Soft particles

Numerical simulations play an important role in Geotechnical Engineering and Geomechanics, e.g. for the prediction of settlements and landslides. A standard tool of numerical simulations is the Finite Element Method. In its usual version for solids, it is based on material meshes, i.e. the considered bodies are endowed with a concomitant mesh, whose deformations are investigated. Considerable difficulties can be faced when the mesh deformations are too large, or if the the mesh deformation is not topology-preserving (i.e. if the individual nodes change their neighbors, e.g. when interior nodes become boundary nodes), as this is the case for some typical problems of Geotechnical Engineering such as landslides and penetrations (e.g. driving of piles or tunnels). For such cases the so-called mesh-free finite element methods are predestined. This group of methods already comprises a very large amount of versions that can be hardly overlooked. Being particularly apt for Geotechnical Engineering, it has not yet been introduced in this field except from very few cases worldwide. In the proposed project, we intend to investigate the applicability of some special versions of mesh-free finite elements in the field of Geotechnical Engineering and Geomechanics. Herein we intend to apply a modern constitutive equation for soils that has been developed by the Austrian partner. We certainly do not intend to check the applicability in geotechnical problems of the entire multiplicity of the many particular versions of mesh-free methods already proposed.

Numerical simulations help to gain insight into complicated phenomena. With properly calibrated constitutive models, they also help to make predictions and, hence, are profitable in design. To handle a real-world problem in numerical simulations, it is discretized in space and time. In a time interval, the governing equations consisting of differential equations are formulated for the study subjects. The equations are then expressed numerically, by evaluating the derivatives in the differential equations using numerical interpolation or approximation methods. Thereafter, the differential equations can be solved subject to some initial and/or boundary conditions. Meshless numerical methods have received great attention since the 1990s.Since we are interested in solving typical geotechnical problems using our own constitutive equation barodesy, we refrained from using any of the widespread codes, which are usually available as black boxes, and we developed our own code SPARC, based on collocation of scattered data and strong formulation of equilibrium. The considered continuum is replaced by scattered mass points that carry all relevant field properties such as density, velocity, stress etc. The needed spatial derivatives are obtained by differentiating local interpolation/approximation functions. The connectivity of the individual particles can change from timestep to timestep allowing thus for large deformations. Despite its simplicity, SPARC was able to yield realistic simulations of a series of soil mechanics tests (oedometer test, biaxial test and triaxial test) including the inhomogeneous deformation that develops in the course of these tests. In addition to these simulations, laboratory model test using fine sand were carried out, in which the cyclic tilt of a retaining wall induces a peculiar motion in the backfill (sand) with closed trajectories.