Influence of cross correlation between soil parameters on probability of failure of simple cohesive and c-ϕ slopes

Abstract

This paper focuses on the calculation of probability of failure of simple unreinforced slopes and the influence of the magnitude of cross correlation between soil parameters on numerical outcomes. A general closed-form solution for cohesive slopes with cross correlation between cohesion and unit weight was investigated and results compared with cases without cross correlation. Negative cross correlations between cohesion and friction angle and positive cross correlations between cohesion and unit weight, and friction angle and unit weight were considered in the current study. The factors of safety and probabilities of failure for the slopes with uncorrelated soil properties were obtained using probabilistic slope stability design charts previously reported by the writers. Results for cohesive soil slopes and positive cross correlation between cohesion and unit weight are shown to decrease probability of failure. Probability of failure also decreased for increasing negative cross correlation between cohesion and friction angle, and increasing positive correlation between cohesion and unit weight, and friction angle and unit weight. Probabilistic slope stability design charts presented by the writers in an earlier publication are extended to include cohesive-frictional (c-[Formula: see text]) soil slopes with and without cross correlation between soil input parameters. An important outcome of the work presented here is that cross correlation between random values of soil properties can reduce the probability of failure for simple slope cases. Hence, previous probabilistic design charts by the writers for simple soil slopes with uncorrelated soil properties are conservative (safe) for design. This study also provides one explanation why slope stability analyses using uncorrelated soil properties can predict unreasonably high probabilities of failure when conventional estimates of factor of safety suggest a stable slope.

A soft computing approach to tunnel face stability in a probabilistic framework

“…The dataset shows a negative correlation between the cohesion and friction angle of q cu ¼ À0:21 (Fig. 6), which complies with the values found in the literature [27]. The positive and negative correlations-shown by the soil cover and tunnel diameter on the one hand, and by dry soil unit weight, cohesion and friction angle on the other handwith the effective support pressure are also supported by previous findings [7,58].…”

Effects of soil heterogeneity on susceptibility of shallow landslides

“…Further investigation of the number of ellipsoids sufficient to cover a region can be done to improve the efficiency of the model. Another limitation is that the 3DPLS model currently does not support cross-correlation among model parameters which may be important in certain situations as shown in Javankhoshdel and Bathurst (2016).…”

Influence of Both Soil Properties and Geometric Parameters on Failure Mechanisms and Stability of Two‐Layer Undrained Slopes

“…Under the static loading condition, for FS � 1, the stability number N c in equation ( 2) expresses the combination of c u , c, and DH, which warrants the slope to be at critical failure (limit equilibrium). When the slope's β and DH of the soil are given, then N c can be calculated readily from Taylor's stability charts [29][30][31][32][33]. However, most of Taylor's original charts are for the homogeneous slopes, and these charts do not provide a common and easy means to assess the critical sliding surface related to a slope stability issue.…”