ESTIMATION OF LIQUEFACTION FROM CASE HISTORIES

A critical parameter in the evaluation of the liquefaction of soils is the residual or liquefi ed shear strength. Liquefaction of granular soils can have extremely detrimental effects on the stability of soil slopes and deposits, and on structures founded on them. This liquefi ed shear strength determines the magnitude of the deformation that the soil will undergo once it has liquefi ed. Current procedures for estimating the liquefi ed shear strength are based on laboratory testing programs or from the back-analysis of case histories of liquefaction failures where in-situ test data were available. The case-histories approach is the procedure that is preferred in practice. However, it has several limitations including the very limited amount of data available, the signifi cant uncertainties involved in the back-calculation of the liquefi ed shear strengths, and the lack of consistent and rational methods in the use of the available data. To address these current limitations, this paper proposes new probabilistic liquefi ed shear strength criteria for liquefi able soils from case histories. The paper presents probabilistic undrained residual or liquefi ed shear strength values of liquefi able soils as function of SPT blow count. The liquefi ed shear strengths were back-calculated using slope stability analysis of previous case histories of fl ow liquefaction failures. Probabilistic procedures, including the First-Order Reliability Method (FORM) and Monte Carlo Simulations (MCS) were used in combination with limit equilibrium methods to analyze case histories of fl ow failure presented in the deterministic companion paper. Depending on the post-failure geometry of the case history, either the simplifi ed infi nite slope stability analysis or the more general Spencer method of slices analysis was used in the back analysis. The Beta Probability Density Function was used to model the statistical distributions and uncertainties in the geotechnical parameters involved in the probabilistic analyses. For FORM, a Bayesian Mapping procedure is used where values of PF are computed from the probability density function of the reliability indices of fl ow failure. The logistic mapping function is obtained by relating the deterministic factor of safety <i>FS </i>to <i>PF </i>for the liquefi ed shear strength relationships. A parameter <i>C</i>1 was introduced to account for model uncertainty in the reliability calculations. Probabilistic <i>Su-LIQ </i>versus minimum (<i>N</i>1)60 criteria were presented for <i>PF </i>contours corresponding to 2 %, 16 %, and 50 %. It was shown that the <i>PF </i>= 50 % relationship is very close to the best fi t relations obtained from the deterministic analysis of the case histories. The probabilistic <i>Su-LIQ </i>versus minimum (<i>N</i>1)60 criteria provide a more rational procedure for estimating the postliquefaction stability of cohesionless soils deposits by providing estimates of the probability of failure in addition to traditional values of factor of safety. The probability of failure can account for the different uncertainties in the back calculation of the liquefi ed shear strength values from case histories, and the natural variability and uncertainties and properties of soil deposits