By means of experimental research and theoretical analysis, the nonuniform evolution characteristics of rock friction and sliding were studied. Using digital speckle correlation (DIC) as observation method, the whole process of friction and sliding of a granite specimen in double-sided shear experiment is studied. A spring slider model considering the microscopic characteristics of interface asperities was established to simulate the microscopic process of rock friction and sliding. By comparing the theoretical analysis results with the experimental results, the effect of interface nonuniformity on rock friction sliding instability is studied. The results demonstrated that, with the increase of nonuniformity of sliding interface, the degree of local instability before stick-slip decreases, the stick-slip period shortens, and the value of shear drop during stick-slip period decreases. The nonuniformity of sliding interface will increase after local instability.
With the development of geotechnical engineering projects in deep underground areas, safety accidents such as landslides and rock burst have occurred more frequently [
The research on the mechanism of rock friction sliding instability has always been one of the hot topics in the field of earthquake and geotechnical engineering. Scholars have carried out a lot of research work in this field and made many research achievements. Brace [
In this paper, using DIC as observation method, the whole process of friction and sliding of a granite specimen in double-sided shear experiment is studied. A spring slider model considering the microscopic characteristics of interface asperities was established to simulate the microscopic process of rock friction and sliding. By comparing the theoretical analysis results with the experimental results, the effect of interface nonuniformity on rock friction sliding instability is studied.
To study the sliding friction characteristics of rock, a double-sided shear friction test is designed, and granite with elastic modulus of about 60 GPa is selected as the experiment specimen. The upper and lower rock blocks are fixed with the size of 300 mm, 50 mm, 50 mm. In addition, there is a sliding rock block in the middle, the size of which is 300 mm, 50 mm, 100 mm. The specimen contains upper and lower sliding interfaces with an area of 0.015 m2. In order to reduce the error, the sliding interfaces were polished with 300# emery paper before the experiment. The experimental conditions are shown in Figure
The experimental model.
As shown in Figure
The picture of the experimental system.
Before the experiment, the loading device and the image acquisition system are timed to ensure that the system time is consistent. At the same time, the image acquisition system is debugged to make the camera face the specimen surface. In the experiment process, firstly, the vertical load of the specimen reaches 25 MPa by force loading mode, and the value of vertical load remains unchanged. Then, the sliding rock block is loaded horizontally by displacement control loading, and the image acquisition system is started to collect speckle images until the end of the experiment.
The whole speckle image of the specimen collected by CCD camera is calculated by DIC, and the horizontal strain data of each pixel of the specimen is obtained. The horizontal strain values of each analysis area in Figure
The expression of nonuniform index
Among them,
It can be seen from Figures
The loading curve and interface displacement evolution curve.
The loading curve and
The analysis shows that the shear stress increases slowly and linearly, the sliding surface is in static friction state, and the value of nonuniformity index is small. Because of the compaction effect of normal stress on the micro-concave-convex body of sliding interface, the nonuniformity index increases approximately linearly. In the stage of nonlinear growth of shear stress, the sliding surface changes from static friction to sliding friction, which makes the region near the loading end show local sliding instability, while the nonuniformity index grows rapidly, and calculation area 4 has obvious fluctuation evolution characteristics. In the periodic stick-slip stage and inter-stick-slip stage, the sliding surface is in a viscous state, and the nonuniformity fluctuates. During the stick-slip period, the slip surface slides and the inhomogeneity drops.
It can be seen that the nonuniformity of sliding interface is closely related to the instability of rock friction and sliding. Further, a spring slider model is established to study the effect of sliding interface nonuniformity on rock friction sliding instability.
Based on the finite element method, the sliding rock block in the specimen model of two-sided shear friction experiment is discretized into finite elements, as shown in Figure
The rock friction sliding spring slider model: (a) unit body; (b) spring slider system.
In the model, the sliders are affected by the force between sliders, interfacial friction, damping force, and inertial force. Among them, the first slider at the loading end is subjected to the external force exerted by the loading system in addition to the above-mentioned acting force. The dynamic equation of the whole system is shown in (
The central difference method is used to simulate the dynamic behavior of rock friction and sliding, and the acceleration and velocity are expressed as follows:
By substituting (
The formula of initial velocity and initial acceleration in (
The friction force
Thereinto,
By comparing the space-time evolution diagram of interface friction [
The calculation method of slider stiffness
The release time
Among them,
The shear stiffness of two-sided shear test is twice that of single-sided shear test, so the calculation method of average stiffness
In order to save the time of solving the model, the loading rate is set to 5 mm/s and the loading step is set to 1 × 10−7 s without affecting the numerical analysis results. The stiffness
Here, Δ
In order to effectively simulate the microscopic behavior of “occlusion-failure-occlusion” of interface asperities, multiple sets of interface springs are connected to each slider in the model, and the interface springs deform with the slider to generate tension. When the tensile force reaches its tensile strength, the interface spring is released. However, after
In order to simulate the strength nonuniformity of interface asperities, Gaussian distribution is used to describe the strength distribution of interface springs. According to the previous calculation method [
The interface spring intensity distribution diagram with standard deviation of different strength distributions.
The spring stiffness of single slider interface is calculated according to the average strength
The interfacial connection spring stiffness distribution diagram with standard deviation of different strength distributions.
Figure
The numerical model loading curve and sliding displacement evolution curve.
Figures
Loading curves of numerical model under different uniformity conditions.
The partial enlarged detail of nonlinear stage.
The slider friction evolution curve: (a) Δ
Viscous slip event shear derating table (kN).
Stick-slip times | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Δ | 18.40 | 8.89 | 13.15 | 5.63 | ||
Δ | 15.92 | 11.15 | 6.72 | 4.04 | ||
Δ | 14.97 | 6.43 | 3.09 | 2.25 | 2.24 | 2.32 |
Take curves in Figure
By comparing the theoretical analysis results with the experimental results of two-sided shear friction, it is considered that the instability process of rock friction and sliding can be deeply studied according to the theoretical model of rock friction and sliding.
By analyzing the loading curve and sliding block friction evolution curve in the nonlinear stage, it is concluded that the specimen will have local instability many times before stick-slip occurs. The degree of local instability will decrease with the increase of interface inhomogeneity. After the specimen undergoes local instability, the interface inhomogeneity will increase.
By observing the loading curve of periodic stick-slip stage, the friction evolution curve of slider, and the shear drop value table of stick-slip event under different uniformity conditions, it is concluded that, with the improvement of the nonuniformity of sliding interface, the stick-slip period of specimen is shortened, and the shear drop value in stick-slip stage is reduced.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (nos. 51474013 and 51774015).