Distinct element rock blasting movement methods, apparatuses and systems

Abstract

To provide methods, systems and apparatuses for designing a blast plan.SOLUTION: A blast modeling system may generate a site model based on blast input data. The blast input data may include blasthole data, bench information, and geology input data. The site model may comprise a plurality of distinct elements representing rock masses. Each element may have a geometric outline formed by connecting endpoints of one or more lines such that the endpoints of the one or more lines are indirectly coupled via arcs. The blast modeling system may simulate a blast using the plurality of elements.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] Related Applications This application claims priority to U.S. Patent Application No. 17 / 324,704, entitled "DISTINCT ELEMENT ROCK BLASTING MOVEMENT METHODS, APPARATUSES, AND SYSTEMS," filed May 19, 2021; U.S. Provisional Patent Application No. 63 / 124,412, entitled "DISTINCT ELEMENT ROCK BLASTING MOVEMENT METHODS, APPARATUSES, AND SYSTEMS," filed December 11, 2020; and U.S. Provisional Patent Application No. 63 / 028,345, entitled "DISTINCT ELEMENT ROCK BLASTING MOVEMENT METHODS, APPARATUSES, AND SYSTEMS," filed May 21, 2020, the contents of which are incorporated herein by reference in their entireties.

[0002] The present disclosure relates generally to explosives and, more particularly, to methods, systems, and apparatus for designing blasting schemes. [Background technology]

[0003] To easily identify the discussion of any particular element or operation, one or more of the most significant digits of a reference number refer to the figure number in which that element is first introduced. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Stiehr, Jon F. “ISEE Blasters' Handbook, 18th Edition”, International Society of Explosives Engineers, Inc., Section I, Part II, Chapter 9, p. 109-134

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 4

Non-Patent Document 5

[0005] [Figure 1] 1 illustrates advanced individual elements of a blast simulation according to one embodiment. [Figure 2] 10 illustrates an arc-arc contact detection technique that may be used by the modeling system to identify contact between arcs of neighboring elements, according to one embodiment. [Figure 3] 1 illustrates an arc-line contact detection technique according to one embodiment. [Figure 4] 1 illustrates a method for detecting line-to-line contact using arc-to-line contact detection techniques according to one embodiment. [Figure 5] 10 illustrates force calculations that a modeling system may use to identify forces imparted to an advanced individual element by contacting the element, according to one embodiment. [Figure 6] 10 illustrates a moment calculation that identifies the moment imparted to an advanced individual element by contacting the element, according to one embodiment. [Figure 7] 1 illustrates a flowchart of a method for blast modeling according to one embodiment. [Figure 8] 1 shows a flowchart of a method for simulating a blast according to one embodiment. [Figure 9] 1 illustrates parameters of an input file that may be received by a modeling system according to one embodiment. [Figure 10] 1 illustrates geological input data according to one embodiment. [Figure 11] 1 illustrates a blast model divided into multiple zones according to one embodiment. [Figure 12] 1 illustrates a partially fragmented blast model according to one embodiment. [Figure 13] 1 illustrates a partially fragmented blast model according to one embodiment. [Figure 14] 1 illustrates a blast pit according to one embodiment. [Figure 15] 1 illustrates a custom blasting model according to one embodiment. [Figure 16] 1 illustrates a top view of a blasting pattern according to one embodiment. [Figure 17] 1 illustrates a blast model with sub-drilled blast holes according to one embodiment. [Figure 18] 1 illustrates a rotation procedure for introducing geological gradients into a blast model according to one embodiment. [Figure 19] 10 illustrates the timing of unloading of individual modeling elements in a blast model according to one embodiment. [Figure 20] 1 illustrates a simulation model of buffer blasting or chalk blasting according to one embodiment. [Figure 21] 1 illustrates a flowchart of a method for creating a model for simulating blasting according to one embodiment. [Figure 22] 1 illustrates an item according to one embodiment. [Figure 23] This shows the procedure for changing the shape of an element during a blasting simulation. [Figure 24] 1 illustrates two circular elements that may be used by the modeling systems and methods described herein. [Figure 25] 1 illustrates three potential three-dimensional shapes that may be used as elements by the modeling systems and methods described herein. DETAILED DESCRIPTION OF THE INVENTION

[0006] Explosives are commonly used in the mining, quarrying, and mining industries to break up rock and ore. Generally, a hole called 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 break up 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 properties, explosive type, explosive quantity, and blast hole start time. The number of possibilities makes blast planning difficult even for experienced blast engineers.

[0007] Blast simulations performed by a modeling system may 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 may be used to identify the location of ore in the final muckpile after the blast occurs, to assist in ore management of tailings ore waste and minimization of mixing of tailings ore with target ore.

[0008] Some blast modeling systems use discrete elements to simulate a blast. Discrete element modeling systems generate a collection of elements that represent the blast site and track the movement of the elements over time to simulate the blast. The movement of the discrete elements is caused by forces applied to the collection and usually also by gravity.

[0009] Some modeling systems use circular elements to represent rock. A blast can be simulated using a population of two-dimensional circular elements that move over time due to explosive load and weight. Circles can be very computationally efficient because interparticle contact can be identified by comparing the center-to-center distance of two circles to the sum of the circle radii. However, circular elements oversimplify the rock mass, resulting in a less accurate simulation. For example, circular elements do not create friction between elements or interact with each other in the same way that uneven rock masses would. Another problem associated with spherical individual elements is that they have no aspect ratio, thus limiting the prediction of bulking or porosity in a population of spherical individual elements. Therefore, circular elements cannot accurately represent the bulking that may occur in the final muckpile after blasting.

[0010] Some modeling systems employ straight-edged discrete elements, such as quadrilateral elements or triangular elements, to represent rock masses. Straight-edged discrete elements are a series of lines connected to each other to form the outline of a shape with a set of angled corners. Systems using straight-edged elements provide more accurate simulations than systems using circular elements. For example, straight-edged discrete elements can have aspect ratios, unlike circular elements. However, detecting contacts between straight-edged 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 computational time than simulations employing spherical elements. Furthermore, straight-edged elements are too rigid and bulky to represent rock flow behavior well.

[0011] Described herein are embodiments for simulating blasting using discrete elements with an advanced geometric paradigm that represent the movement of blasted rock. Advanced discrete elements geometrically include arcs and lines that define the outline of each individual element. Lines are connected via arcs so that the lines do not intersect. Instead, the arcs and lines are used to create two-dimensional discrete elements with one or more straight edges and rounded corners. The rounded corners may be formed using one or more arcs. These advanced discrete elements improve simulation accuracy when compared to circular elements, and are more computationally efficient than straight-edge discrete elements.

[0012] Although the embodiments described herein relate to two-dimensional modeling, the embodiments may be extendable to three dimensions, where the inherent higher fidelity and computational efficiency would provide significant advantages over currently available spherical and block element methods. For example, highly discrete elements in three dimensions may include blocks with rounded corners.

[0013] 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 steps need not be performed only once. Thus, the following more detailed description of various embodiments, as described below and represented in the Figures, is not intended to limit the scope of the present disclosure but is merely representative of various embodiments. While various aspects of the embodiments are presented in drawings, the drawings are not necessarily to scale, unless otherwise noted.

[0014] The embodiments and implementations of the blast planning systems and methods described herein may include various steps, which may be implemented by 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 or a combination of hardware, software, and / or firmware that contain specific logic for performing the steps.

[0015] 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, a magnetic or optical card, a solid-state memory device, or any other type of medium / computer-readable medium suitable for storing electronic instructions.

[0016] Computer systems and computers in computer systems may be connected via a network. Networks suitable 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, virtual private networks, extranets, intranets, or stand-alone machines that communicate with other machines via the physical transport of a medium. In particular, a suitable network may be formed in part or in whole from two or more other networks, including networks using disparate hardware and network communication technologies.

[0017] One suitable network may include one 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.

[0018] Suitable networks may include communications or networking software such as software available from Novell®, Microsoft®, and other vendors, and may operate using TCP / IP, SPX, IPX, and other protocols over twisted pair, coaxial cable, or fiber optic cable; telephone lines; radio waves; satellites; microwave relays; modulated AC power lines; physical media transport; and / or other data transmission "wires" known to those skilled in the art. A network may also encompass smaller networks and / or be connectable to other networks through gateways or similar mechanisms.

[0019] Each computer system includes one or more processors and / or memory, and computer systems 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 general-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 devices may include keyboards, mice, touchscreens, light pens, tablets, microphones, sensors, or other hardware with associated firmware and / or software. Output devices may include monitors or other displays, printers, speech or text synthesizers, switches, signal lines, or other hardware with associated firmware and / or software.

[0020] The computer system may be capable of using floppy disks, tape drives, optical drives, magneto-optical drives, or other means of reading storage media. Suitable storage media include magnetic, optical, or other computer-readable storage devices that have a particular physical configuration. Suitable storage devices include floppy disks, hard drives, 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.

[0021] Suitable software to assist in the practice of the present invention can be 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++, PHP, .Net, database languages, APIs, SDKs, assembly, firmware, microcode, and / or other languages ​​and tools. Suitable signal formats can be implemented 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 will be readily provided by one of ordinary skill in the art.

[0022] 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, for example, one or more physical or logical blocks of computer instructions, which may be organized as routines, programs, objects, components, data structures, etc. that perform one or more tasks or implement a particular abstract data type. A particular software module may include heterogeneous instructions stored in different locations of a computer-readable storage medium, the heterogeneous instructions together performing the module's described function. In practice, 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.

[0023] Some embodiments may be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, software modules may be located in local and / or remote computer-readable storage media. Additionally, data linked together or rendered in a database record may reside on the same computer-readable storage medium or across several computer-readable storage media, and may be linked together in 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 the DBMS provides access to the data contained in the databases.

[0024] 1 illustrates an advanced discrete element 100 according to one embodiment. A discrete element modeling system uses the advanced discrete element 100 to segment 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 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 106 connected by four arcs (i.e., a first arc 108, a second arc 112, a third arc 116, and a fourth arc 122).

[0025] The illustrated embodiment includes two parallel lines. Other embodiments may have one or more lines, and the lines may be angled relative to one another. Each line has two endpoints, and each endpoint is connected to an arc so that the shape has rounded corners or edges. Each rounded corner may be created using one or more arcs. For example, one rounded corner or rounded edge is created by connecting a first arc 108 and a second arc 112.

[0026] Each arc is a distinct curve. In the illustrated embodiment, the arcs are circular arcs that 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 132). The arc center points represent points equidistant from all points on the arc. Each arc also includes a radius (i.e., first radius 110, second radius 114, third radius 118, and fourth radius 124). Because the arcs are circular, the radius of each arc is the same along all points of the arc. Additionally, each arc includes an arc angle (e.g., first arc angle 120). The arc angle is the angle formed by the arc at the center point. As shown, an endpoint of an arc may connect to another arc, as shown by the connection between the first arc 108 and the second arc 112, or an endpoint of an arc may connect to a line, as shown by the connection between the first line 102 and the third arc 116.

[0027] Arc-to-line and arc-to-arc intersections form smooth transitions between different shape contour elements. Each line may be tangent to the endpoint of the arc it connects to, smoothing the transition. Similarly, arc-to-arc transitions may also be smooth. Intersections do not form sharp angles, as would occur if two lines were directly connected to form a vertex. As a result, the shape has 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 connected through arcs to avoid angled corners. Rounded corners are more computationally efficient than sharp corners and may be created using one or more arcs.

[0028] The advanced discrete elements 100 are created from arcs and lines that define the outline of each individual discrete element. Figure 1 depicts one of many possible element shapes that can be created from arcs and lines. Other embodiments of advanced discrete elements may use arcs and lines to create other non-spherical shapes that do not have angled corners. Other shapes that may 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.

[0029] 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 in the simulation model are different shapes. For example, elements of different shapes may be used to model different types of rock. For example, coal may be modeled using rounded quadrilaterals, while another rock in the same simulation may be modeled using rounded hexagons. In some embodiments, at least some of the elements of the same shape are different sizes.

[0030] Individual element shapes formed with discontinuous lines indirectly connected through arcs offer better accuracy than circular elements and computational efficiency advantages over individual elements with only straight lines. Straight lines and varying arc radii provide more realistic aspect ratios when compared to circles, while arcs provide a more efficient method of detecting contact between neighboring elements when compared to elements with only straight lines.

[0031] 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 endpoint node coordinates, designated arc endpoints, arc center points, arc radii, and arc angles.

[0032] 2-4 illustrate various methods for detecting contact between highly individual elements. Two primary inter-element interaction mechanisms for detecting contact between neighboring elements are 1) 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 described in more detail below, line-line contact can also be detected by the arc-line interaction mechanism.

[0033] All of these element interaction detections between highly individual elements are very computationally efficient, much more computationally efficient than interactions between straight-edged individual elements. Highly individual elements also have aspect ratios greater than 1, and have more natural bulking and inter-particle friction than circular elements.

[0034] The described advanced individual elements can increase simulation fidelity in individual element modeling of rock blasting because the elements have aspect ratios that circular elements cannot have and more naturally represent the natural behavior of rock during blast-induced movements such as bulking and inter-element friction.

[0035] Also, due to the computational simplicity, arc-arc and arc-line contact detection speed, and resolution, higher fidelity simulations can be completed in much shorter computational times, implying that much higher fidelity blast simulations can be achieved on cheaper and more portable laptop computers.

[0036] 2 illustrates an arc-arc contact detection technique that a modeling system may use to detect contact between arcs of neighboring elements. As shown, a first element 202 having a first arc 216 is a neighbor of a second element 204 having a second arc 218.

[0037] To detect whether the cores of these two elements contact each other during a simulation time step, the modeling system may determine whether there is an overlap 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 neighboring elements involves 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 neighboring elements to the sum of the first radius 210 and the second radius 212 of the two arcs of the neighboring elements. For example, in some embodiments, arc-arc contact is detected if the sum of the radii is greater than the distance 214.

[0038] 3 illustrates an arc-line contact detection technique that a modeling system may use to detect contact between an arc 310 and a line 312 of neighboring elements. In this illustration, a first element 302 and a second element 304 are neighboring elements whose nearest 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 determine the distance 306 using a dot product.

[0039] When an arc 310 and a line 312 overlap in a simulation, it is called an arc-line contact. The modeling system may detect arc-line contact between neighboring 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 may be detected if the radius 308 is greater than the distance 306.

[0040] Figure 4 shows how line-line contact may be detected by the modeling system using the arc-line contact technique described with reference to Figure 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 computationally less efficient than arc-arc contact detection and arc-line contact detection. Therefore, in some embodiments, line-line contact may be detected indirectly using arc-line contact detection because, when the lines overlap, one or both of the first arc 410 and the second arc 412 overlap with the first line 402.

[0041] 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.

[0042] FIG. 5 illustrates force calculations that a modeling system may use to identify forces imparted to advanced individual elements by contacting elements. The modeling system may calculate the magnitude and direction of the force imparted to each element. The system detects contact between two individual elements 502 and 504 if there is an overlap 506 at the perimeter of the first and second elements 502 and 504 during a simulation time step. The modeling system resolves or eliminates the overlap 506 by applying calculated restoring forces to eliminate the overlap 506. These restoring forces are applied to both the first element 502 and the second element 504.

[0043] As part of the simulation, the modeling system may determine contact and calculate the force imparted to each element by neighboring elements in contact. 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 (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 is equal to the specified spring constant of the material multiplied by the overlap 506.

[0044] 6 illustrates moment calculations that a modeling system may use to determine the moment 604 imparted to an advanced individual element 600 by a contacting element. Each force 606 imparted to an advanced individual element 600 imparts a moment M to the advanced individual element 600, as shown. 604. A moment is imparted at element center 602 by all forces imparted to advanced individual element 600, including force 606 imparted at arc center point 608 caused by contacting elements. In some embodiments, the modeling system calculates the moment for each force separately and then sums the moments to determine the total moment for advanced individual element 600.

[0045] The modeling system is M=F×r Moments 604 may be calculated by calculating: F is the force 606 r 610 is the shortest distance between the vector representing the force 606 and the element center 602 .

[0046] The total moment (ie, sum of the moments) is calculated to determine the rotation of the advanced individual element 600 .

[0047] FIG. 7 shows a flowchart of a method 700 of explosive blast modeling according to one embodiment. A modeling system executing method 700 receives a blast plan including blasthole data and blast site data. The blasthole data may include blasthole parameters such as blasthole spacing, blasthole load, blasthole depth, blasthole diameter, blasthole pattern, blasthole count, stemming information, explosive properties, blasthole angle, blasthole top coordinate, blasthole bottom coordinate, and decking information. The blast pattern may be geometrically defined in a 3D coordinate system X (longitude), Y (latitude), and Z (vertical). The 3D coordinate system may be a local coordinate system with an origin somewhere near the blast pattern, or may be within the mine's coordinate system, which is typically a larger 3D local coordinate system encompassing all of the mine. In the blast pattern design, a line representing a blasthole may be defined by a top coordinate and a bottom coordinate. Most blasting patterns do not have a flat top surface and the angle of each blast hole in the pattern can vary slightly or significantly, therefore a top coordinate and a bottom coordinate may be used to define a blast hole.

[0048] The blast site data may include site bench information, geological properties, geological characteristics, and geological coefficients. Non-limiting examples of bench information include face angle, bench height, bench slope, pit slope, spoil angle, and face element count. Non-limiting examples of geological properties include mineralogy (elements and / or minerals), lithology (primary, secondary, and / or texture), porosity, hardness, attenuation, Young's modulus, shear modulus, bulk modulus, Poisson's ratio, P-wave velocity, S-wave velocity, rock density, rock type, rock strength, rock condition, rock description, joint condition, joint angle, joint orientation, standard deviation of joint spacing, cohesion, vertical joint spacing, horizontal joint spacing, uniaxial compressive strength (UCS), sound velocity, standard deviation of drilling, impact velocity, rock fracture strength, rock reflectivity, rock tensile strength, angle of internal friction, Hugoniot data (e.g., Up min, Up max, Us min, Us max), and soil strength (σ1, σ2, σ3, stress orientation, dip, direction, and roll). " refers to the size, shape, and arrangement of the incorporated mineral crystals that form a rock or other material. Geological data can be used to identify further geological characteristics such as friable and clastic.

[0049] The modeling system generates a site model (e.g., two two-dimensional site models) based on the blast plan by generating a plurality of advanced individual elements (704). Each advanced individual element has a shape formed by connecting endpoints of one or more lines with arcs, such that endpoints of the one or more lines are indirectly connected via the arcs, and the arcs form rounded corners of the shape. The modeling system further simulates the blast using the site model and the plurality of elements (706).

[0050] 8 shows a flowchart of a method 800 for simulating a blast according to one embodiment. The distinct element simulation method tracks the movement and interaction of thousands of distinct elements by stepping through time in pre-calculated stable time steps, typically 1.0E-4 s or less, depending on the mass and stiffness of the individual elements. At each time step, the following method steps are used:

[0051] A system using method 800 searches 806 the entire population of individual elements in the in-situ model for arc-arc and arc-line contacts using the techniques described with reference to Figures 2-4. The system may further identify 808 forces resulting from arc-arc and arc-line contacts using the techniques described with reference to Figure 5. The system may also identify 810 moments for each element using the techniques described with reference to Figure 6.

[0052] A system using method 800 sums 812 the moments and forces of each element. At each time step, each element may have multiple restoring forces and moments applied to it resulting from multiple contacts with surrounding elements. The multiple forces and moments are summed to calculate a total force and total moment.

[0053] The system implementing method 800 moves each element to a new position based on the total force and moment (814). The new position is used during the next time step. Contact between elements leads to overlap. This overlap is resolved or eliminated by applying reaction forces and moments to each element. The system applies the total force and moment to each element, translating and rotating each element a small distance to a new location at the end of the small time step.

[0054] The system using method 800 then determines whether the total run time of the simulation has completed (804). If the duration of the simulation has ended, method 800 ends (802). Otherwise, method 800 adds a time step to the current time period and runs the simulation again using the new positions of the individual elements (816).

[0055] In some embodiments, method 800 may include additional steps. For example, when two arcs intersect, significant friction is not generated. Thus, part of method 800 may include imposing a temporary constraint to simulate the friction caused by rough rock. This enhanced friction behavior may vary based on rock type.

[0056] Figures 9-20 illustrate various procedures that the modeling system may follow to simulate a blast, any of which may be used in combination with the methods described in Figures 7 and 8.

[0057] 9 shows input file parameters 900 that may be received by the modeling system. The input file is used by the modeling system to create a model of a blast simulation. The model shown is a free-form two-dimensional model. The model includes multiple blast holes (e.g., blast hole 902 and blast hole 904) shown in a two-dimensional XY plane. The input file defines the model, including the location, size, and angle of the blast holes.

[0058] The input file may be a blast plan including blast hole data and blast site data. The blast hole data may include the number of rows, load, spacing, stemming information, decking information, explosive properties, blast hole diameter, blast hole angle, top coordinate, and bottom coordinate. The blast site data may include bench information such as face angle, bench height, bench slope, pit slope, spoil angle, and face element count.

[0059] 10 illustrates geological input data 1000 that may be received by the modeling system. The geological input data 1000 may be included in the blast site data input file received by the modeling system. The geological input data includes the geological properties, geological characteristics, and geological coefficients of the site.

[0060] For example, the geological input data 1000 may include a bench slope 1002, a pit slope 1012, and a geological slope 1004. The bench slope 1002 represents the slope of the bench plateau. The pit slope 1012 represents the slope of the pit. The geological slope 1004 represents the slope of the bench formations. In some embodiments, the angles of the bench slope 1002, the pit slope 1012, and the geological slope 1004 may be different from each other. In some embodiments, two or all three of the bench slope 1002, the pit slope 1012, and the geological slope 1004 may have the same angle. For example, the bench slope and the geological slope 1004 may have the same angle.

[0061] Additionally, the geological input data may include properties of the formations (e.g., the first 1006, second 1004, and third 1010 layers of the bench). The formation properties may include the rock type, density, Young's modulus, Poisson's ratio, rock impact velocity, and fracture velocity coefficient of each layer. These properties may be used to specify the arc shape, size, and / or radius of the individual elements used to model the formation.

[0062] 11 shows a blast model 1100 divided into multiple zones (i.e., zones 1102-1110, referred to herein as zones) based on blast hole location. The modeling system may identify zones that represent areas where elements of different sizes will be used in the simulation.

[0063] Elements of different sizes may be used to represent different fragment sizes. The modeling system may use smaller elements in zones to represent rock closest to the blasthole 1112-1120 being fragmented into smaller pieces due to their position relative to the explosive force. Additionally, in some embodiments, these zones may be defined based on the location of the explosives within the blasthole 1112-1120, ignoring parts such as stemming.

[0064] In some embodiments, rock within a zone is represented by elements that are a fraction of the size of the rest of the bench. For example, in the illustrated embodiment, the elements within the zone are half the size of the other elements in the model. In other embodiments, the elements within a zone may be of different proportions based on the energy density, type, and / or amount of explosives in the blasthole associated with the zone. For example, a first zone may be segmented into half-sized elements, while a second zone may be segmented into quarter-sized elements.

[0065] In some embodiments, the element size may be graduated based on the relative position to the charge in the blasthole rather than being two sizes. In these embodiments, zones may or may not be used. The gradient in element size results in the smallest elements near the charge in the blasthole and gradually increasing element sizes based on the distance from the charge in the blasthole.

[0066] 12 shows a partially fragmented blast model 1200. As shown, the modeling system fragments the blast model 1200 by segmenting or creating a mesh of elements that represent the rocks of the model. The elements in the illustrated embodiment are quadrilateral elements with rounded corners. Similar fragmentation can be performed using other non-spherical elements that do not have sharp corners.

[0067] In the illustrated embodiment, the modeling system predicts that the areas of the blast model 1200 outside the first zone 1202 and the second zone 1204 will fracture at a size that is 60% of the desired pass size. Larger elements at the bench face can be cut to align with the bench face.

[0068] The modeling system uses smaller elements in the first zone 1202 and the second zone 1204 to represent a higher degree of fragmentation near the charge within the blasthole. In the illustrated embodiment, the smaller elements are 30% of the desired passage size, which is half the size of the larger elements. The elements that traverse the blasthole may be split and represented as two elements.

[0069] 13 shows a blast model 1300 that has been partially fragmented into multiple elements using various fragmentation techniques. The elements used in the illustrated embodiment represent one type of highly individual element: a quadrilateral element with rounded corners.

[0070] In the first area 1302, the modeling system segmented the top of the bench into four layers. As shown, each layer in the first area 1302 and the second and third areas 1306 and 1304 is offset. For example, in some embodiments, each successive layer may be offset by half an element.

[0071] A second area 1306 represents how the modeling system segments the blast model 1300 near the blast hole. The modeling system may identify elements that cross the blast hole and cut such elements to match the elements surrounding the blast hole. In the illustrated embodiment, these elements in the blast hole are cut or severed at the blast hole with a vertical edge. However, in other embodiments, the elements may be cut at the same angle as the blast hole. Additionally, in some embodiments, if the cut element is below a threshold size or width, the modeling system may simply delete the element.

[0072] A third area 1304 represents how the modeling system segments the blast model 1300 near the bench plane. The modeling system may identify elements that cross the bench plane and cut such elements to match elements within the bench. In the illustrated embodiment, these elements at the bench plane are cut or severed at the bench plane with a vertical edge. However, in other embodiments, the elements may be cut at the same angle as the bench plane. Additionally, in some embodiments, if the cut element is below a threshold size or width, the modeling system may simply delete the element.

[0073] The modeling system may fragment the remaining portions of the blast model 1300 according to the techniques described above.

[0074] FIG. 14 shows how the modeling system may create a blasting pit 1400. The blasting pit 1400 may be formed using immobile elements 1402. The immobile elements 1402 do not move during the simulation. The immobile elements 1402 may also use elements formed using arcs and lines. For example, the immobile elements 1402 may have the same shape as the same elements used to model the bench. Thus, interactions between the immobile elements 1402 and the blasting moving elements may be specified by the modeling elements using arc-arc contacts and arc-line contacts.

[0075] FIG. 15 shows a blast model 1500 with blast holes that vary in parameters. In a blast design, parameters can vary across a blast site. For example, blast design parameters can vary in each row. Some parameters that are variable within a blast plan include load, spacing, stemming, hole angle, hole depth, hole diameter, and explosive type, which can be customized in each row. Load and spacing are defined with respect to the blast hole's location at the bench top, while hole depth and stemming are defined from the bench top (e.g., distance from the bench top). A modeling system such as that described herein can generate custom models that vary blast design parameters and then run blast simulations.

[0076] Figure 16 shows a top view of a blasting pattern 1600. The two-dimensional calculation plane 1602 is a two-dimensional discrete element blasting model (such as the model shown in Figures 9-15) on which the blasting simulation is performed. The modeling system can use the blasting pattern 1600 to take into account the three-dimensional aspects of the bench.

[0077] For example, the modeling system may take into account the three-dimensional aspects of the bench by identifying element masses based on spacing 1604. By accounting for spacing 1604, the modeling system identifies the true mass moved by each blast hole and assigns that mass to elements in the two-dimensional calculation plane 1602. Thus, element displacement in a simulation is a function of spacing. Additionally, increasing element mass may result in a larger time step for the simulation.

[0078] The element mass is Element mass = area x spacing x rock density where: Area is the element area in the two-dimensional calculation plane 1602, Spacing is the distance between blast holes in a row; Rock density is the density of a geological material expressed in terms of elements.

[0079] 17 shows a blast model 1700 with subdrilled blast holes (e.g., blast hole 1706). Subdrilling occurs when the blast hole is drilled below the bottom of the pit 1704. In other words, the blast hole depth plus the stemming is greater than the bench height.

[0080] To simulate a blast with sub-drilled holes, some embodiments of the modeling system may extend the moving element area 1702 below the pit 1704. For example, individual elements moving during a blast simulation may extend beyond the bench surface by the length of the first load width 1708. The first load width 1708 is the space between the first row of blast holes and the face. When the modeling system simulates a blast, the entire modeling element area 1702 is used as the calculation area within which the system identifies element movement. Thus, the sub-drilling extends the calculation area below the pit 1704. In some embodiments, the modeling system may use elements to simulate inter-row time delays. For example, the modeling system may simulate a series of time delay planes that provide data on the element's location and the time to start the second row. For example, FIG. 16 shows the volume of rock moved by individual blast holes. The (off-plane) spacing between blast holes may control the mass of rock moved by the blast hole and, ultimately, the velocity of the GEM element affected by that blast hole.

[0081] 18 illustrates a rotation procedure that a modeling system may employ to create a geological slope for a blast model 1800. In some embodiments, the modeling system may create the model 1800 with zero geological slope. The system may then rotate the model 1800 from a horizontal position 1802 to an angled position 1804. The system may rotate the model 1800 so that the model 1800 in the angled position 1804 may have an angle that matches the geological slope.

[0082] 19 illustrates a procedure for timing the unloading of individual modeling elements in a blast model 1900. As shown, the modeling system may divide the blast model 1900 into multiple burst portions (e.g., first burst portion 1902, second burst portion 1904, third burst portion 1906, fourth burst portion 1908, and fifth burst portion 1910). Before the explosives in the blast hole are detonated, the individual elements have not yet been released. In other words, the individual elements are frozen from movement.

[0083] The unloading of individual elements in a blast section occurs when the simulation detonates explosives in blast holes located in the blast section. The unloading allows the individual elements to begin moving. The simulation may include a time delay that may be delayed between the detonation of each row of blast holes. During initialization of the simulation, the modeling system may set the unloading or "alive time" of each element based on the row delay time.

[0084] Each blast section may include elements located in 1 / 3 of the load behind each row of blast holes and elements in front of the blast holes. Thus, when each blast section reaches its load release time, 1 / 3 of the load behind the blast holes will fragment and move freely with the load fragmentation to the front of the blast holes.

[0085] The modeling system advances the simulation in time at steady time steps. When the row's explosion time is reached, the modeling system releases the elements in the load at the front of the row, plus the elements in the rear third of the load are released to move because they have all reached their "life time." The modeling system releases elements in each explosion section in turn until it reaches a new free surface 1912.

[0086] FIG. 20 shows a discrete element model 2000 generated by a modeling system to simulate blasting without free faces (e.g., buffer blasting or chalk blasting). Buffer blasting or chalk blasting is a blasting technique that does not use free faces. Simulations using hexahedrons for buffer blasting or chalk blasting predict that the ore will move during blasting. This prediction may allow for more precise excavation of the ore.

[0087] This type of blasting technique can be used in gold and copper mining. Gold and copper mining rely on high resolution simulation. Based on the need for high resolution, the rock properties and properties of gold, hexahedral elements can be used.

[0088] Hexahedral elements may include size lines that are indirectly connected with arcs to form polygons with rounded corners. Hexahedral elements may be cut in half to create flat surfaces. Additionally, hexahedral elements that interact with a blast hole (such as blast hole 2002) may be split or cut into two parts.

[0089] FIG. 21 shows a flowchart of a method 2100 for creating a model for simulating a blast. At block 2102, method 2100 receives input data including blast hole data, bench information, and geological input data. At block 2104, method 2100 generates a site model based on the input data, where the site model includes a set of blast holes. At block 2106, method 2100 identifies a zone around each blast hole in the set of blast holes, where each zone has a perimeter at a target distance from the associated blast hole. At block 2108, method 2100 fragments the site model into a plurality of non-circular elements, including arcs and lines, where a first set of non-circular elements within the zone is smaller than a second set of non-circular elements outside the zone. At block 2110, method 2100 simulates a blast using the plurality of non-circular elements.

[0090] 22 is a block diagram of a blasting modeling system 2200 according to one embodiment. The blasting modeling system 2200 may perform the methods and use the techniques described with reference to other figures herein. The blasting modeling system 2200 may include a memory 2203, one or more processors 2204, a network interface 2206, an input / output interface 2208, and a system bus 2209.

[0091] The one or more processors 2204 may include one or more general-purpose devices, such as an Intel®, AMD®, or other standard microprocessor. The one or more processors 2204 may include general-purpose processing devices, such as an ASIC, SoC, SiP, FPGA, PAL, PLA, FPLA, PLD, or other customized or programmable device. The one or more processors 2204 may perform distributed (e.g., parallel) processing to perform or otherwise implement the functions of the embodiments disclosed herein. The one or more processors 2204 may run a standard operating system and perform the functions of a standard operating system. It is recognized that any standard operating system, such as Microsoft® Windows®, Apple® MacOS®, Disk Operating System (DOS), UNIX, IRJX, Solaris, SunOS, FreeBSD, Linux®, ffiM® OS / 2® operating system, etc., may be used.

[0092] The memory 2203 may include static RAM, dynamic RAM, flash memory, one or more flip-flops, ROM, CD-ROM, DVD, disk, tape, magnetic, optical, or other computer storage medium. The memory 2203 may include a number of program modules 2210 and program data 2220. The memory 2203 may be local to the blast modeling system 2200 as shown, or may be distributed and / or remote from the blast modeling system 2200.

[0093] Memory 2203 may include data 2220. Data generated or used by the blast modeling system, such as program module 2210 or other modules, may be stored in memory 2203, for example, as stored program data 2220. Data 2220 may be organized as one or more databases.

[0094] Data 2220 may include blast input data, element data structures 2222, positioning information 2224, and contact, force, and moment data 2226. Blast input data may be entered by a user through input / output interface 2208. In some embodiments, blast input data may include blast hole data, bench information, and geological input data. Element data structures 2222 may include information related to the geometry of each element in the blast model. For example, element data structures 2222 may include line endpoint node coordinates, designated arc endpoints, arc center points, arc radii, and arc angles. Positioning information 2224 may include location information for each element in the blast model. For example, positioning information 2224 may include the coordinates of each element and the orientation of each element. Contact and moment data 2226 may include the contact, force, and moment of each element at the current time step.

[0095] The program modules 2210 may include all or portions of other elements of the blast modeling system 2200. The program modules 2210 may execute multiple operations simultaneously, in parallel, or on one or more processors 2204. In some embodiments, some of the disclosed modules, components, and / or facilities are implemented as executable instructions embodied in hardware or firmware or stored on a non-transitory machine-readable storage medium. The executable instructions may include computer program code that, when executed by a processor and / or computing device, causes the computing system to perform certain processing steps, procedures, and / or operations as disclosed herein. The modules, components, and / or facilities disclosed herein may be implemented and / or embodied as drivers, libraries, interfaces, APIs, FPGAs, configuration data, firmware (e.g., stored in EEPROM), etc. In some embodiments, some of the modules, components, and / or facilities disclosed herein are implemented as machine components such as general-purpose devices and / or special-purpose devices, including, but not limited to, circuits, integrated circuits, processing components, interface components, hardware controllers, storage controllers, programmable hardware, FPGAs, ASICs, etc. Accordingly, the modules disclosed herein may be referred to as controllers, layers, services, engines, facilities, drivers, circuitry, subsystems, etc.

[0096] Module 2210 may include a model generator 2212, a simulation model 2214, and a mass calculator 2216. The model generator 2212 may generate a site model based on blasting input data and fragment the site model into multiple elements. The mass calculator 2216 may calculate the mass of each element.

[0097] The simulation model 2214 may run a simulation of the blast over multiple time steps. For example, the simulation model 2214 may search the field model for arc-arc and arc-line contacts and identify the forces and moments resulting from the arc-arc and arc-line contacts. The simulation model 2214 may also change the position coordinates and orientation of each element to a new position based on the total forces and moments. The new positions are used during the next step.

[0098] The input / output interface 2208 may facilitate user interaction with one or more input devices and / or one or more output devices. Input devices may include a keyboard, mouse, touchscreen, lightpen, tablet, microphone, sensor, or other hardware with associated firmware and / or software. Output devices may include a monitor or other display, printer, speech or text synthesizer, switch, signal line, or other hardware with associated firmware and / or software. For example, in one embodiment, the input / output interface 2208 includes a display that provides a graphical user interface (GUI) showing potential ablation perimeters. The input / output interface 2208 can receive user input data 2222. In some embodiments, the input / output interface 2208 is a touchscreen, and size input is received via the touchscreen. In some embodiments, the input / output interface 2208 can overlay the target ablation perimeter on an image of the tissue.

[0099] The network interface 2206 may facilitate communication with other computing devices, networks, and / or other computing and / or communications networks. The network interface 2206 may comprise a conventional network connection, such as Ethernet (IEEE 1102.3), Token Ring (IEEE 1102.5), Fiber Distributed Data Link Interface (FDDI), or Asynchronous Transfer Mode (ATM). Additionally, the network interface 2206 may be configured to support a variety of network protocols, such as Internet Protocol (IP), Transmission Control Protocol (TCP), Network File System over UDP / TCP, Server Message Block (SMB), Microsoft® Common Internet File System (CIFS), Hypertext Transfer Protocol (HTTP), Direct Access File System (DAFS), File Transfer Protocol (FTP), Real-Time Publish-Subscribe (RTPS), Open Systems Interconnection (OSI) protocols, Simple Mail Transfer Protocol (SMTP), Secure Shell (SSH), Secure Sockets Layer (SSL), etc.

[0100] The system bus 2209 may facilitate communication and / or interaction between other components of the blast modeling system 2200 , including one or more processors 2204 , memory 2203 , input / output interface 2208 , and network interface 2206 .

[0101] 23 illustrates a procedure 2300 for changing the shape of an element 2302 during a blast simulation. In a blast, as rocks roll, slide, and break apart, they become more rounded. The modeling system may approximate this effect on the element 2300 by increasing the radius of each arc during the simulation based on one or more of the corresponding element's movement, the corresponding element's rotation, and the corresponding collision. In other words, as the element 2300 moves and interacts with other elements, the endpoints of the lines move closer together and the radius of the arcs increases.

[0102] Element 2300 may start out as a polygon (e.g., a square) with tightly rounded corners (e.g., corners formed from arcs with small radii). Tightly rounded corners allow the element to fit together better on the bench. However, blast-induced movement of elements with such tightly rounded corners may be somewhat unnatural. Therefore, the modeling system may track the movement, rotation, and collisions of element 2300 and change the shape of element 2300 during the simulation. As the element moves, collides, and rotates, the modeling system may increase the radius of the corner arcs.

[0103] 24 shows two circular elements (i.e., first elements 2404 and 2410) that may be used by the modeling systems and methods described herein. Although the shapes used by the modeling system may have straight lines, the modeling system may be able to use circular elements as well to model rock in a blast simulation.

[0104] For example, the modeling system may handle circular elements by creating a circular element with one arc center point 2408 and two 180 degree arcs (e.g., first arc 2402 and second arc 2404). As shown, the first element 2404 overlaps with the second element 2420. Using the one arc center point and the two arcs, the modeling system can determine the movement of the element using the methods described above.

[0105] Figure 25 shows three potential three-dimensional shapes that may be used as elements by the modeling systems and methods described herein. The illustrated embodiment includes a spherical element 2502, a quadrilateral element 2504, and a cuboid element 2506. The methods and systems described herein may use these shapes to model three-dimensional blasts. As shown, each of these elements may include rounded edges and corners. The radii of the rounded edges and corners may be used to identify element movement using the methods described herein.

[0106] In some embodiments, the spherical element 2502 may be modeled using a three-dimensional hexahedron shape with rounded corners and edges, the contact behavior of which may not be significantly different from a sphere.

[0107] While the examples and embodiments disclosed herein refer specifically to blast simulation, the advanced discrete elements and simulation methods may be applied to a variety of different simulation applications. For example, the elements described herein may be used to simulate the movement of liquids, solutions, gases, materials in storage silos, and powders. The simulation methods may be used in a variety of applications and industries. For example, the simulation methods may be used to simulate earthquakes, oil and gas drilling and recovery, and mineral processing. Embodiments of the discrete elements disclosed herein may also be used to model, understand, and grind ore using grinding entities such as high-strength steel rods or balls in a milling cylinder. Both the ore and grinding entities may be more easily represented by advanced discrete elements. Embodiments relating to discrete elements with rounded corners based on movement and collisions may be particularly useful for milling modeling.

[0108] Some embodiments of a more generalized method for simulating a moving object may include generating a model including a plurality of highly discrete elements, as described with reference to the previous figures. Each element may have a shape formed by connecting the endpoints of one or more lines with arcs, such that the endpoints of one or more lines are indirectly connected via arcs. Simulating the movement of the plurality of elements may be performed by performing a time-step simulation that repeatedly advances through time. At each time step of the simulation, the method may search for and detect arc-arc and arc-line contacts between neighboring elements. The method may also identify forces and moments resulting from arc-arc and arc-line contacts. The forces and moments may be summed to move each element to a new position that is used during the next time step.

[0109] The examples and embodiments disclosed herein should be construed as merely illustrative and exemplary, and in no way as limiting the scope of the present disclosure. Those skilled in the art and having the benefit of this disclosure will understand that changes may be made in the details of the above-described embodiments without departing from the underlying principles of the disclosure herein.

Claims

1. 1. A method of blast modeling, comprising: receiving a blast plan including blast hole data and blast site data; generating a site model based on the blast plan, the site model including a plurality of elements; generating a plurality of arcs, each of the plurality of lines having a shape formed by connecting the endpoints of the one or more lines with arcs such that the endpoints of the lines are indirectly joined by the arcs; simulating a blast using the site model and the plurality of elements; A method comprising:

2. The method of claim 1 , wherein a radius of each arc increases and a length of each of the one or more lines decreases based on translation of corresponding elements, rotation of the corresponding elements, and collision of the corresponding elements.

3. The simulating blasting includes detecting contact between neighboring elements, and detecting the contact includes: detecting arc-arc contacts between said neighboring elements; detecting arc-line contact between said neighboring elements; The method of claim 1 , comprising:

4. 4. The method of claim 3, wherein detecting the arc-arc contact between the neighboring elements comprises comparing a distance between arc center points of two arcs of the neighboring elements to a sum of radii of the two arcs of the neighboring elements, and contact is detected if the sum is greater than the distance.

5. 4. The method of claim 3, wherein detecting the arc-line contact between the neighboring elements comprises comparing a distance between a line of a first element and an arc center of an arc of a second element with a radius of the arc of the second element, and contact is detected if the radius is greater than the distance.

6. 2. The method of claim 1, wherein simulating the blasting includes calculating a force imparted to each element by contacting neighboring elements, the force being calculated based on contact overlap and applied to an arc center point.

7. The method of claim 1 , wherein the shape of each element is a polygon with rounded corners.

8. The method of claim 7 , wherein at least some of the elements are of different shapes.

9. The method of claim 7 wherein at least some of the elements of the same shape are of different sizes.

10. Simulating the blasting includes a time step simulation that iteratively advances through time, and at each time step of the simulation, the method includes: searching the in-situ model for arc-arc and arc-line contacts; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; The method of claim 1 further comprising:

11. a processor; a memory storing instructions; wherein the instructions, when executed by the processor, receiving a blast plan including blast hole data and blast site data; generating a site model based on the blast plan, the site model including a plurality of elements; generating a plurality of arcs, each of the plurality of lines having a shape formed by connecting the endpoints of the one or more lines with arcs such that the endpoints of the lines are indirectly joined by the arcs; simulating a blast using the site model and the plurality of elements; a computing device, the computing device configured to:

12. The computing device of claim 11 , wherein the radius of each arc increases based on one or more of a translation of the corresponding element, a rotation of the corresponding element, and a collision of the corresponding element.

13. The simulating blasting includes detecting contact between neighboring elements, and detecting the contact includes: detecting arc-arc contacts between said neighboring elements; detecting arc-line contact between said neighboring elements; The computing device of claim 11 , comprising:

14. 14. The computing device of claim 13, wherein detecting the arc-arc contact between the neighboring elements comprises comparing a distance between arc center points of two arcs of the neighboring elements to a sum of radii of the two arcs of the neighboring elements, and contact is detected if the sum is greater than the distance.

15. 14. The computing device of claim 13, wherein detecting the arc-line contact between the neighboring elements includes comparing a distance between a line of a first element and an arc center of an arc of a second element to a radius of the arc of the second element, and contact is detected if the radius is greater than the distance.

16. 12. The computing device of claim 11, wherein simulating the blasting includes calculating a force imparted to each element by contacting neighboring elements, the force being calculated based on contact overlap and applied to an arc center point.

17. The computing device of claim 11 , wherein the shape of each element is a polygon with rounded corners.

18. 20. The computing device of claim 17, wherein at least some of the elements are different shapes.

19. 20. The computing device of claim 17, wherein at least some of the elements of the same shape are of different sizes.

20. Simulating the blasting includes a time step simulation that iteratively advances through time, and at each time step of the simulation, the method includes: searching the in-situ model for arc-arc and arc-line contacts; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; The computing device of claim 11 further comprising:

21. A non-transitory computer-readable storage medium containing instructions that, when executed by a computer, cause the computer to: receiving a blast plan including blast hole data and blast site data; generating a site model based on the blast plan, the site model including a plurality of elements; generating a plurality of arcs, each of the plurality of lines having a shape formed by connecting the endpoints of the one or more lines with arcs such that the endpoints of the lines are indirectly joined by the arcs; simulating a blast using the site model and the plurality of elements; A computer-readable storage medium that causes the

22. 22. The computer-readable storage medium of claim 21, wherein the radius of each arc increases based on one or more of a movement of the corresponding element, a rotation of the corresponding element, and a collision of the corresponding element.

23. The simulating blasting includes detecting contact between neighboring elements, and detecting the contact includes: detecting arc-arc contacts between said neighboring elements; detecting arc-line contact between said neighboring elements; 22. The computer-readable storage medium of claim 21, comprising:

24. 24. The computer-readable storage medium of claim 23, wherein detecting the arc-arc contact between the neighboring elements includes comparing a distance between arc center points of two arcs of the neighboring elements to a sum of radii of the two arcs of the neighboring elements, and contact is detected if the sum is greater than the distance.

25. 24. The computer-readable storage medium of claim 23, wherein detecting the arc-line contact between the neighboring elements includes comparing a distance between a line of a first element and an arc center of an arc of a second element with a radius of the arc of the second element, and contact is detected if the radius is greater than the distance.

26. 22. The computer-readable storage medium of claim 21, wherein simulating the blasting includes calculating a force imparted to each element by contacting neighboring elements, the force being calculated based on contact overlap and applied to an arc center point.

27. 22. The computer-readable storage medium of claim 21, wherein the shape of each element is a polygon with rounded corners.

28. 30. The computer-readable storage medium of claim 27, wherein at least some of the elements are different shapes.

29. 30. The computer-readable storage medium of claim 27, wherein at least some of the elements of the same shape are different sizes.

30. Simulating the blasting includes a time step simulation that iteratively advances through time, and at each time step of the simulation, the method includes: searching the in-situ model for arc-arc and arc-line contacts; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; 22. The computer-readable storage medium of claim 21, further comprising:

31. 1. A method of blast modeling, comprising: receiving a blast plan including blast hole data and blast site data; generating a site model based on the blast plan, the site model including a plurality of elements; simulating a blast using the site model and the plurality of elements; Including, simulating the blasting Detecting arc-arc contacts between neighboring elements; detecting arc-line contact between said neighboring elements; A method comprising:

32. 32. The method of claim 31, wherein the radius of each arc increases based on one or more of a translation of the corresponding element, a rotation of the corresponding element, and a collision of the corresponding element.

33. 32. The method of claim 31 , wherein each element has a shape formed by connecting endpoints of two or more lines with arcs such that the lines are indirectly joined via the arcs.

34. 32. The method of claim 31 , wherein detecting the arc-arc contact between the neighboring elements comprises comparing a distance between arc center points of two arcs of the neighboring elements to a sum of radii of the two arcs of the neighboring elements, and contact is detected if the sum is greater than the distance.

35. 32. The method of claim 31 , wherein detecting the arc-line contact between the neighboring elements comprises comparing a distance between a line of a first element and an arc center of an arc of a second element with a radius of the arc of the second element, and contact is detected if the radius is greater than the distance.

36. 32. The method of claim 31 , wherein simulating the blasting includes calculating a force imparted to each element by contacting neighboring elements, the force being calculated based on contact overlap and applied to an arc center point.

37. 32. The method of claim 31 , wherein the shape of each element is a polygon with rounded corners.

38. 38. The method of claim 37, wherein at least some of the elements are different shapes.

39. 38. The method of claim 37, wherein at least some of the elements of the same shape are different sizes.

40. Simulating the blasting includes a time step simulation that iteratively advances through time, and at each time step of the simulation, the method includes: searching the in-situ model for arc-arc and arc-line contacts; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; 32. The method of claim 31 further comprising:

41. a processor; a memory storing instructions; wherein the instructions, when executed by the processor, receiving a blast plan including blast hole data and blast site data; generating a site model based on the blast plan, the site model including a plurality of elements; simulating a blast using the site model and the plurality of elements; and configuring the apparatus to: simulating the blasting Detecting arc-arc contacts between neighboring elements; detecting arc-line contact between said neighboring elements; 12. A computing device comprising:

42. 42. The computing device of claim 41, wherein the radius of each arc increases based on one or more of a movement of the corresponding element, a rotation of the corresponding element, and a collision of the corresponding element.

43. 42. The computing device of claim 41, wherein each element has a shape formed by connecting endpoints of two or more lines with arcs such that the lines are indirectly joined via the arcs.

44. 42. The computing device of claim 41, wherein detecting the arc-arc contact between the neighboring elements comprises comparing a distance between arc center points of two arcs of the neighboring elements to a sum of radii of the two arcs of the neighboring elements, and contact is detected if the sum is greater than the distance.

45. 42. The computing device of claim 41, wherein detecting the arc-line contact between the neighboring elements comprises comparing a distance between a line of a first element and an arc center of an arc of a second element to a radius of the arc of the second element, and contact is detected if the radius is greater than the distance.

46. 42. The computing device of claim 41, wherein simulating the blasting includes calculating a force imparted to each element by contacting neighboring elements, the force being calculated based on contact overlap and applied to an arc center point.

47. 42. The computing device of claim 41, wherein the shape of each element is a polygon with rounded corners.

48. 48. The computing device of claim 47, wherein at least some of the elements are different shapes.

49. 48. The computing device of claim 47, wherein at least some of the elements of the same shape are different sizes.

50. Simulating the blasting includes a time step simulation that iteratively advances through time, and at each time step of the simulation, the method includes: searching the in-situ model for arc-arc and arc-line contacts; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; 42. The computing device of claim 41, further comprising:

51. A non-transitory computer-readable storage medium containing instructions that, when executed by a computer, cause the computer to: receiving a blast plan including blast hole data and blast site data; generating a site model based on the blast plan, the site model including a plurality of elements; simulating a blast using the site model and the plurality of elements; Let them do this, simulating the blasting Detecting arc-arc contacts between neighboring elements; detecting arc-line contact between said neighboring elements; 1. A computer-readable storage medium comprising:

52. 52. The computer-readable storage medium of claim 51, wherein the radius of each arc increases based on one or more of a movement of the corresponding element, a rotation of the corresponding element, and a collision of the corresponding element.

53. 52. The computer-readable storage medium of claim 51, wherein each element has a shape formed by connecting endpoints of two or more lines with arcs such that the lines are indirectly joined via the arcs.

54. 52. The computer-readable storage medium of claim 51, wherein detecting the arc-arc contact between the neighboring elements comprises comparing a distance between arc center points of two arcs of the neighboring elements to a sum of radii of the two arcs of the neighboring elements, and contact is detected if the sum is greater than the distance.

55. 52. The computer-readable storage medium of claim 51, wherein detecting the arc-line contact between the neighboring elements includes comparing a distance between a line of a first element and an arc center of an arc of a second element with a radius of the arc of the second element, and contact is detected if the radius is greater than the distance.

56. 52. The computer-readable storage medium of claim 51, wherein simulating the blasting includes calculating a force imparted to each element by contacting neighboring elements, the force being calculated based on contact overlap and applied to an arc center point.

57. 52. The computer-readable storage medium of claim 51, wherein the shape of each element is a polygon with rounded corners.

58. 58. The computer-readable storage medium of claim 57, wherein at least some of the elements are different shapes.

59. 58. The computer-readable storage medium of claim 57, wherein at least some of the elements of the same shape are different sizes.

60. Simulating the blasting includes a time step simulation that iteratively advances through time, and at each time step of the simulation, the method includes: searching the in-situ model for arc-arc and arc-line contacts; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; 52. The computer-readable storage medium of claim 51, further comprising:

61. 1. A method of blast modeling, comprising: receiving input data including blast hole data, above-bench, and geological input data; generating a site model based on the input data, the site model including a set of blast holes; identifying a zone around each blast hole of the set of blast holes, each zone including a perimeter that is a target distance from an associated blast hole; fragmenting the in-situ model into a plurality of non-circular elements including arcs and lines, wherein a first set of non-circular elements within the zone is smaller than a second set of non-circular elements outside the zone; simulating a blast using the plurality of non-circular elements; and A method comprising:

62. 62. The method of claim 61, further comprising offsetting layers of the plurality of non-circular elements.

63. 62. The method of claim 61, further comprising cutting the element across the bench face or the blast hole.

64. 62. The method of claim 61, further comprising determining the mass of each of the plurality of non-circular elements by multiplying the area of ​​the element by the spacing and rock density.

65. 62. The method of claim 61, further comprising rotating the site model to create a geologic gradient.

66. 62. The method of claim 61, further comprising identifying an unloading time for the plurality of non-circular elements.

67. 62. The method of claim 61, wherein if the blast hole is sub-excavated, the non-circular element is extended below the blast pit and beyond the bench surface by the length of the first load.

68. a processor; a memory storing instructions; wherein the instructions, when executed by the processor, receiving input data including blast hole data, bench information, and geological input data; generating a site model based on the input data, the site model including a set of blast holes; identifying a zone around each blast hole of the set of blast holes, each zone including a perimeter that is a target distance from an associated blast hole; fragmenting the in-situ model into a plurality of non-circular elements including arcs and lines, wherein a first set of non-circular elements within the zone is smaller than a second set of non-circular elements outside the zone; simulating a blast using the plurality of non-circular elements; and a computing device, the computing device configured to:

69. 69. The computing device of claim 68, wherein the instructions further configure the device to offset layers of the plurality of non-circular elements.

70. 69. The computing device of claim 68, wherein the instructions further configure the device to cut elements that cross a bench face or a blast hole.

71. 69. The computing device of claim 68, wherein the instructions further configure the device to determine a mass of each of the plurality of non-circular elements by multiplying an area of ​​the element by a spacing and a rock density.

72. 69. The computing device of claim 68, wherein the instructions further configure the device to rotate the site model to create a geologic gradient.

73. 69. The computing device of claim 68, wherein the instructions further configure the device to identify an unloading time for the plurality of non-circular elements.

74. 69. The computing device of claim 68, wherein if the blast hole is sub-excavated, the non-circular element is extended below the blast pit and beyond the bench surface by the length of the first load.

75. A non-transitory computer-readable storage medium containing instructions that, when executed by a computer, cause the computer to: receiving input data including blast hole data, above-bench, and geological input data; generating a site model based on the input data, the site model including a set of blast holes; identifying a zone around each blast hole of the set of blast holes, each zone including a perimeter that is a target distance from an associated blast hole; fragmenting the in-situ model into a plurality of non-circular elements including arcs and lines, wherein a first set of non-circular elements within the zone is smaller than a second set of non-circular elements outside the zone; simulating a blast using the plurality of non-circular elements; and A computer-readable storage medium that causes the

76. 76. The computer-readable storage medium of claim 75, wherein the instructions further configure the computer to offset layers of the plurality of non-circular elements.

77. 76. The computer-readable storage medium of claim 75, wherein the instructions further configure the computer to cut elements that cross a bench face or a blast hole.

78. 76. The computer-readable storage medium of claim 75, wherein the instructions further configure the computer to determine a mass of each of the plurality of non-circular elements by multiplying an area of ​​the element by spacing and rock density.

79. 76. The computer-readable storage medium of claim 75, wherein the instructions further configure the computer to rotate the site model to create a geologic gradient.

80. 76. The computer-readable storage medium of claim 75, wherein the instructions further configure the computer to identify an unloading time for the plurality of non-circular elements.

81. 76. The computer-readable storage medium of claim 75, wherein if the blast hole is sub-excavated, the non-circular element is caused to extend below the blast pit and beyond the bench surface by a length of a first load.

82. 1. A method for modeling a moving object, comprising: generating a model including a plurality of elements, generating a plurality of arcs, each of the arcs having a shape formed by connecting endpoints of one or more lines with arcs such that the endpoints of the lines are indirectly connected via the arcs; simulating movement of the plurality of elements, Detecting arc-arc contact between neighboring elements; Detecting arc-line contact between said adjacent elements. and simulating by A method comprising:

83. Simulating the movement includes performing a time step simulation that iteratively advances through time, and at each time step of the simulation, the method comprises: searching the in-situ model for the arc-arc contact and the arc-line contact; identifying forces resulting from the arc-arc contact and the arc-line contact; Identifying the moments of each element; summing the moments and the forces of each element; moving each element to a new position based on the total force and total moment, the new position being used during the next time step; 83. The method of claim 82, further comprising:

Images