The response of rock tunnel when subjected to blast loading: Finite element analysis

In the past few decade tunnels were targeted to explosives and that resulted in sizeable structural damage. The increase in the strategic importance of tunnel construction has increased the demand for the blast‐resistant design approach. The present paper considered an internal blast loading on a rock tunnel constructed in Quartzite rock. A three‐dimensional finite element model of the tunnel has been developed in Abaqus. The diameter of the tunnel has been kept constant to a two‐lane transportation tunnel. However, the thickness of the concrete liner, depth of overburden, and mass of explosive charge has been varied to understand the response in different possible conditions. The Jones‐Wilkins‐Lee, Concrete Damage Plasticity, and Mohr‐Coulomb material models have been used for the modeling of trinitrotoluene, concrete, and rock respectively. Blast has been formulated through Coupled‐Eulerian‐Lagrangian technique. The tunnel at 12.5 of the depth of overburden has been found 2.7‐times more blast resistant than 5 m. Moreover, the extent of damage in shallow depth tunnels found to be more than the tunnels at higher depth of overburden.

of the joints play an essential role in the shock wave propagation. Moreover, the distance of propagation, weight of charge and angle made by incidence angle with the strike of joint are the governing factors in shock wave propagation. However, the effect of overburden and tunnel lining thickness was not considered.
Jayasinghe et al, 14 and Shang 15 had also studied the numerical modeling of blast loading on rockmass and concluded that the joint persistence significantly controls the blasting-induced damage in the rockmass. However, all the three studies [13][14][15] had considered rock mass in its natural state. Nevertheless, in case of already constructed tunnel these joints sets had been treated to block the water inflow in the tunnel. 16 Sealing of these joints with grouting, shotcreting, and so on, also improves the rock mass strength, which is desirable for long stability of projects. 17,18 Hence, while investigating the blast response of an already constructed tunnel, the immediate rock mass may be treated as continuous.
Choi et al, 19 carried out finite element study for the blast analysis of underground tunnel. They had studied the effect of different surrounding ground properties and concluded that the blast response of the tunnel depends on the properties of the surrounding ground. However, the vulnerability of the tunnel having different overburden depth and tunnel lining thickness had not been considered. Tiwari et al, 20 studied the effect of rock weathering for the rock tunnel subjected to blast loading. The finite element method was used for blast analysis, and they concluded that shock wave propagation is higher in less weathered rock. The higher attenuation of shock waves had been observed in highly weathered rock. However, there had been rarely available discussion regarding the effect of tunnel lining thickness and overburden depth. Furthermore, several studies were carried out to understand the behavior of rock tunnel during blast loading due to explosives. [21][22][23][24][25] However, the effect of depth of overburden and thickness of tunnel lining had been rarely incorporated in the available literature. Moreover, trinitrotoluene (TNT) had not been adopted as material which is only possible through assigning the properties of TNT and modeling it as a part of a simulation. Further, the modeling of TNT as a material possesses several issues, and the problem of element distortion is the most common. Therefore, Coupled-Eulerian-Lagrangian (CEL) method of modeling needs to be considered to overcome the problem of element distortion which had rarely been considered in the past studies.
In the present paper, a numerical study of the rock tunnel constructed in Quartzite rock has been considered. A detailed finite element model has been presented and validated with available experimental and numerical results. The advanced method of coupled modeling, that is, CEL method, has been adopted for the modeling of the TNT and air inside the tunnel. The effect of thickness of tunnel lining and overburden depth has been incorporated to understand the stability of a rock tunnel under blast loading. Furthermore, the amount of TNT explosive charge has also been varied to observe the extent of the damage.

FINITE ELEMENT MODELING
The finite element software Abaqus/Explicit has been used for the present analysis of rock tunnel subjected to internal blast loading. 26,27 The The element size of the model has been kept as 0.2 m based on the mesh convergence study. The tunnel lining and rock model has meshed with an element type of C3D8R (Eight-node brick element with reduced integration and hourglass control). Moreover, the Eulerian Model of TNT and air has been modeled as EC3D8R (eight-node linear brick element with reduced integration and hourglass control). A mesh convergence study has been carried out to find an optimum size of element for meshing, with mesh size 2 m, 1. as a semi-infinite boundary and it extends to higher depth. However, the sides of the model show significant movement in a vertical direction; therefore, roller support has been applied. Moreover, interaction property has been defined between the different materials for proper interaction. In Abaqus interaction property module, hard contact in the average direction and frictionless in the tangential direction has been assigned. This interaction property gives rise to deformations in the Lagrangian material when Eulerian material flows through it. The finite element model has been shown in Figure 1.
The Mohr-Coulomb constitutive material model has been adopted for the elastoplastic behavior of Quartzite rock. The properties of the Mohr-Coulomb material model have been shown in Table 1 where = deviatoric polar angle, p = equivalent pressure stress, q = Mises equivalent stress, r = third invariant of deviatoric stress, and S = deviatoric stress. The Concrete Damage Plasticity (CDP) model has been used for the modeling of tunnel lining. The stress-strain relation of the CDP model is represented where t and c refer to tension and compression, respectively, t & c are stress vectors, The CDP model properties are listed in Table 2. It has been opted from the author's previously published work. 33 The justification of the values of different parameters has discussed in detail there.
For the simulation of blast loading, the TNT explosive has been modeled in the finite element software by the method of CEL modeling. For the CEL modeling, the Jones-Wilkins-Lee (JWL) constitutive model has been used for the TNT explosive. The properties of TNT explosive are shown in Table 3.
The JWL equation of state (EOS) 34 model is defined as where p = pressure of the TNT explosive, A, B, R 1 , R 2 and are material constants for TNT explosive A and B = magnitudes of pressure, = ratio of the density of the explosive in the solid-state ( _sol) to the current density ( ), e int = specific internal energy at atmospheric pressure. In the JWL EOS, the first two exponential terms on the right-hand side represent high pressure generated during an explosion and the last term on the right-hand side is a low-pressure term, which deals with high volume due to explosion.
The TNT and air inside the tunnel were modeled using CEL method of modeling. The CEL modeling has been incorporated in the present analysis by using Eulerian-Volume-Fraction (EVF) option available in Abaqus. The primary function of the EVF option is to fill the Eulerian part with material which flows through the Lagrangian part of the model and interact with the boundary of other parts. In the case of EVF, the value between 0 and 1 is assigned, which define the number of voids in the material or other words how much material is filled in the Eulerian part. Therefore, in the present study, EVF = 1, has been assigned for the TNT material. EVF = 1 means that the Eulerian part is filled with material, and there is no void space available. Further, the air has been assigned EVF = 0.8, where 20% of void space has been assumed. 3 For the proper interaction between the Eulerian and Lagrangian parts of the model, an interaction property, global hard contact has been assigned. The blast analyses have been carried out for the 30 milliseconds.

NUMERICAL VALIDATION WITH EXPERIMENTAL RESULTS
Experimental study related to blast loadings on full structures had been performed rarely, due to involvement of high expenditure and permissions from local government. However, experiments were carried out on a structural component at lab sale. 35,36 Hence, in the present study, for the validation of the numerical method of blast loading, the experimental study carried out by Reference 35 has been referred. A Reinforced-Cement-Concrete slab of 1 m × 1 m has been modeled with 0.04 m depth, similar to Reference 35. Two-way reinforcement in the form of steel bars having 6 mm dia @ 75 mm c/c has been provided with a clear cover of 20 mm. The concrete has been modeled using CDP material model, and elastic-plastic model based on stress-strain history has been used for reinforcement modeling. The default parameters of concrete compressive strength have been used in the validation. [37][38][39][40] The concrete has 28.3 GPa of Young's Modulus, 4.2 MPa tensile strength, and 39.5 MPa of compressive strength. The steel reinforcement bars have Young's Modulus of 200 GPa and yield strength of 600 MPa. 41 The sides of the slab have fixed boundary conditions and base and the top surface (see fig. 1   three explosive charges assumed in the experimental test and numerical software for validation. The three different TNT explosive charges assumed were 0.20 kg, 0.31 kg, and 0.46 kg having scaled distance as 0.684 m/kg 1/3 , 0.591 m/kg 1/3 , and 0.518 m/kg 1/3 respectively. The TNT and the air have been modeled using CEL method of modeling. The properties of the TNT explosive material are the same as mentioned in Table 3. The mesh size has been finalized based on mesh sensitivity analysis. Moreover, the blast validation has shown results in the vicinity of the experimental and numerical study of Reference 35. Thus, the present study has been validated. Table 4 shows the validation results and compare with Reference 35. Figure 2 shows the displacement contours of the square reinforced cement concrete slab for comparing with Reference 35. The maximum displacement has been represented by deep red contour, while the edges have no displacement due to the applied boundary condition. Therefore, it has been concluded that CEL method of modeling is an accurate method for the simulations having problem of element distortion and large displacements.

RESULTS AND DISCUSSION
A three-dimensional numerical study of the response of underground rock tunnel subjected to internal blast loading has been analyzed. The Mohr-Coulomb material model has been adopted for rock, and CDP Model has been used for tunnel lining. The TNT explosive has been modeled using the JWL material model. Further, the present study incorporates CEL modeling for simulating the blast loading event. Following results have been found out and were discussed. The comparative response of the thickness of tunnel lining, when subjected to a constant (60 kg of TNT) blast load, has been plotted in Figure 3. The deformation decreases as the depth of overburden increases from 5 to 7.5 m @ 70%-73%, and for an increase in depth of overburden from 7.5 to 10 m and from 10 m of overburden depth to 12.5 m, the decrease in deformation has been observed as 23%-28%. Hence, it may be noted that tunnels having a higher depth of overburden are more blast-resistant in comparison to the shallow tunnels. Moreover, for the increase in the tunnel lining thickness initially from 0.22 to 0.35 m, a significant decrease in deformation has been observed, that is, a 20% decrease in deformation. However, a relatively smaller increase in resistance to deformation has been noted for the increase in the tunnel lining thickness from 0.35 to 0.55 m. Hence, it has been concluded that an optimum tunnel lining thickness should be taken into account for less damage due to blast loading.
The comparative results of the deformations caused by the different amount of TNT explosives have been shown in Figure 4. It has been observed that the magnitude of deformations in tunnels has a higher range for 5 m of the depth of overburden. However, a sharp decrease in deformation has been observed for the case of 5-7.5 m increase in depth of overburden. The deformation further decreases with an increase in the depth of overburden, which concludes that stability in the tunnel results from an increase in the depth of overburden. Moreover, the maximum percentage change in the deformation magnitude occurred when the depth of overburden increases from 5 to 7.5 m. Furthermore, lesser change in the magnitude of deformation has been observed in comparison to the former. In terms of safety, tunnel having 12.5 m depth of overburden are 2.7-times safer than tunnel that has 5 m depth of overburden. Therefore, the choice of depth of overburden also contributes to the stability and blast-resistant designing of underground rock tunnels. Figure 5 has been plotted to show the variation of deformations in the tunnel when an internal blast load with a varying charge of TNT explosive has occurred. It has been observed that the magnitude of deformation at the tunnel crown has 10% more value than the ground surface. Also, it has been observed that the zone of deformation along the tunnel alignment has increased linearly for the increase in the amount of TNT explosive. The deformation concentrates in a minor zone at the internal surface of the tunnel irrespective of a small amount of TNT explosive. As the blast load due to an increasing amount of TNT explosive increases in the tunnel, the further extent of deformations transferred to the ground surface, which results in the heaving of the surface instead of settlement. The heaving or bulging of the ground surface has been the common record phenomenon. The concentration of damage at the crown of tunnel results in the spalling of tunnel liner, and sometimes it results in the production of minor cracks. If these cracks further propagate, then it requires to treat the cracks thoroughly. However, the generation of smoke also has a significant contribution to casualties, but the present study is affiliated with civil engineering perspective on the event. Deformation profiles along the tunnel length have been plotted for the different amount of TNT explosive in Figure 6. From this plot, is has been noted that throughout the tunnel length, the deformation increases with increase in TNT. Moreover, it has been observed that the depth of crater formed due to blast loading and its diameter increases with the increase in the amount of TNT explosive charge. However, the response of rock remains symmetrical on both sides of the location of the blasting event. It has been observed that 54 % increase in the magnitude of deformation has been observed due to an increase in an explosive mass by six times. Furthermore, the value of deformation ranges between 10 and 20 mm for the varying mass of TNT explosive charge from 10 to 60 kg. The shock waves due to blast load propagate from the location of blast event to boundary of the rock. This propagation has significant effect near the blast location, and it diminishes toward the boundary. Due to the CEL modeling technique, this propagation of shock waves does not rebound back to the center of the tunnel.

CONCLUSION
A three-dimensional non-linear finite element analysis has been carried out for internal blast loading of Quartzite rock tunnel, through the less conversant CEL modeling technique using the Abaqus/Explicit. The tunnel depth, tunnel lining thickness, as well as a mass of TNT, has been varied to observe the response in different possible conditions. In the present study, tunnels constructed at higher depth of overburden are more blast resistant than tunnel at shallow depth. The effect of an increase in explosive mass has been evident. However, it has been observed that this effect is more significant in a shallow tunnel rather than tunnel having a higher depth of overburden. The thickness of the tunnel liner plays an essential role in blast resistance of rock tunnel, but up to a limit only. Further, the increase in lining thickness makes the section uneconomical and heftier, without any significant contribution in blast resistivity. Hence, for any proposed tunnel, a study should be carried out for optimum thickness of blast resistant liner considering the rock type and overburden. It has been concluded that a rock tunnel having 12.5 m depth of overburden has 2.7-times more resistance against blast loading than 5 m. Moreover, ground surface experiences heaving and the internal face of the tunnel has spikes and crack formation. The deformations at the ground surface have 10% lesser magnitude as compared to the internal surface of the tunnel.
As quartzite is a vital rock type present in major metro projects, its properties vary according to the condition in which it has formed. Therefore, its behavior against the blast load varies from the reported results in the present study depending on the properties of rock.

ACKNOWLEDGEMENT
Authors would like to acknowledge Mr Manojit Samanta Senior Scientist (CBRI-CSIR Roorkee, U.K., India) for assisting in the computational facility.

PEER REVIEW INFORMATION
Engineering Reports thanks the anonymous reviewers for their contribution to the peer review of this work.