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9th GRACM International Congress on Computational Mechanics Chania, 4-6 June 2018

EFFECTS OF THE SOIL-STRUCTURE-INTERACTION PHENOMENON ON RC STRUCTURES WITH PILE FOUNDATIONS 1

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George Markou , Mohammad AlHamaydeh and Dina Saadi

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1

Department of Civil Engineering Universidad Católica de la Santísima Concepción Concepción, Alonso de Ribera 2850, Chile e-mail: [email protected] 2,3

Department of Civil Engineering American University of Sharjah P.O. Box 26666, Sharjah, United Arab Emirates 2

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e-mail: [email protected] email: [email protected]

Keywords: Soil-Structure-Interaction, FEA, Reinforced Concrete, Pile Foundation, Cyclic Loading. Abstract. The Soil-Structure Interaction (SSI) has a significant effect on the overall structural behavior of reinforced concrete buildings, especially under cyclic loading conditions. Considering the SSI effects within experimental setups comprise cumbersome procedures that are usually very difficult to control and monitor. Furthermore, when the foundation type of the structure foresees the use of pilecaps connected to piles, accounting for the SSI effect becomes further complicated to investigate. Consequently, most SSI experiments involve very simple geometry configurations for specimens under monotonic loading conditions. The need for developing new numerical methods that will enable realistic capturing of this phenomenon, is deemed to be of great importance. This research work aims to study the SSI effect for the case of a 6-storey building with a pile foundation undergoing cyclic loads. The numerical model foresees the study of the main shear wall of the structure that is connected to six reinforced concrete slabs and is resting on a pilecap that is connected to three piles found within a soil class E, according to ASCE7-10. By using the hexahedral isoparametric finite element, the structure is discretized in 3D, where the adopted concrete material model is integrated with the smeared crack approach and the steel bars are modelled by using embedded rebar elements. Both soil and concrete foundation are discretized with hexahedral elements, while monotonic and cyclic analyses are performed in order to study the mechanical behavior of the fixed-base structure and the corresponding SSI counterpart structure that is founded on the flexible soil. 1 INTRODUCTION The Soil Structure Interaction (SSI) phenomenon can be of great importance when assessing the capacity of a structure founded on a soil with low mechanical properties [1]. The flexible soil combined with large superstructure loads can cause the foundation system to deform substantially, posing significant effects on the overall structural response. The effect of the SSI on the overall mechanical behavior of structures can vary based on the adopted foundation type [2]. The local stress and strain are redistributed when the foundation is free to deform, affecting the response of the structure. This is of great importance, especially when a reinforced concrete (RC) framing system is designed to undertake seismic excitations which generate high lateral forces. Accounting for SSI effects may be necessary when the dynamic response of a structure, its foundation and its soil collectively contribute to the overall seismic response [3]. Researchers face major difficulties in conducting experimental tests to understand the complicated SSI mechanisms, which develop during seismic excitation. As a result, the majority of experimental tests in existing literature are limited to simple specimens under monotonic loading. The study of the SSI mechanisms is further complicated by the complexity of their geotechnical aspects and prediction of soil mechanical behavior. Modeling the SSI phenomenon through numerical models has been frequently implemented by researchers over the last two decades [1-10]. It is worth noting that the commercial software used to perform SSI analysis have evolved substantially over the years [11-17]. The main challenges associated with nonlinear finite element modeling of full-scale structures founded on soil are attributed to computational inefficiency. The need to account for material nonlinearities of both soil and concrete domains adds further complications. Therefore, modeling the soil domain through springs is the most popular simulation approach given its numerical simplicity. Nevertheless, this approach is found to be impractical and inaccurate when dealing with foundations that have complicated

George Markou, Mohammad AlHamaydeh and Dina Saadi.

geometries (i.e. pile foundation). Thus, capturing complicated SSI mechanisms that develop due to the 3D deformation of the foundation system is not feasible through this numerical method. Hence, the use of hexahedral elements was proposed to discretize the soil and concrete mediums [1, 2]. This FE method helps in achieving an accurate representation of the structural system as well as the soil. When the structure and soil are discretized with 8-noded hexahedral elements, an exact representation of the geometry is achieved [1]. Furthermore, performing static pushover analysis to study the SSI effect in terms of capacity, deformation, energy dissipation and damage can be investigated at a material level. The 3D modeling approach allows for special considerations at the concrete-soil interface, which also affects the overall mechanical response of the SSI system. A previously published work [1] examined the structure with an isolated foundation resting on class E soil, based on ASCE7-10 [18]. The structure was tested under monotonic and cyclic loading, at which the effect of the SSI on the structural response was studied. The same approach is adopted herein, to investigate the mechanical response of a structure supported by deep foundation consisting of three piles. The effects of the SSI phenomenon will be examined and presented through this numerical investigation. The SSI effects play a paramount role in seismic response, especially for nonlinear dynamic analysis and inelastic response assessment where realistic damage estimates are needed for RC structures of various types. All reported findings in such research investigations [19-31] are expected to require re-assessments. 2 NUMERICAL MODEL 2.1 Material Models The 3D detailed discretization that was adopted in this work follows the concept proposed in “Nonlinear FEA of Soil-Structure-Interaction Effects on RC Shear Wall Structures” [1], which demonstrated the use of 8-noded hexahedral finite elements to discretize the structure and the soil domains. The steel reinforcement was modeled by the embedded rebar element. In addition, the model used in this research work demonstrates the use of springs positioned at the pile cap-soil interfaces, to simulate the phenomenon of soil detachment when the interface undergoes tension. Furthermore, the interface of the piles and the soil is modeled through hexahedral elements that were numerically calibrated to account for the friction stresses, but not transfer tension to the soil domain. The pile-soil interface elements are modeled to resist a maximum shear stress after a certain allowable settlement, which was taken as 0.6% of the pile diameter to comply with conditions for numerical analysis described in section 3. The concrete material model, which is integrated within the 8-noded hexahedral elements is based on the proposed algorithmic implementation presented in [2]. The model is based on the concrete material model proposed by Mourlas et al. [32], which was integrated with a flexible crack closure criterion. The criterion was found to induce numerical stability for problems that tackle nonlinear analysis of RC structures under ultimate limit state cyclic loading conditions [32]. To capture the numerical effects of cracking during monotonic and cyclic analyses, the smeared crack approach is adopted [33]. When a crack opens at a given Gauss point (shown in Fig. 1), the constitutive material matrix is modified accordingly to account for the material’s damage [32].

Fig. 1: Local axes for the case of two cracks at a specific Gauss point. [32] According to the concrete model adopted in this numerical investigation, when the 3D stresses at a given Gauss point exceed the concrete’s strength envelope, a crack occurs along the plane perpendicular to the maximum principal tensile stress. The concrete’s strength envelope is computed by Eq. 1, which is based on the Willam and Warkne [34] formulae.

 0u 

2 0c ( 02c   02e ) cos    0c (2 0e   0c ) 4( 02c   02e ) cos 2   5 02e  4 02c 02e

(1) 4( 02c   02e ) cos2   (2 0e   0c )2 where, θ defines the rotational variable of the deviatory stress orientation on the octahedral plane. The terms τ0e (θ=0°) and τ0c (θ=60°) correspond to the states of σ1=σ2>σ3 and σ1>σ2=σ3, respectively. The Menegotto Pinto [35] steel model incorporating the Bauschinger effect (shown in Fig. 2) is used to model


the embedded rebar elements within the concrete hexahedral mesh in the steel model adopted in this paper.

Fig. 2: Menegotto – Pinto steel model. [35] The stress-strain corresponding to the steel model is presented below:

 *  b * 

(1  b) * (1   *R )1/ R

where,

 *  (    r ) / (  0   r ),  *  (    r ) / (  0   r ) and R  R0  a1 / (  2   ) It must be noted that the SSI model, which uses the 8-noded hexahedral elements to discretize the soil domain, is integrated with a von Mises material model. This material model helps in capturing the nonlinear behavior of the soil domain in the case where the ultimate compressive strength of its material is exceeded. 2.2 Finite Element Model The investigation of a 6-storey RC building was performed in this work through two finite element models; the first was the fixed-base (FX) model (illustrated in Fig. 3a) and the second involved discretizing the soil domain with hexahedral elements to account for the SSI effect (illustrated in Fig. 3b). The foundation type that was designed and discretized accordingly consisted of three piles with a diameter of 1.2m connected to a pile cap of size 2.5x9.5x1.6m. The 24m tall shear wall had a section of 400x4500cm and was reinforced based on the design presented in [19-22]. Furthermore, the foundation system was designed based on the ACI 318 provisions [36] and the resulting reinforcement was modeled in 3D as shown in Fig. 4.

(a) (b) (c) Fig. 3: Hexahedral finite element mesh of the (a) fixed-base and (b) SSI models. (c) SSI model’s hexahedral

(2)


mesh without the soil elements.

Fig. 4: Embedded rebar finite element mesh of the SSI model. Model FX SSI

Num. of Concrete Hexa Elements 4,824 5,400

Num. of Soil Hexa Elements 5,228

Num. of Steel Embedded Rebar Elements 56,803 62,405

Table 1: Mesh details Soil Parameter

E

v

qu

Value

65.7 MPa

0.3

964 kPa

Table 2: Soil Properties (Class E) It is noteworthy to state here that the tributary areas of the six slabs connected to the discretized shear wall were also included in the numerical model. This modelling approach was applied to optimize the number of computations and the execution time of the heavy computational demand imposed by the numerical analysis of a full-scale structure. Table 1 shows the number of hexahedral elements and embedded rebar elements used to construct the two aforementioned 3D models. It may be observed that the SSI model consists of a larger number of finite elements, given that the pile foundation and the soil domain are discretized and included within the 3D model. The material properties used to define the soil domain, which are characteristic of an ASCE7-10 Class E soil [18], are summarized in Table 2.The soil domain within the SSI mesh was divided into four different layers, with a total depth of 30m (shown in Fig. 3b). The soil material properties were modified based on the depth of each layer. Thus, the deeper the soil layer, the larger the Young modulus and the larger the corresponding uniaxial compressive strength. Furthermore, each pile had a total length of 20m and the concrete material exhibited an ultimate uniaxial compressive strength of 38 MPa. The steel rebars had a yielding stress of 420 MPa. The tributary areas of the slabs, which have a thickness of 20cm, are based on the design of the 6-storey RC building presented in previously published work [19-22]. The slabs were subjected to dead loads and live loads are consistent with previously published work. The slab edges were restrained in order to capture the mechanical behaviour of a continuous slab, which is expected to develop bending moments and shear. Therefore, the edges were assumed to displace along the x-axis (the direction of the imposed displacements) but not displace along the z-axis. Finally, the displacement-control nonlinear analysis performed in this work demonstrates the application of imposed displacements at the nodes located at the perimeter of each slab.


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NUMERICAL RESULTS AND DISCUSSION

Pushover analysis was performed in order to compare the mechanical response of the structure with and without SSI considerations. The analysis was implemented to numerically assess the mechanical behavior of the two models under static push over analysis. The horizontal monotonic displacements at each slab were computed based on Eq. 3. 𝑘 (3) 𝛿𝑓𝑙𝑜𝑜𝑟 = (𝑥⁄𝐿) where, x is the ground to slab height, L is the total height of the structure and k is a constant, which was set to be equal to 1.2, based on the parametric investigation performed in [1]. 3.1 Push-Over Analysis Fig. 5 shows the base shear force vs horizontal displacement curves obtained numerically through quasi-static push-over analysis. As observed, the SSI model derived a more flexible behavior in comparison to the FX model. This may be attributed to the flexible behavior of the foundation system, which undertakes the superstructure loads as shown in Fig. 6. Based on the numerical findings, it is evident that the deformation of the soil and the foundation system (comprised of the pile cap and piles) affects the overall mechanical behavior of the structure, which was found to be more flexible by 52% in terms of initial stiffness. The stiffness decrease is attributed to the relatively flexible soil and the fact that the soil-pile interface elements reach their friction capacity at an early stage of the analysis. Thus, the piles are mainly transferring the vertical superstructure loads to the soil through the head bearing mechanism. Additionally, the corresponding ultimate base shear of the SSI model was found to be 29.58% smaller compared to the FX model as depicted in Fig. 5. This decrease is attributed to the flexibility induced by the soil domain, which deforms accordingly as the imposed displacements increase. It is also evident that, the SSI model derived a different nonlinear mechanical behavior when the imposed displacements were larger than 150 mm. When the imposed horizontal deformation was 150 mm, the FX model exhibited a sudden drop in terms of capacity, attributed to the longitudinal reinforcement yielding and concrete cracking, a mechanical phenomenon that was noted in a lower degree in the corresponding SSI model. As it was found from the numerical investigation, the fixed-base assumption within the FX model forced the shear wall to develop higher deformations at the ground floor level, where the rebar yielding occurred due to the large bending moment developed at the base of the structure. Furthermore, as it can be seen in Fig. 5, the corresponding capacity drop shifted significantly when the SSI effect is accounted for. This is once more attributed to the overall flexible behavior of the pile foundation when compared to the mechanical behavior of the fixed-base assumption that does not allow any deformation to occur at the foundation level. It must be noted at this point that, the numerical results from the parametric investigation that foresee the analysis of the structure under cyclic loads was also performed but will be presented in a future publication.

Base Shear Force (kN)

30000 25000 20000 15000 10000 SSI B1 pushover

5000

FX B1 pushover

0 0

50

100

150

200 250 300 350 400 450 Horizontal Displacement (mm)

500

Fig. 5: Base shear force vs horizontal displacement curves from push-over analysis. 3.2 Pile Foundation Mechanical Response Fig. 6 shows the deformed shape and the corresponding strain contour of the pile cap and the three piles resulting from the push over analysis. The two deformed shapes given in this figure correspond to the results obtained for the displacement increments corresponding to a 12mm and 60mm horizontal displacement at the roof slab, respectively. To emphasize the deformed shapes, a deformation scale factor of 500x was used. Thus, it can be easily observed that the pile cap develops a shear deformation due to the large bending moment developed at


the base of the RC shear wall. The piles were found to develop a bending deformation since the pile cap displaces along the x-axis (direction of the imposed displacements), forcing the pile heads to displace horizontally as well. The complexity of the under study problem is evident in the complicated 3D deformed shapes, which incorporate several SSI resistance mechanisms. Therefore, even for cases of simple loading such as the push-over, delivering a realistic representation of the behavior of SSI systems requires advanced numerical tools. This also explains why the simplistic spring model approach cannot be used in this type of analysis without compromising numerical accuracy. In addition to the above findings, the numerical investigation also revealed that the damages due to strain concentration agreed with the findings in [1]. According to the numerical analysis presented in this paper, the ground floor shear wall exhibited increased cracks in the FX model, whereas the SSI model exhibited lower strain concentration due to the foundation’s ability to deform. Moreover, the upper floors of the SSI model were found to generate larger deformations due to the flexibility of the soil, which causes redistribution of the internal stresses and in return alters the structure’s deformed shape.

Fig. 6: Deformed shape and von Mises strain contour of the pile foundation for a horizontal roof displacement of (Left) δ = 12 mm and (Right) δ = 60 mm. Deformation scale factor: 500x. 4

CONCLUSIONS

In this work, the SSI effect was numerically investigated by studying a 6-storey RC structure resting on a pile foundation system. The pile foundation was supported by a soil of class E as per the ASCE 7-10 provisions. The superstructure was modeled with 8-noded hexahedral elements, which analyze cracks through the smeared crack approach. The reinforcement bars were modeled as embedded rebar elements. The soil domain was also discretized with 8-noded isoparametric hexahedral elements. Special considerations were accommodated for modeling the friction and potential soil detachments at the concrete-soil interfaces. The SSI effect was modeled and studied numerically, and the obtained results were compared to those of an equivalent fixed base model. Upon successful completion of the parametric investigation presented in section 3.1 (Push-Over Analysis), it was concluded that the SSI model demonstrated a more flexible behavior. The ability of the foundation system to deform causes the soil to develop settlements proportional to the superstructure loads. Based on the numerical findings, the SSI model’s initial stiffness decreased by 52%. In addition, the computed maximum base shear was 29.58% smaller than that obtained from the equivalent FX model. Furthermore, in the SSI system, the shear wall was found to behave in a more flexible manner, yielding lower strain concentrations at the ground floor. Moreover, the deformed shape of the foundation system confirmed the shortcomings of the simplistic spring model in representing the SSI mechanisms. The research presented in this paper is part of a future project to extend the obtained numerical results to further cases of structures with various geometries and reinforcement arrangements. The objective of this project would be to investigate the relationship between superstructure characteristics and the extent to which the SSI effects influence overall structural response, e.g. stress/strain concentration regions, excessive cracking, etc.


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