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A total stress-pore water pressure formulation of coupled consolidation analysis for saturated soils

Authors: Zhang, X., Briaud, J.-L.
Key words: Saturated soils, coupled consolidation, undrained conditions, stress state variables, numerical instability, thermodynamic analogue
Source: The International Journal of Geotechnical Engineering
Volume: 3
Issue: 2
Pages: 15
Date: 2009-04-01
DOI: 10.3328/IJGE.2009.03.02.171-185

A one-phase formulation has been extensively used to deal with consolidation for saturated soils in which incompressible elasticity is used for undrained conditions. An undrained Poissonís ratio close to 0.5 and the equivalent bulk modulus for water are required as inputs. Use of the latter one is inconsistent with assumption of water incompressibility in the soil mechanics for saturated soils. In addition, the formulation often leads to indeterminate problems, which is mainly attributed to the fact that there is no strict and fast rule available to determine the exact values of undrained Poissonís ratio and equivalent bulk modulus for water. At present, determination of undrained Poissonís ratio and the equivalent bulk modulus for water for undrained conditions is highly subjective, and quality of the simulation results relies on the modelersí experience. Special numerical integration techniques are also needed to avoid numerical instability and systematic error associated with the use of the two parameters. By considering saturated soil as a special case of unsaturated soil and using the extensively-used two stress state variable concept in unsaturated soil mechanics, this paper presented a total stress-pore water pressure formulation of coupled consolidation theory for saturated soils. Derivation of governing differential equations and implementation in the finite element method using the thermodynamic analogue were reported, followed by its verification through example analyses of loading under undrained condition and coupled consolidation for a saturated soil. Its potential application in the pavement engineering was explored as well by modeling the pore water pressure increase due to a moving load. In the proposed formulation, any behavior of a saturated soil, including undrained conditions, is expressed by a combination of two drained processes: 1) changes in the total stress under constant pore water pressure, and 2) changes in the pore water pressure under constant total stress. In this way, neither undrained Poissonís ratio nor the equivalent bulk modulus is needed as an input, and the associated numerical instability and systematic error are avoided. No special numerical integration technique is required, and converged solutions can be easily obtained by a few iterations.



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