International Journal of Rock Mechanics and Mining Sciences
Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading
Introduction
Joints can significantly affect the mechanical behavior of rock masses. More specifically, joint properties such as roughness, strength of asperities, separation, matedness, gouge and even the spatial distributions make the behavior of jointed rock masses more complicated. Most of the previous laboratory experiments for the mechanical properties of rock joints have been focused on determining the peak shear strength and the stress–displacement relations under unidirectional shear loading [1]. The comprehensive behavior of rock joints under the cyclic loading condition where the direction of shear load is repeatedly reversed has been rarely reported. Since the large-size underground rock structures such as energy storage cavern and radioactive waste repository require the higher standard of stability against blasting and earthquakes, the cyclic shear [2] and dynamic shear [3] behavior of rock joints become more important for providing the fundamental ideas to understand the natural phenomena of higher loading frequencies.
Hutson and Dowding [4] suggested an exponential wear equation for joint asperity based on the experimental results using artificial joints of sinusoidal shape. Huang et al. [5] tested molded joints of saw-tooth shape under cyclic shear loading and validated the theoretical degradation law for joint asperities proposed by Plesha [6]. Jing et al. [7] investigated the cyclic behavior of natural joints using the replicas of natural joint surfaces. By utilizing these results Jing [8] proposed a conceptual model for the cyclic shear behavior. Kana et al. [9] suggested the interlock-friction model for dynamic shear response, and the importance of the second order asperities on the dynamic shear behavior was explained by Fox et al. [10]. Recently, Homand et al. [11] reported the cyclic shear behaviors of rock joints having sinusoidal shape of asperities. However, the experimental results concerning irregular rough joints with matrix of intact rock properties under cyclic shear loading has rarely been reported.
Algebraic calculation and numerical simulation for the mechanical behavior of jointed rock mass require the constitutive law of rock joints. After Patton [12] proposed bilinear models of saw-tooth joints, several empirical and theoretical constitutive models were developed by Ladanyi and Archambault [13], Barton and Choubey [14], Plesha [6], Amadei and Saeb [15], Jing [7], Qiu et al. [16]. Among these Barton's empirical model [1], [14] has widely been used because it is easy to use and includes several important factors of joint characteristics. However, Barton's model is not formulated incrementally, it is somewhat difficult to implement numerically. Plesha [6] idealized Patton's saw-tooth type asperities and developed a constitutive model based on the classical plastic theory. In his model, the asperity degradation is an exponential function of the exerted work during shearing. Huang et al. [5] verified this exponential degradation law through a series of experiments for joints having saw-tooth type asperities. Though Plesha's model is theoretically complete and highly adaptable to numerical implementation, this model over-predicts the dilation during cyclic shearing and has not been evaluated for the behavior of rough rock joint. Qiu et al. [16] revised Plesha's model by idealizing the sinusoidal asperities, but it would be less practical due to the complexity of constitutive equation.
In this study, a precision direct shear testing system was designed to study the mechanical behavior of rock joint of irregular asperities under cyclic shear loading. A series of cyclic shear tests were conducted using both the saw-cut and the split tensile joint specimens of Hwangdeung granite and Yeosan marble. Prior to shear tests, surface topography of joint was measured using 3D laser profilometer and analyzed statistically. Based on the experimental results, Plesha's [6] plastic constitutive model was revised by considering the second order asperities, and finite element analysis was performed to simulate the laboratory shear tests. The results of numerical analysis for both the monotonic and cyclic shear behavior were compared to the laboratory test results.
Section snippets
Testing system
A servo-controlled direct shear-testing machine was designed and attached to MTS 815 loading frame. Both shear and normal loading systems were controlled by MTS controller (Teststar II). Fig. 1 shows the schematic diagram of cyclic shear testing system. The loading capacity of the testing system is 250 kN in both the normal and shear directions. This test setup can hold the sample size of up to 160×120×120 mm3. The lower shear box is fully attached to the normal loading actuator, and the upper
Surface roughness
Rock joint consists of rough surfaces having numerous asperities from macroscopic scale to microscopic one. The concept of first and second order asperity was firstly introduced by Patton [17] and has been broadly used to delineate the characteristics of joint surfaces [1], [9], [10], [18]. First order asperities imply overall inclination of joint surfaces, while second order asperities refer to the randomly distributed microinclinations. Representative surface roughness profiles of Hwangdeung
Formulation of constitutive equation
The constitutive equation for the behavior of rough rock joint was developed based on the formulation proposed by Plesha [6]. By applying the plastic flow rule and consistency conditions [6], [29], the incremental stress–strain relation can be obtained as follows:where D is the joint stiffness matrix, F is the joint slip function of plastic work and stress, Q is the slip potential function, and H is hardening or softening parameter associated with the
Conclusions
Fundamental mechanisms of joint asperity degradations and their effects on the cyclic shear behaviors of irregular rough rock joints of different intact strengths were investigated. Measured profiles of joint surface using laser profilometer exhibited the typical random topography having the first and the second order asperities according to the conventional definition of joint surfaces. The possible range of second order asperity angles could be evaluated from the average inclination angle at
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