| With the development of IT technology and earth science, finite element modeling has been a powerful tool to study the earthquake mechanism. The earthquake mechanism can be simulated by the finite element modeling based on data of physical process of source, fault types and their mechanics, regional stress field, velocity ratio of P and S waves, underground water level change, temperature effects, stress triggering, and so on. And a great progress has been made. However, because geological structure is complicated and mechanical nature of the rocks is distinct, there are still some big challenges that need to be solved in the finite element modeling of the earthquake mechanism, especially boundary effects and the uncertainties of the parameters.The boundary effect, which is important to the mechanic properties of materials, is widespread among the geological units, such as the crust-mantle boundary, plate boundaries, and mineral boundaries. To study mineral boundary effect can provide important theoretical data for exploring the dynamic process of the Earth’s interior and earthquake mechanism, because the boundary effects can influence deformation mechanisms of rocks or minerals. Now, the boundary effects become a focused topic in earth sciences, too. The reason is that most major earthquakes (Ms>7) occurred on the active faults at plate or block boundaries. The Wenchuan earthquake resulted from rapid release of the accumulated stress at the boundary caused by the eastward extension of the Tibetan Plateau. In some rheological experiments, it was found that the heterogeneous distribution of the stress among mineral grains led to the differential dislocation densities. The boundary effect among the minerals is an important factor controlling the rock mechanics and deformation mechanism. However, boundary effects in rock cannot be investigated by physical experiments so far. The reported numerical simulations for the boundary effect in rock are mainly related to slipping and effect of wetting on shear stress distribution at grain boundaries. The stress distribution at mineral boundaries in rock, however, is rarely studied systematically.In this thesis, the finite element software, ANSYS, was employed to model the 3D stress field of the mineral aggregate at room temperature and 1.6 GPa hydrostatic pressure. The boundary effect of minerals is studied at a mesoscopic scale, which can help to understand the deformation mechanism of rocks, the dynamics in the earth interior and earthquake mechanisms.The principle of finite element method is to separate a continuous region into a set of finite elements. Here, the mineral assemblage is composed of two different minerals which are cubic structure with side length is 1μm. The minerals are arranged in the following order: mineral 1, mineral 2 and mineral 1. The coordinate origin was set at the center because of the symmetrical structure of the assemblage. An octant of the mineral assemblage was taken as a calculation model. The regular grids and SOLID 185 element type in the ANSYS were used during modeling. The regular grid was established by separating the model into 25 parts in X and Z directions, and 25, 1 and 50 parts in Y direction, respectively. In the mineral grain, the grid size was 20 nm×20 nm×20 nm. At the boundary, the grid size was 20 nm×thickness of the boundary layer×20 nm. The grid model consists of 53404 nodes and 47500 elements. The critical point between the mesoscopic scale (10 nm ~ 1000 nm) and macroscopic scale (>1μm) is 1μm (= 1000 nm). At the mesoscopic scale, the non-bond interactive force among molecular controlled the activities of molecule clusters. The mechanic properties of the mineral grains (1μm) were similar to those at the macroscopic scale. Thus, each node in the model can be considered as a molecule cluster. Under the compressive condition, the elements in the mineral assemblage interacted with each other in a given way, and the stress was transfered to the molecule clusters (nodes). Therefore, the stress on each molecule cluster (node) can be modeled when the whole mineral was at certain pressure.In the model, the boundary layer between mineral grains was both the geometrical boundary and physical boundary. The boundary was uniformly composed of mixture of two minerals. So its elastic modulus was calculated using the typical mixture model. The mineral grain and boundary layer were assumed to be contacted by static friction. In ANSYS, the surface-surface connection can be transformed into node-node connection on the surface. It means that the bond between surfaces at the macroscopic scale can be considered as the friction among the molecule clusters at the mesoscopic scale. CONTA 174 and TRAGE 170 in ANSYS were used as the contact elements and the target elements, respectively. In the model, the top of mineral 2 was contacted with the bottom of the boundary layer. The former was the target surface, and the latter was the contact surface. Mineral 1 overlaid the boundary layer. The bottom surface of mineral 1 was the target surface, and the top of the boundary was the contact surface. The algorithm for the contact was the augmented Lagrangian. The contact detection was carried out using Gussian interpolation. The factor of contact stiffness was taken as 0.1. Considering the boundary being the mixture of two minerals, penetration could exist, and tolerance factor was set as 0.1.The minerals used in the study are diopside and forsterite at first. The difference between their Young’s modulus was 38.3560 GPa, and the difference between their Possion’s ratio was 0.0181. The modeling condition was room temperature, and 1.6 GPa hydrostatic pressure. Pure elastic deformation occurred under the pressure. To analyze influence of the thickness, friction coefficient, and the elastic modulus of the boundary layer on the stress distribution, three different modeling cases were considered: (1) The elastic modulus was constant, friction coefficient was 0.65, and thickness varied from 1 nm to 10 nm with a step of 0.5 nm. The relationship between the stress distribution and thickness of the boundary layer was studied based on Mise stress at 5 representative points. (2) The elastic modulus was constant, thickness was 1 nm, and friction coefficient varied from 0.5 to 0.85 with a step of 0.025. Ten points were used to evaluate the relationship between the friction coefficient and Mise stress distribution. (3) Thickness was 1nm, friction coefficient was 0.65, and elastic modulus changed 21 times by adjusting the volume and shear modules based on the Reuss model. Ten points were selected to analyze the influence of the elastic modulus on stress distribution. Then, Diopside-anorthite and anorthite-quartz assemblages were analyzed under the same conditions. The differences of Young’s modulus and Possion’s ratio between diopside and anorthite were 64.9220 GPa and 0.0393, respectively. For anorthite-quartz assemblage, the differences of Young’s modulus and Possion’s ratio between diopside and anorthite were 3.2577 GPa and 0.1618, respectively.The following can be concluded based on the 3D finite element modeling. 1. When an assemblage composed of two cubic minerals experienced pure elastic deformation at room temperature and 1.6 GPa hydrostatic pressure, the stress was distributed unevenly in the assemblage. Stress was mainly accumulated at the grain boundary. The stress distribution at the boundary was not uniform, too. This indicates that the boundary between minerals was a weak zone, and plastic deformation and/or fracture could occur in the zone under compression.2. At the mesoscopic scale, the molecule clusters at the boundaries had larger equivalent stress than those within the minerals. At the boundary, the farther distance to the coordinate origin, the larger equivalent stress was.3. The equivalent stress at the boundary layer and maximum equivalent stress within the mineral assemblage were linearly negative proportion to the thickness of the boundary. The thicker of the boundary, the less maximum equivalent stress of the mineral assemblage was. At the mesoscopic scale, equivalent stress on the molecule clusters at different locations within the boundary layer decreased to different extents according to the distance to the center.4. The equivalent stress at the boundary layer and contact friction stress were linearly positive proportion to the friction coefficient. The closer to the center, the less degree of change was. However, the change extents of both equivalent stress and contact friction stress on the different molecular clusters were almost consistent in the region close to the boundary surface under the pressure directly.5. For the mineral assemblages or rocks composed of minerals with different elastic parameters, the larger difference between the elastic parameters, especially Possion’s ratio, the more the stress concentrated at the boundary layer.6. The relationship between the equivalent stress and elastic parameters at the boundary layers can be described by Gussion’s function. The minimum stress concentration occurred at the boundary layers if the elastic parameters of the boundary layer equal to the average of those of the minerals. |
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