A Parallel Implementation Of Numerical Methods For Analyzing Layered And Heterogeneous Geomaterials And Their Applications

Soils and rocks are characterized by heterogeneity.Under the action of sedimentation and gravity,soils are heterogeneous with depth.Stratified rocks are widely distributed in the Earth's crust and can be classified into sedimentary and metamorphic rocks.Therefore,it is necessary to develop numerical methods for the analysis of mechanical properties of layered and heterogeneous geo-materials.The additional stress fields are a main factor for inducing the deformation and subsidence of foundations.The additional stress fields in a heterogeneous foundation are also an important research topic.Rocks have a larger amount of cracks and joints,which control the stability of rock engineering.For this reason,this thesis develops the numerical methods of heterogeneous media and studies their applications in detail.This thesis firstly introduces the fundamental solution of a multi-layered solid and analyzes a layered halfspace.To verify the accuracy of the fundamental solution for analyzing a halfspace,this fundamental solution is used to calculate a homogeneous halfspace and the results obtained are compared with the Mindlin's solution.It can be found that the results with high accuracy can be obtained.The numerical method LayerSmart3D can be further developed for the analysis of soils whose elastic parameters vary arbitrarily with depth.Various types of integrals can be effectively solved.In order to increase the effectiveness of calculation,adaptive numerical integrals are incorporated into the software LayerSmart3D.Secondly,the parallel numerical method of the software LayerSmart3D is developed.In analyzing a heterogeneous halfspace,the medium is discretized into a n-layered homogeneous halfspace with depth.The layer number n is an arbitrary nonnegative integer.As n increases,the computational effort increases obviously.When a single CPU is used in the calculation of a heterogeneous halfspace,the calculation speed is low obviously.Thus,multiple CPUs can be uesed for the parallelization of the software LayerSmart3D.After the parallelization,the calculation speed is enhanced obviously and the results with high accuracy can be obtained.Thirdly,the software LayerSmart3D is used to analyze elastic fields of a heterogeneous halfspace under the action of different types of loadings.The shear moduli of the halfspace vary linearly and exponentially with depth and the loadings are horizontally and vertically distributed on horizontal loading areas.Additionally,the heterogeneous halfspace subjected to inclined and triangle loadings are also analyzed and the effect of the Poisson's ratio to the elastic fields is also considered.Finally,the software LayerDDM3D for analyzing the crack problems in a layered solid is developed by increasing new types of elements and parallel programming.This software can be only used to analyze the cracked halfspace in layered solids where the crack surfaces are subjected to loadings.In some cases,jointed rocks are subjected to tractions on boundary surfaces.For this reason,the numerical methods LayerSmart3D and LayerDDM3D and the principle of superposition in fracture mechanics are used together for analyzing this type of crack problems.In using this proposed method,LayerSmart3D is used to obtain the stresses in the uncracked halfspace,the principle of fracture mechanics is used to obtain the tractions on the crack surface.Then,LayerDDM3D is used to calculate the discontinuous displacements across the crack surface.On this basis,the fracture properties of cracked halfspaces are analyzed.Squared cracks subjected to circular and square loadings are analyzed.Results show that the positions of cracks in a layered halfspace and the material near the crack tip exert an obvious influence on the stress intensity factors.The density factor of strain energy across the crack tip is calculated and the S-criterion is used for the analysis of critical loadings and directions of crack growth.The proposed numerical methods can be used to effectively and accurately analyze heterogeneous media with depth subjected to complex loadings.In the ensuing,the proposed methods will be further applied to analyze engineering problems in heterogeneous geo-materials.