| Porous medium,as a material composed of the skeleton and a large number of tiny voids,widely exists in nature and engineering applications.Rock and soil,as the foundation and construction material of civil engineering,are closely related to people's production and life,such as the soil excavation,ground settlement,dam seepage deformation,oil-gas exploitation,gas seepage in coal seam,evaporation consolidation of foundations and dam landslides and other issues involved in the practical engineering problems.Before dealing with these issues,we need to understand the following characteristics of the soil:(1)the coupling effect between different phases,such as the solid-liquid coupling,solid-liquid-gas coupling,solid-oil coupling,etc.The deformation of the solid skeleton will directly affect the fluid flow state in the pore space.Conversely,the fluid flow in the pore will also affect the deformation of the solid skeleton,which makes the mechanical behavior of the soil more complicated and changeable than traditional single-phase solids;(2)the high heterogeneity and nonlinearity.Soil materials usually undergo complex and long-term geological activities,so their material properties tend to exhibit heterogeneous characteristics and complex nonlinear behaviors;(3)large-scale and multi-scale characteristics.For modern civil engineering structures and geological hazards,such as the shale gas exploitation with hydraulic fracturing,land subsidence caused by urban groundwater mining,sand liquefaction caused by the seismic,etc.,due to the large-scale property and fine-scale characteristics need fine grids to resolve,the whole model often fails to be solved with conventional numerical methods.Therefore,to develop a new numerical approach with high-efficiency and high-precision is of great significance for understanding and studying the mechanism of soil mechanics and for evaluating the safety and stability of engineering structures.Based on the theoretical basis of the multiscale finite element method.this dissertation studies the multiscale method for the nonlinear problems of single phase solids and saturated porous media.The main research work includes:a general coupling extended multiscale finite element method for the elastoplastic consolidation and dynamic problems of saturated porous media is proposed;a multiscale finite element method with the embedded strong discontinuity model for strain localizations of single phase solid and saturated porous media is proposed;a multiscale finite element method with the embedded strong discontinuity model for fracture problems of single phase solid,and an adaptive multiscale finite element method with the embedding strong/weak discontinuity model for hydraulic fracturing problems are proposed.The main contents of this dissertation are divided into the following five parts:Firstly,a general coupling extended multiscale finite element method for the elastoplastic consolidation and dynamic problems of homogeneous and heterogeneous saturated porous media is proposed.This method differs from the coupling multiscale finite element method in that it requires the construction of two independent sets of solid-and liquid-phase numerical basis functions.Instead,it directly constructs a fully-coupled numerical basis function based on the equivalent stiffness matrix,which can accurately capture the solid-liquid coupling effect and dynamic characteristics within the unit cells.Meanwhile,a generalized formula for constructing a numerical basis function under the framework of multiscale finite element method is established-and all numerical basis functions of a unit cell can be calculated at a time.For nonlinear problems,the displacement and pore pressure decomposition technique is further proposed,and the fine-scale solutions are divided into downscale and perturbation solutions.Finally,numerical tests of elastoplastic consolidation and dynamic problems of homogeneous and heterogeneous saturated porous media show that the proposed method owns good convergence,accuracy and efficiency.The newly developed method in this dissertation is suitable for other multi-phase and multi-field coupled nonlinear problems,and has broad application prospects.Secondly,a multiscale finite element method with the embedded strong discontinuity model for strain localizations in solids is proposed.The main idea of this method is that the discontinuities on the fine-scale meshes are described by the embedded strong discontinuity model.Since the introduced additional degrees of freedom can be eliminated at the elemental level by the condensation technique,the dimension of the equivalent stiffness matrix of the unit cells can be kept constant,which makes the program is convenient to be implemented.On the coarse scale,an enhanced multi-node coarse element technique is proposed,which can dynamically increase the number of coarse nodes according to the position of the discontinuity.The constructed enhanced numerical basis functions can correctly capture the discontinuous characteristics on the fine scale.Local perturbation methods have been developed to update fine-scale solutions.Finally,through the typical strain localization examples,the correctness and effectiveness of the proposed method are validated.Thirdly,based on the newly developed enhanced multi-node coarse element technique and embedded strong discontinuity model,an embedded strong discontinuity multiscale finite element method for the localizations of saturated porous media is proposed.The embedded strong discontinuity model assumes that the displacement field and the flow field are strong discontinuities,while the pore pressure field is still continuous.Because the flow field is not directly introduced into the solving equations,it only needs to be calculated in post-processing,which greatly reduces the solving difficulty.Coupling coarse element technique and enhanced coarse element technique were used to solve the numerical basis functions of non-localizaed unit cells and localized unit cells,respectively.The localization examples of homogeneous and heterogeneous saturated porous media show that the proposed method owns the high accuracy and computational efficiency.Fourthly,for the brittle fracture problems of single phase solids,this dissertation further develops a multiscale finite element method with the embeddded strong discontinuity model.The evolution of cracks on the fine elements is described by the cohesive constitutive equations.The enhanced numerical basis function is used on the coarse elements to describe the discontinuous characteristics of the fine elements on the unit cell,and the flow chart of the algorithm implementation is given in detail.Finally,through the numerical crack propagation tests of simple extension,three-point bending and four-point bending,it is validated that this method can effectively reduce the number of degrees of freedom and computational time.Finally,an adaptive multiscale finite element method with embedded strong/weak discontinuity model is proposed for hydraulic fracturing.This model assumes that the displacement field is strong discontinuity and the pore pressure is weak discontinuity.In order to correctly capture the crack propagation process driven by water,the continuity of the force and the pore pressure at the adjacent cracking element should be ensured.As for this reason,the additional displacement and pore pressure degrees of freedom in the crack element are set as the global degrees of freedom to participate in the global calculations.Meanwhile,an adaptive multiscale finite element method combined with the discontinuity model is proposed.The coarse elements within a certain range from the tip of the crack are changed into the fine elements for calculations.The interface between the coarse and fine elements is coupled with the master-slave constraint relationship.Finally,the correctness of the proposed method is validated through the typical hydraulic fracturing problem. |
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