Journal of University of Science and Technology Beijing Volume 15, Number 3, June 2008, Page 209 Mineral

Corresponding author: Shijie Qu, E-mail: qushijie1229@yahoo.cm.cn Also available online at www.sciencedirect.com 2008 University of Science and Technology Beijing. All rights reserved.

Numerical simulation of parallel hole cut blasting with uncharged holes

Shijie Qu, Xiangbin Zheng, Lihua Fan, and Ying Wang

School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China (Received 2007-05-30)

Abstract: The cavity formation and propagation process of stress wave from parallel hole cut blasting was simulated with AN-SYS/LS-DYNA 3D nonlinear dynamic finite element software. The distribution of element plastic strain, node velocity, node time-acceleration history and the blasting cartridge volume ratio during the process were analyzed. It was found that the detonation of charged holes would cause the interaction of stress wave with the wall of uncharged holes. Initial rock cracking and displacement to neighboring uncharged holes become the main mechanism of cavity formation in early stage. 2008 University of Science and Technology Beijing. All rights reserved.

Key words: parallel hole; cut blasting; cavity formation; numerical simulation

1. Introduction Cut with parallel holes is widely used in tunneling

and shaft sinking operations in different types of rock masses because of the simplicity in drilling and plan-ning and the possibility of obtaining high efficiency of blast holes. However, experiences show that the frag-mentation and efficiency of any tunneling practice are dominated by the performance of those cut holes to a certain extent because these holes are supposed to pro-duce new free surfaces and space for detonation of blast holes initiated thereafter [1].

Tunneling with parallel cut holes means that the rock between uncharged holes and charged cut holes is to be fragmented by stress wave and expansion of the gaseous products from detonation of charged cut holes and to be put forward to the uncharged holes and the original surface, before the cut is pulled out as a result. This cut will perform as free faces and space to which the helpers will blast. This shows that the rock fragmentation from the helpers will be controlled by the performance of cut holes, and affects the pulling of contour holes consequently.

In an effort to improve blast design and control fragmentation of tunneling operations, many re-searches on tunneling with parallel cut holes have been conducted in recent years. The fragmentation mechanism, parameter selection, and fragmentation

simulation of parallel hole cut blasting were studied and discussed by different researchers [2-7]. Through mechanical model study and numerical analyses, Zhang et al. found that area of empty holes needed to be determined with the depth of charged holes in par-allel hole cut blasting [4].

Because of the high temperature and high pressure of the instant process of explosive detonation, diffi-culties still exist for technical experimental methods to assure blast results with effectiveness and reliability. Therefore, an effort to estimate the reasonability of a cut blast design and to optimize the selection of blast-ing parameters, such as drill pattern and charge quan-tity, was made. To achieve the above, computer simu-lation with ANSYS/LS-DYNA 3D nonlinear dynamic finite element software [8] and the process of parallel hole cut blasting with uncharged holes, based on blasting dynamics, were carried out. The results of the research may serve as a reference for stress analyses and parameter selection of parallel hole cut blasting with uncharged holes.

2. Constitutive model and state equation of cut blasting

The media involved in cut blasting include rock, explosives, gaseous products from explosives detona-tion, stemming material, the air in uncharged holes,

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210 J. Univ. Sci. Technol. Beijing, Vol.15, No.3, Jun 2008

and the air outside of the face. Thus, constitutive models for each of the media need be set up and the model matching method of the multiphase system needs be selected.

ANSYS/LS-DYNA, a finite element software, can be used to analyze nonlinear dynamic problems. Two methods, i.e. the Lagrange method and arbitrary La-grangian Eulerian (ALE) method are available for liq-uid-solid matching analyses with ANSYS/LS-DYNA. Element mutation can hardly be avoided as it is ap-plied in numerical calculations of large deformation problems, especially, when elements are unevenly dis-tributed. Therefore, the ALE method is selected, which can fairly deal with possible element mutation during the process of cut blasting of the multiphase media system, and multiphase media matching prob-lems can be solved more effectively.

2.1. The HOLMQUIST-JOHNSON-COOK consti-tutive model of rock

The use of the HOLMQUIST-JOHNSON-COOK constitutive model makes it possible to simulate high stress and large strain and simulate the pressure pro-duced from gas expansion of a dynamic impact proc-ess in concrete and rock. Volumetric strain, stress state of fractured area, and damage within the media can all be described with the pressure equation of the model [9].

Because damage in ordinary dynamic circum-stances, such as the cut blasting, is caused generally by effective plastic strain, the HOLM-QUIST-JOHNSON-COOK constitutive model is ap-plied and its state equation can be written as follows:

(1) State equation for loading and unloading in lin-ear elastic stage.

ep K= (1) where is the standard volumetric strain as

1 0= / - , and 0 are the density and original den-sity, respectively; e c c/K p = , pc and c are the uni-axial compressive strength and volumetric strain at crushing, respectively.

(2) State equation for loading in plastic transferring stage.

1

1 c cc

c

( )( )p

p pp p = + (2)

where p1 is the stress at solidification under impact, c is the volume strain at solidification as

c g 0/ 1 = , where g is the grain density as there are no fissures in the media, and 1p is the volume strain at final crushing as 1p p= .

(3) State equation for unloading in plastic stage.

[ ]max e 1 max(1 ) ( )p p F K FK = + (3) where F is the factor of interpolation as

1max c c( ) /( )pF = , K1 is the volumetric plas-tic modulus, max and pmax are the maximum volumet-ric strain and the maximum pressure before unloading, respectively, and 1p is the volumetric strain as

1p p= . (4) State equation for loading in ideal solid stage.

2 31 2 3p L K K = + + (4)

where is the revised volumetric strain as 1 1( ) /(1 ) = + ; K1, K2, and K3 are constants and

equal to 127, 216, and 257 GPa, respectively, where 1 is the volumetric strain at solidification.

(5) State equation for unloading in ideal solid stage.

max 1 max( )p p K = (5) where max max 1 1( ) /(1 ) = + .

Mechanical properties of the rock and parameters of the state equations are listed in Tables 1 and 2, re-spectively.

Table 1. Mechanical properties of the rock

Density / (gcm3)

Elastic modulus of shearing /

GPa

Elastic modulus /

GPa

Poisons ratio

Internal en-ergy ratio /

(kJg1) 3.217 18.6 46 0.15 1.267

Table 2. Parameters of the state equations

pc Pc / GPa Pi / GPa pi T / GPa Ke / GPa0.006 0.217 0.65 0.2 0.032 12

In Table 2, pc is the compressive stress in rock, pi is the initial ground stress, pc is the volumetric strain corresponding to pc, pi is the volumetric strain corre-sponding to pi, and T is the maximum of statically in-determinate tensile stress.

2.2. Model of explosives detonation

The model *MAT_HIGH_EXPLOSIVE_BURN and the state equation Jones-Wilkins-Lee (JWL) for explosives are used to describe the performance and characteristics of explosives detonation [8]. The state equation JWL can give an accurate description of the characteristics of the explosion products in terms of pressure, volume, and energy. The state equation is applied together with the model, thus the pressure of the explosion products is defined as a function of rela-tive volume and internal energy:

1 2 0

1 21 e 1 eR V R V Ep A B

R V R V V = + + (6)

S.J. Qu et al., Numerical simulation of parallel hole cut blasting with uncharged holes 211

where A, B, R1, R2, and are coefficients, V is the relative volume, and E0 is the density of initial internal energy.

Because the shock wave from detonation is always associated with rapid variation of physical variants, jump and disconnection in pressure and density, as well as particle acceleration, will be caused [10]. To avoid the effect of this phenomenon, an artificial volume viscosity coefficient can be asserted to the terms of pressure and make the rapid jump and dis-connection into a continuous variation in fairly narrow periods. The explosive used in the tunnel blasting is ammonium nitrite #2 with an initial density of = 1200 kg/m3 and detonation velocity of 3200 m/s, whereas the pressure in C-J plane is 5.6 GPa. Parame-ters of the state equation of a detonation of the explo-sive are shown in Table 3.

Table 3. Parameters of the state equation of detonation of the explosive ammonium nitrite #2

A / GPa B / GPa R1 R2 E0 / GPa252.3 3.93 4.82 0.97 0.35 0.752

2.3. Air model

The state equation *MAT_NULL is applied in this model to avoid partial stress calculations, as the lower limit of the stress is determined with resultant pressure. The elements at strength of compression and tension under critical pressure conditions can be justified with failure criterion of the state equation MAT_NULL during the process of air compression and expansion [8]. The density of air is = 1.2 kg/m3 [10]. 2.4. Model of the stemming material

The stemming material used in tunnel blasting is earth, thus, state equation *MAT_SOIL_AND_FOAM is applied to establishment of the model of the stem-ming material and solid-gaseous phase matching can be effectively simulated. In accordance with measured data, the density, elastic modulus, and Poisons ratio of the stemming material, the earth, are 1.85 g/cm3, 1.6 104 GPa, and 0.2, respectively. 3. Numerical simulation of cavity formation

3.1. Conditions

Hole drilling for tunnel blasting was carried out at the level of 274 m of an iron mine with rock drills YT228. The length of the drill is 2.2 m or 1.8 m and the tip of the drill is 38 mm in diameter. The diameter of the blast holes is 40 mm. Cartridges of ammo-nium explosive #2 were used, with the cartridge di-ameter and length of 32 mm and 200 mm, respectively. Electric initiation was applied. The tunnel, at the level

of 274 m, was designed of a triple-center arc form with a figure of 3.74-m width and 3.07-m height. About 50 blast holes of 2.0 m in depth and 46 kg ex-plosive products per round were used. The pulling depth was usually up to 1.2-1.5 m only. The profile of the tunnel was often out of design. The face produced was uneven as maximum over breakage was up to 50 cm. Thus, blast design needs to be optimized and technical parameters need to be changed.

3.2. Drill pattern and charge structure for the sin-gle helix parallel hole cut blasting

This type of cut blasting is characterized in that all cut holes are parallel to each other and perpendicular to the face. One or a number of the cut holes are not charged and are used to provide free faces for the charged holes. The drill pattern and hole charge struc-ture are shown in Fig. 1.

Fig. 1. Drill pattern (a) and hole charge structure (b) of the single helix cut model (unit: cm).

3.3. Finite element model

Double of the size of the tunnels profile is used to define the boundary into the surrounding rock mass, taking the effect of rock mass on the cut blasting process. Meanwhile, the gravity effect of rock mass from the top of the tunnel is neglected.

The cubic element is used to spatially separate ex-plosive charges, rock, stemming material, and the air decking at the bottom of blast holes. Because the cut holes are relatively small to the tunnel, the elements close to explosive charges are defined as fine, and others as coarse (Fig. 2 and Fig. 3). Since the symme-

212 J. Univ. Sci. Technol. Beijing, Vol.15, No.3, Jun 2008

try of the model, half of the model is used for the study (Fig. 4). The length, width, and height of the model are 3.87 m, 4.0 m, and 6.0 m, respectively. The model is separated into 66954 elements in total, in which 1080 are for explosive charges, 1682 are for hole bottom air decks, 360 are for hole stemming, and 63832 are for the rock. The time for simulation of 1 ms is selected, that is approximately equal to the dura-tion for cavity formation and expansion.

Fig. 2. Detailed drawing of the model (unit: cm).

Fig. 3. Element meshing of the model.

Fig. 4. Distribution of plastic strain (t = 988.5 s).

4. Results and analyses

Visualization of the interaction of rock and explo-sive charges is realized with use of the section func-tion of ANSYS/LS-DYNA. The section along the axis of the tunnel for visualization is designed at the height of 100 cm of the model shown in Fig. 2.

4.1. Effective plastic strain

Fig. 4 gives the effective plastic strain distribution at Z = 100 cm when t = 989 s. It shows that the plastic strain area, caused by detonation, increases with the distance from the charge to the uncharged hole. The nearest point of the effective strain occurs at the top of the charged hole No. 7 and the 0.5 m right side of the charged hole No. 6, and the furthest point of the effective strain occurs at 0.57 m below the charge No. 5. The strain decreases with the distance to the uncharged hole. Because of the effect of the re-flected tensile stress from neighboring uncharged holes, the effective plastic strain around the uncharged hole No. 1 appears to be much higher than that further away from it.

Fig. 4 also shows that plastic strain occurred to some extent around the relievers and was favorable to fragmentation. However, the uneven distribution of strain may cause uneven fragmentation and produce an effect to cavity formation in the process.

4.2. History of velocity and acceleration

Fig. 5 shows that the maximum velocity occurs at the node around the charge, and the minimum velocity occurs in the middle of the two neighboring charged holes because of the stress overlapping effect. Hereby, the recorded acceleration in direction Y is used to analyze the stress state on the node indirectly.

Fig. 5. Distribution of node velocity (t = 988.5 s).

S.J. Qu et al., Numerical simulation of parallel hole cut blasting with uncharged holes 213

The node No. 57291 is located adjacent to the hole No. 5, and the node No. 57331 is located adjacent to hole No. 1as node No.57478 is at the middle of the two holes.

Fig. 6 shows that the dynamic load to the node No. 57291 is quite strong at an early stage and thereafter attenuation of the load occurs in a manner similar to dynamic stress from explosive detonation. The load to the node No.57478 is higher than that to the node No. 57331 and the increase in stress occurs after attenua-tion before negative acceleration occurs, which im-plies that tensile stress is caused possibly by reflection of the compressive stress wave from uncharged hole wall.

Fig. 6. Acceleration-time history of the key nodes.

4.3. Analyses on the cavity formation process

The function modes history Var#5 of the post proc-essing software LS-PREPOST, an advanced pre/post processor for ANSYS/LS-DYNA, is used for dynamic visualizing of the explosive charge, uncharged holes, other materials and the whole process of cavity forma-tion (i.e. the space expansion process of these materi-als) by detonation of the explosive charge.

The isoline of stress is produced with LCON, line contours, of ANSYS/LS-DYNA and the entire model with phantom function, thus, variation of the relations between explosive charge and the air can be observed. From Fig. 7 it can also be seen that the boundaries of the explosive charges No. 5 and No. 7 begin to expand towards the uncharged hole before t = 454.95 s, as the charges No. 4 and No. 6 expand circularly from their own center. At this moment, no effect has oc-curred to the uncharged hole because the stress wave is still a distance far away.

The wave fronts from the holes No. 4 and No. 6 reach the perimeters of the uncharged holes, the holes No. 2 and No.6 as t = 747.44 s. Along with expan-sion of the hole perimeters and propagation of the stress waves from the holes No. 5 and No.7, the un-charged hole located in the middle of the model be-

gins to be disturbed and the stress is initiated before fragmentation and displacement of the rock occurs around the uncharged hole.

Fig. 7. Process of cavity formation from parallel hole cut blasting.

As t = 988.54 s, overlapping of the stress waves from adjacent charged holes, with the hole No. 7 be-ing an exception because it is relatively farther away, the stress wave from it is still on the way to the nearest uncharged hole No. 1, and the interaction of the stress waves with the uncharged holes begins to occur. Therefore, it is fair that the disturbance to the un-charged hole No. 1 is less than that to the holes No. 2 and No. 3. In the later stage of the process, overlap-ping of the stress waves from all the charged holes and cracking from charged hole perimeters to neighboring uncharged hole wall in the area around the uncharged hole No. 1 become obvious, before propagation of the stress waves completes. However, it can be found from Fig. 7 that the process is featured with interac-tion of the stress waves with the neighboring un-charged holes and with the priority of cracking from the charged holes to the uncharged holes, which be-comes the main mechanism of cavity formation by parallel hole cut blasting.

5. Conclusions

(1) The result of simulation shows that in the proc-ess of parallel hole cut blasting with uncharged holes, the detonation of charged holes will cause the interac-tion of stress wave with the uncharged hole wall and become the main reason for initial rock cracking and displacement to the uncharged hole.

(2) Unloaded holes, if properly designed, will pro-vide good free face and space for detonation of neighboring charged holes and provide a significant help in the process of cavity formation.

(3) Distance from a charged cut hole to its nearest uncharged hole is an important factor controlling ac-tual outcome of a parallel hole cut blasting practice. Increasing this distance will possibly cause poor

214 J. Univ. Sci. Technol. Beijing, Vol.15, No.3, Jun 2008

cracking within the area and a small cavity can be formed as a result, therefore which may produce a poor pulling of the whole tunnel blasting practice.

(4) Stress overlapping first occurs in the middle of two neighboring charged holes, as the charged cut holes are simultaneously initiated. Therefore, it is proposed that the uncharged holes should be located in the middle of two neighboring charged holes.

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