Modeling blast heave using energy partitioning.

Abstract

The blast modeling system may generate a site model based on blast input data. The blast input data may include blast hole data, bench information, and geological input data. The site model may include a plurality of individual elements representing rock masses. The blast modeling system may simulate a blast by determining an initial pressure in each blast hole caused by the detonation of explosives. The blast modeling system may determine a heave of the blast based in part on the initial pressure and display a simulation based in part on the heave.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims priority to U.S. Patent Application No. 18 / 484,130, entitled "Blast Heave Modeling Utilizing Energy Partitioning," filed October 10, 2023, and U.S. Provisional Patent Application No. 63 / 379,621, entitled "Blast Heave Modeling Utilizing Energy Partitioning," filed October 14, 2022, each of which is incorporated by reference in its entirety herein.

[0002] The present disclosure relates generally to explosives, and more particularly to methods, systems, and apparatus for designing blasting schemes. [Brief explanation of the drawings]

[0003] To easily identify the discussion of any particular element or operation, the most significant digit(s) in a reference number refers to the number of the figure in which that element is first introduced.

[0004] [Figure 1] FIG. 1 illustrates advanced individual elements for blasting simulation, according to one embodiment. [Figure 2] FIG. 1 illustrates an arc-arc contact detection technique that may be used by the modeling system to determine contact between arcs of adjacent elements, according to one embodiment. [Figure 3] FIG. 1 illustrates an arc-line contact detection technique according to one embodiment. [Figure 4] FIG. 1 illustrates a method for detecting line-line contact using arc-line contact techniques, according to one embodiment. [Figure 5] FIG. 1 illustrates force calculations that the modeling system may use to determine the forces applied by contact elements to advanced discrete elements, according to one embodiment. [Figure 6]FIG. 10 illustrates a moment calculation for determining the moment applied by a contact element to an advanced discrete element, according to one embodiment. [Figure 7] 1A-1C illustrate various possible element shapes, according to some embodiments. [Figure 8] 1 is a graph of an exemplary adiabatic curve for an explosion. [Figure 9] 1 is a flowchart for a discrete element method, according to some embodiments. [Figure 10] FIG. 1 illustrates a simulation using GEM elements, according to some embodiments. [Figure 11] 1 is a chart showing investigated bench and mack profiles and GEM predicted bench and mack profiles, according to some embodiments. [Figure 12] 10 is a chart showing the consistency of GEM-predicted face velocities between simulations using circular and hexagonal elements, according to some embodiments. [Figure 13] FIG. 1 illustrates a blast modeled with both circular and hexagonal elements, according to some embodiments. [Figure 14] FIG. 1 illustrates a model using GEM elements, according to some embodiments. [Figure 15] FIG. 14 illustrates a simulation of the model of FIG. 13 using energy partitioning, according to some embodiments. [Figure 16] FIG. 1 illustrates a Mine model, according to some embodiments. [Figure 17] A table of four different explosives. [Figure 18] FIG. 17 is a table containing common rock types used in the simulations of the model of FIG. 16. [Figure 19] 17 is a table with example input variables for a simulation calculation of the model of FIG. 16, according to some embodiments. [Figure 20] 1 is a table of calculated heaves for four explosives in two rock types. [Figure 21] 1 is a graph charting the effects of explosives and rocks on a cast. [Figure 22] 1 is a graph showing the effect rock type has on percent cast for ANFO. [Figure 23] 1 is a graph of percent cast face velocity for two rock types. DETAILED DESCRIPTION OF THE INVENTION

[0005] Explosives are commonly used in the mining, quarrying, and drilling industries to crush rock and ore. A hole, commonly referred to as a "blast hole," is drilled into a surface, such as the earth. Explosives may then be placed within the blast hole. Typically, multiple blast holes are used to crush large volumes of rock and ore. The use of multiple blast holes introduces complexity into blast planning. For example, blasts can vary based on several factors, including blast hole spacing, blast hole load, blast hole depth, blast hole pattern, number of blast holes, geological characteristics, explosive type, explosive quantity, and blast hole start time. The number of possibilities makes blast planning difficult, even for highly trained blast engineers.

[0006] Blast simulations performed by the modeling system can be used to predict the outcome of a blast. The modeling system simulates the blast to predict rock movement and blast-induced heave. The blast modeling system can be used to determine the location of the ore in the final muckpile after the blast has occurred to assist in ore management for waste ore disposal and minimization of mixing of waste ore with target ore. Efficient blasts can be optimized for a particular rock by selecting the correct explosives based on the blast simulation. The explosive selection and pattern can be based on rock properties with respect to fragmentation and heave and the desired blast results.

[0007] Some blast modeling systems use discrete elements to simulate blasts. Discrete element modeling systems generate a collection of elements to represent a blast site and track the movement of the elements over time to simulate the blast. The movement of the individual elements is caused by forces applied to the collection, typically also by gravity.

[0008] Some modeling systems use circular elements to represent rock. A collection of two-dimensional circular elements moving over time due to explosive charges and gravity can be used to simulate blasting. Circular shapes are computationally very efficient because contact between particles can be determined by comparing the distance between the centers of two circles with the sum of the circle radii. However, circular elements oversimplify the rock mass, causing a loss in simulation accuracy. For example, circular elements do not generate friction between elements or interact with each other in the same way as heterogeneous rock masses. Another challenge associated with spherical individual elements is that they do not have an aspect ratio and are therefore limited in predicting bulking or void formation in a collection of spherical individual elements. Therefore, circular elements cannot accurately represent the bulking that may occur in the final muckpile after blasting.

[0009] Some modeling systems employ straight-sided discrete elements, such as quadrilateral or triangular elements, to represent rock masses. Straight-sided discrete elements are a series of lines connected to one another, forming the outline of a shape with a set of angled corners. Systems using straight-sided elements provide more accurate simulations than systems using circular elements. For example, straight-sided discrete elements may have a different aspect ratio than circular elements. However, detecting contacts between straight-sided elements (e.g., contact between a corner of a first element and an edge of a second element, contact between a corner of a second element and an edge of the first element, and contact between an edge of a first element and an edge of a second element) is a highly complex and computationally intensive process. Furthermore, simulations using these types of discrete elements require several orders of magnitude more computation time to complete than simulations employing spherical elements. In addition, straight-sided elements tend to be too stiff and bulky, and do not represent rock flow behavior very well.

[0010] Some embodiments herein use discrete elements with an advanced geometric paradigm to represent the movement of blasted rock in blast simulations. Geologic Element Motion (GEM) is a Discrete Element Method (DEM) feature for blast-induced heave simulations that uses very fast computational algorithms that can efficiently handle many different element shapes. GEM elements (also referred to herein as advanced discrete elements) are created by utilizing alternating arcs and lines.

[0011] GEM elements geometrically contain arcs and lines that define the outline of each individual element. Lines are connected via arcs so that the lines do not cross. Instead, arcs and lines are used to create two-dimensional individual elements with one or more straight-sided edges and rounded corners. The rounded corners may be formed by one or more arcs. These GEM elements improve simulation accuracy compared to circular elements and are computationally more efficient than individual elements with straight edges.

[0012] Although complex GEM shapes are possible, blast modeling requires that the elements represent solid ground with minimal voids within the element array. Thus, GEM blast heave models can be created from packable element shapes such as hexagons, squares, pentagons, triangles, and circles. Hexagons, squares, and circles can be utilized to represent blasted rock.

[0013] Some embodiments include the ability to define the size of the rounded corner radius, as well as the side length of quadrilateral and hexagonal elements. A circle can be created from quadrilateral elements with zero side length and four arcs.

[0014] The explosive gas filling of GEM elements can be achieved by employing a Noble-Abel equation of state (EOS) specific to each explosive formulation. Noble-Abel EOS characteristics have been developed for 40 different blasting-relevant explosive formulations. These formulations include ammonium nitrate / fuel oil (ANFO), AN-only emulsions, double salt (AN+SN) emulsions, and blends of ANFO and AN-only emulsions. Density is either unmodified (i.e., blends) or controlled by chemical gas treatment or microballoons (plastic and glass).

[0015] An explosion simulation may calculate rock movement from knowledge of the gas pressures that move the elements. The simulation may use an equation for the pressure versus volume of the explosion product gases, or an adiabatic curve. This work uses an analytical equation for the adiabatic curve derived from the properties of the explosive. The effect of explosive detonation pressure in spalling the rock ring and generating a shock wave may be called brisance. Some embodiments may incorporate the detrimental effect of brisance on subsequent rock movement.

[0016] Some embodiments may employ energy partitioning between blissance, fragmentation, and heave. This physics-based partitioning may provide accurate modeling of blast results across a wide range of rock and explosive types. It accurately defines the volume, pressure, and energy state of explosive gases in the blasthole following detonation. Rock mechanical and explosive properties may be included in the calculation. Additionally, some embodiments provide a method for better predicting heave.

[0017] Although many of the embodiments herein discuss energy partitioning in the context of discrete element modeling (e.g., GEM), energy partitioning can be used in combination with other simulation techniques. For example, energy partitioning can be used in fragmentation modeling. Energy partitioning can be used to determine detonation energy, explosive type, and / or explosive density for a desired result.

[0018] It will be readily understood that the components of the embodiments, as generally described below and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. For example, the steps of the methods need not be performed in any particular order, or even sequentially, or that a step need not be performed only once. Thus, the following more detailed description of various embodiments, as described below and illustrated in the figures, is not intended to limit the scope of the disclosure but is merely representative of various embodiments. While various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.

[0019] The embodiments and implementations of the blast planning systems and methods described herein may include various steps that may be embodied in machine-executable instructions executed by a computer system. The computer system may include one or more general-purpose or special-purpose computers (or other electronic devices). The computer system may include hardware components that contain specific logic for performing the steps, or may include a combination of hardware, software, and / or firmware.

[0020] Embodiments may be provided as a computer program product that includes a computer-readable medium having stored thereon instructions that can be used to program a computer system or other electronic device to perform the processes described herein. The computer-readable medium may include, but is not limited to, a hard drive, a floppy diskette, an optical disk, a CD-ROM, a DVD-ROM, a ROM, RAM, an EPROM, an EEPROM, a magnetic or optical card, a solid-state memory device, or any other type of medium / computer-readable medium suitable for storing electronic instructions.

[0021] Computer systems, and computers within computer systems, may be connected via a network. Suitable networks for configuration and / or use as described herein include one or more local area networks, wide area networks, metropolitan area networks, and / or Internet or IP networks, such as the World Wide Web, private Internets, secure Internets, value-added networks, hypothetical private networks, extranets, intranets, or even standalone machines communicating with other machines via the physical transport of a medium. In particular, suitable networks may be formed in part or in whole from two or more other networks, including networks using disparate hardware and network communication technologies.

[0022] One suitable network includes a server and several clients, while other suitable networks may include other combinations of servers, clients, and / or peer-to-peer nodes, and a given computer system may function as both a client and a server. Each network includes at least two computers or computer systems, such as servers and / or clients. The computer systems may include workstations, laptop computers, disconnectable mobile computers, servers, mainframes, clusters, so-called "network computers" or "thin clients," tablets, smartphones, personal digital assistants or other handheld computing devices, "smart" consumer electronic devices or appliances, medical devices, or combinations thereof.

[0023] Suitable networks may include communications or networking software, such as software available from Novell®, Microsoft®, and other vendors, including TCP / IP, SPX, IPX, and other protocols over twisted pair, coaxial, or fiber optic cable, telephone lines, radio waves, satellite, microwave relays, modulated AC power lines, physical media transport, and / or other data transmission "wires" known to those skilled in the art. The network may include smaller networks and / or may be connectable to other networks via gateways or similar mechanisms.

[0024] Each computer system includes one or more processors and / or memory, and the computer system may also include various input and / or output devices. Processors may include general-purpose devices such as Intel®, AMD®, or other “off-the-shelf” microprocessors. Processors may include special-purpose processing devices such as ASICs, SoCs, SiPs, FPGAs, PALs, PLAs, FPLAs, PLDs, or other customized or programmable devices. Memory may include static RAM, dynamic RAM, flash memory, one or more flip-flops, ROM, CD-ROM, disk, tape, magnetic, optical, or other computer storage media. Input device(s) may include a keyboard, mouse, touchscreen, light pen, tablet, microphone, sensor, or other hardware with firmware and / or software. Output device(s) may include a monitor or other display, printer, speech or text synthesizer, switch, signal line, or other hardware with firmware and / or software.

[0025] The computer system may be capable of using a floppy drive, tape drive, optical drive, magneto-optical drive, or other means for reading storage media. Suitable storage media include magnetic, optical, or other computer-readable storage devices having a particular physical configuration. Suitable storage devices include floppy disks, hard disks, tapes, CD-ROMs, DVDs, PROMs, RAM, flash memory, and other computer system storage devices. The physical configuration represents data and instructions that cause the computer system to operate in a particular, predefined manner as described herein.

[0026] Suitable software to assist in the practice of the present invention is readily provided by one of ordinary skill in the art using the teachings presented herein and programming languages ​​and tools, such as Modern Fortran, Java, Pascal, C++, C, PHP, .Net, database languages, APIs, SDKs, assembly, firmware, microcode, and / or other languages ​​and tools. Suitable signal formats may be embodied in analog or digital form, with or without error detection and / or correction bits, packet headers, network addresses in specific formats, and / or other supporting data that would be readily provided by one of ordinary skill in the art.

[0027] Aspects of certain embodiments may be implemented as software modules or components. As used herein, a software module or component may include any type of computer instructions or computer-executable code located in or on a computer-readable storage medium. A software module may include one or more physical or logical blocks of computer instructions, which may be organized as, for example, a routine, program, object, component, data structure, etc., that performs one or more tasks or implements a particular abstract data type. A particular software module may include heterogeneous instructions stored in different locations of a computer-readable storage medium, which together implement the module's described functionality. Indeed, a module may include a single instruction or many instructions, distributed across several different code segments, among different programs, and across several computer-readable storage media.

[0028] Some embodiments may be practiced in distributed computing environments where tasks are performed by remote processing devices linked through a communications network. In a distributed computing environment, software modules may be located in local and / or remote computer-readable storage media. In addition, data linked or rendered together in a database record may reside in the same computer-readable storage medium or across several computer-readable storage media and may be linked together within fields of records in a database across a network. According to one embodiment, a database management system (DBMS) allows users to interact with one or more databases and provides access to the data contained in the databases.

[0029] A new discrete element technique has been developed that overcomes the simplified behavior of circular elements, is much more computationally efficient than rectangular elements, and exhibits flow behavior that is more representative of blasted rock. As shown in Figure 1, a 2D GEM element is created by enclosing space with a series of arcs and lines. Figure 1 also shows the data structure for defining the lines and arcs that make up the element.

[0030] FIG. 1 illustrates an advanced discrete element 100, according to one embodiment. A discrete element modeling system using the advanced discrete element 100 segments a two-dimensional site model into multiple elements. The advanced discrete element 100 has a shape formed by connecting the endpoints of one or more lines with arcs, such that the endpoints of the two or more lines are indirectly joined via the arcs and the arcs form rounded corners of the shape. The illustrated embodiment of the advanced discrete element 100 includes a first line 102, a second line 104, and a third line 132 connected by four arcs (i.e., a first arc 114, a second arc 122, a third arc 110, and a fourth arc 118).

[0031] The illustrated embodiment includes two parallel lines. Other embodiments may feature more than one line, and the lines may be at an angle relative to one another. Each line includes two endpoints, and each endpoint is connected to an arc so that the shape features a rounded corner or edge. Each rounded corner may be created using one or more arcs. For example, connecting a first arc 114 and a second arc 122 forms a rounded corner or rounded edge.

[0032] Each arc is a differentiable curve. In the illustrated embodiment, the arcs outline a portion of the circumference of a circle. The illustrated embodiment includes four arcs. Other embodiments may include a different number of arcs. Each arc includes an arc center point (i.e., first center point 126, second center point 128, third center point 130, and fourth center point 124). The arc center point represents a point equidistant from all points on the circular arc. Each arc also includes a radius (i.e., first radius 112, second radius 116, third radius 120, and fourth radius 106). Because the arcs are circular, the radius of each arc is the same along all points on the arc. Additionally, each arc includes an arc angle (e.g., third arc angle 108). The arc angle is the angle formed by the arc at the center point. As shown, the end point of an arc may be connected to another arc, as shown by the connection between the first arc 114 and the second arc 122, or the end point of an arc may be connected to a line, as shown by the connection between the first line 102 and the third arc 110.

[0033] Intersections between arcs and lines, and between arcs and arcs, form smooth transitions between different shape contour elements. Each line can be tangential to the end point of the arc it is connected to to smooth the transition. Similarly, arc-to-arc transitions can be smooth. Intersections do not form sharp angles, as would be formed when two straight lines directly connect to form a vertex. The resulting shape is characterized by a contour with rounded corners, rather than a shape with angled corners. Thus, the lines of the advanced individual elements 100 are not directly connected, but rather are indirectly joined via arcs to prevent angled corners. Rounded corners are computationally more efficient than sharp corners and can be created using one or more arcs.

[0034] The advanced discrete elements 100 are created from arcs and lines that define the outline of each individual discrete element. FIG. 1 shows one of many possible element shapes that can be created from arcs and lines. Other embodiments of the advanced discrete elements may use arcs and lines to create other non-spherical shapes without angled corners. Other shapes that can be created using a combination of arcs and lines include polygons with rounded corners, such as a triangle with rounded corners, a trapezoid with rounded corners, a rectangle with rounded corners, a square with rounded corners, a hexagon with rounded corners, or an octagon with rounded corners.

[0035] In some embodiments, the shapes used for elements of the simulation model may be based on geological data such as rock hardness. In some embodiments, at least some of the elements are different shapes. For example, different rock types may be modeled using elements of different shapes. For example, coal may be modeled with rounded squares, while another rock in the same simulation may be modeled with rounded hexagons. In some embodiments, at least some of the elements of the same shape are different sizes.

[0036] Discrete element shapes formed of discontinuous lines indirectly connected through arcs provide better accuracy than circular elements and computational efficiency advantages over discrete elements having only lines with straight edges. Straight lines and varying arc radii provide more realistic aspect ratios compared to circles, while arcs provide a more efficient method for detecting contact between adjacent elements compared to elements having only lines with straight edges.

[0037] Each advanced individual element 100 in the blast simulation model may be stored in the memory of the modeling system. For example, an advanced individual element 100 may be a data structure that includes line end node coordinates, designated arc end points, arc center points, arc radii, and arc angles.

[0038] In some embodiments, the first step in the contact detection algorithm is a binning process that sorts the GEM elements into fixed square geometric regions, or bins, in space. Detailed contact detection of the elements occurs by searching each bin and its neighboring bins for arc-arc and arc-line contacts. This bin-sorting method is very efficient in searching for contacts between elements because each bin contains only a small number of elements at any time.

[0039] Contact detection and resolution of a GEM element with neighboring elements is shown for a given arc pair and arc-line in Figure 2. This contact detection algorithm has the computational efficiency of circular elements.

[0040] Contact detection and resolution between sides from two GEM elements is not necessary as this will be detected by the previous arc-line contact as shown in Figure 2. This makes the GEM contact detection algorithm more efficient.

[0041] 2-4 illustrate various methods for detecting contact between sophisticated individual elements. Two important inter-element interaction mechanisms for detecting contact between adjacent elements are arc-arc, as shown in FIG. 2, and arc-line, as shown in FIG. 3. Another possible interaction mechanism is line-line, as shown in FIG. 4. However, as will be explained in more detail below, line-line contact can also be detected by the arc-line interaction mechanism.

[0042] Detecting these element interactions between highly discrete elements is all very computationally efficient, much more so than interactions between linearly edged discrete elements. Highly discrete elements also have aspect ratios greater than 1, which means they have greater natural bulking and inter-particle friction than circular elements.

[0043] The described advanced discrete elements will allow simulations to increase the fidelity in discrete element modeling of rock blasting because the elements have aspect ratios that circular elements do not have and will more naturally represent the natural behavior of rock during blast-induced movements such as bulking and inter-element friction.

[0044] Also, the computational simplicity and speed of arc-arc and arc-line contact detection and resolution allows higher fidelity simulations to be completed in substantially less computation time, meaning that significantly more realistic blast simulations can be achieved on cheaper and more portable laptop computers.

[0045] 2 illustrates an arc-arc contact detection technique that may be used by a modeling system to determine contact between arcs of adjacent elements. As shown, a first element 202 having a first arc 216 is adjacent to a second element 204 having a second arc 218.

[0046] To detect whether the arcs of these two elements contact each other during a simulation time step, the modeling system may determine whether an overlap exists between the first arc 216 and the second arc 218. Such overlapping arcs may be referred to as arc-arc contact. Detecting arc-arc contact between adjacent elements includes comparing the distance 214 between the arc center points (i.e., the first center point 206 and the second center point 208) of the first arc 216 and the second arc 218 of the adjacent elements to the sum of the first radius 210 and the second radius 212 of the two arcs of the adjacent elements. For example, in some embodiments, arc-arc contact is detected when the sum of the radii is greater than the distance 214.

[0047] 3 illustrates an arc-line contact detection technique that may be used by a modeling system to determine contact between an arc 310 and a line 312 of adjacent elements. In this illustration, a first element 302 and a second element 304 are adjacent elements, and the closest points along the perimeter of the elements are the arc 310 of the second element 304 and the line 312 of the first element 302. R1 represents the radius 308 of the arc 310, and D represents the shortest distance 306 between the arc center point 314 and the line 312. The modeling system may use a dot product to determine the distance 306.

[0048] When an arc 310 and a line 312 overlap in a simulation, it is called arc-line contact. The modeling system can detect arc-line contact between adjacent elements by comparing the radius 308 of the arc 310 to the distance 306 between the line 312 of the first element 302 and the arc center point 314 of the arc 310 of the second element 304. For example, contact can be detected when the radius 308 is greater than the distance 306.

[0049] 4 illustrates how line-line contact may be detected by a modeling system using the arc-line contact technique described with reference to FIG. 3. Line-line contact occurs when a first line 402 of a first element 406 overlaps a second line 404 of a second element 408. Direct line-line contact detection is less computationally efficient than arc-arc and arc-arc contact detection. Thus, in some embodiments, line-line contact may be detected indirectly using the arc-line contact detection technique because, when the lines overlap, one or both of the first arc 410 and the second arc 412 will overlap the first line 402.

[0050] 3 for one or both of the first arc 410 and the second arc 412. For example, the system may compare the radius of the first arc 410 to the distance between the first line 402 and the center point of the first arc 410, and compare the radius of the second arc 412 to the distance between the first line 402 and the center point of the second arc 412.

[0051] FIG. 5 illustrates force calculations that a modeling system may use to determine forces applied by contact elements to advanced discrete elements. The modeling system may calculate the magnitude and direction of the force applied to each element. The system detects contact between a first element 502 and a second element 504 when an overlap 506 exists around the two discrete elements during a simulation time step. The modeling system resolves or eliminates the overlap 506 by applying restoring forces that are calculated to eliminate the overlap 506. These restoring forces are applied to both the first element 502 and the second element 504.

[0052] As part of the simulation, the modeling system can determine contact and calculate the force applied to each element by the contacting adjacent elements. The force is calculated based on the overlap 506 caused by the contact. In the case of arc-arc contact, the force is applied through the arc center points of the arc-arc contact (i.e., first arc center point 508 and second arc center point 510). In the case of arc-line contact, the force is applied perpendicular to the line through the center of the arc. The magnitude of this restoring force (F) is equal to the material's specific spring constant (K) multiplied by the overlap 506 (Δ). As shown in FIG. 5, F=KΔ.

[0053] 6 illustrates moment calculations that a modeling system may use to determine a moment 604 applied to an advanced individual element 600 by a contact element. Each force 606 applied to the advanced individual element 600 will also generate a moment 604 (M) on the advanced individual element 600, as shown. The moment is applied to the element center 602 by all of the forces applied to the advanced individual element 600, including the force 606 applied to the arc center point 608 caused by the contact element. In some embodiments, the modeling system calculates the moment for each force separately and then sums the moments to determine the total moment for the advanced individual element 600.

[0054] The modeling system may calculate moments 604 by calculating:

number

[0055] The total moment (ie, the sum of the moments) is calculated to determine the rotation of the advanced individual element 600 .

[0056] GEM element shapes that have been utilized to date are square, hexagonal, and circular. Element shape can be controlled by side length and arc radius, as illustrated in Figure 7 for a square. GEM elements can have aspect ratios greater than 1, which involves more natural bulking and inter-particle friction. GEM element contact detection, restoring forces, and explosive loading can be modeled using the Noble-Abel equation of state.

[0057] Energy partitioning between brissance, fragmentation, and heave

[0058] To model the work done to move a load, the adiabatic curve and available heave work of an explosive can be calculated. To mechanistically model an explosive's ability to heave rock, the following can be used: Mechanistic models necessarily include some simplifying assumptions, for example, regarding the size and shape distribution of fragments to be displaced by the product gases. Rock properties are sometimes approximately known, but often must be estimated for general rock types. Thus, the rock to be blasted is often described as hard, medium, or soft, and homogeneous, cemented, or heavily cemented. A realistic description of the blast includes variations in hole placement and depth, as well as variations in the quantity and quality of explosives. The EOS of an explosive describes the detonation and detonation state pressure, detonation velocity, and the decrease in gas pressure as the gas expands (adiabatic curve). Taking the above factors into account, an approximate description of the explosive may be appropriate.

[0059] For heave modeling, the adiabatic curve may have the following attributes: The adiabatic curve may cover the entire expansion from detonation conditions to atmospheric pressure. The adiabatic curve may be based on available data for commercial explosives. The adiabatic curve may reduce to the ideal gas equation at lower pressures. The adiabatic curve may have the total available work calculated to be equal to the heat of reaction (at least for non-aluminized explosives).

[0060] Some embodiments may use the following equations to model detonation properties: These calibrated analytical equations for detonation pressure and velocity may be based on densities, calculated heats of reaction, and simple versions of the product gas mixture for the explosive.

number

number

[0061] For Q, the change in heat of formation (-ΔHf o ) can be used. For oxygen-balanced explosives, M=1 / N, but the above equations for N and M have the consequence that M≠1 / N for oxygen-negative explosives.

[0062] In some embodiments, the EOS has the following form:

number

[0063] This EOS has desirable properties along the entire adiabatic curve.

number

number

[0064] For an adiabatic process, the work done by the product gas may be equal to the change in internal energy Q.

number

[0065] From these two equations, it can be shown that:

number

number

[0066] where the subscripts e and f refer to the detonation state (when the product gas has the same density as the unreacted explosive) and the final state at atmospheric pressure. f These simultaneous equations in can be solved iteratively.

[0067] For a more accurate simulation, the explosion energy division between brissance and heave can be applied. Brissance energy is the energy that expands the blasthole and propagates the shock / stress waves into the rock, causing most of the fragmentation. Heave energy is the energy that remains in the explosive gas products in the form of pressure and heat. This residual gas energy displaces the rock, resulting in a heave or throw.

[0068] The energy of an explosive can be divided into total available work and brissance energy, as explained below. Half of the impact and elastic strain energy can be directed through the load towards the free face, while the other half is dissipated in the rock behind the blast. Also, part of the energy lost in compressing the crushed rock can be returned to the gas as the pressure drops. For these reasons, the following approximation can be adopted for the heave work:

number

[0069] As shown in Equation 8, heave work may be the total available work minus a portion of the brissance energy. In some embodiments, the amount of brissance work subtracted from the total available work to determine the heave work may be half, as described in Equation 8 above. In other embodiments, the percentage of brissance work that may be subtracted from the total available work to determine the heave work may be different. For example, in some embodiments, the brissance work reduction parameter may be in the range of 0.1 to 0.9. In some embodiments, this parameter may be adjustable based on environmental factors. For example, for different rock hardness values, a different percentage of the brissance energy may be removed from the total available work to calculate the heave work.

[0070] As shown in Equation 8, in some embodiments, the heave energy of an explosive can be divided into the total available work (W) and half the brissance energy. This reduction in heave energy can represent a scenario in which half of the energy radiates toward the free surface where movement can occur. Some explosives of interest are characterized in terms of EOS, as described above. The starting borehole pressure for the heave simulation can be calculated using an adiabatic curve based on EOS, which can be unique for each explosive / rock combination.

[0071] Brissance may involve the rock surrounding the hole being fractured and shock waves being emitted into the rock, placing it in a state of elastic strain. Brissance refers to the degree of fragmentation and elastic impact imparted by the explosive, which radiates uniformly in all directions from the blast hole.

[0072] Since the initiation and propagation of (most) radial fractures is slow compared to the time scale of the shock, this shock end state is called quasi-static and is treated as such. The radius of the hole is el (the "elastic" radius), and the gas volume increases to V el,g The pressure increases along the adiabatic curve to P el (up).

[0073] This process can be thought of in three steps: first, a portion of the rock surrounding the hole is sheared and fractured under compression and shear; second, this annulus of fractured rock is compressed, thereby increasing the space available for product gas; and third, the rock beyond the fractured zone is left in a state of elastic strain (due to the passage of the shock wave). This strain further increases the volume available for product gas.

[0074] One method for calculating the fracture zone surrounding a wellbore involves the following calculation.

number

[0075] For the rock to be crushed, R cr Note that / R0>1. In general, R cr / R0>=1.

[0076] In some embodiments, the value of k is R, which is only slightly larger than R for ANFO in very hard rocks. cr From this, it was found that k=0.55. As an integral part of the fracturing process, the fractured rock is also compressed. The volume of the uncompressed fractured rock, V, cr,u is the ring diameter R per unit length of the borehole cr -R0 The change in volume due to compression can be approximated by the following equation:

number

[0077] As the rock fractures and compresses, shock waves are generated that propagate away from the hole. This complex dynamic process can be approximated for modeling. The rock surrounding the fracture zone can be assumed to behave elastically. Using quasi-static assumptions, this elastic compression can be evaluated using widely available equations for thick-walled cylinders. The relevant internal pressure is the borehole pressure along the adiabatic curve. The outer radius of the thick-walled cylinder can be set to infinity. (Using an outer radius equal to the load makes negligible difference to the results.) The change in the internal volume of the cylinder due to elastic compression of the very thick cylinder wall is then given by the following equation:

number

[0078] These equations give the functional relationship between the borehole volume as a result of both fracturing and compaction, the compression of the rock around the hole, and the final state of elastic compression of the rock after the shock wave has passed. Solving these equations simultaneously with the P(V) equation for the adiabatic curve gives the pressure at the end of the brissance, and from that the work done between the CJ state and the brissance state.

[0079] R0 and R cr This ring of fractured rock between is compressed by the product gas according to the dynamic bulk modulus of the rock and the gas pressure. The final step of the Brissance algorithm may be to calculate the state of the borehole after the passage of the shock wave. The rock surrounding the hole may be treated as an elastic body and the load may be treated as a thick-walled cylinder, allowing further changes in hole radius to be calculated.

[0080] Brissence work can be determined by the following formula:

number

[0081] Finally, to provide a heave adiabatic curve for use in GEM, we use a new initial heave state ( h ) can be calculated as follows:

number

[0082] The rock movement simulation algorithm may use the initial and final states of the heave process and the P(V) adiabatic curve linking these two states. heave =W total - 1 / 2W brisance To use 1 / 2W brisance This state can be created along the adiabatic curve so that the temperature is equal to P ih The initial heave state can be characterized by P for different explosive / rock combinations. ih Exemplary values ​​of are shown in FIG.

[0083] For fragmentation and heave modeling, adiabatic curves may be based on data available for commercial explosives using Noble-Abel EOS. Embodiments may generate cast behavior predictions consistent with explosive formulations.

[0084] Implementations of explosive gas element charging may include: the charging from explosive gas products may be calculated taking into account the expansion of the blast hole and the diffusion of gas within the fractured rock; the pressure of the gas may be calculated using an adiabatic curve; the permeability induced by rock fracture may increase as the blast hole expands.

[0085] FIG. 8 is a graph of an exemplary adiabatic curve 800 for an explosion. The adiabatic curve 800 shows the pressure and volume conditions of the explosion. The pressure of the gas can be calculated using EOS, as described above, based on the current specific volume. The total available work 812 for the explosion is calculated based on the detonation point 802 (e.g., P cj , V cj ) until the detonation reaches atmospheric pressure (e.g., endpoint 814).

[0086] Brissence point 804(P Bristance , V Bristance ) may define the end of the brissance state. The area under the adiabatic curve 800 between the detonation point 802 and the brissance point 804 is the brissance work from the explosion. Not all work done during the brissance state (e.g., before the brissance point 804) contributes to the heave of the rock. The brissance energy expands the blasthole and propagates shock / stress waves into the rock, causing most of the fragmentation. Some of this brissance energy will contribute to the heave of the rock.

[0087] As shown, the Brissence work is divided into a first section 808 and a second section 810. In some embodiments, the work done in the first section 808 may be half of the Brissence work, and the work done during the second section 810 may also be half of the Brissence work. heavy =W total - 1 / 2W bristance To determine the initial heave state 806 (i.e., P ih ) is shown along the adiabatic curve 800. In some embodiments, the initial heave state 806 is such that the energy between the initial heave state 806 and the detonation point 802 (or, equivalently, between this state and the brissance point 804) is 1 / 2W brisance can be arranged to be equal to W brisanceis equal to the work between the detonation point 802 and the brissance point 804 (e.g., first section 808 and second section 810). In other embodiments, the first section 808 and second section 810 may be different. For example, the initial heave state 806 may be such that the energy between the initial heave state 806 and the detonation point 802 is 0.1*W. brisance ~0.9*W brisance (i.e., W brisance In another example, the initial heave state 806 may be positioned such that the energy between the initial heave state 806 and the detonation point 802 is somewhere in the range of 10% to 90% of the initial heave state 806. brisance ~0.6*W brisance (i.e., W brisance The saturation voltage may be positioned to be anywhere in the range of 40% to 60% of the saturation voltage.

[0088] The first section 808 can be thought of as the energy used for the impact / stress waves into the rock that generate the majority of the fragmentation before the rock begins to heave. Once the initial heave state 806 is reached, the pressure between the initial heave state 806 and the terminal point 814 can be used to calculate the heave of the rock in the simulation. The heave energy (e.g., total available work 812 minus the first section 808) is what remains in the explosive gas products in the form of pressure and heat. This residual gas energy moves the rock, resulting in the heave or throw. Therefore, the system can use the work between the initial heave state 806 and the terminal point 814 to simulate the heave.

[0089] By using a portion of the brissance energy in the heave calculation, the simulation can produce more accurate results. heave =W total -Y*W bristancewhere Y is a variable less than 1. In some embodiments, half of the brissan work may be removed from the total available work to determine the heave work. In some embodiments, the portion of the brissan work removed from the total available work is between 40% and 60% of the brissan work. In some embodiments, the portion of the brissan work removed from the total available work is between 10% and 90% of the brissan work.

[0090] Using less than the total brisance work can arise from two considerations: first, the dynamic impact energy may impart forward momentum to the loaded rock, which is the half of the rock affected by the shock wave (in 2-D); second, some of the work done in elastically compressing the rock outside the fractured annulus may be recovered due to relaxation of this rock as the pressure is reduced. The heave modeling described in Figures 10-23 shows the results of using the total work minus a portion of the brisance work when determining the heave work.

[0091] 9 shows a flowchart of a discrete element method 900, according to some embodiments. The method 900 may initialize a discrete element model (902). Initializing the model may include generating, creating, or starting the model for simulation. Initializing may include generating details about the model, determining a starting point for the simulation, determining element shapes / sizes, etc. In initializing the model, the method 900 may calculate mass and spring constants, calculate a stable time step, define an explosive charge, and calculate element coordinates.

[0092] The method 900 may integrate 904 the element motion through each time step. For each time step, the method 900 may determine new element coordinates, detect new element contacts, calculate contact removal forces, and define any new explosive charge forces. Element motion may begin after reaching an initial heave state. The heave energy (e.g., W heave =W total -Y*W bristance) may be used as a force to move the element. The method 900 cycles through the time steps until an end time is reached.

[0093] In some embodiments, energy partitioning may be used in a method for loading a blasthole. For example, the method may include determining an explosives loading profile for the blasthole to achieve a desired result and loading the blasthole with explosives according to the loading profile. Determining the explosives loading profile may include simulating the blast by determining total available work from hypothetical detonations of explosives, dividing the total available work by removing a portion of the brisance work from the total available work to generate heave work, such that the simulated blast is based on heave work, and selecting explosives to achieve a simulated blast that approximates the desired result.

[0094] In some embodiments, the brissance work is work performed between a hypothetical detonation and the brissance point of the explosive. In some embodiments, selecting an explosive includes identifying a type of explosive and / or an energy output of the explosive. In some embodiments, the type of explosive is selected from at least one of emulsion explosives, ammonium nitrate prill and fuel oil, water gel-based explosives, or blends and mixtures thereof. In some embodiments, the energy output of the explosive is selected from at least one of explosive density or explosive volume. In some embodiments, selecting an explosive includes selecting multiple energy outputs of the explosive in different portions of the blasthole. In some embodiments, selecting an explosive includes selecting multiple types of explosives in different portions of the blasthole.

[0095] Figures 10-12 show the results of a first blast simulation using GEM and energy partitioning. Figure 10 shows four time snapshots of a GEM simulation of a blast utilizing circular elements and the explosive energy partitioning technique described above. The energy partitioning technique can lead to a more accurate simulation.

[0096] For example, Figure 11 shows a chart 1100 comparing a surveyed bench 1102 and McPile profile 1104 with a modeled bench 1106 and predicted McPile profile 1108. The predicted McPile profile 1108 is based on the GEM and energy partitioning (e.g., W heave =W total - 1 / 2W brisance ) were generated. The cast line, which is the angle of repose of the muck, was assumed to be 45 degrees. The muck profile and calculated percent cast of 45.6%, compared to a measured value of 45%, adds credence to the reliability of energy partitioning and GEM as blast movement prediction tools. An important aspect of these simulations is the inclusive energy partitioning.

[0097] Face velocity is a key metric for understanding, predicting, and improving cast blasts. During this blast, face velocity was measured using a rock-filled, orange-painted box suspended over the face. Figure 12 shows a graph 1200 comparing the measured face velocity 1202 with the GEM-predicted face velocity simulated using circular and hexagonal elements. The high-speed camera-measured velocities span the predicted velocities (e.g., circular simulation velocity 1206 and hexagonal simulation velocity 1204), with three of the measured velocities close to those predicted. However, two of the measured velocities are significantly higher than average, and one is significantly lower. Examination of the bench face in both the GEM modeling and blast photographs leads to a viable explanation. This figure shows substantial face bowing early in the blast. Figure 10 shows face bowing at time 0.74 seconds, but it appears less dramatic than the blast bowing. A possible difference in velocity behavior is that GEM elements in a hexagonal close-packed configuration resist horizontal sliding more than occurs in blasted layered shale.

[0098] The face velocities predicted by GEM closely match the measured face curvature. The three highest face velocity measurements do not produce face curvature and are considered erroneous. An explosive impact impacting a free face may project into the target at a higher velocity than the free face.

[0099] 13 shows the results 1300 of a second blast compared to a muckpile 1302 that was modeled and investigated using both circular and hexagonal elements. The hexagonal elements, which result in a hexagonal profile 1306, do not move as easily as the circular elements, which result in a circular profile 1304, which results in a higher muckpile at the rear of the blast and a lower muckpile at the front. Another way to explain the behavior is that the center of gravity of the muckpile is moving less relative to the hexagonal elements.

[0100] Another example of the corrective impact of this new energy partitioning method is shown in Figures 14 and 15. The heave from this blast was previously underpredicted by 42%, but with the current version of GEM with energy partitioning, it is now 44%. Figure 14 shows a model 1400 using GEM elements, according to some embodiments. Figure 15 shows four time stamps 1500 of a simulation of the model of Figure 14 using energy partitioning, according to some embodiments.

[0101] FIG. 16 shows a coal mine model 1600, according to some embodiments. The model 1600 shows a bench 1604 and a series of blast holes 1602. Because GEM predicts rock movement and heave is important in cast blasting, a typical cast blast was used for the simulation. Simulation results for different cases are shown in FIGS. 17-23. Unless otherwise stated, the bench height of the bench 1604 was set to 40 m (131 ft), the hole angle of the boreholes 1602 was set to 20°, the hole diameter was set to 270 mm (10 5 / 8 in), and the powder modulus was set to 0.693-0.695 kg / m 3 (0.85 cu yd / lb). The cast percentage was calculated from the volume of rock beyond the 45° cast line 1606.

[0102] The available work to heave rock (through energy partitioning) depends on both the explosive and the rock. This approach should give a better understanding of heave than simple use of powder factors combined with heat of reaction or relative strength by weight (RWS). Four different explosives were used to simulate the blast of model 1600 in Figure 16. Figure 17 shows a table 1700 of the four different explosives. The explosives used in the simulation included an ANFO emulsion, a 50 / 50 blend, and a non-ideal blend.

[0103] Figure 18 shows a table 1800 containing common rock types used in the simulations of model 1600 of Figure 16. Table 1800 shows two densities for each rock hardness. While variable densities are common for rock types, a common density was used in some simulation runs to eliminate the effect of rock density on percent cast. The UCS variable represents uniaxial compressive strength. Because blasts have very high strain rates and most rock properties are static values, a Dynamic Increase Factor (DIF) was used in the simulations. Both Young's modulus and UCS in table 1800 were multiplied by the DIF before being used in the brisance calculations for the simulations.

[0104] In most cases, the two extreme rock types from this table, i.e., very soft rock and very hard rock, were used in the test simulations of model 1600. As shown in table 1900 of Figure 19, the four explosive types and the two extreme rock types result in eight main cases considered.

[0105] 19 shows a table 1900 with example input variables for a simulation calculation of the model 1600 of FIG. 16 according to some embodiments. 3 The loads and intervals shown in Table 1900 were selected to achieve a constant powder factor of P ih , W brisance , and W heave The values ​​of were calculated as described above. The table shows that the work of brissance (fragmentation and impact) varies from 6% to 56% of the total available work, with the majority of the work being done by the explosives in the soft rock during the brissance stage, leaving less available energy for heave.

[0106] The results of simulations of model 1600 using inputs from table 1900 are described with reference to Figures 20-23. Simulations were performed using GEM and energy partitioning. These results compare the heave of various explosives in two different rock types. Figure 20 shows table 2000 of calculated heaves for four explosives in two rock types. As shown, ANFO has the highest face velocity and best percent cast for both very soft and very hard rock.

[0107] For soft rocks (at the same fineness factor), there may be little difference in percent cast between the emulsion and 50 / 50 heavy ANFO (see cases 2, 3, and 4 in Table 2000). In the illustrated embodiment, the percent cast of the emulsion is better than that of the heavy ANFO (at the same fineness factor), despite the better RWS of the blend. The casting results from Table 2000 are shown in FIG. 21. FIG. 21 shows graph 2100, which charts the effect of explosives and rock on cast. The points on graph 2100 are from Table 2000 in FIG. 20. The non-ideal blend gives a percent cast that is only 2 percentage points better than the same explosive detonated ideally, but the brissance work (W) for these two cases is 1. brisance ) is 1.14 vs. 1.85 MJ / kg. (See Cases 3 and 4 in Table 1900.) In other words, when heavy ANFO is detonated with a slow detonation and the brisance energy is reduced by about 40%, there is only a slight improvement in heave, as measured by percent cast.

[0108] Table 2000 and graph 2100 also show that for each of the four explosives, the face velocity and percent cast are greater in very hard rock 2104 than in very soft rock 2102. This is further illustrated in FIG. 22 for the five rock types in table 1800 of FIG. 18. FIG. 22 shows graph 2200 illustrating the effect rock type has on percent cast for ANFO. As shown, cast is greater in hard rock than in soft rock. This may be due to less energy being lost to the fragmentation and impact brisance processes.

[0109] FIG. 23 shows a graph 2300 of percent cast face velocity for two rock types (i.e., very hard rock 2304 and very soft rock 2302). The charted point values ​​are from table 2000 in FIG. 20. As shown, face velocity is generally higher for harder rock, but within each rock type, face velocity may not be a good predictor of percent cast, as shown in graph 2300.

[0110] Example

[0111] The following examples relate to particular embodiments and point out particular features, elements, or operations that can be used or otherwise combined in achieving such embodiments.

[0112] Example 1. A method for simulating an explosive blast, the method comprising: initializing a model of a blast site including a plurality of blast holes; identifying explosives to be used in the simulated blast of the model; determining total available work from the detonation of the explosives; dividing the total available work by removing a portion of brisance work from the total available work to generate heave work, the brisance work being work performed between the detonation and a brisance point of the explosives; and simulating the detonation of the explosives based on the heave work.

[0113] Example 2. The method of example 1, wherein heave work is used to determine the heave of an element of the model.

[0114] Example 3. The method of example 1 or 2, further comprising displaying the simulated blast and the resulting muck pile resulting from the heavework.

[0115] Example 4. The method of any one of Examples 1-3, further comprising determining an initial heave condition between the detonation and the brissance point, the initial heave condition being the point at which pressure from the detonation of the explosive begins to move elements of the model.

[0116] Example 5. The method of any one of Examples 1-4, wherein the portion of Brissence work removed from the total available work is between 10% and 90% of the Brissence work.

[0117] Example 6. The method of any one of Examples 1-4, wherein the portion of Brissence work removed from the total available work is between 40% and 60% of the Brissence work.

[0118] Example 7. The method of any one of Examples 1-4, wherein the portion of the Brissance work removed is half of the Brissance work.

[0119] Example 8. The method of any one of Examples 1-7, wherein the model includes a plurality of elements, and simulating the detonation includes determining movement of the elements based on heave work.

[0120] Example 9. A computing device comprising: a processor; and a memory storing instructions, the instructions, when executed by the processor, configuring the device to: initialize a model of a blast site including a plurality of blast holes; identify explosives to be used in simulated blasts of the model; determine total available work from detonations of the explosives; divide the total available work by removing a portion of brisance work from the total available work to generate heave work, the brisance work being work performed between the detonation and a brisance point of the explosives; and simulate the detonation of the explosives based on the heave work.

[0121] Example 10. The computing device of example 9, wherein the heave work is used to determine the heave of an element of the model.

[0122] Example 11. The computing device of example 9 or 10, wherein the instructions further configure the device to display a resulting muck pile resulting from the simulated blast and heave work.

[0123] Example 12. The computing device of any one of Examples 9-11, wherein the instructions further configure the device to determine an initial heave condition between the detonation and the brissance point, the initial heave condition being the point at which pressure from the detonation of the explosive begins to move elements of the model.

[0124] Example 13. The computing device of any one of Examples 9-12, wherein the portion of the brissance work removed from the total available work is between 10% and 90% of the brissance work.

[0125] Example 14. The computing device of any one of Examples 9-12, wherein the portion of the brissance work removed from the total available work is between 40% and 60% of the brissance work.

[0126] Example 15. The computing device of any one of Examples 9-12, wherein the portion of the brissance work that is removed is half of the brissance work.

[0127] Example 16. The computing device of any one of Examples 9-15, wherein the model includes a plurality of elements, and simulating the detonation includes determining movement of the elements based on heave work.

[0128] Example 17. A non-transitory computer-readable storage medium containing instructions that, when executed by a computer, cause the computer to initialize a model of a blast site including a plurality of blast holes, identify explosives to be used in simulated blasts of the model, determine total available work from detonations of the explosives, divide the total available work by removing a portion of brisance work from the total available work to generate heave work, the brisance work being work performed between the detonation and a brisance point of the explosives, and simulate the detonation of the explosives based on the heave work.

[0129] Example 18. The computer-readable storage medium of Example 17, wherein the heave work is used to determine the heave of an element of the model.

[0130] Example 19. The computer-readable storage medium of example 17 or 18, wherein the instructions further configure the computer to display the simulated blast and the resulting muck pile resulting from the heavework.

[0131] Example 20. The computer-readable storage medium of any one of Examples 17-19, wherein the instructions further configure the computer to determine an initial heave condition between the detonation and the brissance point, the initial heave condition being the point at which pressure from the detonation of the explosive begins to move elements of the model.

[0132] Example 21. The computer-readable storage medium of any one of Examples 17-20, wherein the portion of the brissance work removed from the total available work is between 10% and 90% of the brissance work.

[0133] Example 22. The computer-readable storage medium of any one of Examples 17-20, wherein the portion of the brissance work removed from the total available work is between 40% and 60% of the brissance work.

[0134] Example 23. The computer-readable storage medium of any one of Examples 17-20, wherein the portion of the brissance work that is removed is half of the brissance work.

[0135] Example 24. A computer-readable storage medium according to any one of Examples 17 to 23, wherein the model includes a plurality of elements, and simulating the detonation includes determining movement of the elements based on heave work.

[0136] Example 25. A method for loading a blast hole, comprising: determining an explosives loading profile for the blast hole to achieve a desired result; and loading explosives into the blast hole according to the loading profile, wherein determining the explosives loading profile comprises simulating the blast by determining total available work from a hypothetical detonation of explosives; dividing the total available work by removing a portion of the brisance work from the total available work to generate heave work, such that the simulating blast is based on heave work; and selecting explosives to achieve a simulated blast that approximates the desired result.

[0137] Example 26. The method of Example 25, wherein the brissance work is work performed between a hypothetical detonation and the brissance point of the explosive.

[0138] Example 27. The method of example 25 or 26, wherein selecting an explosive comprises identifying the type of explosive and / or the energy output of the explosive.

[0139] Example 28. The method of example 27, wherein the type of explosive is selected from at least one of emulsion explosives, ammonium nitrate prills and fuel oil, water gel-based explosives, or blends and mixtures thereof.

[0140] Example 29. The method of example 27 or 28, wherein the energy output of the explosive is selected from at least one of the density of the explosive or the volume of the explosive.

[0141] Example 30. The method of any one of Examples 25-29, wherein selecting the explosives includes selecting multiple energy outputs of the explosives in different portions of the blasthole.

[0142] Example 31. The method of any one of Examples 25-30, wherein selecting explosives includes selecting multiple explosive types in different portions of the blasthole.

[0143] Example 32. The method of any one of Examples 25-31, wherein the heave work is used to determine the heave of an element of the model.

[0144] Example 33. The method of any one of Examples 25-32, further comprising displaying the simulated blast and the resulting muck pile resulting from the heavework.

[0145] Example 34. The method further includes determining an initial heave condition between a hypothetical detonation and a brissance point; The method of any one of Examples 25-33, wherein the initial heave state is the point at which pressure from a hypothetical detonation of an explosive begins to move elements of the model.

[0146] Example 35. The method of any one of Examples 25-34, wherein the portion of Brissance work removed from the total available work is between 10% and 90% of the Brissance work.

[0147] Example 36. The method of any one of Examples 25-34, wherein the portion of Brissance work removed from the total available work is between 40% and 60% of the Brissance work.

[0148] Example 37. The method of any one of Examples 25-34, wherein the portion of the Brissance work removed is half of the Brissance work.

[0149] Example 38. The method of any one of Examples 25-37, wherein the model includes a plurality of elements, and simulating the hypothetical detonation includes determining movement of the elements based on heave work.

[0150] Embodiments herein provide GEM discrete element rock blast heave modeling that includes energy partitioning. Embodiments herein may more accurately predict the amount of explosive energy that contributes to fragmentation and heave. In some embodiments, the brissance work may be partitioned into fragmentation energy and heave energy. Obtaining accurately partitioned energy may eliminate the need for user-defined coupling coefficients that are adjusted for every blast model to match measured field blast heave results.

[0151] The concept of energy partitioning suggests that energy lost to brissance may not be available for heave. Brissance may be defined as the work done in fracturing the rock surrounding the borehole with an explosive and generating a shock wave (which leaves the load before movement of the load begins). Some embodiments herein propose modeling energy partitioning, i.e., modeling where a portion (e.g., half) of the calculated brissance work contributes to heave while the other half does not contribute to rock movement.

[0152] The implementation of the energy partitioning concept in GEM has been shown not to result in excessive dependence of the results on element size, suggesting that the blasting charge on the rock is carried out in a way that is independent of element size.

[0153] References throughout this specification to an "embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment. Thus, references throughout this specification to an embodiment do not necessarily all refer to the same embodiment.

[0154] Similarly, those skilled in the art with the benefit of this disclosure should understand that in the description of the above embodiments, various features may be grouped together in a single embodiment, figure, or description for the purpose of streamlining the disclosure. However, this method of disclosure should not be interpreted as reflecting an intention that any claim requires more features than are expressly recited in that claim. Rather, as the following claims reflect, inventive aspects lie in combinations of fewer than all features of any single foregoing disclosed embodiment. Accordingly, the claims following this detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment. The present disclosure includes all combinations of independent claims with their dependent claims.

[0155] The recitation in a claim of the term "first" with respect to a feature or element does not necessarily imply the presence of a second or additional such feature or element. Those skilled in the art will recognize that changes can be made to the details of the above-described embodiments without departing from the underlying principles of the disclosure.

Claims

1. 1. A method for simulating an explosive blast, comprising: initializing a model of a blast site including a plurality of blast holes; identifying explosives to be used in a simulated blast of said model; determining total available work from the detonation of said explosive; Dividing the total available work by removing a portion of brisance work from the total available work to generate heave work, the brisance work being work performed between the detonation and a brisance point of the explosive; simulating the detonation of the explosive based on the heave work; and A method comprising:

2. The method of claim 1 , wherein the heave work is used to determine the heave of elements of the model.

3. The method of claim 1 or 2, further comprising displaying the simulated blast and the resulting muck pile resulting from the heavework.

4. 4. The method of claim 1, further comprising determining an initial heave condition between the detonation and the brissance point, the initial heave condition being the point at which pressure from the detonation of the explosive begins to move elements of the model.

5. 5. The method of claim 1, wherein the portion of the brissance work removed from the total available work is between 10% and 90% of the brissance work.

6. 5. The method of claim 1, wherein the portion of the brissance work removed from the total available work is between 40% and 60% of the brissance work.

7. 5. The method of claim 1, wherein the portion of the brissance work that is removed is half of the brissance work.

8. 8. The method of claim 1, wherein the model includes a plurality of elements, and simulating the detonation includes determining movement of the elements based on the heave work.

9. 1. A computing device comprising: a processor; a memory storing instructions that, when executed by the processor, Initialize a model of a blast site containing multiple blast holes; identifying explosives to be used in a simulated blast of said model; determining total available work from the detonation of said explosive; dividing the total available work by removing a portion of brisance work from the total available work to generate heave work, the brisance work being work performed between the detonation and a brisance point of the explosive; simulating the detonation of the explosive based on the heave work; 20. A computing device, comprising:

10. The computing device of claim 9 , wherein the heave work is used to determine the heave of elements of the model.

11. 11. A computing device according to claim 9 or 10, wherein the instructions further configure the device to display a resulting mock pile resulting from the simulated blast and heave work.

12. 12. The computing device of claim 9, wherein the instructions further configure the device to determine an initial heave condition between the detonation and the blissance point, the initial heave condition being a point at which pressure from the detonation of the explosive begins to move elements of the model.

13. 13. A computing device according to any one of claims 9 to 12, wherein the portion of the brissance work removed from the total available work is between 10% and 90% of the brissance work.

14. 13. The computing device of claim 9, wherein the portion of the brissance work removed from the total available work is between 40% and 60% of the brissance work.

15. A computing device according to any one of claims 9 to 12, wherein the portion of the brissence work that is removed is half of the brissence work.

16. 16. The computing device of claim 9, wherein the model includes a plurality of elements, and simulating the detonation includes determining movement of the elements based on the heave work.

17. 1. A non-transitory computer-readable storage medium containing instructions that, when executed by a computer, cause the computer to: Initialize a model of a blast site containing multiple blast holes, identifying explosives to be used in a simulated blast of said model; determining total available work from the detonation of said explosive; dividing the total available work by removing a portion of brisance work from the total available work to generate heave work, the brisance work being work performed between the detonation and a brisance point of the explosive; simulating the detonation of the explosive based on the heave work; A computer-readable storage medium.

18. The computer-readable storage medium of claim 17 , wherein the heave work is used to determine the heave of elements of the model.

19. 19. The computer-readable storage medium of claim 17 or 18, wherein the instructions further configure the computer to display the simulated blast and the resulting muck pile resulting from the heavework.

20. 20. The computer-readable storage medium of claim 17, wherein the instructions further configure the computer to determine an initial heave condition between the detonation and the brissance point, the initial heave condition being a point at which pressure from the detonation of the explosive begins to move elements of the model.

21. 21. The computer-readable storage medium of claim 17, wherein the portion of the brissance work removed from the total available work is between 10% and 90% of the brissance work.

22. 21. The computer-readable storage medium of claim 17, wherein the portion of the brissance work removed from the total available work is between 40% and 60% of the brissance work.

23. 21. The computer-readable storage medium of claim 17, wherein the portion of the brissance work that is removed is half of the brissance work.

24. 24. The computer-readable storage medium of claim 17, wherein the model includes a plurality of elements, and simulating the detonation includes determining movement of the elements based on the heave work.

25. 1. A method for loading a blast hole, comprising: determining an explosives loading profile for the blasthole to achieve a desired result; loading the blast hole with explosives according to the loading profile; Including, Determining an explosives loading profile simulating a blast by determining total available work from a hypothetical detonation of an explosive, and dividing the total available work by removing a portion of brisance work from the total available work to generate heave work, such that simulating a blast is based on the heave work; selecting the explosives to achieve the simulated blast that approximates the desired result; A method comprising:

26. 26. The method of claim 25, wherein the brissance work is work performed between the hypothetical detonation and the brissance point of the explosive.

27. 27. A method according to claim 25 or 26, wherein selecting the explosive comprises identifying the type of explosive and / or the energy output of the explosive.

28. 28. The method of claim 27, wherein the type of explosive is selected from at least one of emulsion explosives, ammonium nitrate prills and fuel oil, water gel based explosives, or blends and mixtures thereof.

29. 29. A method according to claim 27 or 28, wherein the energy output of the explosive is selected from at least one of the density of the explosive or the volume of the explosive.

30. A method according to any one of claims 25 to 29, wherein selecting the explosives comprises selecting multiple energy outputs of explosives in different parts of the blasthole.

31. A method according to any one of claims 25 to 30, wherein selecting the explosives comprises selecting a plurality of explosive types in different parts of the blasthole.

32. A method according to any one of claims 25 to 31, wherein the heave work is used to determine the heave of an element of a model.

33. 33. The method of any one of claims 25 to 32, further comprising displaying the simulated blast and the resulting muck pile resulting from the heavework.

34. 34. The method of any one of claims 25 to 33, further comprising determining an initial heave condition between the hypothetical detonation and a brissance point, the initial heave condition being the point at which pressure from the hypothetical detonation of the explosive begins to move elements of a model.

35. 35. The method of any one of claims 25 to 34, wherein the portion of the brissance work removed from the total available work is between 10% and 90% of the brissance work.

36. 35. The method of any one of claims 25 to 34, wherein the portion of the brissance work removed from the total available work is between 40% and 60% of the brissance work.

37. 35. The method of any one of claims 25 to 34, wherein the portion of the brissance work that is removed is half of the brissance work.

38. 38. The method of any one of claims 25 to 37, wherein the model includes a plurality of elements, and simulating the hypothetical detonation includes determining movement of the elements based on the heave work.

Images