A Meshfree Numerical Approach for Soils at Rest and in Flow

Granular materials are solids as they can permanently sustain shear stress. On the other hand, they can undergo large deformations (like fluids). The transition from small strain, where the inner stresses increases with strain, to large strain, where the stresses remain constant at further deformation (flow), can be considered as phase transition. The most striking similarity is pattern formation, which in granular bodies appears as shear localization. The particular position of granular materials between fluids and solids characterizes many of their scientific and technical applications. They can be placed in fills, slopes and silos, but they can also flow downhill in valleys and pipes. Vessels can move upon sand, but they also can sink into it. Buildings are safely founded on sand but they can also subside into it during liquefaction. The implied large deformations are usually non-topological, i.e. neighborhood relations are not preserved. Therefore, meshfree methods appear to be the appropriate numerical tool for simulations. As compared with the Discrete Element Method, meshfree methods open the possibility to use not only refined constitutive models but also variable initial densities as well as the whole spectrum of continuum mechanics. In the first phase of our research project, we developed a special meshfree method that is characterized by outstanding simplicity. It is a particular implementation of the motion of points whose density, velocity, and stress can be obtained by interpolation of neighborhood configuration. The governing balance equations are used in the strong form. Two codes have been developed, FPM (explicit and linearized implicit) and SPARC (nonlinear). In the continuation phase, applied herewith, the gained insights and achievements will be used to simulate not only quasi-static (slow) deformations but also dynamic (fast) ones, and also to couple them to each other. Coupled problems are characterized by phase transitions of the type solid / quasi-fluid / solid. To model such transitions each method applied so far has to be enhanced, and synergy effects have to be exploited. The list of coupled processes is long and involves e.g. failures of geotechnical structures (landslides), discharge from silos, tunnel collapse, etc. The biggest challenge is of mathematical/physical nature: the loss of controllability of the mechanical behavior of granular materials that occurs in the vicinity of phase transitions (limit states in geotechnical engineering). This loss manifests in various ways: computation instabilities, ill-conditioned matrices, problems of convergence, and the like, and requires special regularization methods.

Numerical methods play a completing role along theory and experiment in analysis of mechanical problems. The numerical approaches can be categorized in two groups of mesh based and meshfree ones. One of the deficiencies of standard mesh-based methods is their difficulty in simulating large deformations, which are the case for most problems in soil mechanics. In contrast to mesh-based methods, the meshfree approaches do not possess connectivities between the material points and should, therefore, be more appropriate for problems associated with large deformations. In this project, a straightforward meshfree method, the Soft Particle Code (SPARC), is developed for simulation of a number of problems in soil mechanics. The simulations comprise conventional laboratory tests, large deformations in vertushka, formation of shear bands, punching, cone penetration, turbulence in granular solids and formation of ptygmatic folds.