Probabilistic Framework for Liquefaction Potential by Shear Wave Velocity

This paper presents a new empirical equation for assessing liquefaction resistance of soils based on shear wave velocity Vs and the results of probabilistic analyses based on this empirical equation. A database consisting of in situ shear wave velocity measurements and field observations of liquefaction∕nonliquefaction in historic earthquakes is analyzed. This database is first used to train and test an artificial neural network to predict the occurrence of liquefaction∕nonliquefaction based on soil and seismic load parameters. The successfully trained and tested neural network is then used to establish the empirical equation. The concept of clean soil equivalence is introduced and used in the development of the empirical equation. The established empirical equation represents a deterministic method for assessing liquefaction resistance of a soil. Based on this newly developed deterministic method, probabilistic analyses of the cases in the database are conducted using the logistic regression approach and the mapping function approach. The results provide a basis for risk-based evaluation of liquefaction evaluation.     

First-Order Reliability Method for Probabilistic Liquefaction Triggering Analysis Using CPT

The potential for liquefaction triggering of a soil under a given seismic loading is measured herein by probability of liquefaction. The first order reliability method (FORM) is used to calculate reliability index, from which the probability of liquefaction is obtained. This approach requires the knowledge of parameter and model uncertainties; the latter is the focus of this paper. An empirical model for determining liquefaction resistance based on cone penetration test (CPT) is established through “neural network learning” of case histories. This resistance model along with a reference seismic loading model forms a performance function or limit state for liquefaction triggering analysis. Within the framework of the FORM, the uncertainty of this limit state model is characterized through an extensive series of sensitivity studies using Bayesian mapping functions that have been calibrated with a set of quality case histories. In addition, a deterministic model for assessing liquefaction potential in terms of factor of safety is presented, and the probability-safety factor mapping functions for estimating the probability of liquefaction for a given factor of safety in the absence of the knowledge of parameter uncertainty are also established. Examples are presented to illustrate the proposed methods.     

CPT-Based Probabilistic and Deterministic Assessment of In Situ Seismic Soil Liquefaction Potential

This paper presents a complete methodology for both probabilistic and deterministic assessment of seismic soil liquefaction triggering potential based on the cone penetration test (CPT). A comprehensive worldwide set of CPT-based liquefaction field case histories were compiled and back analyzed, and the data then used to develop probabilistic triggering correlations. Issues investigated in this study include improved normalization of CPT resistance measurements for the influence of effective overburden stress, and adjustment to CPT tip resistance for the potential influence of “thin” liquefiable layers. The effects of soil type and soil character (i.e., “fines” adjustment) for the new correlations are based on a combination of CPT tip and sleeve resistance. To quantify probability for performance-based engineering applications, Bayesian “regression” methods were used, and the uncertainties of all variables comprising both the seismic demand and the liquefaction resistance were estimated and included in the analysis. The resulting correlations were developed using a Bayesian framework and are presented in both probabilistic and deterministic formats. The results are compared to previous probabilistic and deterministic correlations.     

Validation and Application of Empirical Liquefaction Models

Empirical liquefaction models (ELMs) are the standard approach for predicting the occurrence of soil liquefaction. These models are typically based on in situ index tests, such as the standard penetration test (SPT) and cone penetration test (CPT), and are broadly classified as deterministic and probabilistic models. No objective and quantitative comparison of these models have been published. Similarly, no rigorous procedure has been published for choosing the threshold required for probabilistic models. This paper provides (1) a quantitative comparison of the predictive performance of ELMs; (2) a reproducible method for choosing the threshold that is needed to apply the probabilistic ELMs; and (3) an alternative deterministic and probabilistic ELM based on the machine learning algorithm, known as support vector machine (SVM). Deterministic and probabilistic ELMs have been developed for SPT and CPT data. For deterministic ELMs, we compare the “simplified procedure,” the Bayesian updating method, and the SVM models for both SPT and CPT data. For probabilistic ELMs, we compare the Bayesian updating method with the SVM models. We compare these different approaches within a quantitative validation framework. This framework includes validation metrics developed within the statistics and artificial intelligence fields that are not common in the geotechnical literature. We incorporate estimated costs associated with risk as well as with risk mitigation. We conclude that (1) the best performing ELM depends on the associated costs; (2) the unique costs associated with an individual project directly determine the optimal threshold for the probabilistic ELMs; and (3) the more recent ELMs only marginally improve prediction accuracy; thus, efforts should focus on improving data collection.     

Logistic Regression Model for Evaluating Soil Liquefaction Probability Using CPT Data

A simple model for evaluating liquefaction probability using cone penetration test (CPT) data is developed based on logistic regression analyses of 396 case histories. The proposed model uses the normalized cone penetration resistance and soil behavior type index as input parameters; therefore, only CPT testing is necessary for evaluating the liquefaction probability of a site. The selection of the model parameters and the expression of equations are based on results of probability examinations and rigorous statistical analyses. Moreover, the derivation of the logistic regression model is presented in a system of equations. The incorporation of these procedures in developing the model not only fully satisfies the statistic requirements but also highlights the physical meanings of the model parameters. Comparisons of the proposed probability model with previously proposed deterministic and probabilistic approaches are performed to demonstrate the improvements. For practical purposes, the developed model is implemented to establish the relationship between the factor of safety against liquefaction and the probability of liquefaction.     

Reliability-Based Method for Assessing Liquefaction Potential of Soils

This paper describes a probabilistic method for assessing the liquefaction potential of sandy soils. The proposed probabilistic method is formulated based on the results of reliability analyses of 225 field records, observations of soil performance against liquefaction. The results of the present study show that a meaningful mapping between notional probability and an actual relative frequency measure of the occurrence of liquefaction can be obtained with the proposed method. Twenty case records from the 1989 Loma Prieta earthquake are further analyzed to demonstrate the proposed reliability-based method. The developed method has the potential of becoming a practical tool for engineers involved in the assessment of liquefaction potential.     

Accounting for Soil Aging When Assessing Liquefaction Potential

It has been recognized that liquefaction resistance of sand increases with age due to processes such as cementation at particle contacts and increasing frictional resistance resulting from particle rearrangement and interlocking. As such, the currently available empirical correlations derived from liquefaction of young Holocene sand deposits, and used to determine liquefaction resistance of sand deposits from in situ soil indices [standard penetration test (SPT), cone penetration test (CPT), shear wave velocity test (Vs)], are not applicable for old sand deposits. To overcome this limitation, a methodology was developed to account for the effect of aging on the liquefaction resistance of old sand deposits. The methodology is based upon the currently existing empirical boundary curves for Holocene age soils and utilizes correction factors presented in the literature that comprise the effect of aging on the in situ soil indices as well as on the field cyclic strength (CRR). This paper describes how to combine currently recorded SPT, CPT, and Vs values with corresponding CRR values derived for aged soil deposits to generate new empirical boundary curves for aged soils. The method is illustrated using existing geotechnical data from four sites in the South Carolina Coastal Plain (SCCP) where sand boils associated with prehistoric earthquakes have been found. These sites involve sand deposits that are 200,000?to?450,000?years in age. This work shows that accounting for aging of soils in the SCCP yields less conservative results regarding the current liquefaction potential than when age is not considered. The modified boundary curves indicate that old sand deposits are more resistant to liquefaction than indicated by the existing empirical curves and can be used to evaluate the liquefaction potential at a specific site directly from the current in situ properties of the soil.     

Discriminant Model for Evaluating Soil Liquefaction Potential Using Cone Penetration Test Data

Statistical analysis using a discriminant model is applied to 399 cone penetration test (CPT) data sets of both liquefaction and nonliquefaction cases, including 174 sets from the Chi-Chi earthquake in Taiwan and 225 sets of synthesized data. The discriminant model employed is a multivariate statistical method. In situ testing results of cone tip resistance qc and sleeve friction ratio Rf are adopted as the major parameters for analyses. A model for evaluating liquefaction potential using CPT-qc data is also established in this study, which allows calculated results to be compared with the empirical curves.     

Probabilistic Assessment of Stress Normalization for CPT Data

Currently available cone penetration test (CPT) stress normalization schemes exhibit no consensus on the estimation of the stress normalization component. Depending on which power law stress normalization exponent is used, very different interpretations may result in the analyses where normalized CPT data are used (e.g., CPT-based soil classification and seismic soil liquefaction initiation assessment). Within the confines of this paper, it is intended to clarify and resolve some of these differences, and to propose improved recommendations for CPT stress normalization. For this purpose, available stress normalization databases from theoretical, numerical, and field data analyses approaches were compiled. For the soil types, and stress conditions where compiled database is not conclusive, additional finite element simulations have been performed. The resulting relationship not only eliminates several sources of bias intrinsic to previous, similar correlations, and provides greatly reduced overall uncertainty and variance, it also helps to establish a consensus to the stress normalization issue that have long been difficult and controversial. Key elements in the development of these new correlations are: (1) accumulation of a significantly expanded database of analytical/numerical CPT simulation results, as well as field and chamber test data from homogeneous soil layers; (2) use of improved knowledge and understanding of factors affecting CPT and stress normalization; and (3) use of high-order probabilistic tools (Bayesian updating).     

Mapping Liquefaction Potential Considering Spatial Correlations of CPT Measurements

The past studies of liquefaction phenomena during earthquakes have contributed to the development of simplified methods employing field test data to assess the liquefaction potential. Since the field data are limited by exploration cost, it is of interest to obtain valuable and meaningful distribution of liquefaction potential of an area from the limited data. This study proposes a method for assessing liquefaction potential over an extensive area according to the random field concept. The spatial structures of soil properties are estimated from the available cone penetration test (CPT) measurements. The soil properties at unsampled locations are simulated using Monte Carlo simulation. The reliability against liquefaction at every location within the study area is evaluated to map the liquefaction potential. The comparison between simulated distributions of liquefaction potential and observed liquefaction phenomena is discussed. The spatial correlation of soil property provides more information than the traditional approach that solely uses the field test data. The influences of CPT data, penetration locations, and spatial structures of soil properties on the mapping results of liquefaction potential are also discussed.     

Use of Artificial Neural Networks in the Prediction of Liquefaction Resistance of Sands

A backpropagation artificial neural network (ANN) model has been developed to predict the liquefaction cyclic resistance ratio (CRR) of sands using data from several laboratory studies involving undrained cyclic triaxial and cyclic simple shear testing. The model was verified using data that was not used for training as well as a set of independent data available from laboratory cyclic shear tests on another soil. The observed agreement between the predictions and the measured CRR values indicate that the model is capable of effectively capturing the liquefaction resistance of a number of sands under varying initial conditions. The predicted CRR values are mostly sensitive to the variations in relative density thus confirming the ability of the model to mimic the dominant dependence of liquefaction susceptibility on soil density already known from field and experimental observations. Although it is common to use mechanics-based approaches to understand fundamental soil response, the results clearly demonstrate that non-mechanistic ANN modeling also has a strong potential in the prediction of complex phenomena such as liquefaction resistance.     

Neural Network Embedded Monte Carlo Approach for Water Quality Modeling under Input Information Uncertainty

This paper proposes a neural network embedded Monte Carlo (NNMC) approach to account for uncertainty in water quality modeling. The framework of the proposed method has three major parts: a numerical water quality model, a neural network technique, and Monte Carlo simulation. The numerical model is used to generate desirable output for training and testing sets, and the neural network is used as a universal functional mapping tool to approximate the input-output response of the numerical model. The Monte Carlo simulation then uses the neural network to generate numerical realizations based on a probabilistic distribution of parameters, thus obtaining a probabilistic distribution of the simulated state variables. By embedding a neural network into the conventional Monte Carlo simulation, the proposed approach significantly improves upon the conventional method in computational efficiency. The proposed approach has been applied to uncertainty and risk analyses of a phosphorus model for Triadelphia Reservoir in Maryland. The results of this research show that the NNMC approach has potential for efficient uncertainty analysis of water quality modeling.     

Evaluation of Liquefaction Using Disturbed State and Energy Approaches

The disturbed state concept (DSC) and the dissipated energy approach can provide simplified, fundamental, and mechanistic methods for the identification of the initiation and growth of liquefaction in saturated soils under cyclic and earthquake loading. Both approaches are developed and used for the analysis of liquefaction in the soil deposits at Port Island, Kobe, Japan, during the Hyogo-ken Nanbu earthquake. They are also used to analyze liquefaction of two sands during laboratory cyclic tests using torsional and multiaxial devices. It is shown that the DSC and energy criteria can lead to improved understanding of the mechanism of liquefaction, and to rational and simplified procedures compared to those based on empirical and index properties. Furthermore, the DSC possesses certain advantages over the energy approaches, particularly in terms of its implementation in computer (finite-element) programs for dynamic and liquefaction analysis.     

Prediction of Soil Composition from CPT Data Using General Regression Neural Network

Soil type is typically inferred from the information collected during a cone penetration test (CPT) using one of the many available soil classification methods. In this study, a general regression neural network (GRNN) was developed for predicting soil composition from CPT data. Measured values of cone resistance and sleeve friction obtained from CPT soundings, together with grain-size distribution results of soil samples retrieved from adjacent standard penetration test boreholes, were used to train and test the network. The trained GRNN model was tested by presenting it with new, previously unseen CPT data, and the model predictions were compared with the reference particle-size distribution and the results of two existing CPT soil classification methods. The profiles of soil composition estimated by the GRNN generally compare very well with the actual grain-size distribution profiles, and overall the neural network had an 86% success rate at classifying soils as coarse grained or fine grained.     

Liquefaction Resistance of Clean and Nonplastic Silty Sands Based on Cone Penetration Resistance

Liquefaction of granular soil deposits is one of the major causes of loss resulting from earthquakes. The accuracy in the assessment of the likelihood of liquefaction at a site affects the safety and economy of the design. In this paper, curves of cyclic resistance ratio (CRR) versus cone penetration test (CPT) stress-normalized cone resistance qc1 are developed from a combination of analysis and laboratory testing. The approach consists of two steps: (1) determination of the CRR as a function of relative density from cyclic triaxial tests performed on samples isotropically consolidated to 100 kPa; and (2) estimation of the stress-normalized cone resistance qc1 for the relative densities at which the soil liquefaction tests were performed. A well-tested penetration resistance analysis based on cavity expansion analysis was used to calculate qc1 for the various soil densities. A set of 64 cyclic triaxial tests were performed on specimens of Ottawa sand with nonplastic silt content in the range of 0–15% by weight, and relative densities from loose to dense for each gradation, to establish the relationship of the CRR to the soil state and fines content. The resulting (CRR)7.5-qc1 relationship for clean sand is consistent with widely accepted empirical relationships. The (CRR)7.5-qc1 relationships for the silty sands depend on the relative effect of silt content on the CRR and qc1. It is shown that the cone resistance increases at a higher rate with increasing silt content than does liquefaction resistance, shifting the (CRR)7.5-qc1 curves to the right. The (CRR)7.5-qc1 curves proposed for both clean and silty sands are consistent with field observations.     

Liquefaction Potential Index: Field Assessment

Cone penetration test (CPT) soundings at historic liquefaction sites in California were used to evaluate the predictive capability of the liquefaction potential index (LPI), which was defined by Iwasaki et al. in 1978. LPI combines depth, thickness, and factor of safety of liquefiable material inferred from a CPT sounding into a single parameter. LPI data from the Monterey Bay region indicate that the probability of surface manifestations of liquefaction is 58 and 93%, respectively, when LPI equals or exceeds 5 and 15. LPI values also generally correlate with surface effects of liquefaction: Decreasing from a median of 12 for soundings in lateral spreads to 0 for soundings where no surface effects were reported. The index is particularly promising for probabilistic liquefaction hazard mapping where it may be a useful parameter for characterizing the liquefaction potential of geologic units.     

Database Assessment of CPT-Based Design Methods for Axial Capacity of Driven Piles in Siliceous Sands

Numerous cone penetration test (CPT)-based methods exist for calculation of the axial pile capacity in sands, but no clear guidance is presently available to assist designers in the selection of the most appropriate method. To assist in this regard, this paper examines the predictive performance of a range of pile design methods against a newly compiled database of static load tests on driven piles in siliceous sands with adjacent CPT profiles. Seven driven pile design methods are considered, including the conventional American Petroleum Institute (API) approach, simplified CPT alpha methods, and four new CPT-based methods, which are now presented in the commentary of the 22nd edition of the API recommendations. Mean and standard deviation database statistics for the design methods are presented for the entire 77 pile database, as well as for smaller subset databases separated by pile material (steel and concrete), end condition (open versus closed), and direction of loading (tension versus compression). Certain methods are seen to exhibit bias toward length, relative density, cone tip resistance, and pile end condition. Other methods do not exhibit any apparent bias (even though their formulations differ significantly) due to the limited size of the database subsets and the large number of factors known to influence pile capacity in sand. The database statistics for the best performing methods are substantially better than those for the API approach and the simplified alpha methods. Improved predictive reliability will emerge with an extension of the database and the inclusion of additional important controlling factors affecting capacity.     

Normalizing the CPT for Overburden Stress

Effective overburden stress can have a significant influence on cone penetration test (CPT) measurements. This influence can lead to an incorrect assessment of soil strength/resistance for such purposes as liquefaction triggering analysis. For an accurate measurement of tip and sleeve resistance, unbiased by overburden stress, it is essential to normalize these index measurements appropriately. Presented herein is a comprehensive study reviewing all aspects of CPT normalization. A result of this study is a variable normalization procedure for the CPT that is based on both empirical results and theoretical analysis. This paper presents these results in the form of an improved normalization scheme and discusses its application in practice.     

CPT-Based Probabilistic Soil Characterization and Classification

Due to lack of soil sampling during conventional cone penetration testing, it is necessary to characterize and classify soils based on tip and sleeve friction values as well as pore pressure induced during and after penetration. Currently available semiempirical methods exhibit a significant variability in the estimation of soil type. Within the confines of this paper it is attempted to present a new probabilistic cone penetration test (CPT)-based soil characterization and classification methodology, which addresses the uncertainties intrinsic to the problem. For this purpose, a database composed of normalized corrected cone tip resistance (qt,1,net), normalized friction ratio (FR), fines content (FC), liquid limit (LL), plasticity index (PI), and soil type based on the unified soil classification system was complied. Soil classification was performed by laboratory testing of the standard penetration test disturbed samples retrieved from the boreholes within mostly 2?m of each CPT hole. The resulting database was probabilistically assessed through Bayesian updating methodology allowing full and consistent representation of relevant uncertainties, including (1) model imperfection; (2) statistical uncertainty; and (3) inherent variability. As a conclusion, different sets of FC, LL, PI, and A-line boundary curves along with a new CPT-based, simplified soil classification scheme are proposed in the qt,1,net and FR domain. Probabilistic uses of the proposed models are illustrated through a set of illustrative examples.     

Estimation of Aeroelastic Parameters of Bridge Decks Using Neural Networks

A new method of estimating flutter derivatives using artificial neural networks is proposed. Unlike other computational fluid dynamics based numerical analyses, the proposed method estimates flutter derivatives utilizing previously measured experimental data. One of the advantages of the neural networks approach is that they can approximate a function of many dimensions. An efficient method has been developed to quantify the geometry of deck sections for neural network input. The output of the neural network is flutter derivatives. The flutter derivatives estimation network, which has been trained by the proposed methodology, is tested both for training sets and novel testing sets. The network shows reasonable performance for the novel sets, as well as outstanding performance for the training sets. Two variations of the proposed network are also presented, along with their estimation capability. The paper shows the potential of applying neural networks to wind force approximations.