Unfortunately, all of the above-mentioned equations have limited the applicability and variable accuracy. Despite this shortcut, their use in numerical calculus is extremely beneficial since different particular situations can be investigated in a reasonable time frame and an almost costless manner.

When explosive detonation applications are numerically investigated, one EOS is usually involved, namely Jones–Wilkins–Lee (JWL) [16]. In fact, the use of the JWL EOS is so common that by now almost all hydrocodes have implemented it and several forms can be identified in the literature. However, the most known form of equation is the form of a family of isentropes [17], which is illustrated in Equation (3).

$$p(\mathcal{S}, V) = Ae^{-R\_1V} + Be^{-R\_2V} + \mathcal{C}^\*(\mathcal{S})V^{-(\omega+1)}\tag{3}$$

where *p* is the pressure; *S* refers to the entropy per unit initial volume (*s*/*v*0); *V* is the volume relative to the undetonated state (*v*/*v*0); *A*, *B*, *R*1, and *R*2 are constant fitting parameters; *ω* is an assumed-constant material parameter (Grüneisen function); and *C*\*(*S*) is a parameter dependent only upon the entropy *S*.

Based on the previously mentioned JWL EOS and ideal gas EOS assumptions, the pressure in the front of a traveling blast wave can be accurately evaluated when hydrodynamic simulations are employed. Even though the equation's versatility is impressive, the application of JWL EOS by itself cannot deliver crucial data regarding the initiation of the explosive when subjected to blast wave stimulus. Thus, in order to investigate the blasting cap sympathetic detonation susceptibility, a slightly different EOS was chosen, the Lee–Tarver equation of state [18]. In fact, the Lee–Tarver EOS is basically a JWL EOS that has been upgraded with a supplementary equation, Equation (4), that allows the evaluation of the burning fraction based on the pressure level acting on/inside the explosive [18].

$$\frac{\partial F}{\partial t} = I(1 - F)^b \left(\frac{\rho}{\rho\_0} - 1 - a\right)^x + G\_1 (1 - F)^c F^d p^y + G\_2 (1 - F)^e F^g p^z \tag{4}$$

where *F* is the explosive burning fraction which has a value between 0 and 1.

The importance of JWL EOS and Lee–Tarver EOS for the current blast cap sympathetic detonation study is correlated with the Chapman–Jouguet pressure level that can be used as the Go/No-Go criterion.

The materials used in the numerical simulation are TNT for the donor charge, PETNJJ1 for the acceptor charge, aluminum for the blasting cap walls, and air for the space between the donor and the acceptor. All the equations of state (EOS) and strength models of the materials were adopted from the library of the Autodyn 2021® software.

#### *3.3. Numerical Results*

The obtained numerical results are presented in Table 3. In Figure 5, the pressure levels recorded by two different gauges located inside the acceptor charge are illustrated for two cases. Figure 5a shows the pressure levels in the case of a 200 mm gap between the donor and acceptor, while Figure 5b shows the results for a distance of 500 mm. The peak overpressure was directly measured from the gauges. The pressure wave speed was determined from graphs of pressure in time, for consecutive sensors. By dividing the distance between the sensors by the values of the times at which the maximum values of the pressures were obtained, the shock wave velocities were determined for each case of the acceptor–donor charge. The critical energy fluence was determined by using the maximum pressure value, speed, and the pulse duration of the shock wave. For the calculation of the shock wave pulse duration, the area under the pressure–time curve was numerically evaluated and then approximated with a square-shaped pulse (rectangle with a height

given by the maximum pressure value and length given by the value of pressure-acting time that equals the previously calculated impulse). height given by the maximum pressure value and length given by the value of pressureacting time that equals the previously calculated impulse).

determined from graphs of pressure in time, for consecutive sensors. By dividing the distance between the sensors by the values of the times at which the maximum values of the pressures were obtained, the shock wave velocities were determined for each case of the acceptor–donor charge. The critical energy fluence was determined by using the maximum pressure value, speed, and the pulse duration of the shock wave. For the calculation of the shock wave pulse duration, the area under the pressure–time curve was numerically evaluated and then approximated with a square-shaped pulse (rectangle with a

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 7 of 12

**Figure 5.** Typical examples of numerically recorded pressure history in PETNJJ1 material (gauges 7 and 8 are the first and second gauges from the upper row). **Figure 5.** Typical examples of numerically recorded pressure history in PETNJJ1 material (gauges 7 and 8 are the first and second gauges from the upper row).

#### **4. Discussions 4. Discussion**

As the main goal of the present study is to evaluate the sympathetic detonation tendency of blasting caps, the main focus is on the correlation of experimental and numerical results. As the main goal of the present study is to evaluate the sympathetic detonation tendency of blasting caps, the main focus is on the correlation of experimental and numerical results.

If the experimental approach is a straight forward method that clearly points out the presence of acceptor detonation, the numerical approach is somehow trickier. If the experimental approach is a straight forward method that clearly points out the presence of acceptor detonation, the numerical approach is somehow trickier.

As previously mentioned, the numerical simulation is based on the use of Lee–Tarver EOS [19]. The Lee–Tarver EOS points mainly at the Chapman–Jouguet [19,20] findings that were later included in von Neumann's work [21]. Basically, a stable detonation is achieved when the pressure level reaches a certain value that is specific to each explosive (0.327 Mbar for PETN). Considering this approach, the blasting cap will not be susceptible to sympathetic detonation (in a range of a 0.1 to 0.5 m clearance distance) as long as the pressure recorded by the gauges indicates significantly lower levels (see Table 3). Nevertheless, as experimental tests have proved, the blasting cap detonation manifested at both 100 mm and 200 mm, where, according to numerical simulation, the peak overpressure is less than 0.327 Mbar. As previously mentioned, the numerical simulation is based on the use of Lee–Tarver EOS [19]. The Lee–Tarver EOS points mainly at the Chapman–Jouguet [19,20] findings that were later included in von Neumann's work [21]. Basically, a stable detonation is achieved when the pressure level reaches a certain value that is specific to each explosive (0.327 Mbar for PETN). Considering this approach, the blasting cap will not be susceptible to sympathetic detonation (in a range of a 0.1 to 0.5 m clearance distance) as long as the pressure recorded by the gauges indicates significantly lower levels (see Table 3). Nevertheless, as experimental tests have proved, the blasting cap detonation manifested at both 100 mm and 200 mm, where, according to numerical simulation, the peak overpressure is less than 0.327 Mbar.

Acknowledging the hypothesis involved in the critical energy fluence theory (step pulse shape and constant impedance, mainly) and the 1.5 × 105 J/m2 threshold value for Acknowledging the hypothesis involved in the critical energy fluence theory (step pulse shape and constant impedance, mainly) and the 1.5 × 105 J/m2 threshold value for the energy fluence of PETN (1.75 gm/cm3 ) [22], the calculus based on the numerical data (Figure 5) indicates a very good match with the experimental observation (see Tables 1 and 3). Thus, it is found that for distances of 100 mm and 200 mm, the critical energy values are close to the threshold value for the initiation of the acceptor explosive. On the other hand, the recorded pressures are lower than those corresponding to the C-J state, which indicates a weak detonation. The values of the maximum pressure and the duration of the positive phase of the phenomenon shown in Figure 5a fall within the values presented in the literature for the initiation of solid explosives [23]. Moreover, the shape of

the pressure–time curve in Figure 5a is similar to the ones in Walker and Wasley's work [24] at the point that the initiation of the explosive occurs. Additionally, by analyzing Figure 5, it can be observed that the pressure wave shape acting on the blasting cap has a much different profile from the ones usually recorded during a standard gap test. shape of the pressure–time curve in Figure 5a is similar to the ones in Walker and Wasley's work [24] at the point that the initiation of the explosive occurs. Additionally, by analyzing Figure 5, it can be observed that the pressure wave shape acting on the blasting cap has a much different profile from the ones usually recorded during a standard gap test.

the energy fluence of PETN (1.75 gm/cm3) [22], the calculus based on the numerical data

Tables 1 and 3). Thus, it is found that for distances of 100 mm and 200 mm, the critical energy values are close to the threshold value for the initiation of the acceptor explosive. On the other hand, the recorded pressures are lower than those corresponding to the C-J state, which indicates a weak detonation. The values of the maximum pressure and the duration of the positive phase of the phenomenon shown in Figure 5a fall within the values presented in the literature for the initiation of solid explosives [23]. Moreover, the

(Figure 5) indicates a very good match with the experimental observation (see

Due to the mismatch between the shock wave's front velocity and donor gas products' front velocity, the first to act on the blast cap is the blast wave, and the gas products pressure shortly afterward, depending on the relative position between the donor and acceptor charges, as can be deduced from Figure 6. The pressure wave profile is also shaped by the reflected blast wave, which is clearly indicated by the numerical simulation. Due to the mismatch between the shock wave's front velocity and donor gas products' front velocity, the first to act on the blast cap is the blast wave, and the gas products pressure shortly afterward, depending on the relative position between the donor and acceptor charges, as can be deduced from Figure 6. The pressure wave profile is also shaped by the reflected blast wave, which is clearly indicated by the numerical simulation.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 8 of 12

**Figure 6.** Pressure wave profile (200 mm case). **Figure 6.** Pressure wave profile (200 mm case).

The same outcome can be underlined by theoretical means as well. Therefore, using far-field experimental data (images recorded when the blast wave has already traveled over a 0.6 m distance), the Sedov-Taylor model [25,26], and Gilev's observations [27], one can predict the distance between the incident blast wave and the gas products' border. Useful data regarding the position of the blast wave and the gas products' border can be extracted by solving Equations (5)–(10) [25–29]. In Figure 7, a comparison between experimental results and the application of Equations (5)–(10) for two values of the expansion dimensionality factor is presented. The same outcome can be underlined by theoretical means as well. Therefore, using far-field experimental data (images recorded when the blast wave has already traveledover a 0.6 m distance), the Sedov-Taylor model [25,26], and Gilev's observations [27], onecan predict the distance between the incident blast wave and the gas products' border. Useful data regarding the position of the blast wave and the gas products' border can be extracted by solving Equations (5)–(10) [25–29]. In Figure 7, a comparison between experimental results and the application of Equations (5)–(10) for two values of the expansion dimensionality factor is presented.

$$R\_s(t) = at^b\tag{5}$$

$$a = \left[\frac{{}^{E\_d}\!/(\tau\_0^s l\_0^{3-n})}{\rho}\right]^{1/(n+2)}\tag{6}$$

$$\underset{\tau\_L}{s+2}$$

$$b = \frac{s+2}{n+2} \tag{7}$$

$$l\_0 = \left(\frac{\Im m}{2\pi\rho}\right)^{1/3} \tag{8}$$

$$
\pi\_0 = \frac{l\_0}{\upsilon\_{TNT}} \tag{9}
$$

$$R\_f(t) = R\_{\text{max}} \left( 1 - e^{-kt} \right) \tag{10}$$

where *Rs*(*t*) indicates the shock front radii; *a* and *b* are coefficients; *Ed* is the TNT release energy during detonation (usually 4.1 MJ/kg); *l*0 denotes a length scale; *τ*0 denotes a time scale; *m* is the TNT mass; *ρ* is the TNT mass density; *vTNT* denotes the TNT detonation velocity (6940 m/s); *s* indicates a factor characterizing the rate of energy release: instantaneous energy release (s = 0) and constant-rate energy release (s = 1); *n* is the expansion dimensionality: planar expansion (*n* = 1), cylindrical expansion (*n* = 2), and spherical

expansion (*n* = 3); *Rf* (*t*) indicates the fireball radii; *Rmax* is the fireball stopping radii (0); and k denotes the drag coefficient. pansion (*n* = 3); *Rf(t)* indicates the fireball radii; *Rmax* is the fireball stopping radii (0); and k denotes the drag coefficient.

*0* = ൬ *3 2*൰

> *0* = *0* ்ே்

where *Rs(t)* indicates the shock front radii; *a* and *b* are coefficients; *Ed* is the TNT release energy during detonation (usually 4.1 MJ/kg); *l0* denotes a length scale; *τ0* denotes a time scale; *m* is the TNT mass; *ρ* is the TNT mass density; *vTNT* denotes the TNT detonation velocity (6940 m/s); *s* indicates a factor characterizing the rate of energy release: instantaneous energy release (s = 0) and constant-rate energy release (s = 1); *n* is the expansion dimensionality: planar expansion (*n* = 1), cylindrical expansion (*n* = 2), and spherical ex-

*1 3*ൗ

(8)

(9)

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 9 of 12

It must be stated that the Sedov–Taylor equation can be applied only to the mid-field region according to Equation (11) [28]. It must be stated that the Sedov–Taylor equation can be applied only to the mid-field region according to Equation (11) [28].

$$\left(\frac{3m}{2\pi\rho}\right)^{1/3} \ll R\_s \ll \left(\frac{\Delta H\_d}{p}\right)^{1/3} \tag{11}$$

ሺሻ = ௫ሺ*1* − ି௧ሻ (10)

where ∆*Hd* indicates the total energy released during detonation, afterburning included, (up to 10.1 MJ/kg [30]), and *p* denotes the ambient pressure. where Δ*Hd* indicates the total energy released during detonation, afterburning included, (up to 10.1 MJ/kg [30]), and *p* denotes the ambient pressure.

Using high-speed camera imaging, *Rs* radii can be identified for different time values. Since the TNT charge has a cylindrical shape, a factor *n* = 2 was considered. Additionally, due to the fact that the distances between the TNT charge and the blasting cap are small (less than 0.5 m) for the experimental setup, an instantaneous energy release (s = 0) was set. However, the experimental results plotted against the results provided by Equation (5), which are presented in Figure 7a, show some considerable differences. Using high-speed camera imaging, *Rs* radii can be identified for different time values. Since the TNT charge has a cylindrical shape, a factor *n* = 2 was considered. Additionally, due to the fact that the distances between the TNT charge and the blasting cap are small (less than 0.5 m) for the experimental setup, an instantaneous energy release (s = 0) was set. However, the experimental results plotted against the results provided by Equation (5), which are presented in Figure 7a, show some considerable differences.

**Figure 7.** Experimental vs. Equation (5) results. **Figure 7.** Experimental vs. Equation (5) results.

By closely analyzing the footage in Figure 8, it can be observed that the blast wave shape presents itself neither as a cylindrical shape nor as a spherical one. The mismatch is By closely analyzing the footage in Figure 8, it can be observed that the blast wave shape presents itself neither as a cylindrical shape nor as a spherical one. The mismatch is probably due to the ratio between the length and the diameter of the TNT blast charge, which has a value of 3.57, and also due to the overall small dimensions of the charge. Considering the experimental blast's wave shape, which is more like an ellipsoid, a different value for *n* factor was chosen, namely 2.7. A comparison between predicted and experimental results for the modified value of the *n* factor is presented in Figure 7b, and it is clear that the use of this value leads to a much better approximation of the experimental data.

The *Rf* radii can also be calibrated with the use of the camera footage and finally plotted against *Rs* values, as shown in Figure 9. Predictions using Equation (11) are plotted in the same figure. With the use of Figure 9, one can easily see that the blast wave gradually moves away from the fireball border, which is consistent with the data provided by the numerical simulation.

mental data.

mental data.

**Figure 8.** Blast wave shape (perfect sphere (blue) and real (black)). **Figure 8.** Blast wave shape (perfect sphere (blue) and real (black)). numerical simulation.

**Figure 9.** Blast wave vs. Fireball Radii. **Figure 9.** Blast wave vs. Fireball Radii.

The analytical calculus based on Equations (5)–(10) is confirmed by a numerical approach, as shown in Figure 10. According to Figure 10, the blast wave front gradually speeds up, leaving behind the front of the donor gas products. The analytical calculus based on Equations (5)–(10) is confirmed by a numerical approach, as shown in Figure 10. According to Figure 10, the blast wave front gradually speeds up, leaving behind the front of the donor gas products.

probably due to the ratio between the length and the diameter of the TNT blast charge, which has a value of 3.57, and also due to the overall small dimensions of the charge. Considering the experimental blast's wave shape, which is more like an ellipsoid, a different value for *n* factor was chosen, namely 2.7. A comparison between predicted and experimental results for the modified value of the *n* factor is presented in Figure 7b, and it is clear that the use of this value leads to a much better approximation of the experi-

probably due to the ratio between the length and the diameter of the TNT blast charge, which has a value of 3.57, and also due to the overall small dimensions of the charge. Considering the experimental blast's wave shape, which is more like an ellipsoid, a different value for *n* factor was chosen, namely 2.7. A comparison between predicted and experimental results for the modified value of the *n* factor is presented in Figure 7b, and it is clear that the use of this value leads to a much better approximation of the experi-

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 10 of 12

**Figure 9.** Blast wave vs. Fireball Radii. The analytical calculus based on Equations (5)–(10) is confirmed by a numerical approach, as shown in Figure 10. According to Figure 10, the blast wave front gradually speeds up, leaving behind the front of the donor gas products. As mentioned in Section 3.1, two rows of gauges (six gauges/row) were used for pressure recording in the acceptor charge. This particular choice was due to the close distance between the donor and acceptor charges which resulted in a curved shock wave front, as depicted in Figure 10. As a result of the curved shock wave front, the first susceptible area to interact with the blast wave is the upper front of the acceptor charge. This can be clearly seen in Figure 5, where the higher-pressure values are recorded by gauges no. 7 and 8.

**Figure 10.** Blast wave front vs. TNT gas products front for 100 mm air gap thickness case. **Figure 10.** Blast wave front vs. TNT gas products front for 100 mm air gap thickness case.

#### As mentioned in Section 3.1, two rows of gauges (six gauges/row) were used for pres-**5. Conclusions**

sure recording in the acceptor charge. This particular choice was due to the close distance between the donor and acceptor charges which resulted in a curved shock wave front, as depicted in Figure 10. As a result of the curved shock wave front, the first susceptible area to interact with the blast wave is the upper front of the acceptor charge. This can be clearly seen in Figure 5, where the higher-pressure values are recorded by gauges no. 7 and 8. Sympathetic detonation tendency of the blasting cap for different scenarios is mandatory when the disrupting equipment is used on suspicious packages (IEDs). While experimental tests easily allow the evaluation of blasting cap sensitivity to blast waves, the mix between numerical and experimental approaches can enhance the understanding of the phenomenon.

**5. Conclusions**  Sympathetic detonation tendency of the blasting cap for different scenarios is mandatory when the disrupting equipment is used on suspicious packages (IEDs). While experimental tests easily allow the evaluation of blasting cap sensitivity to blast waves, the mix between numerical and experimental approaches can enhance the understanding of the phenomenon. Based on the relations of the mathematical model, it can be concluded that the shock Based on the relations of the mathematical model, it can be concluded that the shock wave detaches gradually from the donor gas products, the complete detachment being completed at a greater distance than the ones characterized by the blast cap initiation. In the nearby distance of the donor charge, both the shock waves' and the gas products' overpressure act on and initiate the blasting caps, even though not simultaneously, as proved in Figure 6. It is also clearly pointed out that the presence of gas products favors reaching the critical value for sympathetic detonation, according to the critical energy fluence criterion.

wave detaches gradually from the donor gas products, the complete detachment being completed at a greater distance than the ones characterized by the blast cap initiation. In the nearby distance of the donor charge, both the shock waves' and the gas products' overpressure act on and initiate the blasting caps, even though not simultaneously, as The analysis of sympathetic detonation tendency of blasting caps in close vicinity shows that the critical energy fluence criterion is preferable to the Chapman–Jouguet pressure threshold. The critical energy fluence criterion can be applied to test configurations that include not only a dense matter gap but also an air gap.

proved in Figure 6. It is also clearly pointed out that the presence of gas products favors reaching the critical value for sympathetic detonation, according to the critical energy fluence criterion. The analysis of sympathetic detonation tendency of blasting caps in close vicinity shows that the critical energy fluence criterion is preferable to the Chapman–Jouguet pressure threshold. The critical energy fluence criterion can be applied to test configurations **Author Contributions:** Conceptualization, M.L. and E.T.; methodology, E.T. and M.L.; software, E.T and A.C.C.; validation, E.T., M.L. and A.C.C.; formal analysis, E.T., M.L. and B.I.; investigation, M.L., B.I., E.T. and A.C.C.; resources, M.L. and B.I.; data curation, E.T.; writing—original draft preparation, E.T. and B.I.; writing—review and editing, M.L., E.T. and A.C.C.; visualization, E.T., B.I. and A.C.C.; supervision, E.T.; project administration, M.L.; funding acquisition, M.L. All authors have read and agreed to the published version of the manuscript.

that include not only a dense matter gap but also an air gap. **Author Contributions:** Conceptualization, M.L. and E.T.; methodology, E.T. and M.L.; software, E.T **Funding:** The paper was partially supported by a grant of the Romanian Ministry of Innovation and Research, UEFISCDI, project number 33SOL/2021 within PNCDI III.

and A.C.C.; validation, E.T., M.L. and A.C.C.; formal analysis, E.T., M.L., and B.I.; investigation, **Institutional Review Board Statement:** Not applicable.

M.L., B.I., E.T., and A.C.C.; resources, M.L. and B.I.; data curation, E.T.; writing—original draft preparation, E.T. and B.I.; writing—review and editing, M.L., E.T. and A.C.C.; visualization, E.T., B.I. **Informed Consent Statement:** Not applicable.

and A.C.C.; supervision, E.T.; project administration, M.L.; funding acquisition, M.L. All authors have read and agreed to the published version of the manuscript. **Data Availability Statement:** Not applicable.

**Funding:** The paper was partially supported by a grant of the Romanian Ministry of Innovation and **Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

**Institutional Review Board Statement:** Not applicable. 1. Yang, T.; Wang, C.; Li, T. Numerical simulation study of sympathetic detonation in stages. *Def. Technol.* **2021**, *18*, 1382–1393. [CrossRef]

Research, UEFISCDI, project number 33SOL/2021 within PNCDI III.

**Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. 2. Zhang, Z.; Wang, C.; Hu, H.; Yang, T. Investigation of underwater sympathetic detonation. *Prop. Explos. Pyrotech.* **2020**, *45*, 1736–1744. [CrossRef]

**Conflicts of Interest:** The authors declare no conflicts of interest.

## *Article* **Behavior of Sedimentary Rock Tunnel against Rigid Projectile Impact**

**Abdullah H. Alsabhan 1,\*, Md. Rehan Sadique 2,\* , Ali S. Alqarni 1 , Shamshad Alam 1 and Wonho Suh 3**

**Abstract:** The tunnels in present-day cities are experiencing varying degrees of loading conditions ranging from static to extreme loading. Therefore, the stability of underground tunnels needs to be analyzed and understood for safer and strengthened design. The present study was conducted to simulate the impact loading conditions due to a missile traveling at a velocity of 5 Mach for different rock tunnels. The nonlinear continuum finite element analysis has been carried out through Abaqus and Explicit. The four different types of sandstones considered in the present study include Kota, Jamrani, Singrauli, and Jhingurda sandstones. An elastoplastic Mohr–Coulomb constitutive material model has been considered to model the behavior of rock surrounding the tunnel opening. The tunnel has an opening of 7 m in diameter (d), and 50 m in height and breadth, with 50 m of longitudinal length. The deformation and stress in the rock and the damage to the concrete lining have been compared in different cases. The Concrete–Damage–Plasticity (CDP) model and the Johnson–Cook model were considered for modelling of the RC lining and steel reinforcement. It was concluded that Jhingurda sandstone has maximum deformations due to impacts caused by missiles.

**Keywords:** numerical modeling; rock tunnel; sandstone; missile impact

### **1. Introduction**

Due to the rapid migration of the population from rural to urban cities, the demand for better, faster, and safer modes of transportation arises. In addition, the horizontal expansion of residential construction has created a need for subsurface construction. Therefore, the need for the design and research of tunnels and other underground structures has arisen. A number of studies have been carried out by researchers to understand the different aspects of tunnel stability [1–12].

Subsurface structures, especially tunnels and caverns, have been an integral part of the defense strategy of the country. The stability and equilibrium of these structures need to be studied for extreme loading events such as seismic loading, blast, and impact loading. Therefore, a number of researchers have studied the behavior of tunnels under varying types of loading conditions [13–17]. However, there are few studies that depict the performance of underground tunnels constructed in rock when subjected to impact load.

The numerical tools for computation and modelling have been used by researchers to study the stability of tunnels under varying impact loading conditions. Gao et al. [18] studied the behavior of intact rocks under an impact load using a commercial tool, LS-DYNA. They proposed a relationship and a model to study the behavior of intact rocks under impact loads. The model was validated with high accuracy using experimental results. Experimental and numerical simulations have been carried out by Aziznejad et al. [19] using a distinct element code to study the response of rock mass under an impact load. The propagation of cracks in the rock tunnel was studied by Zhou et al. [20] under the impact loading condition, and it was found that the speed of crack propagation is

**Citation:** Alsabhan, A.H.; Sadique, M.R.; Alqarni, A.S.; Alam, S.; Suh, W. Behavior of Sedimentary Rock Tunnel against Rigid Projectile Impact. *Appl. Sci.* **2022**, *12*, 9595. https://doi.org/10.3390/ app12199595

Academic Editors: Ricardo Castedo, Lina M. López and Anastasio P. Santos

Received: 7 March 2022 Accepted: 19 September 2022 Published: 24 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

non-uniform; therefore, cracks may stop propagating suddenly. Zhou et al. [21] considered the change in orientation of the impact with respect to the tunnel model. They categorized different types of failure modes in tunnels under impact loading conditions. Zhou et al. [22] had concluded that the tunnel experiences different types of failure modes due to impact load and found that radial cracks propagate in the tunnel from the edge of the tunnel.

Therefore, it may be summarized that the strength of tunnels in rocks under impact loads has been rarely studied in the open literature. However, there is still a significant scope and a need for further study. Sedimentary rocks cover the majority of metropolitan areas in different countries of the world. However, the impact resistance of these rocks against soft and hard missiles has received little attention from previous researchers. Moreover, sandstone is found in significant areas near the borders of strong military countries like India, Pakistan, and China. Hence, it needs to be studied for impact loading conditions. Consequently, the present paper has considered four different types of sandstone: Jhingurda, Singrauli, Jamrani, and Kota. A missile having 100 kg of weight and a velocity of 5 Mach has been considered to simulate the impact loading conditions for different rock tunnels. The nonlinear elastoplastic continuum FE (finite element) method has been adopted to understand the adverse effects of impact loading on rock tunnels.

#### **2. Impact Loading Simulation**

The impact resistance of four different sandstone rock tunnels has been studied in the present paper. A missile has been modelled based on the description given by Vidanovi´c et al. [23]. The missile has a 0.7637 m length and a mass of 100 kg, modelled as a discrete part. The commercial software Abaqus has been used, and explicit mode has been selected for the simulation. The missile had a 5 Mach velocity before it hit the ground surface above the rock through which a tunnel has been constructed. The geometry of the tunnel has been considered based on the DMRC design specifications and published articles [24–26]. A dynamic explicit analysis has been carried out in the finite element tool Abaqus. In Abaqus, a step is time allotted for a particular analysis. However, according to the demand of output frame, it breaks the overall time allotted in small increments. In the present analysis, the step time is 0.035.

#### *2.1. Geometry*

The rock surrounding the tunnels has been modelled as a bigger size element having a three-dimensional size of 50 m × 50 m × 50 m and 12.5 m of overburden depth. The tunnel has an opening of 7 m in diameter and has been supported by a reinforced concrete liner of 0.35 m in thickness. The liner has an M30 grade of concrete. The concrete liner has reinforcement of steel bars of Weldox 460E grade in the longitudinal and circular directions. The details of the reinforcement and tunnel geometry are presented in Figure 1.

### *2.2. Input Properties of Materials*

The rock mass surrounding the tunnel has been considered as a nonlinear elastoplastic material. The Mohr–Coulomb failure model has been used to incorporate the nonlinearity of four different types of sandstones. The four sandstone rocks considered in the present paper are Jhingurda, Singrauli, Jamrani, and Kota. The input parameters are taken from Rao et al. [27]. Table 1 represents the different physical and mechanical properties of rocks used in the present simulation.

**Figure 1.** Geometry of finite element model for impact loading simulation. (**a**) Abaqus model of Missile, 0.7637 m in length and a mass of 100 kg with 5 Mach velocity (**b**) Tunnel with an opening of 7 m in diameter and supported by a reinforced concrete(M30) liner of 0.35 m in thickness. (**c**) The rock surrounding the tunnels of 50 m × 50 m × 50 m and 12.5 m of overburden depth.

**Figure 1.** Geometry of finite element model for impact loading simulation*.* (**a**) Abaqus model of Missile, 0.7637 m in length and a mass of 100 kg with 5 Mach velocity (**b**) Tunnel with an opening of 7 m in diameter and supported by a reinforced concrete(M30) liner of 0.35 m in thickness. (**c**) The

The rock mass surrounding the tunnel has been considered as a nonlinear elastoplastic material. The Mohr–Coulomb failure model has been used to incorporate the nonlinearity of four different types of sandstones. The four sandstone rocks considered in the present paper are Jhingurda, Singrauli, Jamrani, and Kota. The input parameters are taken from Rao et al. [27]*.* Table 1 represents the different physical and mechanical properties of

rock surrounding the tunnels of 50 m × 50 m × 50 m and 12.5 m of overburden depth.

**Table 1.** Four different sandstone rock surrounding the tunnel opening. rocks used in the present simulation.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 4 of 14

*2.2. Input Properties of Materials*

Similarly, the nonlinear behavior has been considered for steel bars by providing the elastoplastic properties of steel. Table 2 and Figure 2 show the properties of steel reinforcement used in this study. The interaction between the steel bars and concrete of the liner is achieved by embedding the circular and longitudinal reinforcement. The embedment constraint in the interaction module applied the proper bond between the steel and concrete, creating a reinforced concrete liner for the rock tunnel. The Johnson–Cook model [28] has been used for modelling the steel bars and properties are taken from Borvik et al. [29]. Borvik et al. [29] had performed a series of experiments on the steel under different strain rate and at varying temperature range. Similarly, the nonlinear behavior has been considered for steel bars by providing the elastoplastic properties of steel. Table 2 and Figure 2 show the properties of steel reinforcement used in this study. The interaction between the steel bars and concrete of the liner is achieved by embedding the circular and longitudinal reinforcement. The embedment constraint in the interaction module applied the proper bond between the steel and concrete, creating a reinforced concrete liner for the rock tunnel. The Johnson–Cook model [28] has been used for modelling the steel bars and properties are taken from Borvik et al. [29]. Borvik et al. [29] had performed a series of experiments on the steel under different strain rate and at varying temperature range.

**Table 2.** Elastoplastic properties of reinforced steel with Weldox 460 E grade. **Table 2.** Elastoplastic properties of reinforced steel with Weldox 460 E grade.

**Figure 2.** Plastic behavior of steel reinforcement material. **Figure 2.** Plastic behavior of steel reinforcement material.

Moreover, the concrete liner has been considered as M30 grade and its nonlinear elastoplastic behavior has been simulated through the Concrete Damage Plasticity model. It Moreover, the concrete liner has been considered as M30 grade and its nonlinear elastoplastic behavior has been simulated through the Concrete Damage Plasticity model. It also incorporated the damage characteristic of the concrete and, therefore, proved to be useful in studying the overall failure of the internal lining.

The M30 grade of concrete has a mass density of 2500 kg/m3 and a Young's modulus of 26.6 GPa, with a 0.20 Poisson's ratio. Moreover, the dilation angle and eccentricity of 31 degrees and 0.1, respectively, have been considered. The variation in stress and damage corresponding to strain for the M30 grade of concrete are shown in Figures 3 and 4, respectively.

spectively.

spectively.

useful in studying the overall failure of the internal lining.

useful in studying the overall failure of the internal lining.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 5 of 14

**Figure 3.** Input of stress–strain variation for M30 grade of concrete liner used in tunnel. **Figure 3.** Input of stress–strain variation for M30 grade of concrete liner used in tunnel. **Figure 3.** Input of stress–strain variation for M30 grade of concrete liner used in tunnel.

also incorporated the damage characteristic of the concrete and, therefore, proved to be

also incorporated the damage characteristic of the concrete and, therefore, proved to be

The M30 grade of concrete has a mass density of 2500 kg/m3 and a Young's modulus of 26.6 GPa, with a 0.20 Poisson's ratio. Moreover, the dilation angle and eccentricity of 31 degrees and 0.1, respectively, have been considered. The variation in stress and damage corresponding to strain for the M30 grade of concrete are shown in Figures 3 and 4, re-

The M30 grade of concrete has a mass density of 2500 kg/m3 and a Young's modulus of 26.6 GPa, with a 0.20 Poisson's ratio. Moreover, the dilation angle and eccentricity of 31 degrees and 0.1, respectively, have been considered. The variation in stress and damage corresponding to strain for the M30 grade of concrete are shown in Figures 3 and 4, re-

**Figure 4.** Damage parameter variation with strain for M30 grade of concrete. **Figure 4.** Damage parameter variation with strain for M30 grade of concrete. **Figure 4.** Damage parameter variation with strain for M30 grade of concrete.

#### *2.3. Meshing, Loading, Boundary and Interaction Conditions 2.3. Meshing, Loading, Boundary and Interaction Conditions 2.3. Meshing, Loading, Boundary and Interaction Conditions*

The rock mass surrounding the tunnel has been meshed as C3D8R (Continuum Three-dimensional eight-nodded reduced integration solid Brick element), as suggested and used by Zaid and Sadique [30,31], Zaid and Shah [32] and Zaid et al. [33–37]. The element size of 0.7 has been used based on mesh convergence, and this type of mesh is defined as brick-type element, which has eight nodes. The steel bars are modelled as beam-type element, i.e., B31, as suggested and used by Zaid and Sadique [38–40]. The steel bars elements have an element size of 0.05. The missile has been meshed by the R3D4 element type to make it rigid and discrete. The general hard contact and frictionless tangential contact has been assigned to the whole model. The embedment interaction has been used to model the reinforced concrete liner by embedding the steel bars in concrete liner. The base of the rock has a fixed support as the rock mass extends to infinite depth, and the sides of the model have roller supports, which allow vertical movement but restrain other directional movement of rock mass. One set of simulation takes around six and a half CPU hours on a 64GB RAM system with a Dell Precision Tower 7810. General hard contact and frictionless tangential contact have been assigned to the whole model. The rock mass surrounding the tunnel has been meshed as C3D8R (Continuum Three-dimensional eight-nodded reduced integration solid Brick element), as suggested and used by Zaid and Sadique [30,31], Zaid and Shah [32] and Zaid et al. [33–37]. The element size of 0.7 has been used based on mesh convergence, and this type of mesh is defined as brick-type element, which has eight nodes. The steel bars are modelled as beam-type element, i.e., B31, as suggested and used by Zaid and Sadique [38–40]. The steel bars elements have an element size of 0.05. The missile has been meshed by the R3D4 element type to make it rigid and discrete. The general hard contact and frictionless tangential contact has been assigned to the whole model. The embedment interaction has been used to model the reinforced concrete liner by embedding the steel bars in concrete liner. The base of the rock has a fixed support as the rock mass extends to infinite depth, and the sides of the model have roller supports, which allow vertical movement but restrain other directional movement of rock mass. One set of simulation takes around six and a half CPU hours on a 64GB RAM system with a Dell Precision Tower 7810. General hard contact and frictionless tangential contact have been assigned to the whole model. The rock mass surrounding the tunnel has been meshed as C3D8R (Continuum Threedimensional eight-nodded reduced integration solid Brick element), as suggested and used by Zaid and Sadique [30,31], Zaid and Shah [32] and Zaid et al. [33–37]. The element size of 0.7 has been used based on mesh convergence, and this type of mesh is definedas brick-type element, which has eight nodes. The steel bars are modelled as beam-typeelement, i.e., B31, as suggested and used by Zaid and Sadique [38–40]. The steel bars elements have an element size of 0.05. The missile has been meshed by the R3D4 element type to make it rigid and discrete. The general hard contact and frictionless tangential contact has been assigned to the whole model. The embedment interaction has been used to model the reinforced concrete liner by embedding the steel bars in concrete liner. The base of the rock has a fixed support as the rock mass extends to infinite depth, and the sides of the model have roller supports, which allow vertical movement but restrain other directional movement of rock mass. One set of simulation takes around six and a half CPU hours on a 64GB RAM system with a Dell Precision Tower 7810. General hard contact and frictionless tangential contact have been assigned to the whole model. The embedment interaction has been used to model the reinforced concrete liner by embedding the steel bars in the concrete liner.

#### **3. Validation of Dynamic Loading**

In order to validate the present finite element simulation, an experimental study has been simulated using the present methodology and numerical results are compared with the experimental study by Andersson [41], as shown in Table 3. A steel mass weighing 600 kg was considered for impact loading on 0.2 m × 0.2 m area in the middle of a slab. The height of fall was varied from 1 m to 2 m on the concrete slab having a 1.75 m × 1.75 m

cross section and a 0.12 m thickness. The size of the slab, loading conditions, and the properties of the model have been adopted as per the report by Andersson [41]. The height of fall was varied from 1 m to 2 m on the concrete slab having a 1.75 m × 1.75 m cross section and a 0.12 m thickness. The size of the slab, loading conditions, and the properties of the model have been adopted as per the report by Andersson [41].

The embedment interaction has been used to model the reinforced concrete liner by em-

In order to validate the present finite element simulation, an experimental study has been simulated using the present methodology and numerical results are compared with the experimental study by Andersson [41], as shown in Table 3. A steel mass weighing 600 kg was considered for impact loading on 0.2 m × 0.2 m area in the middle of a slab.

**Table 3.** Comparison of results of properties of reinforced steel. **Table 3.** Comparison of results of properties of reinforced steel.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 6 of 14

bedding the steel bars in the concrete liner.

**3. Validation of Dynamic Loading**

#### **4. Results and Discussion 4. Results and Discussion**

Commercial software based on the finite element method, i.e., Abaqus/Explicit, has been used for modelling and analysis. Four different sandstone rocks, Jhingurda, Singrauli, Jamrani, and Kota, were considered. A generally used design specification for metro tunnels has been used based on Delhi Metro Rail Corporation designs. A missile having a 5 Mach velocity and weighing 100 kg has been considered. The simulation has been run for 30 milliseconds, which is the time required by a missile to hit the rock ground from 100 m away. Commercial software based on the finite element method, i.e., Abaqus/Explicit, has been used for modelling and analysis. Four different sandstone rocks, Jhingurda, Singrauli, Jamrani, and Kota, were considered. A generally used design specification for metro tunnels has been used based on Delhi Metro Rail Corporation designs. A missile having a 5 Mach velocity and weighing 100 kg has been considered. The simulation has been run for 30 milliseconds, which is the time required by a missile to hit the rock ground from 100 m away.

Figure 5 has been plotted to compare the deformation variation with time when a missile hits the ground surface for all the sandstone rocks considered in the present study. It has been observed that the amplitude of deformation for Jhingurda sandstone is the maximum, having a magnitude of 2.45 m. Maximum deformations of 1.35 m, 1.03 m, and 0.76 m have been observed for Singrauli, Jamrani, and Kota rocks prospectively at the ground surface. Therefore, Kota sandstone has shown maximum resistance to missile penetration, while Jhingurda sandstone has the least resistance to missile penetration. Figure 5 has been plotted to compare the deformation variation with time when a missile hits the ground surface for all the sandstone rocks considered in the present study. It has been observed that the amplitude of deformation for Jhingurda sandstone is the maximum, having a magnitude of 2.45 m. Maximum deformations of 1.35 m, 1.03 m, and 0.76 m have been observed for Singrauli, Jamrani, and Kota rocks prospectively at the ground surface. Therefore, Kota sandstone has shown maximum resistance to missile penetration, while Jhingurda sandstone has the least resistance to missile penetration.

**Figure 5.** Variation in deformation with time to compare the ground surface behavior under impact loading of 100 kg missile**. Figure 5.** Variation in deformation with time to compare the ground surface behavior under impact loading of 100 kg missile.

The deformation profile is one of the important output results for understanding the internal behavior of a tunnel. Figure 6 shows the comparison of the deformation profiles of four sandstone rocks. The deformation profile for Jhingurda sandstone follows a smooth curvature, while the curvature becomes distorted and non-uniform for other types of sandstone. It has also been observed that as the strength of sandstone increases, the peak deformation gets decreased, while the length of tunnel under disturbance increases with the increase in the strength of sandstone. Moreover, a slight bulging has been observed in all the sandstones except for Jhingurda sandstone. Therefore, it may be concluded that weaker sandstone requires strengthening for a smaller area after an impact loading event, while high-strength sandstone will require repair for a longer portion of the tunnel.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 7 of 14

the tunnel.

the tunnel.

tion.

tion.

**Figure 6.** Comparison of deformation profile generated under the response of impact load**. Figure 6.** Comparison of deformation profile generated under the response of impact load. **Figure 6.** Comparison of deformation profile generated under the response of impact load**.**

Particle velocity is one of the significant output results in the dynamic loading analysis of rock tunnels. Therefore, the peak velocity at the ground surface of different sandstone rocks is shown in Figure 7 for comparison. The peak of the particle velocity graph has been observed at 20.41 milliseconds in each case of sandstone rock. However, the variation of particle velocity follows a separate path for different rocks, but the pattern of the particle velocity plot remains similar in all the cases. Figure 8 represents the peak acceleration at the ground surface when a missile hits the different sandstone rocks. In the case of Jhingurda sandstone, the magnitude of peak velocity and acceleration is greatest. Moreover, the pattern of variation in acceleration and velocity remains similar, and therefore, it is independent of the type of sandstone. Particle velocity is one of the significant output results in the dynamic loading analysis of rock tunnels. Therefore, the peak velocity at the ground surface of different sandstone rocks is shown in Figure 7 for comparison. The peak of the particle velocity graph has been observed at 20.41 milliseconds in each case of sandstone rock. However, the variation of particle velocity follows a separate path for different rocks, but the pattern of the particle velocity plot remains similar in all the cases. Figure 8 represents the peak acceleration at the ground surface when a missile hits the different sandstone rocks. In the case of Jhingurda sandstone, the magnitude of peak velocity and acceleration is greatest. Moreover, the pattern of variation in acceleration and velocity remains similar, and therefore, it is independent of the type of sandstone. Particle velocity is one of the significant output results in the dynamic loading analysis of rock tunnels. Therefore, the peak velocity at the ground surface of different sandstone rocks is shown in Figure 7 for comparison. The peak of the particle velocity graph has been observed at 20.41 milliseconds in each case of sandstone rock. However, the variation of particle velocity follows a separate path for different rocks, but the pattern of the particle velocity plot remains similar in all the cases. Figure 8 represents the peak acceleration at the ground surface when a missile hits the different sandstone rocks. In the case of Jhingurda sandstone, the magnitude of peak velocity and acceleration is greatest. Moreover, the pattern of variation in acceleration and velocity remains similar, and therefore, it is independent of the type of sandstone.

The deformation profile is one of the important output results for understanding the internal behavior of a tunnel. Figure 6 shows the comparison of the deformation profiles of four sandstone rocks. The deformation profile for Jhingurda sandstone follows a smooth curvature, while the curvature becomes distorted and non-uniform for other types of sandstone. It has also been observed that as the strength of sandstone increases, the peak deformation gets decreased, while the length of tunnel under disturbance increases with the increase in the strength of sandstone. Moreover, a slight bulging has been observed in all the sandstones except for Jhingurda sandstone. Therefore, it may be concluded that weaker sandstone requires strengthening for a smaller area after an impact loading event, while high-strength sandstone will require repair for a longer portion of

The deformation profile is one of the important output results for understanding the internal behavior of a tunnel. Figure 6 shows the comparison of the deformation profiles of four sandstone rocks. The deformation profile for Jhingurda sandstone follows a smooth curvature, while the curvature becomes distorted and non-uniform for other types of sandstone. It has also been observed that as the strength of sandstone increases, the peak deformation gets decreased, while the length of tunnel under disturbance increases with the increase in the strength of sandstone. Moreover, a slight bulging has been observed in all the sandstones except for Jhingurda sandstone. Therefore, it may be concluded that weaker sandstone requires strengthening for a smaller area after an impact loading event, while high-strength sandstone will require repair for a longer portion of

**Figure 7.** Comparison of particle velocity at ground surface under present impact loading condi-**Figure 7.** Comparison of particle velocity at ground surface under present impact loading condi-**Figure 7.** Comparison of particle velocity at ground surface under present impact loading condition.

**Figure 8.** Comparison of particle acceleration at ground surface under present impact loading condition. **Figure 8.** Comparison of particle acceleration at ground surface under present impact loading condition.

have a significant influence on the deformation zone. In the cases of Jhingurda, Singrauli, Jamrani, and Kota, the maximum deformation at the crown is 4.94 mm, 2.75 mm, 2.61 mm, and 1.04 mm, respectively. It can be concluded that Kota sandstone has minimum deformation, and therefore, it is the safest sandstone rock under impact loading conditions. However, the area of disturbance is maximum in the case of Kota sandstone, and vibrations may reach the tunnel crown in a shorter time as compared to other sandstones.

Figure 9 shows the deformation contours of Jhingurda, Singrauli, Jamrani, and Kota sandstone when a 100 kg missile moving at the velocity of 5 Mach hits the ground surface

(**a**)

(**b**)

10

15

20

 m/s2) 25

Figure 9 shows the deformation contours of Jhingurda, Singrauli, Jamrani, and Kota sandstone when a 100 kg missile moving at the velocity of 5 Mach hits the ground surface of the rock-containing tunnel. It has been observed that the brittleness and strength of rock have a significant influence on the deformation zone. In the cases of Jhingurda, Singrauli, Jamrani, and Kota, the maximum deformation at the crown is 4.94 mm, 2.75 mm, 2.61 mm, and 1.04 mm, respectively. It can be concluded that Kota sandstone has minimum deformation, and therefore, it is the safest sandstone rock under impact loading conditions. However, the area of disturbance is maximum in the case of Kota sandstone, and vibrations may reach the tunnel crown in a shorter time as compared to other sandstones. **Figure 8.** Comparison of particle acceleration at ground surface under present impact loading condition. 0 5 0.000 0.010 0.020 0.030 Partcile acceleration (x 106Analysis time (s)

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 8 of 14

Jhingurda Singrauli Jamrani Kota

Figure 10 has been plotted to compare the serviceability of reinforced concrete liners under impact loading conditions in the case of different types of sandstone. Tension damage has been observed in each type of sandstone. However, the area of the damaged zone increases with the strength and brittleness of sandstone. Therefore, reinforced concrete liner has maximum tensile damage in Kota sandstone (0.99) and less tension damage in the case of Jhingurda sandstone (0.017). It has been concluded that the consequences of an impacting projectile reach the tunnel lining when constructed in strong and brittle sandstone, or viceversa. In addition, the tensile damage in all the different types of sandstones considered in the present study remains concentrated at the outer periphery of the liner. Figure 9 shows the deformation contours of Jhingurda, Singrauli, Jamrani, and Kota sandstone when a 100 kg missile moving at the velocity of 5 Mach hits the ground surface of the rock-containing tunnel. It has been observed that the brittleness and strength of rock have a significant influence on the deformation zone. In the cases of Jhingurda, Singrauli, Jamrani, and Kota, the maximum deformation at the crown is 4.94 mm, 2.75 mm, 2.61 mm, and 1.04 mm, respectively. It can be concluded that Kota sandstone has minimum deformation, and therefore, it is the safest sandstone rock under impact loading conditions. However, the area of disturbance is maximum in the case of Kota sandstone, and vibrations may reach the tunnel crown in a shorter time as compared to other sandstones.

**Figure 9.** *Cont*.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 9 of 14

**Figure 9.** Deformation contours of (**a**) Jhingurda, (**b**) Singrauli, (**c**) Jamrani and (**d**) Kota when an impact loading occurs due to 100 kg missile. **Figure 9.** Deformation contours of (**a**) Jhingurda, (**b**) Singrauli, (**c**) Jamrani and (**d**) Kota when an impact loading occurs due to 100 kg missile. impacting projectile reach the tunnel lining when constructed in strong and brittle sandstone, or vice-versa. In addition, the tensile damage in all the different types of sandstones considered in the present study remains concentrated at the outer periphery of the liner.

**Figure 10.** *Cont*.

(**a**)

**Figure 10.** Tension damage contours of (**a**) Jhingurda, (**b**) Singrauli, (**c**) Jamrani, and (**d**) Kota sandstone tunnel when an impact loading occurs due to a 100 kg missile. **Figure 10.** Tension damage contours of (**a**) Jhingurda, (**b**) Singrauli, (**c**) Jamrani, and (**d**) Kota sandstone tunnel when an impact loading occurs due to a 100 kg missile.

The in-depth view of lining performance has been studied by comparing the deformation at the reinforcement cage of steel bars in the case of different rocks, as shown in Figure 11. The maximum value of deformation has been noted for Jhingurda sandstone, while the maximum value of deformation remains concentrated at the crown of the tun-The in-depth view of lining performance has been studied by comparing the deformation at the reinforcement cage of steel bars in the case of different rocks, as shown in Figure 11. The maximum value of deformation has been noted for Jhingurda sandstone, while the maximum value of deformation remains concentrated at the crown of the tunnel.

nel.

#### **5. Conclusions 5. Conclusions**

lows:

The present study of finite element simulation for rock tunnel resistance against impact loading has four different sandstone rocks surrounding a 5 m diameter reinforced concrete tunnel lining. The major conclusions drawn from the present study are as fol-The present study of finite element simulation for rock tunnel resistance against impact loading has four different sandstone rocks surrounding a 5 m diameter reinforced concrete tunnel lining. The major conclusions drawn from the present study are as follows:

**Author Contributions:** M.R.S.: drafting—data collection and preparation of the manuscript, writing review and editing, S.A.: drafting—preparation of the manuscript, revision and correction; A.H.A.: composing—reviewing, fund acquisition and modifying; A.S.A.: composing—reviewing, and modifying; W.S.: reviewing and modifying. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors acknowledge the support provided by Researchers Supporting. Project Number (RSP2022R473), King Saud University, Riyadh, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Authors acknowledge the support provided by King Saud University, Saudi Arabia, and Aligarh Muslim University, India, to carry out this study.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

## *Article* **Blast Hole Pressure Measurement and a Full-Scale Blasting Experiment in Hard Rock Quarry Mine Using Shock-Reactive Stemming Materials**

**Younghun Ko 1,\* , Chanhwi Shin 2 , Youngjun Jeong 3 and Sangho Cho 2,4,\***

**Abstract:** By increasing the effectiveness of the energy generated by the explosive charge inserted into a blast hole, stemming increases rock fragmentation. Missing or improper stemming, which can lead to the detonation gas escaping from the blast hole in advance, results not only in the waste of explosive energy and poor fragmentation but also in environmental problems, such as ground vibration, noise, flying rocks, back breaks, and air blasts. In this study, a stemming material based on a shear thickening fluid (STF) that reacts to dynamic pressure was developed. Two blasting experiments were conducted to verify the performance of the STF-based stemming material. In the first experiment, the pressure inside the blast hole was directly measured based on the application of the stemming material. In the second experiment, full-scale bench blasting was performed, and the blasting results of sand stemming and the STF-based stemming cases were compared. The measurement results of the pressure in the blast hole showed that when the STF-based stemming material was applied, the pressure at the top of the blast hole was lower than in the sand stemming case, and the stemming ejection was also lower. Full-scale bench blasting was conducted to compare the two types of stemming materials by evaluating the size of the rock fragments using image processing. The results of the two blasting experiments helped to verify that the blockage performance of the STF-based stemming material in the blast hole was superior to that of the sand stemming material.

**Keywords:** blasting experiment; stemming material; shear thickening fluid; sand; blockage performance

### **1. Introduction**

Stemming is a process applied to blast holes to prevent gases from escaping during detonation. A stemming material helps confine the explosive energy for a longer duration. Without stemming, up to 50% of the explosive energy can escape through the borehole [1]. Proper stemming has been shown to improve explosive efficiency by over 41% [2]. Further, employing even the least efficient stemming materials can boost the usable energy of an explosion by 60%, while the most efficient stemming materials can increase it by up to 93% [3].

Missing or improper stemming, which can lead to the detonation gas escaping from the blast hole in advance, results not only in the waste of explosive energy and poor rock fragmentation but also in environmental problems, such as ground vibration, noise, flying rocks, back breaks, and air blasts [4].

Smaller amounts of explosives may be used to produce the same blasting effects if explosive energy was used more effectively [5,6]. Improvements in fragmentation will

**Citation:** Ko, Y.; Shin, C.; Jeong, Y.; Cho, S. Blast Hole Pressure Measurement and a Full-Scale Blasting Experiment in Hard Rock Quarry Mine Using Shock-Reactive Stemming Materials. *Appl. Sci.* **2022**, *12*, 8629. https://doi.org/10.3390/ app12178629

Academic Editors: Ricardo Castedo, Lina M. López and Anastasio P. Santos

Received: 2 August 2022 Accepted: 26 August 2022 Published: 29 August 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

result in lower second breaking work costs. Proper stemming can reduce costs and improve the productivity and profitability of a mining operation. The main objective of rock-blasting is fragmentation by explosive. The loading and hauling operations of a mining operation, particularly the crushing line, profit greatly from good fragmentation [7]. Additionally, cracks are generated over a larger area in the rock mass using proper stemming. These cracks propagate, interconnect, and cut the rock mass; thus, the block size and distribution after blasting satisfy the construction or mining requirements. Therefore, reasonably selecting the stemming material is of particular importance for improving the blasting effect, increasing the efficiency of explosives, and obtaining ideal blasting fragmentation.

In the mining industry, blast holes are sealed with three different sorts of stemming materials: colloidal, liquid, and solid. Additional research on the performance of stemming materials is required. Li et al. [8] used a water stemming technique that involves putting water-filled polyvinyl plastic bags within blast holes. A water-silt composite-stemmed blasting method for tunnels was proposed [9] to increase rock breakage, reduce dust, and use fewer explosives.

In most cases, using fluid-type stemming inside a blast hole as a stemming material produced good results. Fluid has a higher density than air, and even at extremely high pressures, the compression of water is significantly lower than that of air [10].

Under dynamic loading, Zhu et al. [11] performed an AUTODYN numerical analysis using a variety of stemming materials, such as fluid (water), sand, and air, placed in the area between the internal explosives and the hollow wall inside the blast hole. The water stemming case, which was also the best medium for shockwave transmission, produced the largest fracture area. Additionally, the presence of fluid (water), which results in the deformation and displacement of the rock, causes the shock wave to reflect and bubble pulse, which contributes to the high stress exerted during this process.

The most effective method to evaluate the stemming effect is to conduct field experiments. A stemming performance test of a small-scale model was developed, and the results showed that different stemming materials have different functionalities, which can significantly influence the efficiency of rock breaking [12].

Kopp [13] suggested a simple physical model for predicting the time required to eject stemming. This model depends only on the inertia of the stemming material. The frictional forces that resist the movement were omitted. The stemming performance of the stemming material can be evaluated using the initial ejection velocity of the stemming part at the entrance of the blast hole [14].

The momentum of the stemming structure based on the explosive load can be calculated using the mass of the stemming structure and the initial velocity of the stemming part when the stemming is ejected into the orifice.

As a highly capable method in the mining industry, image analysis techniques have been used to predict rock fragmentation by blasting. These techniques are capable of visual processing, thereby serving as an appropriate alternative to low-accuracy methods [15]. Over the past few decades, various image analysis software packages, such as Split-Online, Split-desktop, Gold-Size, and Wip-Frag, have been developed, and their applications in the mining industry and mineral processing have been reported. The main advantages of these software packages are their integration and lack of disruption [16].

The specific charge is mainly used as an indicator to predict the blasting effect, but the amount of powder used per unit volume of crushed rock cannot properly reflect the influence of energy change in the blasting hole; therefore, the pressure in the blasting hole must be estimated and used to understand this [17]. However, the blasting pressure has relied on calculations rather than direct measurement. Recently, the blasting pressure has been estimated through a numerical analysis approach, but it is difficult to predict the explosion reaction of explosives acting on rocks, an anisotropic material. Therefore, the concepts of abnormal explosion and ideal sealing are used to calculate the pressure in the blast hole, assuming that there is no external influence [18]. Therefore, field experiments are being conducted to directly measure the pressure in the blast hole. However, the pressure probe used is very expensive, and the sensor is only used once because of the extreme conditions generated by the blast, thereby requiring a significant financial investment. Therefore, in most cases, a pressure measurement sensor is inserted into the dummy hole, and the blasting pressure is indirectly measured based on the impact pressure propagated through the rock [19].

In recent years, a new intelligent material named shear thickening fluid (STF) has been widely used in energy absorption research [20–25]. STF exhibits an intense viscosity jump under shock load; as a result, it has been used in various applications, such as liquid body armor [26]. However, limited research on the application of STF for industrial blasting or as a stemming material is currently available.

In this study, a shock-reactive stemming material was developed that behaves similar to water in terms of shockwave propagation and has a high shear strength for dynamic shocks. The STF is characterized by its reversible energy absorption behavior under impulse loading. Its remarkable energy absorption capacity is attributed to viscous dissipation during shear and compression thickening. The STF-based stemming material was developed based on the following advantages. (1) STF has excellent sealing properties as it is a fluid-based material. (2) Its viscosity rapidly changes because of external shock, while material compaction or deformation is minimal with respect to the dynamic gas pressure in the blast hole. (3) Using starch as the main base material reduces costs.

Two blasting experiments were conducted to compare and contrast the blast effects of the developed stemming material and those of commonly used blasting stemming materials. The first is an experiment in which the blast hole pressure and stemming ejection are directly measured, and the second is an experiment to verify the stemming performance by analyzing the assessment of rock fragmentation through a full-scale blasting experiment.

### **2. Materials and Methods**

#### *2.1. STF-Based Stemming Material Rheology Tests*

A dense colloidal dispersion of solid nanoparticles in a carrier fluid is known as an STF [27]. When a shear force is applied, the random distribution of particles in the dispersion initially emerges in an ordered fashion because the hydrodynamic forces are greater than the repulsive forces operating between the interstitial gaps the particles have generated. The order–disorder theory, put forth by Hoffmann in 1972 [28], is represented by this arrangement of particles. Large hydrodynamic forces tend to push out the fluid between the interstitial spaces with rising shear rates, leading to the production of hydroclusters. The hydroclustering mechanism proposed by Brady and Bossis in 1985 is comprised of this phenomenon [29]. These clusters are stress-bearing elements that lead to particle jamming, when additional shearing pressures are applied.

STFs behave by increasing the dynamic viscosity under the application of shear stress. When tightly packed particles combine with enough liquid to cover the spaces between the particles, dilatancy occurs. The fluid serves as a lubricant at low speeds, facilitating easy movement of the dilatant substance.

Because of the increased friction caused by the inability of the liquid to fill the gaps left by the particles at greater velocities, the viscosity also increases. The STF is also non-Newtonian in nature because its viscosity depends on the shear rate or shear rate history. This behavior is a type of deviation from Newton's law and is controlled by factors, such as particle size, shape, and distribution. Empirical studies have also shown that shear thickening effects vary with different particles and additive concentrations, as well as with the molecular chain of the additives [30].

Shear thickening is a reversible phenomenon governed by a power law model. Generally, a non-Newtonian fluid is described using the power law model expressed in Equations (1) and (2).

$$
\pi = \text{K}(\frac{\partial \mu}{\partial y})^n = \text{K}(\mathbf{y})^n = \pi = \text{K}(\mathbf{y})^{n-1} \text{ ( $\mathbf{y}$ )}^1, \ \pi = \mu\_{apparent}(\mathbf{y}), \tag{1}
$$

$$
\mu\_{apparent} = K(\gamma)^{n-1} \tag{2}
$$

௧ ൌ ሺγሻିଵ (2)

where *τ* is the shear stress exerted by the fluid, *K* is the fluid viscosity, *µ* is the shear deformation, *y* is the distance from the reference layer, *∂µ ∂y* is the strain rate, *n* is the flow behavior index, and *µapparent* is the apparent viscosity. deformation, y is the distance from the reference layer, డఓ డ௬ is the strain rate, is the flow behavior index, and ௧ is the apparent viscosity. As shown in Figure 1, the fluid behaves as a Newtonian fluid at *n* = 1 and exhibits

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 4 of 20

As shown in Figure 1, the fluid behaves as a Newtonian fluid at *n* = 1 and exhibits shear thinning properties when 0 < *n* < 1. Moreover, several dispersions and liquid polymers exhibit shear thinning behavior for *n* values between 0.3 and 0.7. However, this depends on the particle concentration and molecular weight of the carrier fluid. shear thinning properties when 0 < *n* < 1. Moreover, several dispersions and liquid poly‐ mers exhibit shear thinning behavior for *n* values between 0.3 and 0.7. However, this de‐ pends on the particle concentration and molecular weight of the carrier fluid.

**Figure 1.** The shear thickening process of a shear thickening fluid. **Figure 1.** The shear thickening process of a shear thickening fluid.

The shear thickening effect of STF is demonstrated by the lower rate of increase in the shear stress in the low‐shear‐strain‐rate regions and a higher rate of increase in the high‐ shear‐strain‐rate regions (Figure 1). Figure 1 also depicts the relationship between the shear stress and shear strain rate of the STF. The potential of a STF to improve the effectiveness of body armor against ballistic impacts and stab resistance has been thoroughly researched [31,32]. Further research is necessary, nevertheless, to fully understand the potential impact of STF on the stemming of blast holes. The motivation of this study is to harness the strength The shear thickening effect of STF is demonstrated by the lower rate of increase in the shear stress in the low-shear-strain-rate regions and a higher rate of increase in the high-shear-strain-rate regions (Figure 1). Figure 1 also depicts the relationship between the shear stress and shear strain rate of the STF. The potential of a STF to improve the effectiveness of body armor against ballistic impacts and stab resistance has been thoroughly researched [31,32]. Further research is necessary, nevertheless, to fully understand the potential impact of STF on the stemming of blast holes. The motivation of this study is to harness the strength of the STF through flexible deployment and relatively easy stemming, which can help dissipate pressure wave loading around the rock mass during an explosion. The rheological behavior of the non-Newtonian fluid was measured using a rheometer.

of the STF through flexible deployment and relatively easy stemming, which can help dis‐ sipate pressure wave loading around the rock mass during an explosion. The rheological behavior of the non‐Newtonian fluid was measured using a rheometer. In this study, the STF-based stemming material was mainly based on corn starch, while xanthan gum and guar gum were blended to increase the viscosity. Sodium benzoate was used to prevent the putrefaction of starch, and nitroglycol and salt were added to prevent freezing in winter.

In this study, the STF‐based stemming material was mainly based on corn starch, while xanthan gum and guar gum were blended to increase the viscosity. Sodium benzo‐ ate was used to prevent the putrefaction of starch, and nitroglycol and salt were added to prevent freezing in winter. The STF samples were sandwiched between a cone plate and the foundation support of a rheometer (Anton-Paar MCR301 rheometer) for rheological experiments. During the studies, the shear rate applied to the sample was increased from 0 to 100 s−1 , and all of the tests were carried out at a temperature of 25 ◦C.

The STF samples were sandwiched between a cone plate and the foundation support of a rheometer (Anton‐Paar MCR301 rheometer) for rheological experiments. During the studies, the shear rate applied to the sample was increased from 0 to 100 s−1, and all of the tests were carried out at a temperature of 25 °C. A schematic of the rheometer and the results of the rheological tests conducted on the STF-based stemming material are shown in Figures 2 and 3. The rheology tests were performed on the STF samples of 30, 45, and 55 wt.% corn starch suspensions. In the case of the 30 wt.% corn starch suspension, no significant shear thickening is observed. However, as the starch content increases, the particle content exceeds the ratio of the dispersion

A schematic of the rheometer and the results of the rheological tests conducted on the

STF‐based stemming material are shown in Figures 2 and 3. The rheology tests were per‐

30 wt.% corn starch suspension, no significant shear thickening is observed. However, as the starch content increases, the particle content exceeds the ratio of the dispersion medium; therefore, the distance between the corn starch particles decreases, and the shear thickening effect increases. For the sample made up of 55 wt.%, a shear thickening effect is attained at

medium; therefore, the distance between the corn starch particles decreases, and the shear thickening effect increases. For the sample made up of 55 wt.%, a shear thickening effect is attained at a critical shear rate of 85 s–1. The STF initially experiences marginal shear thinning, which then grows with the shear rate. In particular, the viscosity of the STF suddenly increases as the shear rate reaches a critical value, indicating a shear thickening phenomenon. However, the viscosity of the STFs sharply decreases after a period of shear thickening. The critical shear rate of the STF sample is approximately 85 s−1 , and the maximum viscosity of the STF samples is 543 Pa. a critical shear rate of 85 s–1. The STF initially experiences marginal shear thinning, which then grows with the shear rate. In particular, the viscosity of the STF suddenly increases as the shear rate reaches a critical value, indicating a shear thickening phenomenon. However, the viscosity of the STFs sharply decreases after a period of shear thickening. The critical shear rate of the STF sample is approximately 85 s−1, and the maximum viscosity of the STF samples is 543 Pa. a critical shear rate of 85 s–1. The STF initially experiences marginal shear thinning, which then grows with the shear rate. In particular, the viscosity of the STF suddenly increases as the shear rate reaches a critical value, indicating a shear thickening phenomenon. However, the viscosity of the STFs sharply decreases after a period of shear thickening. The critical shear rate of the STF sample is approximately 85 s−1, and the maximum viscosity of the STF samples is 543 Pa.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 5 of 20

**Figure 2.** (**a**) Rheometer schematic and (**b**) Anton‐Paar MCR301 rheometer. **Figure 2.** (**a**) Rheometer schematic and (**b**) Anton-Paar MCR301 rheometer. **Figure 2.** (**a**) Rheometer schematic and (**b**) Anton‐Paar MCR301 rheometer.

The STF‐based stemming material image and package products are shown in Figure 4. **Figure 3.** Results of the shear thickening fluid based stemming material's rheological tests. **Figure 3.** Results of the shear thickening fluid based stemming material's rheological tests.

The hammer recoils upon impact with the STF suspension surface, similar to hitting a true solid interface. It is a suspension of starch powder with a diameter range of 5–20 μm in water. The STF was created using a mixture of mechanical and ultrasonic mixing at a concentration of 55 wt.%. This weight percentage was chosen to preserve a viable solution, while ensuring the shear thickening tendency [33]. According to previous experimental results [34] for 52.5– 55 wt.% corn starch, after the impact of rock falling on the suspension surface, the rock The STF‐based stemming material image and package products are shown in Figure 4. The hammer recoils upon impact with the STF suspension surface, similar to hitting a true solid interface. It is a suspension of starch powder with a diameter range of 5–20 μm in water. The STF was created using a mixture of mechanical and ultrasonic mixing at a concentration The STF-based stemming material image and package products are shown in Figure 4. The hammer recoils upon impact with the STF suspension surface, similar to hitting a true solid interface. It is a suspension of starch powder with a diameter range of 5–20 µm in water. The STF was created using a mixture of mechanical and ultrasonic mixing at a concentration of 55 wt.%. This weight percentage was chosen to preserve a viable solution,

of 55 wt.%. This weightpercentage was chosen to preserve a viable solution, while ensuring the shear thickening tendency [33]. According to previous experimental results [34] for 52.5–

recoiled, similar to hitting a true solid interface.

recoiled, similar to hitting a true solid interface.

while ensuring the shear thickening tendency [33]. According to previous experimental results [34] for 52.5–55 wt.% corn starch, after the impact of rock falling on the suspension surface, the rock recoiled, similar to hitting a true solid interface. *Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 6 of 20

**Figure 4.** (**a**) Shear thickening fluid‐based stemming material image and (**b**) package products**. Figure 4.** (**a**) Shear thickening fluid-based stemming material image and (**b**) package products.

#### *2.2. Overview of the Blast Hole Pressure Measurements 2.2. Overview of the Blast Hole Pressure Measurements*

In blasting, stemming constrains the blasting pressure in the blasting hole, leads to crack propagation through the behavior inside the blasting hole under the explosive pressure, and ultimately plays an importantrole in crushing the rock. Therefore, the behavior and control of the explosive pressure acting on the blast hole are important for effective blasting. Laboratory‐ and field‐scale experiments were conducted to measure the pressure in‐ In blasting, stemming constrains the blasting pressure in the blasting hole, leads to crack propagation through the behavior inside the blasting hole under the explosive pressure, and ultimately plays an important role in crushing the rock. Therefore, the behavior and control of the explosive pressure acting on the blast hole are important for effective blasting.

side the blast hole. However, because the sensor that measures the pressure inside the blast hole is expensive, there is a risk of failure owing to a strong impact. Therefore, the explosive pressure is measured using a one‐time polyvinylidene fluoride (PVDF) sensor [35] or by drilling a dummy hole [36]. In this study, instead of using a one‐time sensor or drilling a dummy hole to measure Laboratory- and field-scale experiments were conducted to measure the pressure inside the blast hole. However, because the sensor that measures the pressure inside the blast hole is expensive, there is a risk of failure owing to a strong impact. Therefore, the explosive pressure is measured using a one-time polyvinylidene fluoride (PVDF) sensor [35] or by drilling a dummy hole [36].

the pressure inside the blast hole, nylon tubes and water pressure measurement sensors that can be used multiple times were employed. Thus, the pressure generated by blasting was measured in the blasting hole without sensor damage or additional drilling. In this study, instead of using a one-time sensor or drilling a dummy hole to measure the pressure inside the blast hole, nylon tubes and water pressure measurement sensors that can be used multiple times were employed. Thus, the pressure generated by blasting was measured in the blasting hole without sensor damage or additional drilling.

#### *2.3. Assessment for Rock Fragmentation of Bench Blasting 2.3. Assessment for Rock Fragmentation of Bench Blasting*

In this study, full‐scale bench blasting was performed for each stemming material (sand or STF), and an image‐based blast fragmentation method was applied to compare and evaluate the performance of each stemming material. In this study, full-scale bench blasting was performed for each stemming material (sand or STF), and an image-based blast fragmentation method was applied to compare and evaluate the performance of each stemming material.

Sieving or screening is a direct and accurate method for evaluating the size distribution of particles or their fragmentation. This method is feasible for small‐scale blasts or opera‐ tions; however, it is costly and time‐consuming. Rock fragments are screened through sieves of different mesh numbers for different fragment sizes, and the screened fragments are grouped based on their size. The nature of the blast was predicted by counting the number of fragments of each size [37]. Sieving or screening is a direct and accurate method for evaluating the size distribution of particles or their fragmentation. This method is feasible for small-scale blasts or operations; however, it is costly and time-consuming. Rock fragments are screened through sieves of different mesh numbers for different fragment sizes, and the screened fragments are grouped based on their size. The nature of the blast was predicted by counting the number of fragments of each size [37].

WipFrag is an image analysis system for sizing materials, such as blasted or crushed rocks [38]. It has also been used to measure other materials, such as ammonium nitrate prills, glass beads, and zinc concentrates. WipFrag accepts images from a variety of sources, such as roving camcorders,fixed cameras, images, or digitalfiles.It uses automatic algorithms to iden‐ tify individual blocks and to create an outline "net" using state‐of‐the‐art edge detection. If desired or necessary, manual intervention (editing the image net) can be performed to im‐ prove the fidelity. WipFrag measures a 2D net and reconstructs a 3D distribution using the principles of geometric probability. WipFrag supports two methods: Rossin Rammler and Swebrec. Two parameters were used by Rammler as key performance indicators (KPIs); , known as the characteristic size of the distribution and more specifically D63.2, and , the value of which is the measure of uniformity [39]. Analyzing every fragment in the rock muck WipFrag is an image analysis system for sizing materials, such as blasted or crushed rocks [38]. It has also been used to measure other materials, such as ammonium nitrate prills, glass beads, and zinc concentrates. WipFrag accepts images from a variety of sources, such as roving camcorders, fixed cameras, images, or digital files. It uses automatic algorithms to identify individual blocks and to create an outline "net" using state-of-theart edge detection. If desired or necessary, manual intervention (editing the image net) can be performed to improve the fidelity. WipFrag measures a 2D net and reconstructs a 3D distribution using the principles of geometric probability. WipFrag supports two methods: Rossin Rammler and Swebrec. Two parameters were used by Rammler as key performance indicators (KPIs); *Xc*, known as the characteristic size of the distribution and more specifically D63.2, and *n*, the value of which is the measure of uniformity [39].

pile is fortunately not necessary because it is widely accepted that the mass percentage of frag‐ ments smaller than any given size varies linearly with the fragment size when plotted in the

line can be expressed as in Equation (3).

Analyzing every fragment in the rock muck pile is fortunately not necessary because it is widely accepted that the mass percentage of fragments smaller than any given size varies linearly with the fragment size when plotted in the Rosin–Rammler domain. By measuring only a sufficient number of particles, the slope and intercept of the Rosin–Rammler line can be confidently defined [40]. A Rosin–Rammler line can be expressed as in Equation (3). *Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 7 of 20 ሺሻ ൌ 1 െ exp ቈെ ൬

$$R(X) = 1 - \exp\left[-\left(\frac{X}{X\_c}\right)^n\right] \tag{3}$$

൰

Here, ሺሻ ൌ Cumulative fraction by weight undersize in relation to size *x*

Here,

*R*(*X*) = Cumulative fraction by weight undersize in relation to size *x*. = Size modulus, which defines the characteristic size of the distribution.

*Xc* = Size modulus, which defines the characteristic size of the distribution. = Distribution modulus, which defines the spread of the distribution.

*n* = Distribution modulus, which defines the spread of the distribution. For ሺሻ = 0.5 (i.e., 50% of the fragments passing through the sieve), the value of

For *R*(*X*) = 0.5 (i.e., 50% of the fragments passing through the sieve), the value of *Xc* can be measured as follows: can be measured as follows: ൌ ହ

$$X\_c = \frac{X\_{50}}{0.693^{1/n}}\tag{4}$$

#### **3. Blast Hole Pressure Measurement Experiment 3. Blast Hole Pressure Measurement Experiment**

*3.1. Explosion Pressure Sensor Calibration 3.1. Explosion Pressure Sensor Calibration*

In this study, it was necessary to calibrate the pressure sensor to measure the explosive pressure inside the blast hole. Therefore, prior to this experiment, explosive pressure sensor calibration using water pressure was performed. The explosive pressure sensor was calibrated under the same installation conditions as those of the blasting site. In this study, it was necessary to calibrate the pressure sensor to measure the explo‐ sive pressure inside the blast hole. Therefore, prior to this experiment, explosive pressure sensor calibration using water pressure was performed. The explosive pressure sensor was calibrated under the same installation conditions as those of the blasting site.

Calibration of the explosion pressure sensor was performed by filling the nylon tube connected to the explosion pressure sensor with water, connecting it with a water pump, and pressurizing the pressure port of the explosion pressure sensor under the conditions of 0 MPa, 25 MPa, and 50 Mpa three times each. The average and standard deviation of the results for three calibration tests was 0.984 (±0.0033) Voltage at 0 MPa, 2.98 (±0.0082) Voltage at 25 MPa, and 4.98 Voltage (±0.0144) at 50 MPa. In addition, Nonlinearity was 0.137% FS (Full Scale), and Accuracy was 0.86% FS. The results of the experiments performed are specified in Table 1, and the Voltage to pressure (MPa) correction equation is shown in Figure 5. Calibration of the explosion pressure sensor was performed by filling the nylon tube connected to the explosion pressure sensor with water, connecting it with a water pump, and pressurizing the pressure port of the explosion pressure sensor underthe conditions of 0 MPa, 25 MPa, and 50 Mpa three times each. The average and standard deviation of the results for three calibration tests was 0.984 (±0.0033) Voltage at 0 MPa, 2.98 (±0.0082) Voltage at 25 MPa, and 4.98 Voltage (±0.0144) at 50 MPa. In addition, Nonlinearity was 0.137% FS (Full Scale), and Accuracy was 0.86% FS. The results of the experiments performed are specified in Table 1, and the Voltage to pressure (MPa) correction equation is shown in Figure 5.

**Figure Figure 5. 5.** Explosive Explosive pressure bar calibration results. pressure bar calibration results.

**Table 1.** Results of the Explosion Pressure sensor calibration. **Table 1.** Results of the Explosion Pressure sensor calibration.

#### *3.2. Blast Hole Pressure Measurement System*

The purpose of the experiment was to measure the explosion pressure in a blast hole for each string material and to evaluate the pressure resistance of the stemming material. Conventional sand and STF-based stemming materials were applied to evaluate their resistance capability under explosive pressure. Figure 6 shows the shape of each stemming material. *3.2. Blast Hole Pressure Measurement System* The purpose of the experiment was to measure the explosion pressure in a blast hole for each string material and to evaluate the pressure resistance of the stemming material. Con‐ ventional sand and STF‐based stemming materials were applied to evaluate their resistance capability under explosive pressure. Figure 6 shows the shape of each stemming material.

9 50 4.987

(**a**) Sand stemming material (**b**) STF‐based stemming material

**Figure 6.** Stemming materials used in blast hole pressure measurement experiment. **Figure 6.** Stemming materials used in blast hole pressure measurement experiment.

To measure the explosive pressure data from the blast hole, a pressure meter with cera‐ bar (PMC) model of manufacturer Sensys capable of instantaneous dynamic shock pressure measurement was applied, and the MREL's MicroTrap was used to collect the data and set the detonation time trigger. The hydraulic shock pressure sensor had a pressure measure‐ mentrange of 0–50 MPa. To measure the explosive pressure in the blast hole, the sensor was connected to a nylon tube filled with water using a coupling connector, placed in a watertube. To measure the explosive pressure in the blast hole, the sensor was connected to a nylon tube filled with water using a coupling connector, placed in a water tube. An explosive pressure‐ measuring device through hydraulic pressure was manufactured. Additionally, the manufac‐ tured water tube was protected with an industrial hose made of piezoelectric material to prevent damage when inserted into the blasting hole. Figure 7 shows the measuring tool applied to the blast pressure measuring system in the blast hole through hydraulic pressure. To collect the corresponding explosive pressure data as a time history at the same time as detonation using MicroTrap, a trigger line was attached to the explosion in the blast hole, and the break circuit trigger method was applied in which the connection signal was cut by the detonation of the explosive, and the measurement was finally started. The length of the blast holes drilled for measuring the impact pressure of the stemming To measure the explosive pressure data from the blast hole, a pressure meter with cerabar (PMC) model of manufacturer Sensys capable of instantaneous dynamic shock pressure measurement was applied, and the MREL's MicroTrap was used to collect the data and set the detonation time trigger. The hydraulic shock pressure sensor had a pressure measurement range of 0–50 MPa. To measure the explosive pressure in the blast hole, the sensor was connected to a nylon tube filled with water using a coupling connector, placed in a water tube. To measure the explosive pressure in the blast hole, the sensor was connected to a nylon tube filled with water using a coupling connector, placed in a water tube. An explosive pressure-measuring device through hydraulic pressure was manufactured. Additionally, the manufactured water tube was protected with an industrial hose made of piezoelectric material to prevent damage when inserted into the blasting hole. Figure 7 shows the measuring tool applied to the blast pressure measuring system in the blast hole through hydraulic pressure. To collect the corresponding explosive pressure data as a time history at the same time as detonation using MicroTrap, a trigger line was attached to the explosion in the blast hole, and the break circuit trigger method was applied in which the connection signal was cut by the detonation of the explosive, and the measurement was finally started.

material was 3.2 m, and the explosives charge length was 1 m. The emulsion series Newmite Plus 1 (Φ50 mm, 2.5 kg) manufactured by Hanhwa with an explosion speed of 5700 m/s were applied to the experiment. On top of the explosive, a test stemming material (sand or STF) ment system.

of 0.6 m was applied; a 0.5 m water tube was inserted to measure the pressure caused by the explosion as the water pressure; and in the 1.1 m remaining at the top of the blast hole, general sand stemming was inserted. Figure 8 shows a schematic of the blast hole measure‐

(**c**) Water tube for hydraulic pressure measurement (**d**) Piezoelectric tube for water tube protection

**Figure 7.** Measuring tool applied to blast pressure measuring system. **Figure 7.** Measuring tool applied to blast pressure measuring system.

The length of the blast holes drilled for measuring the impact pressure of the stemming material was 3.2 m, and the explosives charge length was 1 m. The emulsion series Newmite Plus 1 (Φ50 mm, 2.5 kg) manufactured by Hanhwa with an explosion speed of 5700 m/s were applied to the experiment. On top of the explosive, a test stemming material (sand or STF) of 0.6 m was applied; a 0.5 m water tube was inserted to measure the pressure caused by the explosion as the water pressure; and in the 1.1 m remaining at the top of the blast hole, general sand stemming was inserted. Figure 8 shows a schematic of the blast hole measurement system.

**Figure 8.** Schematic of the blast hole measurement system.

(**c**) Water tube for hydraulic pressure measurement (**d**) Piezoelectric tube for water tube protection

**Figure 7.** Measuring tool applied to blast pressure measuring system.

of 0.6 m was applied; a 0.5 m water tube was inserted to measure the pressure caused by the explosion as the water pressure; and in the 1.1 m remaining at the top of the blast hole, general sand stemming was inserted. Figure 8 shows a schematic of the blast hole measure‐

(**a**) Newmite Plus 1 with trigger line (**b**) MREL's MicroTrap

**Figure Figure 8. 8.** Schematic Schematic of the blast hole measurement system. of the blast hole measurement system.

### *3.3. Experimental Results*

ment system.

In this experiment, a hydraulic explosive pressure propagation data measurement system was used to measure the pressure in the blast hole, and a comparative analysis was conducted on the blasting pressure behavior of the sand- and STF-based stemming materials. Table 2 presents the results of the blast hole pressure measurements.

**Table 2.** Result of the explosion pressure measurement in blast hole.

The pressure in the blasting hole is 5.84 MPa for the sand stemming material and 2.80 MPa for the STF-based stemming material. Further, the blasting pressure by sand is two times higher than by STF-based stemming material. This is the pressure transferred to the water tube located above the test stemming material; therefore, a lower measured pressure value means that the loss of explosive pressure in the blast hole due to stemming transfer is lower.

The time taken from detonation to explosion pressure transfer is 12.24 ms in the sand stemming material and 31.82 ms in the STF-based stemming material; the measured value is significantly lower than that of the sand stemming material. This is the explosive pressure transfer time from the lower part of the blasting hole to the upper part of the blasting hole for the explosive detonation of the stemming material. Thus, the longer the measured explosive pressure delay time, the better the ejection resistance. In addition, the duration of the explosive pressure in the blast hole is 16.82 ms when using the sand stemming material and 21.81 ms when using the STF-based stemming material, an improvement of approximately 5 ms. This implies that the explosive pressure acted longer inside the blast hole, as long as the duration of the explosive pressure. Figure 9 shows the time-pressure hysteresis curve inside the blast hole.

**Figure 9.** Time‐pressure hysteresis curve inside the blast hole. **Figure 9.** Time-pressure hysteresis curve inside the blast hole.

### **4. Full-Scale Blasting Experiment**

*3.3. Experimental Results*

**Peak Pressure in Blasting Hole (MPa)**

In this experiment, a hydraulic explosive pressure propagation data measurement sys‐

The pressure in the blasting hole is 5.84 MPa for the sand stemming material and 2.80

The time taken from detonation to explosion pressure transfer is 12.24 ms in the sand

MPa forthe STF‐based stemming material. Further, the blasting pressure by sand is two times higherthan by STF‐based stemming material. This is the pressure transferred to the watertube located above the test stemming material; therefore, a lower measured pressure value means

stemming material and 31.82 ms in the STF‐based stemming material; the measured value is significantly lower than that of the sand stemming material. This is the explosive pressure transfer time from the lower part of the blasting hole to the upper part of the blasting hole for the explosive detonation of the stemming material. Thus, the longer the measured explosive pressure delay time,the betterthe ejection resistance.In addition,the duration ofthe explosive pressure in the blast hole is 16.82 ms when using the sand stemming material and 21.81 ms when using the STF‐based stemming material, an improvement of approximately 5 ms. This implies that the explosive pressure acted longer inside the blast hole, as long as the duration of the explosive pressure. Figure 9 shows the time‐pressure hysteresis curve inside the

that the loss of explosive pressure in the blast hole due to stemming transfer is lower.

**Explosive Pressure Duration in Blasting Hole (ms)**

tem was used to measure the pressure in the blast hole, and a comparative analysis was conducted on the blasting pressure behavior of the sand‐ and STF‐based stemming materi‐

als. Table 2 presents the results of the blast hole pressure measurements.

**Explosive Pressure Arrival Time after Trigger (ms)**

**Table 2.** Result of the explosion pressure measurement in blast hole.

Sand Stemming 5.84 12.24 16.82 STF‐based stemming 2.80 31.82 21.81

> **4. Full‐Scale Blasting Experiment** *4.1. Bench Blasting*

blast hole.

*4.1. Bench Blasting* The aggregate production step comprises blasting, a vibration feeder, a primary crusher, a secondary crusher, belt conveyors, and vibrating screens. The feed size of the jaw crusher operating in the A‐aggregate mine requires a rock fragment size of at least 1000 mm or less. Therefore, to input the jaw crusher for primary crushing, it is necessary to perform secondary work on fragments by hydraulic rock breakers after blasting the rock, which incurs additional The aggregate production step comprises blasting, a vibration feeder, a primary crusher, a secondary crusher, belt conveyors, and vibrating screens. The feed size of the jaw crusher operating in the A-aggregate mine requires a rock fragment size of at least 1000 mm or less. Therefore, to input the jaw crusher for primary crushing, it is necessary to perform secondary work on fragments by hydraulic rock breakers after blasting the rock, which incurs additional costs. Approximately \$25,000 US dollars per month are required to operate large hydraulic rock breakers, and mine A has ten of such equipment. Figure 10 shows the bench blasting design applied to aggregate mine A, and the blasting results are compared by applying sand and STF-based stemming materials to each different bench part. Table 3 lists the main parameters of the full-scale bench blasting experiment. In the blasting experiment, the STF-based stemming was applied to the left part, and general sand stemming was applied to the right part.

part.

costs. Approximately \$25,000 US dollars per month are required to operate large hydraulic rock breakers, and mine A has ten of such equipment. Figure 10 shows the bench blasting design applied to aggregate mine A, and the blasting results are compared by applying sand and STF‐based stemming materials to each different bench part. Table 3 lists the main param‐ eters of the full‐scale bench blasting experiment. In the blasting experiment, the STF‐based stemming was applied to the left part, and general sand stemming was applied to the right

(**b**) Bench section (STF stemming) (**c**) Bench section (sand stemming)

Stemming type ‐ STF or Sand

**Table 3.** Main parameters of the full‐scale bench blasting experiment. **Table 3.** Main parameters of the full-scale bench blasting experiment.

Total charge kg 720 The properties of the rock mass condition can have a significant influence on the frag‐ mentation outcomes of the blast. Rock properties, such as compressive strength, porosity, Young's modulus, Poisson's ratio, and rock fracturing and jointing, can all influence fragmen‐ tation. In this experiment, by performing blasting at the same experimental area, the variation The properties of the rock mass condition can have a significant influence on the fragmentation outcomes of the blast. Rock properties, such as compressive strength, porosity, Young's modulus, Poisson's ratio, and rock fracturing and jointing, can all influence fragmentation. In this experiment, by performing blasting at the same experimental area, the variation in results due to the rock mass condition difference was reduced as much as possible. The type of rock in this quarry mine is gneiss, and the uniaxial compressive strength is approximately 130–160 MPa. The rock density is approximately 2.6 g/cm3 , and the porosity is less than 0.15%. As shown in Figure 11a, a bench slope with a discontinuity direction and similar region was selected as the experimental site. The spacing of the discontinuities was observed to be approximately 1.2–1.5 m each, and they were under completely dry conditions. Figure 11b,c show the resulting image after the blasting. Under the same blasting conditions, the rock fragments in the STF-applied part are generally smaller than in the sand stemming part.

in results due to the rock mass condition difference was reduced as much as possible. The type of rock in this quarry mine is gneiss, and the uniaxial compressive strength is approximately 130–160 MPa. The rock density is approximately 2.6 g/cm3, and the porosity is less than 0.15%. As shown in Figure 11a, a bench slope with a discontinuity direction and similar region was selected as the experimental site. The spacing of the discontinuities was observed to be ap‐ proximately 1.2–1.5 m each, and they were under completely dry conditions. Figure 11b,c show the resulting image after the blasting. Under the same blasting conditions, the rock fragments in the STF‐applied part are generally smaller than in the sand stemming part.

(**a**) Bench slope image of the experimental area

(**b**) Shear thickening fluid stemming (**c**) Sand stemming

**Figure 11.** Bench blasting results obtained by applying different stemming materials. **Figure 11.** Bench blasting results obtained by applying different stemming materials.

#### *4.2. Evaluation of Rock Fragmentation 4.2. Evaluation of Rock Fragmentation*

Muck piles of fragmented rocks were photographed using a single camera from the top surface of the bench and the front. In the images, a reference scale was used for single‐ scale factor analysis by applying a square marker target of 18 cm in width and height. Table 4 shows the image‐based sieving analysis results of the rock fragmentation of the muck pile after full‐scale bench blasting. Figures 12–15 show the analysis of the rock frag‐ ment size distribution. Larger rock fragments are displayed in red in the resulting image. Muck piles of fragmented rocks were photographed using a single camera from the top surface of the bench and the front. In the images, a reference scale was used for single-scale factor analysis by applying a square marker target of 18 cm in width and height. Table 4 shows the image-based sieving analysis results of the rock fragmentation of the muck pile after full-scale bench blasting. Figures 12–15 show the analysis of the rock fragment size distribution. Larger rock fragments are displayed in red in the resulting image.

**Table 4.** Results of rock fragmentation analysis. **Table 4.** Results of rock fragmentation analysis.

Images taken from the top of the bench muck pile are compared. In the bench region to which sand stemming was applied, the characteristic size (*Xc*) for evaluating the fragment size is approximately 2.7 times larger than that in the region to which STF-based stemming material was applied. Moreover, the uniformity index (*n*) for evaluating the particle size distribution of the fragment rocks of the muck pile is 1.66 for the sand stemming region and 1.93 for the STF-based stemming. A higher uniformity index indicates a more uniform distribution of the fragmented rock.

 In the bench region to which sand stemming was applied, the characteristic size (*Xc*) for evaluating the fragment size is approximately 1.3 times larger than that of the region to which the STF-based stemming material was applied; however, the uniformity index shows no significant difference between the two cases. This is expected to affect the uniformity index as a large rock fragment falls to the front of the muck pile after blasting. These large fragments fell from the top of the outermost bench and had relatively little effect on the explosive force. Moreover, it is for this reason that the average fragment size compared, respectively, at the front and top of the bench muck pile image shows a significant difference Similarly, images taken from the front of the bench muck pile are compared. In the bench region to which sand stemming was applied, the characteristic size () for evaluating the fragment size is approximately 1.3 times larger than that of the region to which the STF‐ based stemming material was applied; however, the uniformity index shows no signifi‐ cant difference between the two cases. This is expected to affect the uniformity index as a large rock fragment falls to the front of the muck pile after blasting. These large fragments fell from the top of the outermost bench and had relatively little effect on the explosive force. Moreover, it is forthis reason that the average fragment size compared,respectively, at the front and top of the bench muck pile image shows a significant difference

Images taken from the top of the bench muck pile are compared. In the bench region to which sand stemming was applied, the characteristic size (ሻ for evaluating the frag‐ ment size is approximately 2.7 times larger than that in the region to which STF‐based stem‐ ming material was applied. Moreover, the uniformity index (ሻ for evaluating the particle size distribution of the fragment rocks of the muck pile is 1.66 for the sand stemming region and 1.93 for the STF‐based stemming. A higher uniformity index indicates a more uniform

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 13 of 20

distribution of the fragmented rock.

The WipFrag 3 program automatically generates the histogram graph. The x-axis is a log graph showing the size distribution of the rock fragments. The y-axis is the rate of passing. Large fragments are marked with boxes in Figures 12–15. The size of the large fragments that must be subjected to secondary breaking with a breaker machine before being placed in the jaw crusher line is approximately 1000 mm or more in diameter. When STF is applied as a stemming, the average fragment size decreases, and the number of large fragments that require second breaking work is greatly reduced. The WipFrag 3 program automatically generates the histogram graph. The x‐axis is a log graph showing the size distribution of the rock fragments. The y‐axis is the rate of pass‐ ing. Large fragments are marked with boxes in Figures 12–15. The size of the large fragments that must be subjected to secondary breaking with a breaker machine before being placed in the jaw crusher line is approximately 1000 mm or more in diameter. When STF is ap‐ plied as a stemming, the average fragment size decreases, and the number of large frag‐ ments that require second breaking work is greatly reduced.

(**a**) WipFrag Graph from the top of the muck pile

(**b**) Fragmented rock pile (**c**) WipFrag Net Image

**Figure 12.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench top image of sand stemming case after blasting). **Figure 12.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench top image of sand stemming case after blasting).

(**a**) WipFrag Graph from the top of the muck pile

(**b**) Fragmented rock pile (**c**) WipFrag Net Image (**b**) Fragmented rock pile (**c**) WipFrag Net Image

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 14 of 20

**Figure 13.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench top image of STF stemming case after blasting). **Figure 13.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench top image of STF stemming case after blasting). **Figure 13.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench top image of STF stemming case after blasting).

(**a**) WipFrag Graph from the front of the muck pile

**Figure 14.** *Cont*.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 15 of 20

(**b**) Fragmented rock pile (**c**) WipFrag Net Image (**b**) Fragmented rock pile (**c**) WipFrag Net Image

**Figure 14.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench front image of sand stemming case after blasting). **Figure 14.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench front image of sand stemming case after blasting). **Figure 14.** Rock pile image, contouring, histogram, and cumulative size curve of the fragmented block (bench front image of sand stemming case after blasting).

(**a**) WipFrag Graph from the front of the muck pile

(**b**) Fragmented rock pile (**c**) WipFrag Net Image

(**b**) Fragmented rock pile (**c**) WipFrag Net Image **Figure 15.** Rock pile image, contouring, histogram, and cumulative size curve of fragmented block **Figure 15.** Rock pile image, contouring, histogram, and cumulative size curve of fragmented block (bench front image of STF stemming case after blasting). **Figure 15.** Rock pile image, contouring, histogram, and cumulative size curve of fragmented block (bench front image of STF stemming case after blasting).

#### (bench front image of STF stemming case after blasting). **5. Discussion 5. Discussion**

**5. Discussion** In this study, a material that instantaneously changes from shock load was developed as a blast stemming material and its performance was verified. Then, the pressure in the upper part of the stemming area was directly measured inside the blast hole. There are lim‐ ited case studies that directly measure the pressure in the blast hole during bench blasting. In this study, a material that instantaneously changes from shock load was developed as a blast stemming material and its performance was verified. Then, the pressure in the upper part of the stemming area was directly measured inside the blast hole. There are lim‐ ited case studies that directly measure the pressure in the blast hole during bench blasting. In this study, a material that instantaneously changes from shock load was developed as a blast stemming material and its performance was verified. Then, the pressure in the upper part of the stemming area was directly measured inside the blast hole. There are limited case studies that directly measure the pressure in the blast hole during bench blasting.

Previous research showed that stemming could increase the action time of the dynamic gas pressure in the blast hole and the efficiency of the explosives, reducing explosive consumption, as shown in Figure 16 [5,6]. Figure 16 depicts the time–pressure concept curves according to the stemming condition. In cases of missing or improper stemming, the pressure rapidly attenuates in the blast hole (Figure 16a), but proper stemming can increase the action time of the detonation gas inside the blast hole (Figure 16b). It is estimated that the shock pressure in the blast hole could be sustained for a longer time compared with that in the sand cases owing to the unique characteristics of STF. This is because STF is a smart-fluid type exhibiting an intense viscosity jump when subjected to loading. Previous research showed that stemming could increase the action time of the dynamic gas pressure in the blast hole and the efficiency of the explosives, reducing explosive con‐ sumption, as shown in Figure 16 [5,6]. Figure 16 depicts the time–pressure concept curves according to the stemming condition. In cases of missing orimproper stemming, the pressure rapidly attenuates in the blast hole (Figure 16a), but proper stemming can increase the action time of the detonation gas inside the blast hole (Figure 16b). It is estimated that the shock pres‐ sure in the blast hole could be sustained for a longertime compared with that in the sand cases owing to the unique characteristics of STF. This is because STF is a smart‐fluid type exhibit‐ ing an intense viscosity jump when subjected to loading. Previous research showed that stemming could increase the action time of the dynamic gas pressure in the blast hole and the efficiency of the explosives, reducing explosive con‐ sumption, as shown in Figure 16 [5,6]. Figure 16 depicts the time–pressure concept curves according to the stemming condition. In cases of missing orimproper stemming, the pressure rapidly attenuates in the blast hole (Figure 16a), but proper stemming can increase the action time of the detonation gas inside the blast hole (Figure 16b). It is estimated that the shock pres‐ sure in the blast hole could be sustained for a longertime compared with that in the sand cases owing to the unique characteristics of STF. This is because STF is a smart‐fluid type exhibit‐

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 16 of 20

**Figure 16.** Concept curves of pressure and time: (**a**) without stemming, and (**b**) with stemming. **Figure 16.** Concept curves of pressure and time: (**a**) without stemming, and (**b**) with stemming. (**a**) without stemming (**b**) with stemming

Figure 17 shows the time–pressure results according to the direct measurement of blast hole pressure, where sand‐ or STF‐stemming materials were applied in each experiment. Since the pressure was measured at the upper part of the stemming area, a lower measured peak pressure transmits enough energy to the rock mass around the blast hole and below the stem‐ ming area. Stage I indicates detonation durations. When the shock front arrives at the gauge point, the gauge outputs a peak pressure. Stage II indicates the pressure variation as detona‐ tion propagates from gauge point to blast hole. Note that during this time, the stemming ma‐ terial begins initial ejection from the blast hole. Finally, in stage III the pressure curve rapidly decreases to atmospheric pressure when the stemming part is completely ejected. Figure 17 shows the time–pressure results according to the direct measurement of blast hole pressure, where sand- or STF-stemming materials were applied in each experiment. Since the pressure was measured at the upper part of the stemming area, a lower measured peak pressure transmits enough energy to the rock mass around the blast hole and below the stemming area. Stage I indicates detonation durations. When the shock front arrives at the gauge point, the gauge outputs a peak pressure. Stage II indicates the pressure variation as detonation propagates from gauge point to blast hole. Note that during this time, the stemming material begins initial ejection from the blast hole. Finally, in stage III the pressure curve rapidly decreases to atmospheric pressure when the stemming part is completely ejected. **Figure 16.** Concept curves of pressure and time: (**a**) without stemming, and (**b**) with stemming. Figure 17 shows the time–pressure results according to the direct measurement of blast hole pressure, where sand‐ or STF‐stemming materials were applied in each experiment. Since the pressure was measured at the upper part of the stemming area, a lower measured peak pressure transmits enough energy to the rock mass around the blast hole and below the stem‐ ming area. Stage I indicates detonation durations. When the shock front arrives at the gauge point, the gauge outputs a peak pressure. Stage II indicates the pressure variation as detona‐ tion propagates from gauge point to blast hole. Note that during this time, the stemming ma‐ terial begins initial ejection from the blast hole. Finally, in stage III the pressure curve rapidly decreases to atmospheric pressure when the stemming part is completely ejected.

**Figure 17.** The time–pressure curves of the experimental results according to sand or shear thicken‐ ing fluid (STF) stemming. **Figure 17.** The time–pressure curves of the experimental results according to sand or shear thickening fluid (STF) stemming.

In the case of STF-based stemming, the pressure attenuates more slowly than in the sand stemming case. The pressure acts approximately 5–10 ms longer than the blasting gas pressure for the STF-based stemming than for the sand stemming. Eloranta et al. [41] verified that 1 ms of increased gas retention time in a blast hole increased the fragment work done on the rock mass and reduced waste energy. Therefore, an increase in the gas retention time of approximately 5 ms has a significant impact on rock fragmentation. pressure for the STF‐based stemming than for the sand stemming. Eloranta et al. [41] veri‐ fied that 1 ms of increased gas retention time in a blast hole increased the fragment work done on the rock mass and reduced waste energy. Therefore, an increase in the gas reten‐ tion time of approximately 5 ms has a significant impact on rock fragmentation. The purpose of stemming is to increase blasting efficiency by extending the duration

In the case of STF‐based stemming, the pressure attenuates more slowly than in the sand stemming case. The pressure acts approximately 5–10 ms longer than the blasting gas

The purpose of stemming is to increase blasting efficiency by extending the duration of the explosion gas and forming more cracks in the crushing area. Therefore, the ability to resist the gas pressure emitted in the direction of the blast hole inlet implies the stemming performance, which is directly related to the blast efficiency. In this study, after crushing and cracking under the effect of detonation, the pressure applied to the elastic area was measured using a water pressure sensor from a nylon tube inserted into the water tube, and the pressure acting in the elastic area was measured, as shown in Figure 18. of the explosion gas and forming more cracks in the crushing area. Therefore, the ability to resist the gas pressure emitted in the direction of the blast hole inlet implies the stemming performance, which is directly related to the blast efficiency. In this study, after crushing and cracking under the effect of detonation, the pressure applied to the elastic area was measured using a water pressure sensor from a nylon tube inserted into the water tube, and the pressure acting in the elastic area was measured, as shown in Figure 18.

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 17 of 20

**Figure 18.** Schematic of the measured pressure wave in the blast hole. **Figure 18.** Schematic of the measured pressure wave in the blast hole.

Therefore, the pressure behavior in the blast hole owing to the explosive detonation measured through the hydraulic pressure measurement sensor is the pressure value at which the pressure ejected to the upper part of the blast hole by the explosion is attenuated by the stemming material and not by the direct blast pressure. The low peak pressure measured by the hydraulic sensor implies that the stemming material has an excellent pressure con‐ straint against the explosive pressure ejected to the upper part of the blast hole. This suggests that the explosive pressure applied to the lower part of the blast hole is high. In addition, be‐ cause the explosive pressure delay time measured by the hydraulic pressure sensor is from the trigger to the pressure wave measurement, the longer the delay time from the detonation to the pressure measurement, the more continuous the pressure behavior of the stemming material under the blast hole. Finally, the time at which the explosion pressure returns to at‐ mospheric pressure after the increase indicates the duration of the explosive pressure in the Therefore, the pressure behavior in the blast hole owing to the explosive detonation measured through the hydraulic pressure measurement sensor is the pressure value at which the pressure ejected to the upper part of the blast hole by the explosion is attenuated by the stemming material and not by the direct blast pressure. The low peak pressure measured by the hydraulic sensor implies that the stemming material has an excellent pressure constraint against the explosive pressure ejected to the upper part of the blast hole. This suggests that the explosive pressure applied to the lower part of the blast hole is high. In addition, because the explosive pressure delay time measured by the hydraulic pressure sensor is from the trigger to the pressure wave measurement, the longer the delay time from the detonation to the pressure measurement, the more continuous the pressure behavior of the stemming material under the blast hole. Finally, the time at which the explosion pressure returns to atmospheric pressure after the increase indicates the duration of the explosive pressure in the blast hole. This suggests that, the longer the duration of the explosive pressure, the longer the crack propagation time owing to the gas pressure behavior in the blast hole.

blast hole. This suggests that, the longer the duration of the explosive pressure, the longer the crack propagation time owing to the gas pressure behavior in the blast hole. The measured pressure behavior in the blast hole correlates with the resistance char‐ acteristics of the stemming material. It is judged that the STF‐based stemming material will effectively achieve the purpose of the stemming material by resisting the blasting The measured pressure behavior in the blast hole correlates with the resistance characteristics of the stemming material. It is judged that the STF-based stemming material will effectively achieve the purpose of the stemming material by resisting the blasting pressure and maintaining relatively high pressure in the blast hole for a longer time compared to the conventional sand stemming material.

pressure and maintaining relatively high pressure in the blast hole for a longer time com‐

pared to the conventional sand stemming material.