Influence of Blasting Disturbance on the Dynamic Stress Distribution and Fracture Area of Rock Tunnels

Abstract

In order to study the dynamic stress distribution and the fracture area of rock around the tunnel under different orientations of blasting disturbance, AUTODYN finite difference method software was used to conduct numerical simulation research. Gauge monitoring points were set around the numerical model of the tunnel to conduct real-time monitoring of the stress distribution, displacement and fracture area of the tunnel. Based on the analysis of the stress wave propagation law, the following conclusions are obtained: (1) under the condition of the same blasting loads, the stress and displacement of the tunnel is relatively small when the blasting disturbance source is located above the roof, i.e., the stress state of the tunnel is relatively stable and the fracture area around the tunnel is minimal; (2) from the uniaxial stress around the tunnel and the tunnel peripheral displacement, it can be seen that the displacement caused by horizontal direction stress of the tunnel is the largest, and the deformation is mainly concentrated above the floor and at the shoulder, while the vertical wall part has almost no deformation; (3) for brittle materials such as rock, the arch-shaped stress-bearing surface is more likely to disperse stress, while the straight wall and flat floor of the tunnel cannot well disperse stress, resulting in uneven stress on the stress-bearing surface, uncoordinated deformation and ultimately, failure.

1. Introduction

As a traditional and reliable rock-breaking technology, blasting has the characteristics of low cost and flexibility to adapt to complex geological conditions. Mining tunnels are be distributed at different depth levels, and the construction of these tunnels causes certain blasting impacts on the surrounding rock mass of adjacent tunnels; these impacts will affect the stability of the tunnel. Therefore, the dynamic distribution of tunnels under blasting disturbance is related to construction safety issues of tunnels.

Since the 1970s, dynamic research into rock and soil structure has developed rapidly. In recent years, scholars have carried out corresponding research into the dynamic responses of rock and soil structures under blasting in terms of testing, theoretical analysis, numerical simulation, etc.

Gao [1] simplified engineering tunnel blasting as a two-dimensional plane strain problem, and pointed out that the radial displacement and tangential stress on the inner surface of the lining are positively correlated with the distance from the center of the blasting source. By solving the structural dynamic equation, Fan [2] obtained the dynamic concentration coefficient of the engineering structure, the structural internal force, bending moment, and displacement, and analyzed the influence of the surrounding rock grade, load action position, and positive pressure action time on the dynamic response of the tunnel structure. Mitelman’s [3] research showed that the rock strength characteristics had a certain degree of impact on a tunnel’s anti-blast durability, i.e., the higher the strength of the rock, the stronger the ability of the tunnel to resist loads. By changing the width and height of the rectangular section and the amount of explosives, Uystepruyst [4] provided the positioning laws of the transition zone during the propagation of blasting stress waves. Yang [5] pointed out that the stress release caused by the blasting led to the stress fluctuation at the tunnel excavation boundary, resulting in greater deviation stress and a wider compression shear damage zone than the maximum static stress. Yang [6] studied the impact caused by gas blasting on the vertical deformation of a subway tunnel, and pointed out that the maximum vertical displacement of the tunnel increased nearly linearly with the increase in the intensity of the blasting loads.

With the application of finite element, finite difference, discrete element and other numerical software, numerical simulation, as a technical means to reproduce experimental results, is also widely used in the analysis of tunnel blasting issues. Its effectiveness and accuracy have been verified [7,8,9,10,11]. Therefore, the numerical simulation is an effective and reliable method in tunnel dynamic research.

Gao [12] used the discrete element numerical calculation method to produce a tunnel displacement time–history curve and a maximum normal stress time–history curve; the tunnel displacement amplitude and maximum normal stress changed along the x-axis at a certain time. A numerical model of adjacent tunnels was established by Shin [13], and the particle velocity, displacement and stress of the tunnel-surrounding rock caused by blasting-induced vibration was obtained. Through AUTODYN simulation, Kundersen [14] found that the impact of the blasting wave on the lining structure gradually weakened with the increase in the distance from the blast center. The tunnel lining was in a tension state at the initiation time, and changed from a tension state to a compression state with the passage of time. Based on the DEM-UDEC program, Deng [15] simulated the shear zone around the circular tunnel and the peak particle velocity on the tunnel surface, and found that the joints in the surrounding rock of the tunnel had a great impact on the tunnel damage. Liu’s research [16] showed that the incident angle of stress wave had a great influence on the tunnel, and the dynamic response of the structure at oblique incidence was greater than that at vertical incidence. Koneshwaran [17] used the finite element method of fluid dynamics to simulate the dynamic response and damage of the tunnel arch in the transverse direction, mainly due to high bending stress. When blasting occurs in a square or circular cross-section tunnel, the blasting stress wave takes on different forms, resulting in redistribution of stress. The FEM-DEM coupled numerical simulation method was used to effectively predict the multiple fractures of rock caused by the blasting loads; the crack initiation and propagation was also captured [18]. Verma [19] analyzed the development of a fracture network in the blasting process through drilling and blasting methods, and the stability of the tunnel was affected by the breakage of the surrounding rock, especially the overbreak area. Zhao [20] used LS-DYNA software to analyze the ground side blasting angle and the buried depth of the tunnel; the results showed that the blasting stress waves had changed the stress state around the tunnel, resulting in damage. Based on the empirical calculation formula of blasting dynamic loads, Zhang [21] obtained the time history curve of the shock wave pressure on the tunnel structure, and pointed out that the engineering structure would not be damaged when the shock wave propagating from the blast to the tunnel structure was within a certain range. Luo [22] used the Galerkin method to solve the vibration differential equation using a numerical model, and the conclusion showed that the blasting center distance had a significant impact on the kinematic parameters of the suspension tunnel, i.e., the maximum displacement of the tunnel is approximately inversely proportional to the increase in the blasting center distance.

Research on the dynamic response of rocks around tunnels has been carried out by numerous scholars [23,24,25], and numerous research results have been achieved using numerical simulation methods [26,27,28,29]. However, few studies have been conducted on the dynamic stress distribution and fracture area of rock tunnels under different orientations of blasting disturbance. In this study, the finite difference numerical software AUTODYN was used to simulate the dynamic response of the blasting source at different locations around the tunnel, using a 1:1 tunnel numerical model. Gauge monitoring points at the surrounding rock of the tunnel were set to analyze the displacement change, stress change, and failure mode of the tunnel-surrounding rock in order to study the law of dynamic stress distribution and the fracture areas of rock tunnels, thereby providing theoretical support for the safety and stability of tunnels under dynamic impact loads such as blasting.

2. Tunnel Numerical Simulation

The finite difference code AUTODYN has been applied widely in solving dynamic problems, and its effectiveness has been well validated [7,8,9,10,11,23,25,26,28]. With the help of the finite difference software AUTODYN, a numerical model 1:1 with the actual model was established to conduct dynamic numerical simulation research, and the displacement change, stress change, particle velocity and other aspects of the tunnel-surrounding rock under the action of the blast stress wave were analyzed.

2.1. Establishment of Tunnel Model

In practical mining engineering, the surrounding of the tunnel is often affected by the disturbance of an adjacent tunnel’s excavation or other surrounding dynamic disturbances, including impact loads and blasting loads, as shown in Figure 1. Because of the high loading rate and short response time of blasting loads, damage often occurs in a short time. In this study, the tunnel and blasting source in the actual project were simplified into a plane model at a ratio of 1:1, i.e., the size of the numerical tunnel model was set according to the actual tunnel size, as shown in Figure 2, which means that the size of the tunnel and the propagation time of the blasting stress waves in the numerical simulation software are the same as in reality. Three types of blasting source location were designed, respectively, from the left side of the tunnel, above the roof and below the floor of the tunnel. The simplified model size of the tunnel is shown in Figure 2.

The designed specimen size ensured that the blasting stress wave fully acted on the tunnel after it was completely propagated in the surrounding rock. In the model, the tunnel arch radius is 5 m, the height from the tunnel floor to the arch shoulder is 5 m, and the distance between the #1 blasting source, #2 blasting source, and #3 blasting source and the tunnel arch center is 20 m, with the same charge, so that the blasting stress wave can fully act on the surrounding rock to disturb it. The propagation medium is sandstone, and the P-wave and S-wave speeds of the sandstone were measured by a Sonic Viewer-SX device, as shown in Figure 3. According to the P-wave and S-wave speeds, the dynamic elastic modulus and the dynamic Poisson’s ratio were obtained. The dynamic physical properties of sandstone are shown in

Table 1. Dynamic physical properties of rock.

Elastic Modulus Ed/GPa	Poisson’s Ratio ν	Density ρ/(kg/m3)	Tensile Strength Td/MPa
12.0	0.25	2350	28
Compressive strength P/MPa	Expansion wave velocity Cd/(m/s)	Shear wave velocity Cs/(m/s)	Rayleigh wave velocity CR/(m/s)
80	2551	1546	1411

.

2.2. Boundary Conditions

The simplified engineering model is a square area. After initiation of the blasting source, the reflection of the stress wave will occur at the boundary, which will further affect the accuracy of the numerical simulation and the reliability of the subsequent data monitoring. Therefore, the “Transmit boundary” condition, i.e., the transmission boundary is adopted, which means the stress wave does not reflect after encountering the boundary, but dissipates directly through the boundary.

Since the plane model is used, the medium will be squeezed and deformed under the action of the blasting stress wave initiation of the blasting source, especially in the direction perpendicular to the plane. In order to keep the research within the plane range, the particle motion velocity in the vertical direction of the plane is set to zero, i.e., a constraint boundary condition of z-direction ‘z ≡ 0′ was adopted in the model plane. The boundary conditions imposed by the numerical model are shown in Figure 4.

2.3. Principles of Numerical Simulation

The numerical model is established according to the size of the engineering simplified model, and AUTODYN finite difference software is used for numerical simulation. The 3D model was established and divided into 600,237 tetrahedral mesh cells. Four sizes, 1.5 mm, 1 mm, 0.5 mm, and 0.25 mm, were used in the convergence study, and the size 0.5 mm was used in this study. The mesh at the blasting source and the tunnel side was densified and refined. The model cell division is shown in Figure 5.

The constitutive model relationship of the propagation medium of the numerical model must meet the requirements of its strength and fracture parameters. The surrounding rock material adopts a linear equation of state (EOS), and the strength model adopts an elastic state. Since no stemming and no coupling were applied to the borehole, the blast-induced gas products will leak out; this means that the gas products do not play any role in the crack propagation. Only the shock wave action in this numerical study was simulated. In this study, the modified maximum principal stress failure criterion (MMTS) was used to simulate the fracture criterion of the rock under impact load, that is, when the maximum principal stress of a material element exceeds the maximum tensile strength of the material, the material element will fail.

Because the pressure and the deformation are relatively small, a linear EOS was applied to the rock and models; and it can be written as

$$P\left(\rho \right)=\kappa \left(\frac{\rho }{{\rho }_o}-1\right)$$

(1)

where $\kappa$ is the bulk modulus, and ρ_o and ρ are the density in the initial state and in the current state, respectively.

For the explosive Hexogen of the detonator, a JWL equation of state is applied, and it can be expressed as

$$P=A·\left(1-\frac{\omega }{R_{1}V}\right)·e^{{-R}_1\upsilon }+B·\left(1-\frac{\omega }{R_{2}V}\right)·e^{{-R}_2\upsilon }+\frac{\omega E_0}{V}$$

(2)

where P is the pressure, E₀ is the total initial energy, V is the specific volume of detonation products, A, B, R₁, R₂ and ω are constants, and A = 778.3 GPa, B = 7.071 GPa, R₁ = 7.0, R₂ = 2.0, ω = 0.24.

For the rock specimen, the major principal stress and the maximum shear stress failure criteria were applied in describing the material status, which means that when the major principal stress ${\sigma }_1$ of an element reaches the dynamic tensile strength ${\sigma }_T,$ or the maximum shear stress ${\tau }_{max}$ reaches the dynamic shear strength of the material ${\tau }_c$, the element is failed, i.e.,

$${\sigma }_1\le {\sigma }_T \mathrm{or} {\tau }_{max}\le {\tau }_c$$

(3)

3. Numerical Simulation Results

3.1. Numerical Simulation Stress Contour

After the explosive was initiated, the blast shock wave first acted on the wall of the borehole and caused serious damage to the surrounding rock mass, which is called the fracture zone. At a certain distance from the center of the hole, the shock wave decayed into a stress wave and continued to propagate in the tunnel-surrounding rock beyond the hole. When the blasting stress wave propagated to the tunnel boundary, the compression wave front of the stress wave acted on the tunnel. At this time, the elements around the tunnel began to deform. Then, the longitudinal wave of the stress wave continued to propagate in the medium, causing the state parameters of the medium, such as pressure, tension and particle velocity, to increase to a high value.

When the blasting disturbance source is located from the left side of the tunnel, the stress wave entered the straight wall of the tunnel from the left side. The wall was first compressed, and then the tensile stress gradually increased due to the reflection of tensile waves, while the tensile stress gradually increased at the straight wall of the back blasting side where the diffraction wave forms a negative pressure zone. The stress wave diffracted at the arch crown and arch foot. Due to the arc shape of the arch crown, which can disperse the pressure, and the easy stress concentration at the arch foot, the tensile stress cloud area at the arch crown was significantly larger than at the arch foot, as shown in Figure 6a. When the blasting disturbance source was located above the roof of the tunnel, the stress wave entered the tunnel arch, and the tunnel roof was first compressed and then reflected to form a tensile wave, resulting in a gradual increase in the tensile stress here. The tensile stress increased on the tunnel floor after the negative pressure zone was formed by the diffraction wave, especially at the arch foot, as shown in Figure 6b. When the blasting disturbance source was located below the floor of the tunnel, the stress wave entered the tunnel floor. The floor was first compressed and then reflected to form a tensile wave, resulting in a gradual increase in the tensile stress here. However, after the diffraction wave formed a negative pressure zone above the roof of the tunnel, the tensile stress increased, but the range was small, as shown in Figure 6c. In general, when the blasting disturbance was located above the roof, the tensile stress area and high stress area of the surrounding rock of the tunnel were smaller, which was due to the dispersion effect of the loads applied by the arc arch on the stress wave.

3.2. Numerical Simulation of Failure Modes

From the stress contour in Figure 6, it can be seen that as the blasting stress wave propagates in the surrounding rock, the stress of the tunnel and surrounding rock was redistributed. When the stress applied to the element of the numerical model exceeded the stress threshold, it became invalid, as shown in Equation (3).

When the source of blasting disturbance was located from the left side of the tunnel, the left side of the straight wall was most severely damaged, followed by the right side, and the damage at the arch shoulder and arch foot of the straight wall was most obvious, as shown in Figure 7a. When the blasting disturbance source was located above the roof of the tunnel, there was a small range of damage at the roof and arch foot of the tunnel, and the integrity maintenance was more complete than the other two locations, as shown in Figure 7b. When the blasting disturbance source was located below the floor of the tunnel, the damage of the floor was the most severe, with a smaller range of damage to the arch crown but greater than the range of incident stress waves above the roof. As a whole, when the blasting disturbance is located above the roof, the integrity of the tunnel remains relatively intact, and the damage area of the surrounding rock is much smaller compared to the other two positions, as shown in Figure 7c. However, when the blasting loads act from a horizontal position, the damage degree is significantly more obvious than in the vertical direction, and more attention should be paid to the impact of excavation blasting on the same horizontal tunnel during tunnel supporting.

3.3. Maximum Stress and Displacement around the Tunnel

In order to explore the impact of blasting disturbance on the dynamic distribution of the tunnel, ten gauge monitoring points were set around the numerical model of the tunnel, and the stress distribution results were analyzed through the iterative operation of the numerical software AUTODYN.

As can be seen from Figure 8, the pressure on the blasting side of the tunnel is the largest, and the maximum pressure is mainly concentrated at the arch foot and arch shoulder. For example, when the blasting source was located from the left side, the pressure at monitoring point #3 located at the arch foot was 48.72 MPa. When the blasting source was located above the roof, the pressure at monitoring point #1 located at the arch shoulder was 23.76 MPa. When the blasting source was located below the floor, the pressure at monitoring point #3 located at the arch foot was 48.76 MPa. From the perspective of pressure distribution, when the blast-facing side is an arch, the distribution of compressive stress at the arch is more uniform compared to the other two situations, and the average compressive stress around the roadway is also smaller. The arch can better resist impact loads such as blasting.

It can be seen from Figure 9, the maximum shear stress on the blasting side of the tunnel is mainly concentrated at the arch crown and arch foot. For example, when the blasting source was located from the left side, the shear stress at monitoring point #3 at the arch foot was 28.61 MPa. When the blasting source was located above the roof, the pressure at monitoring point #8 at the arch crown was 27.35 MPa. When the blasting source was located below the floor, the pressure at monitoring point #4 at the arch foot was 28.71 MPa. The distribution of shear stress is independent of the shape of the stressed surface, and the shear stress on the arch is even greater than that on the straight wall. Through monitoring data, it was found that the shear stress values at the symmetrical positions on the blasting side vary greatly; this may be caused by the inconsistent deformation of the tunnel after compression. Therefore, more attention should be paid to improving its shear strength when supporting the roof of the tunnel; this may be achieved through methods such as anchor bolts support.

It can be seen from Figure 10, the horizontal/vertical stress on the blast-facing side of the tunnel is the largest, and the maximum shear stress is mainly concentrated at the arch shoulder and arch foot. For example, when the blasting source was located from the left side, the shear stress at the #3 monitoring point at the arch foot was 82.31 MPa. When the blasting source was located above the roof, the pressure at the #1 monitoring point at the arch roof was 48.82 MPa. When the blasting source was located below the floor, the pressure at the #3 monitoring point at the arch foot was 79.23 MPa. From the comparison between horizontal stress and vertical stress, the maximum vertical stress is 79.23 MPa, and the maximum horizontal stress is 82.31 MPa. The horizontal stress is significantly larger than the vertical stress, indicating that the stability of the tunnel in the horizontal direction is weaker than in the vertical direction when subjected to the same magnitude of loads. Therefore, when blasting construction is carried out near the tunnel, the support strength of the tunnel side wall should be strengthened.

As can be seen from Figure 11, the displacement on the blasting side of the tunnel is the largest, and the maximum shear stress is mainly concentrated at the arch shoulder, arch crown point, and center of the floor. For example, when the blasting source was located from the left side, the shear stress at the #1 monitoring point at the arch shoulder was 109.25 mm. When the blasting source was located above the roof, the pressure at the #7 monitoring point at the arch crown point was 133.62 mm. When the blasting source was located below the floor, the pressure at the #10 monitoring point at the center of the floor was 104.47 mm. From the overall displacement of the tunnel, the horizontal displacement is significantly larger than the vertical displacement, indicating that the tunnel is more prone to deformation in the horizontal direction, which is similar to the analysis results of horizontal stress. Therefore, when blasting construction is carried out near the tunnel, it is necessary to strengthen the deformation observation of the tunnel side wall to prevent the occurrence of disasters such as wall fragmentation.

4. Conclusions

In this paper, AUTODYN finite difference method software is used to numerically simulate the stress distribution and fracture area of a tunnel under blasting disturbance. Through preliminary research, the following conclusions were obtained:

(1) Under the condition of the same blasting loads, the stress and displacement of the tunnel is relatively small when the blasting disturbance source is located above the roof, i.e., the stress state of the tunnel is relatively stable, and the fracture area around the tunnel is minimal.

(2) From the uniaxial stress around the tunnel and the tunnel peripheral displacement, it can be seen that the displacement caused by the horizontal direction stress of the tunnel is the largest, and the deformation is mainly concentrated above the floor and at the shoulder, while the vertical wall part has almost no deformation.

(3) For brittle materials such as rock, the arch-shaped stress bearing surface is more likely to disperse stress, while the straight wall and flat floor of the tunnel cannot well disperse stress, resulting in uneven stress on the stress-bearing surface, uncoordinated deformation, and ultimately, failure.

Therefore, when blasting construction in tunnels is carried out, it is particularly important to pay attention to the mutual disturbance between horizontal tunnels and then strengthen their support in advance as necessary, e.g., by bolstering the arch shoulder and the bottom plate of the tunnel.