Uncertainty Analysis Of Rock Failure Behaviour Using Probabilistic Collocation Method

With the development of mineral exploration and exploitation, energy exploitation, transportation engineering, nuclear waste deep geological disposal, urban construction and underground space, rock mechanics problems are more and more complex. As a result, people are facing many unprecedented problems and challenges in the solution of rock mechanical problems. It’s an urgent issue to develop and improve rock mechanics theory and method to adapt the engineering practices.The heterogeneity of rock material is one of the important reasons to make the rock mechanics problem complex. The parameters of rock mechanics show high heterogeneity and anisotropy in space, which directly affects the mechanical behaviors of rock material and leads to the mechanical behaviors of materials uncertainty. Moreover, the traditional deterministic mechanical model we used doesn’t accord with practice obviously. So the research of uncertainty problem has important practical and theoretical value. We need to introduce the theory and method of random field to characterize the complex mechanical behavior of rocks. Therefore, combining analysis method of stochastic system with geotechnical engineering numerical simulation, fully considering the variability of mechanical parameters of rock in the spatial domain, and establishing a suitable stochastic analysis theory and corresponding calculation method for geotechnical engineering, has become the objective need and development trend.In this paper, probability collocation method based on the Karhunen-Loeve expansion is introduced. It’s applied to analyze the random problem with a combination of the elastic-plastic cellular automaton (EPCA) numerical system. The input random fields are represented via the Karhunen-Loeve expansion, and random output fields are expressed by polynomial chaos expansions. We use probabilistic collocation method to generate collocations. Therefore, the problem is transfered into the deterministic problem on each collocation point. Then the deterministic equations are solved. Finally the output domain statistical results are obtained. Through a series of elastic, elasto-plastic and elasto-brittle-plastic calculations of rocks under mechanical loading, we get the spatial distribution of mean and standard deviation. Compared with the Monte Carlo method, probabilistic collocation method has a lot of advantages. It only requires fewer collocations and can obtain very high accuracy. And this also greatly reduces the computation and improves the computational efficiency.