soil-structure interaction in nonlinear pushover analysis ... · soil-structure interaction in...

4. Uluslararası Deprem Mühendisliği ve Sismoloji Konferansı

11-13 Ekim 2017 – ANADOLU ÜNİVERSİTESİ – ESKİŞEHİR

Soil-Structure Interaction in Nonlinear Pushover Analysis of Frame RC

Structures: Nonhomogeneous Soil Condition

G. Dok1

ve O. Kırtel2

1 Res. Assist., Department of Civil Engineering, Sakarya University, Sakarya

2 Assit. Prof. Dr., Department of Civil Engineering, Sakarya University, Sakarya

Email: [email protected], [email protected]

ABSTRACT:

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 soil-

structure interaction.

KEYWORDS: Soil-Structure Interaction, RC Frame Systems, Nonlinear Pushover Analysis

1. 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., 2001). 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., 2012). 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 (1991). 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., 1999). Static and dynamic deformations of soils can be larger due

to the dynamic stiffness of soil (Wolf J.P, and Meek J.W., 1994) when soils are multilayered and nonhomogeneous

(Gazetas G., 1980). 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 SAP2000 finite element

software.

mailto:[email protected]



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 3D 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.

2.1. Modelling Superstructure

Three dimensional five and eight-story RC structures are designed according to the minimum design conditions

given by Turkish Earthquake Code 2007 (TEC2007). 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 (Z4 soil class) defined in TEC 2007. The peak ground acceleration (A0) for first degree seismicity risk is

taken as 0.4g. 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 1 and Figure 1. Moreover general layouts and plan views of

three dimensional structures are presented in Figures 2 and 3.

Table 1. Material and section properties of superstructure

Name Element Concrete -

Reinforc.

Mod. of

Concrete

(Mpa)

Mod. of

Reinfor.

(Mpa)

Yield Strength

of Reinforc.

(Mpa)

Dimensions

(mm)

Long. – Trans.

Reinforc.

C1 Column C25 – S420 30000 210000 420 600x250 1016–10/10

C2 Column C25 – S420 30000 210000 420 250x600 1020–10/10

C3 Column C25 – S420 30000 210000 420 600x250 1020–10/10

B1 Beam C25 – S420 30000 210000 420 250x500 616–10/10

B2 Beam C25 – S420 30000 210000 420 250x500 620–10/10

P1 Shear

Wall

C25 – S420 30000 210000 420 250x6000 1216–12/15-

10/10

Figure 1– Reinforcement details of structural elements



Figure 2– Plan view and 3D model of structural model

Figure 3– General layout of RC frame of structural systems

2.2. Modelling Substructure

Soil structure interaction for nonhomogeneous soils is considered by using static spring stiffness coefficients

proposed by Gazetas (1991) 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 (1991) are used for this research. Gazetas (1991) 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. 1. Translational, rocking and torsional spring stiffnesses are determined by using

Equations 2&3, 4, 5 respectively for nonhomogeneous soil class and they are tabulated in Table 2. These equations

represent saturated normally and slightly over consolidated clays whose shear modulus can increase relatively fast

at large depths. In Eq. 1, x parameter should be determined by fitting with the test results. The numerical model

using in Sap2000 software package is shown in Figure 4 considering soil structure interaction for nonhomogeneous

soil conditions.



n/10 )

B

zx1(GG (1)

n0vertical,z α1BGν1

54.4K

(2)

n

0horizontal,xB

zα1BG

ν2

9K

(3)

n30rocking,x α1BG

ν1

36K

(4)

n

30torsion α

10

11BG93.7K

(5)

Table 2 – Translation and rocking stiffness of springs represent nonhomogeneous soil conditions

Shear

Modulus G0

(kN/m2)

Shear Wave

Velocity

(m/s)

Poisson

Ratio

Stiffness (kN/m2)

Translation Along Rocking About

x y z x y z

10368 70 0.49 63741 63741 98029 74729 74729 82742

Figure 4 – Finite element model of superstructure considering SSI with plastic hinge assignments

3. 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 2 m by 2 m square. Shear modulus,

translational and rocking stiffnesses are calculated by using Gazetas (1991) 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.

3.1. 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 5. 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.



Figure 5 – Pushover curves

3.2. Structural Demands

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 3 considering soil structure interaction stemming from the inhomogeneity of soil.

Table 3 – Variation of structural demands

Soil Type Rigid Nonhomogenous Variation (%)

5 Storey

Base Shear ( kN ) 1838.20 1888.55 2.74

Roof Disp. (m) 0.36 0.42 16.95

Periyod T (s) 1.199 1.364 13.76

8 Storey

Base Shear ( kN ) 1744.62 1785.78 2.36

Roof Disp. (m) 0.631 0.741 17.43

Periyod T (s) 1.887 2.141 13.46

3.3. 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 (ASCE41-06) for

immediate occupancy, life safety and collapse prevention performance levels as 2%, 3% and 5% 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.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

BA

SE

SH

EA

R (

kN

)

DISPLACEMENT (m)

PUSHOVER CURVE - 5 STORY MODEL

RIGID SOIL- FRAME SYSTEM

NONHOMOGENOUS SOIL-FRAME SYSTEM

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

BA

SE

SH

EA

R (

kN

)

DISPLACEMENT (m)

PUSHOVER CURVE - 8 STORY MODEL

RIGID SOIL- FRAME SYSTEM

NONHOMOGENOUS SOIL-FRAME SYSTEM



Figure 6 – Story displacements for five and eight story structures

Figure 7 – Story drifts for five and eight story structures

3.3. 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-5 storey b) Nonhomogeneous soil-5 storey c) Rigid

soil condition-8 storey d) Nonhomogeneous soil-8 storey

0

1

2

3

4

5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

ST

OR

Y N

UM

BE

R

STORY DISPLACEMENT

Rigid Soil - Frame System

Nonhomogenous Soil - Frame System

0

1

2

3

4

5

6

7

8

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

ST

OR

Y N

UM

BE

R

STORY DISPLACEMENT



0

1

2

3

4

5

0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00%

ST

OR

Y N

UM

BE

R

STORY DRIFT



0

1

2

3

4

5

6

7

8

0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00%

ST

OR

Y N

UM

BE

R

STORY DRIFT





4. 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:

1-) According to comparison of pushover curves, due to SSI effect, the frame system behaves more ductile and

the shear-wall system becomes less rigid.

2-) 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.

3-) The story drift, which are used to determine performance level in ASCE 41-06, 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.

4-) 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. (2001). Modal pushover analysis of sac buildings, California.

C. Vrettos, (1999). ‘Vertical and rocking impedances for rigid rectangular foundations on soils with bounded

nonhomogeneity’, Earthquake Engineering and Structural Dynamics, 28, pp. 1525-1540.

G. Gazetas, (1991). ‘Static and dynamic displacements of foundations on heterogeneous multilayered soils’,

Geotechnique, 30, pp. 159-177.

G. Gazetas, (1991). ‘Foundation vibrations’, Foundation Engineering Handbook, Van Nostrand Reinhold, New

York, pp. 553-593.

J. P. Wolf and J. W. Meek, (1994). ‘Dynamic stiffness of foundation on layered soil half-space using cone

frustrums’, Earthquake Engineering and Structural Dynamics, 23, pp. 1079-1095.

J. Kubin, Y. M. Fahjan and M. T. Tan (2008). “Comparison of practical approaches for modelling shearwalls in

structural analyses of buildings” Proceedings of The Seminar on The 14th World Conference on Earthquake

Engineering, Beijing, China, 12-17 October.

Liping L., Wenjin G., Qiang X., Lili B., Yingmin L., Yuntian W. (2012). “Analysis of elasto-plastic soil-structure

interaction system using pushover method”, Proceedings of The Seminar on The 15th World Conference on

Earthquake Engineering, Lisboa, Portugal, 24-28 September.

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