Abstract
Numerical modeling (finite element analyses) of saturated-unsaturated soils problems generally involves the solution of linear or nonlinear partial differential equations, PDEs. The soil properties for unsaturated soils usually take on a functional form that subsequently requires an iterative procedure to obtain a solution. Special numerical solution techniques are helpful (and in some cases necessary) in order to have confidence that the results of the numerical solution are accurate. The dynamic upgrade of the finite element mesh (and time steps) during the iterative solution process have proven to be of significant value in ensuring the proper convergence of the numerical solution. The unsaturated soil property functions are usually obtained through use of estimation procedures based on the measurement of the soil-water characteristic curve, SWCC. One or more estimation procedures have been proposed in the research literature for soil property functions for each physical process of interest in unsaturated soil mechanics. The numerical modeller must be aware of the relationship between the estimated soil property functions and the solution technique. Boundary conditions required when solving unsaturated soils problems often involve the assessment of moisture and thermal flux conditions computed from meteorological records. There are conditions and requirements that must be quantifiable when solving unsaturated soils problems. The estimation of the unsaturated soil property functions makes the solution of unsaturated soils problems more complex than those of saturated soils.
Highlights
There are several distinct differences between the modeling saturated soil mechanics problems and unsaturated soils problems
This paper describes the differences between these two classes of problems and illustrates numerical modeling techniques that have been found to perform well when modeling problems involving unsaturated soils
Unsaturated soils problems generally require the solution of a nonlinear partial differential equation because of the nonlinear nature of the soil properties
Summary
There are several distinct differences between the modeling saturated soil mechanics problems and unsaturated soils problems (or saturated-unsaturated soils problems). Numerical modeling solutions become nonlinear and require an iterative procedure to obtain a solution Stated another way, saturated soil mechanics can be viewed as linear soil mechanics problems with constant soil properties while unsaturated soil mechanics can be viewed as nonlinear soil mechanics problems. One of the challenges in solving unsaturated soil mechanics problems is related to obtaining solutions that have converged to the “correct solution” This is important when solving transient field problems where the solution from one time step affects subsequent mass balance calculations. Computing techniques such as “automatic mesh refinement”, AMF, have been developed to ensure that the solution of nonlinear partial differential equations can converge to a “correct solution”. Special mesh refinement techniques (e.g., AMR) have proven to be useful in ensuring convergence and ensuring convergence to an accurate (or correct) solution
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