Promotion Hong Shen


Non-Deterministic Analysis of Slope Stability based on Numerical Simulation


  • Prof. Dr.-Ing. Herbert Klapperich
  • Prof. Dr. rer. nat. habil. Rafig Azzam (RWTH Aachen)
  • Prof. Dr.-Ing. Wei Wu (Universität für Bodenkultur Wien)


In geotechnical engineering, the uncertainties such as the variability and uncertainty inherent in the geotechnical property have caught more and more attentions from researchers and engineers. They have found that a single "Factor of Safety" calculated by traditional deterministic analyses methods can not represent the slope stability exactly. Recently in order to provide a more rational mathematical framework to incorporate different types of uncertainties in the slope stability estimation, reliability analyses and non-deterministic methods, which include probabilistic and non probabilistic (imprecise methods) methods, have been applied widely. In short, the slope non-deterministic analysis is to combine the probabilistic analysis or non probabilistic analysis with the deterministic slope stability analysis. It cannot be regarded as a completely new slope stability analysis method, but just an extension of the slope deterministic analysis. The slope failure probability calculated by slope non-deterministic analysis is a kind of complement of safety factor. Therefore, the accuracy of non deterministic analysis is not only depended on a suitable probabilistic or non probabilistic analysis method selected, but also on a more rigorous deterministic analysis method or geological model adopted.

In this thesis, reliability concepts have been reviewed first, and some typical non-deterministic methods, including Monte Carlo Simulation (MCS), First Order Reliability Method (FORM), Point Estimate Method (PEM) and Random Set Theory (RSM), have been described and successfully applied to the slope stability analysis based on a numerical simulation method-Strength Reduction Method (SRM). All of the processes have been performed in a commercial finite difference code FLAC and a distinct element code UDEC.

First of all, as the fundamental of slope reliability analysis, the deterministic numerical simulation method has been improved. This method has a higher accuracy than the conventional limit equilibrium methods, because of the reason that the constitutive relationship of soil is considered, and fewer assumptions on boundary conditions of slope model are necessary. However, the construction of slope numerical models, particularly for the large and complicate models always is very difficult and it becomes an obstacle for application of numerical simulation method. In this study, the excellent spatial analysis function of Geographic Information System (GIS) technique has been introduced to help numerical modeling of the slope. In the process of modeling, the topographic map of slope has been gridded by GIS software, and then the GIS data has been transformed into FLAC smoothly through the programming of the built-in language FISH. At last, the feasibility and high efficiency of this technique has been illustrated through a case study-Xuecheng slope, and both 2D and 3D models have been investigated.

Subsequently, three most widely used probabilistic analysis methods, Monte Carlo Simulation, First Order Reliability Method and Point Estimate Method applied with strength reduction method have been studied. Monte Carlo Simulation which needs to repeat thousands of deterministic analysis is the most accurate probabilistic method. However it is too time consuming for practical applications, especially when it is combined with numerical simulation method. For reducing the computation effort, a simplified Monte Carlo Simulation-Strength Reduction Method (MCS-SRM) has been developed in this study. This method has estimated the probability failure of slope and calculated the mean value of safety factor by the mean of soil parameters first, and then calculated the variance of safety factor and the reliability of slope according to the assumed probability density function of safety factor. Case studies have confirmed that this method can reduce about 4/5 of time compared with traditional MCS-SRM, and remain almost the same accuracy.

First Order Reliability Method is an approximate method which is based on the Taylor's series expansion of performance function. The closed form solution of the partial derivatives of the performance function is necessary to calculate the mean and standard deviation of safety factor. However, there is no explicit performance function in numerical simulation method, so the derivative expressions have been replaced with equivalent difference quotients to solve the differential quotients approximately in this study. Point Estimate Method is also an approximate method involved even fewer amount of calculations than FORM. In the present study, it has been integrated with Strength Reduction Method directly.

Another important observation referred to the correlation between the soil parameters cohesion and friction angle. Some authors have found a negative correlation between cohesion and friction angle of soil on the basis of experimental data. However, few slope probabilistic studies considered this negative correlation between soil parameters in literatures. In this thesis, the influence of this correlation on slope probability of failure has been investigated based on numerical simulation method. It was found that a negative correlation considered in the cohesion and friction angle of soil could reduce the variability of the safety factor and the failure probability of slope, thus increase the reliability of results.

Except the soil properties are correlated between each other, they are always auto-correlated in space, which is described as the spatial variability. As knowledge on this character is rather limited in literature, it is ignored in geotechnical engineering by most researchers and engineers. In this thesis, the random field method has been introduced into the slope numerical simulation to simulate the spatial variability structure, and a numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation was presented. The soil property such as the cohesion and friction angle was discretized to continuous random fields based on local averaging method. In the case study, both of the stationary and non-stationary random fields have been investigated, and the influence of spatial variability and averaging domain on the convergence of numerical simulation and probability of failure was studied.

In rock medium, the structure faces have very important influence on the slope stability, and the rock material can be modeled as the combination of rigid or deformable blocks with joints in distinct element method. Therefore, much more input parameters like strength of joints are required to input the rock slope model, which increase the uncertainty of the results of numerical model. Furthermore, because of the limitations of the current laboratory and in-site testes, there is always lack of exact values of geotechnical parameters from rock material, even the probability distribution of these variables. Most of time, engineers can only estimate the interval of these variables from the limit testes or the expertise's experience. In this study, to assess the reliability of the rock slope, a Random Set Distinct Element Method (RS-DEM) has been developed through coupling of Random Set Theory and Distinct Element Method, and applied in a rock slope in Sichuan province China.


von links nach rechts: Prof. Dr. Herbert Klapperich, Hong Shen mit Frau Huixian Yang und Kind Frei Shen, Oberbürgermeister Bernd-Erwin Schramm mit Gattin