 
          1634
        
        
          Proceedings of the 18
        
        
          th
        
        
          International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
        
        
          (a)
        
        
          (b)
        
        
          0
        
        
          20
        
        
          40
        
        
          60
        
        
          80
        
        
          -20
        
        
          -10
        
        
          0
        
        
          Depth (m)
        
        
          NewFill,
        
        
          
        
        
          =34
        
        
          OldFill,
        
        
          
        
        
          =34
        
        
          ML/CL,PI=10,Su=25 kN/m 2
        
        
          SM, PI=11,
        
        
          
        
        
          =32
        
        
          CH, PI=37, Su=35 kN/m 2
        
        
          A
        
        
          B
        
        
          C
        
        
          D
        
        
          E
        
        
          FS=3.0 (pre earthquake)
        
        
          FS=1.3 (during earthquake, no strength reduction)
        
        
          FS=1.0 (during earthquake, 15% strength reduction)
        
        
          Distance (m)
        
        
          Figure 6 (a) Subsurface condition at Carrefour Shopping Center (b) Extensometer measurements at Carrefour Shopping Center (Martin et al., 2004)
        
        
          Table 2. Summary of input parameters and estimated strength loss of two case histories
        
        
          Case
        
        
          Seismological  information
        
        
          Site/ soil condition
        
        
          Estimated results
        
        
          Mw R
        
        
          PGA
        
        
          Vs
        
        
          OCR
        
        
          PI
        
        
          Nc
        
        
          
        
        
          eff
        
        
          
        
        
          Strength loss
        
        
          -
        
        
          (km)
        
        
          (g)
        
        
          m/sec
        
        
          -
        
        
          -
        
        
          (-)
        
        
          (%)
        
        
          -
        
        
          (%)
        
        
          Berryman
        
        
          7.0
        
        
          0.2
        
        
          0.72
        
        
          240
        
        
          3-5
        
        
          15-30
        
        
          29
        
        
          1-3
        
        
          0.75
        
        
          25-30
        
        
          Carrefour
        
        
          7.4
        
        
          5
        
        
          0.24
        
        
          120
        
        
          1
        
        
          10-37
        
        
          28
        
        
          0.3
        
        
          0.88
        
        
          10-15
        
        
          Bearing-capacity was evaluated using a slope stability
        
        
          approach before the earthquake and during the earthquake with
        
        
          a pseudo-static type analyses. The failure surface was
        
        
          constrained to a depth of 10 m below the ground surface
        
        
          because extensometer measurements indicate that large
        
        
          deformation occurred at this depth. As shown in Figure 6, the
        
        
          FS for slope stability is 3.0 pre-earthquake and becomes 1.0
        
        
          with a 15% estimated strength reduction (as listed in Table 2),
        
        
          compared to 1.3 without considering strength loss during the
        
        
          earthquake. The result suggests that the soil layer exhibited
        
        
          strength loss and that the amount of strength loss simply
        
        
          estimated by the proposed procedure leads to an analysis
        
        
          outcome consistent with the field observations.
        
        
          7 CONCLUSION
        
        
          In this paper we present an analysis procedure to estimate
        
        
          cyclic softening of saturated clays under seismic loading.
        
        
          Unlike common liquefaction potential analysis procedures that
        
        
          use a stress-based approach, the procedure uses a strain-based
        
        
          approach to estimate cyclic softening and associated strength
        
        
          loss. The procedure has two main components: (1) estimation of
        
        
          the shear strain amplitude and the equivalent number of uniform
        
        
          strain cycles within the soil mass induced by an earthquake
        
        
          event; and (2) estimation of the softening and associated
        
        
          strength loss within the soil given the effective shear strain
        
        
          amplitude and the equivalent number of uniform strain cycles.
        
        
          The procedure is successfully implemented in pseudo-static
        
        
          analysis for analyzing one design case and one field case
        
        
          history and is found to generally provide reasonable, first-order
        
        
          estimates of cyclic softening consistent with the field
        
        
          observations.
        
        
          8 ACKNOWLEDGEMENTS
        
        
          This study was mainly performed by the first author during his
        
        
          employment with URS Corporation. The authors acknowledge
        
        
          URS’ support. The authors also would like to acknowledge Mr.
        
        
          Fidèle Nikiema in translating the abstract into French.
        
        
          9 REFERENCES
        
        
          Boulanger, R. W. and Idriss, I. M. (2007) “Evaluation of Cyclic
        
        
          Softening in Silts and Clays” Journal of Geotechnical and
        
        
          Geoenvironmental Engineering, Vol. 133, No. 6
        
        
          Chu, D. B.; Stewart, J. P.; Boulanger, R. W; and Lin P. S. (2008)
        
        
          “Cyclic Softening of Low-Plasticity Clay and Its Effect on Seismic
        
        
          Foundation Performance” Journal of Geotechnical and
        
        
          Geoenvironmental Engineering, Vol. 134, No. 11.
        
        
          Darendeli, M.B. and Stokoe, K.H. 2001. Development of a new family
        
        
          of normalized modulus reduction and material damping curves,
        
        
          University of Texas, Geotechnical Engineering Report GD01-1.
        
        
          Idriss, I. M., Dobry, R., and Singh, R. D. (1978). "Nonlinear behavior
        
        
          of soft clays during cyclic loading." Journal of the Geotechnical
        
        
          Engineering Division, 104(CT12), 1427-1447.
        
        
          Idriss, I. M. and Boulanger, R. W. (2008) Soil Liquefaction during
        
        
          Earthquakes, EERI EERI monograph.
        
        
          Kishida, T. and Tsai, C.C. (2012) “Seismic Demand of the Liquefaction
        
        
          Potential with Equivalent Number of Cycles for Probabilistic
        
        
          Seismic Hazard Analysis”, submitted to J. Geotech. & Geoenv.
        
        
          Engrg., ASCE,
        
        
          Martin II J. R.; Olgun C. G.; Mitchell J. K., and Durgunoglu, H.
        
        
          T.(2004) “High-Modulus Columns for Liquefaction Mitigation”
        
        
          Journal of Geotechnical and Geoenvironmental Engineering, Vol.
        
        
          130, No. 6
        
        
          Liu A.H., Stewart J.P., Abrahamson N.A. and Moriwaki, Y. (2001).
        
        
          “Equivalent number of uniform stress cycles for soil liquefaction
        
        
          analysis” J. Geotech. & Geoenv. Engrg., ASCE, 127 (12), 1017-
        
        
          1026.
        
        
          Matasovic, N. and Vucetic, M (1995) “Generlized cyclic-degradation-
        
        
          Pore- Pressure Generation model for clays” Journal of
        
        
          Geotechnical and Geoenvironmental Engineering, Vol. 121, No. 1,
        
        
          June 1.
        
        
          Mejia, L., Wu, J., Feldsher, T., and Yiadom, A. (2009) “Re-evaluation
        
        
          of the Seismic Stability of Chabot Dam” Proceedings of Annual US
        
        
          Society on Dams Conference, USSD 2009, Nashville, TN.
        
        
          Tokimatsu K. and Seed H.B. (1987.) “Evaluation of settlements in
        
        
          sands due to earthquake shaking”, J. Geotech. Engrg., ASCE,
        
        
          113(8), 861-878.
        
        
          Tsai, C. C. and Mejia, L. (2011) "A Simplified Procedure to Estimate
        
        
          Strength Softening in Saturated Clays During Earthquakes" 5th
        
        
          International Conference on Earthquake and Geotechnical
        
        
          Engineering, Santiago, Chile
        
        
          URS (2008) Berryman Reservoir Replacement Foundation Report
        
        
          Prepared for East Bay Municipal Utility District