Elasto-Plastic Constitutive Modelling of Geotechnical Material - Investigation of the Intermediate Principle Stress Influence and Exploration of the General Parametric Yield Surface Format

Abstract

In the matter of constitutive modelling of frictional material, two major models are the Mohr-Coulomb and the Drucker-Prager yield criteria. However, contradictions arises as the former neglects the intermediate principle stress and all stresses are of equal importance in the latter. Evidently both statements cannot be true and the actual material behaviour is somewhere in between. The Mohr-Coulomb model is in general a better limit stress representation for frictional soil, however, especially conservative in plane strain calculations, where it to some extent has become the norm to increase the angle of friction with some empirical expression. Yield surfaces to better describe the actual material behaviour has been proposed in plenty, however, as more advanced models thrive in academia, these have failed to gain a widespread use by practitioners. In this thesis, a concept of yield surfaces denoted the General Parametric Yield Surface Format, proposed by Lars Damkilde, is explored. Three novel yield surfaces, which encompasses several existing models are formulated and implemented in a numerical framework. When evaluating the numerical performance of a plasticity model, discrepancy, computation time and robustness are of interest, where the latter two are somewhat connected. The first proposed yield surface operates on four parameters, of which two can be omitted to obtain the Mohr-Coulomb model. This model has proven efficient, however, lacks robustness, especially in the analyses of three-dimensional systems. The second proposed yield surface is therefore developed as a smooth continuous approximation of the first model for a numerically robust implementation. It is formulated by employment of a new concept of local corner rounding, which, to the authors knowledge is not presented elsewhere in the literature. Furthermore, this model enables a smooth tension cut-off, and can serve as an optimised material fit, provided the existence of experimental data. The first two models are formulated with linear hydrostatic stress dependency, as a common simplification. A widely accepted formulation of the nonlinear hydrostatic stress dependency for common sands was proposed by Bolton, which is incorporated in the third yield surface formulation. The result of this is an advanced nonlinear model, which operates on the well-known parameters from Bolton, and constitutes the most optimized material calibration conducted in this thesis, and demonstrates the generality of the new yield surface concept. The novel yield surface models are implemented in a computational framework, in MATLAB as well as a Fortran source code for use in Abaqus. The models are calibrated to data from true triaxial experiments and employed in a series of elasto-plastic finite element analysis of typical geotechnical problems, to investigate the influence of the intermediate principal stress and computational performance of the models. The simulation results reveals a vast unused potential in comparison with the Mohr- Coulomb criterion in plane strain conditions, and a considerable increase in general 3D as well. A notable increase in bearing capacity can be obtained if the model is calibrated with standard triaxial tests in both extension and compression, which is not a possibility with the Mohr-Coulomb model. The novel corner rounded model comes with a cost in computation time, however, it is found numerically robust, especially in three-dimensional analyses. It is therefore the recommended model by the authors, as robustness is a desired quality of the numerical implementation.

A master thesis from Aalborg University

Elasto-Plastic Constitutive Modelling of Geotechnical Material - Investigation of the Intermediate Principle Stress Influence and Exploration of the General Parametric Yield Surface Format

[Elasto-plastisk konstitutiv modellering af geotekniske materialer - Undersøgelse af den midterste hovedspændings indflydelse samt udforskning af ``General Parametric Yield Surface Format'']