02 Fakultät Bau- und Umweltingenieurwissenschaften
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Item Open Access Formulation of a dynamic material point method (MPM) for geomechanical problems(2013) Kafaji, Issam K. J. al-; Vermeer, Pieter (Prof. Dr.-Ing.)In geomechanics one often encounters large deformations, soil-structure interaction and dynamical problems, e.g., in pile driving and installation of anchors. Moreover, geomechanical phenomena that include excessive movement of soil masses like landslides can pose a danger to human life and property. The numerical simulation of the physics is challenging, particularly if a saturated soil is subjected to dynamic loading, leading to propagation of different waves in the soil. Because of the reliance of Lagrangian finite element methods (FEM) on a mesh, they are not well suited for the treatment of extremely large deformations of solids. The need for overcoming this limitation urged researchers throughout the last decades to devote considerable effort to the development of more advanced computational techniques. Such techniques include the combination of Lagrangian and Eulerian finite element methods, meshless methods and mesh-based particle methods. The intent of this thesis is to further develop and extend the material point method (MPM), which is a mesh-based particle method, for use in geomechanics. MPM can be conceived as an extension of FEM, in which soil and structural bodies are represented by Lagrangian particles that move through an Eulerian fixed mesh. The physical properties of the continuum reside with particles throughout the computations (deformations), whereas the Eulerian mesh and its Gauss points carry no permanent information. Hence, MPM combines the best aspects of both Lagrangian and Eulerian formulations and avoids as much as possible the shortcomings of them. Three novel MPM development are described in this thesis. In the analysis of geomechanical problems that involve dynamics, absorbing boundaries are introduced to prevent the reflection ofwaves at the selected boundary of the domain. The well-known viscous boundaries, which will continuously creep under load, are modified to viscoelastic boundaries by introducing Kelvin-Voigt elements to limit such non-physical displacements. The novel extension of MPM to model the behavior of saturated soils under dynamic loading is formulated. Enhancement of volumetric strains is adopted to mitigate the spurious pressure oscillations which plague low-order finite element implementations. The algorithm is applied to predict the generation and dissipation of pore pressures in a sea dike under heavy dynamic loading by wave attack. Numerical simulation of pile driving is investigated. Results of shallow and deep penetration are presented. Due to the complex behavior of sand in pile driving, a highly non-linear advanced hypoplastic model is to be used for sand. Explicit Euler forward scheme with sub-stepping technique is used in the integration of this model. MPM is applied to analyze different geomechanical problems, including the collapse of a tunnel face, the instability of a slope and the deep installation of a dynamic anchor. The dynamic MPM can be applied to quasi-static problems. To this end, a local damping procedure for single and two-phase materials is discussed, being applied to reach fast convergence to quasi-static equilibrium. Such convergence is detected by two proposed criteria on force and energy. Mass scaling is presented as a procedure that allows the use of large time step size for problems, in which inertia effect can be disregarded.Item Open Access Formulation and application of a quasi-static material point method(2012) Beuth, Lars; Vermeer, Pieter A. (Prof. Dr.-Ing. )This thesis is concerned with the analysis of quasi-static large deformation problems such as the jacking of piles where inertia and damping effects can be neglected, as opposed to dynamic problems such as pile driving. To this end, a novel type of Material Point Method (MPM) that is specifically adapted to the analysis of quasi-static large deformation problems is developed. The quasi-static MPM can be considered as an extension of the classical Updated Lagrangian Finite Element Method (UL-FEM). As with the UL-FEM, a solid body is discretised by finite elements, but in addition, the solid body is discretised by a cloud of material points which moves through the mesh in the course of a computation. The movement of material points represents the arbitrary large deformations of the solid body. The FE grid is used as with the UL-FEM to compute incremental displacements and strain increments at the locations of material points. In contrast to the UL-FEM, the mesh can be reset into its original state or changed arbitrarily if accumulated distortions of the FE grid cause numerical inaccuracies. Material and state parameters of the solid body as well as applied loads are stored in material points. In contrast to most existing implementations of the MPM, the developed quasi-static variant makes use of implicit rather than explicit time integration, which allows for a considerable reduction of the computation time in case of quasi-static problems. The development of the quasi-static MPM and its validation for simple benchmark problems is the first aim of this thesis. This includes the modelling of soil-structure interaction within the developed method, a feature that is essential to many geotechnical analyses. Here, the novel approach of extending interface elements commonly used in small-strain Finite Element analyses for use with the Material Point Method has been taken. The application of the quasi-static MPM to the simulation of cone penetration testing (CPT) forms the second aim. This widely-used in-situ test consists of pushing a steel rod with a measuring device attached to its tip into the ground with constant velocity. Numerical analyses of cone penetration testing improve the understanding of involved mechanical processes and allow to refine existing or establish new correlations between CPT measurements and soil properties. In the frame of this thesis, cone penetration testing in undrained soft clay is considered with the aim of investigating the relation between the tip resistance and the undrained shear strength of clay. Here, a new soil model that takes into consideration the anisotropic strength of clay has been applied. Thereby, the undrained shear strength of clay and thus measurements of tip resistance are reproduced with a significantly higher accuracy than with previously performed numerical analyses reported so far in literature.