Soil-Structure Interaction in Nonlinear Pushover Analysis of Frame RC Structures: Nonhomogeneous Soil Condition

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1 ABSTRACT: Soil-Structure Interaction in Nonlinear Pushover Analysis of Frame RC Structures: Nonhomogeneous Soil Condition G. Dok ve O. Kırtel Res. Assist., Department of Civil Engineering, Sakarya University, Sakarya Assit. Prof. Dr., Department of Civil Engineering, Sakarya University, Sakarya Determining the real displacement demand and seismic force resisting capacity of structures get more important to obtain performance level of structures when considering soil-structure interaction. Pushover analysis, one method of nonlinear static analysis, is generally used in the assessment of existing buildings. Pushover analysis gives more accurate results when compared to linear analysis methods to achieve seismic performance level of structures. In this study, three-dimensional soil structure interaction due to the soil inhomogeneity problem is carried out with nonlinear pushover analysis to determine effect of story number on performance level of RC structures which are designed as frame systems with five and eight stories. Inhomogeneity of soil is taken account into via impedance functions, which represent static stiffness of foundations for elastic soil behavior. These functions are calculated by considering shear wave velocity, shear modulus, depth of soil and poisson ratio for saturated normally and slightly over consolidated clays for spread foundation. At each foundation horizontal and vertical translations, and rocking stiffness are calculated with these impedance functions. Analysis results are compared in terms of target displacements, story drifts, plastic hinge mechanisms and rotations obtained from pushover analysis of superstructure for five and eight story structures. As a consequence, displacement demand and plastic hinge rotations increase when soil inhomogeneity is considered. In other words, if impedance functions are employed in the analysis, plastic deformations can be observed in elastic deformation regions due to soilstructure interaction. KEYWORDS: Soil-Structure Interaction, RC Frame Systems, Nonlinear Pushover Analysis. INTRODUCTION One of the widely used techniques to determine nonlinear performance of structures under seismic forces is pushover analysis. In this analysis method, seismic demands of a structure is calculated by increasing monotonically lateral seismic effect until a reliable target displacement is achieved. Force distribution due to seismic loads is applied to the structure at story levels in a compatible form of fundamental first mode (Chopra A.K. et al., ). Moreover a pushover analysis method taking into consideration soil-structure interaction (SSI) can be used to make a nonlinear analysis of structures only if an accurate numerical modelling technique is performed (Liping L. et al., ). However, SSI in pushover analysis is generally neglected because of the modeling difficulties of defining the effect of soil condition. One alternative solution to consider this soil condition effect is to use impedance functions for foundations proposed by Gazetas (99). That proposed impedance functions are directly represented by shear modulus of soil. The shear modulus decreases fast with depth of soil in nonhomogeneous soil conditions (Vrettos, C., 999). Static and dynamic deformations of soils can be larger due to the dynamic stiffness of soil (Wolf J.P, and Meek J.W., 99) when soils are multilayered and nonhomogeneous (Gazetas G., 98). In this research, effect of number of story and inhomogeneity of soil are studied to investigate behavior of a three-dimensional reinforced concrete (RC) frame and a shear wall-frame systems by considering SSI. Pushover analysis of the structure having five and eight stories are conducted by using SAP finite element software.

2 . NUMERICAL MODELLING and PARAMETRIC STUDY A single mode nonlinear pushover analysis is used in the research to determine real nonlinear displacement demand under seismic loads. Plastic deformations on structural elements of superstructures are calculated with that displacement demands. Plastic hinge properties of cross sections needed to define nonlinearity of structures is very crucial. Modelling method of superstructure and substructure is explained in detail in this section. In the study eight pushover analyses are performed for five and eight stories RC frame and RC frame-shear Wall D structures considering homogenous and nonhomogeneous soil conditions. The analysis results are compared in terms of nonlinear force-displacement relationship, story drifts, plastic hinge rotation and variation of first free vibration of structure... Modelling Superstructure Three dimensional five and eight-story RC structures are designed according to the minimum design conditions given by Turkish Earthquake Code 7 (TEC7). Shear walls connected to the structural system with infinite rigid beams are modeled via mid-pier frame approach. It is assumed that the structural systems have high ductility, are in first degree seismicity risk zone and were constructed on saturated normally and slightly over consolidated clays (Z soil class) defined in TEC 7. The peak ground acceleration (A) for first degree seismicity risk is taken as.g. Stress-strain relationship of steel reinforcement is assumed as elastic-perfectly plastic. Confined and unconfined behaviors of concrete are modeled by considering Mander et al. approach. Plastic hinge properties of each cross section are defined by considering longitudinal and transverse reinforcements. These plastic hinges are assigned at the each end points of shear walls, columns and beams. The frame highlighted by a red box is selected as a reference axis to be able to make a comparison between analysis results. Cross sectional and reinforcement details of the structural elements are given in Table and Figure. Moreover general layouts and plan views of three dimensional structures are presented in Figures and. Name Element Concrete - Reinforc. Table. Material and section properties of superstructure Mod. of Mod. of Yield Strength Concrete Reinfor. of Reinforc. (Mpa) (Mpa) (Mpa) Dimensions (mm) Long. Trans. Reinforc. C Column C S 6x 6 / C Column C S x6 / C Column C S 6x / B Beam C S x 6 6 / B Beam C S x 6 / P Shear Wall C S x6 6 /- / Figure Reinforcement details of structural elements

3 Figure Plan view and D model of structural model.. Modelling Substructure Figure General layout of RC frame of structural systems Soil structure interaction for nonhomogeneous soils is considered by using static spring stiffness coefficients proposed by Gazetas (99) that are applicable to any solid foundation shape on the surface of a nonhomogeneous half space soil. The relationship between soil and superstructure is defined by means of foundation impedance functions which represent static stiffness of nonhomogeneous elastic soil behavior. Translational and rocking static stiffnesses for spread footing proposed by Gazetas (99) are used for this research. Gazetas (99) calculated that impedance functions by using both dimensions of the footing and shear modulus changing with depth. They are also defined by considering shear wave velocity of soil along with its Poisson s ratio. Shear modulus changing with depth is given in Eq.. Translational, rocking and torsional spring stiffnesses are determined by using Equations &,, respectively for nonhomogeneous soil class and they are tabulated in Table. These equations represent saturated normally and slightly over consolidated clays whose shear modulus can increase relatively fast at large depths. In Eq., x parameter should be determined by fitting with the test results. The numerical model using in Sap software package is shown in Figure considering soil structure interaction for nonhomogeneous soil conditions.

4 z / n G G ( x ) B. Kz,vertical GB α n ν n 9 z Kx,horizontal GB α ν B 6 Kx,rocking GB α n ν n Ktorsion 7.9GB α () () () () () Table Translation and rocking stiffness of springs represent nonhomogeneous soil conditions Shear Shear Wave Stiffness (kn/m ) Poisson Modulus G Velocity Translation Along Rocking About Ratio (kn/m ) (m/s) x y z x y z Figure Finite element model of superstructure considering SSI with plastic hinge assignments. RESULTS Two different structural heights and systems are compared to determine the effect of number of story and inhomogeneity of soil by pushover analysis. Foundation geometry is selected m by m square. Shear modulus, translational and rocking stiffnesses are calculated by using Gazetas (99) formulas which are proposed for nonhomogeneous soil conditions. Firstly the nonlinear incremental single mode pushover analysis are conducted by using finite element software package. Later on effects of inhomogeneity and number of story are determined by comparing of target displacements, story drifts and plastic hinge mechanisms formation for all soil conditions... Pushover Curves The relationship between base shear force and roof displacement is defined by using pushover curves in nonlinear analysis. Pushover curves are used to calculate structural displacement and force demand. Variation of pushover curves considering inhomogeneity of soil and structural height are given in Figure. Additionally the pushover curves obtained from nonlinear analysis are evaluated for different performance of each structural system. The nonlinear displacement demand increases when nonhomogeneous SSI is considered in RC frame systems. However, rigidity of the structural system decreases according to the comparison of pushover curves for Shear Wall-frame system. Moreover the frame system performs more ductile behavior than shear-wall frame.

5 PUSHOVER CURVE - STORY MODEL PUSHOVER CURVE - 8 STORY MODEL BASE SHEAR (kn) 8 RIGID SOIL- FRAME SYSTEM BASE SHEAR (kn) 8 RIGID SOIL- FRAME SYSTEM 6 NONHOMOGENOUS SOIL-FRAME SYSTEM 6 NONHOMOGENOUS SOIL-FRAME SYSTEM DISPLACEMENT (m).. Structural Demands Figure Pushover curves DISPLACEMENT (m) Target displacement values are used to calculate the plastic hinge rotations. These plastic deformations are very essential to determine the real nonlinear performance level of a structure. Target displacements are obtained by measuring of horizontal deflection value at the top of structures. The variation is a ratio that is calculated by dividing the difference between rigid and nonhomogeneous soils to the rigid soil condition values. The variations of base shear, roof displacement and first free vibration period for different structural heights and structural systems are given Table considering soil structure interaction stemming from the inhomogeneity of soil. Storey 8 Storey Table Variation of structural demands Soil Type Rigid Nonhomogenous Variation (%) Base Shear ( kn ) Roof Disp. (m) Periyod T (s) Base Shear ( kn ) Roof Disp. (m) Periyod T (s) Story Drifts Story drift is defined as the difference in horizontal deflection of top and bottom of a story and they are used to determine the nonlinear performance level of a structure. There are some limitations for story drifts in different earthquake codes. That limitations are defined in American Society of Civil Engineers (ASCE-6) for immediate occupancy, life safety and collapse prevention performance levels as %, % and % respectively. Story displacements, and story drifts calculated according to the story displacement for each numerical model of structures are plotted in Figure 6 and 7.

6 STORY DISPLACEMENT STORY DISPLACEMENT Figure 6 Story displacements for five and eight story structures %.%.%.%.%.%.%.%.% STORY DRIFT.%.%.%.%.%.%.%.%.%.%.% STORY DRIFT Figure 7 Story drifts for five and eight story structures.. Plastic Hinge Mechanism Strong column - weak beam is universally accepted analogy to achieve more ductile behavior in RC structures. Analysis results showed that this analogy can be provided if soil-structure interaction due to the inhomogeneity of soil is considered. Additionally, a plastic hinge rotation in a structural system with soil structure interaction can increase with rigid soil condition. For instance, the variation in the plastic hinge formation are shown in Figures 8 for five and eight-story RC structures which are designed as frame and shear wall-frame systems. a) b) c) d) Figure 8 Plastic hinge formation a) Rigid soil condition- storey b) Nonhomogeneous soil- storey c) Rigid soil condition-8 storey d) Nonhomogeneous soil-8 storey

7 . CONCLUSIONS Soil-structure interaction behavior in pushover analysis must be considered especially when soil rigidity decreases due to inhomogeneity and depth. Therefore ignoring soil structure interaction in numerical models can change performance levels of structures in an unconservative way. Furthermore, as the depth of soil increases, the SSI effect gets more apparent than other situations. From analysis results, the following conclusions can be summarized: -) According to comparison of pushover curves, due to SSI effect, the frame system behaves more ductile and the shear-wall system becomes less rigid. -) The roof displacement and the displacement demand obtain bigger values as the soil rigidity decreases when pushover analysis is used considering soil-structure interaction due to the inhomogeneity of soil. Moreover, the difference also gets higher with the increasing number of story. -) The story drift, which are used to determine performance level in ASCE -6, reaches critical limit values when the number of story increases whereas the soil rigidity decreases because of the inhomogeneity of soil especially in frame systems. -) If plastic hinge rotations are compared, plastic hinge formation mechanism changes to column hinge mechanism especially for five and eight-story RC shear wall-frame systems when soil structure interaction is considered. Plastic hinge rotations reach high values as the roof displacement increases. REFERENCES Chopra A.K., Goel R.K. (). Modal pushover analysis of sac buildings, California. C. Vrettos, (999). Vertical and rocking impedances for rigid rectangular foundations on soils with bounded nonhomogeneity, Earthquake Engineering and Structural Dynamics, 8, pp. -. G. Gazetas, (99). Static and dynamic displacements of foundations on heterogeneous multilayered soils, Geotechnique,, pp G. Gazetas, (99). Foundation vibrations, Foundation Engineering Handbook, Van Nostrand Reinhold, New York, pp. -9. J. P. Wolf and J. W. Meek, (99). Dynamic stiffness of foundation on layered soil half-space using cone frustrums, Earthquake Engineering and Structural Dynamics,, pp J. Kubin, Y. M. Fahjan and M. T. Tan (8). Comparison of practical approaches for modelling shearwalls in structural analyses of buildings Proceedings of The Seminar on The th World Conference on Earthquake Engineering, Beijing, China, -7 October. Liping L., Wenjin G., Qiang X., Lili B., Yingmin L., Yuntian W. (). Analysis of elasto-plastic soil-structure interaction system using pushover method, Proceedings of The Seminar on The th World Conference on Earthquake Engineering, Lisboa, Portugal, -8 September.