This study establishes a multiple degrees-of-freedom structural dynamics analytical model to analyse the influence mechanism of different factors on blasting tight bottom and shape of muckpile. The structural displacement response and distribution of internal forces in the bench rock mass are analysed based on several factors including blasting parameters, explosion load, initiation condition, and geological condition. In addition, the structural failure characteristics of the bench rock mass are studied based on a rock strength criterion. The results indicate that the explosive load strength determines the internal forces of the bench rock mass. The use of blasting parameters with large borehole spacing and small row spacing can increase the internal force and deformation of the bench rock and enhance the effect of the breaking and throwing of rock mass. In addition, the strengthening of the lithology of the bottom rocks or weakening of the lithology of the middle rocks can make destroying the bottom rock mass more difficult and increase the probability of blasting tight bottom formation. Adjusting the initiation point to below the weak-lithology segment of the bench can enhance the internal force and displacement of the bottom rock mass, to improve the blasting effect and avoid blasting tight bottom formation. Combined with the bench blasting field test of the Changjiu limestone mine, it verifies the results of the theoretical analysis of the bench blasting rock mass destruction based on structural dynamics. The results can be used as the theoretical basis and technical support for improving the bench blasting effect.
In-situ stress significantly affects rock blast damage but there is a paucity of quantitative assessments of damage evolution in rocks affected by confining pressure. The present paper analyses the effect of envelope pressure on blast-induced rock damage through theoretical analysis and numerical simulations. Damage clouds obtained from numerical simulations are processed using image processing techniques. The concept of the damage variable () is proposed to facilitate the presentation of the image processing results. The damage variable is found to be negatively correlated with the hydrostatic pressure () at the same moment, in equiaxial in-situ stress fields. In contrast, in anisotropic in-situ stress fields, is not negatively correlated with due to the presence of hoop tensile stresses in the rock. The mathematical relationship between and in equiaxial and anisotropic stress fields are established. An anisotropic damage variable () is introduced to describe the effect of the anisotropy ratio () on rock damage, which is found to increase with increasing values of . The sharp increase in equal to 4 and 5 is explained in terms of the state of the rock stress distribution under static loading. This study provides insights into the effect of in situ stress on rock blast damage and presents new approaches for analyzing and presenting the data.
Using blasting caps with electronic delay units, it has become possible to employ wave superposition in rock blasting. This paper presents computer simulations to investigate the hypothesis that fragmentation is improved in areas between blast holes where the tensile waves meet, overlap and interact. In this study, a numerical methodology using the code LS-DYNA was developed. LS-DYNA is a commercially available multi-purpose finite-element code, which is well suited to various types of dynamic modeling. Two different element formulations were used — Euler formulation in, and close to, the blast hole, and Lagrange formulation in the rock volume farther from the blast hole. The models used have a resolution (element size) of 50 mm and comprise approximately 20 million elements. Single and dual blast hole configurations have been studied, and a methodology to calculate possible fragmentation based on model interpretation was developed. The results showed that the amount of explosives and the blast hole spacing had the largest effect on fragmentation. The effect of varying delay times was small and local, implying that a significant increase in fragmentation should not be expected through wave superposition.
The expansion and shock wave coexisting failure theory has been widely recognized. However, it is not clear whether the main cause of rock mass blasting failure is the shock wave or gas pressure. In this paper, the contribution proportions of both loads to rock mass failure were investigated in bench blasting. First, the blasting damage in rock mass was simulated with a fluid-structure interaction (FSI) method. Then, a novel method to quantitatively distinguish between the rock-breaking effects (RBEs) of the shock wave and gas pressure was proposed that was based on the damage results. In addition, under different free surface conditions, the blasting failure volume that was caused by both loads was obtained for three typical rock masses, which included poor, middle, and good rock masses. The results showed that the range of the tensile failure zone by reflected waves was small, and the favorable effects of free surfaces on the failure induced by shock waves were limited. The free surface had a minor beneficial influence on the rock mass failure that was induced by the shock waves. In addition, it had a more favorable influence on the failure that was induced by the gas pressure. Finally, the influence of the free surface and rock mass conditions on the contribution proportions of both loads was discussed. A higher proportion of the RBEs of the shock wave was in the good mass with large wave impedance compared with the poor rock mass with small wave impedance. According to the contribution proportions under different rock masses and free surface conditions, the main cause of rock blasting failure was the gas pressure action, which was verified through the field high-speed photography data. The findings revealed the main cause of rock mass failure in bench blasting and could provide a theoretical basis when seeking effective engineering measures to give full play to the gas pressure action.
A series of numerical simulations of rock blasting has been conducted using the LSDYNA software in order to test the hypothesis proposed by Rossmanith, stating that interaction of stress waves could result in finer fragmentation by controlling the initiation times. The rock material was simulated with the RHT material model. After the calculation, the elements with damage level above 0.6 were removed to simulate complete fracturing of the rock.Firstly, a series of numerical simulations were conducted to model the small-scale tests performed by Johnasson et al. (2013). This work also involved simulating initial damage to the rock through previous blasting, and analyzing the resulting effects. The effect of different delay times showed that through a properly chosen delay time, improved fragmentation could be inferred. Moreover, the initial damage (from the previous row) clearly affected the fragmentation; however, the results indicated that longer delay times (in which the stress wave would have passed the boreholes) also resulted in improved fragmentation, implying that stress wave superposition may not be the primary factor governing the fragmentation. Secondly, full-scale tests conducted at the Aitik open pit mine were modeled. The simulation results indicated that the case of no interacting stress waves (6 ms delay) gavefiner fragmentation at most of the interpretation section cuts compared to the cases of interacting stress waves (0, 1 and 3 ms delay times). Both the simulation results of small scale tests and full scale tests indicate that the stress wave interaction effect due to delayed initiation can result in finer fragmentation compared to simultanious initiation. However, the results also indicate that relatively long delay times, leading to no stress wave superposition, induce even finer fragmentation compared to the use of very short delay times.
A series of numerical simulations of rock blasting using LS-DYNA software havebeen conducted to investigate the effect of short delay time on the fragmentation inunderground mines. The purpose was to test the hypothesis proposed by Rossmaniththat stress wave interaction could result in finer fragmentation by controlling theinitiation times. The blasted rock was simulated with RHT material model. After thecalculation, the elements with damage level above 0.6 were removed to simulate thefracture of the rock.The size of model and the borehole pattern were based on the blasting design of theLKAB Malmberget mine. Several simulations were run to investigate the effects ofinitiation time, primer position and boundary conditions. The results are presented asaccumulated area plots where the level of fragmentation can be observed at certainpositions in the model.The results show that the fragmentation for simultaneous initiation is coarsercompared to initiation with delay times in SLC blasting. It is difficult to identify anyeffect of stress wave interaction from the damage distribution in the blasted blockbecause the borehole pattern is in a fan shape. Thus, the distance between twoadjacent boreholes is not constant and the boreholes are of various lengths. Thenumerical modeling results showed that the fragmentation for the case of 2 ms delaytime is finer than that of simultaneous initiation and the 1 ms delay time case. Thecomparison among the cases with different primer positions shows that if the top ofthe block was set as free face, the bottom primer cases yielded the finer fragmentationthan the top primers cases and the middle primer cases; if the top of the block was setas non-reflecting boundary, the top primer cases yielded the finest fragmentation. Theeffect of overlying waste rock above the block cannot be neglected in simulations.The real boundary conditions of the top of the block and the effect of primer positionneed to be studied further. Some recommendations are proposed for the futureresearch about SLC blasting.
Blasting techniques are widely used to fragment rock masses into smaller pieces. Numerical modelling is an efficient method employed by many researchers in the blasting field. It is difficult for a conventional continuum-based approach such as the finite element method (FEM) to model the rock fragmentation by blasting and the expansion work on the rock by explosive and its detonation products. In this paper, the particle blast method (PBM) was employed to model the behaviour of the detonation and a bonded particle model (BPM) was used to model the brittle material to be blasted. A mortar cylinder with a centrally placed hole for the explosive was modelled and the results were compared to the experimental data. The blast process from crack initiation to fragment formation was analysed. The influence of coupling ratio on fragmentation was also investigated.
Blasting is widely applied in deep rock excavation. The effect of in-situ stresses on the fracturing of rock due to blasting was investigated. A theoretical model was used to explain the effect mechanism of in-situ stresses on crack propagation due to blasting. Four cases with different in-situ stress conditions were numerically investigated. The numerical results indicate that the crack propagation is governed by the blast load in the vicinity of the blasthole while the high in-situ stresses can influence the crack propagation in the far-field. The crack propagation trends towards the direction in which the high initial pressure is applied.
A series of small-scale laboratory tests were carried out to investigate the effects of short delay times on fragmentation. The aim is to test the hypothesis that improve fragmentation through stress wave superposition. These tests have subsequently been modeled using a coupled FEM-BPM-PBM model in LS-DYNA code. In the model, the remaining rock is represented by a finite element model (FEM) and the rock to be blasted is represented by a bonded particle model (BPM). The detonation of explosive is described with a particle blast method (PBM). The fragment size distribution was obtained with a code developed in Perl programming language. The numerical results showed that although the short delay times induced improved fragmentation compared to the simultaneous initiation, the longer delay times also resulted in improved fragmentation, implying that stress wave superposition may not be the primary factor governing fragmentation.
Blasting operations can fragment rock mass into smaller pieces and meanwhile induce vibration anddamage in remaining rock mass. A series of small-scale laboratory tests were carried out to investigatethe effects of short delay times on fragmentation. These tests were modeled using a coupledFEM-BPM-PBM model in the LS-DYNA code. In the model, the remaining rock is representedby a finite element model (FEM) and the rock to be blasted is represented by a bonded particlemodel (BPM). The detonation of explosives is described with a particle blast method (PBM). Thefragment size distribution was obtained with a code developed in Perl programming language. Theblast-induced vibration and damage in the remaining rock mass were evaluated. The results showthat the coupled FEM-BPM-PBM model can be employed to evaluate both fragmentation in theblasted domain and the blast-induced damage and vibration in the remaining rock mass.
The analytic solutions for the dynamic response of a shallow circular lined tunnel with an imperfectly bonded interface subjected to plane SH-waves are presented in the paper. Complex variable method was used and the imperfect interface was modelled with a linear spring model. The case that the rock is harder than the liner was investigated. The effects of the contact stiffness of the interface, the incident angle, the frequency of the incident wave and the depth of the tunnel were investigated. The results indicate when the frequency of incident waves is low, the variation of contact stiffness of the imperfect interface has a slight effect on the distribution of dynamic stress concentration factor (DSCF) in the rock mass but there is a significant effect on the distribution of DSCF in the liner. When the frequency of incident waves is high, the distribution of DSCF is complicated in the rock mass and in the liner. The variation of the depth of tunnel leads to the cyclical variation of DSCF. The incident angle significantly affects the distribution and value of DSCF. The phenomenon of resonance scattering can be observed when the bond of the interface is extremely weak
Rock fragmentation by blasting is determined by the level and state of stress in the rock mass subjected to blasting. With the application of electronic detonators, some researchers stated that it is possible to achieve improved fragmentation through stress wave superposition with very short delay times. This hypothesis was studied through theoretical analysis in the paper. First, the stress in rock mass induced by a single-hole shot was analyzed with the assumptions of infinite velocity of detonation and infinite charge length. Based on the stress analysis of a single-hole shot, the stress history and tensile stress distribution between two adjacent holes were presented for cases of simultaneous initiation and 1 ms delayed initiation via stress superposition. The results indicated that the stress wave interaction is local around the collision point. Then, the tensile stress distribution at the extended line of two adjacent blast holes was analyzed for a case of 2 ms delay. The analytical results showed that the tensile stress on the extended line increases due to the stress wave superposition under the assumption that the influence of neighboring blast hole on the stress wave propagation can be neglected. However, the numerical results indicated that this assumption is unreasonable and yields contrary results. The feasibility of improving fragmentation via stress wave interaction with precise initiation was also discussed. The analysis in this paper does not support that the interaction of stress waves improves the fragmentation.
With the application of electronic detonators and with short delay times, it may be possible to achieve improved fragmentation through stress wave superposition. This hypothesis was studied through a series of small scale laboratory tests. The results from these tests have subsequently been modeled using the numerical FEM code LS-DYNA and the RHT (Riedel-Hiermaier-Thoma) material model, applying a newly developed methodology for three-dimensional computer simulation of blasting. This work also involved simulating initial damage to the rock through previous blasting, and analyzing the resulting effects. The effect of different delay times showed that through a properly chosen delay time, improved fragmentation could be inferred. Moreover, the initial damage (from the previous row) clearly affected the fragmentation; however, the results indicated that longer delay times (in which the stress wave would have passed the boreholes) also resulted in improved fragmentation, implying that stress wave superposition may not be the primary factor governing fragmentation
Rock masses consist essentially of intact rock and discontinuities such as joints. Blasting is mostly used method for the rock excavation. To investigate the effects of joints on the fragmentation by blasting, three models with different joint patterns and one model without joint were created in the LS-DYNA code. In these models, a bonded particle model was used to represent the rock to be blasted, a finite element model was adopted to model the remaining rock mass and a particle blast model was employed to describe the detonation of explosives. To validate the contact model for joints, the fragmentation pattern and the individual particle motion from two single borehole shot models with and without joints were compared. The numerical results indicated that the existence of joints has a significant effect on fragmentation and vibration. The models with joints produced finer fragmentation compared to the model without joints in the paper.
The gravity flow behavior of blasted ore and caved waste in sublevel caving (SLC) mines is complex. The shape of fragmented ore and caved waste is identified as one of the principal factors influencing the gravity flow of ore. To investigate the effect of the particle shapes on the gravity flow, a code was developed to generate polyhedral fragments in different shapes and divide them into internal elements. Then these fragments were imported in the LS-DYNA code to generate SLC models containing blasted ore and caved waste and model the extraction process. To model the non-continuous loading process, the gravity flow was considered to be an intermittent process by setting a switcher at the extraction point. The flow behavior of ore from the numerical modeling is in agreement with the experimental results. The cumulative dilution of ore by waste is up to around 30%, which agrees with the results of the field survey.
A theoretical method for studying the dynamic response of a circular lined tunnel with an imperfectly bonded interface subjected to plane P-waves is presented in the paper. The wave function expansion method was used and the imperfect interface was modeled with a spring model. Two cases were discussed in the paper. In the first case rock is harder than the lining and vice-versa in the second case. The results indicated that the variation in the stiffness of the interface has much influence on the distribution of dynamic stress concentration factors (DSCF) in the rock and the lining. The imperfection of the interface has a more noticeable influence on the DSCF in the rock mass and the lining at high frequency incident wave's scenario than low frequency incident wave's scenario. The resonance scattering phenomena can be observed when the bond is extremely weak. Limiting cases were considered and a good agreement with the solutions available in the literature was obtained.
Ground support systems are commonly used to mitigate the potential consequences of rockburst in burst prone mines. To assess the capacity of ground support systems when subjected to dynamic loading, simulated rockburst tests using blasting were conducted at the Kiruna Mine. In this study, a numerical simulation for one of the field tests was conducted using the LS-DYNA code to investigate the dynamic response of the ground support systems including shotcrete and rockbolts. The numerical results showed a similar particle vibration pattern and a crack pattern to those of the field measurements. The effects of the detonator position and the charge configuration on the dynamic response of ground support systems are also discussed. Numerical results indicated that the peak particle vibrations on the tested panel increase along the direction of detonation propagation. It is difficult to use different charge concentrations in one borehole to investigate the effect of different dynamic loads on the dynamic response of support systems. Numerical results also indicated that 2D numerical modeling for simulated rockburst experiments could overestimate the dynamic response of ground support systems.
A series of tests for a pure emulsion explosive were carried out with PVC confinement to obtain the velocity of detonation (VoD) and the curvature of the detonation front for different charge diameters. The burning process of the pure emulsion explosive has been modelled with a reactive flow model in LS-DYNA code. The parameters in the burning rate function were calibrated with the detonation velocities and the front curvature radii from the tests. The calibrated parameters were used to predict the VOD and the detonation front curvature radii for the emulsion explosive with mortar confinement. The results indicate that both the VoDs and the detonation front curvature radii from numerical modelling are in good agreement with the experimental results for big charge diameters. For small charge diameters, the predicted VoDs are in good agreement with the experimental results while the differences between the predicted and the experimental detonation front curvature radii are obvious
Emulsion explosives are a common industrial explosive and have a non-ideal detonation behaviour. The detonation performance for a given product changes with the charge diameter, ground conditions, confinement and density. The burning process of an emulsion explosive has been modelled with an ignition and growth model in the LS-DYNA code. The parameters in the burning rate function are calibrated by the detonation velocities and the detonation front curvature radii from emulsion explosive tests. A Perl program was developed for an efficient estimation of the parameters, and the results show that the calibrated parameters can predict both detonation velocities and the detonation front curvatures.
To investigate the non-ideal detonation properties of aluminized emulsion explosive, a series of tests for an emulsion explosive with 5% aluminum powder additive were carried out with mortar confinement. The velocity of detonation (VoD) and the curvature of the detonation front for different charge diameters were obtained from the tests with a high-speed camera. The burning process of the aluminized emulsion explosive has been modelled with the ignition and growth (I&G) flow model in the LS-DYNA code. A routine based on the optimization program LS-OPT code was developed to identify the parameters in the burning rate function with the detonation velocities and the front curvature radii from two tests. A Perl code was implemented in the routine and was used to calculate the VoD, fit the detonation front and obtain the detonation front curvature radii. The calibrated parameters were used to predict the VoDs and the detonation front curvature radii for the rest cases. The results indicate that both the VoDs and the detonation front curvature radii from the numerical modelling are in good agreement with the experimental results. The numerical results also indicate that the variety of the burn fraction and the peak pressure with the change of charge diameters is reasonable with the calibrated parameters.
The flow behavior of the ore and waste significantly affect the dilution in sublevel caving (SLC) mines. Drill and blast issues are identified as having a substantial impact upon SLC material flow. In the paper, blast-induced fragmentation in SLC was numerically investigated using the LS-DYNA code. A method was presented to evaluate fragmentation based on the damage description and a fragment identification routine implemented in the LS-PREPOST (a pre- and post-processing tool of LS-DYNA). The effects of the delay time and the primer position on fragmentation were investigated. The results indicated that a long delay time gives a finer fragmentation for the cases discussed in the paper. The results also showed that the middle primer and the top primer in SLC can give a fine fragmentation. The limitations of numerical modelling were also discussed.
The analytic solutions for the dynamic response of a circular lined tunnel with an imperfect interface subjected to a cylindrical P-wave were presented in the paper. The wave function expansion method was used and the imperfect interface was modeled with a spring model. The interface separating the liner from the surrounding rock was considered to be homogeneous imperfect. The dynamic stress concentration factors (DSCF) of the rock and liner were evaluated and discussed. The effects of incident wave’s frequency, bonding conditions and distance between the wave source and the tunnel were examined. The results showed that the low-frequency incident wave leads to a higher DSCF than the high-frequency incident wave. The bonding conditions have a great effect on the dynamic response of the lined tunnel. When the bond is extremely weak, the resonance scattering phenomenon can be observed. When the distance between the wave source and the tunnel, depending on frequency of the incident wave, is considered as large, the cylindrical wave can be treated as a plane wave. Limiting cases were considered and good agreement with the solutions available in the literature was obtained.
In order to assess the capacity of ground support systems when subjected to dynamic loading, simulated rockburst tests by using blasting have been conducted at LKAB Kiirunavaara underground mine. In this paper, a numerical simulation for one of the field tests is conducted using LS-DYNA code to numerically investigate the effect of the different aspects of the charge design including the initiation point and the geometry on the test results. In the simulation, an explosive material model is used to model the detonation of explosive used in field tests and the Riedel-Hiermaier -Thoma (RHT) material model is used to model the dynamic response of the rock mass. The decoupling effect between the explosive and the wall of borehole is also taken into account in the model. The numerical results show a similar particle vibration pattern and a crack pattern to those of the field measurment. The effects of the position of the initiation point and the charge structure on the dynamic response of rock mass are also discussed. The results can be a reference for blast design for future field tests.
To determine the dynamic demand for support design under rockburst conditions, one of the most important issues is the prediction of ground motion parameters at the site of interest. Field monitoring has shown that the peak ground motion at the surface of an excavation in fractured rock is preferentially amplified compared to the motion in solid rock at a similar distance from the source. However, the traditional scaling laws used in rock support design do not account for the effect of free surface (excavation) and fracturing of rock. Recent studies have shown that high ground motion might be generated when a seismic wave crosses through fractures near a free surface in fractured rocks which is very complex and is not well understood. In this paper, particle velocity amplification was theoretically studied by investigating the dynamic interaction between seismic wave and multiple fractures near a free surface using the method of characteristics and the displacement discontinuity model. A harmonic load was applied on a model with a fractured zone near a free surface to investigate this phenomenon. After the harmonic wave propagated normally through multiple parallel fractures, the velocity amplification factor (VAF) was calculated as a function of the ratio of the magnitude of the peak particle velocity at the free surface of the model to the peak input velocity. The VAF can be as high as 3.77 and varies depending on the state of the fractured rock and the characteristics of the seismic wave. Parameter studies were conducted to investigate the effects of seismic load and multiple fractures on wave propagation, especially in terms of the wave frequency, the fracture spacing, the number of fractures and the stiffness of fractures. The results have proved that the interaction of the seismic wave and multiple fractures near the free surface strongly influences the ground motion. Quantitative relationships between the various influential factors and the corresponding VAF were developed. It is anticipated that such relationships can provide criteria to improve the current design procedures and help mining engineers to improve their rock support practice for rockburst-prone areas.
In order to assess the capacity of ground support systems when submitted to dynamic loading, simulated rockburst tests utilizing blasting have been performed for many years in different countries with limited success. In general, the blasts need to be carefully designed in order to reach the goal; however, different blast layouts (e.g. blasthole angle, burden) have been used based on researcher’s experience without conducting detailed analyses, the exception being a field test by CSIR. Recently, field trials have been conducted at the LKAB Kiirunavaara underground mine with some unexpected results which show that either the whole tested panel was destroyed or only a few fractures were formed without any ejections being observed. The aim of this paper is to investigate the failure mechanism in the simulated rockburst tests and improve the blast design by back-analyzing the test results using a coupled numerical modeling technique. The blast was simulated by using finite element method (LS-DYNA) and the dynamic interaction between the blasting generated waves and the opening was simulated by using discrete element modeling (UDEC) with the dynamic input from LS-DYNA. The numerical modeling showed that blasting can create both radial fractures radiating from the blasthole and fractures parallel or sub-parallel to the surface of the tested panel caused by reflected tensile stress waves. By comparing the results of the numerical modeling with the measured data, it is shown that the collapse failure was mainly controlled by the creation of a cone-shaped area formed by radial fractures and the burden seems to be a critical factor. In order to obtain fractures caused by reflected tensile stress waves and reduce blasting induced radial fractures, 2 parallel blastholes are suggested with larger burden (> 5 m) for future tests. Furthermore, the limitation of the current numerical modeling has also been discussed. The coupled numerical technique has shown its advantage when simulating blasting as well as interaction between waves and opening and it can thus be used as a tool for extrapolating results from simulated rockburst experiments if detailed geological structure and ground support system can be incorporated in the model and the model can be well calibrated.
An analytical relation between burden velocity and ratio of burden to blasthole diameter is developed in this paper. This relation is found to be consistent with the measured burden velocities of all 37 full-scale blasts found from published articles. These blasts include single-hole blasts, multi-hole blasts, and simultaneously-initiated blasts with various borehole diameters such as 64 mm, 76 mm, 92 mm, 115 mm, 142 mm and 310 mm. All boreholes were fully charged. The agreement between measured and calculated burden velocities demonstrates that this relation can be used to predict the burden velocity of a wide range of full-scale blast with fully-coupled explosive charge and help to determine a correct delay time between adjacent holes or rows in various full-scale blasts involved in tunnelling (or drifting), surface and underground mining production blasts and underground opening slot blasts. In addition, this theoretical relation is found to agree with the measured burden velocities of 9 laboratory small-scale blasts to a certain extent. To predict the burden velocity of a small-scale blast, a further study or modification to the relation is necessary by using more small-scale blasts in the future.