutrition of the animals, their state of health, but also with the state of preservation of the tissues. In the present study, we selected to compare average values bearing in mind that standard deviations were often high and thus could preclude standard statistical tests.


43

In all the samples studied, the pesticides as dieldrin and endrin were relatively high and the concentrations of the other pesticides were sometimes negligible. In the same sample, dieldrin, unless exception was often in high proportion compared with aldrin, reflecting certainly the presence of this compound in the medium for a long period of time. By contrast, we measured contents in endrin varying from 6 to 1,526 ng.g-1 in the blubber. These values were relatively high as compared to the former pesticides and were similar to those obtained by Hensen [31]: 582 to 1,101 ng.g-1.

The present study demonstrated the persistent nature of the organic compounds in the environment. Some of them, like lindane or dieldrin have been shown to be particularly toxic for many aquatic species from the early stages of the life. In the marine organisms, these recalcitrant compounds, associated with many other toxic compounds have led to the suppression of immune defense [32], the modulation of reproduction [33], and the induction of tumors [34].

Give n our results and the information available, it was difficult to assign to the pesticides the causes of death of the stranded dolphins but the levels of contaminants measured were likely to contribute significantly.

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[19] Wolkers H., Krafft B. A., Van Bavel B., Helgason L. B., Lydersen C., Kovacs K. M., (2008). “Biomarker responses and decreasing contaminant levels in ringed seals (pusa hispida) from Svalbard, Norway.” Journal Toxicology Environmental Health 71: 1009 – 1018.

[20] Dhermain F., Dupraz F., Dupont L., Keck N., Godenir J., Cesarini C., Wafo E., (2011). “Recensement des échouages de cétacés sur les côtes françaises de Méditerranée. Années 2005-2009.” Sci. Rep. Port-Cros natl. Park., Fr 25: 119-139.


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[21] Murphy P. G., (1972). “Sulfuric acid for the cleanup of animal tissues for analysis of acid-stable chlorinated hydrocarbon residues.” J Ass off Anal Chem 55:1360-1362.

[22] Wafo E., Sarrazin L., Diana C., Dhermain F., Schembri Th., Lagadec V., Pecchia M., Rebouillon P., (2005). “Accumulation and distribution of organochlorines (PCBs and DDTs) in various organs of Stenella coeruleoalba and a Tursiops truncatus from Mediterranean littoral environment.” Science of the Total Environment 348: 115 – 127.

[23] Villeneuve J. P., de Mora S. J., Cattini C., (2006). World-wide and Regional Intercomparison for the determination of organochlorine compounds and petroleum hydrocarbons in Tuna homogenate IAEA-435. Marine Environment Laboratory, 4 Quai Antoine Ier, MC-98000 Monaco 2006.

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[26] Fair P. A., Adams J., Mitchum G., Hulsey T. C., Reif J. S., Houde M., Muir D., Wirth E., Wetzel D., Zolman E., Mcfee W., Bossart G. D., (2010). “Contaminant blubber burdens in Atlantic bottlenose dolphins (Tursiops truncatus) from two southeastern US estuarine areas: concentrations and patterns of PCBs, pesticides, PBDEs, and PAHs.” Science of the Total Environment 408: 1577 – 1597.

[27] Ruchel M., (2001). Toxic dolphins- a Greenpeace investigation of organic polluants in South Australian Bottlenose Dolphins.

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[33] Wells R. S., Tornero V., Borrell A., Aguilar A., Rowlers T. K., Rhinehart H., Hofman S., Jarman V. M., Hohnn A. A., Sweeney J. C., (2005). “Integrating life-history and reproductives success data to examine potentiels relationships with organochlorine compounds for bottlenose dolphins (Tursiops truncatus) in Sarasota bay, Florida.” Science of the Total Environment 349: 106 – 119.

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[35] Kajiwara N., Matsouoka S., Iwata H., Rosas F. C. W., Fillmann G., Readman J. W., (2004). “Contamination by persistent organochlorines in cetaceans incidentally caught along Brazilian coastal waters.” Archives of Environmental Contamination and Toxicology 46: 124 – 134.

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MODELING OF REINFORCED CONCRETE STRUCTURES WITH 3D DETAILED FINITE ELEMENT MODELS

George Markou1*1, Manolis Papadrakakis2

1Assistant Professor, Civil Engineering Department, Alhosn University of Abu Dhabi, UAE.

2Institute of Structural Analysis & Seismic Research, National Technical University of Athens, Greece

ABSTRACT: In this paper a detailed finite element modeling is presented for the simulation of the nonlinear behavior of reinforced concrete structures which overcomes limitations of previous models regarding accuracy and computational efficiency. The proposed modeling method uses 8-node hexahedral isoparametric elements for the discretization of concrete. Steel rebars may have any orientation inside the solid concrete elements allowing the simulation of longitudinal as well as transverse reinforcement. Concrete cracking is treated with the smeared crack approach, while steel reinforcement is modeled with the natural beam-column flexibility-based element that takes into consideration shear and bending stiffness. The performance of the proposed modeling is demonstrated by comparing the numerical predictions with existing experimental results in the literature. The results show that the proposed refined simulation predicts accurately the nonlinear inelastic behavior of reinforced concrete structures achieving numerical robustness and computational efficiency.

KEYWORDS: Reinforced concrete, natural beam-column flexibility element, smeared crack, embedded reinforcement.

INTRODUCTION1.

Many numerical models have been developed for the analysis of Reinforced Concrete (RC) structures but none of them have managed to provide the desired combination at an acceptable level of arithmetical accuracy, robustness and computational efficiency in predicting their nonlinear inelastic behavior. 1D beam-column models, based on either concentrated plasticity methods (plastic hinges [1-5]) or distributed plasticity (fiber models [6-10]), have difficulties in predicting the mechanical behavior of 3D RC framed structures due to their inability in capturing shear behavior and local phenomena that affect the global response of the structure. The use of 2D plane stress finite element models [11-15] can avoid some simplified assumptions that are inherent in 1D beam-column models, like the influence of shear stresses, but their inability of capturing the out of plane response made them inadequate for 3D full scale structural analysis. Three-dimensional simulation with solid finite elements, based on triaxial stress-strain relationships and embedded rebars [16-21] provides the highest quality of approximation but it is hindered with high computational cost and in several cases lack of robustness.

The use of 3D material models combined with the smeared crack approach led to inefficient numerical simulations with many Newton-Raphson iterations per load step requiring considerable computational effort even for small-scale finite element models. In this work a 3D 8-noded hexahedral isoparametric element is used for the simulation of concrete based on an improved concrete material model originally proposed by Kotsovos & Pavlovic [16]. The material model of concrete was developed on the basis of experimental tests of concrete under multiaxial stress states [22], where cracking was treated as a complete sudden loss of stress for monotonic loading conditions and the only material parameter that

* Corresponding Author. E-mail: [email protected]


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is required is the cylindrical uniaxial compressive strength of concrete. The reinforcement is modeled with an embedded steel bar simulated with the Natural Beam-Column Flexibility-Based (NBCFB) element. The geometric treatment of the embedded reinforcement allows the rebar elements to have any orientation inside the concrete solid elements [23] while the shear and bending stiffness of the rebars is taken into consideration. The formulation of the NBCFB element follows the nonlinear state determination presented in [24] and the natural mode method which was introduced by Argyris and co-workers [25-26].

The above features of the detailed 3D finite element discretization of RC structures are incorporated into the proposed numerical model and the validation of the obtained numerical results is performed with experimental data of RC structural members, which are found in the literature. The commercial code ATENA v4.1.2 [27] was used in this study in order to conduct numerical comparisons where the superiority of the proposed modeling in terms of accuracy and computational efficiency, is demonstrated.

EMBEDDED REINFORCEMENT IN HEXAHEDRAL CONCRETE ELEMENTS2.

2.1 Generating Embedded Reinforcement

The most noteworthy method for the generation of reinforcement in FE modeling of concrete structures is proposed by Barzegar and Maddipudi [28], which is an extension of the work of Elwi and Hrudey [29]. This approach has the advantage of allowing arbitrary positions for the rebars inside the concrete elements and a free geometry for each hexahedron element. However, a nonlinear search procedure based on the Newton-Raphson method is required in order to calculate the natural coordinates of each steel bar node. Despite the fact that the convergence rate of the nonlinear search is rather high, the computational demand for relatively large-scale structures with thousands of steel bars becomes excessive. In this work the proposed method of Markou and Papadrakakis [30] is used in order to allocate the embedded reinforcement rebars inside each hexahedral element.

2.2 Modeling of Embedded Reinforcement Rebars

Previous simulations with the embedded rebar reinforcement used 2-noded or 3-noded rod elements. Thus, the reinforcement is considered to act as uniaxial element that can only be compressed or tensioned, without taking into consideration shear and bending stiffness. Although it is generally believed that shear resistance of reinforcement is not significant, this is not always the case as it is demonstrated in this work. The discretization of the reinforcement is therefore performed with a NBCFB element which in addition to the consideration of shear and bending it was found to increase the numerical stability of the Newton-Raphson iteration procedure due to its internal nonlinear state determination process. However, the choice of 3D beam elements instead of uniaxial rod elements introduces some implementation issues. When 2-noded or 3-noded rod elements are used, the compatibility conditions between the nodes 1 and 2 of the rod and the corresponding hexahedral nodes (n1-n8) is enforced through the translational degrees of freedom (Fig. 1a), since the rotation of the rod nodes is neglected. On the other hand, when beam elements are used, there must be compatibility between the hexahedral nodal displacements and rotation of the rebar nodes that are located on the hexahedral faces.

In order to calculate the rotation of the rebar node from the displacement of the corresponding hexahedral face that contains it, the rotation of the face has to be computed. Assuming that the angle between the orientation of the rebar and the normal on the master triangle of the hexahedral face (see Fig. 1b) is considered to be fixed before and after deformation, the required rotation can be derived through kinematic constraints. The assignment of a master triangle at each rebar node is performed prior to the

GEORGE MARKOU, MANOLIS PAPADRAKAKIS

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analysis by detecting the three nearest hexahedral nodes of the corresponding face containing the rebar node. These three nodes (n2, n3, n6 in Fig. 1c) represent the master triangle which controls the rotation of the corresponding rebar node. If a rebar node is located inside the hexahedral volume, then only translational kinematic constrains are implemented.

(a) (b) (c)

Figure 1: Embedded rebar elements under imposed transverse deformation:(a) Rod Element, (b) Beam element and (c) Master triangles of beam element nodes 1 and 2.

2.3 Kinematic Relations

In this work, the kinematic relations that connect the beam nodal displacements with the nodal displacements of the hexahedral that contains it, are given from the following expressions

(1)

where uB and UH are the displacement vectors of the beam and hexahedral elements, respectively. The transformation matrix [T] is computed by using the natural isoparametric coordinates of the hexahedral, the beam element and the master triangle nodes (Appendix A).

(2)

2.4 The NBCFB Element

The Natural Beam-Column Flexibility-Based (NBCFB) element [9] is a 2-noded three-dimensional beam finite element with 12 degrees of freedom (6 per node). The computation of its flexibility-based stiffness matrix is done with the use of Gauss-Lobato integration points. The flexibility-based formulation relies on force interpolation functions that strictly satisfy the equilibrium of bending moments and axial force along the element and requires an iterative algorithm in order to calculate the internal forces during the elements state determination [24].

As can be seen in Fig. 2, the circular section of any rebar is transformed into an equivalent square section which is further subdivided into a number of fibers in x and y directions (Eq. 3).

MODELING OF REINFORCED CONCRETE STRUCTURES WITH 3D DETAILD FINITE ELEMENT MODELS

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The material law adopted in this work for the inelastic modeling of the steel rebars is the Menegotto & Pinto [31] material model.

Figure 2: Discretization with fibers of an embedded reinforcement beam element.

CONCRETE CONSTITUTIVE MODEL3.

3D concrete material models combined with the smeared crack approach, introduce numerical instabilities to the Newton-Raphson iterative procedure particularly when the RC reinforcement begins to yield. In some cases divergence of the nonlinear solution was observed when cracking develops locally, thus the structure appears to fail prematurely without entering the failure zone [16]. This is the result of an instability introduced through the constitutive matrix where eventually several diagonal terms of the elemental stiffness matrix takes zero or negative values. In addition to that, when the opening of cracks occurs, abrupt unbalanced forces are created which induce instability in the solution algorithm especially when a large number of cracks open simultaneously.

The Modified Concrete Material Model3.1.

The Kotsovos and Pavlovic material model [16], assumes that the moduli KS and G

S change even when

the stress state is much smaller than the concrete’s compressive strength (0u

<< max ) because their values depend on the hydrostatic and deviatoric stresses (

0,

0). The updating of the hexahedral stiffness

matrices at the early stages of loading demands extra computational effort with no measured effect on the nonlinear structural behavior. Due to the Kotsovos and Pavlovic material model formulation, it is necessary to update the material constitutive matrix of each hexahedral Gauss point according to the change of K

S and G

S moduli. Having to solve an ill-posed numerical problem when cracking occurs, the

uncracked hexahedral elements induce additional numerical instability and increase the computational cost through their material model formulation and the continuous requirement of their stiffness update.

Taking into consideration these numerical difficulties, a modification to the numerical handling of the Kotsovos and Pavlovic material model is proposed. Following an extensive parametric investigation it was concluded that if the ultimate deviatoric stress

0u (Eq. 4) at any Gauss point is less than 50%

of the corresponding ultimate strength, then the elastic constitutive matrix D can be used. It is only when the computed deviatoric stress

0u exceeds the 50% of the corresponding ultimate strength, then

the nonlinear material law is activated and the constitutive matrix is computed by updating the Kt and


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Gt moduli according to [16]. Fig. 3 illustrates the flow chart of the proposed numerical handling of the

material model.

Figure 3: Flow chart of the adopted concrete material model.

SMEARED CRACK MODELING4.

Smeared crack models take into consideration crack openings by modifying the calculation of stiffness matrices and stresses at corresponding integration points. This approach proceeds with the simulation of individual cracks without the need for remeshing. The smeared crack model implemented in this work is based on the work of Rashid [32] as described by Gonzalez-Vidosa et al. [33]. In the framework of an incremental iterative procedure the increments of stresses at each Gauss point are found from the increments of strains through the constitutive matrix D.

A crack occurs when the ultimate deviatoric stress max at a Gauss point has been exceeded (usually


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in tension or in combination of tension and compression). Then a plane is formed (crack’s plane) which is perpendicular to the direction of the maximum tensile stress that exists before the cracking. This tensile stress is set to zero precluding unbalanced forces at the element nodes. The incremental stress-strain relation of Eq. 5 is subsequently properly adjusted to take into consideration zero stress along the perpendicular axis to the plane of crack (axis 3') and a modified shear rigidity G, as shown in Eq. 6, along the plane of crack is applied.

where μ is the Lamé constant. If a tensile state of stress is reached in a different direction than the previous one, then a second crack opens with its corresponding plane being perpendicular to the direction of the new maximum principal tensile stress. If a third tensile stress occurs at the same Gauss point, then a zero stiffness contribution is assumed for this specific Gauss point.

NUMERICAL EXPERIMENTS OF RC BEAMS WITH AND WITHOUT STIRRUPS5.

With these two numerical experiments, we will illustrate the importance of taking under consideration the shear and bending stiffness of reinforcement by treating the rebars as beam elements instead of rod elements. The computational efficiency of the numerical treatment of the proposed formulation will also be demonstrated with these numerical tests. We must note here that, in this numerical study we consider full bond between concrete and reinforcement rebars since the phenomenon does not play an important role on the non-linear behavior of the specific structural members. For both numerical simulations, the tensional strength of concrete was assumed to be equal to 5% of the corresponding cylindrical compressive strength, the remaining shear capacity parameter was equal to 0.05 and the Newton-Raphson energy convergence criterion was set to 10-4.

5.1 RC beam without stirrups under central point load

The first numerical experiment consists of a simply supported beam with no stirrups [16]. Its geometrical features are depicted in Fig. 4. The experimental failure load was reported to be equal to 334kN with a corresponding central deflection of 6.6mm. Fig. 5 shows the FE model which consists of 132 hexahedral elements for concrete and 88 NBCFB elements for the embedded reinforcement. The four longitudinal bars have a diameter of 28.9mm which represents a large reinforcement ratio (1.52%) corresponding to the beam sectional dimensions (309.9mm width and 556.3mm height). Appendix B illustrates how the shear and bending stiffness coefficients of the embedded steel rebar element affect the hexahedral stiffness matrix.

Curve 4 in Fig. 6 was taken by using 27-noded hexahedral elements and rod elements as embedded reinforcement elements [17]. The second and third curves were produced by the commercial code ATENA [27] discretizing the beam with 8- and 20-node hexahedral elements, respectively, rod elements as embedded reinforcement and assuming perfect-bond, while curves 5 and 6 are obtained with the


53

present formulation with rod and beam elements, respectively. The predicted failure load with the proposed modeling method was 338kN with a corresponding deflection of 6.7mm. The failure of the beam (termination of the nonlinear solution procedure) was initiated due to cracking of the beam compressive zone, as illustrated in Fig. 7.

Figure 4: RC beam without stirrups under central point load. (a) Member characteristics, (b) experimentally observed crack pattern at ultimate load [16].

The same problem was solved with the ATENA where the corresponding required time for the solution process, when using 8-node hexahedral elements, was approximately 8 minutes and when using 20-node hexahedral elements the time was about 25 minutes. According to the numerical tests reported in [34] the same problem was solved in 10 minutes with the use of a Pentium 4 extreme processor (3.73GHz) which corresponds to 20 minutes with the processor used in this study.

Figure 5: Beam without stirrups under central loading. FE mesh.

Figure 6: RC beam without stirrups under central point load. Predicted and experimentalload-midspan deflection curves for different FE models.


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Figure 7: RC beam without stirrups under central point load. Crack pattern and deformed shape prior to failure.

The computational effort for this test problem is shown in Table 1, where it can be seen that the required CPU time for solving this nonlinear problem with 30 load increments was 7 seconds.

Table 1: RC beam without stirrups under central point load. CPU time fordifferent tasks of the nonlinear analysis.

Task CPU Time (sec)

Embedded Rebar Element Mesh Generation 0.02

Newton Raphson Non Linear Solution 7.00

Writing Output Data 12.00

Other 0.08

Total Time 20.0

5.2 RC beam with stirrups under central point load

The second numerical test refers to the same beam specimen with stirrups and compression reinforcement, as depicted in Fig. 8. It must be mentioned that local stiffening is applied in the experimental set-up in the region of the central point load and at the support regions. The collapse of this beam member occurred when the central point load reached 467kN with a corresponding midspan deflection of 13.8mm [16].

The failure of the beam was brittle without yielding of the tension bars. Diagonal cracking began at the same load level as for the beam without stirrups (267kN), but did not lead to failure due to the presence of stirrups and compression reinforcement. Fig. 9 shows the FE model that was used for this numerical experiment which consists of 102 hexahedral elements for concrete and 354 NBCFB elements for the embedded reinforcement.


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Figure 8: RC beam with stirrups under central point load. (a) Member’s characteristics and (b) experimentally observed experimental crack pattern at ultimate load.

Figure 9: RC beam with stirrups under central loading. FE model.

As can be seen from Fig. 10, the predicted failure load is equal to 448kN with a corresponding midspan deflection of 13.5mm for the case where the external load is divided into 50 load steps (Curve 4). Similar failure loads were also obtained when the load step increment is increased or decreased confirming the robustness and efficiency of the algorithmic implementation (Curves 3, 4 and 5).Fig. 11 shows the crack pattern prior failure. Cracking in the beam’s compressive zone starts for a total applied load of 300kN, but does not lead to failure of the beam due to stirrups confinement and the compressive contribution of the upper reinforcement. The numerical solution terminates when failure of the compressive bars is manifested which is in good agreement with the experimental mode of failure. The required computational time for the nonlinear solution procedure is depicted in Table 2, which refers to 48 Newton Raphson load steps.

CONCLUSIONS6.

A detailed finite element modeling of concrete is proposed with the following characteristics: (i) An improved numerical handling of a 3D material concrete model for monotonic loading which

was based on the Kotsovos & Pavlovic material model was presented. The proposed material model was integrated with the smeared crack approach and was combined with an isoparametric 8-noded hexahedral element. It was shown that the choice of a brittle material model for concrete is a suitable choice that reproduces objectively experimental results with an acceptable accuracy.

(ii) The modeling of the reinforcement was performed with the use of a 2-noded flexibility-based beam elements, with natural modes and the fiber approach. It was shown that the simulation of the reinforcement with the use of rod elements does not lead to accurate numerical simulations


56

especially for heavily reinforced RC members. The proposed NBCFB element takes into account the shear and bending stiffness of the rebar elements and introduces additional stability to the nonlinear numerical solution through its formulation.

The numerical robustness exhibited by the proposed modeling methodology is attributed to the following reasons: The nonlinear procedure for the calculation of the internal forces of the NBCFB element, the numerical stability induced by the consideration of bending and shear stiffness of the NBCFB elements, the modification of the concrete material model and the handling of the stress redistribution due to cracking.The proposed modeling method managed to predict with very satisfactory accuracy the experimental test results reported in the literature, illustrating its ability to predict failure loads, failure mechanisms and crack patterns with a relative accuracy and computational efficiency, regardless the mesh size and the value of the load step of the incremental iterative nonlinear procedure. This is an important ingredient when dealing with large-scale structures where the sensitivity on the mesh size and on the required number of load increments applied during the analysis plays a crucial role in the feasibility of any detailed finite element simulation for real scale RC structures.

Figure 10: RC beam with stirrups under central loading. Load-deflection curves for different load increments and FE modes.

Figure 11: RC beam with stirrups under central point load. Crack pattern andcorresponding deformed shape at failure load level.


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Table 2: RC beam with stirrups under central point load. CPU time for different tasks of the nonlinear analysis.

Task CPU Time (sec)Embedded Rebar Element Mesh Generation 0.03Newton Raphson Non Linear Solution 17.00Writing Output Data 25.00Other 0.43

Total Time 42.46

ACKNOWLEDGEMENTS7.

The John Argyris Foundation and the Research Funding Department (ELE) of NTUA funded this research work. Their financial support is gratefully acknowledged.

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[31] Menegotto M and Pinto PE. (1973), Method of Analysis for Cyclically Loaded Reinforced Concrete Plane Frames Including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending. Proceedings, IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads, Lisbon.

[32] Rashid, YM. (1968), Ultimate strength analysis of prestressed concrete vessels. Nucl Eng and Des 7, pp. 334-344.

[33] Gonzalez-Vidosa F, Kotsovos MD and Pavlovic MN. (1991), A three-dimensional nonlinear finite-element model for structural concrete. Part 1: main features and objectivity study; and Part 2: generality study. Proceedings of the Institution of Civil Engineers, Part 2, Research and Theory 91, pp. 517-544.

[34] Lykidis G. (2007), Static and Dynamic Analysis of Reinforced Concrete structures with 3D Finite Elements and the smeared crack approach. Ph.D Thesis, NTUA, Greece, [In Greek].

[35] Argyris J., Tenekb L., Olofssond L. (1997), TRIC: a simple but sophisticated 3-node triangular element based on 6 rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells. Comput. Methods Appl. Mech. Engrg. 145, pp. 11-85.

[36] Cotsovos D.M., Zeris Ch.A. and Abas A.A., Finite Element Modeling of Structural Concrete, ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2009, Rhodes, Greece, 22–24 June 2009.


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APPENDIX A

In order to transform the stiffness matrix of the embedded rebar beam element, the transformation matrix [T] (Eq. 2) is required to be computed, which consists of 22 non-zero submatrices with dimension 3x3. From Eq. 2 it can be seen that the translational degrees of freedom of each beam element node are transformed through the use of Eq. A1.

where i = 1, 8 are the 8 hexahedral shape functions and j = 1, 2 denote the embedded rebar nodes.As it can be seen from Eq. A1, matrix , contains the 8 shape function values for each rebar node.In order to transform the rotational dofs of the embedded rebar beam element the definition of a master triangle is necessary in order to compute the rotation along the three global axis. As it was mentioned in this work, for each embedded rebar node j that is located on a hexahedral face, we assign a master triangle. For the case of an 8-noded hexahedral element, each face consists of 4 nodes, thus the three nearest to the rebar beam element node represent the corresponding three master triangle nodes (Fig. 2). In this work, the computation of each master triangle body rotations are calculated through the use of the natural mode theory. In order to estimate the translational modes as functions of the displacements and rotations at vertices 1, 2 and 3 of a triangle [35], it is assumed that the linear displacement field with respect to the local elemental coordinate can be described as:

If the origin of the local coordinate is placed at the element’s barycenter Eq. A2 may be written in the form:

The rigid-body rotation 06 will be estimated by using:

If we write Eq. A2 for every vertex, the result is:

The relation between the rigid-body rotations 04

, 05

and the Cartesian freedoms need to be defined. For this purpose we observe Fig. A which illustrates a rotation

1.

The idea here is to project the rotation on the x, y axes. Observing Fig. A


61

which projects on the local Cartesian coordinate via:

Similarly,

where

Figure A. Rotation 1.

Therefore, the rigid-body rotations 04

, 05

are simply:

Expressing the above equations in matrix format:

where j = 1, 2 embedded rebar beam nodes and Ω is the area of the corresponding master triangle.

Therefore, after the computation of the three transformation matrices j

mR in the global coordinate system


62

(Eq. A11) for each master triangle the computation of the transformation matrix T (12x24) of Eq. 2 is completed. For more details on the natural modes of a triangle see [35].

where is the known cosine matrix.

APPENDIX B

When modeling the reinforcement of a RC structure, the shear and bending stiffness is assumed to be equal to zero, which is considered to be an acceptable approximation. As it is going to be illustrated below, this is not always the case. The computation of the transformed (24x24) stiffness matrix of an embedded rebar beam element will be conducted by using the corresponding methodology described in this work. The material parameters of the simply supported beam without stirrups in the numerical implementation of section 5.1 were used to compute the rebar stiffness coefficients. It was assumed that the hexahedral element edge length was 15cm and the diameter of the embedded rebar element was 28.9mm. After the computation of the transformed (24x24) rebar stiffness matrix, a normalization was applied by dividing all the stiffness coefficients over the longitudinal stiffness coefficient 1,1

K of the rebar element (Eq. B1). For illustrational reasons, when the result of this division was equal to 1, the value of Eq. B1 was set equal to zero.

(a) (b)

Figure B1: (a) Normalized transformed 24x24 beam rebar stiffness matrix.(b) Transformed 24x24 rod rebar stiffness matrix.

Fig. B1a illustrates the normalized transformed rebar stiffness matrix. As it can be seen in Fig. B1a, the stiffness contribution of the shear and bending stiffness coefficients of the embedded beam rebar element is 2.6% of the corresponding longitudinal stiffness coefficient. When the rod element is used


63

for the modeling of reinforcement, the longitudinal stiffness coefficient is distributed as it can be seen in Fig. B1b. In order to illustrate the variation of coefficient c

n in respect to the rebar diameter, the previous parametric

investigation was conducted for different rebar diameters (Ø6-Ø36) and the results are given in Fig. B2. As it can be seen, the increase of coefficient c

n is exponential as the rebar diameter increases. The

maximum value of the coefficient cn is 4.02% for the case of 36mm rebar diameter.

Figure B2: Coefficient cn for different rebar diameters.


2. FINITE ELEMENT FORMULATION

65

A DEVELOPED MICROPLANE MATERIAL MODEL FOR NONLINEAR FINITE ELEMENT ANALYSIS WITH EMPHASIS ON CONFINED REINFORCED CONCRETE

COLUMNS

Omar Al-Farouk Salem Al-Damluji 1*, Ihsan A.S. al-Shaarbaf2, Wamidh Ajil Jassim3

1Former Professor, Department of Civil Engineering, University of Baghdad, Iraq2Assistant Professor, Department of Civil Engineering, Al-Nahrain University, Baghdad, Iraq

3Former Postgraduate Student, Department of Civil Engineering, University of Baghdad, Baghdad, Iraq

ABSTRACT: In this investigation, a constitutive model based on the microplane material model is developed. For the microplane model, simple relations between stress and strain components on planes of multiple orientations (the microplanes) representing the nonlinear material behavior have been developed. The strain components acting on the microplanes are determined by assuming that they are kinematically constrained to the macroscopic strain tensor. Simple, path-dependent, stress-strain relations then determine the microplane stress components on each microplane. A special constitutive model is implemented in the computer code Microplane Material Model (IIIM) which is a finite element program written in Fortran language designed for computer simulations of reinforced concrete structures. Beam, plate, column and panel behaviors are presented in order to demonstrate the capabilities of the proposed numerical constitutive solution scheme and to highlight the response of reinforced concrete members. Ten different types of full scale tied concrete columns have been analyzed and compared with the available test data. The computed results are found to be in good agreement with the experimental data which confirms the adequacy of the model and programs developed.

KEYWORDS: Microplane Material Model- Non-Linear Finite Elements- Confined Columns- Reinforced Concrete.

INTRODUCTION1.

In the last three decades, tremendous progress has been made in modeling concrete and the analysis of reinforced concrete structures. However, the rapid development in the field of structural analysis has not been matched by the development in material modeling for reinforced concrete. Little research has been undertaken in developing elements for confined concrete, particularly when looking beyond the peak load. A proper analysis strongly depends on a workable and reliable numerical model, particularly when the softening behavior of concrete is incorporated in the formulation. Concrete members, which rely on confinement by steel reinforcement for ductility, cannot be modeled in two-dimensions. For studies on earthquake resistance and on ductility of concrete columns, it is important to investigate the post-peak, or strain softening behavior of the columns. The conceptual simplicity of the present general micro-plane model is rewarded by the ease of material identification. This model was proposed by Bazant and Prat [1] and developed by many other researchers later [2, 4, 5, 23, 24, 25 and 26].

* *Corresponding Author: E-mail: [email protected]


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In a finite element representation, the displacements and strains and their virtual counterparts in the three-dimensional brick element may be expressed by the relationships:

in which [Bi ] is the global strain-displacement transformation matrix, and for node i, {d

i } is the vector

of nodal variables, δ{di } is the vector of virtual nodal variables and [N

i] is the global shape function

matrix.

The stress - strain relationship may be written as:

Where

In evaluating the stiffness matrix [K], integration is performed in the natural (local) coordinates system.

Thus, the sub-matrix of the stiffness matrix linking nodes i and j has the form:

Concrete is modelled by 8 and 20-node isoparametric quadratic hexahedral brick elements. Three translations (u, v and w) are considered at each node along the Cartesian coordinates x, y and z. The reinforcement steel bars are modeled by one-dimensional embedded elements built into the three-dimensional concrete elements, and transmitting axial force only.

3. CONSTITUTIVE RELATIONSHIPS

In 1984, a finite element model for the analysis of concrete under uniaxial, biaxial, and triaxial compression and the modeling of reinforced concrete structures was proposed by Bazant and Gambarova [3]. A microplane is an arbitrary plane on which the constitutive properties are defined as shown in Figure (1 a). Instead of defining them by means of a relationship between macroscopic stress and strain, these properties are defined by means of a relationship between the stress and strain components on a microplane, which is conceptually much simpler because there are fewer stress and strain components and the problems of tensorial invariance do not arise at the microplane level. The macroscopic stress-strain relationship is obtained by integrating under some suitable micro-macro constraint over the microplanes of all spatial orientations. If the kinematic constraint is assumed, the microplane stresses represent the projections of the macroscopic stress tensor on the plane considered. The normal and shear strains and on the microplane with unit normal , as shown in Figure (1 b, c), can be obtained as projections of the strain tensor .

OMAR AL-FAROUK SALEM AL-DAMLUJI , IHSAN A.S. AL-SHAARBAF, WAMIDH AJIL JASSIM

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(a) Assumed microstructure (b) Strain components on microplane (c) Stress and strain on microplane

Figure 1. Stress and strain components on a microplane [1]

Each microplane resists not only normal strain but also shear strain, whose vector is assumed to be in the same direction as the vector of shear stress. The normal and shear (tangential) strains, and , on a microplane of unit normal are the resolved components of the macroscopic strain tensor in that direction. This hypothesis which represents a kinematic constraint yields the relationship:

where is the Kronecker’s delta. Additionally, the normal strain is split into two parts, the volumetric

strain and the normal deviatoric strain , the expressions of which are:

The Latin lowercase subscripts refer to Cartesian coordinates ( = 1, 2, 3), and subscript repetition implies summation. is the strain vector on a microplane whose unit normal is . is the tangential vector component of , and is its magnitude. This split for normal strain , proposed by Bazant and Prat [1], makes it possible to obtain any value of the elastic Poisson’s ratio between –1 and 0.5 and, more importantly, has proven essential for allowing a good representation of post-peak softening for both tension and compression. Associated with the three strains and , the three corresponding stresses and are introduced so that their respective products give directly the work done on the microplane. The stress-strain laws at this level are a set of empirical relationships defining the evolution of each one of those three stresses as a function of the three microplane strains exclusively. The relation between the microplane stresses and and the macroscopic stress tensor is obtained by applying the principle of virtual work. Its application to this case is explained when a field of arbitrary virtual strain variation

is prescribed to the model, one obtains the equation [21]:

A DEVELOPED MICROPLANE MATERIAL MODEL FOR NONLINEAR FINITE ELEMENT ANALYSIS

68

where the integral domain represented by represents the upper half hemisphere. This equation could also be valid if all the stress variables were replaced by their differential increments. Finally the new macroscopic stress tensor is obtained by integration of microplane stresses according to Eq. (10) as:

Within the basic framework presented, a very wide range of models can still be defined depending on how the microplane stress–strain relationships are chosen. In this work, the constitutive relationships used at the microplane level have been selected on the basis of those used in Lin and Foster [2]. The stress-strain laws, at the microlevel, are as follows:

3.1. Volumetric Law

This microplane law directly reproduces the macroscopic behavior of the material when only volumetric strains or stresses are present. Therefore, a curve that fits experimental data for hydrostatic tests may be directly introduced as:For compression,

For tension,

where is the initial volumetric modulus of elasticity. and are empirical material parameters. The volumetric law is plotted in Figure 2a. For unloading-reloading, both the tensile and the compressive curves act as envelopes.

3.2. Deviatoric Law

This law is based on the same type of exponential stress-strain envelope curve used for the tensile part of the volumetric behavior, but considering two different sets of parameters for tension and compression as:For compression,

For tension,


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Where is the initial deviatoric modulus of elasticity and are empirical material parameters taken in the same way as for the volumetric law. For unloading-reloading, straight lines are assumed with a certain slope as shown in Figure 2b.

3.3. Tangential Law

It is assumed that the tangential stress vector on a microplane, , remains always parallel to the corresponding tangential strain vector, .This means that:

where is the Euclidean length of the transverse strain vector, , and is the Euclidean length of the transverse stress vector, . Then, the problem, as shown in Figure 2c, is reduced to establishing a one–dimensional relationship between the tangential stress and strain moduli and . The relationship used for that purpose is an exponential curve similar to that used for the other microplane laws as:

where is the initial tangential modulus of elasticity. and are parameters obtained in a similar way to that used for the volumetric and deviatoric laws.

4. TANGENTIAL MACROSCOPIC STIFFNESS TENSOR

For the derivation of the macroscopic tangent stiffness matrix, Eq. (11) must be rewritten in terms of the differential stress increments instead of the total values as:

Then the increments of stresses at the microplane level must be replaced by their incremental expressions in terms of the current tangent modulus and the strain increments at the corresponding microplane level. These are simple scalar expressions for and :

Since both the tangential stress and strain on a microplane are vectors, their incremental relationship must involve a matrix as:

The matrix for the parallel tangential model used in this work is derived basically from Eq.(16) in terms of differential increments as [21]:


70

Introducing Eqs. (19), (20), and (22) into Eq.(11) and then replacing the microplane strain increments according to Eqs. (5)- (9), the final expression of the tangent macroscopic stiffness matrix can be obtained.

Figure 2. Stress - strain laws at the microlevel [1]

The change in the macro-stresses are related to the change in macro-strains. Thus, the final expression becomes:


71

where

To incorporate the model into an existing finite element coding, the tangential stiffness tensor is written in matrix form as [21]:

In fitting of the data, it is convenient to consider and as the basic parameters and choose the ratio

Relating the three initial moduli of the microplane stress-strain laws and to the standard elastic parameters can be achieved by imposing the condition that virgin (uncracked) concrete initially follows a linear elastic behaviour and solving the integral over the hemisphere by hand. By identifying the coefficients of that expression with the coefficient of Lame’s equation of elasticity, the following relations are obtained:


72

Choosing various values of , it was found that good fits are obtained approximately for For the extreme case, .

5. MICROPLANE PARAMETERS

These parameters are scaled to the concrete modulus of elasticity, , where Poisson’s ratio can be taken as = 0.18 for most types of concrete. , and are adjustable empirical constants which take different values for different types of concretes and from fits of the standard triaxial tests. After a significant number of trials [1], the microplane parameters are obtained for the concrete with triaxial compressive strength ranging between 30 and 90 MPa, as shown in Table 1. It is noted that concretes of strengths of 20 to 25 MPa can also be included.

6. NONLINEAR SOLUTION TECHNIQUE

The solution scheme employed in this work is obtained using the Modified Newton-Raphson method where a constant value of stiffness for a specified number of iterations can be assumed. In this approach, the stiffness matrix is not changed after each iteration. However, this is done periodically. This approach


73

depends on an approximate value of the stiffness and multiple iterations to converge. Computationally, multiple iterations at a constant stiffness are significantly more efficient than multiple decompositions. While more iterations are required with the Modified Newton-Raphson method, the method will converge to the same solution as the standard Newton-Raphson method [5]. The method monitors an incremental error ratio and is activated when the error ratio falls into a user specified tolerance. A tolerance of 3-10 % was used in the present study depending on each case. The nonlinear solution has been carried out using a specially modified finite element program written in “FORTRAN 77”. Another method for accelerating convergence is known as the line search method. This method uses linear interpolation to scale an existing incremental solution such that it improves convergence. The method monitors an incremental error ratio and is activated when the error ratio falls into a user specified tolerance. A tolerance of 3-10 % was used in the present study.

7. NONLINEAR SOLUTION TECHNIQUE

In order to independently test the microplane material model, the response of a small scale concrete cylinder and concrete plate under uniaxial, biaxial and triaxial compressions are studied. The model has been calibrated by fitting typical test data available in literature for the following cases: (1) uniaxial compression test of Van Mier (as cited by [1]), (2) biaxial compression and failure envelope tests of Kupfer et al. [4] and (3) triaxial compression test of Lin and Foster [5] obtained on different concretes.

Large scale correlation studies are also conducted with the objective of establishing the ability of the proposed model to simulate the response of reinforced concrete beams and panels. These comparisons are presented in order to demonstrate the capabilities of the proposed numerical solution scheme and to highlight the pronounced effect of the proposed microplane material model on the response of reinforced concrete members. For large scale members, the fitting data were for the (1) three point bending test of Bresler and Scordelis [6], (2) reinforced concrete column tests of Razvi and Saatcioglu under concentric load [7] and (3) reinforced concrete panel tests loaded by a combination of shear and biaxial compression [8].

7.1. Van Mier Compression Cylinder Test (Uniaxial Compression)

A small concrete cylinder of 32 MPa loaded by a concentrated force, tested by Van Mier (as cited by [1]), is considered. The selected segment for the concrete cylinder is shown in Figure (3). The cylinder was modeled using 8-node solid elements with a numerical integration scheme of 2x2x2 Gaussian quadrature. The top and bottom faces of the cylinder are restrained against lateral displacement. Moreover, the bottom nodes are also restrained against vertical movements while the top nodes are enslaved for uniform vertical displacement. Taking advantage of symmetry of loading and geometry, a segment representing one-eighth of the cylinder is modeled by dividing it into 56-brick elements.

In Figure 3, the stress-strain curve of a central point is shown. The load is applied in thirty-four increments up to the failure load of 660 kN. As depicted in the Figure, good agreement with experimental results is obtained throughout the entire loading levels.


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Figure 3. Stress-strain curve for 32 MPa Concrete Cylinder of Van Mier (as cited by [1])

7.2. Kupfer et al Square Plate Test (Biaxial Compression)

The biaxial failure envelope tested by Kupfer et al. [4] is also considered by the present model. The square plate is of dimensions of . The plate is modeled by using 8-node solid three dimensional elements with numerical integration over Gaussian quadrature integration points. Taking advantage of symmetry of loading and geometry, a segment representing one-eighth of the plate is modeled by discretizing the segment into 18-brick elements. The adjacent sides to the center lines of plate are restrained against lateral displacements while the bottom nodes are restrained against vertical movements. The top nodes are free to deform in any direction. Test 1 represents uniaxial compression with = 1.0/0.0, test 2 depicts biaxial compression with = 1.0/0.52 while test 3 models equibiaxial compression with = 1.0/1.0. The compressive stress states in the biaxial stress plane, at a central point in direction, are presented in Figures 4 to 6, in which comparisons between experimental and calculated stress-strain curves are shown. Under biaxial compression, concrete exhibits an increase in compressive strength of up to 25% of the uniaxial compressive strength when the stress ratio is 0.52. When the stress ratio is equal to 1, the concrete compressive strength is approximately 1.16. .

Variable ratios of the stress components were chosen for the analyses. These results are in reasonable agreement with experiments reported by Kupfer et al. [4]. Figure 7 shows the biaxial failure envelope with a non-proportional loading sequence.

7.3. Lin and Foster Compression Cylinder Test (Confined Compression)

Fitting for triaxial compression test data is difficult for two reasons. First, for the same concrete, there are different types of tests to fit simultaneously with the same set of parameters [4, 9 and 10]. Second, the behavior of the uniaxial unconfined compression, which is a limiting special case of the triaxial tests for vanishing confining pressure, is completely different from the behavior of the confined compression case.A solid finite element model is used to model a 60 MPa confined concrete cylinder under axial concentric loading with radial to vertical stress ratio of 0.025, tested by Lin and Foster [5]. The selected


75

cylinder is shown in Figure 8. Figure 8 shows a comparison between the experimental and the calculated stress-strain response. Comparison between the experimental (1000 kN) and numerical ultimate loads (985 kN) indicates an agreeable difference. The load is applied in thirty increments up to failure. The model test results fit very closely to the experimental data. It is shown that the analytical results for concrete stress-strain curve correctly predict the experimental response where they are close to each other.

A three point bending test beam A-1 is investigated by Bresler and Scordelis in 1963 [6]. Specimen A-1 in reference [6] consists of a simply supported beam with a span of 12 ft (3.7 m) which was subjected to a concentrated load at midspan. The geometry and cross sectional dimensions of beam A-1 are presented in Figure 9. Figure 10(a, b) shows the loading and support conditions of this structure. The finite element model shown in Figure 10 represents only half of the structure taking advantage of the symmetry in geometry and loading.


76

Since Adeghe and Collins and Kwak and Filippou did not match the reinforced concrete model observation for the overall structural behavior in these studies (Fig. 11), the comparison of numerical predictions demonstrates the significance of the load-displacement response of a heavily reinforced


77

specimen such as beam A-1. Figure 11 compares the developed numerical results with the measured load-displacement response of beam A-1. Very satisfactory agreement between analysis and experiment is observed. In this analysis, perfect bond is assumed between concrete and the embedded rebars and failure was due to program non-convergence and the mesh density was fine enough for failure load prediction [27, 28 and 29].

7.4. Razvi and Saatcioglu’s Column Specimens CS-19

In order to assess the ability of the proposed finite element model to simulate the behavior of a reinforced concrete column, specimen CS-19, which was tested by Razvi and Saatcioglu in 1998 [7], is selected for this study. The specimen dimensions and the reinforcing arrangement are shown in Figure 12a.

(a) Column Specimen shows (b) Boundary and symmetry (c) 32-brick elements and loading the selected segment conditions arrangement

Figure 12. Finite element idealization of Razvi and Saatcioglu’s column specimen CS-19 [7]

The main longitudinal reinforcement of the column consisted of 8#15 bars with ties stirrups spaced at 85 mm of diameter 11.3 mm as transverse reinforcement were placed to satisfy the confinement. The column specimen was subjected to a constant axial load in order to study the monotonic behavior of the specimen and establish the load-displacement response envelope. The finite element representation of the column specimen is shown in Figure 12c. Concrete is modeled using 8-node three-dimensional isoparametric elements and the longitudinal and transverse reinforcements are modeled using bar elements embedded into the relevant brick element. At stages close to the ultimate load, the stress values at sampling points located within the cover are difficult to evaluate [5, 11 and 12]. Although some computer programs such as “ABAQUS” [13] take concrete cover into account in the analysis, inaccurate results extrapolated over the element surface are obtained based on the values at the integration points. Thus, the used finite element mesh does not include concrete cover. Figure 13 compares the proposed numerical results with the measured load-displacement response of the column specimen CS-19. The proposed finite element analysis shows excellent agreement with the experimental results. The numerical ultimate load of 5280 kN in Figure 13 closely approximates the experimental ultimate load of the specimen. The results are


78

also compared with those of an earlier study using the microplane model developed by Lin and Foster in 1998 [5]. By comparing the results of the other model with the one proposed in this study, it can be concluded that the initial load-deflection behavior of the present model is stiffer than that of Lin and Foster. This is shown in Figure 13.

As mentioned, the current proposed model matches the experimental behavior very well. This can be attributed to the appropriate assumptions of the model presented in this study.

Figure 13. Load-deflection curve of Razvi and Saatcioglu’s column specimens CS-19(as cited by [7])

7.5. Vecchio and Collins Panel-B

In order to investigate the validity of the proposed model and to check if the present model is stress-locking free, a reinforced concrete panel-B tested by Vecchio and Collins in 1982 (as cited by Cervenka [8]) was used for correlation studies. The panel was square in plan and spans 890 mm with a thickness of 70 mm. It was reinforced with two layers of welded wire mesh with a steel ratio of 1.785% in both directions. In the test, external loads were applied through a series of shear rigs along the boundary of the test panels which were built by a series of vertical and horizontal rigid links that were connected to the load control units. The applied biaxial load ratios were controlled by the magnitude of forces applied through the horizontal and vertical rigid links. Panel-B was loaded by a combination of shear and biaxial compression. The dimensions and the applied loads are illustrated in Figure 14a. By taking advantage of symmetry, the finite element analysis is carried out for one quarter of the panel where only 32 brick elements were used in the basic analysis with 64 embedded steel bars through the thickness of the panel. Figure 15 compares the experimental shear stress-strain relationship of the panel with the results of this study and an earlier study carried out by Cervenka [8]. As can be seen, the prediction of the proposed model is in good agreement with measured data and correctly estimates the peak level, i.e. there is no stress locking phenomenon, which is an important feature of the new microplane material model. For all the above analyses, nonlinear simulation using this advanced constitutive model can be efficiently used to support and extend experimental investigations and to accurately predict the behavior of reinforced concrete members.


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(a) Square Panel shows (b) Boundary and symmetry (c) 32-brick elements and loading conditions the selected segment arrangement

Figure 14. Finite element mesh used for 19.3 MPa Panel-B of Vecchio and Collins(as cited by Cervenka [8])

Figure 15. Shear stress-strain curve of Vecchio and Collins Panel-B(as cited by Cervenka [8])

8. CONCLUDING REMARKS FROM VERIFICATIONS

A new constitutive model to describe the behaviour of concrete in multiaxial compression is proposed. The model predicts the load resistance and the deformation capacity of concrete in uniaxial, biaxial and triaxial compression by means of a microplane material model. The model parameters have been optimized so as to predict response close to the typical test data, especially those specimens selected from triaxial tests at various confining pressures. In the optimization, the same values have been used for most of the parameters. The fixed parameters are those for which the optimization yielded nearly the same values for different concretes. The user who needs to optimize the model for a particular concrete needs to adjust only the free parameters. For the user, however, the important points are that, depending on the pressure range, there are only six free parameters which can be identified sequentially. As for the remaining, that is the fixed parameters, the user need not bother. Experimental results are found to be in good agreement with the model prediction.


80

9. APPLICATIONS, RESULTS AND DISCUSSION

It is important to demonstrate the applicability of the proposed concrete constitutive relationships to simulate the response and ultimate load carry capacity of reinforced concrete columns. The newly developed Microplane Material Model for concrete (IIIM) is capable of integrating the effect of confinement, which leads to enhance performance of reinforced concrete members, both in strength and deformability. Numerical simulations are conducted with the developed finite element analysis program. Comparisons between numerical and experimental analyses of ten axially loaded column specimens are presented in which the variables are concrete properties and reinforcement distributions. The selected ten specimens are Sheikh and Uzumeri’s column specimens designated as CS-19 and CS-20, and Razvi and Saatcioglu’s column specimens designated as CS-01, CS-08, CS-13, CS-14, CS-15, CS-17, CS-19, and CS-24, [7, 14]. However, the results of typical cases of Sheikh and Uzumeri’s column specimen CS-20 and Razvi and Saatcioglu’s column specimen CS-24 are presented in details. The results are compared with the available test data.

10. FINITE ELEMENT MESH

The finite element mesh is used with one eighth of the column analyzed due to symmetry about x-y and y-z planes. The column specimens are consisted of two parts: the two end blocks and the test region. Both parts are modeled using 8-node, linear solid elements. Spacing of ties at top and bottom regions of the column specimen is decreased to ensure failure at the mid-height. In order to minimize mesh sensitivity, all the specimens were idealized using 32 brick elements.

11. FINITE ELEMENT MESH

The initial modulus of elasticity of concrete was estimated as Ec

= 5055

, in (MPa). Concrete tensile strength was taken as despite the fact that other relatively different values for these parameters are given in literature [5, 12, 15, 16 and 17]. The defined material model required fourteen material parameters to be identified. These are: (1) characteristic concrete compressive strength( ); (2) concrete tensile strength ( ); (3) Poisson’s ratio (v); (4) modulus of elasticity of concrete (E

c);

(5) modulus of elasticity of the reinforcing steel (Es); and (6) triaxial strength envelope parameters

and .

12. SIMULATION OF THE TESTED SPECIMENS

12.1. Sheikh and Uzumeri’s Column Specimens

In 1980, Sheikh and Uzumeri [14] tested a total of 24 normal strength tied concrete columns under concentric compression. The columns were designed to investigate the parameters of confinement, including the concrete compressive strength, volumetric steel ratio, spacing and yield strength of transverse reinforcement, distribution of longitudinal reinforcement and resulting tie arrangement. The chosen two column specimens were designated as CS-19 and CS-20. The total height was 1900 mm, with a 304 mm square cross-section. Table 2 shows the selected specimens used in the numerical analysis. Twenty-two equivalent nodal forces are applied for each column to simulate the applied axial load. The finite element mesh with the overall geometry of column specimen CS-19 is shown in Figure 12.


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Table 2: Details of the reinforced concrete column specimens of Sheikh and Uzumeri.

12.1.1 Column Specimens CS-19 and CS-20 (Sheikh and Uzumeri)Table 3 shows the macroscopic properties and column characteristics for large-scale normal-strength concrete columns confined by rectilinear reinforcement.

Table 3: Material properties used for modeling test specimens CS-19 and CS-20

Column specimen CS-20 has lower lateral steel spacing and higher tie diameter as compared with column specimen CS-19 (Table 2). Numerical stress-strain curves are compared with the test results in Figure 16 for an experimental stress-strain test point taken in the z-direction [14] as shown in Figure 12. It can be seen from Figure 16 that the numerical results are close to those of experimental test data. At peak load, the numerical axial stresses in the core are 49.9 and 50.1 MPa for specimens CS-19 and CS-20, respectively. As shown in Figure 16, the results are very close to the experimental at the end of analysis. Table 4 shows the microplane material parameters used in the analysis.


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Table 4: Microplane material parameters for column specimens CS-19 and CS-20of Sheikh and Uzumeri.

(a) Column Specimen CS-19 (b) Column Specimen CS-20

Figure 16. Numerical and experimental stress-strain curves ofSheikh and Uzumeris’ column specimens [14]

12.2. Razvi and Saatcioglu’s Column Specimens

In 1998, Razvi and Saatcioglu [7] tested a total of 26 high strength columns under concentric compression. Eight square column specimens have been chosen for the analysis using the finite element method. These column specimens were carefully selected to investigate the effect of amount of steel reinforcement, concrete compressive strength, reinforcement arrangement and spacing of transverse reinforcement. Size effect was also studied. The selected column specimens were 1500 mm high and had a 250 mm square cross-section. These column specimens were reinforced with longitudinal bars and closed stirrups non-uniformly distributed along the height of the specimen. The main reinforcement steel bars were 16 mm in diameter with steel yield strength of 400 MPa. Table 5 shows the selected specimens for the numerical analysis. The finite element mesh and details of steel arrangement are shown in Figure 12 for column specimen CS-19.

12.3 Column Specimens CS-19 and CS-20 (Sheikh and Uzumeri)Material properties for the test specimens used are summarized in Table 6. The passive confinement pressure is generated from the tensile forces that develop in transverse reinforcement. It is,


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therefore, reasonable to expect that the steel yield strength plays an important role in concrete confinement. However, the tensile stress in the transverse reinforcement is generated as a result of lateral expansion which, in turn, is independent of the mechanical properties of concrete. Therefore, the effectiveness of the transverse reinforcement is dependent on the ability of concrete to expand laterally without failure which is a function of concrete confinement [7, 15].The effect of yield strength is investigated by choosing two specimens for the analysis, CS-13 and CS-15, having the same volumetric ratio, arrangement and spacing of reinforcement but differ in their yield strengths. The numerical and experimental stress-strain responses are shown in Figure 17. Comparison between the two column specimens indicate that the specimen confined with 1000 MPa lateral steel, CS-15, showed improved strength over the column specimen CS-13 which was confined with 570 MPa steel. Table 7 shows the microplane material parameters used in the analysis.

Table 5: Details of reinforced concrete column specimens of Razvi and Saatcioglu.

Table 6: Material properties used for modeling test specimens CS-13 and CS-15.


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Table 7: Microplane material parameters for column specimens CS-13 and CS-15 ofRazvi and Saatcioglu.

Specimen

CS-13CS-15

0.000 0.002 0.004 0.006 0.008 0.010Axial Strain

0

20

40

60

Axi

al S

tres

s (M

Pa)

Column Specimen CS-19fc=33 MPa

32 Brick Elements

Experimental

Proposed Microplane Model

0.000 0.002 0.004 0.006 0.008 0.010Axial Strain

0

20

40

60

Axi

al S

tres

s (M

Pa)

Column Specimen CS-20fc=35 MPa

32 Brick Elements

Experimental

Proposed Microplane Model

(a) Column Specimen CS-19 (b) Column Specimen CS-20

Figure 17 Numerical and experimental stress-strain curves of Sheikh and Uzumeris’ column specimens [14].

13. MESH REFINEMENT

In order to assess the ability of the proposed finite element model to simulate the behavior of axially loaded columns and, furthermore, to study the effect of finite element mesh size on the numerical results, three different mesh configurations were investigated, as shown in Figure 18. The column specimen CS-24 of Razvi and Saatcioglu is selected for this study. In all configurations, the number of elements through the cross section of the specimen and the element size along the height direction is progressively increased. The results shown in Figures 19 indicate that the new microplane material model exhibits a satisfactory behavior and leads to response predictions which are essentially independent to the finite element mesh size.

14. HISTORY OF AXIAL STRESSES OVER THE CROSS SECTION

It is interesting to look at the history of axial stresses over the cross section of the specimen. Column specimen CS-24 of Razvi and Saatcioglu is selected for this study. The stresses at the mid-height cross section are plotted using the SURFER-VERSION 7.0 under Windows [18] which extrapolates stress values based on the information at the integration points. The variation of the axial stresses on the


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mid-height cross section is plotted for 64 integration points covering the selected segments used in the analysis. These points are at the same height with regard to the integration coordinates. Axial stress surfaces at 40%, 70% and 100% of the ultimate load capacity are displayed in Figure 20(a-c). Figure (20a-20c) shows surfaces of stress at the cross section located at the middle of column specimen CS-24. Stress values are presented at different levels of loading. As shown in the figures, with increasing dilation, the tie strain increases and the confinement provided to the core increases. At 40% and 70% of the ultimate load, the specimen has almost uniform stress distribution over the cross section. Meanwhile, at 100% of ultimate load, the specimen has stress concentrations around the corners. The axial stress at the stress concentration areas are much larger than the concrete compressive strength which reveals that the confinement is activated in these areas. At ultimate load, the axial stress at the corners was 1.3% greater than the cylinder compressive strength while the axial stress at core of the specimen was much less, with an increase of only 1.18% over the cylinder compressive strength . These figures confirm that the proposed new microplane material model (IIIM) takes into consideration confinement for square tied columns. The obtained enhancement of the stress at the cross section coincides with the results obtained by other researchers [19, 20].


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15. INFLUENCE OF CONCRETE COMPRESSIVE STRENGTH ANDTRANSVERSE REINFORCEMENT

The influence of cylinder compressive strength of concrete and the volumetric ratio of transverse steel on the peak loads Pu and concrete peak stresses are studied for Razvi and Saatcioglu’s column specimen CS-19. For each varied property, three results are obtained from the analysis, as shown in Tables 8 and 9. The results are normalized to the peak load obtained for the maximum value of the three varied properties.

Table 8 shows that when the concrete compressive strength is increased from 92 to 138 MPa, the ratio of the ultimate load is 1.20. However, when the concrete compressive strength is decreased from 92 to 46MPa, the ratio of the ultimate load is 0.74. Table 9 shows that when the volumetric ratio of transverse steel is increased from 0.0324 to 0.0486, the ratio of the ultimate load becomes 1.02. While when the volumetric ratio of transverse steel is decreased from 0.0324 to 0.0162, the ratio of the ultimate load is 0.97. As shown in Figure 21, the finite element solutions reveal that the volumetric ratio of transverse steel has an insignificant effect on the peak load than the concrete compressive strength

which shows more influence on the peak load. High values of lead to a higher peak load and more brittle failure. The numerical results indicate a relatively smaller effect of the tie diameter of transverse reinforcement on the peak load.

Decreasing the volumetric ratio of lateral steel by decreasing tie diameter does not lead to a substantial increase in the concrete confinement between tie levels which are very important for the peak load response. Consequently, the peak load is decreased.

Table 8: Effect of concrete compressive strength on both concrete peak stress and peak loadof Razvi and Saatcioglu’s column specimen CS-19.

(MPa)

46

92

138

Ec(MPa)

322004470055700

Pu(kN)

393052806360

Ultmate loadratio

0.741.001.20

(MPa)

7098.3120.7

Table 9: Effect of volumetric ratio of transverse steel on both concrete peak stress and peak loadof Razvi and Saatcioglu’s column specimen CS-19.

0.0486

0.0324

0.0162

Diameter(mm)

8.011.313.8

Pu(kN)

510052805370

(MPa)

5100

5280

5370

Ultimate loadratio

0.97

1.00

1.02


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Figure 21. Influence of relative concrete compressive strength and relative volumetric ratio oftransverse steel on peak load of Razvi and Saatcioglu’s column specimen CS-19

16. EVALUATION OF PEAK STRESS

The peak stress values determined from the finite element analysis are enlisted in Table 10 for all the ten column specimens analyzed. A comparison is presented in Figure 22 between the predicted stresses using the microplane material model (IIIM) and the ultimate stresses obtained from experimental studies of Sheikh and Uzumeri’s column specimens as well as those tested by Razvi and Saatcioglu column specimens.

Table 10: Comparison of numerical and experimental compressive stress results for reinforced con-crete column specimens.


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Figure 22. Comparison between the numerical and experimental results using theproposed new microplane model for various tests

17. CONCLUSIONS

Based on the work described and results obtained in this investigation, the following conclusions are made.

The new Microplane Material Model (IIIM) is adopted in this study for its simplicity and computa-1. tional efficiency. The new model makes it easy to include the confinement effect and strain soften-ing in tension. In contrast to the previous microplane model, the descending slope of the postpeak softening response can now be controlled independently of the curvature at peak stress, which made possible good fits.

Small and large scales of correlation studies are also conducted with the objective of establishing 2. the ability of the proposed model to simulate the response of reinforced concrete members. These comparisons are presented in order to demonstrate the capabilities of the proposed numerical so-lution scheme and show the effect of the proposed microplane material model on the response of reinforced concrete members.

The three-dimensional 8-node isoparametric finite element is used in the analysis of square rein-3. forced concrete columns with the new microplane model. The computed results for different types of concrete are in good agreement with the experimental data. Hence, the model used is able to realistically predict the stress–strain relationship of confined concrete columns.

Strength gain due to confinement does not appear to be influenced by concrete strength, so long as 4. the confinement reinforcement remains unchanged. Therefore, if the same percentage of strength enhancement is desired, higher strength concrete columns are needed to be confined proportionately more than those with lower strength concretes. Also, the stress gain is not proportional to the con-crete strength. It is observed that stress gain for normal strength concrete is much higher than that of high strength concrete, reaching approximately 20 % for column specimen CS-24.

In the proposed model, it does not take into account the concrete cover and hence what is referred 5. to as corners here are actually the corners of the confined area (sectional area located inside the stir-rups) and not the corners of a realistic section which corresponds to the concrete cover. At ultimate


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load, the specimens stress concentrations around the corners are about 1.3% greater than the cylin-der compressive strength , while the axial stress at core of the specimens was much less, with an increase of only 1.18% over the cylinder compressive strength . This means that the confinement is better in these areas for column specimen CS-24.

18. REFERENCES

[1] Bazant, Z. P., and Prat, P. C., “Microplane Model for Brittle Plastic Material : I. Theory, II. Verification”, Journal of Engineering Mechanics, ASCE, Volume 114, No. EM10, October, 1988, pp. 1672-1702.

[2] Lin, J., and Foster, S., J., “A Three Dimensional Finite Element Model for Confined Concrete Structures”, Internal Report, School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia, 1998, pp. 1-151.

[3] Bazant, Z. P., and Gambarova, P. G., “Crack Shear in Concrete: Crack Band Microplane Model”, Journal of Structural Engineering, ASCE, Volume 110, No. ST9, September, 1984, pp. 2015-2035.

[4] Kupfer, H., Hilsdorf, H. K., and Rusch, H., “Behavior of Concrete under Biaxial Stresses”, Journal of the American Concrete Institute, ACI, Volume 66, No. 8, August, 1969, pp. 656-666.

[5] Lin, J., and Foster, S. J., “A Three Dimensional Finite Element Model for Confined Concrete Structures”, Internal Report, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia, 1998.

[6] Bresler, B. and Scordelis, A.C., “Shear Strength of Reinforced Concrete Beams”, Journal of Structural Engineering, ASCE, Volume 60, No. ST1, 1963, pp. 51-72.

[7] Razvi, S. R., and Saatcioglu, M., “High Strength Concrete Columns with Square Sections Under Concentric Compression”, Journal of Structural Engineering, ASCE, Volume 124, No. ST12, December, 1998, pp. 1438-1447.

[8] Cervenka, V., “Constitutive Model for Cracked Reinforced Concrete”, Journal of the American Concrete Institute, ACI, Volume 91, No. 15, June-July, 1985, pp. 877-882.

[9] Kupfer, H. B., and K. H. Gerstle, “Behavior of Concrete Under Biaxial Stresses”, Journal of Engineering Mechanics Division, ASCE, Volume 99, No. EM4, Proceeding paper 9917, August, 1973, pp. 853-866.

[10] Chen, C. T., and Chen, W. F., “Constitutive Relations for Concrete”, Journal of Engineering Mechanics, ASCE, Volume 101, No. EM4, August, 1975, pp. 465-480.

[11] Kwon, M., and Spacone, E., “Three-Dimensional Finite Element Analysis of Reinforced Concrete Columns”, Journal of Computers and Structures, Volume 80, August, 2002, pp. 199-212.

[12] Lin, J., and Foster, S. J., “Finite Element Model for Confined Concrete Columns”, Journal of Structural Engineering, ASCE, Volume 124, No. ST9, September, 1998, pp. 1011-1017.


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[13] Xie, J., MacGregor, J. M., and Elwi, A. E., “Numerical Investigation of Eccentrically Loaded High Strength Concrete Tied Columns”, Journal of the American Concrete Institute, ACI, Volume 93, No. 4, July-August, 1996, pp. 449-461.

[14] Sheikh, S.A., and Uzumeri, S.M., “Strength and Ductility of Tied Concrete Columns”, Journal of Structural Engineering, ASCE, Volume 106, No. ST5, May, 1980, pp. 1079-1102.

[15] Foster, S. J., Lin, J., and Sheikh, S. A., “Cover Spalling in HSC Columns Loaded in Concentric Compression”, Journal of Structural Engineering, ASCE, Volume 124, No. ST12, December, 1998, pp. 1431-1437.

[16] Ozbolt, J., Mayer, U., and Vocke, H., “Smeared Fracture FE-Analysis of Reinforced Concrete Structures-Theory and Examples”, Institute of Construction Materials, University of Stuttgart, Japan-US Workshop on Nonlinear Analysis or RC Structures, also in Special ASCE Publication: Modeling of Inelastic Behaviour of RC Structures Under Seismic Loads, 2001, pp. 234-256.

[17] Ozbolt, J., Li, Y., and Koar, I., “Microplane Model for Concrete with Relaxed Kinematic Constraint”, Internal Report, Institute of Construction Materials, University of Stuttgart, International Journal for Solids and Structures, Volume 38, Issue 16, April 2001, pp. 2683-2711.

[18] “Statistica Manual”, under Windows-version 5.0, on a workstation, 1998.

[19] Schneider, S. P., “Axially Loaded Concrete-Filled Steel Tubes”, Journal of Structural Engineering, ASCE, Volume 124, No. ST10, October, 1998, pp. 1125-1138.

[20] Huang, Y.-K., Yen, G.-Y., Liu, H.-T., Tsai, K. C., Weng, Y. T., Wang, S. H., and Wu, M.-H, “Axial Load Behavior of Stiffened Concrete-Filled Steel Columns”, Journal of Structural Engineering, ASCE, Volume 128, No. ST9, September, 2002, pp. 1222-1230.

[21] Jassim, W.A., “A Modified Microplane Model for Analysis of Confined Reinforced Concrete Columns”, Doctoral Thesis, Department of Civil Engineering, University of Baghdad, April, 2006.

[22] Phillips, D.V. and Zienkiewicz, O.C., “Finite Element Nonlinear Analysis of Concrete Structures”, Proceedings of the Institution of Civil Engineers, Volume 61, Part 2, 1976, pp.59-88.

[23] Bazant, Z.P., Caner, F.C., Carol, I., Adley, M.D., and Akers, S.A., “Microplane Model M4 for Concrete I: Formulation with Work – Conjugate Deviatoric Stress”, Journal of Engineering Mechanics, ASCE, Volume 126, 2000, pp. 944-953.

[24] Bazant, Z.P. and Caner F.C., “Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity I: Theory”, Journal of Engineering Mechanics, ASCE, Volume 131 (1), 2005, pp. 31-40.

[25] Bazant, Z.P. and Caner, F.C., “Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity II: Computation”, Journal of Engineering Mechanics, ASCE, Volume 131 (1), 2005, pp. 41-47.

[26] Cusatis, G., Beghini, A., and Bazant, Z.P., “Spectral Stiffness Microplane Model for Quasibrittle Composite Laminates – Part I: Theory”, Journal of Applied Mechanics, Transactions ASME, Volume 75 (2), 2008, pp. 021009-1 to 021009-9.


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[27] Hartl, H. “Development of a Continuum-Mechanics-Based Tool for 3D Finite Element Analysis of Reinforced Concrete Structures and Application to Problems of Soil-Structure Interaction”, Doctoral Thesis, Graz University of Technology, Institute of Structural Concrete, Austria, 2002.

[28] Cotsovos, D.M., Zeris, Ch.A., and Abas, A.A., “Finite Element Modeling of Structural Concrete”, ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2009, Rhodes, Greece, 22-24 June, 2009.

[29] Markou, G., “Detailed Three Dimensional Nonlinear Hybrid Simulation for the Analysis of Large-Scale Reinforced Concrete Structures”, Doctoral Thesis, School of Civil Engineering, Institute of Structural Analysis and Seismic Research, National Technical University of Athens, 2011.

A DEVELOPED MICROPLANE MATERIAL MODEL FOR NONLINEAR FINITE ELEMENT ANALYSIS WITH

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SETTING MAXIMUM AND MINIMUM SPEED LIMITS FOR FREEWAY SAFETY IMPROVEMENT.

N. M. Hassan*1, R. A. KadyFaculty of Engineering and Applied Sciences, ALHOSN University,P.O.Box38772 Abu

Dhabi, U.A.E.

ABSTRACT: Speed differentials between vehicles on freeways eventually lead to a higher crash rate. Freeway speed limits aim to reduce the risk of accidents on highway travel. The objective of this research is to examine how setting of the speed limits (minimum and maximum) could help reduce speed dispersion, and thereby providing a safer travel on freeways. A microscopic model is built to simulate the vehicles speed dispersion and measure the percentage of vehicles violating the 3-second rule. The speed limits are investigated via a full factorial design of experiment (DOE). Different DOE scenarios are examined using the simulated model by varying four factors, namely minimum and maximum speed limits and the mean and standard deviation of inter-arrival times between vehicles to determine the possibility of a near crash, quantifying the risk of accidents on freeway travel. The percentage number of vehicles violating the 3-second rule was used as a performance measure to compare the different scenarios. The optimal minimum and maximum speed limits for a specific traffic flow were obtained. The study recommends that the minimum speed limit should be increased when traffic flow rate and variability are low, while the maximum speed limit should also be increased when traffic flow rate is high. As a result, a sensory system of variable speed limits can be used in the segments of the highway system with variability in traffic flow such as construction sites, around rush hour, or public events.

KEYWORDS: Speed Limits, Driving Safety, Speed Variance, Design of Experiments (DOE), Simulation.

1. INTRODUCTION

Speed differentials on highways can eventually lead to an unsafe traffic. An increase in the homogeneity of travelling vehicles is known to lower the risk of traffic accidents [1]. In order to examine this phenomenon, one must look at the root causes of speed dispersion. It could be attributed to speed difference between individual vehicles in the same road segment, or at a certain road section. Larger differences in speed between vehicles result in a higher crash rate. Without exception, a speeding vehicle has a higher crash rate, while for a slowly moving vehicle the evidence is inconclusive [1].

Extensive research has been conducted to examine the effect of speed limits on road safety, and their influence on speed dispersion. Several researchers concluded that higher speed limits result in an increase in fatalities due to the severity of the crash even if it did not lead to an increase in crashes [2]. Letirand and Delhomme [3] stated that excessive and inappropriate speed is a major contributing factor to road accidents, fatalities, and serious injuries. Farmer et al. [4] concluded that increasing the speed of a motor vehicle reduces the time the driver has to respond to an emergency, increases stopping distance, and increases the likelihood and severity of crashing.Other researchers [5] contributed road accidents to either a manipulation error (due to speeding, illegal overtaking, etc.) or a perception error (due to wrong assessment of speed, distance, etc.). For a specific driver with a specific driving skill and perception capability, it is obvious that the probability of a manipulation error and the probability of perception error increase as the speed increases [6, 7]. In

* Corresponding Author: email: [email protected]


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general, safety disbenefits have been associated with an increase in speed limit, while few predicted that higher speed limits may actually save lives by minimizing the speed variance [8, 9]. Upon investigating the minimum speed limit, it was hypothesized that slow moving vehicles would also lead to speed differentials on highways, and could eventually lead to safety and operational problems [10]. According to Ha et al. [11], less variability of speed leads to fewer short headways and lower mean speeds, which translates into fewer crashes [12].

Existing empirical work indicates that reducing the speed limit reduces speed variance, which reduces the risk of accidents. It would appear then that the influence of speed variance on safety exerts downward pressure on the optimal speed limit. However, Graves, et al. [13] concluded unusual results when developed a model of the optimal speed limit which explicitly recognizes the roles of average speed, speed variance, and the level of enforcement. The study revealed that a higher speed limit may be optimal when reducing the variance in highway speeds reduces accidental risk. However, when policing is taken into consideration, the analysis suggests that the effect of speed variance can be to increase the optimal speed limit, not reduce it. Most traffic safety research focused on correlating the speed limits and traffic flow to the number of accidents and deducting inferences based on statistical information from individual studies that are often imprecise [14].

2. BACKGROUND

Speed limits have been used to serve several functions including reducing speed, leading to smoother traffic flow, and providing guide for law enforcement officers [15]. Most of the stated objectives relate back to one overriding purpose, i.e., that is the reduction of the risk of highway travel. In other words, one can relate the function of a speed limit to reducing the risk of highway travel; the risk of accident occurrence. There are a seemingly endless number of factors which affect driving speeds. These tend to fall into categories relating to the driver, the vehicle, the roadway, the traffic, and the environment. Examples of prevailing conditions that affect a driver’s speed are lane width, weather, horizontal alignment, vertical alignment, sight distance, lateral clearance, design speed, behavior, and adjacent environment [16]. For that, it is very hard to devise formulas that would take all those factors into consideration.

Garber and Gadiraju [17] performed a cross-sectional study in which they examined the relationship between crash rate and different speed measures, including speed variance. They measured spot vehicle speeds and 24-hour traffic flow during weekdays, and linked those to the 124 crashes that had occurred on the examined roads in the last 3 years. They found that roads with a larger speed variance had a higher crash rate than roads with a smaller speed variance. The researchers found a negative relationship between average speed and crash rate at the examined roads. However, large speed variances appeared to be associated with relatively low average traffic speeds. The study found that the crash rate and speed variance were lowest when the speed limit was 5–10 mph (≈8–16 km/hr) lower than the design speed. Taylor et al. [18] also found that traffic speed variance is related to the crash frequency. They collected aggregated 24-hour spot speed data of 300 urban single carriageway roads in the UK and linked this to 1590 injury crashes at those roads.The Manual on Uniform Traffic Control Devices (MUTCD) states that “when a speed limit within a speed zone is posted, it should be within 5 mph of the 85th percentile speed of free-flowing traffic [19].” The 85th percentile speed is used as one factor in determining the numerical value of the maximum speed limit that is posted by most transportation agencies. The method requires the measurement of driving speeds on a given roadway to set the maximum speed limit at or near the speed below which 85% of the drivers chose to travel. This eliminates the higher speeds that may be unsafe, but includes a large percentage of the driving public [15]. Parker [20] examined changes in vehicle speeds when speed limits

N. M. HASSAN, R. A. KADY

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are posted within 5 mph (8 km/h) of the 85th percentile speed versus changes in speeds when limits are set at more than 5 mph (8 km/h) below the 85th percentile speed. As with drivers’ compliance, a greater percentage of drivers exceeded the new limits. When speed limits were raised, more drivers were in compliance with the speed limits. Again, these figures do not represent a shift in drivers’ behavior, but a change in how noncompliance is measured, i.e., from the posted speed limits.

It would be nearly impossible to devise a formula for a speed limit that would take into account all of the determining factors, not to mention the feasibility of implementing such a formula [15]. Singh et al. [21] developed an artificial neural network (ANN) models to predict 85th percentile speed (V85) of two-lane rural highways in Oklahoma. Several input parameters, namely, roadway characteristics, traffic conditions, and accident experience were considered in developing the ANN models. Physical roadway characteristics include surface width, shoulder type, and shoulder width. Traffic parameters cover average daily traffic, posted speed, and V85. Pavement condition includes skid number and international roughness index. The location collision rate, statewide collision rate (overall, fatal, and injury), and percentage unsafe speed drivers (USD) were covered in the accident data [21].

As for setting the minimum speed limit, Muchuruza and Mussa [10] revealed that apart from the legal minimum speed limits, their survey did not discover any specific criteria that were used to set (or derive) the existing minimum speed limit values. Half the states in the US would not post minimum speed limit on Interstate freeways, and would rely on the rule adopted from the Uniform Vehicle Code (UVC) for enforcement purposes. The rule states that, ‘‘No person shall drive a motor vehicle at such slow speed as to impede the normal and reasonable movement of traffic [22].’’ Another theme unveiled by the survey results is the fact that there seems to be no relationship between the minimum and maximum speed limits. Muchuruza and Mussa [10] stated that there is a continued need to study the relevance of the minimum speed limit on speed variability in light of the increase in maximum speed limit and the prevailing driving speed characteristics.

3. SIMULATION STUDIES

Computer simulation programs have been used extensively in traffic research. Taylor [23] has classified traffic simulation models into microscopic and macroscopic. In a microscopic model, the movement of individual vehicles is captured, while in a macroscopic analysis, the traffic behavior is studied at an aggregate level. Simulation models have been used for several purposes such as capacity analysis, estimation of lane flow at intersections and approaches, evaluating new strategies for reducing delays, congestion, fuel consumption, and pollution, investigating dynamic traffic management systems problems caused by incidents, heavy traffic, or road work, and studying adaptive intersection signal controls, ramps, and mainline metering. Algers et. Al [24] presented an extensive review of micro-simulation models. Since then, more micro-simulation models have been developed. Many of existing models however have just been developed for specific traffic research problems. Examples of commercial micro simulation tools are AIMSUN2®, FLEXSYT®, FRESIM®, HUTSIM®, INTERGRATION®, PARAMICS®, THOREAU®, TRAF-NETTSIM®, and VISSIM®. AIMSUN2® (Advanced Interactive Microscopic Simulator for Urban and Non-urban Networks) is a combined discrete-continuous simulator. Some elements of the transportation system (vehicles, detectors) in the simulator change states continuously over the simulated time period, while other elements (traffic lights, entrance points) change states discretely at specific points during the simulation time. PARAMICS® claims to simulate the traffic impact of signals, ramp meters, loop detectors linked to variable speed signs, variable message sign (VMS), and constant message sign (CMS), in-vehicle network state display devices, in-vehicle messages advising of network problems, and re-routing suggestions. The traffic flow model VISSIM® is a discrete, stochastic, time step-based microscopic model, with driver-vehicle-units as single entities.


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The model contains a psycho-physical car-following model for longitudinal vehicle movement and a rule-based algorithm for lateral movements (lane changing). Car following and lane-changing together form the traffic flow model, being the kernel of VISSIM® [25]. THOREAU® and AIMSUN2® are microscopic models developed for ITS evaluations. Federal Highway Administration (FHWA) has combined two microscopic traffic simulators for freeways (FRESIM®) and urban networks (NETSIM®) into a more general traffic simulation framework called CORSIM® [26]. INTEGRATION® was initially a mesoscopic simulator which has recently been adopted to add microscopic features by introducing car-following and lane changing behavior. However, input data (capacity, jam density, and speed at capacity) to INTEGRATION are still macroscopic. Furthermore, it has no direct coupling of traffic control logic with driver behavior. MITSIMLab® was developed to capture the real world interaction between the traffic management center and vehicles on the road. It mimics the real world scenario by separating the simulation of traffic and the traffic management system [27].

Lee et al. [28] simulated, using PARAMICS® software, a one-mile long stretch with one ramp, and placed VMS upstream of a particular location of interest to try to reduce the crash potential. Abdel-Aty et al. [29] simulated a 20 mile stretch, using PARAMICS® software, to investigate with both up and downstream introduction of variable speed limits. Speed limits were decreased, increased, or simultaneously decreased and increased (up and down stream, respectively) to investigate all possible cases in order to see the effect of crash potential changing over time. A full factorial experiment was attempted, but because a suitable measure of effectiveness could not be determined, an alternative stepwise approach was used. Deardoff et al. [16] formulated a design of experiment to determine the relationship between the mean free flow speed and the posted speed limit. A microscopic traffic simulation model [30] realistically simulated changes in traffic conditions as an effect of variable speed limits and combined with the crash prediction model for the evaluation of control logics. Results indicated that variable speed limits could reduce crash potential by 5–17%, by temporarily reducing speed limits during risky traffic conditions when crash potential exceeded the pre-specified threshold. It was also found that the greatest safety benefits were obtained when the variable speed limit was set equal to the average of speeds at the upstream and downstream detectors (i.e. transition speed).

To the best knowledge of the authors, traffic simulation research has not addressed the effect of highway speed limits on traffic safety. The objective of the study was to use a discrete-event simulation package, namely ProModel® to determine how speed limits could be set for traffic safety improvement. ProModel® is flexibility in modeling several parameters, easy to use, and has continuous modeling capabilities. The output processor in ProModel® provides both summary and detailed statistics on key performance measures. Outputs from multiple replications and multiple scenarios can be summarized and compared [31]. In this study, an experimental design was implemented. The design parameters considered are traffic flow rate (defined by mean and standard deviation of the inter-arrival times) and speed limits (minimum and maximum). The response variable analyzed is the percentage of drivers violating the 3-sec rule (this is used to indicate the possibility of crash). Field data was gathered to predict the distribution of the inter-arrival times. Exact distribution for the vehicle’s speed could not be used since it would vary based on the posted speed limits. Field data was not available for all the speed limits combinations that were tested. In order to make a reasonable assumption about the speeds, a triangular distribution was used due to the lack of data. The triangular distribution was correlated to the minimum and maximum speed limits posted based on the assumption that the speed limits in speed zones are set based on 85th percentile speed [19]. It was assumed that the maximum speed limit represents the free flow speed which also happens to be 85th percentile speed and the mode of the triangular distribution. The minimum speed limit represents the minimum velocity at which a vehicle will travel, i.e. equal to the minimum speed limit. This assumption is reasonable since the posted speed limit is partially dependent upon free flow speed.


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4. METHODOLOGY

4.1. Data Gathering

Traffic flow data has been collected from two major highways with a maximum traffic speed limit of 120km/hr. Data was gathered by recording the time a vehicle passes a defined land mark. Data has been collected for several weeks during peak hours. The inter-arrival times between vehicles was calculated from the difference between the arrival time of vehicle j at location 1 and the arrival time of the consecutive vehicle at the same location 1 . Statfit® statistical software was used to find the best distribution that describes the collected data.

4.2. Computer Simulation

“Simulation is the imitation of a dynamic system using a computer model in order to evaluate and improve system performance [31].” It is a useful technique to study the system behavior having stochastic property and conduct experiments in a computer rather than real life. In our study, the simulation model is used to examine how the setting of the speed limits and traffic flow on freeways can help reduce the speed dispersion, and thereby provide a safer travel on freeways. ProModel® software was used to build the traffic model to mimic the real system and run multiple experiments (Figure 1).

In order to simulate this system, five main items were defined in ProModel®, namely entities, locations, process, path network, and arrivals. Entities represent anything that the model process which in this case are the vehicles. The speed of the vehicles varies from one to another. Since the exact statistical distribution of vehicles speeds is unknown, and real vehicles speeds data is unavailable, the triangular distribution was selected to define estimates for the minimum (a), most likely (c), and maximum (b) values of vehicles speeds which are available travel speeds. The minimum travel speed was set to the minimum speed limit under the assumption that no vehicle will drive below the speed limit. The most likely travel speed was set to the posted maximum speed limit, under the assumption that most vehicles will travel at the same speed as the posted maximum speed limit. Since the maximum speed limit is the speed below which 85% of the drivers chose to travel, this was used to calculate the maximum speed for the driving vehicle, i.e., setting , then solving for. A triangular distribution which is a continuous probability distribution, with lower limit upper limit and mode was used to model the stochastic behavior of the vehicles as illustrated in Figure 2. The selected values for the triangular distribution were given by T (minimum speed, maximum speed).

Figure 1: Model layout in ProModel®.


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Figure 2: Cumulative distribution function and probability density function ofa triangular distribution.

The locations represent places in the system where entities are routed for processing, storage, or some other activity or decision making. In our case, the locations were defined to represent the highway, i.e., where the different entities would travel. Another location was defined towards the end of the highway to count the numbers of vehicles violating the 3-second rule. The number of possible accidents was later calculated by counting the number of vehicles violating the 3-second rule. Such rule stipulates that a vehicle in front of yours would pass by a roadside point of reference 3 seconds before your vehicle would. A simple algorithm was embedded into the simulation model to count the number of times the 3-second rule is violated, as depicted in Figure 3.

Figure 3: ProModel® code for counting number of misses.

Any time a new entity is introduced into the system, it is characterized as an arrival. An arrival record is defined by specifying the number of new entities per an arrival, frequency of arrivals, locations of arrivals, time of the first arrival, and total occurrences of arrivals. The frequency of an arrival is defined as where represents the vehicle flow (in vehicles/seconds). Data of inter-arrival times between vehicles arriving at a point in a major highway were collected and then fitted to a statistical distribution. The goodness of fit test shows the best distribution (based on Anderson-Darling and Kolmogorov-Simirnov test with a level of significance of 0.05) to be a lognormal distribution. As illustrated in Figure 4, the inter-arrival times between vehicles follow a lognormal distribution L(m, s) with mean (m) and standard deviation (s). Once vehicles arrive to the system, as defined in the arrivals, processing defines the routing of entities through the system and the operations that take place at each location they enter. Entities may not pass each other, even if an entity is traveling at a faster speed than the one in front of it.


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Figure 4: Probability density function of the inter-arrival times between vehicles.

4.3. Model Verification

The simulation model was verified by assuming two inter-arrival times 4 and 2.5 seconds. In both cases, the simulation was assumed to consist of 1 entity with a constant velocity of 200 m/min. The results of both scenarios after 1 minute elapsed run time are illustrated in Figure 5. When the inter-arrival time is more than 3 seconds (4 seconds), none of the vehicle violates the 3-second rule (simulation counter is zero). However, when the inter-arrival time is less than 3 seconds (2.5 seconds), the number of misses equals {4 x (number of vehicles passing -1)}. The total distance modeled is equal to 100 meters. For an inter-arrival time of 4 seconds and a velocity of 200 m/min (3.333 m/sec), the spacing between the vehicles can be calculated as {velocity x time} = 13.3 m, which is equivalent to 7.5 (100/13.3) spacing intervals as seen in Figure 5-run 1. For the inter-arrival time of 2.5 seconds, the spacing between the vehicles is equivalent to 12 (100/8.3) spacing intervals (Figure 5-run 2).

The number of vehicles arriving during the elapsed 1 min (60 sec) is 24 vehicles/lane (or 96 vehicles for 4 lanes) for the 2.5 sec inter-arrival time, and 15 vehicles/lane (or 60 vehicles for 4 lanes) for the 4 sec inter-arrival time, respectively. These numbers validate the ProModel® simulation counter for the number of vehicles passed since {the number of vehicles arrived = number of vehicles that passed the lane + number of vehicles in the queue}. For the 4 sec inter-arrival time, {number of vehicles arrived = number of vehicles passed radar (32) + number of vehicles in queue (7 x 4) = 60 vehicles}, and for 2.5 sec inter-arrival time {number of vehicles arrived = 52+ (11 x 4) = 96 vehicles}.


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Inter-arrival time = 4 sec (run 1)

Elapsed Time

Inter-arrival time = 2.5 sec (run 2)

Elapsed Time

Number of vehicles violating 3-second rule

Number of vehicles violating 3-second rule

Number of vehicles reaching the end of the street segment

Number of vehicles reaching the end of the street segment

Figure 5: Model verification at 4 sec and 2 sec inter-arrival times, respectively.

4.4. Model Validation

In order to validate the model, information about the traffic flow has been collected in a traffic system with with a maximum traffic speed limit of 60 km/hr (the minimum speed limit was not posted). Data was gathered by recording the time when a vehicle passes a certain point. Data has been collected for several weeks during peak hours. Two positions located 50 meters apart were monitored. The data was used to calculate the driving speed of vehicle j between the two reference points. The speed of each passing vehicle j was calculated as where is the recorded time when vehicle j passes by location i, and represents the distance between location i and the consecutive location. The inter-arrival time between vehicles was calculated from the difference between the arrival time of vehicle j at location 1 and the arrival time of the consecutive vehicle at the same location 1 . Statfit® statistical software was used to find the best distribution that describes inter-arrival times. The goodness of fit test shows the best distribution (based on Anderson-Darling and Kolmogorov-Simirnov test with a level of significance of 0.05) to be a lognormal distribution with a mean of 3.187 sec, and a standard deviation of 1.225 sec. Since there was no posting for minimum speed limit, the minimum speed was assumed to be zero km/hr. The speed distribution was assumed to follow a triangular distribution as discussed earlier T (0, 60, 71). The percentage of vehicles violating the 3-second rule (during a two-hour


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period) was 63%. The triangular distribution was entered into the simulation model to describe the entity speed. The lognormal distribution was entered into the model to describe the inter-arrival time. The simulation model was run for 30 replicates and for 2 hrs. The simulation results reveal that 72% of the vehicles violated the 3-sec rule. Comparing the two percentages (field study vs. simulation), a percentage difference of 14% error is found between the simulation model results and the real life data.

4.5. Design of Experiments

After setting up the simulation model in ProModel®, a full factorial design of experiment analysis of four factors was constructed. The factors in the analysis were minimum speed limit (min), maximum speed limit (max), the mean of inter-arrival time (m), and the standard deviation of inter-arrival time (s). Each factor was set at 3 levels to establish a total of 81 runs. A three-level factorial design was preferred over a two-level one especially because of the wide separation between the minimum and maximum values of each level. By choosing a two-level factorial design we run a greater risk of giving the overall illusion of linearity or no interaction, when in fact there is nonlinearity in the interior of the factor level range; such nonlinearity would be masked in the results if we did not simulate the wide area between the factor levels. Table 1 lists the values of the four-factor factorial design. Two random variables are defined in the simulation model; namely entity (vehicle) speed and the arrival frequency using those four factors. The inter-arrival times between vehicles follow a lognormal distribution L(m,s), while the entity speed is a triangular distribution . The response (dependent) variable should be the mean number of misses (vehicles violating the 3-second rule). However, since the number of vehicles generated in the simulation model varies by each experimental run, a more accurate measure would be the percentage of number of misses to the total number of vehicles generated for that run (i), which is calculated as {number of vehicles violates the 3-second rule in run i /total number of vehicles generated in run i}. The simulation model was run for 30 replicates at every combination to obtain the average percentage of misses.

Table 1: DOE factorial design

5. RESULTS AND ANALYSIS

After performing the simulation, a metamodel is derived which is in essence an algebraic model of the simulation model. This algebraic function relates the response variable to the important input factors to serve at least a rough proxy for the full blown simulation. The response function over the parameters range is defined from the simulation results. The purpose of the metamodel is to estimate the response surface. Later the metamodel will be used to learn about how the response surface would behave over various regions of the input factor space and to search for approximately optimal setting of the input factors. Table 2 shows that the statistical model source of variability has been subdivided into several components. The components m and (m x m) represent the linear and quadratic effects of the mean of the inter-arrival times, respectively. The same applies to the other three factors, namely s, min, and max. The P-values at = 0.05 indicate that the mean and standard deviation of inter-arrival times are significant to the percentage of number of misses. The interaction between mean and standard deviation of inter-arrival times is also significant. At a low level of mean of inter-arrival times (m=8) and a high level of inter-arrival time variability (s=2), the percentage of number of misses is decreased. However,


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the minimum and maximum speed limits are insignificant at of 0.05 to the percentage of number of misses. Figure 6 shows the interaction plot between the four factors affecting the percentage of misses. The remaining linear and quadratic components are also insignificant. By removing the insignificant terms or factors from the statistical model, the regression equation for percentage of number of misses is presented in equation (1).

Table 2: ANOVA for response surface regression analysis

Figure 6: Interaction plots between factors for the percentage of misses.


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Figure 7 shows the main factors affecting the percentage of misses. As illustrated earlier, the inert-arrival time is the most dominant factor. As the mean of the inter-arrival time increases, the spacing between the vehicles increases, thereby the percentage of near crash accidents indicated by the percentage of 3-second rule violators decreases. On the other hand, the greater the deviation of the mean value is, the greater the variance in spacing between the vehicles and the higher the risk of a crash, i.e., the higher the percentage of vehicles violating the 3-sec rule.

Figure 7: Main effects plot for the percentage of misses.

Although the significant factors (m and s), seemingly in theory, affect the response variable, the implication of such regression model is not practical. In a real highway system, the inter-arrival times between vehicles are mainly dictated by traffic flow. As a result, in order to identify the combination of minimum and maximum speed limits that jointly optimize percentage of number of misses, a response optimizer analysis was conducted at all combinations of the levels of the mean and standard deviation of inter-arrival times based on the following procedure. The proposed procedure is for optimal setting of the speed limits based on minimizing the percentage of misses (3-sec rule). A metamodel was developed for each combination setting of inter-arrival time (mean and standard deviation) as listed in Table 3.

Vary factors 1 and 2 (from Table 1) for 3 levels while fixing factor 3 and 4 (31- 2= 9 runs).

Perform a response optimizer analysis to define the relationship between the percentage (%) of 2- vehicles violating the 3-second rule (response) and the speed limits (min and max).

Find the speed limits (min and max) that will minimize the percentage (%) of vehicles violating 3- the 3-second rule (from step 2).

Repeat steps 1-3 for factor 3 at levels 2 and 3.4-

Repeat steps 1-4 for factor 4 at levels 2 and 3.5-


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Table 3: Response surface regressions of % of violators vs. minimum and maximum speed limits.

s=2 s=5 s=8

m=4

m=6

m=8

The Metamodel developed and depicted in Table 3, was not only used to give a rough estimate for the percentage of misses for a specific traffic flow but also to find the optimum setting for the minimum and maximum speed limits. Figure 8 shows that for the particular flow rate with a mean inter-arrival time of 4 and a standard deviation of 2, L(4,2) sec, the optimal percentage of misses is around 31 at minimum and maximum speed limits of 65 and 160 km/h, respectively. This procedure was repeated for all the combinations of inter-arrival times listed in Table 3. Results for the optimal setting for the minimum and maximum speed limits that gives minimum percentage of 3-sec rule violators are given in Table 4.

The optimal settings for the minimum and maximum speed limits shown in Table 4 were used further to construct contour plots to illustrate how the setting varies with the mean and standard deviation of the inter-arrival time. Figure 9 illustrates that as the mean inter-arrival time between vehicles increases and the variability decreases (vehicles are arriving uniformly and far apart), the minimum speed limit should be increased to minimize the percentage of misses and vice versa. On the other hand, when both the mean inter-arrival time between vehicles and the variability decrease (vehicles are arriving uniformly and near to each other), the maximum speed limit should be increased so that they will be further away from each other therefore minimizing the misses or risk of having an accident, and the opposite is true (Figure 10).


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Figure 8: Optimization plot of minimum percentage of misses and the corresponding minimum and maximum speed limits.

Table 4: Combinations of minimum and maximum speed limits that give optimalpercentage of misses.

ms = 2 s = 5 s = 8

min speed limit max speed limit min speed limit max speed limit min speed limit max speed limit

4 65 160 40 115 40 129

6 85 95 67 160 40 160

8 76 95 85 95 77 95

Figure 9: Contour plot of minimum speed as a function of mean (m) andstandard deviation(s) of inter-arrival time.


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Figure 10: Contour plot of maximum speed as a function of the mean (m) and standarddeviation(s) of inter-arrival time

5. DISCUSSION

Our results revealed that for a specific flow rate, the minimum and maximum speed limits are significant factors that affect the percentage of vehicles violating the 3-sec rule. Results from other researchers [1, 32, 33] support our findings. Baruya [32] performed a cross-sectional study to assess the relationship between average speed and crash frequency. Results revealed that the crash frequency is mostly affected by traffic flow (a convex increase with increasing flow). In addition, higher speed limit coincides with a higher crash frequency. Shively et al. [33] used a semi-parametric Poisson-gamma model to estimate the relationships between crash counts and various roadway characteristics. The results suggest that key factors for explaining crash rate variability across roadways are the amount and density of traffic, presence and degree of a horizontal curve, and road classification which coincides with our findings. Congested roads both had a higher absolute crash frequency and a larger increase in crash frequency with higher average speeds than fast roads [1]. If the flow rate were a controllable factor, the percentage of vehicles violating the 3-sec rule will be minimized if the mean of inter-arrival time is increased, and its standard deviation is reduced, as illustrated in Figure 7. However, since the flow rate is an uncontrollable factor, an alternative solution would be to vary the speed limit with flow rate based on a certain scheme that takes into account the frequency of changes. One possible approach to achieve this is through evolving traffic technologies like the variable speed limit (VSL). Several transportation systems have already utilized such technology to reduce or increase speeds on the road. In the United States, on the New Jersey Turnpike 120, a variable speed limit sign was used to vary the speed based on accidents, congestion, construction, and weather conditions [34]. In New Mexico, the VSL sign was used from 1989 to 1998 on a section of I-40 to vary the speed limits based on the traffic speed, day versus night, and precipitation rate [34]. On I-70 at the Eisenhower tunnel in Colorado and I-84 in Oregon, a VSL system is implemented that weighted the travelling vehicles and advised trucks to alter their speed accordingly [34]. VSL signs are also used to decrease the upstream traffic in a work or construction zone bottleneck. This technology is also used worldwide for operators to adjust the posted speed limit without changing the physical sign. Nes, et al. [35] studied the effects of introducing dynamic speed limit systems on


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homogeneity of speed limits to determine road safety. They are used in conjunction with Intelligent Transportation Systems to alter the posted speed limit based on congestion, construction, accidents, fog, snow, and ice. Now, the speeds can be changed remotely via email or telephone, at pre-set times of day, or manually. In the near future, VSL signs may be used to alter speed limits based on real time traffic or weather conditions.

6. CONCLUSIONS

In conclusion, the purpose of the study was to set the minimum and maximum speed limits that would reduce the percentage number of misses. Additional factors namely mean and standard deviation of inter-arrival times have been studied. Such factors represent traffic flow in a highway system. Results showed that, in reality, the minimum speed limit of a highway system should be increased when traffic flow rate is low (minimum variability of inter-arrival times). The maximum speed limit of the highway should also be increased but only when the variability of flow of vehicles is high. A major factor that influences traffic safety that needs to be considered when setting speed limits is the traffic flow rate. Variable speed limits based on traffic flow may be an alternative solution that needs further investigations and experimentation.

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