Strength of sand in plane strain conditions: insights from legacy experimental data

The plane strain assumption is widely used in geotechnical engineering for boundary value problems such as retaining structures and embankments. In practice, the peak friction angle of cohesionless soils under plane strain conditions is frequently approximated by increasing the friction angle obtained from triaxial compression tests by a factor 9/8 to account for the experimentally observed strength surplus. This paper demonstrates, both theoretically and experimentally, that this factor is neither constant nor consistently conservative. Using a comprehensive database of legacy experiments -including both independent stress control and plane strain tests, with matching triaxial compression data- a multi-linear regression analysis is performed to identify key predictors of the plane strain strength surplus. In addition to relative density and confining stress, two geometric parameters are significant: (i) the ratio of sample height to the height for a shear band to freely develop across the sample, and (ii) the ratio of sample height to sample length (distance between the zero strain boundaries). Based on these findings, two empirical relations are proposed for estimating the plane strain strength surplus as a function of relative density and confining stress, conditioned on typical sample geometries: one for uniform strain conditions and one for localized strain conditions. A case study on slope stability demonstrates that the effect of selecting either of these empirical relations on the calculated factor of safety is comparable to (in)adequately capturing localized strain behavior in the model environment. This highlights that the appropriate plane strain strength surplus depends both on soil state and the model’s capacity to capture localized strain behavior.