Markove Model For Rock Type Prediction And Optimization On The Location And Number Of Observation Points Based On Information Entropy

The type of tunnel surrounding rock is an important parameter for TBM tunnel engineering,which is frequently used to calculate the duration and cost.As a result,it is of much importance to predict the rock type of tunnel before the construction of tunnel engineering.However,due to the uncertainty of geology prediction,it is rather common that most engineering design projects will take conservative strategy and use the worst expectation as the base for calculation and design,which without any doubt will bring additional cost that is not necessary.A feasible method to predict the surrounding rock type ot tunnel is to transfer the certain class of surround rock type into uncertain probability by assuming that the whole tunnel is a stochastic process.Markov process is a famous and important stochastic process and put forward by Andrew Markov.One interesting feature of markove process is the forward no-memory,which means the future state is only related with the current state and the state before the current state has no influence on the future state.This feature is rather useful because it can simplify the formula deviation a lot.Scholars from MIT took good advantage of the forward no-memory of Markove process and use it to build a mathematical model to predict the surrounding rock type of tunnel by assuming that the whole rock type of the whole tunnel is an Markove process.Generally speaking,this Markove prediction model is divided into three parts.The first part is called a priori model.It provides a general understanding of the whole tunnel and mainly consisted of a transition probility matrix and transition intensity coefficient,which are mainly get from the estimation of experienced experts or statistics of geology exploration data of design insititute.The second part is called sampling.It will choose some observation points and drill holes to get samples and then correct the observation error.The third part is called posterior model which uses the priori model and the results of observation points to predict the surrounding rock type of the tunnel.Based on this Markov prediction model,this article put forward an optimization mothod for the location and number of observation points based on information entropy.Information entropy is a useful value to quantitively describe the uncertainty of the prediction results and,as a result,can help us to find the moset uncertain point.Besides,this paper also simply the integral formula of the information entropy of the whole tunnel and deviate the sum of information entropy to describethe uncertainty of the whole tunnel quantitatively.Finally,this paper applys the markov prediction model and optimization method of the observation points on the second tender of the Yellow River Diversion Project in Shanxi Province.