The Relationships Between the Volumetric Deformation Moduli of Unsaturated Soils
The International Conference on Soil Mechanics and Foundation Engineering in 1936 was perhaps the first international forum which brought unsaturated soil problems to the attention of geotechnical engineers. Since then, the understanding of unsaturated soil behaviour has been improved considerably. The theory for the volume change and shear strength behaviour of unsaturated soils has now developed to the point of potential application in geotechnical practice. A complete understanding of the volume change behaviour of an unsaturated soil requires a knowledge of volumetric deformation moduli on four state planes. These moduli must be determined in either a direct or indirect manner in order to solve practical problems involving volume change, moisture movement, bearing capacity and slope stability analysis. The measurement of these moduli generally requires modification to conventional laboratory equipment. The solution of unsaturated soil problems would be greatly facilitated if the relationships between the various moduli were known. Then it would be possible for all moduli to be determined by a few established conventional soil tests. The main objective of this dissertation is to develop and measure the relationships between the various volume change moduli. The study began with a literature review on the volume change constitutive relations for the soil structure and water phase of an unsaturated soil. Attempts were made to gather information pertinent to the relationships between different moduli. The theory chapter started with an examination of the most acceptable form for the soil structure and water phase constitutive surfaces on both arithmetic and semi-logarithaic scales. Approximate semi-logarithmic constitutive surfaces were then proposed. The geometry of the approximate semi-logarithmic constitutive surfaces is used to relate the moduli associated with a particular phase (i.e., the soil structure or water phase). When a soil. is saturated, the soil structure and water phase moduli with respect to the logarithm of net total stress are related by the relative density, Gs' of the soil. The inter-relationship of the three remaining moduli was then studied. A laboratory test program was designed to obtain experimental data showing the characteristic form of the semi-logarithmic constitutive surfaces on the net total stress and matric suction planes. Two soils, a uniform silt and a glacial till were tested. Specimens were formed by static compaction at half standard Proctor compaction effort with either dry of optimum or at optimum initial water contents. The investigation included specimens being loaded and unloaded under Ko and isotropic conditions. The results were analyzed and used to evaluate the relationships between the moduli. The knowledge of four moduli is needed to completely describe the volume change behaviour of an unsaturated soil in a monotonic volume change process. Special tests are required to determine these four moduli in the laboratory. For instance, the one-dimensional or isotropic compression test, the suction and unconfined shrinkage tests are necessary for solving settlement problems. The use of an approximate semi-logarithmic constitutive surface as a means to relate moduli for the same phase appears to be viable only for the soil structure. The geometry of the approximate soil structure constitutive surfaces is identifiable by two characteristic stress states namely the corrected swelling pressure (i.e., Pś) and the initial stress state translated to the matric suction plane e following a constant volume stress path (i.e., (ua - uw)e/i). Relationships between soil structure moduli can be written e in terms of log (Pś) and log(ua - uw)e/i. The experimental data has revealed empirical relationships between moduli for the water phase. As a whole, six relationships for the eight moduli associated with monotonic volume decrease and increase are suggested. The compressive and swelling indices with respect to the net total stress (i.e., Ct and Cts respectively) can be measured using conventional oedometer or triaxial equipment. These two are regarded as "basic" moduli. The remaining moduli can be estimated from the proposed relationships with the knowledge of the basic moduli and the characteristic stress states, Pś and (ua - uw)e/i.
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