E-Thesis 540 views
Explicit and Implicit Finite Element Techniques Applied to Mechanical and Coupled Geomechanical Problems / NIA FRY
Swansea University Author: NIA FRY
DOI (Published version): 10.23889/SUthesis.63252
Abstract
In this thesis we look at the development and comparison of critical state material models in both explicit and implicit forms, followed by a review and collation of analytical solutions for coupled porous media problems, and finally consider the solution and comparison of porous media problems with...
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Swansea, Wales, UK
2023
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| Institution: | Swansea University |
| Degree level: | Doctoral |
| Degree name: | Ph.D |
| Supervisor: | Li, Chenfeng F. |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa63252 |
| Abstract: |
In this thesis we look at the development and comparison of critical state material models in both explicit and implicit forms, followed by a review and collation of analytical solutions for coupled porous media problems, and finally consider the solution and comparison of porous media problems with both stabilised staggered coupled and fully implicit, monolithic Finite Element schemes. We determine the classes of problems within computational geomechanics where the staggered or fully implicit monolithic coupling schemes are most effective. These techniques can be applied in industries such as civil engineering and the energy-based sector.We start with the governing porous media equations derived in some detail. The porous media governing equations use the balance equations of mass and linear momentum for both fluid and solid phases. Subsequently an overview of the explicit and implicit Cam Clay material model is given along with implementation details. The main drive in these investigations is the comparison of explicit and implicit treatments, and the response when considering like-to-like geotechnical problems. To this end, assessments are carried out over a range of different stress states, establishing for the corresponding equal material properties that a good match is attained between both solution techniques. The validation examples include triaxial cell loading, column compaction and a strip footing loaded to failure. Additionally, we consider the explicit and implicit soft rock SR3 material model overview and implementation details. This next section develops the model step-to-step and discusses different forms in which the implicit SR3 material model could be cast.The geomechanical analytical methods section introduces the fundamental analytical solutions, where the problem description is provided along with the resulting exact solution for each test case. The comparison test cases selected for this thesis include: 1) Consolidation theory with Terzaghi analytical solution, 2) Sedimentation theory with Gibson analytical solution, 3) Coussy wellbore poroelastic analytical solutions, and 4) Mandel-Cryer problem. For the Coussy wellbore poroelastic analytical solutions, the analytical solution is provided for injection of a fluid considering line injection of fluid mass.Furthermore, the formulation of a staggered explicit-implicit and fully implicit, monolithic coupled scheme is described, and its function aimed at porous media is outlined. We explore the non-analytical solutions of two examples consisting of 1) wellbore instability and 2) Biot. Two analyses of the explicit pore pressure are considered 1) the undrained storativity assumption and 2) a storativity which is established on incremental pore pressure solutions of both seepage and deformation governing equations.Finally, the implementation side of the staggered explicit-implicit and fully implicit, monolithic coupled scheme is introduced, as this forms the background of the coupling study with many of the geomechanical analytical solutions. The final section shows the simulation results for the staggered coupling scheme and the fully implicit, monolithic coupled scheme, which consists of the finite element model set-up for each case, the results and conclusion. |
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| Keywords: |
Cam Clay material model, SR3 material model, triaxial cell, column compaction, quadratic convergence, return-mapping algorithm, hydrostatic compression, shear compaction, shear dilation, staggered coupling scheme, fully monolithic coupling scheme, porous media, well-bore instability, Gibson’s sedimentation rate problem, wellbore poroelastic solutions |
| College: |
Faculty of Science and Engineering |