Prediction of factor of safety of a slope with an advanced friction model

Abstract

Landslides and other mass movements are quite prevalent phenomena in hilly areas, and sometimes cause huge losses of both life and property [1]. To mitigate these natural calamities, a precise scientific study that can predict the slope failures is required. Prediction of the mechanical stability of slopes both man made as well as natural is a tedious task after considering the complexity involved in the physical behaviour of the slope forming material as well as their intricate failure mechanisms [1–4]. Traditional approaches to predict stability of a slope are generally based on evaluation of a factor of safety through limit equilibrium analysis (LEA) [1–4]. The factor of safety (FOS) of a slope is defined as the ratio of shear strength to driving stress generally due to gravitational force along the failure plane [1–3]. Physically, FOSo1 signifies the slope to be unstable; however it is stable if FOS41 [1]. The limitation of the LEA is that the analysis is carried out with a single fixed value of shear strength of solids such as rocks and soils, while ignoring the sliding rate dependent failure strength. Experiments on rocks have shown that failure strength (also known as frictional strength) does depend on sliding velocity and time of stationary contact (also known as waiting time) of the sliding interface [5–7]. Moreover, based on these experimental observations, an advanced friction model has been proposed which is known as the rate and state dependent friction (RSF) model. The RSF model is basically a modified form of the Mohr–Coulomb failure criterion [13]. It is to be noted that the RSF model has been extremely successful in recent times for predicting the frictional behaviour of hard and rough solids such as rocks, soils, hard polymers etc. [8–11]. As a result, the RSF model has found widespread applications in the study of mechanics of earthquakes and faulting [10].