Geotechnical variability is a complex attribute that results from many disparate sources of uncertainties. The three primary sources of geotechnical uncertainties are inherent variability, measurement error, and transformation uncertainty. Inherent soil variability is modeled as a random field, which can be described concisely by the coefficient of variation (COV) and scale of fluctuation. Measurement error is extracted from field measurements using a simple additive probabilistic model or is determined directly from comparative laboratory testing programs. Based on an extensive literature review, the COV of inherent variability, scale of fluctuation, and COV of measurement error are evaluated in detail, along with the general soil type and the approximate range of mean value for which the COVs are applicable. Transformation uncertainty and overall property uncertainty are quantified in a companion paper.Key words: inherent soil variability, measurement error, coefficient of variation, scale of fluctuation, geotechnical variability.

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SUMMARYA random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coe cients. Karhunen-Loeve (K-L) series expansion is based on the eigen-decomposition of the covariance function. Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper. The study is based on ÿve common covariance models. The convergence and accuracy of the K-L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process. It is shown that the factors a ecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the covariance function (namely, analytical or numerical). Comparison with the established and commonly used spectral representation method is made. K-L expansion has an edge over the spectral method for highly correlated processes. For long stationary processes, the spectral method is generally more e cient as the K-L expansion method requires substantial computational e ort to solve the integral equation. The main advantage of the K-L expansion method is that it can be easily generalized to simulate non-stationary processes with little additional e ort.

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Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability P f ,s of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of P f ,s are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliability analysis is applied to two slope examples. Results show that the proposed approach estimates P f ,s properly considering the spatial variability of soils and improves the computational efficiency significantly at small probability levels. With the aid of the improved computational efficiency offered by the approach, a series of sensitivity studies are carried out to explore the effects of spatial variability in both the horizontal and vertical directions and the cross-correlation between uncertain soil parameters. It is found that both the spatial variability and cross-correlation affect P f ,s significantly. The proposed approach allows more insights into such effects from a system analysis point of view.

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