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Modelling of blasthole expansion and explosive gas pressurization in jointed media
e
Pergamon
PH:
Int. J. Rock Mech. Min. Sci. Vol. 35, No. 4/5, pp. 497-498, Paper No. 048, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0148-9062(98)00064-3 ISBN: 0080433332 ISSN: 0148-9062/98 $19.00 + 0.00
Modelling of Blasthole Expansion and Explosive Gas Pressurization in Jointed Media A. MORTAZAVIt P. D. KATSABANISt Paper No. 048j Full paper on enclosed CD-ROM Discontinuum modelling methods are advanced modelling techniques which have been introduced during the last decades to simulate the behaviour of jointed media where discontinuities playa significant role in the deformational behavior of the system. In the discontinuum approach, the behavior of rock mass is described by both a continuum material characterization of the intact rock and a discontinuum model for the discontinuities. The discontinuum approach is similar to a continuum approach (i.e. Finite Element, etc.) in the sense that the problem domain is discretized to a system of solid or deformable elements. However, the dimensions of blocks or elements are defined by the size and orientation of existing discontinuities. Displacement fields do not have to be physically continuous; individual blocks may be free to rotate or translate with associated separation at block interfaces. Cundall & Hart (1989) defined the discontinuum approach as methods that are capable of: i) allowing finite displacements and rotations of discrete bodies including complete detachment and ii) recognize the new contacts between blocks automatically as the calculation proceeds. The development of computer models to describe the entire blasting process from detonation to fragmented rock in the muckpile has been an attempt that has only become partially possible in recent times. A complete simulation of the blasting process would include considering all underlying physical and thermodynamic phenomena that contribute to this process. Therefore, a realistic blasting model must be able to describe the detonation process, stress wave propagation and reflection from free boundaries as well as discontinuity surfaces, gas pressurization effects, and blasthole expansion. Recent experimental results indicated that high pressure gases, produced by explosives, playa very significant role in crack development, rock breakage, and subsequent fragmentation and heave. Immediately after the detonation of explosives, high pressure gases are formed which impact the walls of the blasthole. Due to this impact a stress wave is propagated to the surrounding rock mass which typically carries, depending on the rock type, 1/10 to 1/3 of the energy of the explosion. Expanding gases behind the stress wave pressurize the surrounding medium and penetrate into the pre-existing or stress-wave induced discontinuities. Due to its speed the process can be assumed adiabatic. As the blasthole expands and gas penetrates into discontinuities, more area of rock is exposed to pressure and significant energy and momentum exchange occurs within the fragmented material. Consequently, the blasthole chamber expands further and additional cracks may be generated and further propagated. After the momentum exchange with the rock has occurred, the movement of fragments is governed by mechanical interactions of blocks, friction between block edges, and energy loss due to sliding at block interfaces. Thus, the muckpile formation is controlled by the above factors. Important flow parameters to be considered for modelling purposes are; gas viscosity, gas velocity, and frictional properties of discontinuities. Since the expansion of products occurs rapidly, the gas flow effects are not considered important at later times and a greater concern should be exercised to the correct modelling of motion and interaction between blocks. Therefore, the gas pressurization process and throw of material can be divided into two phases: i) Gas expansion and momentum imparted to the fragments. ii) Motion and interaction of fragments until their final rest state in the muckpile. The objective of this paper is to investigate the explosive gas loading mechanism and propose an expansion model for a pressurized blasthole incarcerated in a blocky rock mass. A Discontinuum modelling approach is used in this study to investigate the blasthole expansion and gas pressurization. The Discontinuous Deformation tDepartment of Mining Engineering, Queen's University, Kingston, Ontario, Canada, K7L 3N6 tConference Reference: CAN-411
497
498
NARMS '98
Analysis (DDA method) is modified to allow for blast modelling and gas pressurization effects. DDA is an implicit method in which displacements are the unknowns to be solved. In the DDA method, equations of motion for all blocks are solved simultaneously by minimizing the total potential energy of the blocky system. The interaction between blocks and their boundary are defined in terms of a set of displacement variables. These interactions involve various loading configurations, block physical properties, inertia forces, and displacement constraints at block interfaces and domain boundaries. DDA uses a first order displacement function to describe the block deformation. Total block deformation consists of six components; two rigid body translations in the x and y directions, one rotational component, normal strain in x and y directions, and the shear strain component. Mohr-Coulomb failure criteria is used to model the block interactions along their interfaces and unbalanced forces of system are only dissipated by friction. No artificial damping is used in the method. The DDA formulation is fully dynamic and large displacements are accumulation of displacements over a number of small time steps. The main advantage of DDA is that it uses a set of data that are easily available and physically meaningful. These are; the domain geometry, loading configuration, block material and joints physical properties, and analysis parameters such as: number and size of time step, maximum allowable displacement per step, and contact stiffness. The current version of DDA has several rectifiable shortcomings which are solely a limitation of the implementation, not of the method itself. For example, block deformability is limited due to the use of first order displacement function. This means that stresses and strains are constant within a block. Thus, the model becomes more suited to smaller and regularly shaped blocks. The proposed model for blasthole expansion assumes an adiabatic expansion of explosion products and the blasthole chamber is pressurized uniformly. The gas loading mechanism is treated as an impact problem, as outlined above, and the time intervals used in the analysis are selected reasonably small that the treatment of gas action becomes realistic. The volume of the blasthole chamber is calculated by the "simplex" theory and updated at every time step. Variations in gas pressure upon expansion of the blasthole chamber are calculated from the equation of state of explosive. Key words-discontinuum modelling, contact mechanics, joints, rock blasting, impact dynamic, explosives, gas induced fracturing REFERENCES 1. Cundall, P. A. and Hart, R. D., Numerical Modelling of Discontinua, Key-note Address. In Proc. of 1st U.S. Can! on Discrete Element Meth .. Golden, Colorado, 1989, pp. 1-17.
Pergamon
PH:
Int. J. Rock Mech. Min. Sci. Vol. 35, No. 4/5, pp. 497-498, Paper No. 048, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0148-9062(98)00064-3 ISBN: 0080433332 ISSN: 0148-9062/98 $19.00 + 0.00
Modelling of Blasthole Expansion and Explosive Gas Pressurization in Jointed Media A. MORTAZAVIt P. D. KATSABANISt Paper No. 048j Full paper on enclosed CD-ROM Discontinuum modelling methods are advanced modelling techniques which have been introduced during the last decades to simulate the behaviour of jointed media where discontinuities playa significant role in the deformational behavior of the system. In the discontinuum approach, the behavior of rock mass is described by both a continuum material characterization of the intact rock and a discontinuum model for the discontinuities. The discontinuum approach is similar to a continuum approach (i.e. Finite Element, etc.) in the sense that the problem domain is discretized to a system of solid or deformable elements. However, the dimensions of blocks or elements are defined by the size and orientation of existing discontinuities. Displacement fields do not have to be physically continuous; individual blocks may be free to rotate or translate with associated separation at block interfaces. Cundall & Hart (1989) defined the discontinuum approach as methods that are capable of: i) allowing finite displacements and rotations of discrete bodies including complete detachment and ii) recognize the new contacts between blocks automatically as the calculation proceeds. The development of computer models to describe the entire blasting process from detonation to fragmented rock in the muckpile has been an attempt that has only become partially possible in recent times. A complete simulation of the blasting process would include considering all underlying physical and thermodynamic phenomena that contribute to this process. Therefore, a realistic blasting model must be able to describe the detonation process, stress wave propagation and reflection from free boundaries as well as discontinuity surfaces, gas pressurization effects, and blasthole expansion. Recent experimental results indicated that high pressure gases, produced by explosives, playa very significant role in crack development, rock breakage, and subsequent fragmentation and heave. Immediately after the detonation of explosives, high pressure gases are formed which impact the walls of the blasthole. Due to this impact a stress wave is propagated to the surrounding rock mass which typically carries, depending on the rock type, 1/10 to 1/3 of the energy of the explosion. Expanding gases behind the stress wave pressurize the surrounding medium and penetrate into the pre-existing or stress-wave induced discontinuities. Due to its speed the process can be assumed adiabatic. As the blasthole expands and gas penetrates into discontinuities, more area of rock is exposed to pressure and significant energy and momentum exchange occurs within the fragmented material. Consequently, the blasthole chamber expands further and additional cracks may be generated and further propagated. After the momentum exchange with the rock has occurred, the movement of fragments is governed by mechanical interactions of blocks, friction between block edges, and energy loss due to sliding at block interfaces. Thus, the muckpile formation is controlled by the above factors. Important flow parameters to be considered for modelling purposes are; gas viscosity, gas velocity, and frictional properties of discontinuities. Since the expansion of products occurs rapidly, the gas flow effects are not considered important at later times and a greater concern should be exercised to the correct modelling of motion and interaction between blocks. Therefore, the gas pressurization process and throw of material can be divided into two phases: i) Gas expansion and momentum imparted to the fragments. ii) Motion and interaction of fragments until their final rest state in the muckpile. The objective of this paper is to investigate the explosive gas loading mechanism and propose an expansion model for a pressurized blasthole incarcerated in a blocky rock mass. A Discontinuum modelling approach is used in this study to investigate the blasthole expansion and gas pressurization. The Discontinuous Deformation tDepartment of Mining Engineering, Queen's University, Kingston, Ontario, Canada, K7L 3N6 tConference Reference: CAN-411
497
498
NARMS '98
Analysis (DDA method) is modified to allow for blast modelling and gas pressurization effects. DDA is an implicit method in which displacements are the unknowns to be solved. In the DDA method, equations of motion for all blocks are solved simultaneously by minimizing the total potential energy of the blocky system. The interaction between blocks and their boundary are defined in terms of a set of displacement variables. These interactions involve various loading configurations, block physical properties, inertia forces, and displacement constraints at block interfaces and domain boundaries. DDA uses a first order displacement function to describe the block deformation. Total block deformation consists of six components; two rigid body translations in the x and y directions, one rotational component, normal strain in x and y directions, and the shear strain component. Mohr-Coulomb failure criteria is used to model the block interactions along their interfaces and unbalanced forces of system are only dissipated by friction. No artificial damping is used in the method. The DDA formulation is fully dynamic and large displacements are accumulation of displacements over a number of small time steps. The main advantage of DDA is that it uses a set of data that are easily available and physically meaningful. These are; the domain geometry, loading configuration, block material and joints physical properties, and analysis parameters such as: number and size of time step, maximum allowable displacement per step, and contact stiffness. The current version of DDA has several rectifiable shortcomings which are solely a limitation of the implementation, not of the method itself. For example, block deformability is limited due to the use of first order displacement function. This means that stresses and strains are constant within a block. Thus, the model becomes more suited to smaller and regularly shaped blocks. The proposed model for blasthole expansion assumes an adiabatic expansion of explosion products and the blasthole chamber is pressurized uniformly. The gas loading mechanism is treated as an impact problem, as outlined above, and the time intervals used in the analysis are selected reasonably small that the treatment of gas action becomes realistic. The volume of the blasthole chamber is calculated by the "simplex" theory and updated at every time step. Variations in gas pressure upon expansion of the blasthole chamber are calculated from the equation of state of explosive. Key words-discontinuum modelling, contact mechanics, joints, rock blasting, impact dynamic, explosives, gas induced fracturing REFERENCES 1. Cundall, P. A. and Hart, R. D., Numerical Modelling of Discontinua, Key-note Address. In Proc. of 1st U.S. Can! on Discrete Element Meth .. Golden, Colorado, 1989, pp. 1-17.