ANISOTROPIC, ELASTIC STATES
Descriptiuon:
Anisotropic materials have different elastic parameters in different directions. Anisotropy in soils results from essentially two causes.
1. The manner in which the soil is deposited. This is called structural anisotropy and it is the result of the kind of soil fabric that is formed during deposition. You should recall (Chapter 2) that the soil fabric produced is related to the history of the environment in which the soil is formed. A special form of structural anisotropy occurs when the horizontal plane is a plane of isotropy. We call this form of structural anisotropy transverse anisotropy.
2. The difference in stresses in the different directions. This is known as stress-induced anisotropy. Transverse anisotropy, also called cross anisotropy, is the most prevalent type of anisotropy in soils. If we were to load the soil in the vertical direction (Z direction) and repeat the same loading in the horizontal direction, say, the X direction, the soil would respond differently; its stress–strain characteristics and strength would be different in these directions. However, if we were to load the soil in the Y direction, the soil’s response would be similar to the response obtained in the X direction.
The implication is that a soil mass will, in general, respond differently depending on the direction of the load. For transverse anisotropy, the elastic parameters are the same in the lateral directions (X and Y directions) but are different from the vertical direction.
To fully describe anisotropic soil behavior we need 21 elastic constants (Love, 1927), but for transverse anisotropy we need only fi ve elastic constants; these are Ez, Ex, nxx, nzx, and nzz. The fi rst letter in the double subscripts denotes the direction of loading and the second letter denotes the direction of measurement. For example, nzx means Poisson’s ratio determined from the ratio of the strain in the lateral direction (X direction) to the strain in the vertical direction (Z direction) with the load applied in the vertical direction (Z direction).
In the laboratory, the direction of loading of soil samples taken from the fi eld is invariably vertical. Consequently, we cannot determine the fi ve desired elastic parameters from conventional laboratory tests. Graham and Houlsby (1983) suggested a method to overcome the lack of knowledge of the fi ve desired elastic parameters in solving problems on transverse anisotropy. However, their method is beyond the scope of this book.
For axisymmetric conditions, the transverse anisotropic, elastic equations are
where the subscript z denotes vertical and r denotes radial. By superposition, nrz/nzr 5 Er/Ez.