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Materials and Structures ISSN 1359-5997Volume 48Number 10 Mater Struct (2015) 48:3367-3375DOI 10.1617/s11527-014-0405-5

Falling-weight impact response forprototype RC type rock-shed with sandcushion

Abdul Qadir Bhatti

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ORIGINAL ARTICLE

Falling-weight impact response for prototype RC type rock-shed with sand cushion

Abdul Qadir Bhatti

Received: 27 September 2012 / Accepted: 19 August 2014 / Published online: 11 October 2014

� RILEM 2014

Abstract In this paper, a prototype model of rein-

forced concrete (RC) type rock-shed is numerically

examined by means of three-dimensional elasto-plastic

finite element based model of RC rock-shed structure,

having sand cushion, against the impact of 10 ton heavy

weight. This study is undertaken in order to improve the

knowledge for establishing a rational performance-

based impact resistant design procedure for the RC type

rock-sheds. Following results are obtained from this

study: (1) the model fails in the punching shear mode

when surcharged at the center of roof slab; and (2) the

impact resistant capacity of the free edges of the model

is greater than that at the center, as the free edges can

behavemore flexibly and absorb more impact energy in

comparison with the center of the roof slab.

Keywords Rock-shed � Dynamic nonlinear

analysis � Sand model � Ultimate state � Input impact

energy

1 Introduction

Protection galleries are normally constructed along

the highways in mountainous areas. Rock fall

protection galleries are an efficient measure to

protect roads and railways, mainly if the danger is

locally concentrated. Rock fall in the mountainous

areas is one of the natural hazards which occur due

to strong typhoon, snow avalanches and landslides.

The associated risks due to rock falls are usually

managed by means of structures such as galleries

protecting roads and railways.

A study on the rock fall galleries has shown that

most of the existing galleries consist of reinforced

concrete slabs and are covered with a cushion layer [1,

2]. The cushion layer distributes the contact stresses,

reduces the accelerations in the striking body and

increases the impact time. Normally, granular sand

from the surroundings or gravel is used as cushion

layer. Protection galleries typically span 9 m with a

slab thickness of approximately 0.70 m. The back side

of the galleries is clamped and is supported at the

retaining wall as shown in Fig. 1.

A. Q. Bhatti (&)

Department of Earthquake Engineering, School of Civil

and Environmental Engineering, National University of

Sciences and Technology (NUST), Islamabad, Pakistan

e-mail: draqbhatti@gmail.com; bhatti-nit@nust.edu.pk;

draqbhatti@berkeley.edu

A. Q. Bhatti

Pacific Earthquake Engineering Research Centre (PEER),

University of California, Berkeley, USA

A. Q. Bhatti

Department of Structural and Geotechnical Engineering,

Politecnico di Torino, Corso Duca degliAbruzzi 24,

10129 Turin, Italy

A. Q. Bhatti

Department of Civil Engineering, Islamic University,

Madina, KSA

Materials and Structures (2015) 48:3367–3375

DOI 10.1617/s11527-014-0405-5

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However, usually those shelters have been designed

without considering impact loads due to falling rocks.

In order to establish a rational impact resistant design

procedure for RC type rock-shelter [3], based not only

on allowable stress design but also on ultimate state

design and/or performance based design method, the

impact resistant capacity and/or maximum input impact

energy for the RC structures must be clearly estimated.

At present, the RC structures have been designed

statically based on allowable stress design method.

In recent years, numerical modeling of various

concrete structures under impact loads has been inves-

tigated by using finite element model/discrete element

model (FEM/DEM and few combined. Hence, many

FEM/DEM models for the pre-failure and post failure

transient dynamics of reinforced concrete structures

under impact loading have been developed [2, 4–6]. For

such models, maximum input impact energy for reach-

ing ultimate state was numerically estimated by means

of three-dimensional elasto-plastic finite element

method for existing real RC rock-shelters with sand

cushion under falling heavy-weight impact loading [6–

8] To effectively absorb and disperse the impact forces,

caused due to a rock falling, a cushionmaterial has been

developedwhich is composed of 90 cm thick sand layer

(top) and 20 cm thick gravel as confined material [9].

For numerical analysis, LS-DYNA code was used [10].

The dimension of the RC shelter is 9,000 mm in length,

4,700 mm in height of side-wall and 4,000 mm in

width. 10,000 kg steelweightwas used as fallingweight

having falling height of 20, 50, 100, 150, 200, 250 m. In

this numerical analysis, solid elements were employed

for concrete, falling heavy-weight and sand-cushion,

and beam elements for reinforcing steel. Drucker–

Prager and reinforcing steel yield criteria were used as

material constitutive law for concrete and reinforcing

steel, respectively. Cracks were estimated by allowing

tensile stress cut-off at reaching at the tensile strength. In

this paper, weight impact force, total axial force at the

side walls, displacement wave at the loading point and

crack patterns of the shelter at the time of occurrence of

maximum displacement are outputs [11–13].

The results obtained from this study are as follows;

(1) The serviceability and ultimate limit states were

determined from various cases having energies of

0.196, 2.45, 4.90, 7.35, 9.8 and 12.3 MJ. (2) It was

observed that maximum response generation time of

the impact force and displacement is different for

various input energies. (3) Maximum input impact

energy for reaching ultimate state was numerically

examined by means of three-dimensional elasto-

plastic FE method for RC rock-shed.

2 Outline of prototype RC type rock-shed

The cross-section and absorbing system of the RC rock-

shed are shown in Fig. 1. The geometry of the rock-shed

and height of sidewall beamare shown inFig. 2.TheRC

type rock-shed used for analysis is about 1/2 scale of

prototype and is assumed to be 11,100 mm in length and

7,000 mm height respectively.

In themodel, D32 reinforcing steel for each upper and

lower axial ones were arranged having 100 mmconcrete

cover. The shear re-bars were not used in this study as

shown in Fig. 3. A rectangular shape footing was

constructed so as to be close to perfectly fixed supports,

Fig. 1 RC rock-shed

Fig. 2 Geometry of rock-shed

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as much as possible. The displacement of the slab was

measured at the mid span and impact force P was

estimated using contact force between heavy-weight and

rock-shed [14]. The material properties of concrete, re-

bars, sandandgravel duringanalysis are listed inTable 1.

3 Numerical overview

3.1 FE models

An example of FE numerical analysis model is shown

in Fig. 4. Only half of RC arch tunnel model and

footing, a falling heavy-weight, and a half of support-

ing apparatus were modelled with FE meshes consid-

ering two symmetrical axes. Six and eight node solid

elements were used in the FE model except for axial

and shear reinforcing steel in the footing. Finite

element models with reinforcing steel arrangement are

shown in Fig. 4 [15, 16]. Total number of nodes and

Fig. 3 Details of steel reinforcement

Table 1 Material properties of rock-shed system

Material type Density Elastic

coefficient

Poisson’s

ratio

q (kg/m3) E (GPa) m

RC 2,500 25 0.2

Sand 1,760 10 0.06

Concrete 2,350 13.7 0.167

Reinforcing steel 7,690 206 0.3

Gravel 1,860 0.042 0.45

Falling weight 3,054 210 0.3

Fig. 4 Finite element mesh and reinforcing steel details of

numerical model

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elements of the RC rock-shed model are shown in

Fig. 4 are 128,890 and 88,882 respectively. Numerical

analyses models were precisely formed for each

component based on the dimensions of the RC rock-

shed tunnel model used in the real prototype structure.

However, axial reinforcing steels have been sim-

plified as a square element rather than simple circular

reinforcing steel, having equivalent cross sectional

area of specific round reinforcing steels. Contact

surface is defined between supporting device and

concrete surface; and between striking face of heavy-

weight and concrete surface, in which sliding with

contact and separation can be considered in this

contact surface applied here [17–19]. All nodes among

concrete and axial reinforcing steel were assumed to

be perfectly bonded with each other. Impact force is

numerically surcharged against the RC rock-shed by

adding a predetermined impact velocity to all nodes of

falling heavy-weight which is set on the surface of RC

rock-shed model. Impact response analysis for RC

rock-shedmodel was performed up to 300 ms from the

beginning of impact. The time increment for numer-

ical analysis is almost equal to 0.6 ms which is

determined based on Courant stability condition. The

typical numerical cases are listed in Table 2.

3.2 Modelling of materials

Figure 5 shows the stress–strain relations for each

material: concrete and reinforcing steel. Neither strain

rate effects of concrete and reinforcing steel elements

nor softening phenomenon of the post peak of concrete

were considered for this elasto-plastic impact response

analysis technique. However, to accurately simulate a

damped free vibration of the RC arch tunnel model

after the rebound of heavy-weight, a damping constant

h was considered. The constitutive law for each

material characteristic is briefly outlined below:

3.2.1 Concrete

Stress–strain relation of concrete was assumed by

using a bilinear model in the compression side and a

cut-off model in the tension side as shown in Fig. 5b. It

is assumed that: (1) yielding stress is equal to the

compressive stress f’c which is equal to-20 MPa; (2)

concrete yields at a strain of 0.0015; (3) the tensile

stress is perfectly released when an applied pressure

reaches the tensile strength of concrete; and (4) the

tensile strength is set to be 1/10 of the compressive

strength. Von Mises criterion was applied to the

yielding of concrete [2]. LS-DYNA material model

MAT_SOIL_AND_FOAM_FAILURE was used to

model the concrete elements [6].

3.2.2 Reinforcing steel

For main reinforcing steels an elasto-plastic model

following isotropic hardening rule was applied as

shown in Fig. 5c. Here, the plastic hardening modulus

H’ was assumed as 1 % of young’s modulus (Es). The

yielding condition was judged based on von Mises

criterion. LS-DYNA material model MAT_PLAS-

TIC_KINEMATIC was used to model main and shear

reinforcing steel.

3.2.3 Falling heavy-weight, and anchor plate

The other elements (heavy-weight and anchor plate)

were modelled as elastic body based on experimental

observations. Young’s modulus and Poisson’s ratio

were assumed as 206 GPa and 0.3, respectively. LS-

DYNA material model MAT_ELASTIC was used to

model them.

3.2.4 Sand cushion

Figure 3a shows the constitutive model for sand

cushion. To rationally analyze the stress behaviour

of sand cushion when a heavy-weight collides, second

order parabolic stress–strain relation for sand cushion

[2] was applied in which the constitutive relation is

described in the following expression.

rs ¼ 50e2s ð1Þ

Table 2 Properties and case types of rock-shed system

Case type Falling height

(m)

Impact

(kN)

Location Energy

(MJ)

E-0.2 20 9.8 Centre 0.196

E-2.5 50 49.0 2.45

E-4.9 100 4.90

E-7.4 150 7.35

E-9.8 200 9.80

E-12.3 250 12.3

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Here, rs is stress in sand and es is the volumetric strain

of sand element. The material properties of sand for

impact response analysis were assumed as; Young’s

modulus Es = 10 GPa; Poisson’s ratio; ms = 0.06 and

density qs = 1,600 kg/m3. LS-DYNA material model

MAT_CRUSHABLE_FOAM was used [2].

3.2.5 Strain rate effects and viscous damping constant

Neither strain rate effects of concrete and reinforcing

steel nor softening phenomenon at post-peak of

concrete were considered for impact response analysis

of the RC rock shed models. The post peak softening

of concrete was not considered. Due to low velocity

impact there is no effect on the results [5–7]. In

addition, to accurately simulate impact response

characteristics of the RC rock shed models, a viscous

damping constant h was considered.

4 Overview of numerical results

4.1 Timehistories of impact force anddisplacement

at crown

The numerical analysis results for time histories of

impact force (P) are shown in Fig. 6. The six types

such as E-0.2, E-2.5, E-4.9, E-7.4, E-9.8 and E-12.3

having energies of 0.196, 2.45, 4.90, 7.35, 9.8 and

12.3 MJ respectively were analyzed as shown in

Table 2. The impact force (P) obtained from the

numerical analysis were estimated by summing the

contact reaction forces in the perpendicular direction

caused in the contact interface elements of falling

heavy-weight.

From these figures, it can be observed that the

impact force wave (P) for each case is composed of

few half-sinusoidal waves: an incidental wave having

extremely short duration at the beginning of impact

with high frequency contact within 10 ms; and one

and/or two waves having relatively larger duration

from 10 to 40 ms. The configuration of the wave in

numerical analysis is similar for all cases of increased

input energy. By comparing the impact forces with

impact energy it seems that the former increases with

increase in impact energy. However it is observed that

the time history has varying time duration cycle with

increase in input energy.

In addition, when paying attention to the maximum

impact force after falling weight collides, the genera-

tion time for the main impact wave is 20 ms in case of

E-9.8 and E12.3 but for other cases it is between 20 and

30 ms. The main wave motion shows that the tendency

of dissipation time becomes short with the increase of

input energy and amplitude. For example, in the case of

E-2.5, the continuation time is 25 ms (ms), as compared

to 15 ms in the case of E-12.3, showing a decreasing

trend. Moreover, in the case of E-2.5 the amplitude of

the wave is 5 MN, which is increased by about 5 times

to 25 MN grade in the case of E-12.3. The relation

Fig. 5 Stress strain

relationship of material

models for sand, concrete,

steel

Fig. 6 Impact force time history cases

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between input energy and the maximum impact force is

shown in Fig. 7 indicating a linear relation with respect

to input energy.

Focusing on the displacement shown in Fig. 8, it is

seen that the vibration period after reaching maximum

amplitude vary from 25 to 75 ms. The maximum

displacements for E12.3 case is about 28 mm. The RC

rock-shed vibrate with smaller residual displacement

in case of E-2.5. On the other hand, it is observed from

the numerical analysis results that the RC rock-shed

vibrate as continuous body with larger residual

displacement and high damping after suffering severe

damages. The main reason may be that diagonal shear

cracks occurred near footing and de-bonding of re-bars

from concrete cannot be precisely estimated due to the

assumptions of continuous body and perfect bond

between reinforcing steel and concrete. At the begin-

ning of 10 ms of displacement waveform there is no

significant amplitude and from 20 to 30 ms the

maximum response is observed in all cases of input

energy. Between 70 and 80 ms there is negative

displacement due to rebound of the falling weight

impact. The relationship between residual displace-

ment and input energy remains linear from E-2.5 to

E-12.3 as shown in Fig. 9. However, there is sudden

increase in slope from E-9.8 to 12.3 due to severe

damage occurs when input energy is quite large.

The strain measured at steels located in the top slab

of reinforcement are shown in Fig. 10 for various

cases. Since in the case of E-7.4, E-9.8 and E-12.3, the

strain is exceeding -1,500 microstrains, which is a

plastic level for concrete element as shown in Fig. 5b.

The case of E-7.4 can be used as serviceability limit

state and E-12.3 can be used as performance limit

state. Moreover, it shows that the strain value of

E-12.3 becomes about 2.5 times more that the value as

in case of E-9.8. It is observed that that tendency of

plastic hardening is higher with increase in input

energy.

Fig. 7 Relationship between impact force and input energy Fig. 8 Displacement Time History Cases

Fig. 9 Relationship between residual dispalcement and input

energy

Fig. 10 Strain time history in reinforcing steel cases

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4.2 Crack patterns of side surface of concrete

Based on a constitutive law model assumed for

concrete elements earlier, stress applied in the con-

crete elements will be converted to zero when the

applied pressure in an element reaches the tension cut-

off value. In other words, it is understood that the

element with zero stress has a potential for crack

occurrence. Here, crack patterns can be predicted

based on this concept and the applicability of the

prediction method was discussed by comparing the

crack patterns obtained from experimental results.

Figure 11 shows the contours of the maximum

principal stress at the maximum displacement obtained

Fig. 11 Crack pattern of rock-shed for case types

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from numerical analysis and crack pattern developed on

side-surfaces of the RC rock-shed. In those figures,

white colour stress contour means that the elements are

around zero stress. From those comparisons, it is seen

that the crack patterns observed from rock-shed can be

increased by the increase in input energy. The crack

distributions at the top of slab and around the thickness

are shown in Figs. 11a–e. Major cracks occurred in the

case of E-12.3. When the input energy is small, it is

observed that the compression stress has occurred in the

longitudinal direction. However with increase in input

energy, the compression stress decreases.

5 Conclusions

Applying cushion material is one of the engineering

approaches to ensure the greater safety of important

structures, such as nuclear power plants, fuel tanks,

and rock-shelters. In this study, focusing on the

absorbing system developed for rock-sheds con-

structed over the highways in mountains areas and

along the edge of cliff near seaside, establishment of

a numerical analysis method for this type of system is

developed. Numerical analysis method is proposed to

investigate a rock-shed by performing the falling-

weight impact load FE analysis of prototype RC

rock-shed. The results obtained from this study are as

follows:

1. Residual displacement and input energy

increase linearly but after the case of impact

energy of 9.MJ (E-9.8), it suddenly increases

due to major damage occurred at the top of the

rock-shed.

2. It seems clear that till the case of impact energy

of 7.5 MJ (E-7.5), the rock-shed reached its

ultimate limit state. It can be concluded from

the impact force time history, displacement time

history and crack pattern as shown in Figs. 6, 8,

and 11 respectively, that the case of impact

energy of 7.4 MJ (E-7.4) may be used as the

serviceability limit state and impact energy of

12.3 MJ (E-12.3) may be used as performance

limit state.

3. Here maximum input impact energy for reaching

ultimate state was numerically examined by

means of three-dimensional elasto-plastic FE

method for RC rock-shed designed based on

allowable stress design concept.

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