Distribution Property of Shear Strength Parameters of Q2 and Q3 Loess in Northwest China and Its Application in Reliability Analysis of Natural and Filled Slopes

Abstract

Geological materials have randomness in nature. Statistical analysis can help revealing the variation pattern of the material parameters and the reliability of the slope. In this paper, the probability distribution and variability of shear strength parameters of typical Q2 and Q3 loess in Northwest China were statistically analysed using the collected geological survey data in Yan`an, Shaanxi Province. Resulting probability properties were applied to the reliability analysis for the natural and fill slope in loess area using the Monte Carlo Method. Finally, an optimization analysis was carried out for the fill slope in the background engineering project. Research results show that normal distribution and lognormal distribution can be used to describe the statistical properties of c and φ of Q2 and Q3 loess. Variance of c is large while the variability of φ is relatively small. The influence of the variability of φ on the reliability index of loess natural slope is generally larger than that of c. On the contrary, influence of the variability of c on the reliability index of the fill slope is generally greater than that of φ, which is related to the structural and uniformity of the soil. Finally, relation between slope height and minimum gradient coefficient is linear when the failure probability of fill slope is less than 10%. Results in this study can be used as a reference for the slope design and construction for the cut and fill engineering in loess area.