Use of uniaxial compression test results in stress modelling around openings in nonlinear geomaterials

A phenomenological approach extending linear elastic constitutive equations to nonlinear materials is presented and applied to stress analysis around circular openings. This extension uses stress-dependent Lamé parameters instead of fixed values: a mean effective stress-dependent compressibility modulus C(σ′) and a shear stress-dependent inverted shear modulus, D(τ2)=1/G(τ2). Both C(σ′) and D(τ2) are expressed as power series, allowing several typical pre-peak material nonlinearities to be described with reasonable accuracy. A similar, strain-dependent model is also provided. In the strain-dependent version, the model uses volumetric strain-dependent bulk modulus K(ε) and shear strain-dependent shear modulus, G(γ2). Material parameters of these nonlinear models can be identified from uniaxial compression tests. Numerical examples showing linear and nonlinear stresses around openings in different rocks are presented. It is shown that a model without yield does not necessarily have to underpredict opening stability. Underpredictions depend on the convexity of the rock compression curve and on the degree of rock nonlinearity.