Investigation of model uncertainty for block stability analysis

Abstract

SUMMARYThe application of probabilistic design, such as FORM, is expanding rapidly in the design of geotechnical structures. The analytical solution proposed by Crawford and Bray for analyzing block stability can be used as a performance function to carry out probabilistic design. The solution benefits from considering both clamping forces and joint stiffness. However, imperfect assumptions and simplifications in the solution generate model uncertainties. The amount of model uncertainty must be considered in order to assess a reliable design. The purpose of this paper is to identify when the analytical solution is applicable and quantify the model uncertainty of the solution. The amount of model uncertainty for the analytical solution has been assessed for different conditions. The results show that at a shallow depth with a low value of in situ stress ratio (horizontal stress/vertical stress), the analytical solution predicts that the block is stable whereas DEM shows that the block is unstable. The results of the analyses indicate that in cases with low stress ratio, cases with high anisotropy of joint stiffness or the case of a semiapical angle close to the friction angle, the accuracy of the analytical solution is low. Neglecting key parameters, such as the absolute value of joint shear and normal stiffness, vertical in situ stress and its influence on joint relaxation generate model uncertainty in the analytical solution. The analyses show that by having more information about the key parameters, the model uncertainty factor could be identified more precisely.

GPR‐MCS model of reliability analysis of key blocks and its engineering application

“…There are many stability analysis methods of key block, such as stereographic projection diagram method, body proportion orthogyaphic projection method and key block theory proposed by Shi et al 1 . In order to effectively solve the stable reliability problem of key block, researchers have proposed various theories, modes and solutions in recent years 2–11 . Considering present research, the stability factor of key block without supporting measures can easily be solved by analytical solution.…”

A new analytical solution based on joint relaxation for analyzing symmetrical block stability

“…Kirsch's solution is applicable for circular sections, and the boundary element method (BEM) is available for other geometries to calculate the induced stress. Previous research has shown that the clamping forces from a continuum medium are higher than those from a discontinuous medium . The clamping forces from this stage can therefore not be used to analyze block stability directly but must be corrected in order to take joint relaxation into account.…”

“…The analytical solutions for estimating clamping forces available today are based on continuum mechanics and may overestimate the clamping forces. A comparison of results using the numerical discrete method and Crawford–Bray's analytical solution showed a significant difference in calculated block stability. One explanation could be that clamping forces in a discontinuous medium are generally lower due to stress relaxation of joints than those calculated using continuous mechanics .…”

“…A comparison of results using the numerical discrete method and Crawford-Bray's analytical solution [12] showed a significant difference in calculated block stability. One explanation could be that clamping forces in a discontinuous medium are generally lower due to stress relaxation of joints than those calculated using continuous mechanics [12,13].Crawford and Bray [2] assumed constant clamping forces when in reality clamping forces change from the initial state, due to excavation and block movements. Using a model that is closer to reality…”

Probabilistic analysis of a discrete element modelling of the runout behavior of the Jiweishan landslide

“…In such a case, the particle-particle contact micro-parameters of the PFC model of a landslide are often determined through a trial-and-error process. [4,28] Thus, the calibration of these micro-parameters is strongly affected by the experience of the engineer. The subjective nature in the selection of the micro-parameters (within PFC) could lead to the uncertainty in the simulated landslide runout behavior, especially in the situation where the physical meaning of these contact micro-parameters is not clear.…”