 
          1633
        
        
          Technical Committee 203 /
        
        
          
            Comité technique 203
          
        
        
          where, c
        
        
          0
        
        
          = -3.43, c
        
        
          1
        
        
          = -0.352, c
        
        
          2
        
        
          = -0.402, c
        
        
          3
        
        
          = 0.798, c
        
        
          4
        
        
          = 1.72,
        
        
          and c
        
        
          5
        
        
          = -1.50. The prediction equation can also estimate
        
        
          
            N
          
        
        
          c
        
        
          at a
        
        
          selected depth (z) by introducing the parameter
        
        
          
            s
          
        
        
          
            s
          
        
        
          
            V
          
        
        
          
            z
          
        
        
          
            T
          
        
        
          4
        
        
          
        
        
          (6)
        
        
          where
        
        
          
            V
          
        
        
          s is average shear wave velocity within depth z. In
        
        
          addition, the site effect is accounted for by
        
        
           
        
        
           
        
        
          2.0
        
        
          0.1
        
        
          1
        
        
          
            Sa
          
        
        
          
            Sa S
          
        
        
          
        
        
          (7)
        
        
          S
        
        
          1
        
        
          is the spectral ratio between 1.0 sec spectrum acceleration
        
        
          Sa(1.0) and 0.2 sec spectrum acceleration Sa(0.2). Kishida and
        
        
          Tsai have shown that their prediction equation can estimate
        
        
          similar
        
        
          
            N
          
        
        
          c values as those of Lui et al. for sand (b=0.35) at the
        
        
          ground surface.
        
        
          Figure 4 b for cyclic softening of clay
        
        
          5 ANALYSIS PROCEDURE
        
        
          The procedure to consider strength softening in pseudo-static
        
        
          analysis has four general steps: (1) estimation of the shear strain
        
        
          amplitude and the equivalent number of uniform strain cycles
        
        
          from the peak acceleration at the ground surface and other
        
        
          seismological and site parameters; (2) estimation of strength
        
        
          softening
        
        
          
        
        
          of the soil based on the effective shear strain
        
        
          amplitude, and the equivalent number of uniform strain cycles;
        
        
          (3) estimation of the cyclic soil strength after cyclic softening
        
        
          by multiplying the strength for 1 cycle by
        
        
          
        
        
          .; (4)
        
        
          implementation of reduced strength (representing post-
        
        
          earthquake condition) in pseudo-static analysis. Details on the
        
        
          analysis steps were described in Tsai and Mejia (2011). For
        
        
          preliminary studies, the strength for 1 cycle of most clays may
        
        
          be conservatively assumed equal to their static strength.
        
        
          6 COMPARISON TO CASE HISTORIES
        
        
          In this section, the above analysis procedure to estimate strength
        
        
          softening was implemented in pseudo static analysis and
        
        
          compared with the predicted consequences of such softening
        
        
          with observed ground failure during past earthquakes.
        
        
          1.1
        
        
          
            Berryman Reservoir, California, CA, USA
          
        
        
          Berryman Reservoir, owned and operated by the East Bay
        
        
          Municipal Utility District, USA, is located in the City of
        
        
          Berkeley in Alameda County, California, and is within the State
        
        
          Alquist-Priolo Earthquake Fault Zone of the Hayward fault.
        
        
          Previous seismic hazard investigations concluded that active
        
        
          traces of the Hayward fault bisect the reservoir. Previous and
        
        
          recent field and laboratory investigations indicated that
        
        
          generally stiff cohesive soils (medium to high PI) grading to
        
        
          highly weathered bedrock are present at the site.
        
        
          To evaluate the seismic performance of the embankment,
        
        
          URS (2008) developed a design response spectrum and site-
        
        
          specific earthquake ground motions for input to the dynamic
        
        
          slope stability analyses. Following the Mejia et al. (2009)
        
        
          procedure, two-dimensional dynamic response analyses were
        
        
          performed using QUAD4M to estimate the cyclic stresses and
        
        
          accelerations induced by the design earthquake within the
        
        
          reservoir embankment. This comprehensive analysis indicated
        
        
          that the undrained strengths of the saturated clayey soils could
        
        
          be reduced by as much as 40 percent under the post-earthquake
        
        
          condition. Given the same design scenario as listed in Table 2,
        
        
          strength softening was also calculated using the simplified
        
        
          procedure proposed in this paper. It was found that the strengths
        
        
          of the saturated soils could be reduced by approximately 25-30
        
        
          percent. Although the predicted strength reduction is less than
        
        
          that by Mejia et al.’s procedure, it is still a reasonable, first-
        
        
          order estimate of cyclic softening of stiff clay. The yield
        
        
          accelerations, obtained from pseudo static analyses using
        
        
          UTEXAS4, were 0.16g for the pre-earthquake (no strength
        
        
          reduction) and 0.12g and 0.1 for post-earthquake condition with
        
        
          30% and 40% strength softening, respectively. The critical
        
        
          failure plane is shown in Figure 5.
        
        
          0.1
        
        
          1
        
        
          10
        
        
          1
        
        
          10
        
        
          Figure 5 Pseudo-static analysis considering strength softening at
        
        
          Berryman Reservoir
        
        
          1.2
        
        
          
            Carrefour Shopping Center 1999 Kocaeli
          
        
        
          The Carrefour Shopping Center Lot C case history (Martin et al.
        
        
          2004) provided a unique set of in situ ground deformation
        
        
          measurements in ML/CL and CH strata from settlement
        
        
          extensometers during the 1999 Kocaeli earthquake. This case
        
        
          history provides an excellent example of how fine-grained soils
        
        
          can develop significant strains or fail due to seismic loading,
        
        
          and an opportunity to evaluate the procedures presented herein.
        
        
          As shown in Figure 6a, the soil profile at Lot C includes a
        
        
          surface layer of approximately 2 m of medium dense fill
        
        
          (gravelly clay, GC). The next 5 m of soil consists of saturated,
        
        
          soft to firm, low plasticity silt and clay (ML/CL) having average
        
        
          PI and LL values of 10 and 33, respectively. This layer is
        
        
          underlain by about 1.2 m of loose to medium-dense silty sand,
        
        
          and sand (SP/SM) having a typical equivalent clean sand
        
        
          corrected SPT blow count ((
        
        
          
            N
          
        
        
          1
        
        
          )
        
        
          60,cs
        
        
          ) value of about 12. The sand
        
        
          layer is underlain by about 0.9 m of ML/CL soils, followed by
        
        
          medium to stiff, high plasticity clay (CH) that extends to depths
        
        
          greater than 35 m and has an average PI value of 37.
        
        
          The vertical strains induced in the fine-grained soil layers by
        
        
          the earthquake are largely attributed to undrained shear failure
        
        
          beneath the surcharge, as illustrated in Figure 6a. The settlement
        
        
          records in Figure 6b do show a modest increase in the rate of
        
        
          settlement from just before the earthquake to just after the
        
        
          earthquake. It is reasoned that the earthquake likely induced
        
        
          moderate excess pore pressures and that the increase in
        
        
          settlements was largely due to undrained shear failure induced
        
        
          by bearing-capacity mode of deformation.
        
        
          100
        
        
          No. of cycles (N)
        
        
          Cyclic strain
        
        
          
        
        
          (%)
        
        
          log
        
        
          
        
        
          = a-b*log N
        
        
          b=1
        
        
          b=1
        
        
          b=1
        
        
          
        
        
          =0.9
        
        
          
        
        
          =0.8
        
        
          
        
        
          =0.7
        
        
          
        
        
          =0.6
        
        
          FS=1.7 (preearthquake)
        
        
          FS=1.6, ky=016g (duringearthquake,nostrength reduction)
        
        
          FS=1.4, ky=012g (duringearthquake,30%strength reduction)
        
        
          FS=1.3, ky=010g (duringearthquake,40%strength reduction)
        
        
          WCC (1987)
        
        
          FS=2.14, ky=0.32g
        
        
          where
        
        
          
            V
          
        
        
          s is average shear wave velocity within depth z. In
        
        
          addition, the site effect is accounted for by
        
        
           
        
        
           
        
        
          2.0
        
        
          0.1
        
        
          1
        
        
          
            Sa
          
        
        
          
            Sa S
          
        
        
          
        
        
          (7)
        
        
          S
        
        
          1
        
        
          is the spectral ratio between 1.0 sec spectrum acceleration
        
        
          Sa(1.0) and 0.2 se spectrum acceleration Sa(0.2). Kishida and
        
        
          Tsai have shown that their prediction equation can stimate
        
        
          similar
        
        
          
            N
          
        
        
          c values as those of Lui et al. for sand (b=0.35) at the
        
        
          ground surface.
        
        
          Figure 4 b for cyclic softening of clay
        
        
          5 ANALYSIS PROCEDURE
        
        
          The procedure to consider strength softening in pseudo-static
        
        
          analysis has four general steps: (1) estimation of the shear strain
        
        
          amplitude and the equivalent number of uniform strain cycles
        
        
          from the peak acceleration at the ground surface and other
        
        
          seismological and site parameters; (2) estimation of strength
        
        
          softening
        
        
          
        
        
          of the soil based on the effective shear strain
        
        
          amplitude, and the equivalent number of uniform strain cycles;
        
        
          (3) estimation of the cyclic soil strength after cyclic softening
        
        
          by multiplying the trength for 1 cycle by
        
        
          
        
        
          .; (4)
        
        
          implementation of reduced strength (representing post-
        
        
          earthquake cond tion) in pseudo- ta ic analysis. Details on the
        
        
          analysis steps were described in Tsai and Mejia (2011). For
        
        
          preliminary studies, the strength for 1 cycle of most clays may
        
        
          be conservatively assumed equal to their static strength.
        
        
          6 COMPARISON TO CASE HISTORIES
        
        
          In this section, the above analysis procedure to estimate strength
        
        
          softening was implemented in pseudo static analysis and
        
        
          compared with the predicted consequences of such softening
        
        
          with observed ground failure during past earthquakes.
        
        
          1.1
        
        
          
            Berryman Reservoir, California, CA, USA
          
        
        
          Berry a Reservoir, owned and operated by the East Bay
        
        
          Municipal Utility District, USA, is located in the City of
        
        
          Berkeley in Alameda County, Californ a, and is within the State
        
        
          Alquist-Priolo Earthquake Fault Zone of the Hayward fault.
        
        
          Previous seismic hazard investigations con lud d t at active
        
        
          traces of the Hayward fault bisect the reservoir. Previous and
        
        
          recent field and laboratory investigations indicated that
        
        
          procedure, two-dimensional dynamic response analyses were
        
        
          performed using QUAD4M to estimate the cyclic stresses and
        
        
          accelerations induced by the design earthquake within the
        
        
          reservoir embankment. This comprehensive analysis indicated
        
        
          that the undrained strengths of the saturated clayey soils could
        
        
          be reduced by as much as 40 percent under the post-earthquake
        
        
          condition. Given the same design scenario as listed in Table 2,
        
        
          strength softening was also calculated using the simplified
        
        
          procedure proposed in this paper. It was found that the strengths
        
        
          of the saturated soils could be reduced by approximately 25-30
        
        
          percent. Although the predicted strength reduction is less than
        
        
          that by Mejia et al.’s procedure, it is still a reasonable, first-
        
        
          order estimate of cyclic softening of stiff clay. The yield
        
        
          accelerations, obtained from pseudo static analyses using
        
        
          UTEXAS4, were 0.16g for the pre-earthquake (no strength
        
        
          reduction) and 0.12g and 0.1 for post-earthquake condition with
        
        
          30% and 40% strength softening, respectively. The critical
        
        
          failure plane is shown in Figure 5.
        
        
          0.1
        
        
          1
        
        
          10
        
        
          1
        
        
          10
        
        
          Figure 5 Pseudo-static analysis considering strength softening at
        
        
          Berryman Reservoir
        
        
          1.2
        
        
          
            Carrefour Shopping Center 1999 Kocaeli
          
        
        
          The Carrefour Shopping Center Lot C case history (Martin et al.
        
        
          2004) provided a unique set of in situ ground deformation
        
        
          measurements in ML/CL and CH strata from settlement
        
        
          extensometers during the 1999 Kocaeli earthquake. This case
        
        
          history provides an excellent example of how fine-grained soils
        
        
          can develop significant strains or fail due to seismic loading,
        
        
          and an opportunity to evaluate the procedures presented herein.
        
        
          As shown in Figure 6a, the soil profile at Lot C includes a
        
        
          surface layer of approximately 2 m of medium dense fill
        
        
          (gravelly clay, GC). The next 5 m of soil consists of saturated,
        
        
          soft to firm, low plasticity silt and clay (ML/CL) having average
        
        
          PI and LL values of 10 and 33, respectively. This layer is
        
        
          underlain by about 1.2 m of loose to medium-dense silty sand,
        
        
          and sand (SP/SM) having a typical equivalent clean sand
        
        
          corrected SPT blow count ((
        
        
          
            N
          
        
        
          1
        
        
          )
        
        
          60,cs
        
        
          ) value of about 12. The sand
        
        
          layer is underlain by about 0.9 m of ML/CL soils, followed by
        
        
          medium to stiff, high plasticity clay (CH) that extends to depths
        
        
          greater than 35 m and has an average PI value of 37.
        
        
          The vertical strains induced in the fine-grained soil layers by
        
        
          the earthquake are largely attributed to undrained shear failure
        
        
          beneath the surcharge, as illustrated in Figure 6a. The settlement
        
        
          records in Figure 6b do show a modest increase in the rate of
        
        
          settlement from just before the earthquake to just after the
        
        
          earthquake. It is reasoned that the earthquake likely induced
        
        
          moderate excess pore pressures and that the increase in
        
        
          settlements was largely due to undrained shear failure induced
        
        
          by bearing-capacity mode of deformation.
        
        
          100
        
        
          No. of cycles (N)
        
        
          Cyclic strain
        
        
          
        
        
          (%)
        
        
          log
        
        
          
        
        
          = a-b*log N
        
        
          b=1
        
        
          b=1
        
        
          b=1
        
        
          
        
        
          =0.9
        
        
          
        
        
          =0.8
        
        
          
        
        
          =0.7
        
        
          
        
        
          =0.6
        
        
          FS=1.7 (preearthquake)
        
        
          FS=1.6, ky=016g (duringearthquake,nostrength reduction)
        
        
          FS=1.4, ky=012g (duringearthquake,30%strength reduction)
        
        
          FS=1.3, ky=010g (duringearthquake,40%strength reduction)
        
        
          WCC (1987)
        
        
          FS=2.14, ky=0.32g
        
        
          wh re, c
        
        
          0
        
        
          = -3.43, c
        
        
          1
        
        
          = -0.352, c
        
        
          2
        
        
          = -0.402, c
        
        
          3
        
        
          = 0.798, c
        
        
          4
        
        
          = 1.72,
        
        
          and c
        
        
          5
        
        
          = -1.50. The prediction equation can also estimate
        
        
          
            N
          
        
        
          c
        
        
          at a
        
        
          selected depth (z) by introducing the parameter
        
        
          
            s
          
        
        
          
            s
          
        
        
          
            V
          
        
        
          
            z
          
        
        
          
            T
          
        
        
          4
        
        
          
        
        
          (6)
        
        
          where
        
        
          
            V
          
        
        
          s is average shear wave velocity within depth z. In
        
        
          addition, the site effect is accounted for by
        
        
           
        
        
           
        
        
          2.0
        
        
          0.1
        
        
          1
        
        
          
            Sa
          
        
        
          
            Sa S
          
        
        
          
        
        
          (7)
        
        
          S
        
        
          1
        
        
          is the spectral ratio betw en 1.0 sec spectrum acceleration
        
        
          Sa(1.0) and 0.2 sec spectrum acceleration Sa(0.2). Kishida and
        
        
          Tsai have shown that their prediction equation can estimate
        
        
          similar
        
        
          
            N
          
        
        
          c values as those of Lui et al. for sand (b=0.35) at the
        
        
          ground surfac .
        
        
          Figure 4 b for cyclic softening of clay
        
        
          5 ANALYSIS PROCEDURE
        
        
          The proce ure to consider strength softening in pseudo-static
        
        
          analysis h s four g neral steps: (1) estimation of the shear strain
        
        
          amplitude and the quivalent number of unif rm strain cycles
        
        
          from the peak acceleration at the ground surfac and other
        
        
          se smological and site parameters; (2) esti ation of strength
        
        
          sof ening
        
        
          
        
        
          of the soil based on the effective hear strain
        
        
          ampli ude, and
        
        
          equivalent number of uniform strain cycles;
        
        
          (3) estimation f th cyclic soil strength after cyclic softening
        
        
          by multiplying the strength for 1 cycl by
        
        
          
        
        
          .; (4)
        
        
          implem ntation of educed strength (representing post-
        
        
          earthquake condition) in pseudo-static analysis. Details on the
        
        
          analysi steps were described in Tsai and Mejia (2011). For
        
        
          preliminary studies, the strength for 1 cycle of most clays may
        
        
          be conservatively assumed equal to their static strength.
        
        
          6 COMPARISON TO CASE HISTORIES
        
        
          In this section, the above analysis procedure to estimate strength
        
        
          softening was implemented in pseudo st tic analysis and
        
        
          compared with the predicted consequences of such softening
        
        
          with observed ground failure during past earthquakes.
        
        
          1.1
        
        
          
            Berryman Reservoir, California, CA, USA
          
        
        
          B rryman Res rvoir, owned and operated by the East Bay
        
        
          Municipa Utili y District, USA, is located in the City of
        
        
          Berkeley in Alameda County, California, and is within the State
        
        
          Alquis -Priolo E thquake Fault Zon of the Hayward fault.
        
        
          Previous seismic hazard investiga ons conclu ed that ac ive
        
        
          traces of the Hayward fault bisect the reservoir. Previous and
        
        
          recent field and laboratory investigations indicated that
        
        
          general y stiff coh sive soils (medium to high PI) gradi g to
        
        
          highly weather d bedrock are present at the site.
        
        
          To evaluate the seismic performance of the embankment,
        
        
          URS (2008) developed a design response sp ctrum and site-
        
        
          specific earthquake groun motions for input to the dynamic
        
        
          slope stability analyses. Following Mejia et al. (2009)
        
        
          procedure, two-dimensional ynamic response analyses were
        
        
          performed using QUAD4M to estimate the cycl c stresses and
        
        
          accelerations induced by the design earthquake within the
        
        
          servoir embankment. This comprehensiv analysis indicated
        
        
          that the undrained strengths of th satur ted clayey soils could
        
        
          be reduced by as much as 40 percent under the po t-earthquake
        
        
          ondition. Given the same design scenario as listed in Table 2,
        
        
          streng h soften ng was also calculated using th simplified
        
        
          procedure proposed in th s paper. It was fo nd that the trengths
        
        
          of the saturated soils c ul b reduced by appr ximately 25-30
        
        
          percent. Alth ugh the predicted strength reduction is less than
        
        
          that by Mejia et al.’s procedure, it is s ll a reasonable, first-
        
        
          order estimate of cyclic softening of stiff clay. The yield
        
        
          a celerations, obt ined fr m ps udo static a alyses using
        
        
          UTEXAS4, we 0.16g for the pre- arthquake (no s rength
        
        
          reduction) nd 0.12g and 0.1 for post-earthquake condition with
        
        
          30% and 40% stren th softening, resp ctively. The critical
        
        
          failure plane is shown in Figure 5.
        
        
          0.1
        
        
          1
        
        
          10
        
        
          1
        
        
          10
        
        
          Figure 5 Pseudo-static analysis considering strength softening at
        
        
          Berryman Reservoir
        
        
          1.2
        
        
          
            Carrefour Shopping Center 1999 Kocaeli
          
        
        
          The Carrefour Shopping Ce ter Lot C c se history (Martin e al.
        
        
          2004) provided a unique set f in situ ground deformation
        
        
          measurements in ML/CL and CH strata from settlement
        
        
          ext ns meters duri g he 1999 Kocaeli earthquake. This case
        
        
          hist ry p ovides an excellent xample of how fi e-grain d soils
        
        
          can develop significant strains or fai due to seismic loading,
        
        
          and an opportunity t evaluate the procedur s presented herein.
        
        
          As shown in Figure 6a, the soil profile at L t C includes a
        
        
          surface layer of approximately 2 m of medium dense fill
        
        
          (gravelly clay, GC). The next 5 m of soil consists of saturated,
        
        
          soft to firm, low plasticity silt and clay (ML/CL) having average
        
        
          PI nd LL values of 10 and 33, respectiv ly. This layer is
        
        
          und rlain by about 1.2 m of loose to medium-dense silty sand,
        
        
          and sand (SP/SM) having a typical equivalent clean sand
        
        
          corrected SPT blow count ((
        
        
          
            N
          
        
        
          1
        
        
          )
        
        
          60,cs
        
        
          ) value of about 12. The sand
        
        
          layer is underlain by about 0.9 m of ML/CL soils, followed by
        
        
          medium to stiff, high plastic ty clay (CH) that extends to depths
        
        
          grea er than 35 m and has an av rage PI value of 37.
        
        
          The verti al strain induced in the fine-grained oil lay rs by
        
        
          the earthquak are largely attribut d to undrained she r failure
        
        
          b neath the surcharg , as illustrated in Figure 6a. The s ttlement
        
        
          records in F gu 6b do s ow a modest increas in the rate of
        
        
          s ttlement from just before the earthquake to just after the
        
        
          earthquake. It is reasoned that the eart quake likely induced
        
        
          moderate ex ess pore pr ssures and that the increase in
        
        
          settlements was largely due to undrained shear failure induced
        
        
          by bearing-capacity mode of deformation.
        
        
          100
        
        
          No. of cycles (N)
        
        
          Cyclic strain
        
        
          
        
        
          (%)
        
        
          log
        
        
          
        
        
          = a-b*log N
        
        
          b=1
        
        
          b=1
        
        
          b=1
        
        
          
        
        
          =0.9
        
        
          
        
        
          =0.8
        
        
          
        
        
          =0.7
        
        
          
        
        
          =0.6
        
        
          FS=1.7 (preearthquake)
        
        
          FS=1.6, ky=016g (duringearthquake,nostrength reduction)
        
        
          FS=1.4, ky=012g (duringearthquake,30%strength reduction)
        
        
          FS=1.3, ky=010g (duringearthquake,40%streng h reduction)
        
        
          WCC (1987)
        
        
          FS=2.14, ky=0.32g
        
        
          selected depth (z) by introducing the parameter
        
        
          
            s
          
        
        
          
            s
          
        
        
          
            V
          
        
        
          
            z
          
        
        
          
            T
          
        
        
          4
        
        
          
        
        
          (6)
        
        
          where
        
        
          
            V
          
        
        
          s is average shear wave velocity within depth z. In
        
        
          addition, the site effect is accounted for by
        
        
           
        
        
           
        
        
          2.0
        
        
          0.1
        
        
          1
        
        
          
            Sa
          
        
        
          
            Sa S
          
        
        
          
        
        
          (7)
        
        
          S
        
        
          1
        
        
          is the spectral ratio between 1.0 sec spectrum acceleration
        
        
          Sa(1.0) and 0.2 sec spectrum acceleration Sa(0.2). Kishida and
        
        
          Tsai have shown that their prediction equation can estimate
        
        
          similar
        
        
          
            N
          
        
        
          c values as those of Lui et al. for sand (b=0.35) at the
        
        
          ground surface.
        
        
          Figure 4 b fo cyclic softening of clay
        
        
          5 ANALYSIS PROCEDURE
        
        
          The procedure to consider strength softening in pseudo-static
        
        
          analysis has four general steps: (1) estimation of the shear strain
        
        
          amplitude and the equivalent number of uniform strain cycles
        
        
          from the peak acceleration at the ground surface and other
        
        
          seismological and site parameters; (2) estimation of strength
        
        
          softening
        
        
          
        
        
          of the soil based on the effective shear strain
        
        
          amplitude, and the equivalent number of uniform strain cycles;
        
        
          (3) estimation of the cyclic soil strength after cyclic softening
        
        
          by multiplying the strength for 1 cycle by
        
        
          
        
        
          .; (4)
        
        
          implementation of reduced strength (representing post-
        
        
          earthquak condition) in pseudo-static analysis. Details on the
        
        
          analysis steps were described in Tsai and Mejia (2011). For
        
        
          preliminary studies, the strength for 1 cycle of most clays may
        
        
          be conservatively assum d equal o their static strength.
        
        
          6 COMPARISON TO CASE HISTORIES
        
        
          In thi section, the above analysi p ocedur o estimate str gth
        
        
          softening was impl mented in pseudo static analysis and
        
        
          compar d with the predict d cons qu c s of su h softening
        
        
          with observed ground failure during past e rthquakes.
        
        
          1.1
        
        
          
            Ber yman Reservoir, California, CA, USA
          
        
        
          Berryman Reservoir, owned and operated by the East Bay
        
        
          Municipal Utility District, USA, is located in the City of
        
        
          Berkeley in Alameda County, California, and is within the State
        
        
          Alquist-Priolo Earthquake Fault Zone of the Hayward fault.
        
        
          Previous seismic hazard investigations concluded that active
        
        
          traces of the Hayward fault bisect the reservoir. Previous and
        
        
          recent field and laboratory investigations indicated that
        
        
          To evaluate the seismic performance of the embankment,
        
        
          URS (2008) developed a design response spectrum and site-
        
        
          specific earthquake ground motions for input to the dynamic
        
        
          sl pe stability analyses. Following the Mejia et al. (2009)
        
        
          procedure, two-dimensional dynamic response analyses were
        
        
          performed using QUAD4M to estimate the cyclic stresses and
        
        
          accelerations induced by the design earthquake within the
        
        
          reservoir embankment. This comprehensive analysis indicated
        
        
          that the undrained strengths of th saturated clayey soils could
        
        
          be reduced by as much as 40 erc under th post-earthquake
        
        
          condition. Given the same design sc nario as listed in Table 2,
        
        
          strengt softening was also calculated using the simplified
        
        
          pro edur propos d in this paper. It was found that t stre gths
        
        
          of th aturated soils could be reduced by approximately 25-30
        
        
          perc nt. Although the predicted strength reduction is l ss than
        
        
          that by Mejia et al.’s procedur , t is still a reasonable, first-
        
        
          orde estimate of cyclic softening of stiff clay. The yield
        
        
          accelerations, ob ained from ps udo ta ic na yses u ing
        
        
          UTEXAS4, were 0.16g for the pre-ear hquake (no strength
        
        
          reduction) and 0.12g and 0.1 for p st-earthquake condition w th
        
        
          30% and 40% str ngth softeni g, respectively. The critical
        
        
          failure plane is shown in Figure 5.
        
        
          0.1
        
        
          1
        
        
          10
        
        
          1
        
        
          10
        
        
          Figure 5 Pseudo-static analysis considering strength softening at
        
        
          Berryman Reservoir
        
        
          1.2
        
        
          
            Carrefour Shopping Center 1999 Kocaeli
          
        
        
          The Carrefour Shopping Center Lot C case history (Martin et al.
        
        
          2004) provided a unique set of in situ ground deformation
        
        
          measurements in ML/CL and CH strata from settlement
        
        
          extensometers during the 1999 Kocaeli earthquake. This case
        
        
          history provides an excellent example of how fine-grained soils
        
        
          can dev lop significant strains or fail due to seismic loading,
        
        
          and an opportunity to evaluate the procedures presented herein.
        
        
          As shown in Figure 6a, the soil profile at Lot C includes a
        
        
          surface layer of approximately 2 m of medium dense fill
        
        
          (gravelly clay, GC). The next 5 m of soil consists of saturated,
        
        
          soft to fi m, low plasticity silt and clay (ML/CL) having average
        
        
          PI and LL values of 10 and 33, re pectively. This layer is
        
        
          underlain by about 1.2 m of loose to medium-dense il y sa d,
        
        
          and sand (SP/SM) having a typi l equivalent clean sand
        
        
          corrected SPT blow count ((
        
        
          
            N
          
        
        
          1
        
        
          )
        
        
          60,cs
        
        
          ) value of about 12. The sand
        
        
          lay r is underlain by about 0.9 m of ML/CL soils, followe by
        
        
          medium to stiff, high plasticity clay (CH) that extends to depths
        
        
          greater than 35 m and has an average PI value of 37.
        
        
          The vertical stra ns induced in he fine-grained soil layers by
        
        
          the earthquake are lar ely attributed to undrained shear fail r
        
        
          beneath the surcharge, as illustr d in Figure 6a. The settl ment
        
        
          records in Figure 6b do show a modest increase in the rate of
        
        
          settleme t from just before the earthquake to just after the
        
        
          earthquake. It is rea oned th t the earth ake likely duce
        
        
          mod rate excess pore pressures and that the i crease in
        
        
          settlements was largely d e to undrained shear f ilure induced
        
        
          by bearing-capacity mode of deformation.
        
        
          100
        
        
          No. of cycles (N)
        
        
          Cyclic strain
        
        
          
        
        
          (%)
        
        
          log
        
        
          
        
        
          = a-b*log N
        
        
          b=1
        
        
          b=1
        
        
          b=1
        
        
          
        
        
          =0.9
        
        
          
        
        
          =0.8
        
        
          
        
        
          =0.7
        
        
          
        
        
          =0.6
        
        
          FS=1.7 (preearthquake)
        
        
          FS=1.6, ky=016g (duringearthquake,nostrength reduction)
        
        
          FS=1.4, ky=012g (duringearthquake,30%strength reduction)
        
        
          FS=1.3, ky=010g (duringearthquake,40%strength reduction)
        
        
          WCC (1987)
        
        
          FS=2.14, ky=0.32g
        
        
          where, c
        
        
          0
        
        
          = -3.43, c
        
        
          1
        
        
          = -0.352, c
        
        
          2
        
        
          = -0.402, c
        
        
          3
        
        
          = 0.798, c
        
        
          4
        
        
          = 1.72,
        
        
          and c
        
        
          5
        
        
          = -1.50. The prediction equation can also estimate
        
        
          
            N
          
        
        
          c
        
        
          at a
        
        
          selected depth (z) by introducing the parameter
        
        
          
            s
          
        
        
          
            s
          
        
        
          
            V
          
        
        
          
            z
          
        
        
          
            T
          
        
        
          4
        
        
          
        
        
          (6)
        
        
          where
        
        
          
            V
          
        
        
          s is average shear wave velocity within depth z. In
        
        
          addition, the site effect is accounted for by
        
        
           
        
        
           
        
        
          2.0
        
        
          0.1
        
        
          1
        
        
          
            Sa
          
        
        
          
            Sa S
          
        
        
          
        
        
          (7)
        
        
          S
        
        
          1
        
        
          is the spectral ratio between 1.0 sec spectrum acceleration
        
        
          Sa(1.0) and 0.2 sec spectrum acceleration Sa(0.2). Kishida and
        
        
          Tsai have shown that their prediction equation can estimate
        
        
          similar
        
        
          
            N
          
        
        
          c values as those of Lui et al. for sand (b=0.35) at the
        
        
          ground surface.
        
        
          Figure 4 b for cyclic softening of clay
        
        
          5 ANALYSIS PROCEDURE
        
        
          The procedure to consider strength softening in pseudo-static
        
        
          analysis has four general steps: (1) estimation of the shear strain
        
        
          amplitude and the equivalent number of uniform strain cycles
        
        
          from the peak acceleration at the ground surface and other
        
        
          seis ological and site parameters; (2) estimation of strength
        
        
          softening
        
        
          
        
        
          of the soil based on the effective shear strain
        
        
          amplitude, and t equivalent number of uniform strain cycles;
        
        
          (3) estimation of the cyclic soil strength after cyclic softening
        
        
          by multiplying the strength for 1 cycle by
        
        
          
        
        
          .; (4)
        
        
          implementation of red c d strength (representing post-
        
        
          earthquake condition) in pseudo-static analysis. Details on the
        
        
          analysis steps wer described in Ts i and Mejia (2011). For
        
        
          preliminary studies, the strength for 1 cycle of most clays may
        
        
          be conservatively assumed equal to their static strength.
        
        
          6 COMPARISON TO CASE HISTORIES
        
        
          In this section, the above analysis procedure to estima e strength
        
        
          softening was implemented n pseudo static analysis an
        
        
          compared with the predicted consequences of such softening
        
        
          with observed ground failure during past earthquakes.
        
        
          1.1
        
        
          
            Berryman Reservoir, California, CA, USA
          
        
        
          Berryman Reservoir, owned and operated by the East Bay
        
        
          Municipal Utility District, USA, is located in the City of
        
        
          Berkeley in Alameda County, California, and is within the State
        
        
          Alquist-Priolo Earthquake Fault Zone of the Hayward fault.
        
        
          Previous seismic hazard investigations concluded that active
        
        
          traces of the Hayward fault bisect the reservoir. Previous and
        
        
          recent field and laboratory investigations indicated that
        
        
          generally stiff cohesive soils (medium to high PI) grading to
        
        
          highly weathered bedrock are present at e site.
        
        
          To evaluate the seismi pe formance of the embankment,
        
        
          URS (2008) developed a design resp nse spectrum and site-
        
        
          spe ific earthquake ground otions f r input to the dynamic
        
        
          slope stability analyses. Following the Meji et al. (2009)
        
        
          procedure, two-dimensional dynamic response analyses were
        
        
          performe using QUAD4M to estimat th cyc ic stresses and
        
        
          accelerations induced by the design earthquake within the
        
        
          reservoir embankment. This comprehensive analysis indicated
        
        
          that the undrained strengths of the saturated clayey soils could
        
        
          be reduced by as much as 40 percent under the post-earthquake
        
        
          condition. Given the same design scenario as listed in Table 2,
        
        
          strength softening was also calculated using the simplified
        
        
          procedure proposed in this paper. It was found that the strengths
        
        
          of the saturated soils could be reduced by approximately 25-30
        
        
          percent. Although the predicted strength reduction is less than
        
        
          that by Mejia et al.’s procedure, it is still a reasonable, first-
        
        
          order estimate of cyclic softening of stiff clay. The yield
        
        
          accelerations, obtained from pseudo static analyses using
        
        
          UTEXAS4, were 0.16g for the pre-earthquake (no strength
        
        
          reduction) and 0.12g and 0.1 for post-earthquake condition with
        
        
          30% and 40% strength softening, respectively. The critical
        
        
          failure plane is shown in F gur 5.
        
        
          0.1
        
        
          1
        
        
          10
        
        
          1
        
        
          10
        
        
          Figure 5 Pseudo-static analysis considering strength softe ing at
        
        
          Berryman Reservoir
        
        
          1.2
        
        
          
            Carrefour Shopping Center 1999 Kocaeli
          
        
        
          The Carrefour Shopping Center Lot C case history (Martin t al.
        
        
          2004) provided a unique se of in situ ground deformation
        
        
          measureme ts in ML/CL and CH strata from settlement
        
        
          extensometers during the 1999 Kocaeli earthquake. This case
        
        
          history provides n excel ent example of how fi e-grained soils
        
        
          can develop significant strains or fail due to seismic loading,
        
        
          and an opportunity to evaluate the procedures presented herein.
        
        
          As shown in Figure 6a, the soil profile at Lot C includes a
        
        
          surface layer of appr ximately 2 m of medium dense fill
        
        
          (grav lly clay, GC). The next 5 m of soil consists of saturated,
        
        
          soft to firm, low plasticity silt and clay (ML/CL) having averag
        
        
          PI and LL values of 10 an 33, respectively. This layer is
        
        
          underlain by about 1.2 m of loose to medium-dense silty sand,
        
        
          and sand (SP/SM) having a typical equivalent clean sand
        
        
          corrected SPT blow count ((
        
        
          
            N
          
        
        
          1
        
        
          )
        
        
          60,cs
        
        
          ) value of about 12. The sand
        
        
          layer is underlain by about 0.9 m of ML/CL soils, followed by
        
        
          medium to stiff, high plasticity clay (CH) that extends to depths
        
        
          greater than 35 m and has an average PI value of 37.
        
        
          The vertical strains induced in the fine-grained soil layers by
        
        
          the earthquake are largely attributed to undrained shear failure
        
        
          beneath the surcharge, as illustrated in Figure 6a. The settlement
        
        
          records in Figure 6b do show a modest increase in the rate of
        
        
          settlement from just before the earthquake to just after the
        
        
          earthquake. It is reasoned that the earthquake likely induced
        
        
          moderate excess pore pressures and that the increase in
        
        
          settlements was largely due to undrained shear failure induced
        
        
          by bearing-capacity mode of deformation.
        
        
          100
        
        
          No. of cycles (N)
        
        
          Cyclic strain
        
        
          
        
        
          (%)
        
        
          log
        
        
          
        
        
          = a-b*log N
        
        
          b=1
        
        
          b=1
        
        
          b=1
        
        
          
        
        
          =0.9
        
        
          
        
        
          =0.8
        
        
          
        
        
          =0.7
        
        
          
        
        
          =0.6
        
        
          FS=1.7 (preearthquake)
        
        
          FS=1.6, ky=016g (duringearthquake,nostrength reduction)
        
        
          FS=1.4, ky=012g (duringearthquake,30%strength reduction)
        
        
          FS=1.3, ky=010g (duringearthquake,40%strength reduction)
        
        
          WCC (1987)
        
        
          FS=2.14, ky=0.32g