Study On Noncooperativity Of Factor Of Satety And Reliability Index Of Subgrade Slope

With the rapid development of infrastructure construction represented by high-speed railway and highway in China,the stability of subgrade slope not only affects the vehicle operation,but also relates to the life-safety,and it is also one of the important research topics in geotechnical engineering,which has long been widely concerned.Since geotechnical materials are affected by various uncertain factors,the traditional method offset the influence of uncertainty by setting factor of safety greater than unit.However,the reserved factor of safety is selected based on experience and cannot exhibit the risk levels quantitatively.Therefore,the reliability analysis method is established gradually,which utilizing reliability index,β,to quantify the uncertain factors in probability theory.Slope safety can be ensured withβas an alternative or complement to the traditional factor of safety.Although there is a positive correlation between F_s andβat general soil parameter variability levels,opposite trends can be observed in specific cases namely,the noncooperativity of F_s andβ.How to effectively identify the occurrence conditions of F_s-βnoncooperativity and reduce engineering risks has become an urgent problem to be solved.In this paper,the noncooperative response characteristics of subgrade slope F_s andβare comprehensively analyzed.The main research work and results are as follows:（1）Methods generally used to calculate factor of safety of slopes are introduced based on limit equilibrium.Disadvantages of the deterministic method in considering the uncertainty are analyzed.Uncertain factors in slope engineering are summarized,which can be divided into physical uncertainty,statistical uncertainty and model uncertainty.The basic principle of slope reliability analysis is described,and the process of calculating reliability index by first-order and second-moment method,Monte-Carlo simulation and random field finite element method is introduced,their advantages and disadvantages are analyzed as well.（2）The Fellenius method is used to calculate the factor of safety of a clay soil slope.Based on the performance function,the integral mean value theorem is utilized to simplify the calculation process of the slice method,and the explicit expression of the reliability index is derived.Reliability indexβis composed of three parts:componentβ_c influenced by cohesion c,componentβφinfluenced by friction angleφand the componentβ₀,which implies limit equilibrium state of slopes.The effects of slope height and slope gradient on F_s sndβare analyzed.The results show that F_s decreases when strength and geometric parameters change towards adverse sides,but under specific soil strength parameters condition,βincreases with the increase of slope height,H,which presents the opposite trend compared to F_s,namely,the noncooperativity response characteristics of F_s andβ.（3）The result of single factor sensitivity analysis on geometry and strength parameters shows that as the mean value of internal friction angle,μφ,and the standard deviation of cohesive force,σ_c increase,the trend of F_s-βnoncooperativity becomes more obvious.A multi-factor sensitivity analysis based on orthogonal design was carried out,and the primary and secondary factors were distinguished.The results shows that the sensitivity of the factors affecting F_s-βnoncooperativity isμφ>σφ>1/m>σ_c>H>μ_c.Based on Monte-Carlo simulation,relationship between reliability index and slope height or slope gradient with different strength parameters is analyzed,and the qualitative description of F_s-βnoncooperativity is obtained,which shows that under the conditions which cohesive is relatively small while its variability is relatively large,and friction angle is relatively large while its variability is relatively small,F_s-βnoncooperativity will be observed.Decreasing slope gradient is more suggested rather than decreasing slope height.（4）Effect of geometry and strength parameters on the failure mechanism of the slope is analyzed,and the F_s-βnoncooperativity is attributed to local averaging,which reduces the variability of the average value of the soil strength parameters within the failure domain,as slope height increases,and leading to increasingβ.Key factors of slope geometry and strength that affecting the significance of the local averaging are summarized,and the coefficient,R,defined as ratio of coefficient of variation of c andφmay characterize the significance of the local averaging.（5）Based on Markovian spatial correlation function,soil strength parameters and horizontal and vertical correlation distance are selected to construct lognormal random field of c andφ.The Cholesky decomposition method is adopted to discrete the random field,then assigned to the finite element grid.F_s andβcorresponding to different slope heights when R=1,2,4,and 8 are calculated.Result shows that the failure slip surface is relatively shallow when R is larger.As H increases,the growth rate of failure surface length is greater than that of slopes with smaller R.As a result,as R increases,F_s andβwill gradually change towards noncooperative side.（6）A method identifies the results of random field finite element and quantitatively analyzes the failure mechanism of slopes is proposed.As the slope height increases,the growth rate of the slope failure area A_S and the failure surface length L is larger with the larger R,and the relative growth rate of A_S is significantly greater than that of L,which verifies that the local averaging contributes to F_s-βnoncooperativity.In addition,the ratio R can effectively reflect the significance of the local averaging,which is important to safety ensuring.