Study On The Three-Dimensional Elastic-Viscoplastic Composite Element Method

Composite element method (CEM) is a new numerical simulation method having the merits of numerical manifold method, block element method and finite element method. It can be applied to three dimensional elasto-viscoplasticity continuous deformation analysis and discontinuous deformation analysis. As to great quantities of joints or fissures and system bolts, equivalent simulation could be used. However as to larger scale faults and pre-stressed bolts or anchors, explicit simulation is needed usually. As the scale of rock and soil engineering is greater and greater, more and more complicated geology condition including many faults intersected each other is to be overcome. It is very difficult to simulate all important faults, bolts, and anchors explicitly. Even forced to realize it, strange shape elements will be inevitable which may cause much negative influence. Even worse, when the configuration of a structure is often modified, it will cost much time and manpower to remesh. It is rather more difficult to simulate explicitly a complicated rock masses structure and the media in it than the structure itself. CEM transfers the difficulty form pre-process to computation, or in another words, from man to computer, which simplifis the pre-process work and heighten the efficiency.Comprehensive researches are conducted in this dissertation in order to realize the idea of the three dimensional elasto-viscoplasticity CEM.Firstly, a review of different currently and widely used numerical methods those are propitious to the mechanical analysis of the continuum or the discontinuous media structures, is made. The basic principles, the advantages, the disadvantages and the applicability of these methods are analyzed. Then the significance and the cause of the research work are expounded. The birth and development of CEM are also introduced briefly.Secondly, a detailed presentation for the principle theory of CEM is made and the main formulae are deduced. The principle of CEM is shown as following: suppose a domain containing several sub-domains having different mechanical characteristics. A composite element is defined to cover the whole domain. The sub-domains are defined as sub-elements. Every sub-elemnt has a set of nodes separately corresponding to nodes of the composite element. The displacements in each sub-element are interpolated from the nodal displacements assigned to the composite element and the interpolate function is the shape function of the conventional FEM defined in the whole composite element. The loads acting at each sub-element are transferred to the respective nodal values of the composite element, and theequilibrium equation can be established according to the virtual work principle. By solving the equations nodal displacements of composite element can be got, the displacements, the strains as well as the stresses in the each sub-element can be also calculated.Thirdly, the principle of CEM is used to establish a fully-grouted rock bolt element model which comprises rock material, bolt material, rock-grout interface and bolt-grout interface. The composite element can be incorporated into the conventional finite element analysis easily with hierarchical technique. When one element contains no bolt segments, the composite element will be degenerated into the conventional finite element. The existed different kinds of explicit bolt finite element have a common characteristics that nodes are fixed and some nodes are used by both bolt and surrounding rock. So the bolt or anchor will cause much limit to finite element mesh generation, especially for three dimensional complicated structures. The bolt composite element treats rock, bolt, grout, bolt-grout and rock-grout as five sub-elements whose elasto-viscoplastic deformations are considered separately. When analyzing the rock structure, mesh may be generated without bolt firstly, then the inclination, direction and coordinates of anchor head should be inputted. After geometry operation, the information of intersections between bolt and mesh will be got. By this way it will not bother to modify the mesh, which means more convenient to use such explicit bolt element in three dimensional situations. Even if the number and direction of bolts are changed in the optimal reinforcement design, the computation grid will be kept unchanged. In this way, pre-process of the larger scale reinforced rock structures becomes relatively convenient and feasible. The results of example by CEM agree well with the in site test and FEM.Fourthly, a composite element algorithm for the jointed rock masses is proposed. Discontinuity is the common name of joint and fault in rock masses. For a long time it is a hard problem to simulate discontinuities in the deformation and stability analysis of rock foundation, slope and underground structure. In finite element analysis, two ways are often used: one is the equivalent model that numbers the influence of discontinuity in continuous deformation without considering their exact positions; anther is the explicit model that use special element to simulate the discontinuity accurately. Usually the former is applied to simulate joint and the later to big fault and interlayer. In view point of engineering, the key point of explicit simulation is the pre-process. The difficult comes from two aspects: one is many bended and extending far discontinuities exist in rock masses; another is the special element used now has fixed nodes along the extending direction of discontinuity, and some nodes are common by boththe discontinuity and its surrounding rock. The difficult and the complication of structure make pre-process cost much time and manpower even by the assistance of some powerful FEM software. The most remarkable feature of the algorithm in this dissertation is that each composite element has the possibility of containing several discontinuities segments such as faults and joints. The main advantages of the composite element method is that it can be incorporated into the conventional finite element analysis procedure, and the mesh generation of the large scale rock structures with considerable number of discontinuities requiring explicit treatment in the calculation will not be restricted by the number, position and orientation of the discontinuities.Fifthly, the pre-process of CEM for jointed rock is implemented. The main advantage of CEM is the convenient and effective preprocess compared with FEM. When analyzing rock structure, mesh may be generated firstly without considering the discontinuities. Then the inclination, direction and coordinates of corner points should be inputted. After operation of pre-process, the information of intersection between discontinuities and mesh will be got. Because of the arbitrary of discontinuities, intersection situations may be very complex: an element may contain several discontinuities intersected with each other and an element may be divided into several odd blocks. These geometry information should be judged and recorded well and truly so that CEM computation can be done. By this way mesh can be kept unchanged, which means more convenient to use such a method in three dimensional situations. There is no much profound innovation on the CEM pre-process theory, but it is important miscellaneous to realize the program and the workload is not less than writing the computation code. The application of pre-process program on the BaoZhusi complicated dam foundation shows the merits.Sixthly, the pre-process and computation program of CEM for jointed rock are applied on several examples whose complexity increase step by step. The first example is one composite element including one or two discontinuities which is pressed. The results errors are between 0.005 % ~0.03 % contrasting with the exact solution. The second example is a dam foundation containing one fault which is loaded by gravity and water pressure of reservoir. CEM and FEM are used separately to simulate explicitly the structure. The displacements and stresses of the structure by two methods agree well and the stresses curves of the fault are very close, too. The third example is BaoZhusi complicated dam foundation that contains eleven faults and one interface of materials, which is loaded by gravity and water pressure of reservoir. CEM andFEM are used separately to simulate explicitly the structure and the mesh density of two methods is close. The results include the displacements, stresses and safeties of whole structure, displacements and stresses of key points, stresses curves of every fault. The comparison shows the validity and the robustness of the new method, which is the sound base of engineering applications.Finally, the pre-process and computation program of CEM for jointed rock are applied on PuBugou large-scale underground cavern engineering. The three dimensional composite element mesh contains all six generator units. Mesh simulates main cavern, main transformer chamber, bus bar gallery, tail gates chamber, diversion tunnel, tailrace tunnel, which contains 39690 elements and 41580 nodes, thereinto 8517 composite elements. Excavation is divided into eight steps and reinforcement is applied after every excavation step. The operation between seven faults and mesh is carried out in pre-process, and its results are inputted into the computation of CEM. The former practice shows that it is very difficult to simulate explicitly the tunnels and three faults intersected with them by FEM, but CEM is able to deal with this structure involving seven such faults in the dissertation. The results list the displacements, stresses and plastic regions of every generator unit section, stresses and safeties of every fault. The computation results accord with impersonality law, which shows the effect of the method further.Although by CEM some successes have been achieved, yet most of the results are situated at beginning stage and many problems need to study deeply, such as crack analysis, thermal problem, and dynamic response of structures, bolt crossing joint problem, p-version adaptivity ect. It is also very important to realize the practicality of CEM and integrate all functions into the visualized software, to facilitate and to accelerate the application in the engineering practice.