New peak shear strength criteria for anisotropic rock joints

Abstract

In general, roughness profiles of rock joints consist of non-stationary and stationary components. At the simplest level, only one parameter is sufficient to quantify non-stationary joint roughness. The average inclination angle I, along with the direction considered for the joint surface, is suggested to capture the non-stationary roughness. Most of the natural rock joint surface profiles do not belong to the self similar fractal category. However they may be modelled by self-affine fractals. Using a new term called specific length, it is shown that even though the fractal dimension D is a useful parameter, it alone is insufficient to quantify the stationary roughness of non-self similar profiles. Also, it is shown why contradictory results for the estimation of D of non-self similar profiles appear in the literature. To estimate D accurately for non-self similar profiles, it seems necessary to use scales of measurement less thanthe crossover length of the profile. Because the crossover dimension of joint roughness profiles can be extremely small, in practice it may be quite difficult to measure roughness at scales of less than the crossover dimension and thus to estimate D accurately. To overcome the aforementioned problems, it is suggested to combine D with a parameter which is negatively correlated to D and also has the potential to compensate for the errors caused by an inaccurate D, and to use the combined parameter to quantify stationary roughness in practice. Four new strength criteria which take the following general form are suggested for modelling the anisotropic peak shear strength of rock joints at low normal effective stresses (0–0.4 times unconfined compressive strength): τ = σ tan φ + a(SRP) c log 10 σ J σ d + I where σ, τ, σ J, φ and SRP denote, respectively, the effective normal stress on the joint, peak shear strength, joint compressive strength, basic friction angle, and the stationary roughness parameter. The following four options are suggested to represent the term a(SRP) c: az 2 ′c, aK d bD c, aK s bD c or aK ν bD c. Joint roughness data should be used to estimate the roughness parameters I, z 2 ′, k d, K s, K ν and D in different directions on the joint surface. Parameter D reflects the rate of change in length in response to a change in the scale of measurement r. Because z 2 ′, K d, K s and K ν are scale-dependent parameters, they can be used to model the scale effect. The coefficients a, b, c and d in the strength criteria should be determined by performing regression analysis on experimental shear strength data. In practice, to allow for modelling uncertainties, the new equations should be used with a factor of safety of about 1.5.