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


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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Center for Engineering Strong Motion Data


Degree of Freedom


Hybrid Frequency–Time Domain


Hybrid Time–Frequency Domain


National Research Institute for Earth Science and Disaster Resilience


Pacific Earthquake Engineering Research Center


Peak Ground Acceleration


Single Degree of Freedom


Stiffness Ratio (same as a0)


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


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)


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


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


Mass matrix for 4-DOF structure-soil model

m :

Effective lumped structural mass

m f :

Mass of foundation block


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


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


  1. Lai CG, Martinelli M (2013) Soil-structure interaction under earthquake loading: theoretical framework. Alert Doctoral School, Aussois

    Google Scholar 

  2. Yashinsky M (1998) Thelomaprieta, california, earthquake of october 17, 1989- highway systems, professional paper 1552-B. Washington, U.S, Geological Survey

    Google Scholar 

  3. Gazetas G, Mylonakis G (2001) Soil-Structure Interaction Effects on Elastic and Inelastic Structures. 4th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego.

  4. Mylonakis G, Gazetas G (2000) Seismic soil-structure interaction: beneficial or detrimental? J Earthquake Eng 4:377–401

    Google Scholar 

  5. Badry P, Satyam N (2017) Seismic soil structure interaction analysis for asymmetrical buildings supported on piled raft for the 2015 Nepal earthquake. J Asian Earth Sci 133:102–113

    Article  Google Scholar 

  6. ATC (1978) Tentative provisions for the development of seismic regulations for buildings, ATC 3-06. Applied Technology Council, California

  7. ASCE (2016) Minimum design loads for buildings and other structures, ASCE/SEI 7–16. American Society of Civil Engineers, Virginia

    Google Scholar 

  8. Anand V, Kumar S (2018) Seismic soil-structure interaction: a state-of-the-art review. Structures 16:317–326

    Article  Google Scholar 

  9. Sharma N, Dasgupta K, Dey A (2018) A state-of-the-art review on seismic SSI studies on building structures. Innovative Infrastructure Solut 3(22):1–16

    Google Scholar 

  10. Veletsos AS, Verbic B (1973) Vibration of viscoelastic foundations. Earthquake EngStructDynam 2(1):87–102

    Article  Google Scholar 

  11. ASCE (2010) Minimum design loads for buildings and other structures, ASCE/SEI 7–10. American Society of Civil Engineers, Virginia

    Google Scholar 

  12. Jarernprasert S, Bazan-Zurita E, Bielak J (2013) Seismic soil-structure interaction response of inelastic structures. Soil Dynamics Earthquake Eng 47:132–143

    Article  Google Scholar 

  13. Khosravikia F, Mahsuli M, Ghannad MA (2017) Probabilistic evaluation of 2015 NEHRP soil-structure interaction provisions. J EngMech 143(9):04017065

    Google Scholar 

  14. Aydemir ME (2013) Soil structure interaction effects on structural parameters for stiffness degrading systems built on soft soil sites. StructEngMech 45(5):655–676

    Google Scholar 

  15. Hassani N, Bararnia M, Amiri GG (2018) Effect of soil-structure interaction on inelastic displacement ratios of degrading structures. Soil Dynamics Earthquake Eng 104:75–87

    Article  Google Scholar 

  16. Nakhaei M, Ghannad MA (2008) The effect of soil-structure interaction on damage index of buildings. EngStruct 30:1491–1499

    Google Scholar 

  17. Boulanger RW, Curras CJ, Kutter BL, Wilson DW, Abghari A (1999) Seismic soil-pile-structure interaction experiments and analyses. J Geotechnical GeoenvironmentalEng 125(9):750–759

    Article  Google Scholar 

  18. Tang L, Ling X, Xu P, Gao X, Wang D (2010) Shake table test of soil-pile groups-bridge structure interaction in liquefiable ground. Earthquake EngEngVib 9:39–50

    Google Scholar 

  19. Durante MG, Sarno L, Mylonakis G, Taylor CA, Simonelli AL (2015) Soil-pile-structure interaction: experimental outcomes from shaking table tests. Earthquake EngStructDynam 45(7):1041–1061

    Article  Google Scholar 

  20. Martakis P, Taeseri D, Chatzi E, Laue J (2017) A centrifuge-based experimental verification of soil-structure interaction effects. Soil Dynamics Earthquake Eng 103:1–14

    Article  Google Scholar 

  21. Ciampoli M, Pinto PE (1995) Effects of soil-structure interaction on inelastic seismic response of bridge piers. J StructEng 121(5):806–814

    Google Scholar 

  22. Dutta SC, Roy R (2002) A critical review on idealization and modelling for interaction among soil-foundation-structure system. ComputStruct 80:1579–1594

    Google Scholar 

  23. Han Y (2002) Seismic response of tall building considering soil-pile-structure interaction. Earthquake EngEngVib 1:57–64

    Google Scholar 

  24. Zhao X, Wang S, Du D, Liu W (2017) Simplified analysis of frame structures with viscoelastic dampers considering the effect of soil-structure interaction. Earthquake EngEngVib 16:199–217

    Google Scholar 

  25. Jaya KP (2000) Dynamic behaviour of embedded and pile foundations in layered soil using cone models. Dissertation, Indian Institute of Technology Madras, Chennai.

  26. Nimtaj A, Bagheripour MH (2013) Non-linear seismic response analysis of the layered soil deposit using hybrid frequency-time domain (HFTD) approach. Eur J Environ Civil Eng 17(10):1039–1056

    Article  Google Scholar 

  27. Bernal D, Youssef A (1998) A hybrid time frequency domain formulation for non-linear soil-structure interaction. Earthquake EngStructDynam 27:673–685

    Article  Google Scholar 

  28. Wolf JP (1994) Foundation vibration analysis using simple physical models. Prentice Hall Inc, New Jersey

    Google Scholar 

  29. Meek JW, Wolf JP (1994) Cone models for embedded foundations. J Geotechnical Eng 120(1):60–80

    Article  Google Scholar 

  30. Wolf JP (1985) Dynamic Soil-Structure Interaction. Prentice Hall Inc, New Jersey

    Google Scholar 

  31. Meek JW, Wolf JP (1994) Material damping for lumped-parameter models of foundations. Earthquake EngStructDynam 23(4):349–362

    Article  Google Scholar 

  32. NIST (2012) Soil-structure interaction for building structures, NIST GCR 12–917-21. NEHRP Consultants Joint Venture, Maryland

    Google Scholar 

  33. Stewart JP, Fenves GL, Seed RB (1999) Seismic soil-structure interaction in buildings II: Empirical findings. J Geotechnical GeoenvironmentalEng 125:38–48

    Article  Google Scholar 

  34. Anand V, Kumar S (2018) Elastic seismic response of moment resisting framed structures with soil-structure interaction. 11th National Conference on Earthquake Engineering, Los Angeles.

  35. Ladhane KB, Sawant VA (2016) Effect of pile group configurations on nonlinear dynamic response. Int J Geomechanics ASCE 16(1):04015013

    Article  Google Scholar 

  36. PEER Ground Motion Database, Pacific Earthquake Engineering Research (PEER) Center. Available from URL:

  37. COSMOS VDC, Consortium for Strong Motion Observation System- Virtual Data Center, Center for Engineering Strong Motion Data (CESMD). Available from URL:

  38. K-NET, Kyoshin Network, National Research Institute for Earth Science and Disaster Resilience (NIED). Available from URL:

  39. Tang Y, Lam N, Lumantarna E, Tsang HH (2016) Generation of Synthetic Earthquake Accelerograms based on up-to-date Seismological Ground Motion Models. Australian Earthquake Engineering Society 2016 Conference, Melbourne

  40. Cini C (2006) Generation of synthetic earthquake accelerograms. Dissertation, Indian Institute of Technology Madras, Chennai.

  41. Seismosoft (2018) SeismoArtif 2018-A computer program for generation of artificial accelerograms. Available from URL:

  42. IS 1893–1 (2016) Criteria for earthquake resistant design of structures, Part I: General provisions and buildings. Bureau of Indian Standards, New Delhi

    Google Scholar 

  43. EN 1998–1 (2004) Design of structures for earthquake resistance, Part I: General rules, seismic actions and rules for buildings, Eurocode 8. European Committee for Standardisation, Brussels

    Google Scholar 

  44. Apsel RJ, Luco JE (1987) Impedance functions for foundations embedded in a layered medium: an integral equation approach. Earthquake EngStructDynam 15:213–231

    Article  Google Scholar 

  45. Jennings PC, Bielak J (1973) Dynamics of building-soil interaction. Bulletin of SeismolSoc Am 63(1):9–48

    Google Scholar 

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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).

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