  Engineering problems are often characterized by significant uncertainty in
their material parameters. A typical example coming from geotechnical
engineering is the slope stability problem where the soil's cohesion is modeled
as a random field. An efficient manner to account for this uncertainty is the
novel sampling method called p-refined Multilevel Quasi-Monte Carlo (p-MLQMC).
The p-MLQMC method uses a hierarchy of p-refined Finite Element meshes combined
with a deterministic Quasi-Monte Carlo sampling rule. This combination yields a
significant computational cost reduction with respect to classic Multilevel
Monte Carlo. However, in previous work, not enough consideration was given how
to incorporate the uncertainty, modeled as a random field, in the Finite
Element model with the p-MLQMC method. In the present work we investigate how
this can be adequately achieved by means of the integration point method. We
therefore investigate how the evaluation points of the random field are to be
selected in order to obtain a variance reduction over the levels. We consider
three different approaches. These approaches will be benchmarked on a slope
stability problem in terms of computational runtime. We find that the Local
Nested Approach yields a speedup up to a factor five with respect to the
Non-Nested approach.
