Keywords: consolidation, heterogeneity, soil profile, elastic modulus, soil permeability, lognormal distribution, Monte Carlo simulation, thin layer method.

When vertical loads are applied on a layer of soil, they cause time dependent soil deformations. Because air or water or spaces are within soil particles structure, vertical loads induce void volume reduction and soil grains rearrangement. These deformations depend basically on the type of soil, drainage conditions, and intensity of applied loads. Such a process is called consolidation and its result is soil settlement.

Geotechnical engineering deals with natural processes and material properties of geological formations which must be interpreted from limited observations and few data availability. Due to prohibitive cost of sampling and measurement errors, deterministic representation of spatial variability of soil properties is not feasible. Hence, reliable degree of consolidation and final settlement of a layer of soil can not be obtained from a deterministic approach. However, probabilistic techniques enables modeling uncertainties by analyzing their dispersion effect.

This paper deals with one-dimensional consolidation of an heterogeneous soil profile, modeled as a set of superposed layers extending horizontally to infinity, and having random properties. The spatial variability of soil properties is considered only in the vertical direction. Under these assumptions, soil profile consolidation analysis is carried out via Monte Carlo simulations combined with the Deterministic Thin Layer Method (DTLM) [1,2], which seems suitable for solving of the problem. Soil properties of interest are elastic modulus and soil permeability, modeled herein as spatially random fields, by choosing the lognormal distribution which enables analyzing their large variability [3]. The statistics regarding final settlement and time corresponding to 100% of the degree of consolidation, are investigated by performing a parametric study, which integrates the influence of, variation coefficient of both elastic modulus and soil permeability. It appears that consolidation statistics are reasonably well represented by the proposed simulation technique. Obtained results for the model often encountered in practice, model with simple drainage, indicate that the heterogeneity significantly influences consolidation of soil profile, generating a quite different way of soil grain rearrangement and water pressure dissipation in comparison to the homogeneous case, and causing a delay in consolidation process.

The performed parametric study indicates that whatever the variability of soil permeability is, as the coefficient of variation of elastic modulus increases, the induced settlement increases too, which means that the simulated soil medium becomes softer. Also, as the coefficients of variation of both elastic modulus and soil permeability increase, time corresponding to 100% of consolidation degree gets important. Furthermore, results obtained show that for highly heterogeneous medium, the consolidation process takes a very long time before its achievement.

1

E. Kausel, J.M. Roësset, "Stiffness matrices for layered soils", Bulletin of Seismological Society of America, 71(6), 1743-1761, 1981.

2

E. Kausel, "Thin layer method: Formulation in the time domain", International Journal for Numerical Methods in Engineering, 37, 927-941, 1994. doi:10.1002/nme.1620370604

3

G.A. Fenton, "Simulation and Analysis of Random Fields", Ph.D. thesis, Princeton University. 1990.

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