Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Influence of Motion Energy and Soil Characteristics on Seismic Ground Response of Layered Soil


The present study focuses on assessing local site effects (especially large-scale soil heterogeneity) and motion characteristics on seismic ground response using nonlinear one-dimensional numerical analysis. All nonlinear and curve-fitting parameters used for soil models were verified using the Class C1 prediction of centrifuge test results available in the literature. The comparison demonstrates that the available MKZ (pressure dependent Modified Kondner Zelesko) formulation with non-Masing hysteresis loading and unloading rule can reliably compute the 1-D ground response of cohesionless soil. Horizontal soil layers with different relative densities were considered next in various hypothetical models to assess the effect of subsurface properties on responses. One novel aspect of this study is that 51 different ground motions with a wide range of variation in their spectral accelerations, frequency contents, and duration characteristics were used to evaluate the effect of ground motion characteristics on the soil response. The results reveal that layering conditions play a significant role in modifying the seismic ground response of heterogeneous soil, especially when the loose liquefiable sand layer is sandwiched between two non-liquefiable soil layers. Relations were obtained to quantify the effect of different seismic inputs and varying site conditions on seismic ground response. The best correlation was obtained between the maximum excess pore water pressure (EPWP) development and the damage potential (Arias intensity) of an input ground motion. These relations can be used for estimating seismic ground response of an identical soil profile to that used in the present study for known design motion characteristics.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17




\(a_{1}, a_{2}, a_{3}\) :

Coefficient for nonlinear regression equation

\(a\left( t \right)\) :

Ground motion acceleration at time t



Adjusted R2 :

Generally the best indicator of the fit quality when additional coefficients were added to a model

\({\text{AI}}\) :

Arias intensity

\({\text{AI}}_{{{\text{input}}}}\) :

Input Arias intensity

\({\text{AI}}_{{{\text{response}}}}\) :

Response Arias intensity

\(b_{1} ,b_{2}\) :

Coefficient for the nonlinear regression equation

\(C_{i}\) :

Fourier amplitude of the entire accelerogram

\(c_{{\text{v}}}\) :

Coefficient of consolidation of the soil layer

c n :

Viscous damping of the nth layer

D :

Damping ratio

D r :

Relative density


Excess pore water pressure

\(f_{i}\) :

Discrete Fourier transform frequencies between 0.25 and 20 Hz

G :

Shear modulus

G max :

Maximum shear modulus of sand at small strains

G n :

Shear modulus of the nth layer

H :

Total height of the soil column

H n :

Height of the nth layer

\(k_{{2, {\max}}}\) :

Coefficient determined from the soil’s void ratio or relative density

k n :

Stiffness constant of the nth layer

M n :

Mass of the nth layer


Nonlinear analysis

P1, P2,P3 :

Nonlinear parameters used in pore pressure generation and dissipation model


Pore pressure transducer


Pore water pressure

R 2 :

Square of the correlation between the response values and the predicted response values

r u :

EPWP ratio

\(T_{{\text{e}}}\) :

The total time duration of a ground motion

\(T_{{\text{m}}}\) :

Mean period

\(T_{{m}_{input}}\) :

Mean period of input motion

\(T_{{m}_{response}}\) :

Mean period of response


Verification of Liquefaction Analyses by Centrifuge Studies

V sn :

Shear wave velocity of nth layer

β, s, b, d :

Nonlinear parameters used in the material model

\(\rho_{n}\) :

Unit weight of the nth layer

\(\varphi\) :

Internal frictional angle

\(\sigma_{{\text{h}}}^{{\prime}}\) :

Effective stress acting on the horizontal direction

\(\sigma_{{\text{m}}}^{{\prime}}\) :

Mean principal effective stress

\(\sigma_{{\text{v}}}^{{\prime}}\) :

Effective stress acting on soil on the vertical direction


  1. 1.

    Shiuly A, Sahu RB, Mandal S (2014) Effect of soil on ground motion amplification of Kolkata city. Int J Geotech Earthq Eng 5:1–20. https://doi.org/10.4018/ijgee.2014010101

  2. 2.

    Jain KS, Murthy CVR, Arlekar JN, et al (1999) Chamoli (Himalaya, India) earthquake of 29 March 1999. EERI Spec. Earthq. Report, EERI Newsl. 33:1–18. https://www.nicee.org/eqe-iitk/uploads/EQR_Chamoli.pdf

  3. 3.

    Mahajan AK, Virdi NS (2001) Macroseismic field generated by 29 March, 1999 Chamoli earthquake and its seismotectonics. J Asian Earth Sci 19:507–516. https://doi.org/10.1016/S1367-9120(00)00049-3

  4. 4.

    Prasad SK, Vijayendra K V, Nayak S (2019) Issues on seismic site characterization. In: Frontiers in geotechnical engineering. Springer, pp 217–248. https://doi.org/10.1007/978-981-13-5871-5-11

  5. 5.

    Jain SK (2016) Earthquake safety in India: achievements, challenges and opportunities. Bull Earthq Eng 14:1337–1436. https://doi.org/10.1007/s10518-016-9870-2

  6. 6.

    Bielak J, Xu J, Ghattas O (1999) Earthquake ground motion and structural response in alluvial valleys. J Geotech Geoenviron Eng 125:413–423. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:5(413)

  7. 7.

    Yasuda S, Harada K, Ishikawa K, Kanemaru Y (2012) Characteristics of liquefaction in Tokyo Bay area by the 2011 Great East Japan Earthquake. Soils Found 52:793–810. https://doi.org/10.1016/j.sandf.2012.11.004

  8. 8.

    Tabatabaiefar SHR, Fatahi B, Samali B (2013) Lateral seismic response of building frames considering dynamic soil-structure interaction effects. Struct Eng Mech 45:311–321. https://doi.org/10.12989/sem.2013.45.3.311

  9. 9.

    Mehrzad B, Haddad A, Jafarian Y (2016) Centrifuge and numerical models to investigate liquefaction-induced response of shallow foundations with different contact pressures. Int J Civ Eng 14:117–131. https://doi.org/10.1007/s40999-016-0014-5

  10. 10.

    Adampira M, Derakhshandi M, Ghalandarzadeh A (2019) Experimental study on seismic response characteristics of liquefiable soil layers. J Earthq Eng. https://doi.org/10.1080/13632469.2019.1568930

  11. 11.

    Bard P, Campillo M, Cha´vez-Garcia FJ, Sa´nchez-Sesma F, (1988) The Mexico earthquake of September 19, 1985—a theoretical investigation of large- and small-scale amplification effects in the Mexico city valley. Earthq Spectra 4:609–633. https://doi.org/10.1193/1.1585493

  12. 12.

    Hashash YMA, Park D (2001) Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment. Eng Geol 62:185–206. https://doi.org/10.1016/S0013-7952(01)00061-8

  13. 13.

    Ghosh B, Klar A, Madabhushi SPG (2005) Modification of site response in presence of localised soft layer. J Earthq Eng 9:855–876. https://doi.org/10.1080/13632460509350569

  14. 14.

    Govinda Raju L, Ramana G V, Hanumantha Rao C, Sitharam TG (2004) Site-specific ground response analysis. Curr Sci 87:1354–1362. https://eprints.iisc.ac.in/2711/1/P4currsci.pdf

  15. 15.

    Juang CH, Yuan H, Lee D-H, Lin P-S (2003) Simplified cone penetration test-based method for evaluating liquefaction resistance of soils. J Geotech Geoenviron Eng 129:66–80. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:1(66)

  16. 16.

    Sun C-G, Chung C-K (2008) Assessment of site effects of a shallow and wide basin using geotechnical information-based spatial characterization. Soil Dyn Earthq Eng 28:1028–1044. https://doi.org/10.1016/j.soildyn.2007.11.005

  17. 17.

    Lo Presti DC, Lai CG, Puci I (2006) ONDA: Computer code for nonlinear seismic response analyses of soil deposits. J Geotech Geoenviron Eng 132:223–236. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(223)

  18. 18.

    Seed HB, Idriss IM (1970) Soil moduli and damping factors for dynamic response analyses. Report No. EERC 70/10, Earthquake Engineering Research Center, Berkeley, Calif. https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/PB197869.xhtml

  19. 19.

    Sugito M, Goda H, Masuda T (1994) Frequency dependent equi-linearized technique for seismic response analysis of multi-layered ground. In: Doboku Gakkai Rombun-Hokokushu/Proceedings of the Japan Society of civil engineers, pp 49–58. https://www.iitk.ac.in/nicee/wcee/article/1806.pdf

  20. 20.

    Assimaki D, Kausel E, Whittle A (2000) Model for dynamic shear modulus and damping for granular soils. J Geotech Geoenviron Eng 126:859–869. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:10(859)

  21. 21.

    Filali K, Sbartai B (2017) A comparative study between simplified and nonlinear dynamic methods for estimating liquefaction potential. J Rock Mech Geotech Eng 9:955–966. https://doi.org/10.1016/j.jrmge.2017.05.008

  22. 22.

    Dammala PK, Kumar SS, Krishna AM, Bhattacharya S (2019) Dynamic soil properties and liquefaction potential of northeast Indian soil for non-linear effective stress analysis. Bull Earthq Eng 17:2899–2933. https://doi.org/10.1007/s10518-019-00592-6

  23. 23.

    Qi C, Lu W, Wu J, Liu X (2015) Application of effective stress model to analysis of liquefaction and seismic performance of an earth dam in China. Math Probl Eng 2015:1–7. https://doi.org/10.1155/2015/404712

  24. 24.

    Das A, Chakrabortty P (2016) One-dimensional seismic energy transmission along heterogeneous layered soil. Int J Students Res Technol Manag 4:49–55. https://doi.org/10.18510/ijsrtm.2016.432

  25. 25.

    Hashash YMA, Groholski DR, Phillips C (2010) Recent advances in non-linear site response analysis. In: Fifth Interantional Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics and Symposium in Honor of Professor I.M. Idriss. pp 1–22. https://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=2952&context=icrageesd

  26. 26.

    Hashash YMA, Musgrove MI, Harmon JA, et al (2016) DEEPSOIL 6.1, User Manual. https://deepsoil.cee.illinois.edu/Files/DEEPSOIL_User_Manual_v6.pdf

  27. 27.

    Putti SP, Satyam N (2018) Ground response analysis and liquefaction hazard assessment for Vishakhapatnam city. Innov Infrastruct Solut 3:14. https://doi.org/10.1007/s41062-017-0113-4

  28. 28.

    Rayhani MHT, El Naggar MH, Tabatabaei SH (2008) Nonlinear analysis of local site effects on seismic ground response in the Bam earthquake. Geotech Geol Eng 26:91–100. https://doi.org/10.1007/s10706-007-9149-0

  29. 29.

    Arulanandan K, Scott RF (1993) Verification of numerical procedures for the analysis of soil liquefaction problems. In: International Conference on the verification of numerical procedures for the analysis of soil liquefaction problems. Davis, California

  30. 30.

    Afacan KB, Brandenberg SJ, Stewart JP (2014) Centrifuge modeling studies of site response in soft clay over wide strain range. J Geotech Geoenviron Eng 140:04013003. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001014

  31. 31.

    Hashash YMA, Dashti S, Romero MI et al (2015) Evaluation of 1-D seismic site response modeling of sand using centrifuge experiments. Soil Dyn Earthq Eng 78:19–31. https://doi.org/10.1016/j.soildyn.2015.07.003

  32. 32.

    Elgamal A, Yang Z, Parra E (2002) Computational modeling of cyclic mobility and post-liquefaction site response. Soil Dyn Earthq Eng 22:259–271. https://doi.org/10.1016/S0267-7261(02)00022-2

  33. 33.

    Drosos VA, Gerolymos N, Gazetas G (2012) Constitutive model for soil amplification of ground shaking: Parameter calibration, comparisons, validation. Soil Dyn Earthq Eng 42:255–274. https://doi.org/10.1016/j.soildyn.2012.06.003

  34. 34.

    Chakrabortty P, Popescu R, Phillips R (2011) Liquefaction study of heterogeneous sand: centrifuge. Geotech Test J 34:227–237. https://doi.org/10.1520/GTJ102925

  35. 35.

    Chakrabortty P, Popescu R (2012) Numerical simulation of centrifuge tests on homogeneous and heterogeneous soil models. Comput Geotech 41:95–105. https://doi.org/10.1016/j.compgeo.2011.11.008

  36. 36.

    Popescu R, Prevost JH, Deodatis G (2005) 3D effects in seismic liquefaction of stochastically variable soil deposits. Geotechnique 55:21–31. https://doi.org/10.1680/ravige.34860.0008

  37. 37.

    Lambe TW (1973) Predictions in soil engineering. Géotechnique 23:151–202. https://doi.org/10.1680/geot.1973.23.2.151

  38. 38.

    Taboada VM, Dobry R (1993) Experimental results of Model No 1 at RPI. In: Arulanandan K, Scott RF (eds) International conference, verification of numerical procedures for the analysis of soil liquefaction problems. Balkema A, Davis, California

  39. 39.

    Stevens DK, Wilson DW, Kutter BL (2001) Comprehensive investigation of nonlinear site response—Centrifuge data report for the DKS04 model test. Rep. No. UCD/CGMDR-01, 3. Davis. https://ucdavis.app.box.com/s/21cvbid1k4ls27ijgbmmx9klh2svrs32

  40. 40.

    Strong-motion virtual data center. https://strongmotioncenter.org/vdc/scripts/earthquakes.plx Accessed 25 Jul 2019

  41. 41.

    Cooke HG (2010) Ground improvement for liquefaction mitigation at existing highway bridges. Dissertation, Virginia Tech.https://vtechworks.lib.vt.edu/handle/10919/28417

  42. 42.

    Elgamal A, Yang Z, Lai T et al (2005) Dynamic response of saturated dense sand in laminated centrifuge container. J Geotech Geoenviron Eng 131:598–609. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:5(598)

  43. 43.

    Arulmoli K, Muraleetharan KK, Hosain MM, Fruth LS (1992) VELACS: verification of liquefaction analyses by centrifuge studies, laboratory testing program soil data report. Project No. 90–0562, The Earth Technology Corporation, Irvine, California. https://doi.org/10.13140/2.1.3740.8320

  44. 44.

    Stewart JP, Kwok AO-L, Hashash YMA, et al (2008) Benchmarking of nonlinear geotechnical ground response analysis procedures. PEER report 2008/04, College of Engineering University of California, Berkeley, USA: Pacific Earthquake Engineering Research Center. https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/PB2012106298.xhtml

  45. 45.

    Ghazavi S (2015) Evaluation of site response analysis programs in predicting nonlinear soil response using geotechnical downhole array data. Dissertation, University of Nevada. Available at https://hdl.handle.net/11714/2529

  46. 46.

    Kramer SL (1996) Geotechnical earthquake engineering. Prentice-Hall international series in civil engineering and engineering mechanics, New Jersey

  47. 47.

    Tasiopoulou P, Taiebat M, Tafazzoli N, Jeremic B (2015) On validation of fully coupled behavior of porous media using centrifuge test results. Coupled Syst Mech 4:37–65. 10.12989/csm.2015.4.1.037

  48. 48.

    Zienkiewicz OC, Shiomi T (1984) Dynamic behaviour of saturated porous media; The generalized Biot formulation and its numerical solution. Int J Numer Anal Methods Geomech 8:71–96. https://doi.org/10.1002/nag.1610080106

  49. 49.

    Jeremić B, Cheng Z, Taiebat M, Dafalias YF (2008) Numerical simulation of fully saturated porous materials. Int J Numer Anal Methods Geomech 32:1635–1660. https://doi.org/10.1002/nag.687

  50. 50.

    Taiebat M, Shahir H, Pak A (2007) Study of pore pressure variation during liquefaction using two constitutive models for sand. Soil Dyn Earthq Eng 27:60–72. https://doi.org/10.1016/j.soildyn.2006.03.004

  51. 51.

    Dafalias YF, Manzari MT (2004) Simple plasticity sand model accounting for fabric change effects. J Eng Mech 130:622–634. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:6(622)

  52. 52.

    Rahmani A, Ghasemi Fare O, Pak A (2012) Investigation of the influence of permeability coefficient on the numerical modeling of the liquefaction phenomenon. Sci Iran 19:179–187. https://doi.org/10.1016/j.scient.2012.02.010

  53. 53.

    Manzari MT, Dafalias YF (1997) A critical state two-surface plasticity model for sands. Géotechnique 47:255–272. https://doi.org/10.1680/geot.1997.47.2.255

  54. 54.

    Shahir H, Pak A, Taiebat M, Jeremić B (2012) Evaluation of variation of permeability in liquefiable soil under earthquake loading. Comput Geotech 40:74–88. https://doi.org/10.1016/j.compgeo.2011.10.003

  55. 55.

    Arias A (1970) A measure of earthquake intensity. In: Hanson R (ed) Seismic design for nuclear power plants. MIT Press, Cambridge, pp 438–483

  56. 56.

    Rogers JD, Karadeniz D, Kaibel CK (2007) Seismic site response modeling for three Missouri river highway bridges. J Earthq Eng 11:400–424. https://doi.org/10.1080/13632460601031748

  57. 57.

    Kokusho T, Fujita K (2002) Site investigations for involvement of water films in lateral flow in liquefied ground. J Geotech Geoenviron Eng 128:917–925. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:11(917)

  58. 58.

    Konrad JM, Dubeau S (2003) Cyclic strength of stratified soil samples. In: Locat J, Mienert J, Boisvert L (eds) In submarine mass movements and their consequences. Advances in natural and technological hazards research. Springer, Dordrecht, pp 47–57. https://doi.org/10.1007/978-94-010-0093-2_6

  59. 59.

    Rathje EM, Abrahamson NA, Bray JD (1998) Simplified frequency content estimates of earthquake ground motions. J Geotech Geoenviron Eng 124:150–159. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:2(150)

  60. 60.

    Das A, Chakrabortty P (2017) Numerical determination of the effect of seismic frequency content in free field dynamic response of layered soil. In: Proceedings of a Conference on numerical modeling in geomechanics (CoNMiG-2017). Roorkee, India

  61. 61.

    Balakrishnan A, Kutter BL (1999) Settlement, sliding, and liquefaction remediation of layered soil. J Geotech Geoenviron Eng 125:968–978. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:11(968)

Download references


The author(s) greatly acknowledge the University of Illinois at Urbana-Champaign for the open-source software DEEPSOIL, the Department of Higher Education (Govt. of India) and IIT Patna for providing the funding for the present research work to carry out the doctoral research study of the first author for which no specific grant number has been allotted.

Author information

Correspondence to Pradipta Chakrabortty.



See Table 3.

Table 3 Detailed ground motion characteristics of all input motions used in this study

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Das, A., Chakrabortty, P. Influence of Motion Energy and Soil Characteristics on Seismic Ground Response of Layered Soil. Int J Civ Eng (2020). https://doi.org/10.1007/s40999-020-00496-6

Download citation


  • Lumped mass model
  • Nonlinear analysis
  • Large-scale heterogeneity
  • One-dimensional model
  • Numerical analysis