The classical Richards equation describes infiltration into porous soil as a nonlinear diffusion process. Recent experiments have suggested that this process exhibits anomalous scaling behaviour. These observations suggest generalizing the classical Richards equation by introducing fractional time derivatives. The resulting fractional Richards equation with appropriate initial and boundary values is solved numerically in this paper. The numerical code is tested against analytical solutions in the linear case. Saturation profiles are calculated for the fully nonlinear fractional Richards equation. Isochrones and isosaturation curves are given. The cumulative moisture intake is found as a function of the order of the fractional derivative. These results are compared against experiment.

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Experimental results obtained in a series of displacement controlled oedometric tests on soft rocks are presented. Four different materials characterised by a high void ratio have been examined; three natural soft rocks and an artificial one. The materials under investigation were conchyliates stone, calcarenite, pumice stone and Gasbeton. In order to monitor the stress path as well, a soft oedometer ring was designed and constructed for the measurement of the radial stresses. The observed behaviour can be divided in three phases. After an initial phase in which the mechanical response is essentially elastic, a second phase starts, in which bonds are progressively broken, so that in the axial stress–strain curve a stress decrease is recorded and in some cases, a sort of ‘curl’ appears in the stress path. This is associated to the occurrence of strain non‐homogeneities in the form of compaction bands. In the final part of the experiment the axial stress increases exponentially and the stress path returns to be linear, as the one expected for a cohesionless material. The experimental behaviour is reproduced by means of an elastoplastic strain‐hardening/softening constitutive model and the occurrence of compaction bands is theoretically predicted.