Numerical Investigations of the Dynamic Shear Behavior of Rough Rock Joints

Abstract

The dynamic shear behavior of rock joints is significant to both rock engineering and earthquake dynamics. With the discrete element method (DEM), the dynamic direct-shear tests on the rough rock joints with 3D (sinusoidal or random) surface morphologies are simulated and discussed. Evolution of the friction coefficient with the slip displacement shows that the 3D DEM joint model can accurately reproduce the initial strengthening, slip-weakening, and steady-sliding responses of real rock joints. Energy analyses show that the strengthening and weakening behavior of the rock joint are mainly attributed to the rapid accumulation and release of the elastic energy in the joint. Then, effects of the surface roughness and the normal stress on the friction coefficient and the micro shear deformation mechanisms, mainly volume change and asperity damage, of the rock joint are investigated. The results show that the peak friction coefficient increases logarithmically with the increasing surface roughness, but decreases exponentially with the increasing normal stress. In addition, the rougher rock joint exhibits both higher joint dilation and asperity degradation. However, high normal stress constrains the joint dilation, but promotes the degree of asperity degradation significantly. Lastly, the effects of the 3D surface morphology on the shear behavior of the rock joint are investigated with a directional roughness parameter. It is observed that the anisotropy of the surface roughness consequently results in the variation of the peak friction coefficient of the joint corresponding to different shearing directions as well as the micro shear deformation mechanisms, e.g., the extent of joint dilation.

Appendix

According to Eq. (1), the elastic energy is calculated as:

$$E^{\text{el}} = \frac{1}{2}\sum\limits_{{N{\text{c}}}} {\left( {\frac{{F^{{{\text{n}}2}} }}{{K^{\text{n}} }} + \frac{{F^{{{\text{s}}2}} }}{{K^{\text{s}} }}} \right)}$$

(A.1)

where $\sum\nolimits_{{N_{\text{c}} }} {}$ refers to summation over all contacts. Refer to Eq. (1) for the definition of the other parameters (the same as below).

The kinetic energy is calculated as:

$$E^{\text{k}} = \frac{1}{2}\sum\limits_{{N_{\text{P}} }} {(mV^{2} + I\omega^{2} )}$$

(A.2)

where m, I, V, and ω are the mass, moment of inertial and translational velocity, and the rotational velocity of particles, respectively. $\sum\nolimits_{{N_{\text{P}} }} {}$ refers to the summation over all particles.

The frictional dissipation is calculated as:

$$E^{\text{f}} = \sum\limits_{{N_{\text{c}} }} {F_{i}^{\text{s}} \left( {V_{i}^{\text{s}} \Updelta t - \Updelta U_{i}^{\text{s}} } \right)} + \sum\limits_{{N_{\text{P}} }} {F_{j}^{\text{d}} V_{j} \Updelta t}$$

(A.3)

where $V_{i}^{\text{s}}$ is the relative shear velocity of two contacting particles (i = 1, 2, 3), $F_{j}^{\text{d}}$ is the damping force, and V _j is the ball velocity. j = 1, 2, 3 represents the translational degrees of particles, while j = 4, 5, 6 represents the rotational degrees of particles. $\Updelta t$ is the time step.

The breakage energy is calculated as the elastic energy lost in the bond-breakage process:

$$E^{\text{br}} = \frac{1}{2}\sum\limits_{{N_{\text{c}} }} {\left( {\frac{{(F_{\hbox{max} }^{\text{n}} )^{2} }}{{K^{\text{n}} }} + \frac{{(F_{\hbox{max} }^{\text{s}} )^{2} }}{{K^{\text{s}} }}} \right)}$$

(A.4)

where $F_{\hbox{max} }^{\text{n}}$ and $F_{\hbox{max} }^{\text{s}}$ are the normal and the shear bond strengths, respectively.