| The rockmass contains numerous cracks and joints. The propagations and interactions of these discontinuities significantly affect the stability of rock slope. These cracks are of three dimensions in essence. Few of them can be simplified into 2D cases. Moreover, the 2D crack model cannot predict the fracture of mode III. The rock is a nontransparent natural material. A crack couldn’t be manually embedded previously in it and the internal crack propagation couldn’t be observed. Hence, it is necessary to adopt the 3D fracture model to numerically study the propagation and interaction of 3D cracks. However, when using the conventional finite element method, the calculation of stress intensity factor and the local mesh adjustment are computationally intensive. To avoid these difficulties, the present thesis employs the virtual internal bond theory plus the element partition method to study 3D fracture propagation and interaction.The augment virtual internal bond(AVIB) is established based on the improved Xu-Needleman potential. The original AVIB adopts the Xu-Needleman potential to describe the energy of micro bond. But the Xu-Needleman has a critical limitation that the normal traction is not become zero when the tangent separation is big enough. This violates reality. To break through this limitation, the improved Xu-Needleman cohesive law is used to characterize the cohesive bonds and the macro constitutive relation is derived. The corresponding micro-macro parameter relationship is derived. The improved Xu-Needleman cohesive law is a coupled one, namely that the normal traction(or the shear traction) is related both the normal and shear deformation. To simplify it, a non-coupled cohesive law is developed and the corresponding constitutive model is derived.The 3D element partition method(EPM) takes advantage of the geometry character of the tetrahedron element to develop a four node contact element. When using this method,the cracked body can be directly meshed regardless of geometric integrity of jointed rockmass, avoiding the setup of joint element and remeshing problem. This advantage becomes especially significant when the number of cracks is large. With this improved AVIB constitutive model and the 3D-EPM, the interactions between vertically parallel elliptic cracks are studied. The simulation results suggest that when the parallel cracks are vertically aligned, they propagate independently in wrapping wing pattern. But there is neither prior propagation nor coalescence path. In contrast to the aligned vertically parallel crack cases, the nonaligned vertically parallel crack case has prior propagation and coalescence path. The crack always propagates toward and coalesces with its adjacent crack by which a wing crack array is formed. During the wing-array cracks propagation and coalescence, the other crack’s growth is restrained to a certain extent due to the release of stress concentration. To investigate the 3D crack propagation subjected multiaxial stress state, the simplified Augment Virtual Internal Bond(AVIB) model in conjunction with the three-dimensional element partition method is used to simulate the propagation process of an embedded π plane crack subjected to true triaxial stress. The simulation results suggest that the fracture firstly initiates at the tip of the pre-existing planar crack and then propagates in wrapping mode along the maximum principle stress. With increasing the intermediate principle stress, the ’wrapped’ extended crack rotates to the direction of the intermediate principle stress. The triaxial compressive strength of rock is also related to the intermediate principal stress. When the intermediate stress is smaller than a certain value(approximately 0.5c?), the triaxial compressive strength almost grows linearly with intermediate principal stress. After the intermediate principal stress exceeds a certain value(approximately 0.8c?) and the triaxial strength decreases with intermediate stress increasing. The simulated results provide valuable reference for the analysis of embedded planar crack propagation in rock under high compressive in-situ stress. Beside the flat crack, there are curved cracks embedded in the rockmass. To simulate the curved crack, a mathematical description of curved crack is established and the effect of curved crack is introduced into the numerical model. It’s found that the curved crack propagates on non-planar path and always is perpendicular to the direction of maximum principal strain.By the same way, the propagations of these embedded cracks under shear stress are investigated. Different influence factors such as crack numbers, crack inclination, crack size, crack distance and normal stress are considered and analyzed, it is revealed that the propagation patterns of 3D embedded cracks under shear stress are related to the inclination of crack relative to the shear force. When the inclination is smaller than 90 degree, the father crack firstly propagates in wrapping wing pattern. Then, many parallel arrays of descendent cracks, which are vertical to the relative slip direction of the father crack faces, anti-symmetrically initiate on part of the upper and the lower father crack faces, respectively. With the inclination increasing, the distribution area of the descendent cracks moves from the lower to the upper part of the father crack face. With shear stress increasing, a prior propagation path, vertical to the father crack face, is formed near the middle transect of the father crack face. Finally, these prior extended descendent cracks adjacent to different father cracks coalesce together in zigzag mode at rock bridges. However, when the inclination is bigger than 90 degree, the father cracks only independently propagate along their minor axis directions. The extended crack is coplanar with the father crack. In all inclination cases, no apparent tensile fracture propagates at the two major axis tips of the original crack. The features of crack propagation obtained and the conclusions drawn in the present paper are significantly valuable for the evaluation of jointed rock slope stability and land slide.To examine the performance of the present method in simulating dynamic fracture, the present thesis uses the improved AVIB in conjunction with the 3D-EPM to simulate a dynamic propagation process of an embedded crack by the explicit integral scheme. The simulation results demonstrate that the present method is capable of capturing the characters of the dynamic embedded crack growth.The 3D-EPM is advantageous in 3D fracture simulation, but it fails to account for the deformation of the two sub-blocks generated by the element partition. As consequence, the error increases with increasing the element size. To address this problem, improve tetrahedral element partition method is proposed, it is assumed that the deformation of each sub-block is only related to the local environment at the same side of crack. So, a local Least Square interpolation method is used to relate the deformation of sub-block to its adjacent nodes. The corresponding stiffness matrix and node force vector of a partitioned element is derived. By this method, the deformation of the sub-blocks is successfully accounted, which makes precision of EPM free of the element size. The present thesis provides an efficient simulation method for 3D fracture and the conclusions drawn in this thesis is of significant importance for practical engineering analysis. |
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