In engineering blasting, the determination of the range of rock blasting fracture zone has important guiding significance for blasting construction. This paper proposes a method that can accurately and directly obtain the range of rock blasting fracture zone. Based on the theory of elastic wave propagation, test rods which are made of appropriate material are selected and prepared. A certain number of boreholes are drilled for subsequent insertion of the test rods along the direction perpendicular to the free surface of the excavation at a certain distance from the blast hole. Based on the field blasting test results, the deepest fracture position of the test rod is used as the boundary of the blasting fracture zone, and the range of the rock blasting fracture zone is obtained. A numerical analysis model is established according to the Mohr–Coulomb constitutive relationship and the Von Mises yield criterion. Then, the range of the fracture zone and the maximum horizontal radius of the fracture zone are analyzed and obtained. The numerical analysis results are compared with the field measured data. It is demonstrated that the range of the fracture zone obtained by the numerical simulation is in good agreement with the blasting test results of the pre-embedded test rods. The research results can provide references for the safety control of blasting and excavation of rock slopes.
Because blasting has the merits of fast excavation speed, high efficiency, and low cost, it has been widely used in the process of rock slope excavation and open-air pit mining. However, blasting inevitably affects and damages the slope. The study of the maximum horizontal radius and range of the slope fracture zone can guide on-site blasting excavation and is of great significance to retain the integrity of the bedrock and ensure the engineering safety. It is also a problem that the engineering community is generally concerned about. When the explosive is buried adjacent to the ground free surface, the phenomenon of rupture, bulging, and throwing will occur according to the distance between the explosion center and the free surface. Livingston [
Regarding the theoretical description of the damage caused by explosive loads to rock masses, it is currently mainly quantified by damage variables. Researchers have made certain progress in this regard. For example, Taylor et al. [
On the basis of previous research results, this paper attempts to propose a more accurate and intuitive test method to determine the range of rock blasting fracture zone. In the area near the blast hole, the pre-embedded test rod was drilled along the direction perpendicular to the free surface of the excavation. The rupture depth of each test rod at different positions from the blast hole was obtained through the field blasting test, and the range of the rock fracture zone under the blasting load was obtained. The results will provide construction references for safe blasting excavation of rock slopes.
According to the wave impedance, compressive strength, and dynamic compressive strength of the rock at the test site, the appropriate test rod material is selected and test rods with similar materials are prepared in the laboratory. The ratio of the dynamic compressive strength of the test rod to the dynamic tensile strength of the rock is required to be close to the transmission coefficient of the stress wave at the interface between the test rod and rock. The transmission coefficient is determined by the ratio of the wave impedance of the test rod material to the rock.
At a certain distance from the blast hole, each test hole is drilled along the direction perpendicular to the free surface of the excavation. The test holes have the same depth as that of the blast hole and are numbered in an increasing order with the distance from the blast hole. The prepared test rods are numbered accordingly based on their respective test holes. The diameter of the test hole and blast hole drilled by the field drill is slightly larger than the diameter of the test rod. After each test rod is placed into the test hole separately, the gap between them is filled with gravel so that the test rod is in close contact with the original rock. After blasting, the maximum rupture range of the test rod is taken as the range of blasting fracture zone of the rock.
The rock is in a three-dimensional stress state of tension and compression. Due to the impact load, the surrounding rock is in a strongly compressed state. The explosive stress is much greater than the dynamic compressive strength of the rock. Subjected to the great explosive stress and the action of the high temperature and high pressure produced by the explosive gas, the rock is crushed. Outside the crushing zone, the explosive stress in the rock is less than the dynamic compressive strength of the rock and the tensile stress generated in the rock is greater than the dynamic tensile strength of the rock. As a result, the rock is subjected to tensile failure [
Stress state at any point in the rock mass.
According to the Von Mises criterion, there are inequalities expressed by equation (
As shown in Figure
Reflection and transmission of elastic waves: (a)
Since the compressive strength of the test rod is much smaller than that of the rock on-site, the intensity of the transmitted stress wave after the explosion stress wave passes through the interface between the test rod and the rock is much greater than the dynamic compressive strength of the test rod. Therefore, the test rod will be mainly subjected to compressive failure. When the original on-site rock is at the position of the test rod, the intensity of the stress wave passed is smaller than the dynamic compressive strength of the rock. It thus cannot directly crush the rock. However, it can still damage the rock. The relatively large radial compression results in radial compressive strains and tangential tensile strains in the rock layer surrounding the crushing zone. Once the generated tangential tensile stress is greater than the dynamic tensile strength of the rock, radial cracks will be generated, which form the fracture zone. Therefore, the original rock corresponding to the rod position is mainly subjected to tensile failure.
When the ratio of the dynamic compressive strength of the test rod to the dynamic tensile strength of the rock and the ratio of the transmitted wave stress to the incident wave stress (i.e., transmission coefficient) are close, it can be considered that the fracture position of the test rod under the blasting load and its corresponding field rock is the same, so the fracture position and fracture range of the test rod can be used to judge the fracture range of the rock on-site.
A limestone mine in Bazhong, Sichuan, is a hillside open-pit mine. The mine mainly yields limestone and flint limestone. The rock mass in the mining area has a steeply dipping layered structure. The fractures are generally developed, but the connectivity is poor, and no secondary folds and faults are seen. The integrity of the rock formation is good, and the geological structure is relatively simple. The blasting scheme adopts a top-down open-pit mining method with horizontal steps, following the principle of simultaneous mining and stripping with stripping first. The on-site blasting test was selected on a platform with an elevation of 1278 m, and the test location is shown in Figure
Mine test site: (a) test platform; (b) test position.
Photograph of the blast hole taken upward from the inside.
The field blasting test uses 2# rock emulsion explosive, and the drilling and blasting parameters are shown in Table
Drilling and blasting parameters of the field blasting test.
Blast hole diameter (cm) | Blast hole depth (m) | Dose (kg) | Blockage length (cm) |
---|---|---|---|
14 | 2 | 10 | 40 |
Physical and mechanical parameters of the limestone rock.
Elastic modulus | Poisson’s ration | Density | Internal friction angle | Cohesion | Tensile strength |
---|---|---|---|---|---|
38.5 | 0.296 | 2680 | 55 | 16.25 | 5.57 |
Compressive strength parameters of limestone rock samples in natural state.
In the field blasting test, the gypsum rod was used as the test rod. The gypsum rods are prepared by mixing gypsum and water with a certain gravimetric ratio. Three kinds of gypsum rods are made by adopting water-gypsum ratios of 0.7, 1.0, and 1.3, respectively. The physical parameters of the gypsum rods with the three water-gypsum ratios are shown in Table
The physical parameters of the gypsum rods with different water-gypsum ratios.
Water-gypsum ratio | Elastic modulus | Poisson’s ratio | Density | Compressive strength |
---|---|---|---|---|
0.7 | 2.31 | 0.250 | 1408.8 | 4.08 |
1.0 | 1.49 | 0.198 | 1127.1 | 1.65 |
1.3 | 1.23 | 0.169 | 1015.4 | 1.25 |
The longitudinal wave velocity of the stress wave in the elastic medium is as follows:
In engineering blasting, the loading rate in crushed zone is high, which is taken as
The longitudinal wave velocity in the rock measured by sonic tester on-site is
Calculated parameters of the original rock and test rods with different water-gypsum ratios.
Water-gypsum ratio | Wave impedance ratio | Transmission coefficient | Dynamic compressive strength | |
---|---|---|---|---|
0.7 | 5.10 | 0.327 | 18.930 | 0.566 |
1.0 | 7.09 | 0.247 | 7.656 | 0.229 |
1.3 | 8.20 | 0.217 | 5.800 | 0.173 |
It can be seen from Table
The preparation procedure of the test rod is as follows. (1) A PVC pipe with a length of 1.0 m and an inner diameter of 0.14 m was cut and split into two halves along the center line. After brushing a layer of oil on the inner side of the pipe, it was then wounded with adhesive tape for bonding. (2) One end of the PVC pipe was sealed, and an iron wire was fastened at the center of sealed end. (3) Gypsum slurry was then poured into the PVC pipe. When grouting, the iron wire was kept in a centered and tensed state, while vibrating and stirring until the gypsum was uniformly formed. (4) The gypsum rods were taken out and cured naturally for 7 days. Two 1.0 m length gypsum rods are connected to a 2.0 m long gypsum rod through the embedded iron wire.
At a distance of 1.0 m from the blast hole, test holes were drilled along the direction perpendicular to the free surface near the excavation. In the field blasting test, the orientation angle of the connection line between the blast hole and the nearest test hole is 60°. The test hole spacing is 0.6 m. Before the test, the prepared gypsum rods were numbered 1∼4 according to their distances from blast hole from the near to the distant. The diameter of the gypsum rod was 0.14 m, and the test holes and blast hole were all 2.0 m deep. The layout of the on-site shallow hole blasting test is shown in Figure
Schematic diagram of the field blasting test: (a) plan view; (b) sectional view.
Gypsum rod before the blasting test.
After the field blasting test, the free-surface fracture zone on the top of the blast hole is shown in Figure
Fracture diagram after the blasting test: (a) radial crack; (b) circumferential crack.
Gypsum rod after the blasting test: (a) field observation; (b) measured data.
It can be seen from Figure
In Figure
The combination of field test and numerical analysis can more accurately reproduce the damage range of the rock under the blasting load. Therefore, the numerical analysis is conducted to further validate the accuracy of using test rod to obtain the fracture range of the original rock on-site under the blasting load.
The Chapmam–Jouguet (C-J) theory can qualitatively explain the physical phenomenon of explosive detonation. The C-J model of detonation regards the detonation surface as a sudden interface [
The peak shock pressure,
The field blasting test adopts a coupled charge structure and uses a triangular load to approximate the blasting load. The impact pressure loading curve on the blast hole wall can be simplified to a triangular loading curve, as shown in Figure
Equivalent diagram of blasting load.
The explosion load increases rapidly at the moment of blasting, assuming the rise time of the explosion load
The ratio of the rise time to the total action time of the commonly used triangular explosion load [
Calculated by equations (
Assuming that the rock is an isotropic material, the Mohr–Coulomb constitutive model is adopted in this work to analyze the constitutive stress-strain relationship of rock materials.
In order to simplify the calculation, a 1/4 cylinder is taken as the calculation model based on the symmetry. In order to reduce the influence of the model boundary, based on the size of the crushing zone and the fracture zone produced by rock blasting, the 1/4 cylinder with the radius of 8.0 m and the height of 8.0 m is used as the model for simulating the field blasting. The blast hole radius is set to be 0.07 m according to the actual on-site geometry. The vertical boundary of the model restricts the horizontal displacement. The lower boundary restricts the vertical displacement. The circumferential boundary adopts a static viscous boundary to reduce the influence of boundary reflection waves on the calculation results. The top horizontal plane is set as the free surface, and the particle velocity on each boundary in the initial state is set to be 0.
In the dynamic analysis with large strain, simply setting a very small damping ratio can meet the requirements. Rayleigh damping [
The size of the grid element has a great effect on the numerical simulation results. To reach decent accuracy, the following relationship [
Blasting vibration velocity waveforms and dominant frequencies were obtained by employing the blasting vibration tester (UBOX-5016; see Figure
The arrangement of on-site blasting vibration tester.
Field blasting vibration test results: (a) horizontal radial vibration of the particle; (b) horizontal tangential vibration of the particle; (c) vertical vibration of the particle.
It can be seen from Figure
The cylindrical shell modeling method is adopted. The inner and outer radii of the shell are 0.07 m and 8.0 m, respectively. The number of grid elements in the radial direction is 20, and the size of the individual grid is increased by a ratio of 1.1 from center outward. The vertical plane is evenly divided into 10 grid elements within a depth of 2 m. In the depth range below 2 m, the size of the individual grid is increased downward by the ratio of 1.05. The centripetal part of the shell below the depth of 2 m is filled. The counterpart within the depth of 2 m is not filled to reserve the blast hole. The radius of the filling part is 0.07 m. The number of grids in the radial direction is 2, and the mesh division method is the same as that of the shell below the depth of 2 m. At the same time, the annulus sector is equally divided into 30 parts. The portions closer to the blast hole are divided more densely so as to ensure the accuracy of the calculation results and reduce the calculation convergence time. The minimum size of the model mesh is 0.03 m, and the maximum mesh size is 0.85 m. The numerical analysis model is shown in Figure
The meshing diagram of the numerical model.
The Von Mises yield criterion is used as the rock failure criterion to depict the rock fracture zone in the numerical analysis. Figures
The development of rock mass fracture zone in bird’s-eye view: (a) 0.5 ms; (b) 0.8 ms; (c) 1.5 ms; (d) 2.0 ms; (e) 2.5 ms; (f) 3.0 ms.
The development of rock mass fracture zone in head-up view: (a) 0.5 ms; (b) 0.8 ms; (c) 1.5 ms; (d) 2.0 ms; (e) 2.5 ms; (f) 3.0 ms.
It can be seen from Figures
Comparison of the range of fracture zones in the blasting test.
It can be seen from Figure
This paper proposes a method that can accurately and directly obtain the range of the fracture zone of the rock slope under the blasting load. The basic principle of the method in which embedded test rods are drilled around the blast hole and subjected to blasting load is based on the reflection and transmission theory of the stress wave of different media interface. Based on the field blasting test and the numerical simulation presented in this study, the following conclusions can be drawn: Based on the closeness between the transmission coefficient of the stress wave through the test rod-rock interface and the ratio of the dynamic compressive strength of the test rod to the dynamic tensile strength of the rock, the fracture range of the test rod after blasting can be used as the range of the surrounding rock fracture zone after the slope blasting. In the field blasting test, the range of the surrounding rock blasting fracture zone conforms to the general distribution pattern of the surrounding rock fracture zone under blasting load. The relative error between the field blasting test results and the numerical analysis results in this paper is less than 18%, indicating that the proposed test method has a good accuracy. The test method described in this paper adopts shallow hole blasting, and this method is also applicable to deep hole blasting.
The data sets used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (no. 51909192) and the Open Project of Engineering Research Center of Phosphorus Resources Development and Utilization of Ministry of Education (no. LKF202004).