Experimental and numerical investigation on dynamic behaviors of the concrete wall in underground coal mine with hydraulic blasting demolition

3.1.1. Momentum equation

In the continuum mechanics, momentum equation is:

where ${\sigma }_{ij,j}$ one order partial derivative of Cauchy stress component ${\sigma }_{ij}$ with respect to the coordinate variable in the $j$th direction, $f_i$ is the volume force vector of unit mass, $x_i$ is acceleration vector, and $\rho$ is the density of air.

3.1.2. Conversation equation

Conversation equation of mass is:

where $\rho$ is the current density of air, ${\rho }_0$ is the initial density of air, $J=\left|\partial x_i/\partial x_j\right|$ is the relative volume, $x_i$ is the space coordinate in the $i$th direction, $x_j$ is the matter coordinate in the $j$th direction, and $\partial x_i/\partial x_j$ is the strain gradient with respect to $x_j$.

3.1.3. Energy equation

Energy equation is:

This equation is mainly used for the equation of state and calculations for the balance of total energy, where $V$ is volume, ${\epsilon }_{ij}$ is strain rate tensor, $q$ is volume viscous resistance and $p$ is hydrodynamic pressure.

However, the expression between deviatoric stress tensor and hydrodynamic pressure is given by:

ANSYS/LS-DYNA is a finite element computation code for dynamics suitable for impact, explosion and other instantaneous problems, is used to carry out the numerical simulation process. In LS-DYNA, there are three classes of methods are available for generating the grids and mesh, include Euler, Lagrange and Arbitrary Lagrange-Euler (ALE) method, Details of the models of fluid-solid interaction can be found in the LS-DYNA theoretical manual [16]. In this study, the ALE method is employed to simulate the process of the methane explosion, the propagation of air shock waves through tunnel in this process, and the interaction of explosion shock waves with the sealing wall [17]. Wang researches the shock wave propagation process and analyses the seismic effects of shallow underground explosions [18].

The ALE algorithm consists of a classical Lagrange step in which the mesh moves along with the modeled material, a rezone step in which the mesh is modified to preserve good quality through the computation of Euler time step, and a remapping step in which the solution is conservatively transferred from the old mesh to the new rezoned one, and thereby analysis for the fluid-solid coupling transient.

3.2.1. Shock tube

The dynamite device is made of high strength alloy steel, MAT_JOHNSON_COOK* is selected to describe material, the state equation *EOS_GRUNEISNE. is defined as below [19]:

where, ${\overline{\epsilon }}^p$ is equivalent plastic strain. ${\epsilon \text{'}}^{*}$ is dimensionless plasticity ratio of ${\epsilon }_0^{\text{'}}=1.0s^{-1}$. ${\epsilon \text{'}}^{*}={\overline{\epsilon }}^p/{\epsilon }_0^{\text{'}}$; $T^{*}$ is relative temperature, $T^{*}=\left(T-T_{room}\right)/\left(T_{melt}-T_{room}\right)$; $A$ is yield stress, Pa; $B$ is strain hardening coefficient. $n$ is strain hardening index. $C$ is strain rate correlation coefficient. $m$ is temperature correlation coefficient. Specific parameters see in Table 1.

3.2.2. Dynamite

High energy dynamite materials is applied to describe TNT dynamite, JWL state equation is applied to describe the expansion of detonation product, it is assumed to detonation product propagate at constant velocity and the before detonation. Equation of state JWL is defined as follows [20]:

where, $P$ is pressure, $V$ is the relative volume, $e$ is the internal energy of the unit volume of dynamite, $A$, $B$, $R_1$, $R_2$ and $\omega$ are the constant in laboratory. Parameters in the calculation Eq. (19) are shown in Table 2.

3.2.3. Water

Liquid water is selected as the blasting medium, water is defined as empty material model (*MAT-NULL), and equation of state for water is described by Gruneisne [21]:

The equation of state for the expansion material is [22]:

where, ${\rho }_0$ is the initial density of the water, $C$ is the intercept of the curve $V_S-V_P$, namely the propagation velocity of shock wave in water $\upsilon$ is Poisson’s ratio; $S_1$, $S_2$ and $S_3$ are the coefficients of the intercept of the curve $V_S-V_P$. ${\gamma }_0$ is Gruneisen coefficient; $\alpha$ is the first order volume correction for ${\gamma }_0$ and $\mu =\rho /{\rho }_0-1$. $E$ is the internal energy per unit mass. Material parameters are shown in Table 3.

3.2.4. Concrete wall

Concrete is the mainly material of sealing wall, JOHNSON_HOLMQUIST_CONCRETE is selected as the constitutive model, called model JHC, which can be used to simulate the damage behavior under high strain rate, large deformation and high impact strength of brittle materials such as concrete. The continuous damage degradation effect of material strength is increased based on the JH-1 model, which can be applied to describe the failure process of brittle materials with load. During the loading process in the experiment, the material is elastic, before stress reaches the yield limit. With the accumulation of damage, the material begins to deteriorate until it is completely broken. The theoretical formula of JHC constitutive model is shown as follows:

where, ${\sigma }_i^{*}$ is the standard full strength, ${\sigma }_f^{*}$ is standard failure strength, $D$ is damage factor, and $\text{0}\le D\le \text{1}$; ${\sigma }_k^{HEL}$ is Hugoniot elastic limit stress, $\mathrm{\Delta }{\epsilon }_p$ is material plastic strain, ${\epsilon }_{{}_p}^f$ is constant pressure damage plastic strain under standard pressure $p$, $A$, $B$, $C$, $M$, $N$, are constants of material. $p^{*}$ is standard pressure. ${\dot{\epsilon }}^{*}$ is real time strain rate of reference strain rate 1 s^-1. $K_1$, $K_2$, $K_3$ are constant. $\rho$ is real-time density; ${\rho }_0$ is initial density. Material parameters of concrete wall are shown in Table 4.

3.4.1. Fluid-structure interaction effect

Fig. 6 shows the interaction between the shock wave and the hole wall in the blasting hole, which shows that the explosion field and the pore wall are mutually restricted and influenced. As the dynamite explode, detonation products expansion occurs, at the same time, on the one hand, energy is absorbed by water in the inner hole and began to spread around rapidly, on the other hand, high temperature and high pressure gas diffuse in high-speed after the explosion.

Fig. 6Fluid-structure coupling effect of water – dynamite – pore wall

a) 0 µs

b) 30.8 µs

c) 39.6 µs

d) 60 µs

e) 180 µs

f) 279.2 µs

As can be seen from the Fig. 6, in the stage 0-40 µs, the blasting hole is destroyed sharply under the blasting stress wave, and tends to be stabilized gradually, which can be explained as follows: (1) Blasting holes squeezed by shock tube. (2) The strength parameters of the wall is far less than that of the shock tube shock. (3) Energy absorbed by wall is much larger than that of blast hole after detonation of shock tube. Therefore, pressure wave generated quickly through the water impact hole wall with the help of energy of dynamite in the shock tube, thus causing cracks of the hole wall, and the stress wave in the medium. Radial and tangential stress produced as the propagation of stress wave in the medium, and the tensile strength of the whole wall is far lower than the compressive strength, shear strength is also much smaller than the compressive strength. Meanwhile, high pressure gas produced equipment acts on the internal water in the detonating device, and propagates along the two directions before and after through the reserved hole at the bottom of the pressure relief port, directly work on the hole wall, therefore, hole wall damage increases rapidly in the initial stage and tends to be stable gradually.

3.4.2. Dynamic response of the wall under blast load

3.4.2.1. Stress field

Fig. 7 shows the stress contours of the wall under hydraulic blasting, as can be seen from the figure, with the interaction between the explosion shock wave and the sealing wall, equivalent stress of the wall increased gradually at first and tended to balance thereafter. At the moment of 30 μs after the explosion, the water absorbs energy of the shock wave and begins to act on the hole wall. After 40 μs, the shock wave penetrates the shock tube and begins to spread to the wall. After that, the wall starts to crack and expands, and the stress increases gradually. Due to the action of the crack tip, stress increases to a certain degree tend to a balance.

Fig. 7Stress contours of concrete wall with hydraulic blasting load

a) 30.8 μs

b) 39.6 μs

c) 60 μs

d) 180 μs

e) 279.2 μs

3.4.2.2. Displacement field

Fig. 9 shows the displacement contours under hydraulic blasting. As can be seen from the figure, with the interaction between dynamite shock wave and hole wall, deformation of hole wall increased gradually until failure occurs, cracks expanded from the hole wall around to the whole wall.

As can be seen from the above Fig. 10 and Fig. 11, the distance farther away from the hole, the smaller the stress, velocity, displacement. Due to the existence of the transmission, the further point has the hysteresis, the time of 3 elements reaches the maximum value are also different. Displacement, velocity and stress of all elements decrease rapidly, and the displacement, stress and vibration velocity attenuation are very small when the elements are close to the wall.

Fig. 8Monitoring elements concrete wall with hydraulic blasting load

Fig. 9Displacement contours of concrete wall with hydraulic blasting load

a) 30.8 μs

b) 39.6 μs

c) 60 μs

d) 180 μs

e) 279.2 μs

3.4.3. Laws of energy variation

Fig. 12 shows the time-energy curves of the kinetic energy, internal energy and total energy of the wall.

As can be seen from the Fig. 12, energy in the whole blasting process includes 4 following aspects: (1) The crushing and plastic flow of medium. (2) Shock waves, elastic deformation of medium particle. (3) Gas product in medium broken to release into the air from air shock wave in the blasting process. (4) Crushing and throwing flying of the medium. The above four aspects, the crushing and throwing of medium is a hard (with the exception of a few unnecessary throw), the other is useless work. Blasting of shock tube will not work on the wall of the hole and caused excessive grinding. Energy produced by shock tube is consumed in the elastic deformation, wall breaking and cracking, throwing of medium. Therefore, the sum of total energy of the wall and the shock tube and water is much less than the total energy of the dynamite after the explosion.

Fig. 10Comparison of the stress, displacement and velocity of the different elements in the middle section of the wall

a) Stress

b) Displacement

c) Velocity

Fig. 11Comparison of the stress, displacement and velocity of the different elements in the front face of the wall

a) Stress

b) Displacement

c) Velocity

Fig. 12Energy variation laws of concrete wall with hydraulic blasting load

4.3.1. Failure modes

The results of the experiment are shown in Table 6.

Table 6Experimental results and description of each working condition

	Program 1	Program 2	Program 3	Program 4	Program 5
Front face
Back face
Description	The maximum length in horizontal direction is 72 cm, the maximum Vertical distance is 32 cm, the maximum depth is 20 cm; safety distance is 20 meters; no noise, no dust and no vibration	Blasting diameter is 70 cm, the depth is 20 cm, the maximum depth on back face is the formation is 18 cm, maximum horizontal length is 70 cm, the maximum vertical distance is 40 cm, safety distance is 1.7 meters	No blasting funnel, and the cracks transverse through the entire wall, the wall is divided into two parts, and the upper part wall is divided into about two parts by vertical crack	No blasting funnel, irregular blasting crater occur on the back, the maximum depth is 17 cm, the horizontal length is 75 cm, vertical distance is 35 cm. noise is 78.9 dB	The diameter of blasting funnel on front face is the 15 cm, no blasting funnel on the back face, noise is 86.1 dB, 11.39 ppm CO, the effect is not ideal

4.3.2. The blasting demolition process

When the shock tube is excited, pressure generated in the tube will penetrate quickly wave through the water first to hole wall, resulting in the initial cracking of the hole wall, and stimulate the stress wave in the medium. Radial and tangential stress produced by stress wave in the medium, the tensile strength of the wall body is far lower than the compressive strength, shear strength is also much smaller than the compressive strength. Therefore, when the radial stress is larger than the dynamic compressive strength of the medium, the medium will be destroyed. When the tangential tensile stress is larger than the dynamic tensile strength of the medium, fracture will form.

At the same time, high pressure expansion gas produce in the device, act on the detonating device in internal water, transfer through the reserved hole at the bottom of the pressure relief port along the two directions, directly to the hole wall, forcing water to seep into the crack, cracking form into cracks, change into the stress concentration area of crack tip. When the stress intensity factor of fracture is larger than concrete has been blasting the fracture toughness of the medium, cracks will continue to extend. When the forward extension of the development of cracks encountered the free surface of the wall, the wall will be broken, the medium throwing under high pressure gas. When the stress wave is larger than the dynamic tensile strength of the wall, the reflection of the tensile wave is larger than that of the wall.

4.3.3. Difference

The blasting effect is closely related to the structure material and the strength of the wall. In the same condition of blasting parameters, experiment 3-5 and experiment 2 are designed with brick and concrete, and the breaking effect was different. Blasting effect, parameters and loading are related to the experiment 2 when compared with the experimental 1, difference in value $L$ is only 3 cm, not only broken funnel in the back of the wall, but also the blasting effect is not inferior to the positive. In experiment 2, the quantity of dynamite is larger, and the width of crack is larger. But if the broken parameter is not reasonable, difference in the effect of blasting the wall before and after the demolition will be great.

Fig. 14The minimum resistance line of the wall to be demolished

In experiment 1, according to the characteristics of the equipment and blasting design, the front and back of the wall are free surface. Reserved hole on the bottom of the front wall and the back distance are far from inconsistent. The distance form pressure relief mouth position on the detonating device to the free surface is different, the distance from bottom of the reserved hole to the two minimum resist line is different and the difference between the two line of least resistance is rather larger, according to the principle of directional blasting control, we can draw the conclusion that the blasting effect of front face on the wall is much better than that of the back face. Due to the reserved hole on the front face of wall, so it weakens the strength to a large extent, leads to the failure of formation of blasting funnel. Fig. 14 shows the 2 minimum resistance lines of wall.

In experiment 2, blasting parameters are improved compared with the experiment 1, reduce the reserved hole bottom distance away from the back of the wall, decrease the difference between the two line of least resistance, and therefore strengthen the blasting effect of the back of wall. Blasting funnel forms on the front and back of the wall, the demolition effect is more ideal, so the design of the blasting parameters of experiment 2 is reasonable.

The blasting parameters of experiment 2 and experiment 3 are identical, but due to the wall is made up of high strength concrete, the wall is separated by the formation of obvious cracks in the but not throwing.

4.3.4. Damage range

When the hydraulic shock tube in the medium of blasting, stress wave generated at first, parameters of medium on the wave front will not be mutation when affected by the impact of waves, but elastic deformation and destruction by using blasted medium will occur on concrete wall. Water pressure blasting device requires a reserved hole with radius of 2.5 cm, 500 MPa pressure peak on the hole wall according to the experimental dose. The Poisson's ratio of concrete and brick is 0.2. The radial stress and tangential tensile stress of the stress wave in different distance from the blasting holes are shown in Fig. 15.

As can be seen from Fig. 15, the large the distance away from the hole wall, with the increase of the distance away from the dynamite center, radial stress and shear stress are decreased exponentially. The smaller the ratio, of the distance, the larger attenuation of the stress is. Radial stress and shear stress will increase at the same position in the medium. At the same pressure peak value, radial stress should be larger than the tangential stress at different distance away from the dynamite center.

Fig. 15Radial stress and tangential stress at different distances

4.3.5. Crack range

When the radial stress is larger than the dynamic compressive strength of the material, the radial stress is higher than that of the material. When the tangential tensile stress is larger than the tensile strength of the material, the radial fracture is formed. The stress wave damage can be determined according to the Eq. (27) [24]:

As for the calculating result and analysis above, the radial stress of hole wall is larger than the dynamic compressive strength of medium, radial stress in the distance to hole wall 0.8 cm generated at is equal to the dynamic compressive strength of medium, tangential stress away from the hole wall 7 cm is larger than dynamic tensile strength of concrete. Therefore, the medium in the range of 0.8 cm from the hole wall may be damage when subjected to compressive load, the maximum length of 3.7 cm of cracks will form.

At the same time when the formation of radial cracks, high pressure expansion gas act on water, force water seep into the fracture, the fracture bursting crack forms, change into crack tip stress concentration area. When the stress intensity factor of fractured ends is larger than the burst fracture toughness of medium, the gap will continue to extend and expand. Due to the water is selected as broken medium for blasting device, so gas pressure drops slowly in the whole process of gas expansion, water is pressed into the cracks, extend the length of the crack. According to the observation result of cracks in the wall, the maximum length of crack is larger than 72 cm. According to the above analysis, the range of hydraulic blasting damage is shown in Fig. 13.

In Fig. 16, the maximum distance from crushing zone formed in blasting medium to the hole wall is 0.8 cm. B is radial crack area of stress wave, maximum distance to the center hole is 7 cm. C is crack zone under high-pressure gas extension. The length can be larger than 72 cm in the experiment. Its action sphere and the experiment have a smaller difference. At the same time, scopes of stress wave and expansion gas and consistent with hydraulic blasting theory, indicating that the reasonable calculation can provide a theoretical method for the following parameters design and blasting process of in-depth study.

Fig. 16Damage range of non-dynamite blasting

4.3.6. The effect of reflected wave

The wave impedance can be calculated according to the density of medium and the velocity of longitudinal wave. Generally speaking, the density and velocity of concrete are 2400 kg/m³ and 4000 m/s, respectively, for air are 1.205 kg/m³ and 340 m/s. Wave impedance is significantly larger than that of air. When the stress wave transmits in concrete to spread in the air, the reflection wave will be tensile wave. The value of reflected can be calculated through the above data and the formula. When initial pressure of the hole wall is 500 MPa, the reflection Paula stress is 11.61 MPa 20 cm away from the explosion center. Because the reflected tensile wave stress is less than the dynamic tensile strength of the medium, the falling phenomenon of the wall surface will not occur, which is in accordance with the experimental result of concrete blasting.

Fig. 17The procedure and blasting effect on underground mine

As for the brick masonry walls, stress wave affect as well, gas expansion and the reflection of tensile wave effect. Due to the particularity of the experimental architecture, the brick wall can be seen as a whole. Compared with concrete wall, the compressive tensile strength of brick is small, so the formation of the broken area is larger, more cracks in the fracture zone, the crack is wider, and the front and rear surfaces can form a better blasting funnel.