Study On Plastic Limit Analysis For Reliability Of Geotechnical Slope

China is now in the period of rapid development of infrastructure construction.A large number of soil slopes and rock slopes have appeared in the construction of railways,highways,water conservancy,hydroelectricity and mines.The instability of rock and soil slopes will cause humans serious loss of life and property.The instability of rock and soil slopes are related to many random parameters,and the reliability analysis of slope is getting more and more attention.Under the support of the National Natural Science Foundation(51564026),this paper applies the limit analysis theory in plastic mechanics to the field of reliability analysis of rock and soil slopes,and the systematic and in-depth study on the plastic limit analysis method of slope reliability is made.The main work of this paper is as follows:(1)Based on the lower bound theorem of plastic mechanics,a theoretical model of the lower bound method for the plastic limit analysis of soil slope reliability is established.Taking the shear parameters of soil materials as random variables,and the stress vector of finite element nodes are taken as decision variables,the lower bound method stochastic programming model of soil slope reliability analysis which satisfies with the equilibrium equations,yield conditions,common boundary stress discontinuity conditions and stress boundary conditions is established,An efficient numerical solution method of the lower bound method stochastic programming model based on Monte Carlo method is proposed.And the lower bound solution of the reliability index of soil slope is obtained.(2)Based on the upper bound theorem of plastic mechanics,a theoretical model of the upper bound method for the plastic limit analysis of soil slope reliability is established.Taking the shear parameters of soil materials as random variables,and the velocity vector and plastic multiplier of finite elements are taken as decision variables,the upper bound method stochastic programming model of soil slope reliability analysis which satisfies with the plastic flow constraint conditions of finite elements and velocity discontinuities,the velocity boundary conditions and Functional balance principle is established,An efficient numerical solution method of the upper bound method stochastic programming model based on Monte Carlo method is proposed.and the upper bound solution of the reliability index of soil slope is obtained.(3)Research on estimation method of reliability evaluation index of soil slope based on the plastic limit analysis theory.The concept of failure probability of soil slope element is put forward for the first time,and the calculation method of unit failure probability matching with the kinematically admissible velocity fields of upper bound method is deduced.At the same time,the method of slope failure pattern identification based on slope failure consequence is proposed,which reveals the evolution law of failure mode,failure probability and failure risk of soil slope under the conditions of complex soil layers and shear parameters variability.(4)The lower bound method model and upper bound method model of reliability plastic limit analysis of soil slope considering the randomness of groundwater level and the randomness of shear parameters are established.The effect of groundwater is the key factor of the instability of soil slopes.In this paper,it is assumed that the ground water level of the slope is of a truncated normal distribution,the random seepage field of the soil slope is calculated to obtain the random amount of pore water pressure at each point of the soil body.The mathematical programming model of the lower and upper bound method under the action of the random seepage fields are established based on the effective stress principle.The law of the reliability index of the soil slope with the random variation of the groundwater level is obtained through the solution of models,at the same time the relationship between the failure mode and the failure risk of the soil slope and the groundwater level is obtained.(5)Due to the randomness and variability of parameters,reliability analysis of jointed rock slopes generally contains multiple failure modes.This reliability problem cannot be effectively treated by traditional methods,such as limit equilibrium method(LEM)and finite element method(FEM).A numerical method for performing reliability analysis of jointed rock slope is proposed by combining the plastic limit analysis theory,rigid finite element discretization,mathematical programming theory and Monte Carlo method.The shear parameter s of interfaces are set as random variables,and the mathematical programming model of the lower and upper bound method of the reliability analysis of the joint rock slope are constructed according to the lower limit theorem and the upper limit theorem,and the lower bound solution and the upper bound solution of the reliability index of the jointed rock slope are s olved by using the Monte Carlo method.Through the deep analysis of classical examples,it is shown that compared with LEM and FEM,the method mentioned in this paper is more reasonable and accurate to evaluate the reliability of jointed rock slope s.(6)Based on the upper bound method,the centroid velocity field of rigid block element is calculated.The calculation method of unit failure probability of the element for jointed rock slope is proposed.The failure probability of the element in the jointed rock slope is obtained.The failure probability cloud map of jointed rock slope is drawn for the first time.The failure probability cloud map of the slope rock mass is also proposed.At the same time,the identification method of the failure mode of the jointed rock slope is proposed,and all the failure modes of the slope and the failure probability of each rock block are accurately solved.Through the research,the theoretical framework of the plastic limit analysis of the reliability of the geotechnical slope is preliminarily established,and the failure analysis of the slope based on the element failure probability method is realized.The research results enrich the methods of slope reliability analysis and have important scientific significance and application value for slope safety evaluation.