Numerical solution of cylindrical cavity expansion in sands: effects of failure criteria and flow rules

Brenton Ryan Cook

Cavity expansion in soil is an important area of interest within the field of geotechnical engineering. Detailed understanding of this boundary value problem would allow engineers to better interpret in-situ test data from devices such as the pressuremeter and the cone penetrometer. Cavity expansion theory can also be extended to important and complex design problems commonly encountered in practice such as driven/cast in place lateral pile capacities, in addition to applications for tunneling. Early research into cavity expansion in soils involved developing closed form solutions for clays assuming linear elastic, perfectly plastic behavior. Later, rigorous analytical solutions for the cavity expansion problem were introduced which made a concerted effort to capture the effects of confinement pressure and density to characterize the behavior of sands. More recently, finite difference models have been presented that are more versatile for conducting studies on the influence of various parameters on cavity expansion. A recent finite difference model proposed by researchers from Purdue University discretized the plastic region around an expanding cavity into thin shell elements. Iterations across each shell were carried out using an empirical friction angle relation in conjunction with a flow rule and failure criterion. Recognizing that there exist numerous friction angle models, flow rules and failure criteria, it is of interest to investigate how their combinations influence results when implemented into a cavity expansion analysis. This study modified the finite difference model with the objective of investigating the influence of different friction angle models, flow rules and failure criteria within a cylindrical cavity expansion algorithm for sand assuming drained conditions. Results from the proposed algorithm were evaluated including limit pressures for different combinations of depth and relative density. It was found that the choice of flow rule had little impact on predicted results, whereas the choice of failure criterion did have influence. Recognition of such modeling nuances allows for algorithms, such as the one presented in this study, to predict soil conditions in the field with increased confidence.

Numerical solution of cylindrical cavity expansion in sands: effects of failure criteria and flow rules

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