modelling gas pressure effects on explosive rock breakage

International Journal of Mining and Geological Engineering, 1988, 6, 73-79

SHORT C O M M U N I C A T I O N

Modelling gas pressure effects on explosive rock breakage

Introduction

In an endeavour to define the role of gas pressure in explosive rock breakage, several research projects have been undertaken at The Ohio State University. Britton et al. (1984) measured explosive-generated gas pressures and developed calculations for borehole pressures. The calculations used the initial and the final thermodynamic states of an explosive reaction without definition of rate-dependent detonation parameters.

Britton (1983) used the same method to calculate pressures for evaluation of relationships between gas pressure and breakage, work or work ratio and breakage, and work or work ratio and gas pressure for a range (1-3) of decoupling ratios (borehole diameter/charge diameter). In all cases, the correlation between the variables was high when compared to the explosive- generated gas pressure. Shock energy seemed to play an insignificant role, especially in decoupled holes having a ratio of 2 or greater.

To establish further the importance of gas pressure as the primary element in the mechanism of the fracture of rock, a computer model was developed (Haghighi, 1985) to describe quantitatively interrelationships between breakage and gas pressure. Four general cases were considered, and these are illustrated in Fig. 1: (a) borehole pressure operated on the rock only at the surface of the borehole; (b) the rock was twice cracked vertically; (c) the rock was cracked vertically four times; and (d) gas flowed into the four cracks one-third and two-thirds of the distance to the face. Significant breakage and rock movement effects occurred as the length to burden ratio (L/B) was increased from 1.2 to 10 in increments of 0.4. Rock in the burden was modelled to resemble a beam with different stiffness qualities for different lengths.

The radial cracks which in practice form about the borehole could not be disregarded in the model, but were essential features to successful prediction of rock breakage behaviour. The calculations showed that the cracks need not fill completely with explosive-generated gas before the cracks reach the free face and vent. Partial expansion of the explosive-generated gases into the newly available crack volume was required to obtain the effects which corresponded closely to photographs of bench blasts.

The paper shows that for a constant, medium-ranged L/B ratio, gas expansion and beam bending more nearly explain the process of rock breakage than do shock energy and vibrational models. The modelling was done using Supertab 7 and Superb, a computer-generated finite element analysis system which approximated exact solutions to the bending beam calculation.

Previous work by Ash and Smith (1976) had applied beam-bending theory to the action of explosives in overburden removal. Ash (1975) had previously shown that burden rock acted qualitatively like a beam with realistic trends in stress levels within the rock. Ash also created a

Keywords: Explosive; pressure; modelling; rock; breakage

02694)316/88 $03.00+ .12 ©1988 Chapman and Hall Ltd.

74 Haghighi, Britton and Skidmore

finite dement model which displayed similar effects. Both models which realistically showed crushing about the borehole, however, generated displacements far below those observed in practice. These models were apparently deficient in estimated forces available from the pressurized gases in the borehole, or in representation of model geometry or operation.

Basic model parameters

The present model characterizes a blast in a single hole 102 mm in diameter. The hole length to burden ratio was initially set in a middle range of column stiffness at 3.2. The hole length (see Fig. 1) extended in the Z direction while the breadth and width described an xy-plane. The burden, the distance from the centre of the borehole to the free face, was fixed at 3.05 m. The

oF S ..ETRYJ I I I I I 1

DIRECTION OF ROCK MOVEMENT

~zy

Z y L x

(a)

OF SYMMETRY

Y IzLX L

c % CRACK I E

%% I % I

% I

" I

DIRECTION OF ROCK MOVEMENT Z

yl--x (b)

Modelling gas pressure effects on explosive rock breakage 75

RADIAL~~ i AXISJ CRACKS I OF SYMMETRY

Y z~X

'%.

xxxx.

DIRECTION OF

ROCK MOVEMENT

(e)

Zy ~x

Z

yL____x Fig. 1. Finite element model configurations: (a) homogeneous rock; (b) rock face containing two vertical orthogonal cracks; (c) containing four vertical cracks.

stemming length and sub-drilling depth were maintained at 2.4 m and 1.2 m, respectively. Bench height was 9.75 m.

The rock was considered homogeneous, elastic and isotropic, possessing a modulus of elasticity of 17 GN m -2 and a Poisson's ratio of 0.27. The explosive used was ammonium nitrate-fuel oil (ANFO) composed of 94.5% ammonium nitrate and 5.5% fuel oil. ANFO normally has a unit weight of 800 to 850 KN m -a, but 800 was used in this model. The pressure produced by the ANFO was calculated to be 2.9 GPa and pressure was considered to be constant without heat or gas loss or adiabatic pressure drop in each case.

Discussion

The first case did not utilize radial cracks. The results (Fig. 2a) dearly showed that displacement was greatest at the nodes representing the borehole surface. The model achieved a maximum displacement value of a very low 0.58 cm. Even smaller displacements were observed at the nodes which represented the free surface or burden face. Gas pressure decreased due to borehole expansion. Each calculated interaction denoted a time change of about 12 ms during which the geometric configuration of the borehole changed and the pressure dropped to a point just large enough to move the rock, but not large enough to crush rock further. In this case the model did not represent actual field blasting conditions since the displacements at the free face were negligible, and an unrealistically symmetrical expansion occurred about the borehole.

Based on the performance and results of the first model application, changes were made to weaken the rock mass by introducing radial cracks from the borehole to the face (Fig. lb). The two orthogonal cracks lay in a vertical plane along the Z-axis and extended the length of the powder column. The bottom of the crack corresponded to the ground floor level, not to the borehole bottom, which was sub-drilled. The effect of the cracks is to promote rock movement in the face direction and to stimulate non-symmetrical expansion about the borehole axis. Results


(a)

(b)

Illllllll II II~lll II

Illlllll II Illlllll II Illll Illl II Illl III II

II

Ill,Ill II IIIIlllU II HIIIIIII II

r iiiiiiiiiili!!!!


MAXIMUM : +3.62

IIllltlll II Ulllltlll IJ II I I IlllllllJl II IJ

Z

L-x (c)

Z

L-x (d)

II II IIIIIitl II

I ll IlllmlllllY II IIII IllAlll II Iflll~ffhl

1111 IIIt~IV - II It IIIIII/I ]I II II flllUNI I

It IIIIIIII I I1 IIII]111

Fig. 2. X-Z views of deformed geometrical configurations: (a) homogeneous rock; (b) rock face containing two vertical orthogonal cracks; (c) rock face containing four vertical cracks; (d) face containing four pressurized vertical cracks.


showed that displacements were greater overall, and movement occurred at the free face. It should be noted that at the first iteration or impact, the displacement was the largest. As in the first case, displacements were larger at the borehole wall than at the free surface and the displacement maximum was located near the middle of the explosive column. An XY-view at this location is shown in Fig. 2b.

The second case gave a more reasonable result than did the first case, but the expanded borehole configuration was not fully representative of a well-designed field blast. Crushing at the back of the borehole was extensive, and the displacement at the free surface was considerably less than customarily occurs in actual blasting systems.

The third case considered four radial cracks (Fig. lc). Each crack was located at an angle incremented by 22.5 ° from the centre of the borehole to the burden face. The borehole was pressurized by explosive gas pressure but the cracks were not pressurized. Results showed increasingly realistic behaviour of displaced rock compared to the second case. Displacements were greater, and the expanded borehole was not only non-symmetrical, but greater movement was observed (see Fig. 2c) in the direction of the free face, while crushing at the back of the borehole was reduced.

Maximum displacement was noticed after the first iteration near the middle of the explosive column. Displacement magnitude was increased about 3% over the second case. Maximum displacement was larger at the borehole wall than at the free surface. The behaviour is understandable, since the number of pre-existing radial cracks had increased and the rock mass to be moved became less rigid. As a result, movement occurred preferentially in the direction of the bench face. Volume created by borehole expansion allowed gas expansion. With lower sustained pressure due to increased expansion of the borehole, the explosive worked more efficiently on the rock in the preferred direction and reduced back-breakage near the borehole.

A comparison of results from case 3 with field data showed that displacements were improved, but still inadequate. Therefore, the final model included partial pressurization of the cracks as well as the borehole itself. The cracks were pressurized to less than total borehole-to-face distance because gas leakage at the face was considered undesirable as a realistic model for field tests.

The modelling process determined what fraction of the crack distances should be pressurized. As shown in Fig. lc, each sector consisted of three finite elements. Therefore, the crack surfaces were divided into three regions in the XY-plane. The borehole was pressurized completely and the cracks to 1/3 and 2/3 total crack length. Pressurization to 1/3 crack length showed improvements, including adequate face movement and an absence of rock crushing, but the pressurization of 2/3 crack length gave the best representation of a confined shot. The following factors were noticed in a comparison of 1/3 to 2/3 crack pressurization. For the 2/3 crack pressurization (Fig. 2d), the location of maximum displacement shifted away from the borehole to the free face and its magnitude, near the middle of explosive column, increased from 1.17 to 3.19 m.

References

Ash, R.L. (1975) The Influence of Geological Discontinuities on Rock Blasting. Unpublished PhD Thesis, University of Minnesota, Minneapolis, Minnesota, USA.

Ash, R.L. and Smith, N.S. (1976) Changing borehole length to improve breakage: a case history. Proceedings of Second Conference on Explosives and Blasting Technique, Louisville, Kentucky, USA.


Britton, Robert R. (1983) The Effects of Decoupling on Rock Breakage, MSc Thesis, The Ohio State University, Columbus, Ohio, USA.

Britton, R.R., Skidmore, D.R. and Otuonye, F.O. (1984) Simplified calculation of explosive generated temperature and pressure. Mining Science and Technology 1, 299-303.

Haghighi, Rahim (1985) Investigation of Relationships Between Rock Fragmentation and Burden Stiffness Ratio in Confined Bench Blasting, PhD Thesis, The Ohio State University, Columbus, Ohio, USA.

1TRW Defense System Group, Mail Station DH4/2936, One Space Park, Redondo Beach, CA 90278, USA

2Mining and Mineral Resources Research Institute, The Ohio State University, Columbus, Ohio 43210

R A H I M H A G H I G H I 1 R O B E R T R. B R I T T O N 2

D U A N E S K I D M O R E 2

Received 6 October 1987

modelling gas pressure effects on explosive rock breakage

Documents