Probabilistic analysis of one-dimensional large-deformation consolidation considering permeability relationship's variability

The large-deformation consolidation theory is fundamental for many applications involving the poromechanical couplings but faces great challenges in making accurate predictions in practices due to significant uncertainties of material permeability, k. The permeability could take random values at constant void ratio, e, due to random microscopic flow channels, moreover, its statistics vary with evolving microscopic structure subjected to volumetric compression during large-deformation consolidation, which is referred to as permeability's volumetric variability in this work. Current consolidation-related probabilistic models are focused exclusively on the properties' spatial variability and limited to infinitesimal deformations. Here, we formulate a random largedeformation consolidation model, RANDCON, by combining the random field theory with an existing piecewise linear formulation in the Monte Carlo framework, which will simulate the large-deformation consolidation as a random process. In this model, we treat e as a spatial-like dimension to establish a generalized nonstationary random field where the statistical moments of k changes with e (i.e., random k - e relations) to embrace volumetric variability. We choose the piece-wise linear formulation that directly updates k from the generalized random field, which, being different from the conventional random field approach, is performed at every time step. The statistical results from an example shows that (1) variabilities of k yields an overall delayed consolidation due to local clogging, which could be aggravated by the associated fluctuations of e, (2) "too significant" clogging can, conversely, suppress the clogging by creating a permeable near-surface zone with increased e (k) from fluctuations; (3) the converse clogging effect also explains distinct effects of scale of fluctuation on changes of average consolidation rate in different cases. Practical significances mainly include that the deterministic approach might underestimate the time to reach full consolidation.