Finite Element Study of Using Concrete Tie Beams to Reduce Differential Settlement Between Footings

AMIN H. ALMASRI* AND ZIAD N. TAQIEDDIN**

*Assistant Professor, Department of Civil Engineering, Jordan University of Science and Technology, Irbid, Jordan. Email: ahalmasri@just.edu.jo, corresponding author.

**Assistant Professor, Civil Engineering Department, Applied Science University, Amman, Jordan. Email: z_taqieddin@asu.edu.jo

Abstract:- Buildings footings are usually susceptible to soil settlement; uniform or differential. The latter settlement is the one that causes higher stresses in building elements, and is classified as a main reason for structural failures. Some codes suggest using tie beams to increase structural integrity and reduce differential settlement. Hence, this paper investigates how tie beams between footings can improve structural resistance to settlement using finite element analysis of three dimensional structural models. In addition, seismic analysis is run to investigate tie beams behavior under earthquake loading in enhancing structural performance of foundation system. Results indicate that tie beams can reduce differential settlement greatly under both static and dynamic conditions.

Key-words: Tie Beams, Finite Element, Seismic Analysis, Differential Settlement, Earthquakes

1 Introduction

Soil is usually considered a heterogeneous material with settlement behavior that is hard to be predicted with any great accuracy. Since soil is a relatively weak material compared to building materials such as concrete, steel, and wood; footings are required to transfer and distribute gravity loads of buildings to soil layers. This load can be different from one footing to another, causing a differential settlement between the different footings. One practical way to improve settlement resistance is to increase the structural stiffness in the vertical direction by using reinforced concrete tie beams. These beams usually connect isolated footings and sometimes even strip footings as shown in Fig 1.

Literature shows no closed form analysis and design procedures when dealing with tie beams. But despite that using tie beams is generally a

common practice rather than a structural requirement, some codes and standards suggest using them in specific conditions. For example, Indian Standards IS 1893 (2002) state that spread footings or pile caps shall be interconnected with ties in some specific seismic zones for soil types other than rocks. In addition, these ties shall be able to carry an axial force (tension and compression) equal to a seismic factor Ah/4 times the larger of the column or pile cap load. Massachusetts state building code requires that all ties shall be capable of resisting, in tension or compression, a force equal to 10% of the larger column dead plus live load. The force to be resisted by the ties in International Building Code 2009 equals to the lesser of the product of the larger footing design gravity load times a seismic coefficient, SDS, divided by 10 and 25 percent of the smaller footing design gravity

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load. FEMA requires individual pile caps, drilled piers, or caissons to be interconnected by ties capable of carrying, in tension or compression, a force equal to the product of the larger pile cap or column load times a seismic factor S divided by 4.

Heidebrecht and Rutenberg [2] used the travelling wave assumption to propose a simple structural model to evaluate the axial force acting on tie beams interconnecting spread footings due to differential ground motion. The approach was intended to find the percent of gravity load to be the design axial forces on tie beams. The axial force was rather modest, while shear forces between footing and soil may be quite large depending on maximum column displacements and superstructure rigidity.

Thevendrana and Wanga [3] obtained a solution, by two independent approaches, for the optimal cross-sectional area of a simply supported tie-beam that minimizes the maximum deflection, subject to a volume constraint and the longitudinal elongation of the tie-beam not exceeding a given value.

2 Finite Element Analysis

Full three dimensional models of nine footings are created. Every footing supports one column and the nine columns support a solid slab that carries distributed load of 50 kN/m2. Every footing has an area proportioned to the load that is carried. Hence, the center footing will have twice the area of an edge footing, which in turn has twice the area of a corner footing. Beneath the footing is a large soil layer that is fixed at the lower surface and carries the footings at top. Dimensions of all elements are presented in Table 1. In order to simplify analysis, both materials (foundation concrete and soil) are assumed to be homogeneous, with properties listed in Table 2. Two structural models are constructed as shown in Fig 2; one without tie beams, and the other with tie beams. The models are meshed using an 8-node linear brick with reduced integration and hourglass control, with total number of elements of 53822 and 57472 for model without tie beams and

with tie beams, respectively. Sweep meshing technique is used to construct the models where inter-element continuity is ensured. Full contact is assumed between the soil elements and footings elements. Results of displacement and stresses are obtained through the center line of the models as illustrated in Fig 3. The lower surface of soil layer is fixed against translations and rotations as a boundary condition.

After static analysis, seismic one is performed using Koyna earthquake horizontal and vertical acceleration record, as shown in Fig 4. Only first 10 seconds of the record is considered in the analysis to reduce the time needed for the simulation, where peak acceleration reaches about 0.4g.

Table 1: Model geometry and dimensionsGeometry Depth or

height (m) Length (m) X width (m)

Soil layer 4 30 X 30Center footing 0.5 2 X 2Edge footing 0.5 1.4 X 1.4Corner footing 0.5 1 X 1Columns 3 0.5 X 0.5Tie beams 0.5 8.55 X 0.3Slab 0.25 20 X 20

Table 2: Material properties Property Foundation

Concrete Soil

Modulus of elasticity (GPa)

25 0.04

Poisson ratio 0.15 0.33Unit weight (kN/m3)

24 17

Strip footing

Isolated footings Tie beams

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Figure 1: Tie beams between footings

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Figure 2: Structural models (a) without tie beams, and (b) with tie beams

Figure 3: Path line where settlement and stresses are

obtained

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Figure 4: (a) Horizontal and (b) vertical ground acceleration record of Koyna earthquake.

3 Results and discussion

Vertical displacement of the structure is illustrated in Fig 5-a, and normal stress is illustrated in Fig 5-b under static loading along the centerline of the model. Results show that using tie beams reduces both absolute settlement and differential settlement. Total settlement of middle footing without using tie beams is about 0.043m compared with 0.027m for the edge footing, with differential settlement of 0.016m. This is reduced to 0.002m differential settlement when using tie beams in addition to reducing total settlement to about 0.025m or 42% for the center footing. On the other hand, the variation between normal stress under the different footings is almost negligible. Using tie beams reduces the maximum normal stress under footings by about 30%, but increases the stress between the footings since it applies some pressure on soil. It should be noted that the columns transfer some moments from the slab to the footings, which introduces some nonuniformity to the stress beneth the footings. The vertical displacement contour is shown in Fig 6 for structural model with tie beams for illustration purposes.

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Figure 5: (a) Settlement of footings and (b) normal stress under footings with and without using tie

beams under static conditions

Figure 6: Settlement contour for half of the model

Seismic analysis is carried out using Konya horizontal and vertical ground acceleration records. Normal stress along the centerline of the models is obtained with time as shown in Fig 7. The results show that normal stress oscillates highly during earthquake in the absence of tie beams. This oscillation is reduced significantly when using tie beam as illustrated in Fig 7-b, in addition to

reducing the normal stress value itself. Normal stress envelope (maximum and minimum) due to earthquake is shown in Fig 8, where the difference between the maximum and minimum stress under footings is clear to be about 400 kPa when no ties are used, compared to less than 50 kPa when tie beams are present. It is obvious that tie beams eliminate the effect of earthquake to a large degree and keep the stress envelope close to the static results.

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Figure 7: Normal stress along distance during earthquake (a) without and (b) with tie beams

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Figure 8: Normal stress envelope during earthquake (a) without and (b) with tie beams

4 Conclusions

Tie beams have been used to increase the integrity of foundation systems for a long time. Its effect in improving foundation resistance to settlement was investigated under static and dynamic loading. It was found that tie beams can really reduce both total and differential settlements under static loading. However, bigger advantage for tie beams was found under seismic conditions, where it can reduce the effect of earthquakes significantly, which is the reason why they are a requirement in building codes for buildings in high seismic activity zones.

5 References

[1] The massachusetts state building code, user’s guide, to 780 cmr, sixth edition

[2] A. C. Heidebrecht and A. Rutenberg, “Evaluation of foundation tie requirements in seismic design,” Canadian Journal of Civil Engineering, 1993, 20:73-81, 10.1139/l93-008

[3] V. Thevendrana and C.M. Wanga, “Optimal design of tie-beams,” International Journal of Solids and Structures, Volume 22, Issue 11, 1986, Pages 1343-1356

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