Research On The Second-order Reliability Method Of Slopes Considering The Spatial Variability Of Soil Properties

The spatial variability of soil parameters is of great significant to the stability of a slope.To characterize the spatial variability,the random filed is commonly used and discretized into a large number of random variables,which leads a “curse of dimensionality” to the system reliability analysis of slopes.Most of the existing researches analyze the system reliability of spatially variable soil slopes using the Monte Carlo simulation,and the traditional reliability analysis methods seem limited due to the “curse of dimensionality”,though they are efficient and simple in computation.Besides,the failure mode of the slope is commonly influenced by the spatial variability of soil parameters.At present,the distribution law of the failure mode considering the spatial variability of soil parameters is not clear,and there is a lack of efficient representative slip surface identification method.The researches in this dissertation focus on the topics of the system reliability analysis,the identification of the important failure modes and the risk assessment of slopes with spatially varied soils.The limit equilibrium method and the second-order reliability method are used to study the reliability analysis of slopes and the efficient identification of representative slip surface(RSS).The main research contents and results are listed below.(1)The random limit equilibrium method(RLEM)for system reliability analysis and risk assessment of slope is proposed based on the circular slip surface assumption and the non-circular slip surface assumption.In this method,the K-L expansion method is adopted to simulate the random field of soil properties,and the Genetic algorithm is used to search the critical slip surface.The influence of different slip surface assumptions on the system reliability is discussed with 4 typical slope cases,and it is also found that the location of the critical slip surface is influenced by both the average effect of soil parameters and the fluctuation effect of the random fields.(2)Aiming at applying the second-order reliability method(SORM)to the reliability analysis of the individual failure mode,the random field is local averaged along the slip surface and the local averaging variables are used to reduce the number of random variables.The equations to calculate the correlation coefficient of different failure modes are derived based on the local averaging variables,and the reliability analysis for slope system with multiple failure modes is conducted based on the reliability analysis and the correlation analysis.The results show that for the undrained slope,the local averaging along the whole slip surface can characterize the spatial variability of soil parameters along the slip surface if the error caused by distribution fitting of the local averaging variables is ignored.However,for the drained slope,the slip surface should be divided into several segments to ensure the accuracy of the random field simulation by local average method.(3)A multimodal optimization method for RSS identification and risk assessment is proposed.In this method,by considering the influence of the synergy between the reliabilities and the correlation coefficients between different slip surfaces on the system failure probability,the task of RSS identification is transformed as a multimodal optimization problem,and the potential slip surfaces that make great contributions to the system failure probability are determined as RSSs.The contributions of each RSS to the system failure probability are taken as the weights of the corresponding failure consequences,and the failure risk is evaluated by summarizing all the weighted failure consequences.The results show that the proposed method is valid to evaluate the system reliability and risk of the slope.When the number of RSSs increases,the evaluated failure probability converges to the overall failure probability of the slope,and the converge speed increases with the correlation length of the random field.(4)An efficient method for RSS identification based on the modified Hassan & Wolff model is proposed.By reordering the RSSs according to their contributions to the failure probability of the slope system,the convergence curve of the evaluated failure probability with the number of RSSs is obtained,and the system reliability analysis and risk assessment are conducted by the RSSs and the convergence curve.The method is used to conduct the reliability-based design optimization of an embankment slope.The results show that the modified Hassan & Wolff model is efficient to identify the RSS by considering the average effect of the soil parameters and the fluctuation effect of the random fields on the location of critical slip surface,and it can meet the efficiency requirement for engineering application.