Local Stability Analysis And System Reliability Assessment Of Long-segment Subgrade Slopes

Local instability of subgrade soil slopes has become one of the main risk sources affecting the operational safety of railways,and it is of great engineering value and practical significance to carry out the research on the system reliability assessment of cross-regional long subgrade slopes.Considering the typical characteristics of large variability of soil parameters,small geotechnical survey sample size and random distribution of local independent instability events along the longitudinal direction,the momentary weighting method(MWM)for slope reliability analysis,which can significantly reduce the transfer of statistical uncertainty to the result space,is studied according to the sample moment estimation bias distribution and Bayes conditional probability theory.Based on the judgment of the main shape of the threedimensional sliding surface with ellipsoid at both ends and cylinder in the middle,an analytical method for local reliability analysis of the subgrade soil slope is constructed.Based on the number of independent local instability predicted by numerical simulation,the subgrade slope is equally discretized,and the K/N model is used to establish the system reliability assessment method,in which the number of allowable local instabilities and generalized system failure probability are evaluation indices.In view of the current engineering practice of using limit state method for reliability design of subgrade slopes,the traditional partial factor calibration method may lead to dangerous situations that the slope reliability index is far below the target one.An improved calibration method based on three principles is proposed,which can effectively avoid the adverse negative deviation of slope reliability index beyond the permissible threshold.This paper lays the theoretical foundation for the systematic application of probability theory in the system reliability assessment and design,from the perspectives of parameter characteristics,survey features,instability modes,and practical applications.The main work and results are as follows:Ⅰ)Reliability analysis of subgrade soil slopes considering moment estimation deviation with small parameter sample1)According to the law that the deviations between the mean and variance of a normal population and the corresponding sample moments obey the t and χ2 distributions respectively,the probability relationship between the occurrence of the event that a small sample may come from different population,and the greater the deviation between the population parameters and the sample moments is less likely.Based upon Bayes’ conditional probability theory and full probability formula,the calculation method of slope reliability indices that can consider the influence of sample moment estimation bias is established.2)For simple soil slopes with uniform properties,the spaces of slope reliability indices calculated by the MWM and the conventional method is compared and analyzed,indicating that the MWM can effectively narrow the range of reliability indices and significantly reduce the transfer of statistical uncertainty to the reliability analysis results.The reliability indices obtained by MWM are closer to the true value by up to 33.5%than the simple method in specific cases.Ⅱ)Local stability reliability analysis of subgrade soil slope based on cylindricalellipsoidal slip shape1)For long subgrade slopes with statistically homogeneous soil parameters and constant cross-sectional dimensions,based on the numerical simulation using random finite element method(RFEM)and engineering experience,a sliding surface shape judgment with cylindrical in the middle and ellipsoid at both ends of subgrade soil slopes is proposed.Based on the local average theory,the relationships between the slope geometries,soil parameters and the total resistance and sliding moments are derived.The analytical expressions of mean safety factor Fb,standard deviation Fb and reliability index βb with the longitudinal length b as the key variable are established.By setting the derivative of βb to b to be zero,the formulas for computing the geometric parameters of the critical slip surface are derived,forming an improvement of the Vanmarcke method(VM),which is denoted by IVM.VM assumes that the sliding surface is cylindrical in the middle and vertical at both ends.2)According to IVM,b is positively related to the horizontal scale of fluctuation(δh)of soil strength parameters.The ratio of longitudinal half-length axis to vertical half-length axis of ellipsoid is constantly less than one,i.e.,two ends are part of flat ellipsoids.Since the friction effect of two ends is stronger than the slip effect,βb is larger than the cross-sectional slope reliability index(β).As the end effect decreases with increasing b,βb gradually converges to β.Compared with VM,the b obtained by IVM is slightly larger but close to,and βb is reduced by up to 20%,indicating that IVM can search for more dangerous slip surface,which is more significant when δh is smaller.Compared with RFEM,the βb calculated by IVM is still unconservative.Ⅲ)System reliability assessment of long subgrade soil slopes based on K/N discrete model1)Under the condition of spatial variability of soil parameters,local instability events on long subgrade slopes occur randomly and independently in the longitudinal direction.For long subgrade slopes with statistically homogeneous soil parameters and constant cross-sectional dimensions,based on the number of local instabilities predicted by RFEM,a subgrade slope is equally divided into n sections that statistically contain only one potential instability event.The relationship between the generalized system reliability(R(Gsys))and the section slope reliability(R(sec))and the number of allowable instability sections m is analyzed using the K/N model.The system reliability assessment method of long subgrade slopes with m and R(Gsys)as measurement indicators is established,where m represents the expectation of the stability degree of long subgrade slopes,and R(Gsys)characterizes the confidence level that the value of m is not exceeded by the actual number of local instabilities.2)For the problem of system reliability assessment of the existing subgrade slopes,R(Gsys)increases with m,i.e.,the occurrence probability of the actual number of instability events exceeding m decreases.R(Gsys)shows an S-shaped non-linear increasing law with the increase of R(sec).In the dramatic increase phase,a small decrease of R(sec)can cause a significant decrease of R(Gsys),and thereby deteriorate the system safety.For the system reliability design problem of new subgrade slopes,the target reliability index of section slopes(βT(sec))is calculated based on the generalized system target reliability index(βT(Gsys)and the design instability amount(m).βT(sec)is positively and negatively correlated with βT(Gsys)and m,respectively,i.e.,by accepting a small amount of local instabilities can considerably reduce βT(sec)and thus obtain a more economical design plan.Ⅳ)Partial factor calibration of subgrade slopes based on negative deviation regulation of reliability index1)For the reliability design of sub grade soil slopes,the partial factors are determined according to the traditional single principle of residual minimum.The negative deviation characteristics of the slope reliability index(β)around the target value(βT)are analyzed,suggesting that the risk condition of β below βT over 0.5 accounts for 33%.The method of determining the partial factor based on the negative deviation setting limit,the residual tends to be low and the coefficients are similar is proposed.Taking typical subgrade slopes as example,it is verified that the new method can effectively avoid the adverse negative deviation from exceeding the tolerance threshold.For the problem of inconsistent calibration results of partial factors due to the difference of variable loads on embankments and cuttings,a method of obtaining unified partial factors of sub grade slopes based on the comprehensive optimization search in the low residual region is proposed.2)For the commonly encountered cases with small to medium variation of soil parameters,the βT ≈2.2 corresponding to the slope safety factor F=1.1511.25.The resistance partial factors of subgrade slopes are calibrated as γc=1.25,γφW=1.20,γφQ=1.05,and the sliding partial factors are calibrated as γW=1.03,γQ=1.05.