Study On The Analysis Model Of Stochastic Temperature Fields And Displacement Fields In Permafrost Regions

In permafrost regions, the problem about the thermal stability and mechanical stability of embankments need to be solved as soon as possible. Some researchers from home and abroad made a large number of researches. However, very few people have considered the randomness of parameters for frozen soil. In fact, there are many uncertainties for general geotechnical engineering. Especially for the permafrost engineering, the engineering properties are very complex and special because of the existence of ices, which cause a strong discreteness and randomness. In this paper, the embankments in permafrost regions are the research object. The randomness of thermal and mechanical parameters is considered. Based on the stochastic analysis theory, the calculation models of random temperature fields, random stress fields and random displacement fields are presented. It can provide a theoretical basis for long-term stability of actual engineering design in permafrost regions.Firstly, the random field theory and the local average method are used to describe and disperse the stochastic parameters. A local average method of triangular elements is proposed. The analytical calculation and numerical calculation for the covariance matrix of triangular elements of the local average random field is provided by the transformation of coordinates and the gauss numerical integration. The results show that the quadrilateral random field grids cannot match up with the triangular finite element grids. The numerical characteristics of the contained triangular finite elements aren’t equal each other, and every contained triangular finite element isn’t identical with the quadrilateral element of the random field in the same place. The triangular random field grids can perfectly match up with triangular finite element grids. The numerical characteristic of triangle unit is accurate and the calculation program is simple.Secondly, we model the soil properties as random fields and the upper boundary conditions as stochastic processes. The stochastic finite element program is compiled by Matrix Laboratory(MATLAB) software, and the random temperature fields of an embankment in a permafrost region are investigated by Neumann stochastic finite element method(NSFEM). The results show that the mean temperature is roughly the same as the conventional deterministic temperature. The locations of more standard deviation are different when the coefficients of variation are the same. When the coefficients of variation are different, the bigger the coefficients of variation are, the bigger the standard deviations are. The thermodynamic property of warm frozen soil is strongly related to the temperature, frozen soil and thawed soil have a big difference. There is a lot of warm frozen soil under the embankment and foundation. It is more reasonable to take the probabilistic aspects of the parameters and conditions into account because a lot of warm frozen soil is subsistent.Thirdly, based on the modified Cambridge model and the double yield surface theory, we consider the influence of cohesive strength and internal friction angle on frozen soil, and describe the deformation characteristics by the εv- lnp line. The yield surface hardening parameter obtaining from normal consolidation path is modified. We obtain the potential yield surface hardening parameter in combination with critical state parameters, which can reflect inherent features of permafrost. A dense parameter and a potential strength are defined by the relationship between the current yield surface and referential yield surface. A permafrost model which could show the shear dilatancy softening properties and shear contraction hardening properties is established. We obtain the incremental stress-strain relationship for the constitutive model based on the classic elastic-plastic theory. Combining with the algorithm of elastic plastic finite element, the numerical calculation process of constitutive model is discussed in detail.Finally, we consider the influence of random temperature on the basic mechanical parameters for frozen soil. The mechanical parameters are considered as random fields. The stochastic finite element program is compiled and the random stress fields and random displacement fields of an embankment in a permafrost region are investigated by NSFEM. The results show that the temperature change has a great effect on the distributions of mean and standard deviation for vertical displacement. The change of mean settlement can be divided into settlement, frost heave and subsidence stages for cross-section specific location. When the coefficients of variation are different, the bigger the coefficients of variation are, the bigger the standard deviations are. The standard deviation of vertical displacement increases with time given climatic warming.