Spatial variability of liquefaction potential in regional mapping using CPT and SPT data

Cone penetration test (CPT) and standard penetration test (SPT) are widely used for the site specific evaluation of liquefaction potential and are getting increased use in the regional mapping of liquefaction hazard. This paper compares CPT and SPT-based liquefaction potential characterizations of regional geologic units using the liquefaction potential index (LPI) across the East Bay of the San Francisco Bay, California, USA and examines the statistical and spatial variability of LPI across and within geologic units. Overall, CPT-based LPI characterizations result in higher hazard than those derived from the SPT. This bias may result from either mis-classifications of soil type in the CPT or a bias in the CPT simplified procedure for liquefaction potential. Regional mapping based on cumulative distribution of LPI values show different results depending on which dataset is used. For both SPT and CPT-based characterizations, the geologic units in the area have broad LPI distributions that overlap between units and are not distinct from the population as a whole. Regional liquefaction classifications should therefore give a distribution, rather than a single hazard rating that does not provide for variability within the area. The CPT-based LPI values have a higher degree of spatial correlation and a lower variance over a greater distance than those estimated from SPTs. As a result, geostatistical interpolation can provide a detailed map of LPI when densely sampled CPT data are available. The statistical distribution of LPI within specific geologic units and interpolated maps of LPI can be used to understand the spatial variability of liquefaction potential.     

System identification estimation of soil properties at the Lotung site

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input–output data sets) using both time-invariant and time-variant parametric modeling methods (system identification). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratios were calculated for 8 events with M_L ranging from 4.5 to 7.0. Shear stiffness ranged between 0.5 and 6 MN/m, inversely proportional to PGA. The equivalent viscous damping ratio varied from 2 to 30% of critical damping, proportional to PGA. Degradation of soil behavior, while less pronounced with increasing depth, consistently occurs above a peak input acceleration of 0.07 g. Although “non-linear” behavior is evident above 0.17 g, Event 7 (0.21 g) is accurately predicted using a linear constant parameter model estimated from the smaller Event 8 aftershock ground motions.     

Spatial correlation of shear-wave velocity in the San Francisco Bay Area sediments

Ground motions recorded within sedimentary basins are variable over short distances. One important cause of the variability is that local soil properties are variable at all scales. Regional hazard maps developed for predicting site effects are generally derived from maps of surficial geology; however, recent studies have shown that mapped geologic units do not correlate well with the average shear-wave velocity of the upper 30 m, V_s(30). We model the horizontal variability of near-surface soil shear-wave velocity in the San Francisco Bay Area to estimate values in unsampled locations in order to account for site effects in a continuous manner. Previous geostatistical studies of soil properties have shown horizontal correlations at the scale of meters to tens of meters while the vertical correlations are on the order of centimeters. In this paper we analyze shear-wave velocity data over regional distances and find that surface shear-wave velocity is correlated at horizontal distances up to 4 km based on data from seismic cone penetration tests and the spectral analysis of surface waves. We propose a method to map site effects by using geostatistical methods based on the shear-wave velocity correlation structure within a sedimentary basin. If used in conjunction with densely spaced shear-wave velocity profiles in regions of high seismic risk, geostatistical methods can produce reliable continuous maps of site effects.     

Consistency of dynamic site response at Port Island

System identification (SI) methods are used to determine empirical Green's functions (EGF) for soil intervals at the Port Island Site in Kobe, Japan and in shake table model tests performed by the Port and Harbor Research Institute (PHRI) to emulate the site during the 17 January 1995 Hyogo‐ken Nanbu earthquake. The model form for the EGFs is a parametric auto‐regressive moving average (ARMA) model mapping the ground motions recorded at the base of a soil interval to the top of that interval, hence capturing the effect of the soil on the through‐passing wave. The consistency of site response at Port Island before, during, and after the mainshock is examined by application of small motion foreshock EGFs to incoming ground motions over these time intervals. The prediction errors (or misfits) for the foreshocks, the mainshock, and the aftershocks, are assessed to determine the extent of altered soil response as a result of liquefaction of the ground during the mainshock. In addition, the consistency of soil response between field and model test is verified by application of EGFs calculated from the shake table test to the 17 January input data. The prediction error is then used to assess the consistency of behaviour between the two cases. By using EGFs developed for small‐amplitude foreshock ground motions, ground motions were predicted for all intervals of the vertical array except those that liquefied with small error. Analysis of the post‐liquefied ground conditions implies that the site response gradually returns to a pre‐earthquake state. Site behaviour is found to be consistent between foreshocks and the mainshock for the native ground (below 16 m in the field) with a normalized mean square error (NMSE) of 0.080 and a peak ground acceleration (PGA) of 0.5g. When the soil actually liquefies (change of state), recursive models are needed to track the variable soil behaviour for the remainder of the shaking. The recursive models are shown to demonstrate consistency between the shake table tests and the field with a NMSE of 0.102 for the 16 m to surface interval that liquefied. The aftershock ground response was not modelled well with the foreshock EGF immediately after the mainshock (NMSE ranging from 0.37 to 0.92). One month after the mainshock, the prediction error from the foreshock modeled was back to the foreshock error level. Copyright © 2001 John Wiley Sons, Ltd.     

Sampling Bias and Class Imbalance in Maximum-likelihood Logistic Regression

Logistic regression is a widely used statistical method to relate a binary response variable to a set of explanatory variables and maximum likelihood is the most commonly used method for parameter estimation. A maximum-likelihood logistic regression (MLLR) model predicts the probability of the event from binary data defining the event. Currently, MLLR models are used in a myriad of fields including geosciences, natural hazard evaluation, medical diagnosis, homeland security, finance, and many others. In such applications, the empirical sample data often exhibit class imbalance, where one class is represented by a large number of events while the other is represented by only a few. In addition, the data also exhibit sampling bias, which occurs when there is a difference between the class distribution in the sample compared to the actual class distribution in the population. Previous studies have evaluated how class imbalance and sampling bias affect the predictive capability of asymptotic classification algorithms such as MLLR, yet no definitive conclusions have been reached.     

Three-dimensional liquefaction potential analysis using geostatistical interpolation

We applied three-dimensional geostatistical interpolation to evaluate the extent of liquefiable materials at two sites that liquefied during the 1994 Northridge Earthquake. The sites were the Balboa Blvd site and the Wynne Ave. site located in the alluvial San Fernando Valley. The estimated peak ground accelerations at the sites are 0.84 g (Balboa Blvd) and 0.51 g (Wynne Ave.). These sites were chosen because surface effects due to liquefaction were not predicted using available techniques based on thickness and depth of liquefiable layers (Ishihara [Ishihara K. Stability of natural deposits during earthquakes. Proceedings of the 11th international conference on soil mechanics and foundation engineering, vol. 1. Rotterdam, The Netherlands: A.A. Balkema; 1985. p. 321–76.]) and the Liquefaction Potential Index (Iwasaki et al. [Iwasaki T, Tatsuoka F, Tokida K, Yasuda S. A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. In: Proceedings of the second international conference on microzonation, San Francisco; 1978. p. 885–96.]). During the earthquake, both sites experienced surface effects including ground cracking and extension as a result of liquefaction. Foundations and buried utilities were damaged at both sites. The sites were investigated after the event by researchers with the United States Geologic Survey using standard penetration tests (SPT) and cone penetration tests. In this paper, liquefaction potential was estimated for each soil sample using results from SPTs according to the updated Seed and Idriss simplified procedure. The probability of liquefaction was estimated by applying an indicator transform to the results of the liquefaction potential calculation. We compared our results to detailed geologic mapping of the sites performed by other researchers. Using geostatistical interpolation to estimate the probability of liquefaction is a useful supplement to geologic evaluation of liquefaction potential. The geostatistical analysis provides an estimate of the continuous volume of liquefiable soil along with an assessment of confidence in an interpolation. The probability of liquefaction volumes compare well with those predicted using geologic interpretations.