Probability Distribution Model Of Shear Strength Of Loess And Its Application

In order to study the stability of the slope engineering in the loess area,this paper discusses the research status of slope stability and reliability analysis of theory,analysis of the probability distribution model of shear strength parameters of loess slope and its application in reliability.The results of the reliability analysis based on Monte-Carlo are compared with results of the strength reduction finite element method.The applicability of the probability model of the Loess shear strength index distribution is studied.The primary coverage of the paper include:The paper first researches probability distribution model of shear strength indexes of loess.The probability distribution model of c、φvalues are non negative,unimodal,non symmetry,continuity,and generally skewed.The probability distribution model of remolded loess is basically consistent with that of original loess and the main subject of this paper is the original loess.The test results show that the normal distribution and the lognormal distribution can be applied to the shear strength index.But the Weibull distribution can be applied partly.Furthermore,the fitting degree of normal distribution and lognormal distribution is higher.Therefore,the normal distribution and lognormal distribution should be taken into account first.When the sample size is different,the test values of normal distribution and lognormal distribution are basically the same.Considering the excellent properties of normal distribution,the article should use the normal distribution as the distribution probability model.The correlation and the variability of c、φvalues of Q₂ and Q₃ original loess are analysed.The c、φvalues are negatively related.The c、φvalues of backfill are positive correlation under saturated condition and negative correlation under non saturated condition.On the whole,the greater the absolute value of the relevance of c、φ,the more stable the slope is.The variance of c is large while the variability ofφis small.The influence of the variability ofφon the stability of loess natural high slope is generally larger than that of c.The influence of the c-value variability on the stability of the fill slope is generally greater than that ofφ.The safety factor of increases with the increase of slope coefficient,and there is a great relationship between the two sides.The reliability analysis of safety factor is a standard general project.The lower the slope is,the smaller the minimum slope coefficient when failure probability is under 10%and the smaller the error of the platform slope and non platform slope is.A typical example analysis shows that,in addition to the main parameters of cohesion force and internal friction angle,the order of influence on stability from size of the slope:the dilatancy angle,Poisson’s ratio and modulus of elasticity in the finite element analysis.The effect of elastic modulus can be neglected.The probability distribution model of Q₃ loess shear strength index is input into finite element model for numerical simulation.The normal and lognormal distribution is suitable to calculated safety factor,which agree well with the probability distribution model of soil shear strength index.The reliability analysis based on Monte-Carlo method is highly consistent with the result of strength reduction finite element method,which increases the credibility of Monte-Carlo method in reliability analysis.The results of this study can be used as the basis for design and construction of the slope,and research methods can provide a reference for similar projects.