Slope Stability Analysis Based On Moment Methods With Discrete Random Field

The evaluation of slope stability has been a very important research content in geotechnical engineering.In addition,the analysis process of it has significant uncertainty.There are many uncertain factors that affect slope stability.Such as,rock and soil performance parameters,slope stability analysis model,pore pressure,external loads,etc.At present,the common mathematical models describing the uncertainty of soil parameters are divided into two categories: random variable models and random field models.The random variable model neglects the spatial variability of soil parameters,and considers that the soil parameters of the same soil layer are completely related in the spatial area.The random field model can effectively simulate the spatial variability of soil parameters and is more scientific and reasonable than the random variable model.The reliability analysis of slope stability is a complex problem involving multi-parameter correlation and implicit limit state equation.In addition,the spatial variability of geotechnical parameters makes the problem more troublesome with the random fields discretion.The point estimation method can easily consider the correlation between geotechnical parameters through Rosenblatt transformation or Nataf transformation.Nowadays,the moment method based on point estimation has shown advantages over the implicit limit state equation involving multi-random variables for its high efficiency and reasonable analytical results.In view of the advantages of the mentioned moment method,this paper applies the four fourth-order moment methods to the stability analysis of slope stability based on High-order moment standardization method,Edgeworth expansion method,Pearson system method and Third-order polynomial normal transformation method.And the calculation accuracy and application range of the four fourth-order moment methods are analyzed and compared through examples.However,the moment method is usually applied to the random variable model.At present,there is no research on the moment method of the random fields model.Therefore,according to the concise relationship between variance function,the fluctuation scale and the correlation function in the local average process theory,a random field layering discrete method for moment method is proposed and the corresponding moment method for reliability analysis of slope stability is present.The slope of the actual project is a three-dimensional form.Simplifying the three-dimensional slope stability problem into a two-dimensional form for analysis and calculation will inevitably produce errors.Currently,three-dimensional slope stability reliability analysis considering the spatial variability of geotechnical parameters is rarely Some scholars have studied it.The two-dimensional limit equilibrium method is extended to three-dimensional situation.The slope stability reliability analysis considering the spatial variability of soil parameters is performed for the three-dimensional long slope.The main conclusions of this paper are as follows:(1)For the slope random variable model,the four fourth-order moment methods all have great calculation accuracy,and the High-order moment standardization method is relatively optimal.Because Pearson system method and Third-order polynomial normal transformation method have a certain scope of application,there is no solution to the stability analysis of the slope stability,and Third-order polynomial normal transformation method has the narrowest scope of application.(2)The discrete method considers each layer of soil parameters as a random variable,and can effectively describe the spatial variability of soil parameters through a large-scale mesh.By adjusting the layer thickness,different spatial variability simulations can be achieved.The discreteness is simple and efficient,and it is compatible with the moment method.(3)Considering the correlation between the end effect of the slope and the length of the soil parameters along the length of the failure section of the slope.The three-dimensional slope reliability index is obviously greater than the two-dimensional slope reliability index,indicating that the use of two-dimensional reliability indicators to evaluate the stability of slope stability is too conservative,and the greater the coefficient of variation of soil parameters,the greater the increase in the three-dimensional reliability index than the two-dimensional reliability index.