Nonlinear shear stress reduction factor (rd) for assessment of liquefaction potential in Christchurch Central Business District


  • James N. Dismuke Golder Associates, Christchurch, NZ



Simplified procedures for evaluating liquefaction triggering potential use the nonlinear shear stress reduction factor, rd, to estimate the peak earthquake-induced cyclic shear stress within the soil strata. Previous studies have derived rd by considering the response of representative ground profiles subjected to input ground motions with a range of ground motion characteristics. In this study, site–specific rd for serviceability limit state (SLS) and ultimate limit state (ULS) design ground motions are developed using site response models of the Christchurch Central Business District (CBD). The site response models are generated for typical geologic conditions of Christchurch CBD with shear wave velocity, Vs, profiles developed from the results of multichannel analysis of surface waves (MASW) surveys conducted across Christchurch CBD. A total of 528 simulations were conducted using 1D nonlinear time domain site response analyses using a suite of input ground motions that are representative of controlling ground motion scenarios for seismic hazard of Christchurch. The results of the ground response analyses are used to determine Christchurch CBD-specific rd relationships for liquefaction triggering assessments. The proposed relationships provide a better estimate of the cyclic stress ratios induced below Christchurch CBD when subjected to design SLS and ULS ground motions as compared to typical practice using generic liquefaction assessment methodologies.


Seed, H. B., and Idriss, I. M. (1971). “Simplified procedure for evaluating soil liquefaction potential,” J. of Soil Mech. and Foundation Div., ASCE 97(SM9), 1249– 1273.

Idriss, I. M. (1999). “An update to the Seed-Idriss simplified procedure for evaluating liquefaction potential,” Proceedings, TRB Workshop on New Approaches to Liquefaction, Publication No. FHWARD-99-165, Federal Highway Administration, January.

Cetin, K. O., and Seed, R. B. (2004). “Nonlinear shear mass participation factor, rd, for cyclic shear stress ratio evaluation,” Soil Dyn. and Earthquake Eng. 24(2) 103– 113. DOI:

Ministry of Business, Innovation, and Employment (2012). Guidance for repairing and rebuilding houses affected by the Canterbury earthquakes.

Schnabel, P. B., Lysmer, J., and Seed, H. B. (1972). ‘‘SHAKE—A computer program for earthquake response analysis of horizontally layered sites.’’ Rep. No. EERC 72-12, Earthquake Engrg. Res. Ctr., University of California, Berkeley, Richmond, Calif.

Youd, T. L., et al. (2001). “Liquefaction resistance of soils; summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils,” J. Geotech. Geoenviron. Eng., ASCE 127(10), 817–833.

Golesorkhi, R. (1989). “Factors Influencing the Computational Determination of Earthquake-InducedShear Stresses in Sandy Soils,” Ph.D. thesis, University of California at Berkeley, 395 pp.

Idriss, I.M., and Boulanger, R.W. (2010). “SPT-Based Liquefaction Triggering Procedure,” Report No. UCD/CGM-10-02, Center for Geotechnical Modeling, University of California at Davis.

Idriss, I. M., and Boulanger, R.W. (2008). “Soil liquefaction during earthquakes,” Monograph MNO-12, Earthquake Engineering Research Institute, Oakland, CA, 261 pp.

Cetin, K., Seed, R., Der Kiureghian, A., Tokimatsu, K., Harder, L., Jr., Kayen, R., and Moss, R. (2004). “Standard Penetration Test-Based Probabilistic and Deterministic Assessment of Seismic Soil Liquefaction Potential.” J. Geotech. Geoenviron. Eng., 130(12), 1314– 1340. DOI:

Moss, R.E.S., Seed, R.B., Kayen, R.E., Stewart, J.P., Der Kieureghian, A., and Cetin, K.O. (2006). “CPT-based probabilistic and deterministic assessment of in situ seismic soil liquefaction potential,” J. Geotech. Geoenviron. Eng., ASCE 132(8), 1032-051 DOI:

Kayen, R., Moss, R., Thompson, E., Seed, R., Cetin, K., Kiureghian, A., Tanaka, Y., and Tokimatsu, K. (2013). “Shear-Wave Velocity–Based Probabilistic and Deterministic Assessment of Seismic Soil Liquefaction Potential.” J. Geotech. Geoenviron. Eng., 139(3), 407– 419. DOI:

Hashash, Y.M.A, Groholski, D.R., Phillips, C. A., Park, D, Musgrove, M. (2012) “DEEPSOIL 5.1, User Manual and Tutorial,” 107 p.

Brown, L.J. and Weeber, J.H. (1992). “Geology of the Christchurch Urban Area,” Institute of Geological and Nuclear Sciences Ltd., Lower Hutt.

Tonkin and Taylor Limited (2011). “Christchurch Central City Geological Interpretive Report,” prepared for Christchurch City Council, December.

Canterbury Earthquake Recovery Authority (CERA), (2013). “Canterbury Geotechnical Database,” (Feb 23, 2013).

Toro, G.R. (1995). “Probabilistic models of site velocity profiles for generic and site-specific ground-motion amplification studies,” Upton, New York: Brookhaven National Laboratory.

Kottke, A.R., and Rathje, E.M. (2008). “Technical Manual for STRATA,” Pacific Earthquake Engineering Research Center Report 2008/10, October

Robertson, P.K. (2009). “Interpretation of Cone Penetration Tests – a unified approach,” Canadian Geotech. J., 46 pp 1337-1355.

Darendeli, M. B. (2001). “Development of a new family of normalized modulus reduction and material damping curves,” Ph. D. Dissertation, University of Texas at Austin.

Hashash, Y.M.A., Phillips, C. and Groholski, D. (2010). “Recent advances in non-linear site response analysis,” Fifth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Paper no. OSP 4.

Menq, F. -Y. (2003). “Dynamic properties of sandy and gravelly soils,” Ph. D. Dissertation, University of Texas at Austin.

NZS 1170.5. (2004) "Structural design actions, Part 5: Earthquake actions - New Zealand". Standards New Zealand: Wellington, New Zealand, 82.

Stirling, M.W., Gerstenberger, M., Litchfield, N.J., McVerry, G.H., Smith, W.D., Pettinga, J., and Barnes, P. (2007). “Updated probabilistic seismic hazard assessment for the Canterbury region,” GNS Science Consultancy Report 2007/232. Environment Canterbury report U06/6.

Stirling, M., McVerry, G., Gerstenberger, M., Litchfield, N., Van Dissen, R., Berryman, K., Barnes, P., Wallace, L., Villamor, P., Langridge, R., Lamarche, G., Nodder, S., Reyners, M., Bradley, B., Rhoades, D., Smith, W., Nicol, A., Pettinga, J., Clark, K., and Jacobs, K., (2012). “National Seismic Hazard Model for New Zealand: 2010 Update,” Bulletin of the Seismological Society of America, Vol. 102, No. 4 1514-1542, August.

PEER (2013). “PEER Ground Motion Database,” <, Feb. 23 2013.

Stewart, J.P., Kwok, A.O.L., Hashash, Y.M.A., Matasovic, N., Pyke, R., Wang, Z., Yang, Z. (2008). “Benchmarking of Nonlinear Geotechnical Ground Response Analysis Procedures,” Pacific Earthquake Engineering Research Center Report 2008/04, August.

GeoNet (2013). “Strong-Motion Data,” <>, Feb. 23 2013.

Bradley, B.A. (2010) "NZ-specific pseudo-spectral acceleration ground motion prediction equations based on foreign models" Report No.2010-03, Department of Civil and Natural Resources Engineering, University of Canterbury: Christchurch, New Zealand. 324.

Rathje, E.J., and Kottke, A.R. (2013), “STRATA,”

Bradley, B.A. and Cubrinovski, M. (2011). “Near-source Strong Ground Motions Observed in the 22 February 2011 Christchurch Earthquake,” Seismological Research Letters; 82(6): 853-865. DOI:




How to Cite

Dismuke, J. N. (2014). Nonlinear shear stress reduction factor (rd) for assessment of liquefaction potential in Christchurch Central Business District. Bulletin of the New Zealand Society for Earthquake Engineering, 47(1), 1–14.