In order to study the dynamic crack propagation law in fissured rock under the different fillings, a borehole with 7 mm diameter was processed in the center of a polymethyl methacrylate (PMMA) specimen. The preexisting fissure with different angles (
A large number of randomly distributed joints and fissures make the rock mass to show properties of the discontinuity, anisotropy, and inhomogeneity. For the fissured rock, when the stress waves travel to the fissure surface, the stress waves can produce the phenomena of reflection, refraction, diffraction, and transmission [
Song and Kim [
Although many researchers have studied largely the blast-induced crack propagation law in fissured rock mass, they mostly studied the influence of single variable on crack propagation, such as stress wave incident angles [
PMMA and rock exhibit an anisotropic behavior and brittle characteristic under explosive loading [
PMMA specimen (unit: mm).
The variables of the specimens.
Fillings |
|
| ||||
---|---|---|---|---|---|---|
Air/soil/water | 0 | 20 | 30 | 40 | 50 | 60 |
45 | 20 | 30 | 40 | 50 | 60 | |
90 | 20 | 30 | 40 | 50 | 60 |
The experimental procedures are as follows: The laser lathe was applied to incise the PMMA specimen and prefabricate the borehole and preexisting fissure, which requires walls of the borehole and preexisting fissure to be smooth and perpendicular to the specimen surface; Sellotape was pasted tightly on the backside of preexisting fissure in each soil-filled specimen and water-filled specimen; gaskets were used to form a holder for underlaying the specimen via its four corners to the same height on the ground, which aimed at preventing the bottom of the detonator from touching the ground to change the main charge zone position. To the air-filled group, ① a #8 instantaneous electric detonator was fixed with the same batch, the similar resistance values in the center of the borehole and the detonator must be perpendicular to the specimen surface, and all the main charge zones of the detonator were required to align the thickness of the specimen in the same position; ② the specimen was put on the holder; ③ a thin wood plate that had a slightly bigger hole than the borehole with the same size of the specimen was covered above the specimen to prevent the detonator debris from scratching in the explosion; and ④ the detonator was initiated, and the specimen was recycled after explosion. To the soil-filled group, firstly soil was filled in preexisting fissure completely, which requires soil to be consistent with the thickness of the specimen so that it does not invade into the rear paste area of Sellotape, and then, the steps ①, ②, ③, and ④ were followed in the air-filled group. To the water-filled group, firstly the steps ① and ② were followed in the air-filled group; then, a syringe was used to fill water in the preexisting fissure completely, and it was ensured that no bubbles exist in the fissure; and lastly, the steps ③ and ④ were followed in the air-filled group.
The crack propagation effects of the experimental specimens after explosion are shown in Figures
Air-filled PMMA specimens after explosion.
Soil-filled PMMA specimens after explosion.
Water-filled PMMA specimens after explosion.
The mechanical properties of the fillings affect the discontinuity degree of the specimen, which was measured by the wave impedance. The wave impedances of four media are shown in Table
Four kinds of media wave impedance relationship at room temperature.
Medium |
|
|
|
Δ |
---|---|---|---|---|
PMMA | 1190 | 2320 | 2.7608 × 106 | — |
Air | 1.25 | 340 | 425 | 2.760375 × 106 |
Soil | 1800 | 1000 | 1.8 × 106 | 0.9608 × 106 |
Water | 998 | 1497 | 1.494006 × 106 | 1.266794 × 106 |
Figure
Relationship between fillings and the total number
As shown in Figure
Relationship between
In the actual blasting project, the wing crack propagation in the fissured rock mass seriously affects the rock fragment range and the later engineering support, so it is necessary to analyze the far-end wing crack. In the case of two far-end wing cracks in the 0° group, for the convenience of studying, the numbers show the average values in Figures
Relationship between fillings and far-end wing crack. (a)
Relationship between
In Figure
In Figure
In order to further reveal the blast-induced crack propagation law in the fissured rock mass under the explosive loads, the nonlinear dynamics software AUTODYN is used for numerical simulation according to the corresponding parameters of the experimental specimen, involving materials including PMMA, fillings (air, soil, and water), and explosive.
To better cooperate with the tensile crack softening failure model, the linear equation of state (EOS) is applied in PMMA [
The tensile crack softening model is applied as the PMMA failure model, and the detailed description of this model is in [
Dynamic parameters of PMMA.
Density, |
Poisson’s ratio, |
Dynamic elastic modulus, |
Dynamic shear modulus, |
Dynamic bulk modulus, |
P wave velocity, |
S wave velocity, |
---|---|---|---|---|---|---|
1190 | 0.31 | 6.1 |
2.328 |
5.35 |
2320 | 1260 |
Strength parameters of PMMA.
Dynamic tensile strength, |
Dynamic shear strength, |
Fracture energy, |
---|---|---|
45 |
80 |
133 |
Air For air, the EOS is described by the ideal gas: where Soil The soil is described by the shock EOS and the Drucker–Prager strength model. The concrete parameters are shown in Table Water A polynomial EOS is applied to water: For For where in the above two formulas
Parameters of the soil model.
Density, |
Grüneisen gamma, |
|
|
Shear modulus, |
Pressure 1 (Pa) | Pressure 2 (Pa) | Pressure 3 (Pa) | Yield stress 1 (Pa) | Yield stress 2 (Pa) | Yield stress 3 (Pa) | Hydrotensile limit (Pa) |
---|---|---|---|---|---|---|---|---|---|---|---|
1800 | 0.11 | 1614 | 1.5 | 0.24 |
−1.149 |
6.88 |
1 |
0 | 6.88 |
6.2 |
−100 |
Parameters of the water model.
Density, |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
998 | 2.2 |
9.54 |
14.57 |
0.28 | 0.28 | 2.2 |
0 |
The explosive is ammonium nitrate-fuel oil (ANFO) explosive, and the EOS is described by JWL:
Parameters of ANFO.
Density, |
Detonation velocity (m/s) |
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
931 | 4160 | 5.15e9 | 5.15e9 | 1.891e9 | 3.907 | 1.18 | 0.333 |
According to the experimental specimen, the 2D model and noncoupling charge structure are applied. The diameters of the borehole and explosive are 7 mm and 6 mm, respectively. A variety of grid sizes were applied to simulate the crack propagation, and we found that too big or too small grid sizes would lead to unsatisfactory or nonideal crack results compared with the experimental crack results. Meanwhile, we also did the convergence computation through all kinds of grid sizes. Based on the above previous works before simulation, we chose 1.5 mm as the grid size at last and the total number elements were 78655. The mesh method is sweep, the boundary condition is the free boundary, and the calculation time is 100
(a) Material location; (b) gird mesh.
The numerical simulation results are shown in Figures
Material status of air-filled PMMA after explosion. (a)
Material status of soil-filled PMMA after explosion. (a)
Material status of water-filled PMMA after explosion. (a)
Because the explosion of the detonator in experiment has less gas and the calculation time is relatively shorter in numerical simulation, it is considered that the stress wave is the most important factor in blast-induced crack initiation and propagation. From the experimental and simulative results, it can be concluded that the crack propagation process can be divided into two stages through the time points that whether the reflected stress wave formed in the preexisting fissure has common interaction with the compressive stress wave or not. The first is the phase of the compressive stress wave, and the second is the phase of the common interaction between compressive stress wave and reflected stress wave.
After detonator or explosive detonation, the shock wave compresses on the borehole wall intensely to develop the crushed zone around the borehole because of the shear stress. The shock wave attenuates the stress wave during the process of the crushed zone formation. The stress wave compresses radially the media outside the crushed zone to cause the tangential stress, and once the tangential stress reaches the dynamic tensile strength of the medium, it will lead to radial crack initiation and propagation. Then, the reflected stress wave and the compressive stress wave act together to promote the crack propagation again.
Considering the different positions between preexisting fissure and borehole, the reflected stress wave that travels back to the borehole is different, and radial crack propagation mechanism is also different, so it is necessary to discuss the influence of the distance, angle, and fillings on crack propagation. Distance
In numerical simulation, take the air-filled specimens at Angle
Relationship between peak pressure and
When Fillings
When
Relationship between peak pressure and fillings.
In numerical simulation, the damage-time curve is obtained by setting the initiation point of the far-end wing crack as the gauss point. Taking the air-filled specimen at
The fitting curve of damage-time in the air-filled specimen at 45° and
The dynamic tensile damage evolution process is reflected fully in Figure
The curve of damage-pressure in the air-filled specimen at 0° and
Figure
Typical curves of pressure-time at different angles (air-filled specimens at
The effects of distance, angle, and fillings on the initial damage and fracture time of the initiation point of the far-end wing crack are discussed below. Generally, the distance that the stress wave travels to the far end of the preexisting fissure also increases as the distance
The compressive stress wave travels to the preexisting fissure, and the pressures are firstly generated at the initiation points of the both ends. The pressure is gradually converted to the tensile force as the reflected stress wave generated in the prefabricated crack continues to pressure on initiation points. As time goes on, the initiation point begins to damage, and the damage value increases rapidly, and finally the damage value reaches 1. During the whole process, the stress concentration occurs at the crack initiation point. When the stress strength exceeds the dynamic tensile strength of PMMA, the wing cracks begin to initiate and propagate. In the crack propagation process, the shear stress is produced by the shear-slip caused by the uneven stress at the crack tip, which indicates that the wing crack propagates in a tensile-shear mode. When the stress strength is lower than the dynamic initiation strength, the wing crack arrests.
Through the analysis of the physical experiment and numerical simulation, for most of the specimens, the wing crack propagation direction exists in two situations: when the distance
In Figure
Relationship between fillings and the total number
In Figure
Relationship between
In Figure
Relationship between fillings and length of far-end wing crack. (a)
It is well known that the reason for the decrease in the far-end wing crack length when the distance
Relationship between fillings and pressure (all pressures are absolute values, but in fact, the pressure values are negative in (b) and (c)). (a)
In Figure
Relationship between
Figure
Relationship between fillings and
Figure
Relationship between
Compared with the experimental results, the numerical simulation can reflect better the entire variation law of blast-induced crack propagation that the total number The wing crack is a kind of mixed mode crack by propagating in the tensile-shear mode. The similar propagation path of the far-end wing crack is related to the direction of the compressive stress wave propagation at the same angle. The length of the far-end wing crack in air-filled specimens is larger than that in the soil-filled and water-filled specimens, which shows that the damage range caused by explosion is the largest under this condition. The damage-time curve of the initiation point of the far-end wing crack presents “S”-type change, and the damage-pressure curve of the initiation point can fully reflect the law of the dynamic tensile damage evolution process. The specimen discontinuity degree is measured by the wave impedance difference value between the three fillings and PMMA, and the greater the difference value, the smaller the discontinuity degree and the greater the reflected wave energy. It is generally believed that the larger the angle and the smaller the distance, the greater the reflected wave energy should be in the three kinds of filling specimens, but meanwhile the greater the transmitted stress wave energy also is. So there is a mutual restraint relationship between the distance
The authors declare that they have no conflicts of interest.
The authors gratefully acknowledge the support of NSAF (no. U1530140) and the Beijing Institute of Applied Physics and Computational Mathematics through the contract of HG7017105.