Particle finite element method in geomechanics

Research Doctorate - Doctor of Philosophy (PhD)Despite the wide application of the finite element method (FEM) in geotechnical engineering, the numerical analysis usually stops at the point when soil flow occurs and results in overall `failure'. In many cases, the so-called failure only represents a specific time point of the deformation process and the soil flow itself is of interest as well. A typical example is a landslide in which a transition of the soil behaviour is experienced from solid-like to liquid-like, and then back to solid-like. For such problems, a correct understanding of the triggering mechanism is important. However, the prediction of the sliding process as well as the estimation of the final deposit are also of great concern. Unfortunately, the traditional Lagrangian FEM cannot handle problems involving both solid-like and liquid-like behaviour. This is to a large extent, due to the following two issues: (1) Severe mesh distortion and boundary evolution as a result of large changes in geometry. (2) Difficulties in solving the highly nonlinear and non-smooth discrete governing equations in an efficient and robust manner. In this thesis, a new continuum approach that addresses the above two issues explicitly is proposed for handling problems involving the solid-liquid transitional behaviour in geomechanics. More specifically, the first issue is solved via the so-called Particle Finite Element Method (PFEM) originally proposed for the solution of fluid dynamics problems involving free surfaces. The key feature of the PFEM is that mesh nodes are treated as a cloud of particles which can move freely and even separate from the domain to which they originally belong. At each time step, the computational domain is detected based on those particles; then, the conventional FEM is used to solve the problem on the identified domain. Regarding the second issue, mathematical programming formulations for the dynamic analysis of elastoplastic behaviour are developed with a wide utilisation of the Hellinger-Reissner variational theorem. The resulting formulations can be cast as a second-order cone program and solved via appropriate optimization methods. Unlike the conventional Newton-Raphson based FE scheme, the convergence of the solution of the scheme developed is guaranteed regardless of the quality of the initial solution. Formulations for both plane strain and axisymmetric problems are developed. Moreover, the contact between deformable bodies and rigid boundaries is also taken into account. A number of challenging problems in plane strain cases are solved successfully, which demonstrates the capabilities of the proposed approach. Furthermore, the approach is used to reproduce laboratory tests involving the collapse of axisymmetric granular columns. A quantitative comparison between the simulated results and the existing experimental data is conducted. Finally, an actual natural disaster event, the Yangbaodi landslide, is considered and analysed in some detail