Rock stiffness is important in design as it affects the stresses and deformation around openings. Many rocks are anisotropic and those of sedimentary origin are frequently highly nonlinearly elastic. Traditionally elastic properties are inadequately measured using uniaxial test methods. This paper examines the results of uniaxial, triaxial and hydrostatic testing for the elastic behaviour of rock based on the assumption of orthotropic behaviour. The effects of fluid pressure on effective stress are also discussed. The mathematics are presented for each case. The testing methods involve step-wise loading of triaxial or hydrostatic samples that are fitted with strain gauges. The effects of fluids on deformation are determined by gas injection. The simple hydrostatic test process enables rock fragments to be tested to determine their anisotropy. This however requires an estimation of at least one of the values of Poisson's ratio.
Rocks are complex composites of different minerals. As a consequence their mechanical properties are highly variable. This variability extends through varying elastic to post elastic behaviour. For a general elastic solid there are six stresses and six engineering strains which are linked by either a compliance (Equation 1) or stiffness matrix, each with 36 terms. Because of the symmetry of these matrixes the number of terms may be reduced to 21. Practically this is still a very large number of parameters to determine from a physical test on a piece of rock, particularly as this piece of rock is frequently a cylindrical core or more conveniently a fragment.(equation)The general formulation of Equation 1 means that quite complex effects can be accounted for. For example a normal stress to a plane may cause a shear strain in that same plane. More realistically shear stress acting on a plane may lead to strain (dilation or compaction) perpendicular to the plane.
If we make the convenient, but not necessarily correct, approximation that the rock behaves in an orthotropic manner, then the number of independent terms in the compliance matrix drops from 21 to nine (allowing for symmetry) as shown in Equation 2. Three of these are shear terms that are difficult to measure directly, but may be estimated. The orthotropic approach does however mean that the options such as dilation or compaction perpendicular to the plane on which shearing acts are assumed to be zero.