In the drilling and blasting excavation of underground rock mass, the stress wave produced by the blasting holes usually propagates in the form of cylindrical wave, while the rock mass surrounding the underground engineering is initially subjected to the in situ stress. To explore the propagation and attenuation law of cylindrical stress wave in the in situ stressed rock mass, a model test of cylindrical blasting stress wave propagation across the intact and jointed rock mass under different initial stresses was carried out. First, the attenuation law of the cylindrical stress wave in the intact rock mass under different confining pressures is analysed, and then the influence of the confining pressure scales, the angle, and the number of joints on the propagation law of the cylindrical blast wave in the jointed rock mass is studied. The experimental results show that the physical attenuation of the cylindrical wave in the intact rock mass decreases and then increases as the confining pressure increases from zero. Under zero confining pressure, the transmission coefficient of the cylindrical wave in the jointed rock mass decreases with the increase of joint angle, and the transmission coefficient increases with the increase of the joint angle under confining pressure. As the confining pressure increases from zero, the transmission coefficient shows a trend of increasing firstly and then decreasing.
Within Earth’s crust, the underground rock mass is usually in a certain initial in situ stress environment. In geophysics, earthquake engineering, underground engineering blasting excavation, and rock dynamics, it is of great significance in the research of the propagation and attenuation of blasting stress wave in in situ stressed rock mass.
The natural rock mass contains a large number of joints which have a great impact on the mechanical properties of rock mass and the propagation of stress wave [
The underground in situ rock mass during blasting excavation is subjected to complicated loading conditions, which mainly include in situ stress and blasting loading [
At present, experimental research on the propagation law of stress wave primarily uses the Split Hopkinson Pressure Bar (SHPB) apparatus [
Therefore, a model test of cylindrical blasting stress wave propagation across the jointed rock mass under different initial stresses is carried out, and the influencing factors, such as the scale of the initial stress, the angle, and the number of joints, are discussed, respectively. In contrast, the propagation of cylindrical stress wave in the intact rock mass under the same loading conditions is also studied. This study is helpful for better understanding stress wave propagation across in situ stressed rock mass and is of considerable importance to the design of the blasting excavation of rock mass in underground engineering.
The multifunctional testing machine for rock and soil is adopted to provide steady and uniformly distributed static boundary loads in the model test, as shown in Figure
Multifunctional testing machine for rock and soil.
The loading diagram for the test sample.
Horizontal loading mode.
The prototype used in the model test is the underground engineering rock mass excavated by the drilling and blasting method. By referring to the physicomechanical parameters of several typical deep underground engineering rock masses in China [
Physicomechanical parameters of prototype used in the model test.
Type | |||||||
---|---|---|---|---|---|---|---|
Prototype | 120 | 12 | 50 | 30 | 30 | 0.223 | 2600 |
The horizontal loading mode is adopted in the model test; that is, the model test samples are placed horizontally, and then static and dynamic loads are applied. Hence, the gravity of the model test samples is borne by the restrained steel girders on both sides of the loading equipment, and the stress similarity coefficient
In this paper, similar materials are mainly made of cement mortar and supplemented with some additional materials to simulate the intact rock. In the model test, the mixture ratio of the cement mortar in accordance with the similarity theory was determined through the orthogonal test, in which the cement: sand: water: plasticizer ratio = 1 : 4: 1.2 : 0.0267. Through the following series of tests, the physical and mechanical parameters of the cement mortar material with the chosen mixture ratio are determined.
The uniaxial compressive strength of the similar materials is measured by a uniaxial loading test, as shown in Figure
Uniaxial loading test.
The typical stress-strain curve is shown in Figure
Typical stress-strain curves of the test sample under uniaxial compression.
At the same time, the Poisson ratio of the model material can be determined by the stress-strain curve of the uniaxial loading test. The Poisson ratios of the model materials were 0.197, 0.209, 0.205, and 0.201, with an average of 0.203.
The tensile strength of the model material is measured by a split test. A total of ten specimens are made, and the size of each specimen is
Split test.
To measure the internal friction angle and cohesion force of the similar materials, a two-sided shearing test is carried out, and the size of sample is
Two-sided shearing test.
The axial load applied was 0, 1, 2, 3, and 4 MPa and the two-sided shearing tests at each applied axial load were carried out 4, 3, 3, 4, and 4 times, respectively. The critical shear force
Relationship between shear strength and axial stress.
As shown in the above figure, the shear strength increases with the increase of axial stress. According to the Mohr–Coulomb strength criterion, the relationship between shear strength and axial stress is calculated as
The physicomechanical parameters and stress similarity coefficient
Physicomechanical parameters and stress similarity coefficient of the similar materials.
Type | |||||||
---|---|---|---|---|---|---|---|
Similar material | 5.864 | 0.613 | 5.226 | 23.2 | 1.49 | 0.203 | 1980 |
20.5 | 19.6 | 9.6 | — | 20.1 | — | — |
The prototype used in the model test is the underground engineering rock mass subjected to the in situ stress, and the joints in the rock mass are usually in the closure state under compression. Consequently, the joints in the model test samples are also considered as closed joints. To ensure that the joint simulation materials do not deform or break during the manufacturing process of the model test samples, mica plates with certain strength and a thickness of 1 mm are used to simulate the joint in the rock mass. To determine the normal loading mechanical properties of the mica plate, a circular sheet with a diameter of 50 mm and a thickness of 1 mm is fabricated, as shown in Figure
Normal mechanical properties test of the joint simulation material. (a) Circular mica plates. (b) Normal loading test.
The typical normal stress and deformation curves of the joint simulation materials are shown in Figure
Normal stress and deformation curve of the joint simulation material.
The two model test samples were designed as shown in Figure
Arrangement of measuring points (unit: mm). (a) T1 sample. (b) T2 sample.
In the two samples, four measuring lines are arranged on the strain test section, and four strain measuring points are embedded in each line and numbered from 1 to 16 to measure the radial strain of the model test sample caused by cylindrical stress wave. On the stress test section, two pressure measuring points are arranged on each line and numbered from 17 to 24 to measure the radial stress, which coincides with the projection of the strain measuring point before and after the joint in the thickness direction of the model test samples.
In the T1 and T2 samples, in addition to one measuring line not being arranged on the joints, the other three measuring lines are arranged on 1 or 2 joints, as shown in Figure
To avoid the expansion of joints in the model test samples under the blast load and reduce the influence of the reflected stress wave at joints on different measuring lines affecting the stress wave propagation on other measuring lines, the joint length in the model test samples should not be too large and was set as 200 mm. At the same time, the measuring points arranged before and after the joints in the model test samples are located on the central line of the joints as shown in Figure
Before pouring the model test samples, the position of the joint is determined first, and the mica plates are fixed by the homemade device to constrain the displacement during the sample pouring process, as shown in Figure
Layout of the joints in the model test samples. (a) T1 sample. (b) T2 sample.
Both model test samples are divided into 3 layers for pouring, as shown in Figure
Schematic diagram of layered pouring (unit: mm).
To avoid the different cohesion strength between each layer of model test samples during layered pouring, the layered surface of the similar materials is made into a rough surface with a thickness of approximately 5 mm, as shown in Figure
Surface treatment of similar materials poured in layers. (a) Fabrication of rough surface. (b) Finished rough surface.
Owing to the complicated and high cost of making model test samples, the scheme of repeatedly applying blasting load to single test samples under different scales and distributions of static load is adopted to improve the efficiency of the model test. The cylindrical stress wave applied in the test sample is generated by using an electric detonator to detonate four detonating fuses with a total length of 1.6 m. The TNT (trinitrotoluene) equivalence is approximately 17.6 g, and the charge is kept constant during the test. The main model test steps are as follows. The four detonating fuses are tied together and fixed in the seamless steel pipe in the centre of the test sample through the wooden centring stent, as shown in Figure After the model test sample is fixed on the multifunctional testing machine for rock and soil, the preset static load is applied. To facilitate the full deformation of the model test samples, the static loads are divided into two stages and slowly loaded to the design value. The first stage is loaded to one-half of the preset value and lasts for 15 min; the second stage is loaded to the design value and finally stabilized for 30 min. Keep the model test samples under a stable static load, and then detonate the detonating fuses. At the same time, the DH 5960 dynamic data acquisition instrument is used to collect the dynamic stress and strain time-history curve of each measuring point in the model test samples under the blasting load. When the dynamic data collection is finished, the three restrained steel beams near the seamless steel tube in the model test samples are removed; then the quick-drying material in the steel pipe is smashed by an electric drill, and removed manually.
Schematic diagram of charge structure.
After the above four steps are completed, the wooden centring stent with detonating cords can be placed again in the seamless steel tube, and the quick-drying material can be poured. When the strength of quick-drying material reaches the strength required by the model test, the next blasting test can be carried out.
In the model test, the boundary static loads applied to the T1 and T2 samples are the same and are shown in Table
Boundary static loads of test samples.
Number | Experiment load (MPa) | Initial in situ stress (MPa) | ||
---|---|---|---|---|
Vertical | Horizontal | Vertical | Horizontal | |
1 | 0 | 0 | 0 | 0 |
2 | 0.75 | 0.75 | 15 | 15 |
3 | 1.5 | 1.5 | 30 | 30 |
4 | 3 | 3 | 60 | 60 |
To determine whether the propagation of the cylindrical stress wave produced by the detonating fuses in all directions is uniform in the model test samples, the strain measuring points 1, 5, 9, and 13 which are of same distance to the explosion source in the two test samples are taken as the research objects. The strain time-history curves of each measuring point without confining pressure are shown in Figure
Time-history curves of measuring points near explosion source without confining pressure. (a) T1 sample. (b) T2 sample.
The strain peaks of measuring points 1, 5, 9, and 13 in the T1 sample are −228.82 × 10−6, −225.99 × 10−6, −233.91 × 10−6, and −232.03 × 10−6, respectively. From the strain waveforms shown in Figure
The strain time-history curves of the strain measuring points 1, 5, 9, and 13 in the T2 sample are shown in Figure
The stress and strain measurement points are arranged in the test samples, and the pressure measuring points record the variation of stress wave amplitude value with time, which can directly show the variation law of the amplitude of the cylindrical blast wave. However, due to the limitations of test conditions, only two pressure measuring points are arranged on each measuring line in the test samples, which is not enough to obtain the propagation law of the cylindrical blasting wave. Therefore, the peak values of the four strain measurement points in the intact rock mass measuring line are chosen to study the propagation and attenuation law of the cylindrical stress wave.
Without the initial stress, the strain time-history curves of the radial strain measuring points 13, 14, 15, and 16 in the intact rock mass of the T1 sample are shown in Figure
Time-history curves of radial strain of measuring point in intact rock mass without initial stress.
It can be seen in the above figure that the peak strain of each measuring point decreases with the increase of the propagation distance of the cylindrical stress wave without initial stress. When the cylindrical stress wave propagates from measuring point 13 to 16, the amplitude of the peak strain is reduced by 77.2%. To facilitate the study, the absolute value of the strain peak value is used to analyse the attenuation of cylindrical stress wave in intact rock mass.
The attenuation law of the strain peak of the measured points in the intact rock mass of the T1 test sample under different confining pressures is shown in Figure
Attenuation law of the cylindrical stress wave in the intact rock mass under different confining pressures.
When cylindrical stress wave propagating across intact rock mass, geometric attenuation and physical attenuation both occur as the propagation distance increases. The geometric attenuation is caused by the expansion of the cylindrical stress wave front, which is independent of the physicomechanical properties of the propagating medium and the boundary conditions.
The mechanical parameters of the cylindrical stress wave front are all attenuated by the coefficient
The physical attenuation mechanism of the cylindrical stress wave in the intact rock mass is caused by the friction effect of the stress wave on the microcrack surface inside the propagating medium [
The physical attenuation of the cylindrical wave in the intact rock mass is affected by the mechanical properties of the propagation medium and the boundary conditions. The geometric attenuation part is eliminated from the attenuation of the peak strain at the measuring points shown in Figure
Physical attenuation law of cylindrical wave in intact rock mass under different confining pressures.
It can be seen in Figure
When the confining pressure increases from 0 to 3 MPa and the cylindrical stress wave propagates from measuring point 13 to measuring point 16, the decreased amplitude of the peak strain is 26.8%, 25.6%, 25.2%, and 30.7%, respectively. It can be seen that the physical attenuation of the cylindrical wave in the intact rock mass decreases first and then increases with the increase of the confining pressure.
The peak strain of the measuring points under different confining pressures in Figure
Variation law of physical attenuation coefficient under different confining pressures.
With the change in confining pressure, the physical attenuation coefficients of the cylindrical wave in the intact rock mass basically meet the cubic function of one variable, as shown in the following:
As seen in Figures
The reason for this phenomenon is that there are a large number of microcracks inside the intact rock mass, and when the stress wave propagates across the intact rock mass, it will drive the microcracks to slide overcoming the frictional forces. In this process, part of the cylindrical stress wave energy is converted into heat energy, resulting in a decrease in its amplitude. When the confining pressure is low the microcracks in the rock mass are closed, the dynamic stress required for the sliding of the microcracks is also increased, and the number of microcracks that can slip under the stress wave is reduced, so the physical attenuation of the stress wave decreases. With the increase of confining pressure, the closed microcracks in the intact rock mass are expanded and the new microcracks are initiated, and the number of microcracks that can slip under the stress wave increases, so the attenuation of the stress wave increases accordingly.
Because of the existence of joints, the transmission and reflection occur when stress wave passing through the joints will lead to the attenuation of stress wave amplitude. In the absence of confining pressure, the propagation and attenuation law of cylindrical wave in intact rock mass and 30° single jointed rock masses is shown in Figure
Attenuation law of cylindrical wave in the intact and 30° single-joint rock mass without confining pressure.
Different from the intact rock mass, the ratio of the peak values of the stress measuring points before and after the joints with different angles and numbers in the T1 and T2 samples are taken as the transmission coefficient, to study the propagation law of the cylindrical wave in the jointed rock mass intuitively.
As a comparison, the transmission coefficients of cylindrical wave in intact rock masses are also obtained. The variation law of transmission coefficient of intact and jointed rock mass in T1 and T2 samples under different confining pressures is shown in Figure
Variation law of transmission coefficient of intact and jointed rock mass under different confining pressures. (a) T1. (b) T2.
It can be seen in Figure
The reason for the above phenomenon is that the attenuation of the cylindrical stress wave in the jointed rock mass mainly consists of three parts: the physical attenuation resulting from propagation of stress wave in intact rocks, the attenuation resulting from interaction between stress waves and joints, and the geometrical attenuation resulting from the expansion of wave fronts. Meanwhile, it can be seen in Section
For the jointed rock mass, when the confining pressure increases from 0 to 1.5 MPa, the attenuation of the cylindrical wave propagating across joints decreases, and the physical attenuation in rocks also reduces, with the result that the attenuation of the cylindrical wave in jointed rock mass decreases, and the transmission coefficient increases. When the confining pressure increases from 1.5 to 3 MPa, the physical attenuation of cylindrical stress wave in the rocks increases, the attenuation at joints continues to decrease and the transmission coefficients of the jointed rock mass decrease, indicating that the increment of physical attenuation of cylindrical wave in rocks is greater than the decrement of the attenuation at joints.
When the confining pressure is 0, 1.5, and 3 MPa, the variation law of the transmission coefficients in jointed rock mass with the angle of joint in T1 and T2 test samples is shown in Figure
Effect of the number and angle of joints on transmission coefficient.
Figure
It can also be seen in Figure
According to the propagation characteristics of cylindrical stress wave, the model test samples including the intact rock mass and jointed rock mass were designed, and a model test of cylindrical stress wave propagation under different initial stresses was conducted. Then, through the stress and strain measuring points embedded in different positions of the model samples and the dynamic data acquisition technique, the propagation and attenuation law of the cylindrical wave in the intact and jointed rock mass under initial stress was studied. The model test carried out in this paper can provide a new idea and method for studying the propagation law of stress wave in jointed rock mass under static loads; moreover, the model test results are helpful for understanding the propagation and attenuation mechanisms of cylindrical stress wave across in situ stressed jointed rock mass. The following conclusions can be drawn: The initial stress has a significant impact on the propagation and attenuation of cylindrical stress wave in intact and jointed rock mass, and the rocks and joints of jointed rock mass are in different mechanical states under different initial stresses, which leads to a change in the propagation law of stress wave. The attenuation of the cylindrical stress wave in the jointed rock mass mainly consists of three parts: the physical attenuation resulting from the propagation of the stress wave in rocks, the geometrical attenuation resulting from the expansion of the stress wave fronts, and the attenuation resulting from the interaction between stress wave and joints. The geometric attenuation is only related to the geometry of the stress wave front, while the physical attenuation in rocks and the attenuation at the joints are affected by the initial stress. For the intact rock mass, a polynomial function can be used to describe the relationship between the confining pressure and the physical attenuation coefficient. With the increase of the confining pressure, the physical attenuation of the cylindrical wave decreases first and then increases. The transmission coefficients of the cylindrical wave in jointed rock mass are related to joint angles, quantities, and confining pressures. Without the confining pressure, the transmission coefficient decreases with the increase of the joint angle. When the confining pressure exists, the transmission coefficient increases with the increase of joint angle. With the increase of confining pressure, the transmission coefficient shows a trend of increasing firstly and then decreasing. The transmission coefficient also decreases as the number of joints increases.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest.
This study was supported by the Natural Science Foundation of Hubei Province, China (2020CFB428), the National Natural Science Foundation of China (51774222), the Research Start-Up Foundation of Jianghan University (1027-06020001), and the Postdoctoral Innovation Research Post of Hubei Province of China (20201jb001).