Nonlinear SoilStructure Interaction Analysis of Multistorey Shear Wall Buildings with Site Specific Ground Response
Abstract
Influence of local geology and soil conditions play a major role in varying the intensity of ground shaking. In the present study, by utilizing the geotechnical data of a specific site, amplification of earthquake motion is found out by ground response analysis. Seismic structural response variation in multistory shear wall buildings with different shear wall locations is determined from nonlinear soilstructure interaction (SSI) analysis using the ground motion with the highest peak ground acceleration obtained from the site. Geotechnical data from twenty bore holes at the site with depth varying between 7–15 m below ground level are considered. This specific site is very near to the Arabian Sea coast with a lot of variation in the geotechnical profile. Symmetric plan multistorey reinforced concrete shear wall buildings of aspect ratio (h/d) ranging from 1 to 4 resting on raft foundation with shear walls placed symmetrically along the exterior frames, core and all four corners of the exterior frames are considered. Further, the structural responses obtained from SSI analysis and conventional method of assuming rigidity at the base of a structure is compared. Results show the significance of positioning of shear wall in symmetric buildings which attracts the least earthquake forces, with the consideration of nonlinear behavior of the underlying soil medium.
1 Introduction
Local site conditions influence the significant characteristics of ground motion, such as amplitude, frequency content and duration. The magnitude of this influence depends on the material and geometrical properties of the underlying soil profile at the site and the characteristics of input motion.
Approximation of sitespecific dynamic response of layered soil deposit is denoted as a sitespecific response analysis. Time histories rendered from ground response analysis constitute the ground surface motions. A case study of ground response analysis of a site in Ahmedabad city during the Bhuj earthquake was carried out by Raju et al. (2004) to determine the varying degree of damage in multistorey buildings in the close proximity of the Sabarmati river area due to amplification of ground motion. Similar study was carried out by Uthayakumar and Naesgaard (2004) to determine the significant amplification in the earthquake motion in Fraser river delta, British Columbia. Ground response analysis using the SHAKE2000 software was carried out by Roy and Sahu (2012) to determine the local site effects for the Kolkata Metropolitan District area. This study also stated the engineering importance of sitespecific ground response analysis, difficulties faced in conducting a complete ground response analysis and steps to be followed in conducting a meaningful site amplification study.
It’s the usual practice to analyse buildings by considering the base to be fixed. Nevertheless, in reality, sub layer soil property influences the response of the structure to a greater extent by its natural ability to deform. The possible severities of omitting the effects of SSI in seismic design of buildings were noted by many researchers such as Mylonakis et al. (1997) and Roy and Dutta (2001a, b) etc. Flexibility of soil causing the lengthening of lateral natural period of the structure due to the reduction in overall lateral stiffness was shown in the studies carried out by Bielak (1975) and Stewart et al. (1999a, b). Seismic soilstructure interaction study of massive concrete structures supported over raft foundation using finite element software to determine the stress resultants in the raft was carried out by Rajasankar et al. (2007) Finite element transient analysis of segmental retaining walls using RambergOsgood model to simulate the nonlinear hysteretic behaviour of soil was carried out by Helwany et al. (2001) using computer program DYNA3D and the results were further compared with laboratory shake table tests. Nonlinear timedomain soilstructure interaction analysis of embedded reactor structures subjected to earthquake loads using a simple hysteretic soil model based on the RambergOsgood formulation was carried by Solberg and Hossain (2013).
In the present study, site specific ground motion was generated from ground response analysis using ProSHAKE software. To suffice this, geotechnical data from twenty bore holes at the site with depth varying between 7–15 m below ground level were considered. Time history record of Elcentro earthquake motion was scaled down to a peak acceleration of 0.1 g and was used in the ground response analysis due to the unavailability of recorded strong ground motion data in the study area. Ground motion, thus generated possessing the highest PGA was further used in the finite element soilstructure interaction analysis of multistorey shear wall buildings. To simulate the nonlinear hysteretic behaviour of soil, RambergOsgood soil model was employed in SSI analysis. The effects of local site conditions in varying the seismic response of the buildings were evaluated. Position of shear walls, drawing the least earthquake forces on the buildings was also identified.
2 Ground Response Analysis
 V_{s}

is the shear wave velocity and
 N

is the standard penetration test value of soil.
3 SoilStructure Interaction Analysis
When structure is held on soil deposit, the inability of foundation to respond to the deformations of soil stratum as in free field motion causes the movement of the base of structure to vary from the free field motion. As well, the dynamic responses of the structure itself cause deformation of the supporting soil. This phenomenon, in which the response of soil influences the motion of the structure and response of the structure influences the motion of the soil, is referred as soilstructure interaction (SSI). In the analysis of integrated structurefoundationsoil system, present study adopts the direct method of SSI and the soil is represented by elastic continuum finite element model with nonlinear material behavior.
3.1 Structural Idealization
Geometric properties of building components
h/d  Columns (m)  Shear wall thickness (m)  

Up to 3 story  Above 3 story  
1  0.32 × 0.32  0.32 × 0.32  0.15 
2  0.40 × 0.40  0.35 × 0.35  0.20 
3  0.50 × 0.50  0.40 × 0.40  0.20 
4  0.60 × 0.60  0.50 × 0.50  0.25 
Raft foundation slab:  0.3 m  
Roof and floor slab:  0.15 m  
Beams:  0.23 × 0.23 m 
3.2 Geotechnical Idealization
Details of soil parameters
Soil description  Shear wave velocity (Vs) (m/s)  Poisson’s ratio μ  Unit weight (ρ) (kN/m^{3})  Young’s modulus (Es) (kN/m^{2})  Bulk modulus (K) (kN/m^{2})  Reference shear stress, τ_{y} (kN/m^{2}) 

Sandy silt (Layer1)  212  0.35  18  2.23E + 05  2.47E + 05  4096 
Sandy silt (Layer2)  299  0.35  18  4.43E + 05  4.92E + 05  8190 
Reference shear strain ɣ_{y} (%) = 0.05  
Stress Coefficient (α) = 0.8499  
Stress Exponent (r) = 2.2822 
3.3 Finite Element Model
4 Methodology

One dimensional equivalent linear ground response analysis was executed using ProSHAKE program to determine the amplification of ground motion due to local site condition.

Eigen value analysis to determine the fundamental natural period of the building which forms the significant element in determining the seismic loads coming on structures.

Finite element soilstructure interaction (SSI) analysis of multistoreyed concrete shear wall buildings at the site was performed to determine the responses in building due to the effect of soil flexibility and varying shear wall locations employing surface ground motion with highest peak ground acceleration (PGA) generated using ProSHAKE software.
Damping ratio equivalent to 5% of critical damping was presumed for both the structure and soil. Acceleration time histories were applied at the interface in the global X direction of the integrated SSI system.
5 Results and Discussions
Site specific SSI analyses were carried out on threedimensional finite element integrated soilfoundationstructure models to determine the response of the system during ground motion. Multistorey buildings of different aspect ratios with three different shear wall positions were considered. The variations in responses of buildings due to the effect of soil flexibility and various positions of shear wall are expressed in terms of variation in natural period, base shear and roof deflection.
5.1 Natural Period
Highest variation in the value of natural period is found in SWI shear wall configuration, i.e., shear wall at the core and the lowest in bare frame buildings revealing that the influence of soil on bare frame buildings is less than that on the shear wall buildings at this site.
5.2 Base Shear
Buildings with shear wall at the core (SWI) show the least value of base shear as compared to the other shear wall configurations considered. The least variation in base shear is also found in SWI shear wall configuration for all buildings except for aspect ratio of 1. Base shear for bare frame buildings are lower that in shear wall buildings, due to lower seismic weight of the bare frame building. Seismic weight forms the vital component in the base shear generation. Base shear values obtained by conventional fixed base analysis are higher than SSI analysis making conventional analysis results as more conservative.
5.3 Roof Deflection
Roof deflection is found to be the least in shear wall buildings with shear wall placed at core (SWI) and the highest in shear wall buildings with shear wall at corners of exterior frame (SWC). Roof deflections of buildings incorporating SSI effect are higher than the conventional fixed base condition due to the inclusion of flexibility in the structural system.
6 Conclusions

Natural period variation between the conventional fixed base analysis and SSI analysis is less for bare frame buildings and it increases with increase in stiffness of building by the addition of shear walls. In shear wall buildings, natural period is the highest in shear wall buildings with shear wall placed at corners of exterior frame and the lowest in shear wall building with shear wall at the core.

In general with SSI effect, base shear is the least in shear wall buildings with shear wall placed at core. Base shear values found by conventional fixed base condition for all buildings are higher than those considering SSI effects and hence conservative.

Roof deflections are considerably reduced by inclusion of shear walls in buildings and increased by inclusion of soil flexibility in structural systems. Buildings with shear wall placed at the core have the least roof deflection for this specific site.
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