This document discusses modeling the dynamic break in underground ring blasting operations. It presents a 3D visualization method using a Kleine field to model the potential break zone around blastholes, which can be used with cavity monitoring surveys to assess dilution and recovery. It examines circular and elliptical break geometries. The document also discusses challenges with underground blasting patterns and powder factors due to complex geometries and the confined nature of drilling. It presents methods for estimating break dimensions and powder factors using different geometric shapes to model the break zone.
This document discusses modeling dynamic rock break from underground metal mining blasts. It describes challenges with underground blasting including non-uniform energy distribution, difficultly determining burden distances, and importance of priming location. The objectives of underground mining blasts are also outlined. The document then examines using geometric shapes and isosurfaces to calculate powder factors and model blast break. It proposes using scalar fields defined on 3D grids to best fit isosurfaces to cavity monitoring surveys for blast modeling and calibration.
This document discusses rock excavation methods, focusing on blasting techniques. It describes how the geologic structure of the rock mass is the most important consideration for blasting. Factors like discontinuity sets, orientations, and slope dip can influence the success of blasting and potential for slope failures. The document provides illustrations of how different joint orientations can impact end break, back break, and the final slope face quality when blasting.
This document discusses modeling the dynamic break in underground ring blasting operations. It presents a 3D visualization method using a Kleine field to model the potential break zone around blastholes, which can be used with cavity monitoring surveys to assess dilution and recovery. It examines circular and elliptical break geometries. The document also discusses challenges with underground blasting patterns and powder factors due to complex geometries and the confined nature of drilling. It explores methods for more accurately representing blast energy distribution and break using geometric shapes instead of just powder factor calculations.
Assessment of powder factor in surface bench blasting using schmidt rebound n...eSAT Journals
Abstract Rock mass characterisation helps in selection and optimum usage of explosive in bench blasting. There are various methods to characterize the rock mass but use of Schmidt hammer in rock characterization before blasting may be a good option. Schmidt hammer, since its simplicity and capability of instant data production, has so far been a powerful tool utilized by many researchers to predict compressive strength of rocks. In this light the present study was conducted in opencast coal mines to see the effect of Schmidt hammer rebound number or transformed compressive strength of rocks on powder factor. The correlation was found sufficiently reliable to enable the determination of optimum powder factor for surface bench blast in different rock types maintaining the required blasting results in terms of fragmentation. Keywords: Powder factor, Schmidt hammer, Rebound number, Rock mass, Overburden bench
Control and Prediction of Blast Fragmentation and It's effect on the Comminut...James Dunford
This technical report discusses controlling and predicting blast fragmentation and its impact on comminution. Section 1 covers bench blast theory, including geometric controls, explosive properties, and rock mass properties. Section 2 discusses comminution theory, including the three laws of comminution and Bonds Law. Section 3 examines how varying geometric controls, explosive type, detonator choice, and delay timing can affect fragmentation. Optimizing these factors can improve comminution efficiency. The report then covers several models for predicting fragmentation and compares their benefits and limitations.
The document discusses developing a safety concept for combined piled-raft foundations, which act as a composite structure consisting of piles, slab, and subsoil. It proposes using a global safety factor approach and reliability index to define acceptable load and resistance values. Future work is needed to establish design standards through additional research involving measurements, model tests, and numerical simulations.
This document discusses techniques for controlled blasting to improve environmental and safety standards. It describes methods like line drilling, trim blasting, pre-splitting, and muffle blasting that are used to control adverse impacts from blasting such as overbreak, ground vibrations, noise, and rock fractures. These techniques involve parameters like drill hole spacing, charge weight, and accurate delay timing to help fragment rock while minimizing damage to surrounding areas.
Firing patterns and its effect on muckpile shape parameters and fragmentation...eSAT Journals
Abstract Proper use of firing pattern vis-à-vis the blast requirements can provide optimal blast performance in terms of fragmentation, throw, wall control etc. This is largely attributed to the importance of firing burden in any blast round. By changing the firing patterns the firing burden, and, thereby the ratio of spacing to burden is also subject to change. Proper initiation timing is as important for fragmentation as the burden, spacing, sub drilling, stemming etc. Simultaneous initiation leads to the problems, such as, coarser fragmentation, blasting of a large number of holes at a given time which leads to the other problems. The present research study which was conducted in three limestone quarries where major problems such as of improper fragmentation, poor wall control, and poor heave characteristics of the muckpile were observed. Designed firing pattern was not able to provide the requisite fragmentation, and, even the throw. Modifications in firing pattern were implemented to obtain the required blast results. Keywords: Firing pattern, fragmentation, progressive relief, throw, drop, muckpile
This document discusses modeling dynamic rock break from underground metal mining blasts. It describes challenges with underground blasting including non-uniform energy distribution, difficultly determining burden distances, and importance of priming location. The objectives of underground mining blasts are also outlined. The document then examines using geometric shapes and isosurfaces to calculate powder factors and model blast break. It proposes using scalar fields defined on 3D grids to best fit isosurfaces to cavity monitoring surveys for blast modeling and calibration.
This document discusses rock excavation methods, focusing on blasting techniques. It describes how the geologic structure of the rock mass is the most important consideration for blasting. Factors like discontinuity sets, orientations, and slope dip can influence the success of blasting and potential for slope failures. The document provides illustrations of how different joint orientations can impact end break, back break, and the final slope face quality when blasting.
This document discusses modeling the dynamic break in underground ring blasting operations. It presents a 3D visualization method using a Kleine field to model the potential break zone around blastholes, which can be used with cavity monitoring surveys to assess dilution and recovery. It examines circular and elliptical break geometries. The document also discusses challenges with underground blasting patterns and powder factors due to complex geometries and the confined nature of drilling. It explores methods for more accurately representing blast energy distribution and break using geometric shapes instead of just powder factor calculations.
Assessment of powder factor in surface bench blasting using schmidt rebound n...eSAT Journals
Abstract Rock mass characterisation helps in selection and optimum usage of explosive in bench blasting. There are various methods to characterize the rock mass but use of Schmidt hammer in rock characterization before blasting may be a good option. Schmidt hammer, since its simplicity and capability of instant data production, has so far been a powerful tool utilized by many researchers to predict compressive strength of rocks. In this light the present study was conducted in opencast coal mines to see the effect of Schmidt hammer rebound number or transformed compressive strength of rocks on powder factor. The correlation was found sufficiently reliable to enable the determination of optimum powder factor for surface bench blast in different rock types maintaining the required blasting results in terms of fragmentation. Keywords: Powder factor, Schmidt hammer, Rebound number, Rock mass, Overburden bench
Control and Prediction of Blast Fragmentation and It's effect on the Comminut...James Dunford
This technical report discusses controlling and predicting blast fragmentation and its impact on comminution. Section 1 covers bench blast theory, including geometric controls, explosive properties, and rock mass properties. Section 2 discusses comminution theory, including the three laws of comminution and Bonds Law. Section 3 examines how varying geometric controls, explosive type, detonator choice, and delay timing can affect fragmentation. Optimizing these factors can improve comminution efficiency. The report then covers several models for predicting fragmentation and compares their benefits and limitations.
The document discusses developing a safety concept for combined piled-raft foundations, which act as a composite structure consisting of piles, slab, and subsoil. It proposes using a global safety factor approach and reliability index to define acceptable load and resistance values. Future work is needed to establish design standards through additional research involving measurements, model tests, and numerical simulations.
This document discusses techniques for controlled blasting to improve environmental and safety standards. It describes methods like line drilling, trim blasting, pre-splitting, and muffle blasting that are used to control adverse impacts from blasting such as overbreak, ground vibrations, noise, and rock fractures. These techniques involve parameters like drill hole spacing, charge weight, and accurate delay timing to help fragment rock while minimizing damage to surrounding areas.
Firing patterns and its effect on muckpile shape parameters and fragmentation...eSAT Journals
Abstract Proper use of firing pattern vis-à-vis the blast requirements can provide optimal blast performance in terms of fragmentation, throw, wall control etc. This is largely attributed to the importance of firing burden in any blast round. By changing the firing patterns the firing burden, and, thereby the ratio of spacing to burden is also subject to change. Proper initiation timing is as important for fragmentation as the burden, spacing, sub drilling, stemming etc. Simultaneous initiation leads to the problems, such as, coarser fragmentation, blasting of a large number of holes at a given time which leads to the other problems. The present research study which was conducted in three limestone quarries where major problems such as of improper fragmentation, poor wall control, and poor heave characteristics of the muckpile were observed. Designed firing pattern was not able to provide the requisite fragmentation, and, even the throw. Modifications in firing pattern were implemented to obtain the required blast results. Keywords: Firing pattern, fragmentation, progressive relief, throw, drop, muckpile
- A new blasting technique called the Power Deck was developed to eliminate subgrade drilling, improve fragmentation, reduce explosive consumption, and lower ground vibrations.
- Single hole and full-scale blast tests were conducted to evaluate the Power Deck system. Results showed reductions in subgrade drilling, ground vibrations up to 33%, explosive consumption by 16-25%, and improved fragmentation up to 25%.
- The tests utilized various instrumentation including high-speed video cameras, seismic monitors, and fragmentation analysis to carefully analyze the results of blasts using the Power Deck technique versus standard blasting.
This document provides a blasting and production schedule for a proposed limestone quarry. It outlines quarry parameters such as bench height and angle. It then details the blast design, including hole diameter, burden, spacing, and explosive parameters. Calculations are shown to determine scaled distance and maximum instantaneous charge. The production schedule involves excavating 20,000 tonnes of limestone per month using a track shovel, loader, and haul trucks. Fragmentation is also addressed. In summary, this document comprehensively designs the blasting and mining processes for a limestone quarry to meet production targets in a safe and efficient manner.
The document discusses rock mass properties and the Hoek-Brown failure criterion for estimating the strength of jointed rock masses. It presents the generalized Hoek-Brown criterion equation and describes how to determine the intact rock properties of uniaxial compressive strength (σci) and the Hoek-Brown constant (mi) from triaxial test data or estimates. It also discusses estimating the Geological Strength Index (GSI) of the rock mass.
Subsidence is one of the major environmental issues related to underground mining industry. This presentation gives an insight to causes, nature, effect of subsidence and some mitigation measures.
This document discusses the Hoek-Brown failure criterion for estimating the strength and deformation properties of rock masses. It provides details on:
1) Estimating the intact rock strength (ciσ) and Hoek-Brown constant (mi) from triaxial test data on rock cores.
2) Methods for estimating ciσ and mi when direct testing is not possible.
3) Factors that influence rock mass strength estimates such as rock type, discontinuity spacing, and scale of the structure being analyzed.
Fluid and structural modeling of cavitating propeller flowsPhuong Dx
This document summarizes previous research on modeling cavitating propeller flows and hydroelastic effects. It presents the objective to develop a coupled boundary element-finite element model to predict cavitation patterns and hydroelastic response of propellers. An overview is given of the boundary element formulation used, including the assumptions of potential, incompressible, and cavitating sheet flow. Boundary conditions at wetted surfaces and cavities are described. Validation with experiments is discussed.
Numerical and Analytical Solutions for Ovaling Deformation in Circular Tunnel...IDES Editor
Ovaling deformations develop when waves propagate
perpendicular to the tunnel axis. Two analytical solutions are
used for estimating the ovaling deformations and forces in
circular tunnels due to soil–structure interaction under
seismic loading. In this paper, these two closed form solutions
will be described briefly, and then a comparison between these
methods will be made by changing the ground parameters.
Differences between the results of these two methods in
calculating the magnitudes of thrust on tunnel lining are
significant. For verifying the results of these two closed form
solutions, numerical analyses were performed using finite
element code (ABAQUS program). These analyses show that
the two closed form solutions provide the same results only
for full-slip condition.
This document discusses design considerations for large underground caverns excavated in weak rock at depths of 100-300m below the surface for hydroelectric projects. It addresses the stability of caverns and surrounding rock mass given in situ stress conditions, effects of nearby slopes, and determining appropriate pillar sizes between excavations. The key design factors are the strength of the rock mass, influence of structural features like joints and bedding planes, sequence of excavation and support, and stress changes induced by nearby slopes and excavations. Pillar size between caverns must consider stresses imposed and stability of the rock mass.
The document discusses the design of anchored sheet pile walls. It provides steps for designing anchored sheet pile walls in both cohesionless and cohesive soils. For cohesionless soils, it describes how to calculate active and passive earth pressures, determine the embedded depth, and calculate the anchor force and maximum bending moment. For cohesive soils, it similarly describes calculating active and passive pressures, determining the embedded depth through iteration, and sizing the sheet pile. The document also provides an example design for each soil type.
This document discusses how different explosive energies used in blasting can influence the strength of resulting rock fragments and the throughput of a SAG mill. Experimental studies found that higher explosive energies produced weaker rock fragments through cracking and damage. To validate this, granite samples were blasted using explosives with different velocities and the fragments were tested. Comminution parameters showed the fragments were weaker when higher energies were used. Modelling found this pre-conditioning of fragments could increase SAG mill throughput by up to 20%.
Hand scaling and mechanical scaling are commonly used stabilization methods to remove loose rock from slopes. Scaling is effective for 2-10 years as a temporary measure. Trim blasting can also be used to remove larger sections of rock too big for scaling. Reinforcement systems work to strengthen slopes internally by increasing resistance along fractures, while external systems protect from erosion. The most effective stabilization strategies alter slope geometry or add reinforcement or drainage systems.
The document discusses the shear strength of discontinuities in rock masses. It defines key terms like basic friction angle (φb), residual friction angle (φr), cohesion (c), and introduces Barton's method for estimating shear strength which accounts for joint roughness coefficient (JRC) and joint compressive strength (JCS). Small scale laboratory tests are used to determine φb, while JRC and JCS are estimated visually in the field. The shear strength of rough surfaces is higher than smooth surfaces due to surface asperities. Shear strength decreases if discontinuities are filled with soft materials like clay.
This document summarizes design guidelines for supporting tunnels based on rock mass quality as measured by the Rock Mass Rating (RMR) system. It provides updated charts and relationships for determining:
(i) Rockbolt, shotcrete, and steel rib support requirements based on excavation span and RMR;
(ii) Recommended tunnel shapes based on RMR; and
(iii) Methods for estimating properties like rock load and shotcrete/bolt capacities as a function of RMR.
The guidelines are intended to provide practical design aids for tunnel engineers based on accumulated experience using RMR over 40 years, complementing but not replacing numerical modeling approaches.
1) Not all of the explosive energy is used for rock fragmentation, as some is lost through early venting of gases from the blasthole before pressures drop sufficiently.
2) Numerical modeling shows peak blasthole pressure only lasts 1-2 milliseconds, during which time fractures form around the blasthole. Containing gases during this critical period is important for maximizing energy transfer to the rock.
3) Explosives with higher density and velocity of detonation are better able to transfer energy to the rock quickly before venting occurs, compared to lower density explosives like ANFO.
The document discusses shear strength of discontinuities in rock masses. It introduces concepts like shear strength of planar surfaces, shear strength of rough surfaces, Barton's estimate of shear strength which relates shear strength to joint roughness coefficient (JRC) and joint compressive strength (JCS). It discusses estimating JRC and JCS in the field and how these parameters are influenced by scale. It also summarizes the shear strength of filled discontinuities and the influence of water pressure on shear strength.
This document presents revisions to the Hoek-Brown failure criterion for rock masses. It resolves uncertainties in applying the criterion and incorporating it into numerical models. The revised criterion sets out a recommended calculation sequence and defines equations to determine rock mass strength parameters like cohesive strength and friction angle from the Geological Strength Index rating of rock mass quality. It also distinguishes between undisturbed and disturbed rock masses using a new disturbance factor.
This document provides an overview of mat foundations. It discusses common types of mat foundations including flat plate, flat plate thickened under columns, beams and slab, and slab with basement walls. It describes how to calculate the bearing capacity of mat foundations and differential settlement. Methods for structural design of mat foundations are presented, including the conventional rigid method and approximate flexible method. Examples are provided to illustrate how to design combined footings, calculate bearing capacity, and structurally design mat foundations.
The effect of soil improvement on foundation super structure designIAEME Publication
This document summarizes a study on the effects of soil improvement on raft and folded plate foundation design. The authors used Winkler and continuum modeling methods to analyze raft foundations with and without soil strength increases below high settlement areas. They found that localized soil improvement significantly reduced settlement and allowed for reductions in foundation and superstructure material requirements like concrete and steel reinforcement. Selectively increasing soil stiffness parameters like modulus of subgrade reaction (ks) and modulus of elasticity (E) provided benefits to both flat raft and folded plate foundation designs in terms of reduced settlement, moments, and reinforcement needs.
A study-of-the-behaviour-of-overlying-strata-in-longwall-mining-and-its-appli...Agustino Rosas
This study investigated the behavior of rock strata above a longwall coal mining face. Instruments were installed in boreholes above an active longwall face in China to monitor the movement of rock layers over time. The data showed three zones of behavior: 1) an abutment pressure zone with little movement near the face, 2) a bed separation zone where rock layers began to separate as the face passed, and 3) a consolidation zone further away where the layers reconsolidated. By analyzing the displacement curves, a structural model was created to examine how forces are distributed between the rock blocks as mining progresses. This model can help explain some phenomena observed during longwall mining such as ground subsidence and roof pressure development.
This document provides guidelines for surface blast design in mining operations. It discusses elements such as free face, hole diameter and burden ratio to face height, burden and spacing ratios, subdrilling, stemming, decking, powder factor calculations, choice of blast patterns including staggered and square, use of delays between holes and rows, and references for further information. The guidelines aim to optimize fragmentation while maintaining costs and safety.
Research on mean partical size after drilling & blasting by Abhijit palAbhijit Pal
Rock fragmentation is important for mining efficiency. Factors like blast design, explosives used, and rock properties affect fragment size. A report from Tata Steel showed mean fragment sizes ranging from 15-49 cm for overburden and coal over 10 days. Software can analyze muckpile photos and provide fragmentation data like size distributions and percentages. Understanding fragmentation allows optimizing blasting for maximum production.
- A new blasting technique called the Power Deck was developed to eliminate subgrade drilling, improve fragmentation, reduce explosive consumption, and lower ground vibrations.
- Single hole and full-scale blast tests were conducted to evaluate the Power Deck system. Results showed reductions in subgrade drilling, ground vibrations up to 33%, explosive consumption by 16-25%, and improved fragmentation up to 25%.
- The tests utilized various instrumentation including high-speed video cameras, seismic monitors, and fragmentation analysis to carefully analyze the results of blasts using the Power Deck technique versus standard blasting.
This document provides a blasting and production schedule for a proposed limestone quarry. It outlines quarry parameters such as bench height and angle. It then details the blast design, including hole diameter, burden, spacing, and explosive parameters. Calculations are shown to determine scaled distance and maximum instantaneous charge. The production schedule involves excavating 20,000 tonnes of limestone per month using a track shovel, loader, and haul trucks. Fragmentation is also addressed. In summary, this document comprehensively designs the blasting and mining processes for a limestone quarry to meet production targets in a safe and efficient manner.
The document discusses rock mass properties and the Hoek-Brown failure criterion for estimating the strength of jointed rock masses. It presents the generalized Hoek-Brown criterion equation and describes how to determine the intact rock properties of uniaxial compressive strength (σci) and the Hoek-Brown constant (mi) from triaxial test data or estimates. It also discusses estimating the Geological Strength Index (GSI) of the rock mass.
Subsidence is one of the major environmental issues related to underground mining industry. This presentation gives an insight to causes, nature, effect of subsidence and some mitigation measures.
This document discusses the Hoek-Brown failure criterion for estimating the strength and deformation properties of rock masses. It provides details on:
1) Estimating the intact rock strength (ciσ) and Hoek-Brown constant (mi) from triaxial test data on rock cores.
2) Methods for estimating ciσ and mi when direct testing is not possible.
3) Factors that influence rock mass strength estimates such as rock type, discontinuity spacing, and scale of the structure being analyzed.
Fluid and structural modeling of cavitating propeller flowsPhuong Dx
This document summarizes previous research on modeling cavitating propeller flows and hydroelastic effects. It presents the objective to develop a coupled boundary element-finite element model to predict cavitation patterns and hydroelastic response of propellers. An overview is given of the boundary element formulation used, including the assumptions of potential, incompressible, and cavitating sheet flow. Boundary conditions at wetted surfaces and cavities are described. Validation with experiments is discussed.
Numerical and Analytical Solutions for Ovaling Deformation in Circular Tunnel...IDES Editor
Ovaling deformations develop when waves propagate
perpendicular to the tunnel axis. Two analytical solutions are
used for estimating the ovaling deformations and forces in
circular tunnels due to soil–structure interaction under
seismic loading. In this paper, these two closed form solutions
will be described briefly, and then a comparison between these
methods will be made by changing the ground parameters.
Differences between the results of these two methods in
calculating the magnitudes of thrust on tunnel lining are
significant. For verifying the results of these two closed form
solutions, numerical analyses were performed using finite
element code (ABAQUS program). These analyses show that
the two closed form solutions provide the same results only
for full-slip condition.
This document discusses design considerations for large underground caverns excavated in weak rock at depths of 100-300m below the surface for hydroelectric projects. It addresses the stability of caverns and surrounding rock mass given in situ stress conditions, effects of nearby slopes, and determining appropriate pillar sizes between excavations. The key design factors are the strength of the rock mass, influence of structural features like joints and bedding planes, sequence of excavation and support, and stress changes induced by nearby slopes and excavations. Pillar size between caverns must consider stresses imposed and stability of the rock mass.
The document discusses the design of anchored sheet pile walls. It provides steps for designing anchored sheet pile walls in both cohesionless and cohesive soils. For cohesionless soils, it describes how to calculate active and passive earth pressures, determine the embedded depth, and calculate the anchor force and maximum bending moment. For cohesive soils, it similarly describes calculating active and passive pressures, determining the embedded depth through iteration, and sizing the sheet pile. The document also provides an example design for each soil type.
This document discusses how different explosive energies used in blasting can influence the strength of resulting rock fragments and the throughput of a SAG mill. Experimental studies found that higher explosive energies produced weaker rock fragments through cracking and damage. To validate this, granite samples were blasted using explosives with different velocities and the fragments were tested. Comminution parameters showed the fragments were weaker when higher energies were used. Modelling found this pre-conditioning of fragments could increase SAG mill throughput by up to 20%.
Hand scaling and mechanical scaling are commonly used stabilization methods to remove loose rock from slopes. Scaling is effective for 2-10 years as a temporary measure. Trim blasting can also be used to remove larger sections of rock too big for scaling. Reinforcement systems work to strengthen slopes internally by increasing resistance along fractures, while external systems protect from erosion. The most effective stabilization strategies alter slope geometry or add reinforcement or drainage systems.
The document discusses the shear strength of discontinuities in rock masses. It defines key terms like basic friction angle (φb), residual friction angle (φr), cohesion (c), and introduces Barton's method for estimating shear strength which accounts for joint roughness coefficient (JRC) and joint compressive strength (JCS). Small scale laboratory tests are used to determine φb, while JRC and JCS are estimated visually in the field. The shear strength of rough surfaces is higher than smooth surfaces due to surface asperities. Shear strength decreases if discontinuities are filled with soft materials like clay.
This document summarizes design guidelines for supporting tunnels based on rock mass quality as measured by the Rock Mass Rating (RMR) system. It provides updated charts and relationships for determining:
(i) Rockbolt, shotcrete, and steel rib support requirements based on excavation span and RMR;
(ii) Recommended tunnel shapes based on RMR; and
(iii) Methods for estimating properties like rock load and shotcrete/bolt capacities as a function of RMR.
The guidelines are intended to provide practical design aids for tunnel engineers based on accumulated experience using RMR over 40 years, complementing but not replacing numerical modeling approaches.
1) Not all of the explosive energy is used for rock fragmentation, as some is lost through early venting of gases from the blasthole before pressures drop sufficiently.
2) Numerical modeling shows peak blasthole pressure only lasts 1-2 milliseconds, during which time fractures form around the blasthole. Containing gases during this critical period is important for maximizing energy transfer to the rock.
3) Explosives with higher density and velocity of detonation are better able to transfer energy to the rock quickly before venting occurs, compared to lower density explosives like ANFO.
The document discusses shear strength of discontinuities in rock masses. It introduces concepts like shear strength of planar surfaces, shear strength of rough surfaces, Barton's estimate of shear strength which relates shear strength to joint roughness coefficient (JRC) and joint compressive strength (JCS). It discusses estimating JRC and JCS in the field and how these parameters are influenced by scale. It also summarizes the shear strength of filled discontinuities and the influence of water pressure on shear strength.
This document presents revisions to the Hoek-Brown failure criterion for rock masses. It resolves uncertainties in applying the criterion and incorporating it into numerical models. The revised criterion sets out a recommended calculation sequence and defines equations to determine rock mass strength parameters like cohesive strength and friction angle from the Geological Strength Index rating of rock mass quality. It also distinguishes between undisturbed and disturbed rock masses using a new disturbance factor.
This document provides an overview of mat foundations. It discusses common types of mat foundations including flat plate, flat plate thickened under columns, beams and slab, and slab with basement walls. It describes how to calculate the bearing capacity of mat foundations and differential settlement. Methods for structural design of mat foundations are presented, including the conventional rigid method and approximate flexible method. Examples are provided to illustrate how to design combined footings, calculate bearing capacity, and structurally design mat foundations.
The effect of soil improvement on foundation super structure designIAEME Publication
This document summarizes a study on the effects of soil improvement on raft and folded plate foundation design. The authors used Winkler and continuum modeling methods to analyze raft foundations with and without soil strength increases below high settlement areas. They found that localized soil improvement significantly reduced settlement and allowed for reductions in foundation and superstructure material requirements like concrete and steel reinforcement. Selectively increasing soil stiffness parameters like modulus of subgrade reaction (ks) and modulus of elasticity (E) provided benefits to both flat raft and folded plate foundation designs in terms of reduced settlement, moments, and reinforcement needs.
A study-of-the-behaviour-of-overlying-strata-in-longwall-mining-and-its-appli...Agustino Rosas
This study investigated the behavior of rock strata above a longwall coal mining face. Instruments were installed in boreholes above an active longwall face in China to monitor the movement of rock layers over time. The data showed three zones of behavior: 1) an abutment pressure zone with little movement near the face, 2) a bed separation zone where rock layers began to separate as the face passed, and 3) a consolidation zone further away where the layers reconsolidated. By analyzing the displacement curves, a structural model was created to examine how forces are distributed between the rock blocks as mining progresses. This model can help explain some phenomena observed during longwall mining such as ground subsidence and roof pressure development.
This document provides guidelines for surface blast design in mining operations. It discusses elements such as free face, hole diameter and burden ratio to face height, burden and spacing ratios, subdrilling, stemming, decking, powder factor calculations, choice of blast patterns including staggered and square, use of delays between holes and rows, and references for further information. The guidelines aim to optimize fragmentation while maintaining costs and safety.
Research on mean partical size after drilling & blasting by Abhijit palAbhijit Pal
Rock fragmentation is important for mining efficiency. Factors like blast design, explosives used, and rock properties affect fragment size. A report from Tata Steel showed mean fragment sizes ranging from 15-49 cm for overburden and coal over 10 days. Software can analyze muckpile photos and provide fragmentation data like size distributions and percentages. Understanding fragmentation allows optimizing blasting for maximum production.
This document discusses blasthole drilling and initiation patterns in surface blasting. It covers the following key points:
1) The layout of drill holes, burden, spacing and their ratio have an important effect on blasting results. A staggered pattern with a spacing to burden ratio of 1 to 1.5 provides the best coverage of fractured areas.
2) When blastholes are fired independently, a cylindrical "plug" of broken ground is created around each hole. The optimal burden results in maximum ground fracturing and heaving of loosened rock.
3) Blasthole initiation patterns can be used to control the degree of interaction between adjacent holes and the overall blast performance. The intra-row delay controls interaction between
The document discusses tunnelling and geological aspects of tunnelling. It provides details on the history and types of tunnels, benefits of tunnels, tunnel construction equipment, and geological considerations for tunnel design including rock mass characterization, structural mapping, discontinuity analysis, and instability mechanisms. Key blocks and maximum wedge theories are described for evaluating potential rock failures around tunnel excavations.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
New burn cut blast design in drives enhances drilling blasting efficiency wit...partha sharma
A new Burn-Cut blast pattern has been designed for drives, declines and ramps in underground metal mines, to replace a design (of Decked-Burn with more number of holes), which was giving number of blast failures, such as ‘Under_Blast’ - difficult to handle. The new Burn-cut design contains less number of blast-holes and Reamer than earlier Decked-Burn-cut. Decked system has been removed to make the charging operation easier. This enables to increase explosives energy in a hole and to reduce stemming length in order to eliminate above blast failures. Moreover, requirement of Detonators is reduced, as Decked system has been abolished. Total explosives quantity has been reduced marginally. Thus, drilling efficiency and cost effectiveness has been achieved. Entire process has been done by changing the original pattern / system in three phases.
Composite dome Shape and Pressure Vessels Optimizationalilimam2
This document presents a multi-level optimization strategy for composite pressure vessels with nonmetallic liners. In the first level, different head shapes (geodesic and ellipsoidal) and winding angles are compared based on maximizing a "modified shape factor" objective function calculated using finite element analysis. In the second level, the stacking sequence and number of layers are further optimized for the best head shape and winding angle selected in level 1. The goal is to optimize design variables like head shape, winding angle, layer thickness, number of layers, and stacking sequence to improve burst pressure, internal volume, and reduce vessel weight.
The document discusses factors that influence blast design and describes the various components of bench blast design. It provides background on how the blast design must balance parameters to achieve desired fragmentation. The factors affecting blast design are classified as uncontrollable geological variables and controllable variables like hole diameter, burden, spacing, stemming, and firing system. Formulas are provided for calculating the values of bench blast design components like burden, spacing, subdrilling, hole depth, and stemming height using the Ash approach. Examples are worked out using initial assumptions of a 115mm hole diameter, emulsion explosive, and medium rock density. The document concludes with discussing powder factor calculation and the basic steps for successful blast design.
The application of the SRV in the development of the shale gasIJRES Journal
1) Stimulated Reservoir Volume (SRV) is a hydraulic fracturing technique used to develop shale gas reservoirs. It aims to form a complex three-dimensional fracture network to increase the effective reservoir volume and gas production.
2) SRV involves using multi-stage fracturing in horizontal wells to create a network of natural and artificial fractures. This increases the contact area between the fractures and shale gas resources.
3) While SRV has been successfully used in shale gas development, more research is still needed to optimize fracture network formation and improve fracturing technologies for different shale reservoirs.
The document discusses techniques for open pit mining blasts, including:
- Major factors like attitude, communication, blast design, and geological effects influence blast efficiency
- Proper blast design considers uniform energy distribution, confinement, energy level, and design adjustments for conditions
- Geological effects like rock properties, structure, water, and seam orientations impact blasting results more than explosive properties
- Basic blast design considerations include bench height, hole diameter, burden, spacing, stemming, and decking
IRJET- Effects of Excavation-Geometry on Blast- Geometry with Reference t...IRJET Journal
This document discusses the effects of excavation geometry on blast geometry with reference to blast hole diameter and bench height. It analyzes data collected from coal mines in India to investigate the relationship between these factors and develop a new multiple regression model. The study finds that blast hole depth and spacing are statistically significant predictors of hole diameter. While burden is included in the final model, its impact is less significant. The regression model can help mining professionals accurately design blasting operations.
This technical paper discusses methods for estimating the amount of urea stored in a silo. It explains that the packing arrangement and bulk volume of urea depends on factors like inter-particle friction. It then provides three methods for calculating the urea quantity based on the shape of the urea pile: 1) for a simple conical shape, 2) for a triangular cross-section with length L, and 3) for a bottom portion parallel to the silo plus a conical top portion. The paper concludes that accurately estimating urea quantities is challenging due to non-symmetrical shapes and varying densities, but provides conceptual frameworks for making rough calculations.
This technical paper discusses methods for estimating the amount of urea stored in a silo. It examines how the packing arrangement and bulk density of urea prills depends on factors like inter-particle friction. It also outlines considerations for measuring solids piles, like the angle of repose. The paper then provides specific methods for estimating urea quantity based on the shape of the pile, including formulas for conical or triangular shapes. Dimensions needed for calculating the volume of a sample silo are also given.
The document discusses planning for surface mine mechanization using a balancing diagram. It describes how a balancing diagram can be used to determine suitable seating positions for draglines to maximize overburden removal and coal exposure while minimizing rehandling. The balancing diagram shows dragline cuts, spoil geometry, bench heights, and helps estimate coal exposure rates and workload distribution between draglines. Steps are provided for developing a balancing diagram, including calculating dragline production and deciding cut widths, bench heights, and dragline positions.
FACTORS USED IN ESTIMATING THROUGHPUT FOR CUTTER SUCTION DREDGES William Wetta
Many factors contribute to limitations in the throughput of cutter suctions dredge. While most performance data available from cutter suction dredge manufactures outlines theoretical design throughput, others factors need to be considered when estimated expected throughput. This is obviously important for estimating purposes but also to understand what factors cause limitations on the performance of the dredges. This paper will go into detail on understanding the effects on bank height and its relation to throughput rates. The paper will address cutter limitations by showing the affect of throughput on a dredge that is excavating material with high compaction rates with cutter systems under and properly designed to meet the required breakout forces. The paper will address the effects of different material types and how the material classifications affect the performance of the dredge. This paper will also detail pump limitations and the overall system designs required for optimal equipment efficiency. Other factors that will be addressed include; dredge pump location with respect to dredging depth, pipeline choice, pipeline length, dredge repositioning time, cut width and the overall efficiency of the dredging system.
This document describes an algorithm for optimizing the shape of composite pressure vessel domes. The algorithm uses genetic algorithms and finite element analysis to optimize design parameters like control point weights, winding angle, and dome depth that define the dome shape using a rational B-spline curve. The objective is to maximize shape factor, which is the ratio of internal volume to weight. Constraints include geometric limits, winding conditions, and failure criteria evaluated using Tsai-Wu analysis. The algorithm is applied to a compressed natural gas pressure vessel to efficiently define the optimal dome shape.
This paper presents an algorithm for shape optimization of composite pressure
vessels head. The shape factor which is defined as the ratio of internal volume to weight of
the vessel is used as an objective function. Design constrains consist of the geometrical
limitations, winding conditions, and Tsai-Wu failure criterion. The geometry of dome shape
is defined by a B-spline rational curve. By altering the weights of control points, depth of
dome, and winding angle, the dome shape is changed. The proposed algorithm uses genetic
algorithm and finite element analysis to optimize the design parameters. The algorithm is
applied on a CNG pressure vessel and the results show that the proposed algorithm can
efficiently define the optimal dome shape. This algorithm is general and can be used for
general shape optimization
Its a presentation about the design aspect of open cast mine. The author believes it will surely help the mining engineering students at the beginning level.
Similar to Modeling of Dynamic Break in Underground Ring Blasting (20)
Modeling of Dynamic Break in Underground Ring Blasting
1. Modeling of Dynamic Break in Underground Ring Blasting
Abstract
Underground blasting operations are challenging from the standpoint of the distribution of explosives
energy representative of ring blasting. Energy from both shock and pressure regimes of commercial
explosives may appear concentrated in the collar region of a typical ring blast and diluted at the toes of
holes due to the oblique geometries of blastholes. The non-homogenous nature of ore in which explosives
are distributed via drillholes, adds to the complexities of generating particulate profiles from fragmented
material with consistencies that are predictable from blast pattern to blast pattern - well suited for specific
underground handling equipment and mill processing. In an ideal world, it would be the blasting
operations themselves that represent the primary crushing mechanism, or at least mitigate mechanical
crushing that can comprise a large component of the cost in generating suitable muck.
This paper presents a dynamic break view in 3D that allows a planner to visualize the potential break zone
around a blasthole generated by an explosive load using a Kleine field. Simple as it sounds, this
methodology provides information that can be used in conjunction with cavity monitoring surveys (CMS)
to potentially judge dilution due to overbreak as well as recovery for a typical blast. As examples, there
are two break geometries that are examined regarding circular breaks and elliptical breaks around
blastholes. Using a Kleine field to define break, a planner generated isosurface can be generated and
compared to CMS data for calibration and prediction, using AEGIS 3D ring design software.
Underground Blasting Operations
Powder factor limitations for underground blasting operations are listed with some observations;
• Patterns can be very complex and are constrained by the shape of the orebody as well as drift
size and sublevel heights
• Perimeter control is used mostly in development operations and not generally used in stope
blasting which may include Sublevel Cave (SLC), Open Stope Slot and Slash (OSS) as well as
Vertical Retreat Mining (VRM)
• Mass blasts can be large and multilevel in scope – fragmentation is qualitatively and
quantitatively appraised as broken material is mucked out via scooptram by the scooptram
operator
• Energy distribution from detonating explosives tends to be concentrated at the collar due to the
confined nature of drilling from drifts and diluted at the toes because of the oblique geometry of
rings
• Powder factors are not easily calculated and are either estimated from toe to toe dimensions or
calculated from the total volume of muck broken and the amount of explosives used
• Powder factors in many underground blasting operations appear to be twice those of surface
blasting operations – break is hole to one-half the distance to an adjacent hole
• Free face for next row of drillholes (in a ring) is not visible; distance to next ring to detonate is
not known
• The future of underground mining operations is to go deeper such that great attention is being
focused on ground stability - especially with regard to blast design
There are severe constraints with regard to the design of underground blasting operations from the
standpoint of ground support, ore block modeling - as well as production requirements that are dependent
on the number of active workplaces. Safety is paramount. It becomes important to ensure that blasting
2. operations limit overbreak and dilution, including the restriction of overbreak into support structures.
Recovery of valuable ore without dilution is the targeted goal of ring blasting design.
The Powder Factor Dilemma
In underground mining operations, the preference is to define PF (powder factor) as the weight of
explosive required per unit volume or weight of ore used to fragment either a cubic meter or tonne of solid
material. Thus, the units become kg/m3
or kg/tonne using metric units, or lbs/yd3
and lbs/ton in imperial
units. Note that there is no direct association of explosive energy in the formula when powder factor is
used as shown below:
𝑷𝑭 =
𝑾 𝑬𝒙𝒑𝒍𝒐𝒔𝒊𝒗𝒆
𝑽 𝒐𝒓𝒆, 𝑾 𝒐𝒓𝒆
; (𝟏)
Where:
PF = powder factor (
𝑘𝑔
𝑚3
;
𝑙𝑏𝑠
𝑦𝑑3
) , (
𝑘𝑔
𝑡𝑜𝑛𝑛𝑒
;
𝑙𝑏𝑠
𝑡𝑜𝑛
)
W𝐸𝑥𝑝𝑙𝑜𝑠𝑖𝑣𝑒 = weight of explosives used in blast (kg; lbs)
𝑉𝑜 𝑟𝑒, 𝑊𝑂𝑟𝑒 = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑜𝑟𝑒 𝑏𝑙𝑎𝑠𝑡𝑒𝑑 (𝑚3
, 𝑡𝑜𝑛𝑛𝑒; 𝑦𝑑3
, 𝑡𝑜𝑛)
Not being able to refer to energy in the formula causes problems not only from the oblique nature of ring
design but also for predicting the degree of overbreak for individual stoping operations. It becomes quite
apparent that blasthole geometry plays an extremely important role with regard to the focus of blast energy
and how it will be distributed. The direction of blast motion becomes an important factor in insuring that
blasting energy is propagated to the right free face (away from both topsill and bottomsill). PF is usually
calculated on a per ring or per blast basis for a specific explosive type.
Different rock or ore types may require different weights of explosives to generate equivalent
fragmentation profiles. If a low strength explosive is used, it may require blasting patterns to shrink in
order to get the same fragmentation level as that produced by a higher strength explosive.
Rectangular Volume – 1
𝑽 = 𝑩𝑺𝑳 ; (𝟐)
L = explosive column height
S = spacing
B = burden
Cylindrical Volume – 2
𝑽 = 𝝅𝑹 𝟐
𝑳 ; (𝟑)
L = explosive column height
R = radial break
Prolate Ellipsoid Volume – 3
𝑽 =
𝟒
𝟑
𝝅 ×
𝟏
𝟐
𝑳 × 𝑹 𝟐
; (4)
L = column height
B = burden, S = Burden, S = B = R
Figures 1, 2 and 3 illustrating some geometries to define powder factor.
3. The objective is to arrive at a calculation that is more likely to represent the action of a detonating
explosive column in terms of geometrical ‘break’- in which break represents the requisite number of crack
pathways that provides a fragmentation profile required for mine handling equipment. Figures 1, 2 and 3
attempt to rationalize rectangular volumes, which may be suitable for surface mining such that patterns
are either square, rectangular and/or staggered, to geometric shapes that represent break action that is
radially outward from a blasthole in a ring.
Underground mining operations demand drilling accuracy. Blastholes 100 mm (4 in) diameter are common
for open stoping operations and can be long – sometimes over 5 times the length of blastholes drilled in
open cast mining.
Drilling straight holes at the proper location can sometimes prove to be difficult. Figures 4, 5 and 6 below
show the different types of errors that contribute to inaccuracies in blasting patterns responsible for
distributing explosive energy throughout a rock/ore mass. In opencast mining operations, holes rarely
exceed 20 m in depth.
Figure 4 Figure 5 Figure 6
Figure 4 illustrating typical drilling errors.
Figure 5 shows break cylinders that are in and out of the ring plane as shown in Figure 4.
Figure 6 indicates a ring longitudinal section (sideways view) in which holes are in and out of the
ring plane seen in underground blasting operations.
For the case of underground PF’s, ring geometries can be quite different and difficult to design.
Blastholes are not drilled to the same depth; the resulting geometry conforms to a quadrilateral forming a
trapezium (a quadrilateral without parallel sides). Ring burden is used to calculate the volume addressed
for each hole in a ring to define a representative PF .
To get an accurate powder factor, the total explosives used in an underground blast is divided by the total
tons produced. This number can only be determined accurately when a stope has been completely mucked
out.
4. Figure 7 shows some of the different quadrilateral shapes that can sometimes be used to calculate powder
factor for rings.
Figure 7 shows examples of four-sided shapes that may be used to calculate powder factor with
the trapezium being very common for underground ring design.
Figures 8, 9 and 10 illustrate the trapezium type geometries that must addressed. Figure 10 is useful
showing concentrations of energy and/or lack of it.
Figure 8 Figure 9 Figure 10
Figure 8 shows a trapezium formed by connecting the collars and toes of two holes.
The right angled distance between rings provides the burden component. Right angle
distance between toes is assumed to provide the spacing component.
Figure 9 illustrates a ring design in which the fragmentation suffers not only to drilling
but also loading. In this case holes were not fully charged because of blocked holes with
the belief that the next ring will take care of the drilling/loading problem.
Figure 10 shows an actual ring with ‘break overlap’ simulated for each hole defined by
‘break’ cylinders. Collars can be staggered to avoid concentration of energy in this
region. In this view, it is easy to visualize the break around a blasthole based on a
planner’s experience.
5. For the cylindrical volume in which radial break is Rradial.cylinder, using Figure 2 for the Figure 10 cylindrical
break example above, the formula for an equivalent radial break based on the volume calculation for an
equivalent volume enclosed by a rectangular block (total confinement) is;
𝑩 × 𝑺 × 𝑳 = 𝝅 × 𝑹 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓
𝟐
× 𝑳 ; (5)
𝑹 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓 = √
𝑩 × 𝑺
𝝅
; 𝒇𝒐𝒓 𝒄𝒚𝒍𝒊𝒏𝒅𝒓𝒊𝒄𝒂𝒍 𝒃𝒓𝒆𝒂𝒌 ; (𝟔)
And, in a similar manner, the prolate ellipsoidal volume calculated such that B and S are equal and in the
prolate case will represent the burden and spacing such that B2
represents the break as shown below;
𝑩 × 𝑺 × 𝑳 =
𝟒
𝟑
𝝅 ×
𝟏
𝟐
𝑳 × 𝑹 𝒆𝒍𝒍𝒊𝒑𝒔𝒐𝒊𝒅
𝟐
; 𝒇𝒐𝒓 𝒂 𝒑𝒓𝒐𝒍𝒂𝒕𝒆 𝒆𝒍𝒍𝒊𝒑𝒔𝒐𝒊𝒅 ; (𝟕)
𝑹 𝒆𝒍𝒍𝒊𝒑𝒔𝒐𝒊𝒅 = √
𝟑 × 𝑺
𝟐 × 𝝅
; 𝒇𝒐𝒓 𝒆𝒍𝒍𝒊𝒑𝒔𝒐𝒊𝒅𝒂𝒍 𝒃𝒓𝒆𝒂𝒌 ; (𝟖)
By way of an example, using a ring pattern for sublevel cave mining with a toe spacing of 2.7 m (8.9 ft),
with a 2.4 m (7.9 ft) burden between rings - with the longest hole in the ring having a length of 30.5 m
(100 ft), and using the rectilinear figure, the volume would be 198 m3
. With this volume as common to
the other figures, the radial breaks can be approximated in Table 1. PF is based on a fully coupled emulsion
explosive at a density of 1.25 gm/cm3
in a 100 mm (4 in) borehole 30.5 m (100 ft) long.
Table 1 showing break dimensions in terms of common geometric shapes.
Geometrical Shape
Volume
(m3
)
Radial Break
(m)
Powder Factor
(kg/tonne)
Rectangular
𝑽 = 𝑩 × 𝑺 × 𝑳
198 1.51
Cylindrical
𝑽 = 𝝅 × 𝑹 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓
𝟐
𝑳
𝑹 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓=√
B × S
π
=1.44
Prolate Ellipsoidal
𝑽 =
𝟒
𝟑
𝝅 ×
𝟏
𝟐
𝑳 × 𝑩 𝟐
R 𝒆𝒍𝒍𝒊𝒑𝒔𝒆=√
𝟑 × 𝑺
𝟐 × 𝝅
=1.77
Using Internal Energy of a Commercial Explosive to Develop an Energy Factor
It becomes obvious that blasting patterns can be expanded using explosives that have higher densities of
charge - even though the energy per unit of weight may be lower. The PF formula previously outlined
contains no information concerning explosive energies. It is difficult to compare the PF for an ore type
6. using an ANFO or an emulsion based on PF alone with different energies as well as densities. Weight of
ANFO cannot be compared to the same weight of emulsion, for example. It would be most convenient for
explosive energy be brought into the calculation.
One of the problems using explosive internal energy is that commercial explosives are non-ideal meaning
that detonation velocity increases gradually as the diameter of a charge increases. There is a critical
velocity in which an explosive will detonate at a ‘critical’ diameter. This fact is usually noted in an
explosive manufacturer’s technical data sheet advising a user against loading an explosive in diameters
below a critical one - along with a priming specification. The effect of varying detonation velocities, in
specific diameters of charge, can be included in the energy (Eexp) calculation by taking into account the
volumetric extent of reaction (N) which is represented by the following formula;
𝑵 = (
𝑽𝑶𝑫∅
𝑽𝑶𝑫𝒊𝒅𝒆𝒂𝒍
)
𝟐
; (𝟗)
Where:
𝑽𝑶𝑫∅ = 𝒅𝒆𝒕𝒐𝒏𝒂𝒕𝒊𝒐𝒏 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒊𝒏 𝒄𝒉𝒂𝒓𝒈𝒆 𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 ∅
𝑽𝑶𝑫𝒊𝒅𝒆𝒂𝒍 = 𝒊𝒅𝒆𝒂𝒍 𝒅𝒆𝒕𝒐𝒏𝒂𝒕𝒊𝒐𝒏 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 − 𝑽𝑶𝑫 𝒊𝒔 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒊𝒏 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒊𝒏𝒈 𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓𝒔
The density and energy values in an explosive datasheet are commonly given for the unreacted explosive.
Hence, the bulk internal energy for unreacted explosive can be obtained from the above equation and can
then be applied using the equation shown below;
𝑬𝒊𝒏𝒕 = 𝝆 𝒆𝒙𝒑 × 𝑬 𝒆𝒙𝒑 × (
𝑽𝑶𝑫∅
𝑽𝑶𝑫𝒊𝒅𝒆𝒂𝒍
)
𝟐
× 𝟎. 𝟐𝟑𝟗 ;
𝑴𝑱
𝒎 𝟑
; (𝟏𝟎)
Where:
𝑬 𝒆𝒙𝒑 = 𝒃𝒖𝒍𝒌 𝒊𝒏𝒕𝒆𝒓𝒏𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 ;
𝒄𝒂𝒍
𝒈𝒎
𝝆 𝒆𝒙𝒑 = 𝒆𝒙𝒑𝒍𝒐𝒔𝒊𝒗𝒆 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 ;
𝒈𝒎
𝒄𝒎 𝟑
Assigning an emulsion explosive with the parameters used in Table 1 and in conjunction with equation
10, the energy factor (EFbreak) can be calculated for a loaded blasthole assuming that the VODφ =
¾VODideal and VODφ = VODideal shown in Table 2 determining break energy factors for both cases;
Table 2 presents break volume and break energy factor (EFbreak) of a single 100 mm blasthole
example using an emulsion explosive such that VODφ is set to ¾VODideal and VODideal.
V of Bbreak
(m3)
ρexp
(gm/cm3)
Eexp
(cal/gm)
VOD∅
(m/s)
VODideal
(m/s)
Etotal.emulsion
(MJ/m3)
EFbreak.emulsion
(MJ)
198 1.17 690 4125 5500 111 27
198 1.17 690 5500 5500 198 47
7. The same analysis can be done using ANFO with the following properties and keeping the VOBbreak the
same – as indicated below and shown in Table 3.
Table 3 presents break volume and break energy factor (EFbreak) of a single 100 mm blasthole
example using an ANFO explosive such that VODφ is being set to ¾VODideal and VODideal.
Visualizing Break as a Production Estimation Tool for Underground Blasting Operations
Current blasting practices for underground blasting operations require drilling holes of a given diameter
and with a very specific ring geometry that is usually oblique. This produces a drillhole pattern which is
loaded with explosives and sequenced to generate a fragmentation profile that should be matched to
materials handling equipment for a particular mining method. Many designs are obtained through trial and
error based on historical results using a powder factor method. Software (the AEGIS suite) has been
designed not only to mitigate the trial and error practice, but also to re-invent traditional methods of blast
design in a very special way. In many cases there usually is a concentration of explosive energy in the
collars with less energy at the toes of downholes (illustrated in Figures 9 and 10).
Using isosurfaces for radial break that a planner may estimate to visualize break are shown in Figure 11.
Figure 12 represents an actual laser cavity scan (CMS–cavity monitoring survey) overlay including the
planner’s visualized break.
Figure 11 Figure 12
Figure 11 shows a 1.5 m break isosurface for a 3 m × 3 m ring pattern.
Figure 12 places laser cavity scan (CMS-green) overlay on estimated planner break.
V of Bbreak
(m3)
ρexp
(gm/cm3)
Eexp
(cal/gm)
VOD∅
(m/s)
VODideal
(m/s)
Etotal.ANFO
(MJ/m3)
EFbreak.ANFO
(MJ)
198 0.85 880 3375 4500 101 24
198 0.85 880 4500 4500 178 43
8. Using Break Based on a Kleine Field
It would be useful to generate a break field to determine whether or not there is excessive dilution resulting
in poor recoveries as well as poor recoveries due to underbreak of a specific blast design. Using PF as a
criteria, a Kleine break field can be generated to determine how closely a CMS fits.
A Kleine field is generated for a specific volume around the blast. This field is the basis of an isosurfacing
mechanism in the 3D ring design software. A best fit function looks at the CMS and attempts to find an
isosurface that best fits the CMS mesh. A symmetric difference approach is used between the CMS mesh
and the Kleine isosurface. The isosurface that has the best percentage fit will be found after thousands of
iterations.
For a Kleine field, it is convenient to consider a point source charge first, for any point P in proximity to
a charge. If the point source fractures a spherical region of rock that ends at this arbitrary point, then the
PF for that point source is simply the mass of the charge divided by the volume of the sphere. EF could
be used as well – this work is in progress.
For a cylindrical source, the cylindrical charge can be divided up into a collection of point sources where
each is treated as a point source and the 3D PF is defined as the sum of the contributions of all the point
charges. For a charge of radius r0, with an explosive density ρe, the 3D PF contribution of any charge
segment of length dx is defined by.
𝑷𝑭𝒊(𝑷) =
𝟏𝟎𝟎𝟎 ∙ 𝝆 𝒆 ∙ 𝝅 ∙ 𝒓 𝟎
𝟐
∙ 𝒅𝒙
𝟒
𝟑 𝝅𝒓 𝟑
; (𝟏𝟏)
Where r is the distance from point P to the charge segment. Defining the linear concentration of the
charge (q) as the kg of explosive per meter of charge.
𝒒 = 𝟏𝟎𝟎𝟎𝝆 𝒆 ∙ 𝒓 𝟎 ; (𝟏𝟐)
The above formula simplifies to:
𝑷𝑭𝒊(𝑷) =
𝒒 ∙ 𝒅𝒙
𝟒
𝟑
𝝅𝒓 𝟑
; (𝟏𝟑)
The choice of the charge segment length is arbitrary, then let dx→0, and the sum of all the charge
contributions can be expressed as an integral:
𝑷𝑭𝒊(𝑷) = ∫
𝒒 ∙ 𝒅𝒙
𝟒
𝟑 𝝅𝒓 𝟑
𝒍
𝟎
; (𝟏𝟒)
Then l is the length of the charge. The value r will be different for each point along the charge. Let Z be
the linear offset of the point P from the toe of the charge, and R0 is the distance from P to the line through
the center of the charge. Figure 13 illustrates the geometry.
The unit vector 𝒗 (direction of line through charge) and 𝒖 (offset of P from the toe of the charge) make
the computation of 𝑍 and 𝑅0
2
fast and efficient in any orientation.
𝐙 = 𝐮 ∙ 𝐯 , 𝐑 𝟎
𝟐
= |𝐮 ∙ 𝐮 − 𝐙 𝟐
| ; (𝟏𝟓)
9. Kleine’s model has an analytical solution as follows;
𝑷𝑭𝒊(𝑷) =
𝟑𝒒
𝟒𝑹 𝟎
𝟐
(
𝒁
√𝑹 𝟎
𝟐
+ 𝒁 𝟐
−
𝒁 − 𝒍
√𝑹 𝟎
𝟐
+ (𝒁 − 𝒍) 𝟐
)
; (𝟏𝟔)
The most desirable feature of Kleine’s 3D powder factor field is it is defined as the sum of all the PF
contributions of all charges within a blast. This means that where there are a number of charges in close
proximity to each other and overlap, the 3D PF increases. This is quite handy in showing concentration of
energy in the collar regions of rings where the practice is to stagger explosive loads – hole to hole.
Figure 13 shows the geometry for a solution to a Kleine field.
Comparisons, Best Fit and Match Percent
For computing best-fit, the following definition applies. If an isosurface matches a CMS exactly, then a
perfect fit is the result. Likewise, if there is no intersection between the 2 surfaces, then there is no perfect
fit or a very poor one. In order to compare two meshes, both are converted to a voxel approximation.
Essentially the meshes are reduced to small cubes, or voxels, approximating the mesh shapes. The size of
voxels controls the accuracy of the approximation and comparison. The smaller the voxels, the more
accurate. However there is a tradeoff - more voxels require more computational time. Boolean operations
such as union and intersection can be unstable with meshes, whereas the voxels approximating the meshes
have stable Boolean operations. Calculations consider the number of voxels where the 2 cavities do not
agree divided by the number of voxels contained in either cavity. This is the volume of the symmetric
difference divided by the volume of the union of the 2 cavities. This is shown in the following illustrations.
10. Figure 14 Figure 15 Figure 16
Figure 14 represents the CMS from Figure 12 voxelized - using planner’s break of 1.5 m.
Figure 15 illustrates the Kleine field overlay on a planner’s estimated break of 1.5 m.
Figure 16 presents the Kleine field voxelized overlay on above break.
In Figure 14, the green blocks represent the part of the mesh that is in host rock. The red voxels represent
the parts of the CMS that are in ore.
In Figure 16, this is the voxelized Kleine field from Figure 15 indicating which parts of the mesh are in
ore (red) and which parts are in host rock (green).
As a comparison, the planner’s estimated radial break can easily be increased to 2 m in order to give a
CMS overlay for this new radial break to give the comparison below (comparison between Figure 11 and
Figure 17).
Figure 17 Figure 18
11. Figure 19 Figure 20
Figure 17 represents the CMS overlay (green) on 2 m radial break (red).
Figure 18 shows the voxelized CMS overlay (gold) with voxelized break (blue).
Figure 19 represents the CMS overlay (gold) on the Kleine filed (green).
Figure 20 shows the voxelized CMS (gold). The Kleine field was subtracted leaving only the
parts of the CMS that were not in common with the Kleine field.
Having tools that compare a planner’s estimated break to a CMS along with using field predictions (such
as the Kleine) are very valuable for optimizing blasting operations.
For example, a CMS can be used to calibrate the blast simulation model. The model can then be used to
predict the final excavation break and, if the fragmentation characteristics of the various rock types are
known, the predicted amount of fines and oversize as well. This would allow a blasting engineer to fine-
tune the blast design for a best match of fragmentation to energy distribution and sequencing. Figure 21
shows the results for a typical simulation.
If this is continuously repeated blast by blast, the confidence in the model will increase as well as
potentially give better prediction accuracy.
Figure 21 gives results of comparisons between a Klein field prediction and a CMS using
a laser scan of a stope after ore has been completely mucked.
12. Note that the match was estimated to be roughly 63%. The additional data presented in the table
contributes to the degree of precision of volumes required by the calculations to predict match percent.
Additional simulations using the following procedure would gradually improve the match percent that is
determined using the voxelization process for both the CMS survey and the Kleine Field;
1. After a production blast, a CMS data field from a laser scan is imported as a mesh into
software,
2. Using the blast parameter information for interpolation of a Kleine field (either using PF or EF
criteria) in order to generate a Kleine mesh based on blasthole layout and PF.
3. Determine the match percent using as voxelized CMS and Kleine field.
4. Change Kleine field parameters to obtain the best fit in order to guide the charging for the next
blasting operation.
Recommendations for Future Work - Break Generation Using Crack Probability
A probability function may be able to be determined that represents 100% of the cracks passing through
an elliptical shape (or any shape) close to the blasthole - with the probability falling off as the radial
distance increases from the blasthole.
Work by other authors revised this idea using seismic tomography to get damage envelops and criteria
with large charges. Such work proved that there was a minimum break fit of 100 percent passing through
a well-defined shape (dependent of primer position) with a maximum break fit of less than 5 percent with
increasing radial distances from a blasthole.
At some distance between these limits there is a blast pattern geometry that will generate a specific
fragmentation required by loading and hauling equipment. The problem is to find that pattern based on
probabilities of break using crack length distribution as a criteria as well as pattern geometry including
primer position and delay sequencing.
It would be presumed that for a specific fragmentation the break probability based on crack length would
be a defined number. This gets around trying to pin a precise number for a pattern dimension. It is a good
way of working with geology from the standpoint of structure which would play a big role in influencing
crack length probabilities.
The idea illustrated here is to show that at progressive radial distances out into a rock/ore mass the crack
distribution might possibly be represented by a probability distribution. At a specific blasting pat-tern
distance generating a fragmentation profile that fits an underground material handling system, there should
be a distribution of cracks have a specific length that defines the distribution required based on the
explosive properties, rock/ore properties and drilling layout. This preliminary model is shown in Figure
22.
13. Figure 22 shows elliptical break (defined in Figure 3 in the top frame whereas the frame
below represents the Y axis as percent probability, with the X axis being crack length in
meters.
14. References
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