Drained behaviour of sand

The objective of the project has been to improve the procedure applied at NGI when the drained capacity (failure) in sand is computed.

Closed form expressions for the bearing capacity factors entering the general bearing formula from Brinch Hansen (DGI Bulletin 28) are traditionally applied when the drained bearing capacity in sand is computed. These bearing capacity factors are based on perfect plasticity. A key problem when analysing real soil problem with elasto-plasticity as for instance using the Mohr Coulomb or the Hardening Soil model in Plaxis is that the dilatancy angle is different from the friction angle. The material may then be unstable and the capacity becomes mesh dependent as in more typical softening problems.

This year two model tests on sand have been simulated to see the performance of existing material models for sand in the state of failure. The plan was to study the performance of more advanced models as the Hypo-Plastic model from Karlsruhe, however this was not possible due to limited resources.

Figure 1 shows the calculated shear bands using the Hardening Soil model in Plaxis and the obtained shear bands from one of the tests in (20061273-1). The inclination of the shear bands is about 58 from the horizontal which is lower than = 45 + /2 = 66, where =42.5.

The angle agrees instead well with the critical angle obtained from the bifurcation analysis (or acoustic tensor) = 45 + (+)/4 = 58, where =8. However, in order to fit the global stress/strain (load/displacement) response, a more advanced model including post peak strain softening behaviour is required. Furthermore, in order to achieve a mesh independent solution some kind of regularisation techniques have to be utilised.

Figure: Back-calculation of plane strain drained extension tests on sand using the Hardening Soil model in Plaxis. Calculated and observed shear bands at the end of the test.