Verification of an XFEM Based Slope Stability Analysis Method

Abstract

There are multiple numerical methods for analysing the stability of slopes. Commonly used methods for assessing the slope stability are the slip surface method, strength reduction methods or methods based on load increments. What those methods have in common is that the stability of a slope is assessed by a factor of safety or critical stability number. These dimensionless factors give an indication of the global stability of a slope. A critical stability number is computed through load increments while a factor of safety is based on the strength parameters of the soil. A relatively new XFEM-based method for analysing slope stability is being implemented in the finite element software of Diana FEA. Unique with respect to the other methods is that this method detects onset of localisation and captures the propagation of the slip surface. Therefore, this method is referred to as the propagation method in this work. The propagation method consist of three main procedure steps. First, onset of localisation is detected during incremental loading of the model and the direction of the localisation plain is obtained. In step two, enrichment elements are implemented at the location of localisation, which are able to reproduce a jump in the displacement field. This is followed by a search algorithm for detection of localisation in adjacent elements. From here on, the implementation of the enrichment elements continues till a fully developed slip surface is present, resulting in global failure of the slope. Those procedure steps need to be tested and verified. The objective of this thesis is to verify onset of localisation on element level and to provide a method for verification of the point of global failure in analyses with the propagation method. Onset of localisation is verified with analytical expressions and with numerical results. A critical stability number is used to assess the slope stability in analyses with the propagation method. A relation between the critical stability number and the factor of safety is needed, to be able to compute a factor of safety with the propagation method which is similar to a factor of safety of the slip surface method and a strength reduction method. This relation is obtained through the definitions of those factors. This creates possibilities to asses the stability of a slope with the propagation method by a factor of safety and this factor of safety can be verified with the results of a strength reduction method and a slip surface method. In addition, benchmarks are generated with the aforementioned slope stability analysis methods, which can be used for verification of the factor of safety of the propagation method. The benchmarks are the result of parameter and convergence studies. In the parameter studies, the effect of the Poisson ratio and the dilatancy angle on the factor of safety is studied. This is done by computing the maximum vertical displacements during stability analyses with various values of the Poisson ratio and the dilatancy angle. Those displacements are plotted versus the corresponding factor of safety. The resulting plots provide characteristic information which can be used for verification of the propagation method. The convergence studies are performed in order to obtain reliable factors of safety that can serve as a benchmark. The factors of safety are computed for various mesh sizes and different convergence criteria. From the results, a reliable factor of safety is obtained that can be used as a benchmark for the corresponding finite element model. In the end, a development version of the propagation method is tested and the results are verified with a benchmark which is generated with a finite element model containing interface elements.