Reliability Analysis Of Slopes Based On Spatial Random Field-Bayesian Theory

Seasonal rainfall and water level change are the two main factors that trigger landslides in the Three Gorges reservoir area,but in-depth analysis of fluid-solid coupling behavior of unsaturated soil slope considering both is a significant challenge.To that end,it requires not only a rational mechanical model but also the accurate geotechnical parameters.This paper establishes a random field-Bayesian framework to calibrate key geotechnical parameters,such as Young's modulus,saturated permeability coefficient and internal friction angle,which could assimilate systematically the direct reconnaissance data,indirect monitoring data and prior knowledge.There are three key elements in the Bayesian framework:unsaturated fluid-solid coupling model of forward analysis,multivariate conditional discretization and nonparametric likelihood method.Deterministic and stochastic analyses were carried out on the Shiliushubao slope,located in the Three Gorges reservoir area,as the background project.The main conclusions of the deterministic analysis are as follows:(1)Under the conditions of long-term water level change and rainfall(the data in2012),the safety factor of the Shiliushubao slope fluctuated from 1.755 to 1.338,reaching a maximum of 1.755 at the beginning of January and a minimum of 1.338 on the 243th day.(2)Under the condition of short-term heavy rainfall(the average daily rainfall of 100mm for five consecutive days),the safety factor of the rainfall will gradually decreases with the rain,and the safety factor will drop to the minimum value of 1.227on the last day of rainfall.When the rainfall stops,the safety will be safe.The coefficient is gradually increasing.(3)In the deterministic analysis,the landslide radius of the most dangerous sliding surface is 948.4m,and the landslide volume of the potential landslide body is35395m~3.The main conclusions about the stochastic analysis are as follows:(1)The random field-Bayesian theory dynamically calibrates nine statistical features:mean of Young's modulus,saturated and internal friction angles,vertical range ratio,and correlation coefficient between geotechnical parameters.The statistical characteristics corresponding to Young's modulus are more sensitive to indirect monitoring data-vertical displacement than saturated permeability coefficient and internal friction angle.(2)The posterior statistical characteristics of the geotechnical parameters are used to predict the displacement of the slope surface.The average value of the predicted displacement is 109 mm,and the true value of the envelope is monitored by111 mm in one standard deviation of 4.2 mm.(3)The lowest safety factor would be 1.182 under summer heavy rain given the posterior average values the saturation permeability coefficient,the internal friction angle and the correlation coefficient between them.The sliding radius is 992m,and the landslide amount is 15000m~3.As the rainstorm ends,the matric suction increases and the safety factor will rise by 8%to 12%.(4)The response surface method or Monte Carlo algorithm based on random variables will underestimate the reliability index of the slope safety factor.The average value of the reliability index calculated by the response surface method is1.621,which cannot meet the requirement of the minimum value of 2.7 of the reliability index required by China's specifications.However,based on the random-Bayesian field method,considering the conditional data and spatial variability of key geotechnical parameters,the reliability index calculated by the subset Monte Carlo will reach the stability requirement of 2.70~4.27.In summary,the safety factor calculated by deterministic analysis method is larger than that by stochastic analysis.The sliding radius is small and the amount of landslide is large.However,in stochastic analysis,the reliability index calculated by classical statistics is conservative and cannot consider the constraints of conditional data.The results of Geostatistics meet the requirements of China's norms,and the slope will remain stable even if it is subjected to heavy rainfall without any intensive measures.Therefore,the stochastic field-Bayesian theory based on Geostatistics has great practical value in engineering.