Evaluation of a Gauss integration scheme in MPM for strain dependent soils: Assessment of slope instability including secondary failure mechanisms

A realistic quantification of the probability of flooding due to slope instability for dike assessment and design requires the calculation of the complete failure process after slope instability. To investigate which factors determine the extent of the damage of a dike profile due to an initial slope failure and the rate of an initial slope failure it is proposed to apply MPM (Deltares, 2022). The goal for the longer term is an approach to determine the probability of flooding due to slope instability, including subsequent failure mechanisms, especially secondary slope failures. To work on this goal five steps are defined in Deltares (2022). This report describes the work on the first step. For the assessment of realistic cases, complex geometries must be modelled, and strainsoftening behaviour must be taken into account. Softening is the decrease of the shear strength when the peak shear strength has been exceeded. Softening does occur in Dutch soils, especially at large strains. The “critical state” SHANSEP constitutive model which is used in Dutch practice uses the ultimate state strength (softened strength) of the material. This is a conservative approach. A computation with MPM with the correct initial strength and softening can therefore provide a decrease of the probability of flooding. The approach is thereby impactful for Dutch user practice. The MPM formulation proposed by Martinelli and Galavi (2022) is capable of modelling complex geometries, but it has limitations when strain-softening constitutive models are adopted. In this formulation, the state variables are averaged during the calculations within each computational element. It follows that softening does not occur only in material points with high deviatoric strains, but it is distributed to other material points as result of the element averaging. In this report, a new MPM integration scheme is proposed, developed within the same framework of Martinelli and Galavi (2022), but it does not modify state variables in the material points due to element averaging. An example of soil column collapse is illustrated in this report, which develops multiple failure mechanisms (progressive failure), and it highlights that the new formulation better captures softening behavior in soil. This MPM approach can be then used, in a following study, to assess the failure process of a real dike.

Dit is een rapport van Kennis voor Keringen (Rijkswaterstaat/Deltares).
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