Keywords: geotechnical engineering, clay, analytical solutions, soft soil, consolidation, degree of consolidation, large strain consolidation.

Over the last 30 years or more, great strides have been made on the theoretical development of one-dimensional large strain consolidation of soft soils. Several investigators have contributed to the advancement (e.g. Gibson et al. 1967, 1981, 1995; Mesri and Rokhsar, 1974; Carter et al., 1977; Schiffman, 1980; Cargill, 1984; Chopra and Dagush, 1992), but it appears that the inherently intractable form of the governing equation has so far prevented the development of analytical solutions of large strain consolidation, even for idealized cases.

The objective of this paper is to show the development of some fully explicit analytical solutions of one-dimensional large strain consolidation. To develop the solutions, the authors idealized the coefficient of volume compressibility, the coefficient of permeability of the soil and the applied loading sequences. This is then combined with a transform that reduces the governing equation to a form identical to the Terzaghi's consolidation equation from which explicit analytical solutions for the excess pore pressure, settlement, average degree of consolidation and void ratio are derived.

These solutions are useful in their own right while also providing an efficient method to validate numerical solutions of large strain consolidation analyses. A few numerical examples are given comparing the results of large and conventional small strain theory. Parametric studies have been undertaken showing that unlike in conventional small strain theory, the average degree of consolidation defined by stress (i.e. Up) and that defined by strain (i.e. Us) in large strain theory are not identical. The studies show that the settlement predicted by large strain theory is smaller than that given by small strain theory, and both the development of settlement and the dissipation of excess pore water pressure in large strain consolidation are faster than in small strain consolidation. It is also found that the discrepancy between the consolidation theories of large strain and small strain decreases with decreasing compressibility of soil and magnitude of applied load.

1

Cargill, K. W., 1984. Prediction of consolidation of very soft soil. J. Geotech. Eng., ASCE, 110:6:775-795. doi:10.1061/(ASCE)0733-9410(1984)110:6(775)

2

Carter, J. P., J. C. Small and J. R. Booker, 1977. A theory of finite elastic consolidation. Int. J. Solids Structures, 13:467-478. doi:10.1016/0020-7683(77)90041-5

3

Chopra, M. B. and G. F. Dargush, 1992. Finite-element analysis of time- dependent large-deformation problems. Int. J. Num. Ana. Methods Geomech., 16:101-130. doi:10.1002/nag.1610160203

4

Gibson, R. E., G. L. England and M. J. L. Hussey, 1967. The theory of one- dimensional consolidation of saturated clays: I. Finite non-linear consolidation of thin homogeneous layers. Geotechnique, 17:2:261-273.

5

Gibson, R. E., R. L. Schiffman and K. W. Cargill, 1981. The theory of one- dimensional consolidation of saturated clays: II. Finite nonlinear consolidation of thick homogeneous layers. Canadian Geotechnical Journal, 18:2:280-293. doi:10.1139/t81-030

6

Gibson, R. E., L. J. Potter and C. Savvidou, 1995. Some aspects of one- dimensional consolidation and contaminant transports in wastes. Compression and Consolidation of Clayey Soils, Yoshikuni and Kusakabe(eds), Rotterdam: Balkema, 2:1-19.

7

Mesri, G. and A. Rokhsar, 1974. Theory of consolidation for clays, J. Geotech. Eng. Division, ASCE, GT8:889-903.

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