A frost heave model which simulates formation of ice lenses is developed for saturated salt-free soils. Quasi-steady state heat and mass flow is considered. Special attention is paid to the transmitted zone, i.e. the frozen fringe. The permeability of the frozen fringe is assumed to vary exponentially as a function of temperature. The rates of water flow in the frozen fringe and in the unfrozen soil are assumed to be constant in space but vary with time. The pore water pressure in the frozen fringe is integrated from the Darcy law. The ice pressure in the frozen fringe is determined by the generalized Clapeyron equation. A new ice lens is assumed to form in the frozen fringe when and where the effective stress approaches zero. The neutral stress is determined as a simple function of the unfrozen water content and porosity. The model is implemented on an personal computer. The simulated heave amounts and heaving rates are compared with experimental data, which shows that the model generally gives reasonable estimation.

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SUMMARYThe paper presents an optimization routine especially developed for the identi"cation of model parameters in soil plasticity on the basis of di!erent soil tests. Main focus is put on the mathematical aspects and the experience from application of this optimization routine. Mathematically, for the optimization, an objective function and a search strategy are needed. Some alternative expressions for the objective function are formulated. They capture the overall soil behaviour and can be used in a simultaneous optimization against several laboratory tests. Two di!erent search strategies, Rosenbrock's method and the Simplex method, both belonging to the category of direct search methods, are utilized in the routine. Direct search methods have generally proved to be reliable and their relative simplicity make them quite easy to program into workable codes. The Rosenbrock and simplex methods are modi"ed to make the search strategies as e$cient and user-friendly as possible for the type of optimization problem addressed here. Since these search strategies are of a heuristic nature, which makes it di$cult (or even impossible) to analyse their performance in a theoretical way, representative optimization examples against both simulated experimental results as well as performed triaxial tests are presented to show the e$ciency of the optimization routine. From these examples, it has been concluded that the optimization routine is able to locate a minimum with a good accuracy, fast enough to be a very useful tool for identi"cation of model parameters in soil plasticity.

An algorithm is outlined for the implicit integration of isotropic plasticity models for an arbitrary choice of mixed stress and strain control variables. Drained as well as undrained behaviour is considered. The closest-point-projection method in conjunction with a completely strain-driven format is used in a core algorithm. In the drained case strain response variables are determined via iterations to satisfy equilibrium of prescribed and calculated stresses that correspond to the strain response variables. In the undrained case, on the other hand, strains and pore pressure are determined via simultaneous iterations to satisfy equilibrium and the incompressibility condition. The algorithm is applied to a new generalized cam-clay model, and various iteration techniques are assessed. In particular, Newton iterations which employ the matrix of algorithmic tangent stiffness moduli are shown to compete favourably with more conventional methods.

SUMMARYCoupled flow of water, chemicals, heat and electrical potential in soil are of significance in a variety of circumstances. The problem is characterized by the coupling between different flows, i.e. a flow of one type driven by gradients of other types, and by the dual nature of certain flows, i.e. combined convection and conduction. Effective numerical solutions to the problem are challenged due to the coupling and the dual nature.In this paper, we first present a general expression that can be used to represent various types of coupled flows in soil. A finite element method is then proposed to solve the generalized coupled flows of convection-conduction pattern. The unknown vector is first decomposed into two parts, a convective part forming a hyperbolic system and a conductive part forming a parabolic system. At each time step, the hyperbolic system is solved analytically to give an initial solution. To solve the multi-dimensional hyperbolic system, we assume that a common eigenspace exists for the coefficient matrices, so that the system can be uncoupled by transforming the unknown vector to the common eigenspace. The uncoupled system is solved by the method of characteristics. Using the solution of the hyperbolic system as the initial condition, we then solve the parabolic system by a Galerkin finite element method for space discretization and a finite difference scheme for time stepping.The proposed technique can be used for solving multi-dimensional, transient, coupled or simultaneous flows of convection-conduction type. Application to a flow example shows that the technique indeed exhibits optimality in convergence and in stability.