Site Effects for the Sacramento-San Joaquin Delta - Earthquake Spectra

Site Effects for the Sacramento-San Joaquin Delta Tadahiro Kishida,a) M.EERI, Ross W. Boulanger,b) M.EERI, Norman A. Abrahamson,c) M.EERI, Michael W. Driller,d) e) M.EERI, and Timothy M. Wehling, M.EERI

Seismic site response and site effects models are presented for levees in the Sacramento-San Joaquin Delta where the subsurface soils include thick deposits of highly organic soils. Sources of uncertainty that contribute to the variation of seismic wave amplification are investigated, including variations in the input ground motions, soil profiles, and dynamic soil properties through Monte Carlo simulations of equivalent-linear site response analyses. Regression models for seismic wave amplification for levees in the Delta are presented that range from a function of peak outcrop acceleration alone to a vector of response spectra ordinates and soil profile parameters. The site effects models were incorporated into a probabilistic seismic hazard analysis for a representative location, and the relative impacts of the various models on the computed hazard are evaluated. 关DOI: 10.1193/1.3111087兴 INTRODUCTION The Sacramento-San Joaquin Delta is a critical link in California’s freshwater delivery system, home to a unique ecosystem, and an area experiencing increasing urbanization pressures. The Delta consists of a complicated network of channels and reclaimed islands that collects water from about 40% of California’s surface area and directs it to San Francisco Bay. There are about 1700 km of levees and over 60 islands with ground surface levels up to 8 m 共25 feet兲 below adjacent water ways (California 1992). Levee failures during an earthquake are a major concern because rapid inundation of the inner islands has the potential to significantly reduce the freshwater supply for California, in addition to damaging the natural habitat, crops and civil infrastructure (e.g., Lund et al. 2007). The California Department of Water Resources performed preliminary seismic stability evaluations of the levee system and concluded that the seismic wave amplification at sites underlain by highly organic soils was a major source of uncertainty in seismic hazard evaluations for the delta (California 1992). Seismic site effects have been recognized as being particularly important for soft soil conditions, such as exist in the Delta. Idriss (1991) related nonlinear seismic wave amplification through soft soil sites to the peak horizontal ground acceleration (PGA) at a a)

Graduate Student Researcher, University of California, Davis, One Shield Avenue, Davis, CA 95616 Professor, University of California, Davis, One Shield Avenue, Davis, CA 95616 c) Pacific Gas and Electric, San Francisco, CA 94177 d) Senior Engineer, California Dept. of Water Resources, 1416 9th Street, Sacramento, CA 95814 e) Senior Engineer, California Dept. of Water Resources, 1416 9th Street, Sacramento, CA 95814 b)

301

Earthquake Spectra, Volume 25, No. 2, pages 301–322, May 2009; © 2009, Earthquake Engineering Research Institute

302

KISHIDA ET AL.

corresponding rock outcrop based on earthquake observations and one-dimensional site response analyses. Fiegel (1995) related nonlinear seismic wave amplifications for soft soil sites to the input motion PGA and earthquake magnitude based on dynamic centrifuge model testing of soft clay profiles subjected to peak base accelerations up to about 0.6 g. Arulnathan (2000) obtained similar results based on dynamic centrifuge model testing of highly organic soil profiles shaken with peak base accelerations up to about 0.5 g. Fiegel (1995) and Arulnathan (2000) showed that equivalent-linear site response analyses were capable of reasonably approximating the nonlinear seismic wave amplification observed in these centrifuge models of soft clay and highly organic soil. Baturay and Stewart (2003) showed that 1-D equivalent-linear site response analyses provided improved accuracy, relative to empirical models, in predicting spectral accelerations (at periods less than about 1 s) at soft soil sites where strong ground motion records had been obtained. Nonlinear site response analyses provide a more realistic representation of the hysteretic behavior of soft soils during strong shaking and are therefore expected to provide more accurate predictions of site response. A recent assessment of nonlinear one-dimensional site response analyses by Stewart and Kwok (2008) evaluated the relatively accuracy of five nonlinear site response programs and an equivalent-linear site response program against sets of vertical array data. They demonstrated the importance of code usage and parameter selection protocols for nonlinear site response analyses in practice, and subsequently concluded that nonlinear analyses may provide improved estimates of ground motion relative to equivalent-linear analyses when ground strains approach about 1% (or as low as 0.2–0.3% in deep soil sites). The development of a regional-scale site effects model for Delta levees would ideally be based on a combination of strong ground motion records from Delta levees and numerical simulations using analysis methods that had been verified against such records. The potential value of strong ground motion records to seismic risk studies led the California Department of Water Resources to install downhole arrays at three locations in the 1990s. Records have only been obtained for very small shaking levels to date, and equivalent-linear analyses of such records have produced reasonably good agreement. Recordings at stronger shaking levels are still needed to evaluate the relative accuracy of one- and two-dimensional equivalent-linear and nonlinear analysis methods for predicting levee responses when ground strains become large. The prediction of seismic levee responses is particularly important for evaluating the potential for triggering of liquefaction within levee fill and foundation soils, which become a primary concern as peak accelerations exceed only about 0.1 g. There are advantages to evaluating site response effects for levees using both equivalent-linear and nonlinear methods at this time. Equivalent-linear methods are expected to provide reasonable estimates of seismic responses up through a range of shaking levels that are important to liquefaction triggering evaluations, and can be more easily used in Monte Carlo simulations to study the propagation of various sources of uncertainty. Nonlinear methods can directly simulate levee deformations from yielding soils and liquefaction, which is an important advantage for development of fragility relationships (URS 2008). The combination of equivalent-linear and nonlinear analysis methods provides a basis for evaluating the consistency of the predicted trends and relationships over the range of conditions where consistency is expected.

SITE EFFECTS FOR THE SACRAMENTO-SAN JOAQUIN DELTA

303

General methods for incorporating site amplification effects in probabilistic seismic hazard analyses (PSHA) have been developed and implemented for a range of site conditions. McGuire et al. (2001) describe methods for developing uniform hazard spectra on soil that are consistent with the uniform hazard spectra for the underlying rock: one general approach was to develop ground motion estimation equations for the applicable soil conditions and then use those directly in the PSHA, and the other general approach was to perform the PSHA for rock and then translate the results to the applicable soil conditions. Cramer (2003) illustrated the potential importance of including site amplification uncertainty in the computation of hazard at two sites by comparing results for an implementation of the McGuire et al. (2001) fully probabilistic approach (i.e., the first general approach listed above) to those obtained by applying a deterministic median amplification factor to the probabilistic rock motions. Bazzurro and Cornell (2004) propagated uncertainties in ground motions and dynamic soil properties through nonlinear one dimensional site response analysis and estimated the variance in site amplification factors at soil sites. In this study, seismic site response and site effects models are evaluated for levees in the Sacramento-San Joaquin Delta where the subsurface soils include thick deposits of highly organic soils (or peat). The site response and site effects models are expressed relative to an outcrop of the underlying stiffer deposits which generally correspond to a site D classification by NEHRP (2003). One-dimensional (1-D) equivalent-linear site response analyses were performed using a broad range of input motions, soil profiles, and realizations of dynamic soil properties through Monte Carlo simulations. The dataset of numerical analysis results is used to develop a series of site effects models for levee profiles that range from a function of peak outcrop acceleration alone to a vector of response spectra ordinates and soil profile parameters. The relative contributions of different sources of uncertainty to the total variance in the one-dimensional site amplification factors are described. The site effects models, after adjustment for the two-dimensional (2-D) effects of typical levee geometries, are incorporated into a probabilistic seismic hazard analysis for a representative location to evaluate the relative impacts that the various site effects models have on the computed hazard. The application of these models and their limitations are discussed. DYNAMIC SITE RESPONSE ANALYSES Monte-Carlo simulations of 1-D site response were performed using the equivalentlinear, wave equation analysis method in Shake (Schnabel et al. 1972). The selection of soil profiles, soil properties, and input ground motions for the Delta conditions are described in this section. Regression models for amplification factors on PGA and spectral accelerations (all linear-elastic with 5% of critical damping) are derived from the analysis results in the following section. The results of these equivalent-linear analyses are expected to be reasonable at low to moderate shaking levels (e.g., PGA less than about 0.3 g in this study) that produce ground strains generally less than about 1% (Stewart and Kwok 2008). Analysis results were nonetheless extended to larger shaking levels for

304

KISHIDA ET AL.

Figure 1. Location of soil profiles at Sacramento-San Joaquin Delta (base map from California 1992).

this study, with the recognition that these equivalent-nonlinear analysis results were to be used in combination with nonlinear analysis results for the evaluation of levee performances (e.g., URS 2008). VARIATION OF SOIL PROFILES

Eighteen soil profiles were selected from levees on thirteen different islands in the Delta, at the approximate locations shown in Figure 1. All the profiles were obtained from borings through the crests of levees. Figure 2 shows a typical levee cross-section, illustrating the gentle slopes on either side of the levee crest. The profiles for four locations are shown in Figure 3 to illustrate the range of subsurface conditions encountered in the Delta. In general, the levee fills were 2 to 8 m thick and comprised primarily of sands, silts, clays, and organic soils. The highly organic or “peat” layers were 1 to 9 m thick and had organic contents of 10% to 90%. The highly organic layers were sometimes underlain by a layer of soft to stiff silty clays. All profiles are underlain by an inter-


305

Figure 2. Cross section of levee at Sherman Island.

Figure 3. Soil profile realizations given discrete measurements of (a) densities at Bacon Island, (b) densities at Twichell Island, (c) shear wave velocities at Clifton court, and (d) shear wave velocities at Sherman Island. Black lines are realizations at 0.1 m intervals, and black bullets are point measurements.

306

KISHIDA ET AL.

Figure 4. Normalized modulus reduction curves for (a) low organic content soils (b) high organic content soils.

layered deposit of primarily stiff silty clays and dense sands below approximately 20 to 30 m depth that has Vs values generally corresponding to site class D of the NEHRP site classification (2003). Input ground motions were specified for an outcrop of this underlying strata (i.e., a site D outcrop), such that only the upper 20 to 30 m are modeled in the site response analyses. Shear wave velocities were measured by the suspension logging method at four locations and estimated by empirical correlations for the other locations. The peat deposits consolidated beneath levee fills have typical shear wave velocities of 40 to 110 m / s which are about 5 times higher than those of unconsolidated free-field peat deposits. The soft silty clays that sometimes underlie the peat layers also have low shear wave velocities, typically in the range of 70 to 190 m / s. Shear wave velocities for the overlying levee fill and the upper portions of the deeper stiff clay/dense sand deposits ranged from 80 to 150 m / s, and 140 to 290 m / s, respectively. Total densities 共␳兲 for the levee fill, highly organic soils, and underlying stiff clay/dense sand deposits ranged from 1.20 to 2.15 Mg/ m3, 1.00 to 1.35 Mg/ m3, and 1.50 to 2.20 Mg/ m3 respectively. VARIATION OF SOIL PROPERTIES

Uncertainty in the estimation of dynamic soil properties was included by developing multiple realizations of soil properties for each soil profile. In general, five different realizations were used for each soil profile. Expected values for the normalized modulus reduction 共G / Gmax兲 and damping ratio 共␰兲 versus shear strain 共␥兲 relationships were obtained from Kishida et al. (2009a) for highly organic soils, Vucetic and Dobry (1991) for inorganic clay, and EPRI (1993) for sand. The normalized modulus reduction and damping relationships for highly organic soils, as shown in Figures 4 and 5, include depen-


307

Figure 5. Damping ratio curves for (a) low organic content soils (b) high organic content soils.

dence on organic content (OC) and vertical consolidation stress 共␴vc ⬘ 兲. Expected values for the small strain shear modulus 共Gmax兲 were estimated using empirical correlations that were calibrated to the available Vs data from the Delta, as described in Kishida et al. (2009a) for highly organic soils and Kishida (2008) for inorganic soils. G, ␰, and ␳ were modeled as log-normally distributed with different standard deviations for the highly organic soils and the inorganic soils. Correlation matrices between the residuals of G and ␰ at different ␥ levels were obtained separately for highly organic soils and inorganic soils. Details on the above correlations and distributions are provided in Kishida (2008) and Kishida et al. (2009a). Spatial correlation was modeled as exponential decay within the same geological layer (Vanmarcke 1977). Typical values for the scale of fluctuation are 1 – 2 m in the vertical direction (Phoon and Kulhawy 1999). A value of 2.0 m was selected for this study based on analysis of the available in situ test data. Each realization of dynamic soil properties for a given soil profile was produced by randomly generating a set of residuals in G, ␰, and ␳ at 0.1 m depth intervals based on the established covariance matrix (i.e., from the specified standard deviations, the correlation matrices between residuals of dynamic properties, and the spatial correlations matrix). This process required first generating a realization for other soil characteristics, such as OC for the organic soils and PI for the inorganic clays, because they are predictor variables for the dynamic properties. When OC or PI information was not available from the borings, values were generated by inverse prediction based on other available information (e.g., ␳ or Vs measurements, soil type) to ensure that realistic parameter combinations were produced. For borings with point measurements of ␳ or Vs, the re-

308

KISHIDA ET AL.

duced uncertainty in these properties was accounted for by generating the realizations conditional on the measured values. The effects of this conditional estimation are illustrated in Figure 3 showing the range of realizations for two profiles with ␳ measurements and two profiles with Vs measurements. Dynamic properties were then averaged over 1.0-m-thick intervals for use in the site response analyses. It is worth noting that the methodology used herein for generating realizations of soil properties is different from the procedure by Bazzurro and Cornell (2004). This study varied the residuals in the dynamic soil properties, whereas Bazzurro and Cornell (2004) varied the model parameters. VARIATION AND CHARACTERIZATION OF GROUND MOTIONS

A subset of two hundred and sixty four horizontal ground motions from 54 earthquake events were selected from the approximately 3500 horizontal motions measured at sites with NEHRP site D classifications in the PEER (Pacific Earthquake Engineering Research) NGA database (Pacific 2005). The selected data set has earthquake moment magnitudes 共Mw兲 ranging from 4.3 to 7.9, distances to the source ranging from 1.1 km to 296 km, and peak ground accelerations (PGA) ranging from 0.004 g to 1.8 g. The choice of ground motion intensity measures for a given engineering application can be evaluated in terms of their efficiency and sufficiency, as discussed by Luco and Cornell (2007). Vector-valued intensity measures can have certain advantages. For example, Bazzurro and Cornell (2002) showed that using a vector of spectral accelerations for representing the probabilistic seismic hazard resulted in improved predictions of seismic demands on buildings, and Kramer and Mayfield (2007) showed how to combine a vector of PGA and Mw in the probabilistic evaluation of liquefaction hazards. When using vectors of ground motion intensity measures, it is ideal that the vector components be independent to avoid strong multi-collinearity in subsequent regression analyses. An intensity measure based on spectral ratios was developed for use in a vector with PGA for predicting site amplification effects. In practice, the PGA and spectral accelerations at structural periods 共T兲 of 0.2 and 1.0 s (i.e., Sa共0.2兲 and Sa共1.0兲) are conveniently available for describing design spectra in NEHRP Seismic Design Provisions (2003). The covariance matrix ⌺ for PGA, Sa共0.2兲, and Sa共1.0兲 for NEHRP site D recordings in the NGA database was obtained as follows.

冤

1.18 1.20 1.00 ⌺ = 1.20 1.30 0.95 1.00 0.95 1.41

冥

共1兲

PGA, Sa共0.2兲, and Sa共1.0兲 are all positively correlated with the correlation greater than 0.7. The smallest eigenvalue is about two orders of magnitude smaller than the other two eigenvalues, which suggests that two independent indices may be sufficient to provide a good description of the distribution. If PGA is considered as the primary contributing factor for nonlinear soil behaviors, the objective was to find additional spectral


309

measures that are nearly independent of PGA. The covariance matrix of PGA, Sa共0.2兲, and Sa共1.0兲 can be used to obtain two components that are orthogonal (independent) to PGA. The other two components can be expressed by linear combination of PGA, Sa共0.2兲, Sa共1.0兲 as follows (Johnson and Wichern 2002).

冤

1 0 0 ⌺ = 0 a1 a2 b0 b1 b2

冥冤

1.18 1.20 1.00 1.20 1.30 0.95 1.00 0.95 1.41

冥冤

冥

1 0 0 ⬘ 0 a1 a2 b0 b1 b2

共2兲

where the vector a and b are unit vectors. Since the number of unknown parameters is five, the number of equations with the condition of no correlation is three, and the number of equations for the unit vectors is two, the following vectors are obtained.

冤冥冤

ln共PGA兲 1 0 0 ln共I1兲 = 0 − 0.64 0.77 − 0.76 0.63 0.14 ln共I2兲

冥冤

ln共PGA兲 ln共Sa共0.2兲兲 ln共Sa共1.0兲兲

冥

共3兲

The components I1 and I2, which are independent of PGA, can be approximated as the ratio Sa共1.0兲 / Sa共0.2兲 and the ratio Sa共0.2兲 / PGA, respectively. Thus it is convenient and practical to define an index S1 that approximates the orthogonal component I1,

S1 = Sa共1.0兲/Sa共0.2兲

共4兲

The correlation between ln共PGA兲 and ln共S1兲 was obtained as −0.20 for NEHRP site D recordings in the NGA database, which is small enough to be considered as independent. The correlations between ln共PGA兲 and ln共Sa共0.2兲 / PGA兲 was similarly obtained as −0.61, which shows dependence. Subsequent use of this ratio in regression models for site response showed that it provided little benefit over the use of S1 and PGA, which is consistent with the previously noted observation that only two independent indices would likely be needed to provide an adequate description of the distribution in the PGA, Sa共0.2兲, and Sa共1.0兲 data. Since S1 and PGA are approximately independent, the conditional mean values given PGA are approximately the expected values from the disaggregation results in design procedures. The index S1 is not affected by scaling of the time history of accelerations. REGRESSION ANALYSIS OF SITE EFFECTS 1-D PGA AMPLIFICATION FACTORS AND UNCERTAINTIES

The variations of the computed 1-D PGA amplification factors 共AFPGA兲 against different ground motion variables for the outcropping site D conditions are shown in Figure 6. Figure 6a shows that AFPGA tends to decrease with the increase of PGA at an NEHRP site D outcrop, showing the nonlinearity of site amplification. Similar nonlinear trends are observed in Figure 6b for AFPGA versus Sa共0.2兲 at an NEHRP site D outcrop and, to a lesser degree, in Figure 6c for AFPGA versus Sa共1.0兲. From these plots, PGA appears to be a better estimator than Sa(0.2) or Sa共1.0兲 for the nonlinear site amplification factors.

310

KISHIDA ET AL.

Figure 6. Variation of PGA amplification factors against predictor variables.

Figure 6d shows that AFPGA tends to increase as the spectral ratio index S1 for the site D outcrop motions increases. Since S1 is not strongly correlated to PGA, the variation of AFPGA against S1 cannot be explained by only using PGA at NEHRP site D as a predictor variable in the regression models. Similar increasing trends for AFPGA are observed with the increase of earthquake magnitude and distance shown in Figures 6e and 6f. However, the trend against S1 is stronger than the trends against Mw and distance indicating that S1 is the second component to be used in the regression analysis of site effects. Regression models for AFPGA factors were developed using five alternative sets of predictor variables with varying degrees of efficiency and sufficiency. Beginning with a simple linear site effect model, the sources of uncertainty were evaluated using the form,

ln共AFPGA兲 = 0.164 + ␶profile + ␶property + ␧motion

共5兲

where ␶ denotes the random effect assigned to soil profiles and properties, respectively. The median site effect was 1.18 with the total standard deviation of 0.390. Approximately 40%, 7%, and 53% of the variance in AFPGA is contributed by the soil profiles, soil properties, and ground motions, respectively. This model is clearly insufficient because it neglects the nonlinear site effects, but is nonetheless included for comparative purposes. The second regression model relates AFPGA to the outcrop PGA alone,


ln共AFPGA兲 = − 0.414 − 0.540 ln共PGA + 0.245兲 + ␶profile + ␶property + ␧motion

311

共6兲

and has a lower standard deviation of 0.367. Approximately 50%, 9%, and 41% of the variance in AFPGA is contributed by the soil profiles, soil properties, and ground motions, respectively. This model includes nonlinearity in the site amplification, but it is still insufficient because it cannot capture the dependence of AFPGA on S1, Mw, or distance shown in Figure 6. The third and fourth models use a vector of two intensity measures to achieve a reasonable degree of sufficiency. The third model adds the dependence on Mw that is visible in Figure 6e,

ln共AFPGA兲 = − 1.19 − 0.573 ln共PGA + 0.245兲 + 0.121MW + ␶profile + ␶property + ␧motion 共7兲 and therefore had a smaller standard deviation of 0.354. Approximately 55%, 9%, and 36% of the variance in AFPGA is contributed by the soil profiles, soil properties, and ground motions, respectively. The fourth model instead used the outcrop PGA and spectral ratio index S1, which Figure 6e showed had a stronger effect on AFPGA than Mw. The resulting model,

ln共AFPGA兲 = − 0.105 − 0.397 ln共PGA + 0.245兲 + 0.186 ln共S1兲 + ␶profile + ␶property + ␧motion 共8兲 has a smaller standard deviation, 0.336, than the third model. Approximately 64%, 10%, and 26% of the variance in AFPGA is contributed by the soil profiles, soil properties, and ground motions, respectively. The observed trends of increasing AFPGA with increasing S1 or Mw is expected because increases in these parameters, for the same PGA, correlate with stronger long-period components of motion and longer durations of shaking, which together produce stronger responses for the site conditions encountered. The fifth model incorporates an index of the site characteristics by using the average VS value to a specified depth z. Values of z ranging from 5 m to 30 m were evaluated, with a depth of 10 m providing a reasonable choice for correlating to differences in the computed dynamic responses. The resulting VS10 values primarily serve to differentiate sites on the basis of the levee fill quality and peat deposit, whereas deeper averaging intervals provided less distinction between the soft soil conditions encountered throughout the Delta. The resulting model,

ln共AFPGA兲 = 2.56 − 0.397 ln共PGA + 0.245兲 + 0.186 ln共S1兲 − 0.571 ln VS10 + ␶profile + ␶property + ␧motion

共9兲

has the lowest standard deviation, 0.315, of the five models, assuming that Vs10 is known exactly. In application, the uncertainty in Vs10 will contribute to the uncertainty in the computed AFPGA. If the potential errors in a measured value of Vs10 are represented by a coefficient of variation of 0.10, then the standard deviation in the computed AFPGA is increased to 0.320. In either case, approximately 61%, 10%, and 29% of the variance in

312

KISHIDA ET AL.

Figure 7. Variation of residuals in PGA amplification factors by Equation 8 (using vector of PGAsite D and S1) against predictor variables.

AFPGA is contributed by the soil profiles, soil properties, and ground motions, respectively. The residuals of AFPGA based on Equation 9 are plotted in Figure 7. Note that the trend in AFPGA against Mw and distance in Figure 6 is removed by including S1 in the regression analysis. The median amplification factors computed using the four nonlinear AFPGA relationships are plotted against the PGAsiteD for comparison in Figure 8. The median AFPGA共PGAsiteD兲 is intermediate to the values obtained using AFPGA共PGAsiteD , Mw兲 with Mw = 5.5, 6.5, and 7.5, and follows a similar nonlinear shape with increasing shaking intensity (Figures 8a and 8b). The AFPGA共PGAsiteD , S1兲 with S1 = 0.36, 0.62, and 0.88 (Figure 8c) are similar to those for AFPGA共PGAsiteD , Mw兲 with Mw = 5.5, 6.5, and 7.5 (Figure 8b), as the selected S1 values are typical of the median values expected for these Mw when PGAsiteD is about 0.1 g. The AFPGA共PGAsiteD , S1 , Vs10兲 with Vs10 = 105 m / s (median value) are very similar to those using AFPGA共PGAsiteD , S1兲 shown in Figure 8d. The effect of varying Vs10 to 89 and 121 m / s for this model are illustrated in Figure 8d, showing that the median AFPGA for Mw of 6.5 increases or decreases by a factor of about 0.92 and 1.10 respectively for these two cases.


313

Figure 8. Median amplification factors of PGA for the median Sa from NEHRP site D to Delta levee crests. SPECTRA AMPLIFICATION FACTORS

The most general model for PGA amplification was extended to the other spectral ordinates using the following form.

ln共AF兲 = b0 + b1 ln共PGA + 0.245兲 + b2 ln共S1兲 + b3 ln VS10

共10兲

The regression parameters for the amplification factors on PGA, Sa共0.2兲, Sa共1.0兲, and Sa共5.0兲 and correlations between residuals are listed in Table 1 and Table 2 respectively. Contour lines of equal amplification factors obtained by Equation 10 for PGA, Sa(0.2), Sa(1.0) and Sa(5.0) are shown in Figure 9 for different combinations of the intensity measures (PGA and S1 at NEHRP site D outcrop) and for a value of Vs10 = 100 m / s. The AFPGA and AFSa共0.2兲 values tend to increase with increasing S1, whereas the AFSa共1.0兲 and AFSa共5.0兲 values are essentially independent of S1. Figure 10 shows the expected values for AFPGA, AFSa共0.2兲, AFSa共1.0兲, and AFSa共5.0兲 Table 1. Parameters for site amplification factor from NEHRP site D to Delta levee crests T (sec)

b0

b1

b2

b3

␴ (contributions to ␴2 from soil profiles, properties, grounds motions)

0 0.2 1.0 5.0

2.56 3.30 4.05 0.17

−0.397 −0.416 0 0

0.186 0.153 −0.0113 −0.0586

−0.571 −0.796 −0.763 0

0.315 (61%, 10%, 29%) 0.381 (63%, 12%, 25%) 0.236 (57%, 23%, 20%) 0.212 (8%, 5%, 87%)

314

KISHIDA ET AL.

Table 2. Correlations of residuals for site amplification factor from NEHRP site D to Delta levee crests T (sec)

0

0.2

1.0

5.0

0 0.2 1.0 5.0

1 0.56 0.37 0.23

0.56 1 0.16 0.20

0.37 0.16 1 0.45

0.23 0.20 0.45 1

against the PGA at NEHRP site D for different earthquake magnitudes, Vs10 = 100 m / s, and using Abrahamson and Silva’s (1997) attenuation relationship for deep soil sites with strike-slip faulting to compute the expected values for PGA and S1. The amplification factors for PGA and Sa共0.2兲 increase with increasing earthquake magni-

Figure 9. Amplification factors from NEHRP site D to Delta levee crests 共VS10 = 100 m / s兲.


315

Figure 10. Median amplification factors for the median Sa from NEHRP site D to Delta levee crests with VS10 = 100 m / s.

tude, whereas the amplification factors for Sa共1.0兲 and Sa共5.0兲 are relatively independent of earthquake magnitude. Significant dependence of AFPGA on earthquake magnitude and frequency content has been reported for soft soil sites (e.g., Idriss 1991, Fiegel 1995), but not for stiff soil sites (e.g., Abrahamson and Silva 1997, Bazzurro and Cornell 2004, Choi and Stewart 2005). Expected values for spectral accelerations at different distances from the source and for different earthquake magnitudes are shown in Figure 11 for an outcrop of deep soil (based on Abrahamson and Silva 1997) and for the crest of a Delta levee based on the amplification factors derived in this study. Ground motion tends to be amplified for all period ranges when the shaking intensity is small (e.g., larger distances and smaller Mw). When the shaking intensity is strong (e.g., small distances and larger Mw), spectral accelerations at shorter periods tend to be deamplified while spectral accelerations at longer period such as 1.0 second continue to be amplified. 2-D CORRECTION FOR PGA AMPLIFICATION ON LEVEES

The dynamic response of Delta levees in the transverse direction can be expected to differ from the one-dimensional approximation used herein. Kishida et al. (2009b) performed parametric analyses using two-dimensional, equivalent-linear, dynamic finite element analyses and developed relationships for the ratio of the amplification factors

316

KISHIDA ET AL.

Figure 11. Spectral accelerations at levee crests based on 1D analysis and at a NEHRP site D outcrop (based on Abrahamson and Silva (1997) deep soil site with strike-slip faulting).

computed using 2-D models versus 1-D models for the profile directly beneath a levee crest. The ratio of the PGA amplification factors for 2-D versus 1-D was approximately 1.19 independent of the PGA. The small effect of two-dimensions seems reasonable given that the slopes of Delta levees are often relatively flat and the response is strongly affected by soft soils that extend laterally beneath the levee and adjacent free-field. Previous research has reported 1-D to 2-D correction factors on peak crest accelerations of 1.25 for moderately steep slopes in landfills (Rathje and Bray 2001) and 1.5 for steep slopes in cemented sands (Ashford and Sitar 1994), but the significant differences between landfills, cemented sand slopes, and levees mean that the results may not be directly comparable. Combining the derived linear 2-D/1-D correction with the 1-D amplification models in Equations 5–9 (including the uncertainty in Vs10) produced models for the PGA at a 2-D levee crest with standard deviations of 0.574, 0.538, 0.500, 0.441, and 0.430, respectively, given the spectral accelerations at a NEHRP site D outcrop (Kishida et al. 2009b). IMPACT OF SITE EFFECT MODELS ON HAZARD The impact of the different site effects models on seismic hazard is illustrated by an example hazard analysis for one representative levee location on Sherman Island in the western Delta. For the purpose of this comparison, the seismic hazard at a NEHRP site D outcrop was computed using the Abrahamson and Silva (1997) deep soil attenuation model and the source model from the USGS open file (1996). Conditional probability was used for computing seismic hazard when the ground motion intensity was represented by a vector of PGA and S1. Correlations between residuals of spectral accelerations were previously presented by Baker and Cornell (2006), but the correlations used herein were computed from the residuals obtained by detrending the PEER flatfile data set relative to the Abrahamson and Silva (1997) attenuation model (Watson-Lamprey, personal communication). Amplification factors for levee crests combined the 1-D site amplification factors with the AF2-D / AF1-D correction presented previously. Figure 12 shows a comparison of the resulting PGA seismic hazard curves for the NEHRP site D


317

Figure 12. Comparison of PGA hazard curves for a Delta levee crest using four different site effect models.

outcrop and for the levee crest based on four site amplification models: AFPGA is a constant (Equation 5), AFPGA depends on PGAsite D (Equation 6), AFPGA depends on PGAsite D and Mw (Equation 7), and AFPGA depends on PGAsite D and S1 (Equation 8). For a mean annual frequency of exceedance of 0.0021 (i.e., 10% in 50 year motion), the expected PGA values are 0.43 g at a site D outcrop and 0.86 g, 0.65 g, 0.58 g, and 0.52 g at the levee crest for the four site amplification models, respectively. The differences between the levee crest results for the different site amplification models become much smaller for more frequent events and much larger for less frequent events. The expected PGA values at the levee crest progressively decreases between each of these four site amplification models because the models progressively become both more sufficient and efficient (e.g., as represented in their lower standard deviations). Use of a constant AFPGA increasingly over-estimates the seismic hazard as the frequency of the event decreases, because nonlinear site response is important at these higher shaking intensity levels. The nonlinear AFPGA model based on PGAsite D alone produced the highest hazards of the three nonlinear models because it had the largest variance of the three models and was insufficient in its representation of the nonlinear site effects. The vector model based on PGAsite D and S1 produced smaller hazard results than the vector model based on PGAsite D and Mw, with the differences being largely due to the former model being slightly more efficient (e.g., lower standard deviation) than the latter model. It should also be noted that the site effects models and hazard results are for levee responses in the absence of liquefaction or slope instability; these hazard results can be used to assess the potential for triggering of liquefaction or for use in uncoupled methods of estimating slope deformations, while recognizing that the actual crest motions under very strong shaking would be significantly reduced by the occurrence of slope yielding or liquefaction. The effect of variance in the site amplification models is illustrated in Figure 13 showing the PGA hazard curves computed using the PGA model (Equation 6) with stan-

318

KISHIDA ET AL.

Figure 13. Comparison of PGA hazard curves for a Delta levee crest using the PGA site amplification model showing the effect of varying the site amplification model’s standard deviations.

dard deviations of 0.54, 0.45, and 0.35. The PGA hazard progressively reduces with decreasing uncertainty in the site amplification model, as expected. Comparing these PGA hazard curves with those in Figure 12, which were obtained using the other site amplification models, shows that their sequence (or relative positions) is consistent with the order of their respective standard deviations. The potential benefits of having in situ shear wave velocity measurements and including that data in the site amplification model (Equation 9) are illustrated in Figure 14 showing the PGA seismic hazard curves for site-specific measured Vs10 values of 89 m / s, 105 m / s, and 121 m / s. These Vs10 values are the 16th-, 50th-, and 84thpercentile values for the sites included in this study. For comparisons, the PGA seismic

Figure 14. Expected PGA hazard curves for different site-specific VS10 values.


319

Figure 15. Effect on seismic hazard of eliminating the uncertainty in dynamic soil properties while retaining the uncertainty from ground motions and soil profile variability.

hazard curve computed using the site amplification model based on PGAsite D and S1 (i.e., without a site-specific shear wave velocity value, Equation 8) is also shown on this Figure 14. When the site-specific Vs10 value equals the expected value for Delta conditions, then the inclusion of the Vs10 information in the site amplification model resulted in approximately the identical hazard because the standard deviation in AFPGA was only reduced from 0.441 to 0.430. However, if the site-specific Vs10 value is much smaller than the expected value, then the computed hazard is larger because the lower Vs10 value is known to produce greater PGA amplification. The opposite conclusion is, of course, reached when the site-specific Vs10 value is larger than the expected value. For a mean annual frequency of exceedance of 0.0021 (i.e., 10% in 50 year motion), the expected PGA values are 0.57 g, 0.52 g, and 0.48 g for the three Vs10 values, respectively, which is a range of almost 20%. The effect of including Vs10 values is smaller for more frequent events and larger for less frequent events, as expected. Hazard comparisons were also used to evaluate the potential benefits that might be achieved by performing additional experimental research on the dynamic soil property relationships, followed by an updating of the site effects models. For example, the standard deviation in the site amplification model based on PGAsite D and S1 (Equation 8) would be reduced from 0.441 to 0.428 if there was zero uncertainty in the dynamic soil property relationships. The small reduction in AFPGA uncertainty is due to soil profile and ground motions variability being more dominant sources of uncertainty. The PGA hazard was subsequently shown in Figure 15 to be only slightly reduced if the variance in the general dynamic property relationships was eliminated, provided that the median AFPGA was unaffected. Site-specific testing of dynamic properties could identify a bias in the assumed dynamic soil property models that would shift the median AFPGA and therefore affect the PGA hazard more. Nonetheless, these results illustrate how the uncertainties in the input ground motions and the subsurface soil profiles for Delta levees are dominant concerns for a regional-scale site effects model.

320

KISHIDA ET AL.

SUMMARY AND CONCLUSIONS Nonlinear seismic site effect models were developed for levees in the SacramentoSan Joaquin Delta, where the subsurface soils include thick deposits of highly organic soils (or peat). Monte Carlo simulations of equivalent-linear dynamic response analyses with uncertainties in the ground motions, soil profiles, and soil properties were used to produce a dataset from which a hierarchy of regression models for seismic wave amplification was developed. These amplification factors, relative to a NEHRP site D outcrop, included a linear (constant) model, a function of PGAsite D, vectors of PGAsite D with either Mw or S1, and a vector of PGAsite D, S1, and shear wave velocity index Vs10. These site effects models were incorporated into a probabilistic seismic hazard analysis for a representative location in the western Delta to illustrate the relative impacts that the various site effects models had on the computed hazard. An amplification factor model based on PGAsite D only was insufficient because the residuals showed significant remaining dependence on Mw, distance to source, and spectral ratio, S1 = Sa共1.0兲 / Sa共0.2兲. Vectors that combined PGAsite D with either Mw or S1 were sufficient for describing the nonlinear amplification behavior, with the vector of PGAsite D and S1 being a slightly more efficient predictor of site amplification factors. The PGA seismic hazard curves generated using the vector of PGAsite D with S1 were consequently smaller than those generated with the other two nonlinear site effects models. Variability in soil profiles was the major source of uncertainty in the derived nonlinear seismic wave amplification factors for this regional application. Ground motion variability was the second major source of uncertainty, while dynamic soil properties (given the soil profile is known) made only a minor contribution to the total variance in seismic wave amplification factors. The inclusion of the site-specific shear wave velocity index Vs10 in the site amplification model was only able to slightly reduce the model’s variance when estimating spectral accelerations at shorter periods. The accuracy of these site effects models, as derived from equivalent-linear analyses, is expected to be reasonable at low to moderate shaking levels that produce ground strains less than about 1% (e.g., PGA less than about 0.3 g). Nonlinear analyses are required to develop confidence in the extension of these models to stronger shaking levels and for the direct evaluation of levee deformations (e.g., URS 2008). In either case, the collection of strong ground motion recordings on Delta levees remains an important goal for the verification of dynamic analysis methods and site effects models. ACKNOWLEDGMENTS This research was supported by the California Department of Water Resources (CDWR), State of California. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the State of California. The authors appreciate the suggestions and assistance of Dr. Jennie Watson-Lamprey with portions of the analyses. The above support and contributions are greatly appreciated.


321

REFERENCES Abrahamson, A. N., and Silva, W. J., 1997. Empirical response spectral acceleration relations for shallow crustal earthquakes, Seismol. Res. Lett. 68, 94–127. Arulnathan, R., 2000. Dynamic Properties and Site Response of Organic Soils, Ph. D. thesis, University of California, Davis. Ashford, S. A., and Sitar, N., 2002. Simplified method for evaluating seismic stability of steep slopes, J. Geotech. Geoenviron. Eng. 128, 119–128. Baker, J. W., and Cornell, C. A., 2006. Correlation of response spectral values for multicomponent ground motions, Bull. Seismol. Soc. Am. 96, 215–227. Baturay, M. B., and Stewart, J. P., 2003. Uncertainty and bias in ground-motion estimates from ground response analyses, Bull. Seismol. Soc. Am. 93, 2025–2042. Bazzurro, P., and Cornell, C. A., 2002. Vector-valued probabilistic seismic hazard analysis, Seventh U. S. National Conference on Earthquake Engineering (7NCEE), U. S. National Conference on Earthquake Engineering, proceedings: Urban Earthquake Risk, 1313–1322. ––—, 2004. Ground motion amplification in nonlinear soil sites with uncertain properties, Bull. Seismol. Soc. Am. 94, 2090–2109. California, 1992. Seismic Stability Evaluation of the Sacramento-San Joaquin Delta Levees, Phase I Report: Preliminary Evaluations and Review of Previous Studies, Division of Design and Construction, California Department of Water Resources, 203 pp. Choi, Y., and Stewart, J. P., 2005. Nonlinear site amplification as function of 30 m shear wave velocity, Earthquake Spectra 21, 1–30. Cramer, C. H., 2003. Site-specific seismic-hazard analysis that is completely probabilistic, Bull. Seismol. Soc. Am. 93, 1841–1846. Electric Power Research Institute (EPRI), 1993. Guidelines for Site Specific Ground Motions, Rept. TR-102293, 1–5, Pala Alto, CA. Fiegel, G. L., 1995. Centrifugal and Analytical Modeling of Soft Soil Sites Subjected to Seismic Shaking, Ph. D. thesis, University of California, Davis. Idriss, I. M., 1991. Earthquake ground motions at soft soil sites, in Proceedings of the Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, 2265–2272. Johnson, R. A., and Wichern, D. W., 2002. Applied Multivariate Statistical Analysis, 5th edition, Prentice Hall, Inc., Upper Saddle River, NJ, 767 pp. Kishida, T., 2008. Seismic Site Effects for the Sacramento-San Joaquin Delta, Ph. D. thesis, University of California, Davis, in review. Kishida, T., Boulanger, R. W., Abrahamson, N. A., Wehling, T. M., and Driller, M. D., 2009a. Regression models for dynamic properties of highly organic soils, J. Geotech. Geoenviron. Eng. 135, 533–543. Kishida, T., Boulanger, R. W., Abrahamson, N. A., Driller, M. D., and Wehling, T. M., 2009b Seismic response of levees in the Sacramento-San Joaquin Delta, Earthquake Spectra, in press. Kramer, S. L., and Mayfield, R. T., 2007. Return period of soil liquefaction, J. Geotech. Geoenviron. Eng. 133, 802–813. Luco, N., and Cornell, C. A., 2007. Structure-specific scalar intensity measures for near-source and ordinary earthquake ground motions, Earthquake Spectra 23, 357–392.

322

KISHIDA ET AL.

Lund, J., Hanak, E., Fleenor, W., Howitt, R., Mount, J., and Moyle, P., 2007. Envisioning Futures for the Sacramento-San Joaquin Delta, Public Policy Institute of California, San Francisco, CA. McGuire, R. K., Silva, W. J., and Constantino, C., 2001. Technical Basis for Revision of Regulatory Guidance on Design Ground Motions: Hazard- and Risk-consistent Ground Motions Spectra Guidelines, NUREG/CR-6728, prepared for the U. S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, Division of Engineering Technology. National Earthquake Hazards Reduction Program (NEHRP), 2003. Recommended Provisions for Seismic Regulations for New Buildings and Other Structures with Accompanying Commentary, Building Seismic Safety Council for Federal Emergency Management Agency, Washington, D. C. Pacific Earthquake Engineering Research Center (PEER), 2005. Next Generation Attenuation (NGA) Strong Ground Motion Database, University of California, Berkeley, http://peer.berkeley.edu/nga/index.html. Phoon, K., and Kulhawy, F. H., 1999. Characterization of geotechnical variability, Can. Geotech. J. 36, 612–624. Rathje, E. M., and Bray, J. D., 2001. One- and two-dimensional seismic analysis of solid-waste landfills, Can. Geotech. J. 38, 850–862. Schnabel, P. B., Lysmer, J., and Seed, H. B., 1972. SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites, Report No. UCB/EERC-2/12, Earthquake Engineering Research Center, University of California, Berkeley, December. Stewart, J. P., and Kwok, A. O. L., 2008. Nonlinear seismic ground response analysis: code usage protocols and verification against vertical array data, Geotechnical Earthquake Engineering and Soil Dynamics 4, Geotechnical Special Publication No. 181, Zeng D., Manzari M. T., and Hiltunen D. R., editors, ASCE. URS, 2008. Delta Risk Management Strategy Phase 1, Risk Analysis Report (Draft 4), prepared by URS Corporation/Jack R. Benjamin and Associates, Inc., for California Department of Water Resources, July. U. S. Geological Survey (USGS), 1996. Fault Parameters used in USGS 1996 Seismic Hazard Maps, http://earthquake.usgs.gov/research/hazmaps/products_data/1996/faults.php. Vanmarcke, E. H., 1977. Probabilistic modeling of soil profiles, J. Geotech. Engrg. Div. 103, 1227–1246. Vucetic, M., and Dobry, R., 1991. Effect of soil plasticity on cyclic response, J. Geotech. Engrg. 117, 89–107.

(Received 5 March 2008; accepted 20 November 2008兲