Finite Element Method for the Prediction of Volume Change in Expansive Soils
Hung, Vu Quang
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Expansive soils are present in many parts of the world, particularly in semi-arid areas. An expansive soil is generally unsaturated due to desiccation and contains clay minerals that exhibit high volume change when in contact with water. There has been a worldwide interest in research on expansive soils, and many methods of heave prediction have been proposed. The proposed heave prediction methods are either based on matric suction measurements or one-dimensional oedometer test results. While heave problems in engineering practice are often two-dimensional or three-dimensional in character (i.e., roadways, airport runways or houses), all of the suggested methods can only be used to predict one-dimensional heave. Few attempts have been made to solve heave problems that are two or three dimensional in nature. A new method for the prediction of volume change in an unsaturated soil is proposed in this study. The proposed method makes use of the finite element method with elastic modulus functions (i.e., elastic modulus with respect to net normal stress, E and elastic modulus with respect to matric suction, H). The proposed method can predict both one-and two-dimensional heave. The elastic modulus functions are computed from conventional oedometer test results. The theoretical formulation of the method is based on the equilibrium equations for the soil structure and the constitutive equations for an unsaturated soil. Solutions of one and two-dimensional volume change problems are obtained using a general-purpose partial differential equation solver, called PDEase2D. Several typical examples and case histories that are found in published literature are analyzed using the proposed method for one-dimensional heave. The results agree well with the results obtained from the analytical method proposed by Fredlund, Hasan and Filson (1980). Measured ground movements related to two case histories are also analytically modelled. In this study, two-dimensional volume change problems are analyzed in an uncoupled manner (i.e., a seepage and deformation analyses are performed separately). The matric suction conditions in a soil are predicted by performing a transient unsaturated seepage analysis. The deformations due to changes in net normal stress and matric suction are then predicted by performing a stress-deformation analysis. The coefficient of permeability function and the coefficient of water storage function are required for the seepage analysis, along with appropriate boundary conditions. Elastic modulus functions are required for the stress-deformation analysis. Five two-dimensional examples covering typical volume change problems associated with unsaturated soils are analyzed and discussed. The examples represent typical conditions encountered in engineering practice such as deformation due to loading, unloading, wetting, drying, and both loading and wetting. The analytical results appear to be reasonable (Note: there are no two-dimensional data sets available for verification). The deformations associated with collapsing soil and soft clays can also be performed using the prediction technique presented in this study. For example, the settlement problem of Hanoi city, Vietnam can be conducted using the non-linear soil model suggested in this study. The results of this study also show that there appears to be a new way to solve geotechnical problems using the finite element method. Difficult problems such as finite element mesh design, time step design in a transient problem, non-linearity, and graphical presentation of analysis results are related to the mathematics and computer science disciplines. Geotechnical engineers should adopt the research associated with mathematics and computer science whenever possible and concentrate on solving more specific geotechnical problems. As an example, the general-purpose partial differential equation solver, PDEase2D, has proven to be a powerful computing tool for seepage and stress-deformation analysis for highly non-linear unsaturated soil problems.