A new constitutive law for the nonlinear normal deformation of rock joints under normal load

In view of the deviation of the fitting results of the classical exponential model and the hyperbolic model (the BB model) from several experiment data during intermediate stress period, a new constitutive model for the nonlinear normal deformation of rock joints under normal monotonous load is established with flexibility-deformation method. First of all, basic laws of the deformation of joints under normal monotonous load are discussed, based on which three basic conditions which the complete constitutive equation for rock joints under normal load should meet are put forward. The analysis of the modified normal constitutive model on stress-deformation curve shows that the general exponential model and the improved hyperbolic model are not complete in math theory. Flexibility-deformation monotone decreasing curve lying between flexibility-deformation curve of the classical exponential model and the BB model is chosen, which meets basic conditions of normal deformation mentioned before, then a new normal deformation constitutive model of rock joints containing three parameters is established. Two main forms of flexibility-deformation curve are analyzed and specific math formulas of the two forms are deduced. Then the range of the parameters in the g-δ model and the g-λ model and the correlative influence factor in geology are preliminarily discussed. Referring to different experiment data, the validating analysis of the g-δ model and the g-λ model shows that the g-λ model can be applied to both the mated joints and unmated joints. Besides, experiment data can be better fit with the g-λ model with respect to the BB model, the classical exponential model and the logarithm model.