| Author: | Wang, Zeyu |
| Title: | Two-dimensional implicit stable node-based smoothed particle finite element method in geomechanics |
| Advisors: | Yin, Zhen-yu (CEE) |
| Degree: | Ph.D. |
| Year: | 2023 |
| Subject: | Engineering geology -- Mathematical models Soil mechanics -- Mathematical models Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xix, 233 pages : color illustrations |
| Language: | English |
| Abstract: | There are many geotechnical problems involving large deformation, such as the footing installation, cone penetration, post-failure behaviours of landslide, etc. The numerical simulation of large deformation in geomechanics is challenging due to the composition of multiple nonlinearities, including that from geometry, material, kinetics, and contact. Many advanced numerical methods are accordingly developed, including the Arbitrary Lagrangian-Eulerian method (ALE), material point method (MPM), particle finite element method (PFEM), to name a few. However, some drawbacks, such as the high computational cost due to the variable mapping and high-order interpolation, numerical instability in the nodal integration, and overly rigid solution with the low-order interpolation, still hinder the further application of these methods. It is always worthwhile to develop numerical approaches for geotechnical large deformation analysis with better accuracy, efficiency, and stability. This study aims to develop a fully implicit continuum-based numerical approach named stable node-based smoothed particle finite element method (SNS-PFEM), which addresses all of the aforementioned challenges. The nodes of linear triangular mesh are regarded as the particles which not only discretize the whole computational domain but also carry all the essential variables following their movement. The Lagrangian mesh evolves with the deformation of the computational domain using some re-meshing techniques which could guarantee the quality of the element. The node-based strain smoothing method is used to improve the accuracy of the solution. The pure linear interpolation is adopted, and all the numerical integration can be easily implemented by the multiplication of constants and geometric dimensions, therefore the requirement of using the quadrature points is minimized. All the physical variables are directly carried by the nodes and conveyed in the one-to-one corresponding manner, avoiding the sophisticated variable mapping in the traditional re-meshing process. A number of numerical challenges in this method are successfully overcome, and a code suite of SNS-PFEM for the 2-D problem is gradually developed. The main contributions are listed as follows: (1) A fully implicit solid-phase SNS-PFEM with a novel nodal integration stabilization scheme is developed, which is numerically robust and computationally efficient. (2) The hydro-mechanical coupled SNS-PFEM for saturated soil is developed. An element-based polynomial pressure projection with nodal integration to stabilize the pore pressure is proposed. The coupled SNS-PFEM is efficient with nonlinear soil constitutive models and different drainage capacities. (3) The defect of volumetric locking of SNS-PFEM is successfully circumvented with selective integration and bubble function techniques. (4) The implicit dynamic approach of SNS-PFEM is developed with the time marching scheme of generalized-α method, which is unconditionally stable with the large time step. (5) The axisymmetric SNS-PFEM for both the single-phase and hydro-mechanical coupled problems are proposed. (6) The node-to-segment contact algorithm is incorporated into the coupled SNS-PFEM to simulate the soil-structure interaction problems with large deformation. (7) The coupled SNS-PFEM is applied to simulate the test embankments on soft structured clay, including the Murro embankment and the embankment at Hong Kong Chek Lap Kok international airport. Among all the present mesh-based large deformation methods, the SNS-PFEM is unique in that it not only shows prominent numerical stability but also avoids variable mapping. The computational stability and efficiency are highlighted by comparing the results of SNS-PFEM with other methods, including the PFEM and NS-PFEM. Several challenging geotechnical problems are simulated, demonstrating the ability of the proposed method in tackling the significant nonlinearity arising from large deformation, material, and contact in both static and dynamic analysis with different drainage capacities. |
| Rights: | All rights reserved |
| Access: | open access |
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