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Evaluation of seismic response of inelastic structures considering soil-structure interaction

Abstract

Structural deformations and soil displacements arising out of ground shaking are intertwined. This interplay is termed as seismic soil-structure interaction (SSI). Over last few decades, the conventionally perceived beneficial nature of SSI has been challenged with evidences of damaged sites from various earthquakes. This paper evaluates effects of SSI on seismic response of hardening single degree of freedom systems located in diverse geologies. The assessment is performed using substructure approach in terms of inelastic force reduction factor such that structure attains certain ductility levels. It is observed that soil-structure systems can afford a lesser reduction in design seismic forces compared to fixed-base structures. Components of total displacement arising out of structural deformation, footing translation and footing rotation are also evaluated. With increase in SSI effects, contribution of structural deformation is found to decline sharply. Footing rotation is observed to be very significant in structure-soil systems with larger SSI effects. The soil-structure system is modelled using a discrete physical model which enables inelastic response to be obtained in time domain while considering frequency dependence of impedance functions.

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Abbreviations

CESMD:

Center for Engineering Strong Motion Data

DOF:

Degree of Freedom

HFTD:

Hybrid Frequency–Time Domain

HTFD:

Hybrid Time–Frequency Domain

NIED:

National Research Institute for Earth Science and Disaster Resilience

PEER:

Pacific Earthquake Engineering Research Center

PGA:

Peak Ground Acceleration

SDOF:

Single Degree of Freedom

SR:

Stiffness Ratio (same as a0)

SSI:

Soil-Structure Interaction

a 0 :

Non-dimensional frequency

C EL :

Elastic seismic design coefficient

C̃EL :

Pseudo-elastic (μ ̅D = 1) seismic design coefficient

C EL, max :

Maximum elastic seismic design coefficient

C SSI :

Inelastic seismic design coefficient considering SSI

C y :

Initial assumption of yield strength of structure

C̃̃y :

Yield strength of structure/seismic coefficient (Jarernprasert et al., 2013)

[C]:

Damping matrix for 4-DOF structure-soil model

c :

Damping coefficient of structure

c 0h :

Dashpot coefficient for sway DOF in soil-foundation system

c 0r :

Dashpot coefficient for rocking DOF in soil-foundation system

c 1r :

Dashpot coefficient for internal DOF in soil-foundation system

D μ :

Ductility Damage Index

e :

Embedment depth of foundation

{F g}:

Force vector for 4-DOF structure-soil system

f c :

Eccentricity for coupling between sway and rocking dashpots

f k :

Eccentricity for coupling between sway and rocking springs

f m :

Height of lumped foundation mass and moment from foundation base

G :

Shear modulus of soil

g :

Acceleration due to gravity

H :

Total height of structure

h :

Effective modal height of structure

I 1r :

Moment of mass for internal DOF in soil-foundation system

I f :

Mass moment of inertia of foundation block in rocking

[K]:

Stiffness matrix for 4-DOF structure-soil model

k :

Lateral stiffness of structure

k 0h :

Spring coefficient for sway DOF in soil-foundation system

k 0r :

Spring coefficient for rocking DOF in soil-foundation system

k r :

Stiffness quantity used to evaluate k0r and c0r

[M]:

Mass matrix for 4-DOF structure-soil model

m :

Effective lumped structural mass

m f :

Mass of foundation block

R SSI :

Response reduction factor for structure, considering SSI

r 0 :

Radius of equivalent cylindrical foundation

S a :

Elastic spectral acceleration

T :

Natural period of structure

u :

Deformation in structure/displacement in fixed-base structure

u f :

Horizontal displacement of foundation mass in an SSI system

u g :

Ground displacement during a seismic event

u max :

Maximum structural deformation in a fixed-base structure

ũmax :

Maximum structural deformation in an SSI system

u t :

Total lateral displacement of lumped structural mass in an SSI system

ũ y :

Yield structural displacement in an SSI system

v s :

Shear wave velocity of soil

{X}:

Displacement vector for 4-DOF structure-soil system

x :

Displacement of fixed-base SDOF structural system

γ 0h, γ 0r, γ 1r, μ 1r :

Parameters used to compute coefficients in 3-DOF soil-foundation model

∆Mϑ :

Trapped mass moment of inertia to account incompressibility in soil

η 0 :

Hysteretic material damping ratio of soil

μ D :

Ductility demand in structure

μ̅D :

Mean ductility demand in structure (averaged across ground motions)

μT :

Target/design ductility in structure

ν :

Poisson’s ratio of soil

ρ :

Mass density of soil

φ :

Rotation of foundation in an SSI system (rocking mode)

φ 1 :

Rotation along internal DOF in an SSI system

ω 0 :

Ratio of soil shear wave velocity to radius of equiv. cylindrical foundation

ω n :

Cyclic natural frequency of structure

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Acknowledgements

The authors gratefully acknowledge resources provided by Indian Institute of Technology Madras and Ministry of Human Resources and Development (MHRD), Govt. of India.

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Vishwajit Anand, Satish Kumar S R helped in concept formulation. Vishwajit Anand numerically analysed the study. Satish Kumar S R gave expert guidance. Vishwajit Anand preparation the document.

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Correspondence to Vishwajit Anand.

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Anand, V., Satish Kumar, S.R. Evaluation of seismic response of inelastic structures considering soil-structure interaction. Innov. Infrastruct. Solut. 6, 83 (2021). https://doi.org/10.1007/s41062-020-00423-7

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Keywords

  • Soil-structure interaction
  • Inelastic structure
  • Force reduction factor
  • Displacement components
  • Time history analysis