Experimental Study on Shear Stress-Displacement, Creep and Shear Slip Instability Behavior of Rock Fractures

Rock mass inherently contains discontinuities, and shear sliding of rock masses along discontinuities is the most common failure mode of rock mass in engineering practice (such as slope, dam and tunnel). In this study, the mechanical and failure properties of rock fractures were examined through direct shear tests, pre-peak tiered cyclic shear tests and multistage loading shear creep tests. The results show that the deformable memory of rocks can be observed from shear stress-shear displacement curves, namely reloading curves continued to increase along the loading curve of the last cycle under the pre-peak tiered cyclic shear loading. The envelopes of shear stress-shear displacement curves were similar to the variation trend of shear stress-shear displacement curves obtained in the direct shear test. Besides, the variation trend of residual shear displacement (RSD) and relative residual shear displacement (RRSD) before slip instability were obtained by the data analyses of rock mass under pre-peak tiered cyclic shear tests. It is found that the change in the friction and sliding state of rock fracture is the main reason for the uctuation of shear stress-shear displacement curves. The Chen's method was used to process the multistage loading shear creep curves and the three creep stages were analyzed. Moreover, the complex creep models in some previous studies were discussed and the data of shear creep tests were successfully tted to the classical Burgers model. This study provides a guidance for the study on the shear instability of rock fractures under different shear loading paths.


Introduction
Rock masses contain discontinuities inherently, such as faults, fractures, bedding planes and other planes of weakness [2; 5; 11; 15; 23]. For example, the Baihetan Hydropower Station, a very large construction project, indicated by eld geological investigations that many discontinuities developed in the rock masses [4]. In the open-pit mine located to the west of Fushun City, China, the Cretaceous rock mass between reverse faults F 1 and F 1A was imposed a substantial impact by strong shear stresses, resulting in a large amount of fractured rock mass [16]. The shear strength of rock joints was lower compared with the intact rock materials, and shear failure of rock masses along pre-existing fractures was one of the most common failure modes in rock slopes, rock dams and tunnels [8]. Thus, it is important to understand and predict the shear behaviours of rock masses containing joints for the design and stability analysis of rock structures.
In recent years, great effort has been paid to investigate the mechanical features, energy evolution and morphology characteristics of rock fractures from various perspectives, e.g. complete shear stress-shear displacement curves, energy dissipation and absorption, and change regularity of surface roughness [1; 24; 25; 27]. Similar to intact coal sample easily in uenced by con ning pressure and external stress level, it is general accepted that in uencing factors, such as shear load, applied shear stress level and cyclic shear stress may stronger affect the mechanics and failure properties of rock fractures (Meng et al., [7].
Due to the di culty to obtaining natural rock fractures, the cement mortar fractures or rock fractures obtained by arti cial splitting was mainly used to carry out relevant tests [26].
In terms of direct shear tests, Zhou et al. [26] prepared the irregular serrated structural planes with three different asperity heights made of cement mortar to perform direct shear tests to study the effect of structural plane to the slip burst, and the mechanism of in-situ slip burst was analyzed preliminarily.
Afterwards, Meng et al. [6] carried out shear tests under constant normal loading (CNL) on tensile joints in three different types of rock, the test results indicated that the maximum AE hit rate of marble joints was attained before the peak shear stress when the normal stress was 1 MPa, and the AE hit rate became quiet during the ultimate sliding stage. Moreover, Meng et al. [10] carried out direct shear tests on split granite joints at various shear rates (0.001-0.1 mm/s) under different normal stresses, and the in uences of the shear rate on the shear strength, post-peak shear behaviour and acoustic emission characteristics are analysed and discussed. Recently, Meng et al. [9] conducted direct shear tests under constant normal stress condition on arti cial splitting cement mortar fractures and monitored the AEs during the shear failure process. Furthermore, rock fractures was usually subjected to tiered cyclic stress, such as s periodical change of the reservoir level and reciprocating motion of the train [19]. Thus, it is of considerable signi cance to study the impacts of tiered cyclic stress on the mechanical behaviours of rock fractures. Zhai et al. [20] conducted experiments on jointed marble specimens using servo-controlled testing machine to investigate the energy and deformation characteristics of rock joints under multi-stage shear loading-creep-unloading conditions. Additionally, to study the evolution characteristics of interface slip eld under cyclic loading, a double shear model test study of granite specimen under constant con ning pressure was designed and carried out by Yang et al. [17]. More recently, Zhai et al. [19] experimentally investigated rock samples with arti cially prefabricated fractures by RDS-200 servocontrolled rock direct shear experimental apparatus, measured displacement characteristics and energy evolution under pre-peak tiered cyclic shear loading at a constant normal loading. And like intact coal and rocks, creep of discontinuities is also a part of the fundamental properties for rock fractures, which was prone to contribute to the large deformation of slope and surrounding rock of underground tunnel, or even landslide hazard [22], and delay failure may took place several days or years. Many scholars in this eld have conducted large quantity of research work, and they have gained rich achievements. For example, Wang et al. [12] induced two types of fractures by means of modi ed shear and indirect tension and assembled the fractured rock samples following their initial formation and direct shear tests were performed under a constant normal force and stepwise increased shear creep loadings. Zhang et al. [21] conducted restrictive shear creep experiments to investigate the creep characteristics of key unit rocks in the slope potential slip surface and established creep models re ecting the creep-failure time and progressive-failure characteristics of rock. More recently, Wang et al. [13] investigated the three creep stages of shear creep tests in detail and proposed a method for predicting the accelerating creep stage, established an empirical creep model, and so on.
As illustrated by the above analysis, extensive research has been conducted on mechanical and failure features of the rock fractures by different authors. Nevertheless, minimal investigations exist which simultaneously deal with the shear stress-shear displacement, creep, and cyclic shear failure characteristics. Therefore, in this study, direct shear tests, pre-peak tiered cyclic shear tests and multistage loading shear creep tests are conducted on the rock fractures obtained by arti cial prefabrication method to study the shear failure characteristics and instability behaviour under various loading paths. The results of this study will contribute to the understanding of failure instability mechanism of rock fractures under different shear loading paths, and are of great signi cance for the prevention and control of slip instability hazards of rock mass with fractures in geotechnical engineering.

Sample preparation
The marble samples used in this test were collected from a quarry of Nanzhao county, Henan province, China. The results of apparatus testing showed that the main components of the marble were calcite, dolomite and magnesite. The marble sample was gray, with a particle size of 0.2-0.5 mm and a uniform texture. The cylindrical samples with a diameter of 50 mm and a height of 100 mm were machined according to ISRM (International Society for Rock Mechanics) requirements. The smoothness and atness between the upper and lower surfaces were controlled within a tolerance of ±0.05 mm and ±0.02 mm, respectively ( Fig. 1).

sample treatment
The intact marble sample was placed in the self-made splitting grinding tool to prepare rock fracture, as shown in Fig. 2(a). The tool was composed of upper and lower parts with the same shape and cylindrical grooves. Wedge-shape steel wire with the same arc degree was embedded in the middle of the groove and slightly protruded from the arc surface of the grooves. The section line in the middle of the rock sample coincided with the steel wire, guaranteeing the application of uniform linear compression stress on the side surface of the sample perpendicular to the axis. As shown in Fig. 2(b), under the action of the press machine, the formed fracture was parallel to the upper and lower ends of the sample, which was similar to the natural shape. Fig. 2(c) shows the simpli ed diagram of the rock sample with fractures.

Experimental device
The RDS-200 rock mechanics shear test system produced by the American GCTS company was used in this experiment. Fig. 3 shows the experimental instrument and the simpli ed diagram of test devices in this experimental system, respectively.
The normal and shear loading of the testing system are 100 kN and 50 kN controlled by an electrohydraulic servo control system, and the displacement and loading accuracy are 10 −3 mm and 10 −4 MPa, respectively. This testing system has advantages of easy operation and simple programming process, as well as high reliability and accuracy. The whole testing system is composed of normal and shear mechanisms, including control cylinders, load sensor, displacement sensor, load conduction arm, pin, pressure head and base.

Testing scheme
Twelve samples with rock fractures were prepared in this experiment. To achieve a certain number of stages in the tiered loading experiment, six samples were used for the direct shear test to measure the shear strength of fractures, which provides a reference for the classi cation of shear stress in the tiered shear loading test. The normal stress was constant in the direct shear test and was set at 2.6, 5.2, 7.8, 10.4, 13.0 and 15.6 MPa, respectively. The shear direction was controlled by the shear rate at a speed of 0.5 mm/min and the shear displacement was 5 mm at the end of shear test.
The other two samples were used for the tiered cyclic shear test, and the normal stress was 1. show the loading paths of multistage loading shear creep tests and tiered cyclic shear tests, respectively. The speci c experimental procedures are shown in Table 1.  Figure 6 shows the complete shear stress-shear displacement curves of rock fractures under various normal stress. It can be seen that the shape of pre-peak curves of rock fractures under various normal stress are similar, while the shape of post-peak curves is different obviously. The pre-peak curves of rock fractures can be roughly divided into four stages: compaction stage, uniform rising stage, shear stress decline stage and residual strength stage. With the increase of the shear deformation, the shear stress increases rapidly. When the shear stress reaches the peak value, the shear resistance of rock fracture decreases signi cantly, and then irregular post-peak deformation or slipping phenomenon occurs.
In addition, the shear stress-shear displacement curves of rock fractures under the lower normal stress (e.g. σ = 2.6 MPa and 5.2 MPa) experiences a smoother decrease after the peak, and the slope shapes of the curves are concave; while the shear stress decreases sharply in an extremely short shear displacement or time under the higher normal stress (e.g. σ = 13.0 MPa and 15.6 MPa), resulting in a large gradient of descent. When the shear stress exceeds the peak shear strength, the shear failure occurs, and then slides along the fracture plane under the action of small shear stress. The small shear stress required to keep the sliding is the residual shear strength. The higher the normal stress, the higher the residual strength. As long as the normal stress exists, the shear fracture surface of rock still has the shear resistance.
During the shear process, there are many mechanical processes, such as elastic deformation of microbulges, splitting, generation and migration of particles, relative dislocation of rock fractures. As a result, the uctuation in the residual shear strength curve is caused.
3.2 Tiered cyclic shear stress-shear displacement curves 3.2.1 Overall characteristics Fig.7 shows the tiered cyclic shear stress-shear displacement curves of samples TS151 and TS301 at different cycle stages. As shown in Fig. 7, during the rst cycle, the loading and unloading curves did not form a closed loop, and a large amount of residual shear displacement was observed. In a complete loading and unloading cycle, the loading curve did not coincide with the unloading curve, and the unloading curves were always lower than the loading curves due to the obvious plastic shear displacement of the rock fracture. The reloading shear stress-shear displacement curves continued to increase along the loading curve of the last cycle, indicating that the rock fractures had memory functions under prepeak tiered cyclic shear loading. The pre-peak tiered cyclic shear loading has little in uence on the shear deformation behavior of rock fractures. The outer envelope of shear stress-shear displacement curves and direct shear curves have the same characteristics. Since the two samples have the similar shear displacement variations, the shear displacement change of rock fracture in the sample TS301 is described in detail (see Fig. 8). The envelope of shear stress-shear displacement curves can be roughly divided into four stages, that is, ( ) compaction stage, ( ) uniform rising stage, ( ) shear stress decline stage and ( ) friction sliding stage.
3.2.2 Residual shear displacement (RSD) and relative residual shear displacement (RRSD) Residual shear displacement (RSD) is de ned as the δ when the shear stress is unloaded to 0 MPa and RRSD is de ned as the difference between the adjacent RSD (the RSD is equal to the RRSD during the rst cycle). As presented in Fig. 7, the loading and unloading curves deviate far from each other during the rst cycle. When the shear stress is unloaded to 0 MPa, a large RSD can be observed, which is mainly caused by the coupling compaction. Fig. 9 shows the RSD and RRSD of samples. It can be seen that the RSD increases linearly with the increase in the number of cycles. The RRSD is larger at the initial cycles and then decreases rapidly with the increase of cycles. Due to the existence of interspace between micro convexes of rock fractures, RRSD is relatively larger during the initial loading. With the increase of cycle numbers, RRSD decreases gradually and tends to be stable due to the extrusion action of the micro convex of rock fractures.

Shear slip during loading and unloading stages
As mentioned above, the loading and unloading curves of rock fracture in sample TS301 are described in Fig. 8. The shear stress-shear displacement curves of sample TS301 in loading and unloading stages are shown in Fig. 10(a) and (b), respectively. It can be seen that the morphological characteristics of shear stress-shear displacement curves are similar in the loading or unloading stage. and the curves can be roughly divided into two sections with the slip position as the boundary. At the slip position, the smaller change of shear stress leads to larger shear displacement, which was called shear slip, but this shear slip dose not lead to shear instability failure of rock fractures. For instance, in the forth curve in the unloading stage, shear displacement decreases signi cantly (0.859 -0.753 mm), while the shear stress decreases slightly (0.29 -0.22 MPa). The shear stress at the place of the slip occurrence is basically maintained within a certain range, and the shear stress does not change with the cycle progression. When sliding occurs in the shear loading, the shear stress of the TS301 sample is about 0.43 -0.46 MPa; when the sliding occurs in the shear unloading, that of the TS301 sample is about 0.22 -0.29 MPa. The rapid increase of shear displacement in the loading or unloading stage is different from the shear slip instability caused by the loading of the last cycle. The increasing shear stress can be sustained by fracture after a short slip, whereas the large displacement can be caused in the last stage, resulting in a high possibility of serious damage in engineering practice.
The underlying reasons for the uctuation in curves can be explained from the angle of friction state changes. When the shear stress was lower, the coupling fractures are in the state of static friction, and shear displacement is mainly caused by the rock fracture; there is a small elastic displacement of the randomly distributed bump and convex body, indicating the great compaction of coupling fracture. At this time, wear particles in the fracture were caused by the increasing shear displacement, and the number of particles increased with the increase of shear stress. With the increase of shear stress, the fracture is in the state of static friction and sliding friction alternately. However, the effect of static friction on the fracture surface was weakened by wear particles, and the overall sliding rate increases rapidly. With the increase of the shear stress, shear stress-shear displacement curves present a nearly linear increasing trend, and static friction is changed into sliding friction. Then the in uence of wear particles on shear displacements and shear slip rates of convexes was weakened. Therefore, the change of friction state of the rock fractures is the main cause of the uctuation of shear stress-shear displacement curves. Figure 11 and Fig. 12 show the original creep curves and the curves obtained by Chen's method. The shear displacement of rock fracture is also sensitive to stress (e.g. normal or shear stress) and time (such as creep and relaxation) [22]. In general, the idealized shear creep curve of rock fracture usually exhibits four principal phases, which are the same as the uniaxial and triaxial creep curve of intact rock and coal [22]: (1) instantaneous shear displacement because of instantaneous shear stress; (2) primary creep stage with sharp displacement increments, but at a decelerated displacement rate; (3) steady-state creep stage at low, or near-constant displacement rate; (4) accelerated creep stage with rapid displacement increment until failure occurs, or failure during shear stress application.

Creep curves
Similar to the coal sample, it was almost unrealistic for all rock fracture samples to achieve the ideal accelerated creep through prejudging the shear stress and the time given for the rock fracture to creep. As shown in Fig. 12, the sample CS152 does not experience the ideal tertiary creep in the timescale. In the nal loading process, the shear stress rst rises sharply to the maximum value, and then suddenly decreases, indicating the occurrence of the failure phenomenon. The samples CS151, CS301 and CS302 all reach the ideal accelerated creep. Considering that the accelerated creep curves of the three samples are similar, only the sample CS301 is analyzed.
Generally speaking, when the rock fracture is subjected to instantaneous shear stress, the shear displacement shows a jump, e.g. the AB stage in Fig. 13. When the imposed shear stress was constant, the primary creep occurs at a decelerating displacement rate, i.e. BC segment, and point B is the initiating point of creep. The steady-state creep is apparent (CD curve) as time goes on. Then the sample is gradually transformed from steady-state creep to accelerated creep (DE curve).

Analysis of creep model
Based on shear creep curves obtained by Chen's method in Fig. 12, it can be seen that the marble fractures obtained by the arti cial prefabrication method have distinct visco-elastic behavior at various shear stress levels. To describe visco-elastic shear creep behavior of rock fractures, the Hookean body and Newton body are usually connected in series or parallel to form all kinds of visco-elastic creep models, such as the Maxwell model, Kelvin model.
Complex creep models have been used to t the creep curves under different stress states in previous studies, and the determined model parameters irregularly change with the stress state. The suitability of the model can only be judged according to the tting accuracy of the curve. It should be emphasized that if multiple parameters in the tting formula are determined only for a set of data or a curve, the formula can certainly be in good agreement with the set of data or curve, but the correctness and rationality of the formula cannot be proved, or the formula can not be applied to any other occasions.
To refer to such a formula as a "mechanical model or theory" is to misunderstand the meaning of "model" and "theory". However, choosing complex formulas and too many undetermined parameters to pursue too high tting accuracy may completely distort the variation law of parameters expressed by tting formulas [18]. In this research, the traditional Burgers model was chosen to study the visco-elastic shear creep behavior of rock fractures (see Fig. 14). On the basis of shear creep test curves, the regression inversion method was used to identify the parameters based on the 1stopt tting software. In the identi cation, one of the squares of correlation coe cient (R 2 ) is regarded as the discrimination criterion [14]. It needs to be noted that R 2 tends to 1.0, which means that the theoretical model agrees better with the experimental data. In accordance with Fig.  15 and Eq. (1), the creep parameters for the Burgers model at each creep stage can be identi ed. Fig. 15 shows the comparison between the predicted curve by the Burgers creep model and experimental result under different shear stress, and the tting results are listed in Table 2. As shown in Fig. 15, it can be seen that the Burgers creep model has a good agreement with experimental results.

Conclusions
The main goal of this study is to investigate the shear failure characteristics and instability behaviour of rock fractures obtained by arti cial prefabrication method under various loading paths (including direct shear, pre-peak tiered cyclic shear and multistage loading shear creep simultaneously). The operations mainly consisted of three series of tests (listed in Table 1) where normal stress was held constant in each project. Based on these analysis, the following conclusions are drawn: (1) The shape of pre-peak shear stress-shear displacement curves of rock fractures are similar under various normal stress. These curves can be divided into compaction stage and uniform rising stage.
However, the post-peak curves are different signi cantly and irregular post-peak deformation or slip phenomenon occurs. The shape of these curves is concave after the post-peak shear stress under the lower normal stress; while the shear stress decreases sharply within an extremely short shear displacement or time under higher normal stress. Regardless of direct shear, pre-peak tiered cyclic shear or multistage loading shear creep, all rock fractures show transient failure features after peak shear stress in the shear stress-shear displacement curves.
(2) The deformable memory of rocks can be observed from shear stress-shear displacement curves, that is, the reloading curves continue to increase along the loading curves of the last cycle under pre-peak tiered cyclic shear loading. The pre-peak tiered cyclic shear loading has little effect on the shear deformation behavior of rock fracture, and the outer envelopes of shear stress-shear displacement curves are similar to those obtained in the direct shear test, and the envelope lines of pre-peak tiered cyclic shear stress-shear displacement curves can also be divided into compaction stage, uniform rising stage, shear stress decline stage and friction sliding stage. Generally, the RSD and RRSD are affected by cyclic numbers; with the increasing number of cycles, the RSD increases and the RRSD decreases.
(3) When the shear stress is loaded or unloaded to a certain stress level, the shear displacement increases or decreases rapidly, while the sudden instability of the rock fracture will not occur. The shear slip is caused by the transformation of static friction, and the uctuation of shear stress-shear displacement curves is mainly caused by the sliding friction and the change of friction and sliding state of rock fracture.
(4) The data of shear creep tests are successfully tted to the Burgers model, exhibiting visco-elastic characteristics. The tting results show that G M is far less than that of other shear creep parameters.
However, η M is much larger than other shear creep parameters and can be used to re ect the variation of the shear displacement rate of the secondary creep; η M linearly increases with the rise in shear stress. On the contrary, with the increase of shear stress, both elastic shear displacement and viscous ow increase, G K and η K have the randomness and volatility.
The range of shear stress level applied to the rock fractures, and the timescale applied to the investigation of creep might somewhat limit the ndings. Therefore, future work may be conducted using different types of rock fractures to study its mechanical features, and with a broader range of normal and shear stress, as well as enough time given to the rock fractures to shear creep. Nevertheless, these ndings in the present paper provide a theoretical framework for future studies to assess the geomechanics and failure mechanisms of rock fractures.   Test equipment and simpli ed diagram: (a) shear test system. (b) simpli ed diagram of the testing system [3]. Shear stress paths of multi-step creep tests Figure 5 The tiered loading-unloading cycles for shear testing Figure 6 Shear stress-shear displacement curves of marble fractures Tiered cyclic shear stress-shear displacement curves The four stages of overall curves Page 18/22 The original creep curves