Explicit dynamics based numerical simulation approach for assessment of impact of relief hole on blast induced deformation pattern in an underground face blast

The exploitation of geo-resources is dominantly done using drilling and blasting. The breakage of rock mass by blasting has many challenges. The optimal breakage in an underground development face/tunnel blast is dependent on the relief area provided to the blast holes. This paper has discussed the impact of the number and diameter of the relief holes on the breakage pattern of the rock. The numerical simulation with varying numbers and diameter of relief hole was carried out for this purpose. The isosurface output from numerical simulation was plotted. The plot was used to compare the extent of deformation under varying conditions of relief holes. The analysis shows that the higher number of relief holes with optimum diameter gives more controlled deformation than single relief hole with larger diameter. The nearfield vibrations were also recorded by placement of seismographs. The waveform analysis of the recorded vibration was carried out. The redesigning of the blasting pattern was done using the results of numerical simulation and waveform analysis. The redesigned pattern consists of four relief holes of 115 mm diameter. It was found that the number of cut blast holes firing simultaneously should not be more than two in order to get the optimum breakage for the modelled condition. The blasting output with the revised design has resulted into the considerable improvements in the pull and reduction of overbreak. The revised pattern has addressed the issues of the socket formation at the site. The manuscript covers numerical simulation based approach for assessment of blast induced deformation in an underground face blast under different variations of diameter and numbers of relief holes. The numerical simulation based output reveals that the blast face shows more controlled deformation while using multiple number of relief holes of optimum diameter as compared to a single large daimeter relief hole. The numerical simulation output in this paper has been used to redesign the blasting pattern of the face blast of a Lead-Zinc underground mine. The manuscript covers numerical simulation based approach for assessment of blast induced deformation in an underground face blast under different variations of diameter and numbers of relief holes. The numerical simulation based output reveals that the blast face shows more controlled deformation while using multiple number of relief holes of optimum diameter as compared to a single large daimeter relief hole. The numerical simulation output in this paper has been used to redesign the blasting pattern of the face blast of a Lead-Zinc underground mine.


Introduction
The exploitation of mineral resources by underground needs the development of drives/drivages. These drivages works as the access to the orebody from the main access (shaft or decline) of the mine. The excavation in tunnel or drives of an underground metal mine is dominantly performed by drilling and blasting technique. The controlled blasting technique is practiced to optimise the blast induced deformation. The higher extent of deformation in rock strata is termed as overbreak. This overbreak leads to the irregular profile of the tunnel. On the other hand, blast designers also pose the problems of under breakage along the direction of excavation. This results in to the pull reduction and socket formation. The optimal rock breakage aims to maximize the pull and minimize the overbreak from the blast. The optimisation needs site specific investigations relating the geotechnical parameters of the rock mass. Bieniawski (1968) suggested that the study of fracture propagation characteristic of rock can lead to improve the efficiency of rock breaking using drilling and blasting.
The excavation in drivages of underground metalliferous mine dominantly follows the Burn-Cut pattern. This pattern has a set of cut holes containing empty (relief) as well as blast holes. Since the tunnel/drive excavation has free face along the single direction as compared to two free faces in case of bench blasting, the optimum explosive energy utilisation in the face blast requires additional free face (Murthy and Dey 2002;Verma et al. 2018). This requirement is accomplished by drilling the relief holes, which are kept uncharged during the process of blasting. Accordingly, the dimension of relief holes including its diameter, depth and the area of relief plays significant role in achieving the optimum rock breakage due to blasting (Singh 1995). However, the optimum relief hole dimension for a blast face is a function of rock mass properties, explosive properties, presence of geological discontinuities etc. Accordingly, the assessment of breakage pattern in a burn cut face blast with respective rock and explosive combinations will provide an idea for the optimum relief hole dimension. Sharma (2005) studied the impact of multiple relief holes on the breakage pattern of a face blast. Author found that the multiple relief holes in place of a single large diameter relief hole are more relevant in order to prevent freezing in the spongy rock mass (Sharma 2005;Allen 2014).
The pattern of induced deformation during burn cut face blasting would vary depending on the rock mass properties. The dominant rock mass properties which influences the deformation pattern includes dynamic compressive strength, dynamic tensile strength, elastic modulus, poison's ratio etc. Verma et al. (2016) found that the ultrasonic wave velocities are also important parameter influencing the strata requirement for detonation velocity of explosive. The development blast faces of the underground metalliferous mines are also under the influence of insitu stresses. These insitu stresses also have impact on the damage pattern of a face blast. Researchers have explained that the prestressed strata are prone to show higher magnitude of overbreak under similar explosive loading condition (Mandal and Singh 2009;Abdel-Meguid et al. 2003;Xiao et al. 2019). Mandal and Singh (2009) emphasized to do excavations in small sections and phases in order to minimize overbreak and reduce peripheral damages under highly stressed strata conditions. Verma et al. (2014) found that the presence of geological discontinuities also has impact on excavation profile of a face blast. The explosive parameters also influence the induced damage due to blasting. Researchers such as Mandal et al. (2005), Bullock and Rostami (2013), Himanshu et al. (2021a), Singh (2018, Vishwakarma et al. (2020) etc. discussed the impacts of detonation velocity, energy of explosive and accuracy of delay detonators on blasting outputs.
Various researchers have used statistical and numerical approach for predictions of blast induced damages. Statistical algorithms such as-neural network, genetic algorithms, colony optimisation algorithm, random decision tree, particle swarm optimisation, support vector machine etc. has been used extensively for prediction of blasting outputs under different scenarios (Rezaeineshat et al. 2020;Saghatforoush et al. 2016;Monjezi et al. 2010;Kumar et al. 2021;Zhang et al. 2020;Hasanipanah et al. 2015). These statistical algorithms are based on the data analysis for the experimental blasts carried out at the site. The numerical models however have advantage of simulating the rock mass conditions of the site with specific parametric condition. The parameters in the numerical models can be explicitly distinguished. The respective blasting outputs with the variation of any parameter can be recorded using this approach.
Researchers such as Himanshu et al. (2021b), Xia et al. (2021), Das and Singh (2021) Pan et al. (2021), Wang et al. (2018), Onederra et al. (2013), etc. have used numerical simulation approach for assessment of blast induced damages under various conditions. Mitelman and Elmo (2014) have used a hybrid finite discrete element based modelling for predicting damage induced by blasting in tunnelling operation. Xu et al. (2015) predicted blast induced rock fracture near a tunnel using numerical simulation.

Explicit dynamics
The explicit dynamics solver has been used for the numerical simulation in this study. The solver uses the Central Difference Time Integration scheme for computation of nodal acceleration. In this solver, the forces are computed at the nodes (resulting from internal stress, contact, or boundary condition), and the nodal acceleration are derived by dividing forces by mass. Once the nodal acceleration is determined, the nodal velocity and displacement at a time is further computed using integration. The dynamic loading condition has been simulated in this study. The material subjected to dynamic/high impact loading shows non-linear behaviour. In implicit modeller, the non-linear equations are solved by converting it as linear approximation using Newton-Raphson method. Accordingly, the iterations are required in each time step to achieve convergence. However, the non-linear equations are uncoupled in explicit solvers. So, no iteration or convergence check in each time step is required in such case. Accordingly, the explicit solver is more efficient for solving non-linear equations from high impact loadings. Hence, this solver has been used in this study.

Experimental site details
The outcomes of the numerical simulation were used to redesign the face blasting pattern of an experimental site. The site was located at Rajpura Dariba mine. The physico-mechanical properties of the rocks were also tested for the same mine. The mine is located in the southern extremity of Rajpura-Dariba Bethunmi metallogenic belt in Rajsamand district of Rajasthan state of India.
Dariba-Bethumni metallogenic belt comprises an assemblage of medium to high grade metamorphic equivalents of orthoquartzites, carbonates and carbonaceous facies rocks belonging to Bhilwara super group. This cover sequence is underlain by basement rocks (gneisses and schist) of Mangalwar Complex. The Lead-Zinc mineralisation occur in this belt in various sizes and grades. The orebody mainly contains calc-silicate bearing dolomite and graphite mica schist horizons. The geological map of Dariba-Bethumni metallogenic belt is shown in Fig. 1 (Sugden et al. 1990;Gupta et al.1995;Mishra et al. 2006).
The mine area mainly constitutes a sequence of meta-sediments consisting of mica schist, calcareous biotite schist and graphite mica schist (from footwall to hangingwall). Calc-silicate bearing dolomite occurs within the graphite mica schist horizon towards its contact with the calcareous biotite schist.

Existing face blasting method of the experimental site
The development face blasting at the experimental site is carried out to make drivages and cross-cuts. The drivages are made in the contact of the ore body to have the initial access to the ore body. Cross-cuts are usually driven across the ore body.  Sugden et al. 1990;Gupta et al, 1995;Mishra et al. 2006) properties are shown in The ends of the specimens were flattened and the sides of the specimen were smoothened. The diameter of the specimen was measured to the nearest 0.01 mm and used for calculating the cross-section area. The height of the specimen was determined to the nearest 0.01 mm. In case of uniaxial compressive strength testing, the load on the specimen was applied continuously at a uniform loading rate such that failure occurred within 5-10 min of loading. Alternatively, the loading rate was within the limit of 0.5-1.0 MPa/ sec. Tensile Strength of rock samples was analyzed by the indirect Brazilian Tensile Strength investigation as per IS: 10,082-1981 norms (Bureau of Indian Standard, 1981). The numerical models with varying relief hole diameter as 40 mm, 70 mm, 89 mm, 105 mm and 165 mm were prepared. The diameter of the charged blast holes was kept 40 mm in each case. The number of relief holes were varied as-one relief hole, two relief holes, three relief holes and four relief holes. A view of arrangement of cut holes (including relief holes (R) and blast holes) is shown in Fig. 2. The explosive materials were modelled as detonation products in numerical simulation. Jones-Wilkins-Lee (JWL) Equation of State (EOS) is a dominant constitutive model used for the detonation products. So, JWL EOS was used for the explosives in the numerical models (Castedo et al. 2018;Artero-Guerrero et al 2017;Hu et al 2015;Pramanik and Deb 2015;Sanchidran and Lopez 2006). This EOS is represented as a relation among pressure, volume and energy. The expression for JWL EOS is shown in equation I.
where A, B, R1, R2 and x are constants.P = pressure.V = Volume.E = Energy. The JWL EOS parameters for the explosive have been used in the model from the literature. Cylindrical tests are done to evaluate the parameters of JWL EOS (Davis and Hill 2001). The parameters of this EOS used in the numerical model is given in Table 2.
Sand was used as the stemming material in the numerical model. The physical properties of ''Sand'' was taken from the library of Ansys software (Ansys Autodyn Manual v 18.0).
The explicit dynamics numerical simulation module consists of Lagrange and Euler domain. In simulation consisting of different materials, solid part unlike ore/rock is modelled under Lagrange domain. The fluid or gaseous part is modelled under Euler domain. Explosive and stemming materials were modelled under Euler domain in this numerical model.
Fixed support and impedance boundary conditions were used in this numerical model. Fixed support conditions were imposed to restrict the deformation within the modelled volume. The reflection/refraction of incoming blast waves were restricted by providing impedance boundary condition. These boundary conditions were provided in all the faces of the modelled block except the free face.

Analysis of the numerical simulation results
The combinations of blast holes and cut holes in the cut portion of the burn-cut pattern were varied in different numerical models. The deformation pattern under different conditions were plotted and compared to get the optimised pattern. The trend of variation in deformation under different parametric combinations have been studied. The deformation pattern recorded as the model output reflects only tensile deformation against the relief holes. The plot of maximum principal elastic strain from a model output is shown in Fig. 3. The analysis of maximum principle elastic strain of the rock under blast loading shows that the tensile strain is developed only along the relief holes. This is because the stress wave due to blasting propagates from the detonation point to free face, which is along stemming portion and along relief hole. The propagating stress wave in such case is compressive in nature. The stress wave gets reflected from free face under tension. Since the compressive strength of the rock mass is much larger than the tensile strength, the deformation within the rock mass takes place along tension.
The actual blasting of the cut holes includes delay sequence among the holes. However, the simulation with field delay timing in explicit dynamics is not possible. Hence, the blast holes were allowed to be fired simultaneously in the model.
The output deformation pattern from the model was analysed in terms of the pull achieved and the overbreak. The comparative deformation contour along the pull and periphery of the cut holes for two different conditions of relief holes is shown in Fig. 4.
The comparison reveals that there is minimal deformation along pull as well as periphery direction in the burn cut pattern having relief holes of 40 mm diameter as compared to the pattern having relief holes of 165 mm diameter. The deformation contour was plotted along with the scale and the attempt was made to assess the extent of deformation. However, it was  realised that the plotted contour doesn't include all the area that has been deformed. The plot will show no deformation, even if there is deformation in the model but the magnitude of deformation is less than the second lowest value in the contour band. Isosurface of zero-deformation was plotted to address this issue. An Isosurface is a surface that represents points of constant value within a volume of space. Isosurface plots of non-deformed zones for burn cut face blast with four relief holes of different diameter is shown in Fig. 5. The comparison of the void spaces in the plot shows that the extent of deformation increases with increment in the diameter of the relief holes.
To further investigate the exact extent of breakage under different conditions, capped isosurfaces of zero deformation were plotted. The capped isosurface is the isosurface with capping on the void portion. The capped isosurface for all the parametric conditions were plotted along explosive charging and periphery of blast holes' directions. The analysis of capped isosurface along explosive charging direction suggests that the complete deformation in the rock mass upto charge length doesn't takes place when the relief hole diameter is 40 mm. The complete deformation is observed under all other conditions with different relief hole diameter. The comparative isosurface plot along explosive charging direction with the assessment of deformation extent under two different conditions is shown in Fig. 6.
The capped isosurface has also been plotted to investigate the extent of damage along the periphery of the cut blast holes. The plotted isosurface under different variations of relief holes is shown in Fig. 7. The extent of deformation from the plot has been   40 mm, shows the uniform deformation along blast holes as well as relief holes. This is due to the same free face provided by relief holes as well as charged holes in stemming portion. The figure shows that the tensile stress wave produces deformation at much larger extent when the diameter of relief holes is 165 mm.
The analysed extent of deformation under different variants of relief holes is shown in Fig. 8. The comparison suggests that the extent of deformation increases with the increment in the number and diameter of relief holes. The figure also suggests that the extent of deformation is larger in case of a single large relief hole than using multiple relief holes of smaller diameter. Accordingly, it can be concluded that after achieving the complete pull from the burn cut face blast, multiple numbers of smaller diameter relief holes will give more controlled deformation than the single large diameter relief hole. Jimeno et al. (1995) have also drawn similar conclusion. Authors suggested the equivalent diameter for the group of relief holes. The equivalent diameter is computed using equation II. The plot of extent of deformation in rock mass with the equivalent diameter of relief holes is shown in Fig. 9. The plot shows that the parameters are related with correlation coefficient of 0.76.
where D eq = equivalent diameter of relief hole.n = number of relief holes.D = diameter of relief holes. Further, the maximum magnitude of deformation occurred in the rock mass under different conditions has also been compared. The trend of maximum deformation under different conditions is shown in Fig. 10. The trend shows that the magnitude of deformation increases with the increment in the number and diameter of relief holes. The increment trend is sharper for the case of increase in the diameter of relief holes as compared to that of the numbers of relief holes.

Redesigning of blasting pattern using simulation results
The existing burn-cut blast design pattern practiced at the study site was redesigned using the simulation results. View of a development face blast of the study site is given in Fig. 11. The existing pattern consists of 56 charged blast holes of 40 mm diameter with 04 relief holes of 89 mm diameter. There were issues of socket formation as well as overbreak from the face blast at the site. The existing drilling and delay pattern practiced at the mine is shown in Fig. 12. The identification of sockets was done to investigate the cause of its formation. The most of the sockets were in the holes nearby of the cut portion, which reveals that there was overbreak while blasting of the cut portion. This overbreak might have caused to restrict the detonation of the nearby charged blastholes, which have resulted into the socket formation. The extent of damage output from the numerical model has been compared to estimate the optimum cut blasting pattern to reduce the deformation. The extent of deformation output from the numerical model is due to simultaneous detonation of thirteen blast holes. The numerical simulation with the practical delay timing is not possible with Ansys-Explicit Dynamics module. Hence, the simultaneous detonation was provided in the model to all the cut blast holes. Based on the dependency of rock breakage on critical peak particle velocity (Holmberg and Persson 1978), the blast induced deformation can be considered proportional to the maximum charge weight per delay. Accordingly, the deformation while firing of two blastholes of cut simultaneously will be 1/6.5th of that of the simulation results. The extent of deformation using this computation for firing of two cut holes simultaneously against four relief holes of 115 mm diameter will be 2.4 square meter. Accordingly, the deformation will be 0.1 m more than the cut boundary extent using this pattern. Hence, this pattern can be considered as optimum for the blasting face of the study site. The nearfield vibrations were monitored for the experimental blasts at the site by placement of seismographs. The waveform analysis of recorded near field vibration data has been carried out to explore the possibility of design modifications for reduction of overbreak. The recorded waveform for an experimental development face blast is shown in Fig. 13. The analysis of the recorded waveform shows two sharp peaks of vibration. One peak is due to the blast of cut holes and another peak is due to the blast of perimeter holes. The vibration peaks have been compared with the face blasting pattern shown in Fig. 12. The peak due to the blast of cut holes is due to firing of four cut holes simultaneously against the insufficient free face generated by relief holes of 89 mm diameter. The peak due to firing of perimeter holes can be considered as the main reason behind the overbreak due to the blast. The review of the existing blast design reveals that the number of holes blasted at delay no. 21 and 22 is 16 and 15 respectively, which is much larger to increase the charge weight per delay thereby increasing The increased level of vibration will result into enhanced over break. So, the design was modified to distribute the delay sequence such that the charge weight per delay along periphery holes should be reduced. The revised blast design based on the results of waveform analysis and numerical simulation is shown in Fig. 14. The blast design consists of four relief holes of 115 mm diameter. The firing of only two cut blast holes simultaneously was suggested in the revised blast design. However, maximum 8 blast holes were suggested to be fired in the blast design, thereby reducing the maximum charged weight per delay by half. The results of the experimental trials under existing and revised blast design patterns were compared. The comparison has also been made with variations in numbers of relief holes. A view of the cut blast face with three and four numbers of relief holes is shown in Fig. 15. The relief hole diameter was varied as 89 mm and 115 mm. Altogether twenty blasts were conducted to compare the results. The blasting outputs under different conditions is shown in Table 3. The outcomes have been measured in terms of pull achieved and overbreak generated. The results show that there are considerable improvements in the pull and reduction of socket formation while using four relief holes of 115 mm diameter. Although, the overbreak generation is mainly influenced by the charging pattern in periphery holes. But, the controlled movement of the face after blast of each cut also contributes in the overbreak reduction. Accordingly, the revised pattern has also addressed the issues of overbreaks.
The resulting nearfield vibration has also been reduced with the revised blast design. The waveform of nearfield vibration recorded at a distance of 30 m from the blast face with the revised blast design is shown in Fig. 16. The analysis shows that the  Fig. 13. The waveform analysis also reveals that the variation in magnitude of vibration while blasting of different cuts is relatively uniform. This leads to the controlled deformation of the rock mass.

Conclusions
The number and diameter of relief holes plays pivotal role in blast induced deformation pattern of a burn cut blast. The relief hole works as the free face to ensure tensile breakage of the rock mass under the blast loading. Numerical simulation and analysis of parametric response for different combinations of relief holes is capable of optimising the burn cut blast design Fig. 13 Recorded waveform for the experimental blast featuring the delay timings of the blast holes pattern. Accordingly, the numerical simulation approach with finite element based modeller Ansys-Explicit dynamics was used in this study. The deformation prediction under different scenario has been made for a lead-zinc mine site. The model was simulated for blast of cut holes with different relief hole combinations. The model was provided with isotropic elastic rock mass condition. The explosive parameters were modelled under JWL equation of state. The model result shows that the deformation in rock increases with the increment in the number and diameter of the relief holes. The comparative analysis of the deformation shows that the larger number of relief holes with small diameter gives more controlled deformation than the single relief hole of large diameter. The numerical modelling based output has been used to redesign the existing blast design of the experimental site. The assessment of extent of deformation from numerical modelling shows that the four number of relief holes with diameter of 115 mm is optimum for the modelled rock mass condition. The number of cut blast holes firing simultaneously should not be more than two in order to get the optimum breakage. The waveform analysis of the recorded nearfield vibrations from experimental site was also carried out. Two dominant peaks of vibration were observed in the recorded waveform. The peaks were due to the blasts of cut holes and periphery holes. The peak in cut blast hole region is due to the insufficient movement of rock mass under four relief holes of 89 mm diameter. The peak due to blast of periphery holes is because of larger number of blast holes firing at a delay. The blast design pattern was revised based on the results of numerical simulation and waveform analysis. The overbreak reduction has been achieved using the revised blast design pattern. The issues of socket formation have also been addressed with the revised pattern.
The methodology used in this paper can be used to optimise blast design parameters for a face/tunnel blast. Since, the blasting output is strata dependent, the numerical simulation can be a useful tool to give the insight about the optimum blast design for a face/tunnel blast.