High-performance computer technology for determining mechanical behaviour of soils and rock masses

Abstract

The invention relates to a method, system and computer-readable storage means for determining the mechanical and / or dynamic condition of a rock mass, with low error and acquisition time, for decision-making on production and safety with respect to a domain, which comprises the steps of: obtaining a detailed virtual representation of the domain to be studied; identifying geomechanical units and geological faults in the domain; defining within the detailed virtual representation of the domain a limit Ω containing an interior area / volume that includes a border and geomechanical properties to be studied; generating study spaces; generating models from the spaces; generating independent meshes; processing and transforming the independent meshes by means of processors; and obtaining a plurality of vectors / matrices of displacement, deformations and / or forces that represent the mechanical / dynamic condition of the rock mass for decision-making on production and safety with respect to the domain.

Description

[0001] HIGH-PERFORMANCE COMPUTER TECHNOLOGY TO DETERMINE THE MECHANICAL BEHAVIOR OF SOILS AND ROCK MASSES

[0002] DESCRIPTIVE MEMORANDUM

[0003] FIELD OF INVENTION

[0004] The present invention relates to the geomechanics, geotechnical, structural geology, mining, and civil engineering industries. Specifically, the present invention relates to a computer-readable method, system, and storage medium that allows for the determination of the mechanical and / or dynamic condition of a rock mass with low error and low acquisition time. This enables informed decision-making regarding production and safety within a given area of ​​study, while also reducing the amount of data to be processed and increasing the speed, performance, and accuracy of the data processing system, which in turn implies an increase in the aforementioned response time.

[0005] BACKGROUND

[0006] Large investment projects require the design, execution, maintenance, operation, and expansion of excavation work in the Earth's crust. This is the case in mining, civil works, infrastructure, energy, and hydrocarbons. In any of these activities, the structural stability or stress state of the structures is of vital importance, because if they are not designed, executed, or operated properly or safely, collapses can occur.

[0007] Currently, the state-of-the-art computer tools available for calculation and design in geotechnics and geomechanics suffer from major restrictions, such as considering discretizations that are too large, on the order of thousands of cubic kilometers (km³). 3spurious boundary conditions, simplifications in soil mechanics, etc., significantly hinder the accuracy of results, mesh resolution, and calculation time. This also increases data consumption and the saturation of telecommunications networks when this data is transmitted, leading to excessive increases in safety factors and limiting the analysis of different structural scenarios, given the high processing time required to obtain the results necessary for decision-making at the mine site. The resulting increase in costs and design constraints in engineering are even greater, implying an additional cost of millions of dollars for mining, civil works, and infrastructure projects in general.

[0008] Hence the need for a method that can reduce calculation time and mesh resolution by up to an order of magnitude, while increasing accuracy.

[0009] The overall view of any task that involves altering the geostructural conditions of the Earth's crust where it is located - in large or medium-scale mining, civil works, hydrocarbons, geothermal energy, etc. - leads us to complex dynamic systems made up of multiple operational centers, technological units, and procedures of diverse nature that must coexist together in a coordinated and collaborative manner.

[0010] These dynamic systems are constantly exposed to the threat of loss of equilibrium and operational stability, as they are comprised of countless unit operations and processes susceptible to disturbances or alterations, which, however small, generally cause negative effects of some impact. This is especially true regarding the sustainability of the operation.

[0011] In mining, in particular, among the frequent extreme events that directly impact productivity, we can cite the incorrect allocation of ore blocks to waste dumps or processing plants based on their average grade, the presence of uncrushable material (very hard metallic elements that cannot be crushed), the interruption of transport routes, subsidence, mass wasting, unforeseen fractures in slopes, soil, and subsoil, blasting with long-range consequences, etc. These events are costly and, generally, can be remedied within periods of days, weeks, or months. The same applies to other areas of industry and human activity where the natural formation of the Earth's crust is altered.

[0012] In the aforementioned context, one of the most pressing and complex problems lies in the fields of geomechanics, geotechnics, and structural geology. More precisely, it is the challenge of detecting, locating, identifying, and, if possible, quantifying in real time, threats to operations whose origin and development are situated within the soil or rock mass where a mining operation is located. This includes non-outcropping natural faults, stress accumulation, deformation accumulation, rock fractures resulting from mining activity, the presence of groundwater, and other factors. All of these phenomena threaten the operational continuity of mining operations. It is important to note that losses due to operational downtime in the mining sector are estimated in the tens of millions of dollars per year.

[0013] To meet the challenge outlined in the previous paragraph, it is essential to ensure the timeliness, reliability, and quality of essential data and key indicators—threat, risk, and management indicators—used in decision-making processes. Without this, it is impossible to maintain adequate control over the vulnerabilities and risks that constantly threaten these complex, dynamic systems.

[0014] Currently, this difficulty is addressed by combining professional experience of specialists, instrumental measurements obtained in situ and in real time, standard numerical modeling tools, heuristics, rheological knowledge and structural geological history of the rock mass.

[0015] STATE OF THE ART

[0016] There are a number of standard computational simulation tools on the market - mostly commercial software - that have a certain degree of acceptance among professionals in the fields of geomechanics, geotechnics and structural geology.

[0017] However, these tools rely on mathematical techniques that are limited in their ability to handle the complexity of the geomechanical, geotechnical, and structural geological issues involved. This means they are not efficient, as they require high computational resources and response times on the order of days for three-dimensional (3D) simulations. Furthermore, they almost always require the support of specialists with a significant time commitment.

[0018] All these tools use standard numerical methods to discretize the partial differential equations that describe the mechanical behavior of soil and subsoil. These methods can be classified into three categories: continuous, discontinuous, and hybrid. In continuous methods, as the name suggests, the soil or rock mass is modeled as a continuous medium, although some discontinuities can be implicitly incorporated. The three most important continuous methods are finite difference, finite element, and boundary element methods (FDM, FEM, and BEM, respectively). In discontinuous methods, the discontinuities or fractures in the medium are explicitly incorporated into the model, with interfaces or contacts existing between the blocks that make up the soil or rock mass.Some relevant discontinuous methods are discrete element methods (DEM) and discrete fracture network methods (DFN). Hybrid methods combine more than one method from the two previous categories. The most common are FEM / BEM, FEM / DEM, and BEM / DEM hybrid methods. Given a specific geomechanical or geotechnical problem, the choice of a continuous, discontinuous, or hybrid method will depend primarily on the size, or scale, of the discontinuities relative to the size, or scale, of the problem being addressed. In general, there are no absolute advantages of one type of method over another. However, most commercial simulation software applicable to geomechanics, geotechnics, and structural geology is based on one of the following three standard numerical methods:

[0019] • Finite Difference Method (FDM), the oldest of the numerical methods used in geomechanics and countless other fields. In this technique, the differential equations describing the physical phenomenon are discretized by differences at neighboring nodes of a rectangular grid. This reduces the set of differential equations to a linear system of equations, which can then be solved by any classical method designed for this purpose.

[0020] • Finite Element Method (FEM), by far the most widely used numerical method in geomechanics and solid mechanics in general. In this technique, the continuous medium is discretized into small elements that intersect at their nodes (usually triangles or quadrilaterals), assuming that, through appropriately chosen interpolation functions, the displacements at any point of an element can be accurately obtained from the displacements at the nodes.

[0021] • Distinct Element Method (DEM), a numerical method developed to solve problems in rock mechanics. In this technique, the solid medium is treated as an assembly of rigid or deformable blocks / particles. The interactions between motion and deformation are described by appropriate constitutive models.

[0022] Among the commercial simulation software used in geomechanics, geotechnics, and structural geology—which employs the standard numerical methods described above, also known as Gold Standard (prior art)—we can identify two categories. On the one hand, there are multiphysics simulation software programs, meaning they can address problems in multiple areas of physics and engineering. The main ones are:

[0023] • ABAQUS FEA, part of the SIMULIA simulation software suite, developed by the French company Dassault Systèmes, is a software that uses finite element analysis for engineering problems in a wide range of industrial applications.

[0024] • ANSYS, developed by the American company ANSYS, Inc., is an engineering simulation software suite that allows you to deal with problems in a wide range of areas of physics, such as fluids, structures and electronics, among others, using finite elements for structures and finite volumes for fluids.

[0025] • ADINA, developed by the US company ADINA R&D, Inc., is a simulation software for linear and non-linear finite element analysis of solids and structures, heat transfer, fluid dynamics, electromagnetism and fluid-structure interactions and thermo-mechanical couplings.

[0026] COMSOL Multiphysics, developed by the Swedish company COMSOL, Inc., is a finite element simulation software package for various physics and engineering applications, especially coupled, or multiphysics, phenomena. It specifically includes a geomechanics module.

[0027] On the other hand, there are the Gold Standard (previous art / world standard) or commercial simulation software programs developed specifically for geomechanics, geotechnics, structural geology, and related fields. They generally have a two-dimensional (2D) and a three-dimensional (3D) version. The main ones are: • FLAC2D / FLAC3D, developed by the American company ITASCA, are numerical modeling software programs for advanced geotechnical analysis of soil, rock, groundwater, and earth support. They use an explicit finite difference formulation that allows for the modeling of complex behaviors.

[0028] • RS2 / RS3, developed by the Canadian company Rocscience, are finite element method-based programs for rock and soil applications. They can be applied to a wide range of civil engineering and mining projects, including excavation design, slope stability, and groundwater infiltration.

[0029] • PLAXIS 2D / PLAXIS 3D, developed by the Dutch company PLAXIS, are software programs based on the finite element method for analyzing deformations and stability in geotechnical engineering and rock mechanics. Their potential applications range from excavations and foundations to tunnels, mining, and reservoirs.

[0030] All these gold standard or commercial software programs are capable of simulating the mechanical behavior of a specific area of ​​the Earth's crust through the computational resolution of a more or less realistic mathematical model. The degree of complexity of such a model is defined by the user and can vary depending on the simplifications assumed. A more realistic model will be more complex and will take longer to deliver results. It is common for the resolution of a detailed, three-dimensional model of a large-scale project to require several days or even weeks of simulation to produce results. This assumes that the numerical methods used are consistent.For these reasons, users resort to certain simplifications, such as considering two-dimensional models of cross-sections, or three-dimensional models, but only of specific and delimited areas of the work, which, although they reduce calculation time, do not ensure accuracy or reliability in the results.

[0031] The computer-readable storage method, system, and medium of the present invention reduces energy consumption and time, and improves accuracy compared to prior art solutions. Consequently, the present invention allows the determination of the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for productive and safety decision-making regarding a domain under study, also reducing the amount of data to be processed, increasing the speed, performance, and accuracy of the data processing system, which in turn implies an increase in the previously mentioned response time.

[0032] SUMMARY DESCRIPTION OF THE INVENTION

[0033] The present invention discloses a method for determining the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for making productive and safety decisions regarding the domain under study, comprising the steps of: obtaining a detailed virtual representation (detailed description) of a domain under study; identifying geomechanical units and geological faults in the domain under study; defining a boundary Ω within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary and complexities to be studied, where the boundary δ is continuous (and where the space outside said boundary is considered homogeneous and isotropic); generating a first study space, contained within the interior volume / area such that the boundary is within the first study space;generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are located within said second study space of the plurality of second study spaces; generate a base model, from the first study space (a simplified model eliminating geological faults / singularities); generate a plurality of secondary models, from the plurality of second study spaces;Generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one feature of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation); process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) - 2D / 3D cases, or mixtures thereof);Transform, through at least one processor, the information from each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or 3D), which also consider boundary conditions at the edges of the Q boundary (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

[0034] It should be noted that the boundary conditions of the domain under study are simple; however, since the distances are too large, the processing time increases considerably. Therefore, it is important to delimit the domain under study in order to determine the mechanical and / or dynamic condition of the rock mass with a low error and low acquisition time for making productive and safety decisions regarding the domain under study.

[0035] To delimit the domain under study, one of two techniques is applied: the Steklov-Poincaré vector or the PML (Perfectly Matched Layer) technique. This allows reducing the size of the truncated domain, decreasing the number of discretization points and lowering calculation times. Furthermore, two cases are distinguished, corresponding to the solution of the method associated with the problem of one of the preferred configurations (direct):

[0036] 1. Elastostatic Case: where stresses and strains depend only on position (x), and the movement of a load in the domain under study O is slow enough that its time evolution is negligible. 2. Elastodynamic Case: where stresses and strains depend on both position and their time evolution (x, t); therefore, the movement of a load in the domain under study over time is relevant.

[0037] The method of the present invention, together with its various restrictions, preferred configurations and mixtures thereof, allows the resolution of the aforementioned direct problems in shorter times than known in the art, allowing the analysis of from a few critical cases to all possible critical cases, and where the execution time of the method for obtaining results is reduced from days to a few hours, with the purpose of making decisions in real time.

[0038] DESCRIPTION OF THE FIGURES

[0039] Figure 1 shows a simplified axisymmetric split scheme.

[0040] Figure 2A shows an example domain used in calculation with Abaqus.

[0041] Figure 2B shows an example domain used in calculation using the present invention.

[0042] Figure 3A shows an example of a mesh used in Abaqus

[0043] Figure 3B shows an example of the mesh used in the present invention.

[0044] Figure 4A shows the horizontal displacement obtained with Abaqus.

[0045] Figure 4B shows the horizontal displacement obtained with the present invention (GEOMRI-MC2E).

[0046] Figure 5A shows the vertical displacement obtained with Abaqus.

[0047] Figure 5B shows the vertical displacement obtained with the present invention (GEOMRI-MC2E).

[0048] Figure 6A shows the Von Mises effort obtained with Abaqus.

[0049] Figure 6B shows the Von Mises effort obtained with the present invention (GEOMRI-MC2E).

[0050] Figure 7 shows comparative graphs of horizontal displacement U1 on the pit (bottom and slope), where the present invention is indicated as: GEOMRI-MC2E. Figure 8 shows comparative graphs of vertical displacement U2 on the pit (bottom and slope), where the present invention is indicated as: GEOMRI-MC2E. Figure 9 shows comparative graphs of Von Mises stress on the pit (bottom and slope), where the present invention is indicated as: GEOMRI-MC2E.

[0051] Figure 10 shows comparative graphs of horizontal displacement U1 on the artificial hemispherical boundary, where the present invention is indicated as: GEOMRI-MC2E.

[0052] Figure 11 shows comparative graphs of vertical displacement on the artificial hemispherical boundary, where the present invention is indicated as: GEOMRI-MC2E.

[0053] Figure 12 shows comparative graphs of Von Mises stress on the artificial hemispherical boundary, where the present invention is indicated as: GEOMRI-MC2E.

[0054] Figure 13A shows a simplified three-dimensional open-cut diagram, cross-section.

[0055] Figure 13B shows a simplified three-dimensional open pit scheme, and a view from above.

[0056] Figure 14A shows an example domain used in calculation with Abaqus.

[0057] Figure 14B shows an example domain used in the calculation with the present invention.

[0058] Figure 15A shows an example of the mesh used in Abaqus.

[0059] Figure 15B shows an example of the mesh used in the present invention.

[0060] Figure 16A shows a horizontal displacement U1 obtained with Abaqus.

[0061] Figure 16B shows a horizontal displacement U1 obtained with the present invention.

[0062] Figure 17A shows a horizontal displacement U2 obtained with Abaqus.

[0063] Figure 17B shows a horizontal displacement U2 obtained with the present invention.

[0064] Figure 18A shows a vertical displacement U3 obtained with Abaqus.

[0065] Figure 18B shows a vertical displacement U3 obtained with the present invention.

[0066] Figure 19A shows a Von Mises stress obtained with Abaqus.

[0067] Figure 19B shows a Von Mises stress obtained with the present invention.

[0068] Figure 20 shows a comparison of horizontal displacement U1 on the pit (bottom and slope) (along the semi-major axis and gradient), where the present invention is indicated as: GEOMRI-MC2E. Figure 21 shows a comparison of vertical displacement U3 on the pit (bottom and slope) (along the semi-major axis and gradient), where the present invention is indicated as: GEOMRI-MC2E.

[0069] Figure 22 shows a comparison of Von Mises stress on the pit (bottom and slope) (on the semi-major axis and slope), where the present invention is indicated as: GEOMRI-MC2E.

[0070] Figures 23A and 23B show some open-pit geometries 1, from a project in the Antofagasta Region.

[0071] Figure 24A shows a domain used in Abaqus for first real cut, general view.

[0072] Figure 24B shows a domain used in Abaqus for the first real open pit, zoomed-in view of the open pit.

[0073] Figure 25A shows a domain used in the present invention for first actual cut, general view.

[0074] Figure 25B shows a domain used in the present invention for the first actual open pit, zoomed-in view of pit B.

[0075] Figure 26A shows a displacement U1 obtained with Abaqus in the pit

[0076] Figure 26B shows a displacement U1 obtained with the present invention in open pit.

[0077] Figure 27A shows a displacement U2 obtained with Abaqus in real open pit 1.

[0078] Figure 27B shows a displacement U2 obtained with the present invention in actual pit 1.

[0079] Figure 28A shows a displacement U3 obtained with Abaqus in real open pit 1.

[0080] Figure 28B shows a displacement U3 obtained with the present invention in actual pit 1.

[0081] Figure 29A shows the Von Mises stress obtained with Abaqus in real open pit 1.

[0082] Figure 29B shows the Von Mises stress obtained with the present invention in actual pit 1.

[0083] Figures 30A and 30B show the real open pit geometry 2, from a project in the Metropolitan Region.

[0084] Figure 31A shows a domain used in Abaqus for second real cut, in general view.

[0085] Figure 31B shows a domain used in Abaqus for the second actual open pit, zoomed in on the open pit. Figure 32A shows a domain used in the present invention for the second actual open pit, general view A and zoomed in on the open pit B.

[0086] Figure 32B shows a domain used in the present invention for a second actual open pit, zoomed-in view of the pit.

[0087] Figure 33A shows a displacement U1 obtained with Abaqus in real open pit 2.

[0088] Figure 33B shows a displacement U1 obtained with the present invention in actual pit 2.

[0089] Figure 34A shows a displacement U2 obtained with Abaqus in real open pit 2.

[0090] Figure 34B shows a displacement U2 obtained with the present invention in actual pit 2.

[0091] Figure 35A shows a displacement U3 obtained with Abaqus in real open pit 2.

[0092] Figure 35B shows a displacement U3 obtained with the present invention in actual pit 2.

[0093] Figure 36A shows the Von Mises stress obtained with Abaqus in real open pit 2.

[0094] Figure 36B shows the Von Mises stress obtained with the present invention in actual pit 2.

[0095] Figure 37 shows a two-dimensional exterior domain representing, for example, the cross-section of an underground tunnel in deep mining.

[0096] Figure 38 shows a locally perturbed two-dimensional semi-infinite domain representing, for example, the cross-section of a pit in open-pit mining.

[0097] Figure 39 shows a two-dimensional exterior domain truncated by a Qc transmission layer (marked in green) for applying the method of this application. Figure 40 shows a locally perturbed two-dimensional semi-infinite domain truncated by a Qc transmission layer (marked in green) for applying the method of this application.

[0098] Figures 41A and 41B show an example of a Qc transmission layer for DGN technique. It is bounded by circular boundaries for outer domains (Fig. 41A) and by semicircular boundaries for semi-infinite domains (Fig. 41B).

[0099] Figures 42A and 42B show an example of a Qc transmission layer for DGN technology. It is bounded by elliptical boundaries for exterior domains (Fig. 42A) and by semi-elliptical boundaries for semi-infinite domains (Fig. 42B). Figures 43A and 43B show an example of an Oc transmission layer for DGN technology. It is bounded by rectangular boundaries. The exterior domain case is shown in Fig. 43A, and the semi-infinite domain case in Fig. 43B.

[0100] Figure 44 shows the flow diagram of the operation of the present invention. Figure 45 shows the process diagram of Example 2.

[0101] Figure 46 shows the weight of the Caterpillar CAT 797F truck, used in mining, simulated as loads on rectangular surfaces, representing the contacts of the 6 tires with the gravel.

[0102] Figure 47 shows a truck used in mining, Caterpillar CAT 797F.

[0103] Figure 48 shows the specifications of the mining truck, source specification CAT 797F.

[0104] Figure 49 shows the Vertical displacement (close-up), what is observed with yellow colors, are the displacements associated with the weight of the support per wheel and the advance of the truck from figure 48.

[0105] Figure 50 shows the Vertical displacement (close-up), what is observed with yellow colors, are the displacements associated with the weight of the support per wheel and the advance of the truck from figure 48.

[0106] Figure 51 shows the Vertical displacement (close-up), what is observed with yellow colors, are the displacements associated with the weight of the support per wheel and the advance of the truck, of the truck in figure 48.

[0107] Figure 52 shows the Vertical displacement (close-up), what is observed with yellow colors, are the displacements associated with the weight of the support per wheel and the advance of the truck, of the truck in figure 48.

[0108] Figure 53 shows the vertical displacement (3D diagonal cut).

[0109] Figure 54 shows the direction of travel of the mining truck.

[0110] Figure 55 shows the vertical displacement (3D diagonal cut) of the mining truck.

[0111] Figure 56 shows the displacement in cm.

[0112] Figure 57 shows the vertical displacement (3D diagonal cut).

[0113] Figure 58 shows a 3D graphical representation of vertical stress.

[0114] Figure 59 shows a vertical effort (close-up)

[0115] Figure 60 shows representation on the x,y,z axes

[0116] Figure 61 shows a representation on the x, y, and z axes in planar format. Figure 62 shows a representation of the truck's direction of travel with a lower mesh.

[0117] Figure 63 shows a close-up of Figure 62.

[0118] Figure 64 shows another close-up of Figure 62.

[0119] Figure 65 shows some virtual load cells.

[0120] Figure 66 shows the displacement and vertical stress curves in virtual load cells under the right front tire.

[0121] Figure 67 shows the displacement and vertical stress curves in virtual load cells under the outer right rear tire.

[0122] Figure 68 shows the displacement and vertical stress curves in virtual load cells under the right front tire, at a second time.

[0123] Figure 69 shows the displacement and vertical stress curves in virtual load cells under the outer right rear tire, at a second time.

[0124] Figure 70 shows the case of the truck without cargo.

[0125] Figure 71 shows the case of the truck with maximum load.

[0126] Figure 72 shows the direction of advance of the CAEX.

[0127] Figure 73 shows the CAEX stability metric transverse to the advance.

[0128] Figure 74A shows the case of the front axle without load.

[0129] Figure 74B shows the case of the rear axle without load.

[0130] Figure 75A shows the case with maximum load on the front axle.

[0131] Figure 75B shows the case with maximum load on the rear axle.

[0132] Figure 76 shows the structural geological information: From 2D to 3D.

[0133] Figure 77 shows the geomechanical information, of the minimum of the Mohr-Coulomb stability indicator [MPa], in dry open pit.

[0134] Figure 78 shows, in a referential way, the reconciliation of the measurements of the field instruments in real time with the calculation data.

[0135] Figure 79 shows the Regional Stress Field.

[0136] Figure 80 shows the high-definition discretization mesh of the present invention.

[0137] Figures 81A and 81B show the regional stress field.

[0138] Figures 82A, 82B, 82C and 82D show the global stress results in 3D.

[0139] Figures 83A, 83B, 83C, and 83D show the results obtained in 142 minutes. Figures 84A and 84B show cross-sections of production areas in the mine; Figure 84A shows a top view, and Figure 84B shows a side view.

[0140] Figure 85 shows the Von Mises stress comparison on the vertical segment.

[0141] Figure 86 shows the comparison of the Mohr-Coulomb failure criterion in the vertical segment.

[0142] Figure 87 shows the topography of an open-pit mine with geomechanical and geotechnical units, determined using standard techniques

[0143] Figure 88 shows the displacement measurements at surface points (2D).

[0144] Figure 89 shows the mine design challenge: open pit stability, Figure 90 shows the mine design challenge with names: open pit stability.

[0145] Figure 91 shows the Mohr-Coulomb failure criterion diagram.

[0146] Figure 92 shows the geomechanical information, of the minimum of the Mohr-Coulomb stability indicator [MPa], in wet open pit.

[0147] Figure 93 shows the wet / wet open pit mining plan.

[0148] GENERAL DESCRIPTION OF THE INVENTION

[0149] The technology of the present invention is based on a method that seeks to describe the mechanical behavior of the continuous media that make up the Earth's crust, soil, and / or subsoil surrounding the work site, construction project, or excavation under study. This method efficiently reduces the amount of data to be processed, increasing the speed, performance, and accuracy of the data processing system, which comprises at least one computer hardware processor. This is achieved by reducing the processing and communication overhead between computer system processes executed by the data processing system and / or between devices within the data processing system, thereby improving upon conventional techniques for performing data processing operations that utilize two- or three-dimensional boundaries defining a boundary and a bounded domain. The method in question is described below in general terms.Considering an unbounded region or domain (i.e., of infinite size) representing the soil, subsoil or earth crust around the work of interest, which may be two-dimensional (2D) or three-dimensional (3D), that is, it will correspond to a subset of a real d-dimensional space IR. d where {2,3} denotes the dimension. Denoting by Q c ]Rrf the unbounded domain and by F c afi that part of its boundary that corresponds to the edge of the task, which must be bounded (i.e., of finite size). Calling in general xe O the position vector in the unbounded domain. For d = 2 we have x = (xi, X2) and for d = 3 we have x = (xi, X2, xs). We denote |x| the length of the vector x, that is, its Euclidean norm.

[0150] The following section presents two particular cases of unbounded domains like those just described, which are of particular importance. Figure 37 shows the case of an exterior domain in ℝ 2That is, the complement of a bounded domain. This type of domain is unbounded in all directions of the plane. Such is the case, for example, of the cross-section of an underground tunnel in deep mining, where the ground surface is far enough above ground that its effect on the modeling cannot be considered. In this case, the boundary T simply corresponds to the edge of the tunnel. Another notable example of an unbounded domain is the case of a semi-infinite domain, such as a half-plane in ℝ². 2 or a half-space in IR 3 In this type of unbounded domain, one of the spatial variables (specifically the vertical variable, typically X2 in ]R 2 and xs in IR 3The domain is such that the unboundedness occurs in only one direction (towards +°° or -°°), while for the remaining variables, the unboundedness is in both directions (towards +°° and -°°). This type of domain is of particular importance in this context, as it is used to represent the soil and subsoil considering the surface. The case where there is a local or bounded geometric disturbance located on or near the surface, representing the work site, excavation, or construction, is relevant. Figure 38 presents an example of a semi-infinite domain corresponding to a locally disturbed half-plane, where the disturbance corresponds to the cross-section of an open-pit mine. In this case, the boundary r coincides with the surface of the open pit and does not include the boundary of the undisturbed half-plane, which extends to infinity on both sides and is shown as a dashed line in Figure 38.While these two examples of unbounded domains are two of the most important cases for industry and society, the present method also applies to other types of unbounded domains that describe areas of soil, subsoil and earth crust around work sites, excavations or construction projects.

[0151] Given then an unbounded domain Q with the characteristics described above, what is considered by the method to describe the mechanical behavior of the continuous medium(s) that make it up is generically written as follows:

[0152] Equations of static equilibrium at O ​​- Boundary conditions on F -Decay conditions when -0

[0153] The method also includes the following elements:

[0154] • Static equilibrium equations: Partial differential equations valid in the unbounded domain Q, which account for the conservation of momentum in the static case, typically in terms of the displacement field u and the stress tensor α. The physical variables u and tr are related to each other through a constitutive law that describes the mechanical behavior of the continuous medium under study when subjected to tension. The most standard case is that of a linear elastic solid, resulting in the equations of elasticity, elastic equilibrium, or Navier equations. However, other linear or nonlinear behavior laws are also considered, such as those for elastoplastic solids, viscoelastic solids, porous solids, and fluid-filled cavities, representing the continuous medium(s) that make up a given zone of the soil, subsoil, or Earth's crust in general.

[0155] • Boundary conditions (also known as boundary, contour or frontier conditions): Relationships involving the physical variables valid on the surface r of the work or excavation.

[0156] • Decay conditions: An asymptotic, or far-field, behavior is established for the variables uy / oa at positions x GQ at large distances from the work site or excavation, which must correspond to a decay to zero of some kind. These conditions are necessary to obtain solutions with finite energy, that is, solutions that have physical meaning.

[0157] The present invention uses a methodology in which the unbounded domain Q is truncated by a transmission layer Qc£M that surrounds the work area under study. Figures 39 and 40 show examples of transmission layers for the unbounded domains presented in Figures 37 and 38, respectively.

[0158] This layer has a non-zero thickness, as shown in Figures 39 and 40. That is, it is a surface in ℝ² and a volume in ℝ³. The unbounded domain Q is then divided into an unbounded outer domain Cie, a domain corresponding to the transmission layer Qc, and a bounded inner domain Ci, which is the one that is ultimately discretized. That is, we will have the decomposition Q = QiuQc3QcQe. For its part, the transmission layer Qc will be delimited by two boundaries, an inner and an outer one. These boundaries correspond to curves in ℝ² and surfaces in ℝ³. In general, we say that both boundaries are (d-1)-manifolds in M. Furthermore, both must have at least Lipschitz regularity.

[0159] Within the transmission layer, a Perfectly Matched Layer (PML) technique is used, adapted to the case of second-order elliptic static equilibrium problems, whether linear, semilinear, or nonlinear. This allows for the appropriate truncation of the bounded domain Qi, circumscribing the decay to infinity of the solution in the unbounded domain Qe to the transmission layer Qc. Further details for certain particular cases of transmission layers are given in the following subsection.

[0160] Within the bounded domain Qi, any standard discretization method for bounded domains can be used. The finite element method is most commonly used due to its numerous advantages in solid mechanics, but the finite difference method, the finite volume method, the discrete element method, or other discretization methods can also be employed.

[0161] The Qc transmission layer described above, which is the essential component of the DGN technique, is obtained by following these steps:

[0162] • The interior domain Qi is discretized using a regular mesh, consistent with the numerical method to be used in the computational solution. This defines the set formed by the union of all the elements or discretization cells that constitute the mesh;

[0163] • The border It is made up of a set of regular geometric elements of More precisely, if d=2, they will be straight or curved segments. If d=3, they will be triangles, quadrilaterals, or other polygons, flat or curved.

[0164] • On each of the regular geometric elements defined on a series of points is defined in , denoted If it is Consider the normal vector to the internal boundary at point p, which we call The affine vector subspace of dimension 1 is considered to be defined as

[0165] • Using an appropriately defined contraction diffeomorphism: the unbounded set, i.e., the interval, contracts locally to the bounded segment, that is, to the interval (0,5p).

[0166] • The above generates a discrete transformation of the static equilibrium equations and the decay conditions to infinity from the unbounded domain Qe to the bounded domain Qc, as the outer domains are homologated with the domains through the contraction diffeomorphism

[0167] • By using dispersion relations deduced from conservation laws, constitutive laws and hypotheses about functional spaces (finite energy solutions), a system of differential equations is solved, which allows the behavior of the original solution to be represented at infinity.

[0168] • This allows us to circumscribe the solution of the differential problem originally posed in the unbounded domain to the bounded domain formed by It is worth noting that the aforementioned contraction diffeomorphism is generated in such a way that it functions as a generalization of a PML (Perfectly Matched Layef) to a second-order elliptic static equilibrium problem, whether linear, semi-linear or non-linear.

[0169] The following section details certain specific cases of transmission layers delimited by standard-shaped boundaries, which can be easily parameterized. Some notable examples are:

[0170] Circular / Spherical Boundaries: This corresponds to a particular case of the previous one, specifically when the semi-axes of the ellipses or ellipsoids are equal. Two radii λ₁ and λ₂ are established such that λ₁ > λ₂ > 0. In the two-dimensional case, the transmission boundary is delimited by the two concentric circles with radii λ₁ and λ₂ for an external domain, and by the two lower concentric semicircles with radii λ₁ and λ₂ for a semi-infinite domain, as shown in Figures 41A and 41B. The thickness of the transmission layer is constant and is given by λ = λ₂ - λ₁. It should also be noted that the center of these circles or semicircles should be located at a central point of the work area or excavation under study.

[0171] The extension to the three-dimensional case is natural. In that case, the transmission boundary will be delimited by the concentric spheres of radii 7θ1 and R2 for an external domain, and by the lower concentric hemispheres of radii Zθ1 and R2 for a semi-infinite domain. Again, the center of these spheres or hemispheres should be located at a central point of the work area of ​​interest.

[0172] Elliptical / ellipsoidal boundaries: For the two-dimensional case, a pair of horizontal semi-axis lengths a1, a2 are established such that a1 > a2 > 0, and a pair of vertical semi-axis lengths b1, b2 such that b1 > b2 > 0. The transmission layer is bounded by the two concentric ellipses of semi-axes a1, b1, and a2, b2 for an outer domain, and by the two concentric lower semi-ellipses of semi-axes a1, Z > 1, and a2, b2 for a semi-infinite domain, as shown in Figures 42A and 42B. The thickness of the transmission layer in this case will not be constant; however, the lengths of the semi-axes can be chosen so that the thickness remains relatively constant. Again, the center of these ellipses or semi-ellipses should be located at a central point of the work or excavation under study.For the three-dimensional case, the extension of the above is natural, with the exception that this time it is necessary to consider three pairs of semi-axis lengths, one pair for each dimension of space. That is, a1, a2 such that a2 > a1 > 0, b1, b2 such that b2 > b1 > 0, and c1, c2 such that c2 > c1 > 0. Thus, the transmission boundary is delimited by the two concentric ellipsoids with semi-axes a1, b1, c1, and a2, b2, c2 for an exterior domain, and by the two lower concentric semi-ellipsoids with semi-axes a1, b1, c1, and a2, b2, c2 for a semi-infinite domain.

[0173] Polygonal / Polyhedral Boundaries: In this case, the transmission layer will be delimited by polygonal boundaries for two-dimensional domains and by polyhedral boundaries for three-dimensional domains. The options for polygons or polyhedra are infinite, and the specific choice will depend on the geometry of the structure or excavation under study.

[0174] However, we specifically mention the case of rectangular boundaries, as it is a logical choice due to its simplicity and applies to most cases. For the two-dimensional case, a horizontal distance a>0 and a vertical distance ¿>0 are defined, both intended as reference distances between a central point of the structure or excavation and the inner boundaries of the transmission layer. A constant thickness is also defined. <5> 0. For an exterior domain, the transmission layer is bounded by the rectangle of width 2a and height 2b, and the rectangle of width 2(a+5) and height 2(b+8). For a semi-infinite domain, the transmission layer is bounded by the lower half-rectangle of width 2a and height b, and the lower half-rectangle of width 2(a+5) and height b+8, as shown in Figures 43A and 43B.

[0175] Extending the above to the three-dimensional case is a natural progression. Two horizontal distances a, b > Q and one vertical distance c > 0 are considered, as well as a constant thickness 8 > 0. For an outer domain, the transmission layer is delimited by the rectangular parallelepiped with width 2a, length 2b, and height 2c, and the rectangular parallelepiped with width 2(a+5), length 2(b+8), and height 2(c+5). For a semi-infinite domain, the transmission layer is delimited by the lower rectangular half-parallelepiped with width 2a, length 2b, and height c, and the lower rectangular half-parallelepiped with width 2(a+8), length 2(b+8), and height c+8. The flow diagram of the operation of the present invention is shown in Figure 44.

[0176] The criteria for soil failure include:

[0177] • Coulomb

[0178] • Rankine

[0179] Within the criteria for failure in rock masses:

[0180] • Mohr-Coulomb

[0181] • Hoek and Brown Failure Criteria for Discontinuities

[0182] • Mohr-Coulomb

[0183] • Jaeger

[0184] • Patton

[0185] • Landayi and Archambault

[0186] • Barton and Choubey

[0187] This method is efficiently solved to decrease the amount of data to be processed, increasing the speed, performance, and accuracy of a data processing system comprising at least one computer hardware processor, by reducing the overhead of processing and communication between computer system processes that are executed by the data processing system and / or between devices of the data processing system, and thus improving conventional techniques for performing data processing operations that use limits in two or three dimensions that define a boundary and a bounded domain.

[0188] DETAILED DESCRIPTION OF THE INVENTION

[0189] The present invention discloses a method for determining the mechanical and / or dynamic condition of a rock mass with low error and acquisition time for making productive and safety decisions regarding a domain under study, comprising the steps of: obtaining a detailed virtual representation (detailed description) of a domain under study; identifying geomechanical units and geological faults in the domain under study; defining a boundary Ω within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary (representing the edge of the surface or excavated cavity) and complexities to be studied, where the boundary Ω is continuous (and where the space outside said boundary is considered homogeneous and isotropic); generating a first study space, contained within the interior volume / area such that the boundary is within the first study space;generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are located within said second study space of the plurality of second study spaces; generate a base model, from the first study space (a simplified model eliminating geological faults / singularities); generate a plurality of secondary models, from the plurality of second study spaces;Generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one feature of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation); process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) - 2D / 3D cases, or mixtures thereof);Transform, through at least one processor, the information from each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or 3D), which also consider boundary conditions at the edges of boundary O (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

[0190] Where the virtual representation corresponds to a mesh with variable resolution (CAD) of the domain under study and the limit is Q which has a constant thickness 5

[0191] In a preferred configuration, thickness 5 is 0, generating a transparency boundary to truncate the domain under study.

[0192] In another preferred configuration, the thickness δ is greater than 0, generating a transmission layer to truncate the domain under study.

[0193] In another preferred configuration, the domain under study is a 2-dimensional domain, where the limit δ is a geometric or amorphous representation in 2 dimensions.

[0194] In another preferred configuration, the boundary Ω is a circle, square, ellipse, or portions and / or combinations thereof.

[0195] In another preferred configuration, the boundary O is a circle or a semicircle, whose radius is at least the maximum distance within the first study space.

[0196] In another preferred configuration, without limiting the scope of the invention, the domain under study is a 3-dimensional domain, where the boundary Ω is a geometric or amorphous representation in 3 dimensions.

[0197] In another preferred configuration, the boundary Ω is a sphere, cube, ellipsoid, or portions and / or combinations thereof.

[0198] In another preferred configuration, the boundary Ω is a sphere or a hemisphere, whose radius is at least the maximum distance within the first study space, and the boundary δ is a continuous Lipschitz boundary. In another preferred configuration, without limiting the scope of the invention, a mesh of the plurality of independent meshes may be one of the following: a free mesh (only the boundary / base model), a mesh with the boundary and at least one complexity to be studied (a model that includes a boundary with fluid (water pockets, liquid hydrocarbon pockets, underground rivers, aquifers, among others), with a geological fault, with a change of medium, any natural disruption of the Earth's crust, or any human activity (tunnels, mine shafts, explorations, among others) where the natural conformation of the Earth's crust is altered, and combinations thereof), a mesh with the boundary and a plurality of complexities to be studied, or mixtures thereof, where,The meshing of the plurality of independent meshes can be discretized / meshed more finely in the vicinity of the boundary, where the meshing of the plurality of independent meshes can be discretized / meshed more finely in the vicinity of a complexity to be studied.

[0199] Discretization of the mesh of the plurality of independent meshes increases the mesh pitch as it moves away from the boundary and / or the complexities to be studied.

[0200] The discretization of the mesh of the plurality of independent meshes corresponds to a mesh of triangles in 2D or a mesh of tetrahedra in 3D.

[0201] In another preferred configuration, the method further comprises: graphically representing (holographically 2D / 3D), by means of a visualization screen or graphical interface, the displacements, deformations and / or stresses of material / load, wherein the representation of material displacements comprises the representation by displacement area and by depth, forming a displacement volume indicative of the depth range and / or effect on the domain under study that these displacements imply when caused during a movement of a surface load, wherein the representation of material deformations comprises the representation by area of ​​the deformations and by depth, forming a deformation volume indicative of the depth range and / or effect on the domain under study that these deformations imply when caused during a movement of a surface load.In another preferred configuration, the representation of material stresses comprises the representation by area of ​​stresses and by depth, forming a volume of stresses indicative of the depth range and / or effect on the domain under study that these stresses imply caused during a movement of a surface load, where the domain under study also comprises the temporal evolution.

[0202] In another preferred configuration, the temporal evolution is represented as a plurality of states that contain the detailed virtual representation of the domain under study for different time instants, where the time instants of each state of the plurality of states are at least 1 second apart.

[0203] In another preferred configuration, the time instants of each state in the plurality of states are equal or the time instants of each state in the plurality of states are different.

[0204] In another preferred configuration, material displacements are described as a function of time, by means of a quasi-static analysis (temporal variation is negligible, and they are considered as individual frames / states per unit of time) of the temporal evolution.

[0205] In another preferred configuration, material displacements are described as a function of time by fitting at least one of: a time-dependent variable or a function dependent on at least one time-dependent variable in the time evolution (where the fitting can be done, for example, using Green's functions), wherein material deformations are described as a function of time by a quasi-static analysis (time variation is negligible, and they are considered as individual frames / states per unit of time) of the time evolution, wherein material deformations are described as a function of time by fitting at least one of: a time-dependent variable or a function dependent on at least one time-dependent variable in the time evolution (where the fitting can be done, for example, using Green's functions), whereinMaterial stresses are described as a function of time, through a quasi-static analysis (temporal variation is negligible, and they are considered as individual frames / states per unit of time) of the temporal evolution; it can also be that material stresses are described as a function of time, through an adjustment of at least one of: a variable as a function of time or a function dependent on at least one variable as a function of time, in the temporal evolution (where the adjustment can be made, for example, by means of Green's functions).

[0206] A system for determining the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for productive and safety decision-making with respect to a domain under study, comprising at least one processor and at least one computer-readable storage medium that stores instructions that, when executed by the at least one processor, cause the at least one processor to perform the steps of: obtaining a detailed virtual representation (detailed description) of a domain under study; identifying geomechanical units and geological faults in the domain under study;define a boundary Ω within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary (representing the edge of the excavated surface or cavity) and complexities to be studied, where the boundary Ω is continuous (and where the space outside said boundary is considered homogeneous and isotropic); generate a first study space, contained within the interior volume / area such that the boundary is within the first study space; generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are within said second study space of the plurality of second study spaces;generate a base model, from the first study space (a simplified model eliminating geological faults / singularities / complexities); generate a plurality of secondary models, from the plurality of second study spaces; generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one characteristic of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation);Process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) cases - 2D / 3D, or mixtures thereof); transform, through at least one processor, the information of each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or 3D), which also consider boundary conditions at the edges of the Q boundary (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

[0207] In a preferred configuration, the virtual representation corresponds to a mesh with variable resolution (CAD) of the domain under study, where the Q boundary has a constant thickness 5.

[0208] In another preferred configuration, thickness 5 is 0, generating a transparency boundary to truncate the domain under study, where thickness δ is greater than 0, generating a transmission layer to truncate the domain under study.

[0209] The system also includes a display screen or graphical interface, to graphically represent (holographically 2D / 3D) the displacements, deformations and / or material / load stresses.

[0210] The system further comprises a computer, smartphone, or tablet for graphically (holographically 2D / 3D) representing material displacements, deformations, and / or stresses / loads. In a preferred configuration, the at least one processor further comprises a neural network for learning and iterating the method according to any one of claims 1 to 34.

[0211] A computer-readable storage medium for determining the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for productive and safety decision-making regarding a domain under study, containing instructions that, when executed by at least one processor, cause the at least one processor to execute the steps of: obtaining a detailed virtual representation (detailed description) of a domain under study; identifying geomechanical units and geological faults in the domain under study; defining a boundary Ω within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary (representing the edge of the surface or excavated cavity) and complexities to be studied, where the boundary Ω is continuous (and where the space outside said boundary is considered homogeneous and isotropic);generate a first study space, contained within the interior volume / area such that the boundary is located within the first study space; generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are located within said second study space of the plurality of second study spaces; generate a base model, from the first study space (a simplified model eliminating geological faults / singularities / complexities); generate a plurality of secondary models, from the plurality of second study spaces;Generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one feature of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation); process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) - 2D / 3D cases, or mixtures thereof);Transform, through at least one processor, the information from each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or 3D), which also consider boundary conditions at the edges of the Q boundary (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

[0212] This method is efficiently solved to decrease the amount of data to be processed, increasing the speed, performance, and accuracy of a data processing system comprising at least one computer hardware processor, by reducing the overhead of processing and communication between computer system processes that are executed by the data processing system and / or between devices of the data processing system, and thus improving conventional techniques for performing data processing operations that use limits in two or three dimensions that define a boundary and a bounded domain.

[0213] Different options described for different technical characteristics may be combined with each other, or with other options known to a person normally versed in the subject, without this limiting the scope of the present application.

[0214] In the context of this request, and without limiting its scope, "at least one" shall be understood to mean one or more of the elements referenced. Therefore, the number of elements referenced does not limit the scope of this request. Furthermore, if more than one element is provided, those elements may or may not be identical, without limiting the scope of this request.

[0215] The grammatical articles "a," "an," "the," and "the," as used herein, are intended to include "at least one," "at least one," "one or more," or "one or more," unless the context indicates or requires otherwise. Therefore, the articles are used herein to refer to one or more of the grammatical objects of the article. By way of example, "a component" means one or more components, and thus more than one component may be contemplated and used in an implementation of the invention. Furthermore, the use of a singular noun includes the plural, and the use of a plural noun includes the singular, unless the context of use requires otherwise.

[0216] The use of terms such as: "includes", "which includes", "including", "has", "which has", "having", "contains", "which contains", "containing", "comprising" or "comprising", even incorporating some grammatical equivalents of these, should generally be understood as open and non-limiting, e.g., not excluding additional unmentioned elements or steps, unless explicitly stated or understood otherwise in the described context.

[0217] In the context of this application, and without limiting its scope, "plurality" shall be understood to mean two or more of the elements referred to herein. Consequently, the number of elements of the plurality referred to does not limit the scope of this application, provided it is greater than or equal to two. Furthermore, these elements of the plurality may or may not be identical to one another without this limiting the scope of this application.

[0218] When the term "approximately" or "around" is used before a quantitative value, these teachings also include the specific quantitative value, unless specifically stated otherwise. As used herein, the term "approximately" or "around" refers to a variation of ±10% of the stated nominal value, unless a range is explicitly stated herein. Unless otherwise stated, if the term "approximately" or "around" is mentioned before the first extreme value of a numerical interval, or a set of numbers, regardless of their mode of representation (e.g., ratios of the type A:B or A / B, where A and B are whole numbers or decimals, among other numerical representations), this term refers to all the numbers stated, and in the case of numerical intervals, to both the first and second extreme values ​​of the interval.For example, a mentioned interval of "approximately X to Y" should be read as "approximately X to approximately Y".

[0219] In various places in this document, values ​​are described in groups or ranges. It is specifically intended that the description include each and every member of such groups and ranges individually and in subcombinations, and any combination of the different extreme values ​​of such groups or ranges. For example, an integer in the range of 0 to 40 is specifically intended to individually describe 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, and 40, and an integer in the range of 1 to 20 is specifically intended to individually describe 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20. The above also applies to decimal numbers with up to two decimal places, that is, up to the hundredth.

[0220] To designate intervals and / or ranges, various expressions can be used, such as "X - Y", "from X to Y", "from X to Y", "from X - Y", "between X and Y", and others used for this purpose.

[0221] Although this application mentions separate modes of implementation, it should be understood that any mode of implementation, and its characteristic features, may be freely combined with any other mode of implementation and its characteristic features, even in the absence of an explicit statement to that effect. It should be understood that the order of the steps or the order in which certain actions are performed is irrelevant as long as these teachings remain operative.

[0222] In addition, two or more steps or actions can be carried out simultaneously.

[0223] The use of any and all examples, or exemplary language in this document, such as "as" or "including," is intended solely to better illustrate the disclosure herein and does not limit the scope of the invention unless expressly stated. Nothing in the specification should be construed as indicating that any unclaimed element is essential to the practice of the invention herein.

[0224] APPLICATION EXAMPLES

[0225] The following are examples of the application of this method. These examples are provided for illustrative purposes only, to provide a better understanding of the invention, but should in no case be considered as limiting the scope of the protection sought. Furthermore, specifications of different technical features described in the examples may be combined with each other, or with other technical features previously described, without limiting the scope of the protection sought.

[0226] EXAMPLE 1 shows a comparison between Abaqus Simulia (as one of the best industry standards) and the calculation technology of the present invention: elastic analysis of stresses and strains in open-pit mining. These comparisons are shown in four real-world cases.

[0227] This example presents the comparisons made between the present invention and the Abaqus Simulia software in the numerical solution of a geomechanical application, which consists of an elastic analysis of displacements and stresses in a mine pit. Using both tools, three cases of increasing geometric complexity were solved: a simplified axisymmetric pit, a simplified 3D pit, and a real 3D pit. The results obtained for each case were compared, as well as the calculation times used by each tool.

[0228] The problem considered for comparing the two methodologies, which consists of calculating displacements and stresses in a mine pit, is mathematically modeled as a geometric perturbation on the surface of an elastic half-space. It is assumed that the entire medium is subjected to an initial geostatic stress, which is then modified by the geometric perturbation and the action of gravity. Because this domain is unbounded, it must be truncated to generate a bounded domain that can be meshed and numerically analyzed. In the case of Abaqus, the usual strategy is to truncate the domain using a cube or parallelepiped large enough so that the outer boundaries have minimal influence on the pit area. Standard boundary conditions are typically imposed on these boundaries, such as setting displacements in some or all directions.The present invention, on the other hand, makes use of exact boundary conditions for elasticity in a half-space, which are imposed on a hemispherical outer surface that can be located as close to the crack area as desired. As a result, the same problem can be solved in a much smaller domain, with a mesh with far fewer nodes, and therefore in a much shorter computation time. This example aims to demonstrate this advantage in a concrete application.

[0229] CASE 1: SIMPLIFIED AXISYMMETRIC SPLIT

[0230] This case consists of an axisymmetric open pit with simplified geometry, whose cross-section corresponds to a single slope, as shown in Figure 1. The three-dimensional domain is obtained as a solid of revolution, that is, by rotating the section around the vertical axis of rotation, indicated by the orange dashed line. This domain is unbounded both downwards and to the right. The geometric parameters are the horizontal distance d between the axis of rotation and the slope, the depth of the open pit H, and the slope angle (see Figure 1). In all tests The following dimensions were assumed for this case:

[0231] It is further assumed that the domain is occupied by an isotropic and homogeneous linear elastic medium, with density Young's modulus and Poisson's ratio In all tests performed for this case, the following values ​​were assumed: A gravitational acceleration and a lateral pressure coefficient equal to one were also assumed. This parameter is necessary to impose the initial geostatic stress, see figure 1. Simplified axisymmetric pit scheme.

[0232] To solve this problem using Abaqus, domains like the one shown in Figure 2A were considered. The original (unbounded) domain is truncated by a square of side i, which, as already mentioned, must be large enough so that the generated artificial boundaries do not influence the area of ​​interest, i.e., the open pit. Regarding the boundary conditions to be imposed, the lower boundary is assumed to be fixed in both directions, while the right vertical boundary is considered fixed only in the horizontal direction, as shown in Figure 2A. In order to measure the sensitivity of the solution with respect to the parameter L and to compare it with the solution obtained with the present invention, the following increasing values ​​were considered:

[0233] To solve the same problem using the present invention, an artificial boundary equal to a quarter of a circle with radius [missing information] was considered. The resulting domain is shown in Figure 2B. Note that, for the purposes of For comparison, a quarter circle of equal radius was also considered in the domain of Abaqus, as shown in Figure 2A.

[0234] Regarding the meshes, triangular finite elements were used in both cases. Furthermore, a mesh size of 10 m was chosen for the pit bottom and slope, and a mesh size of 28 m for the quarter-circle, so that both meshes would coincide as closely as possible over the portion corresponding to the domain of the present invention. Over the outer boundaries of the Abaqus domain, the mesh size was made coarser since this area is farther from the area of ​​interest. An example of the mesh used in Abaqus is shown in Figure 3A, while Figure 3B shows the mesh used in the present invention.

[0235] The results obtained with Abaqus for (greater mastery) and with the The results of the present invention are presented below. Figures 4, 5, and 6 show the horizontal displacement, vertical displacement, and Von Mises stress, respectively. In all cases, the results obtained with Abaqus are shown on the left, and the results obtained with the present invention are shown on the right. A good agreement between the results for the three variables is observed. It is expected that the scale of values ​​for the Abaqus results will have a wider range, as it is associated with a much larger domain.

[0236] Furthermore, the same variables were qualitatively compared along the pit edge and the quarter-circle. This was done for the results obtained with Abaqus for different values ​​of 1 and those obtained with the present invention. Figures 7, 8, and 9 present comparisons of the two displacement components and the Von Mises stress, respectively, along the segment encompassing the pit bottom and the slope. Comparisons of the same variables, but along the quarter-circle, are presented in Figures 10, 11, and 12, respectively. In these six graphs, the x-axis represents a normalized distance. In the case of the pit bottom and the slope (Figures 7 to 9), the left end (distance 0) corresponds to the center of the pit bottom (when generating the solid of revolution), and the right end (distance 1) corresponds to the highest point of the slope (which would be a circle when generating the solid of revolution).The point where the bottom ends and the slope begins occurs at a distance of approximately 0.345. This point is easily recognizable on the Von Mises stress graph (Figure 9), as it represents a stress peak. In the case of the quarter circle (Figures 10 to 12), the left end corresponds to the horizontal plane (distance zero) and the right end corresponds to the vertical axis of axisymmetry (distance one).

[0237] In these figures, an interesting phenomenon can be observed, which is particularly evident in the graphs of the vertical displacement (Figures 8 and 11). As the length L in Abaqus increases, the solution obtained becomes increasingly closer to the solution calculated with the present invention, whose accuracy stems from the fact that the present invention uses exact boundary conditions. That is, it is necessary to consider increasingly larger domains, with the consequent increase in mesh nodes, to achieve good accuracy. If we look specifically at Figure 11 at the zero distance (far left), we see that the present invention calculates a displacement of approximately 3.4 cm. The calculation with Abaqus and the smallest domain (L = 2000 m) gives a value of approximately 1.1 cm, so the relative error is on the order of 65%. For its part, for the calculation with the largest domain (L = 20880 m), Abaqus gives a value of approximately 1.1 cm.3.2 cm, which corresponds to a relative error of approximately 6%. To obtain even smaller relative errors, it would be necessary to further enlarge the domain.

[0238] In this analysis, the computation time variable has been deliberately omitted, since, given that the domains are two-dimensional, all simulations take only seconds. This will not be the case in the analyses that follow, where the domains are three-dimensional, making the differences in computation time between Abaqus and the present invention more relevant. CASE 2: SIMPLIFIED 3D OPEN

[0239] The second case involves a pit with simplified geometry similar to the previous case but genuinely three-dimensional, that is, without symmetry with respect to an axis of rotation. Unlike the solid of revolution obtained in the previous case, where the pit bottom corresponds to a circle, in this case the bottom corresponds to an ellipse. The slope is also taken with a fixed angle. Figures 13A and 13B present a schematic drawing of this geometry, including a cross-section (Figure 13A) and a top view (Figure 13B). We are assuming that this pit lies on the surface of an unbounded half-space. The relevant geometric parameters in this case are the major and minor semi-axes of the elliptical bottom, a and b, respectively, the pit depth H, and the slope angle (see Figure 13). In all tests performed for this case, the following dimensions were assumed:

[0240] As in the previous case, we assume that the domain, this time three-dimensional, is occupied by an isotropic and homogeneous linear elastic medium, with density ρ, Young's modulus E, and Poisson's ratio ν. In all the tests performed for this case, the following values ​​were assumed: An acceleration due to gravity was also taken. lateral pressure coefficients equal to 1 in both horizontal directions, this for the purpose of imposing the initial geostatic stress.

[0241] To solve this problem using Abaqus, the original unbounded domain was truncated by a cube of side length £, which must be sufficiently large for the same reasons explained earlier. Figure 14A shows an example of the domain used in Abaqus. Regarding the boundary conditions in this case, the vertical walls of the cube are assumed to be fixed in the direction normal to the surface, while the bottom of the cube is taken to be completely fixed in all three directions, as can be seen in Figure 14A.

[0242] Again, the sensitivity of the solution with respect to the parameter i and was compared with the solution obtained with the present invention, for which the following increasing values ​​were considered: To solve the same problem using the technology of the present invention, an artificial boundary equal to a hemisphere of radius S = 1QQ0 m was considered. The resulting domain is shown in Figure 14B. In addition, for comparison purposes, a circle of the same radius in the horizontal plane and around the crack in the Abaqus domain was also considered, as shown in Figure 14A.

[0243] Regarding the meshing, tetrahedral finite elements were used in both Abaqus and the present invention. In both cases, a uniform mesh size of 10 xn was used over the entire pit (bottom and slope), and a mesh size of 58 ni was used over the hemisphere, ensuring a high degree of overlap between the two meshes within the area corresponding to the domain of the present invention. A coarser mesh size was used over the artificial boundaries of the Abaqus domain (vertical walls and lower base). An example of the mesh used in Abaqus is shown in Figure 15A, while Figure 15B shows the mesh used in the present invention.

[0244] For the purpose of comparing the simulations performed with Abaqus with the simulation performed with the present invention, Table 1 shows the number of mesh nodes and the calculation time for each simulation. It can be observed that the present invention achieves a significant reduction in the number of mesh nodes and, consequently, in the calculation time.

[0245] The results obtained with Abaqus for L - 24000 m (largest range) and with the present invention are presented below. Figures 16, 17, and 18 show the two horizontal components (U1 and U2) and the vertical component (U3) of the displacement, respectively. The Von Mises stress is shown in Figure 19. In all cases, the results obtained with Abaqus are shown on the left and the results obtained with the present invention are shown on the right. Again, a good degree of agreement is observed between the results for these variables from a qualitative standpoint.

[0246] Additionally, qualitative comparisons of these variables were performed on certain segments of the open pit surface. This was done for the results obtained with Abaqus for different values ​​of .1 and those obtained with the present invention. Figures 20, 21, and 22 present comparative graphs of the horizontal displacement component U1, the vertical displacement component U3, and the Von Mises stress, respectively. The segment on which this comparison is made begins at the center of the open pit bottom, passes through the semi-major axis of the ellipse, and rises along the slope until it reaches the flat surface of the half-space. The displacement component U2 is not shown because, due to the symmetries considered, it is identically zero.

[0247] It can be observed that the curves look similar to the axisymmetric case (Figures 7 to 9). The phenomenon previously observed in the vertical displacements is again evident. Figure 21 shows that as the Abaqus domain increases, the solution becomes increasingly closer to the solution calculated with the present invention. At the far left of this graph, which corresponds to the center of the pit bottom, the present invention calculates a value of approximately 1.31 cm, while the values ​​calculated with Abaqus vary little from each other, with the closest value (with in approximately 1.28 cm, which corresponds to a relative error of 2%. It is worth noting that, according to Table 1, the present invention calculates the solution in 14% of the time taken by Abaqus with the largest domain. Furthermore, the agreement of the solutions for the horizontal component of the displacement (Figure 20) is quite high. And with respect to the Von Mises stress (Figure 22), the peak is again observed in the area where the bottom ends and the slope begins. The agreement is also quite high among all the solutions.

[0248] CASE 3: FIRST REAL 3D CUT

[0249] The third case considers a first real geometry of a mine pit. Starting with CAD files containing the pit surface, tools specific to the present invention were used to construct 3D geometry files suitable for finite element meshing. These files were exported in STEP format and then imported as parts into Abaqus to perform the simulations. Except for the greater geometric complexity of this case, the mathematical modeling of the problem and its computational simulation are analogous to the simplified 3D case, both for Abaqus and for the present invention.

[0250] Figures 23A and 23B show the surface of the first open pit analyzed, which corresponds to a project in the Antofagasta Region. Its approximate dimensions are 520 m long, 310 m wide, and 110 m deep. As in previous cases, an isotropic and homogeneous elastic surrounding medium was assumed, with density ρ, Young's modulus E, and Poisson's ratio ν. For this open pit, the following values ​​were taken. As before, an acceleration of gravity was taken with lateral pressure coefficients equal to 1 in both horizontal directions.

[0251] For the simulation in Abaqus, a single cube of length L = 6000 m was used, while for the present invention a hemisphere of radius was considered. Figure 24 shows the domain used in Abaqus, including a view general view A and approaches to the pit area B. The domain used in the present invention is shown in Figure 25, including a general view and an approach.

[0252] Regarding the mesh, both in Abaqus and in the present invention, a uniform mesh size of 3m was used across the entire surface of the open pit. On the artificial boundaries of the Abaqus domain, a coarser and variable mesh size was used. The resulting mesh has a total of 2,290,398 nodes. For the artificial hemispherical boundary of the present invention, a uniform mesh size of 20m was used. The resulting mesh has a total of 141,281 nodes. The simulation with Abaqus took a computation time of 115 min, while the simulation with the present invention took a computation time of approximately 17 min, about 15% of the time taken by Abaqus.

[0253] The results obtained with Abaqus and the present invention are shown below. Figures 26, 27, and 28 (A top, B bottom) show the horizontal displacement components U1, U2, and U3. The Von Mises stress is shown in Figure 29. In all cases, the upper graph corresponds to Abaqus and the lower graph corresponds to the present invention. It can be seen that the solutions have a high degree of agreement in all cases.

[0254] CASE 4: SECOND REAL 3D CRACK

[0255] The fourth case considers a second real-world geometry of a mine pit. Using CAD files containing the pit surface, tools specific to the present invention were used to construct 3D geometry files suitable for finite element meshing. These files were exported in STEP format and then imported as parts into Abaqus to perform the simulations. Except for the greater geometric complexity of this case, the mathematical modeling of the problem and its computational simulation are analogous to the simplified 3D case, both for Abaqus and for the present invention.

[0256] Figure 30 shows the surface of the second open pit analyzed, which corresponds to a project in the Metropolitan Region and has a slightly more complex geometry than Case 3. Its approximate dimensions are 600 m long, 520 m wide, and 160 m deep. A linear elastic medium was assumed with the following parameter values: density, Young's modulus. Poisson's ratio v - 03, plus an acceleration of gravity Lateral pressure coefficients equal to 1 in both horizontal directions. It should be noted that the Young's modulus in this case is much lower than the values ​​considered before; this is because it is a pit located in soil and not in rock mass.

[0257] For the simulation in Abaqus, a single cube of length was again used, whereas for the present invention a hemisphere was considered. with radius s = 45© m this time. Figures 31A and 31B show the domain used in Abaqus, including an overview and close-ups of the pit area. Figures 32A and 32B present the domain used in the present invention, including an overview and a close-up.

[0258] To mesh this geometry, both in Abaqus and in the present invention, a variable mesh size was used on the open pit itself, ranging from a minimum of 3 m to a maximum of 6 m, depending on the required level of resolution in each area. On the artificial boundaries of the Abaqus domain, a coarser mesh size was used, ranging from 200 m to 300 m. The resulting mesh has a total of 2,344,382 nodes. A uniform mesh size of 20 m was used on the artificial hemispherical boundary of the present invention. The resulting mesh has a total of 232,345 nodes. The simulation with Abaqus took 158 minutes to complete, while the simulation with the present invention took approximately 35 minutes, about 22% of the time taken by Abaqus.

[0259] The results obtained with Abaqus and the present invention are shown below. Figures 33, 34, and 35 (A top, B bottom) show the horizontal displacement components U1, U2, and U3. The Von Mises stress is shown in Figure 36. In all cases, the upper graph corresponds to Abaqus and the lower graph corresponds to the present invention. A good agreement between the solutions is observed in all cases.

[0260] The following are another series of application examples of the present invention.

[0261] In the following examples the method and system of the present invention was used and to facilitate the understanding of the present invention the following process diagram is shown in Figure 45.

[0262] EXAMPLE 2. CAEX trucks on gravel dump.

[0263] Stability Analysis

[0264] • Possibility of using CAEX trucks to transport sterile material to the tailings dump.

[0265] • Virtual load cells: Vertical displacement and stress curves.

[0266] • Circulation of CAEX trucks with and without cargo on the gravel dump: Is the gravel capable of safely supporting truck traffic?

[0267] • CAEX stability metric in the longitudinal direction of the advance.

[0268] • CAEX stability metric in the direction transverse to the advance

[0269] • Use of the present invention to evaluate truck traffic scenarios. The weight of the Caterpillar CAT 797F truck, used in mining, simulated as loads on rectangular surfaces, representing the contacts of the 6 tires with the gravel, is shown in Figure 46 and the truck in Figure 47.

[0270] Figure 48 shows the specifications of the mining truck, source specification CAT 797F.

[0271] Longitudinal contacts are assumed to be 25% to 30% of the tire width.

[0272] Vertical displacement:

[0273] The Vertical displacement (approach), which is observed with yellow colors, are the displacements associated with the weight of the support per wheel and the advance of the truck, see figures 49 and 50.

[0274] The Vertical displacement (approach), which is observed with yellow colors, are the displacements associated with the weight of the support per wheel and the advance of the truck, see figures 51 and 52.

[0275] The vertical displacement (3D diagonal cut) is shown in Figure 53.

[0276] The direction of travel of the mining truck is shown in Figure 54.

[0277] The vertical displacement (3D diagonal cut) of the mining truck is shown in Figure 55.

[0278] The displacement in cm is shown in Fig. 56

[0279] The vertical displacement (3D diagonal cut) is shown in Figure 57.

[0280] After observing the displacement of the mining truck, a 3D graphical representation of the vertical stress is generated, see figure 58, its respective close-up in figure 59 and its representation on the x,y,z axes can be seen in figures 60 and 61, which provide the following parameters:

[0281] The vertical stress (3D diagonal cut) is observed again in Figure 58, where a representation of the truck's forward direction is subsequently shown with a lower mesh in Figure 62 and a close-up in Figures 63 and 64.

[0282] The description and figures 45 to 64 are to graphically show what is achieved virtually below.

[0283] Virtual load cells

[0284] • Virtual load cells were placed in the center of each contact surface at the midpoint of the advance.

[0285] • Depths of 0.5 m, 1.5 m and 2.1 m, as in the previous study.

[0286] • 18 virtual load cells in total.

[0287] The displacement and vertical stress curves in virtual tire load cells are shown in Figures 66 to 69.

[0288] The results of the displacement and vertical stress curves in virtual load cells under the right front tire, figure 66, are:

[0289] The results of the displacement and vertical stress curves in virtual load cells under the outer right rear tire, figure 67, are:

[0290] The results of the displacement and vertical stress curves in virtual load cells under the right front tire, in a second time, figure 68, are: The results of the displacement and vertical stress curves in virtual load cells under the outer right rear tire, in a second time, figure 69, are:

[0291] Longitudinal stability metric of the high tonnage extraction truck (CAEX) during forward motion.

[0292] The safety of the CAEX truck's advance through the gravel dump is evaluated against the threat of loss of stability due to forward and backward movements (parallel to the advance), therefore a metric was used that measures the maximum difference in vertical displacement between the front axle and the rear axle of the CAEX truck.

[0293] The contact surfaces of the tires with the gravel were considered when the CAEX truck is halfway through its advance, and the maximum difference in vertical displacement between the front and rear surfaces was calculated.

[0294] In these tests, the following three representative Poisson ratio values ​​for the gravel were used:

[0295] This maximum difference in vertical displacement is plotted against the time required for the complete forward movement of the CAEX truck, for cases with the truck unloaded and fully loaded. The unloaded case is shown in Figure 70, and the case with the truck fully loaded is shown in Figure 71.

[0296] The stability metric considered, that is, the maximum difference in vertical displacement between the front and rear axles of the CAEX, is greater as the Poisson ratio ν decreases. For the CAEX truck traveling without a load and the ν values ​​considered, the differences in displacement between the front and rear axles do not exceed 7 cm. And for the CAEX truck traveling with maximum load and the ν values ​​considered, the differences in displacement between the front and rear axles almost doubled, exceeding 13 cm.

[0297] By establishing a maximum permissible threshold for this metric, it is possible to determine whether the transit of the CAEX truck, with and / or without cargo, is stable with respect to longitudinal or parallel movements. See Figure 72.

[0298] The safety of the advance of the CAEX truck through the gravel dump was evaluated against the threat of loss of stability due to lateral movements (i.e., transverse to the advance).

[0299] The cause of the lateral movements of the CAEX truck was assumed to be possible differences in the degree of compaction of the gravel under the right and left tires.

[0300] These differences are modeled by variations in the Poisson ratio of the gravel within a range, under both right (vd) and left (v¡) tires.

[0301] These two values ​​are assigned to the right and left halves of the rectangular circulation area.

[0302] The stability metric of the CAEX transverse to the advance is shown in figure 73.

[0303] The range of variation for both Poisson ratios vd and v1 was expanded to [0.30, 0.49], in increments of 0.01, i.e., 20 values ​​in total. For each of the 400 ordered pairs (vd, v1), the maximum difference in vertical displacement (in absolute value) between the right and left tires, corresponding to the same axle (front or rear), was established as the stability metric or indicator for the CAEX truck with no load and with maximum load. The graph for the no-load case is shown in Figures 74A and 74B, and for the case with maximum load, it is shown in Figures 75A and 75B.

[0304] When the CAEX truck is unloaded, the greatest differences in vertical displacement between the right and left tires occur on the rear axle. These differences reach up to 4 cm on the front axle and up to 7 cm on the rear axle. When the CAEX truck is fully loaded, the differences in vertical displacement between the right and left tires are almost the same on both axles, reaching up to 8 cm.

[0305] By establishing a maximum allowed threshold for this metric, it is possible to determine if the transit of the CAEX truck with and / or without cargo is stable with respect to lateral or perpendicular movements to the advance.

[0306] A third metric was proposed to quantify the stability of CAEX truck traffic on the gravel dump, related to the gravel's resistance to the stresses caused by the weight of the CAEX truck as it travels across the dump. Through the simulation of various scenarios and the application of this method to the calculation of the complete stress tensor, it was possible to determine whether the failure envelope associated with the Mohr-Coulomb failure criterion is exceeded for each CAEX traffic scenario. This requires precise data on the cohesion and angle of internal friction of the gravel that makes up the dump.

[0307] EXAMPLE 3

[0308] Radical reduction of operational downtime and improvement of the quality of response to extreme events in mining and civil works.

[0309] Geological information: Geomechanical information: Structural information: From 2D to 3D. From the study of some Reconciliation of the

[0310] From a 2D graph to a few possible cases, up to 3D video measurements of the critical path of all field data in real time with temporal evolution. See possible cases. From days to hours of analysis. See Figure 76. Trial and error to systematic real-time reconciliation. See Figure 78. Success story #1: DET, The Regional Stress Field, from Figure 79, showing the study volume of the Abaqus domain: 14,525 km² 3 , while the volume of the domain of the present invention is: 134 km 3(less than 1%), this difference in study volume is one of the great advantages of the present invention's analysis without affecting the quality of the results. Moreover, it improves and brings the results even closer to real-world values.

[0311] The high-definition discretization mesh adapted to the present invention is shown in Figure 80.

[0312] Discretization of real topography, approx. 1,120,000 discretization points.

[0313] Success story #1: DET, Regional stress field is shown in Figures 81A and 81B, the 3D global stress results are shown in Figures 82A, 82B, 82C and 82D, and the calculations were performed in 142 minutes, demonstrating the high speed and savings in calculations, facilitating the delivery of results in an optimal time for decision-making, both for the safety of the operators or people located in the study area and for economic decision-making.

[0314] Cross-sections of production areas in the mine are shown in Figure 84A, a top view, and Figure 84B, a side view.

[0315] Stress indicators calculated using the present invention (MC2E) and prior art (Gold Standard) were compared over a vertical segment starting at the surface and passing through the mine (down to 1,500 m deep). See Figures 85 and 86.

[0316] The initial geomechanical and geotechnical baseline provided by a mining company in the Antofagasta Region, Chile:

[0317] • Topography of an open-pit mine with geomechanical and geotechnical units, determined using standard techniques. (See figure 87)

[0318] • Displacement measurements at surface points (2D). (See figure 88)

[0319] The mine design challenge—open-pit stability—is shown in Figure 89, and the names are shown in Figure 90. Figure 91 shows the Mohr-Coulomb failure criterion diagram, where the results for dry ground show a larger angle (see Figure 77), while for ground with pockets of water (fluid), the angle is smaller (see Figures 92 and 93).

[0320] This demonstrates the importance of the present invention, since the correct calculation of the slope angle determines pit stability, thereby ensuring its safety and maximizing the performance of the mining operation, whether in dry or wet conditions, meaning with the presence of water pockets, which implies a smaller angle to maintain said stability.

Claims

CLAIMS 1. A method for determining the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for making productive and safety decisions with respect to a domain under study, CHARACTERIZED in that it comprises the steps of: obtaining a detailed virtual representation (detailed description) of a domain under study; identifying geomechanical units and geological faults in the domain under study; defining a boundary within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary (representing the edge of the surface or excavated cavity) and complexities to be studied, where the boundary is continuous (and where the space outside said boundary is considered homogeneous and isotropic); generate a first study space, contained within the interior volume / area such that the boundary is within the first study space; generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are within said second study space of the plurality of second study spaces; generate a base model, from the first study space (a simplified model eliminating geological faults / singularities); generate a plurality of secondary models, from the plurality of second study spaces;generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one feature of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation); Process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) cases - 2D / 3D, or mixtures thereof); transform, through at least one processor, the information of each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or 3D), which also consider boundary conditions at the edges of the Q boundary (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

2. The method according to claim 1, CHARACTERIZED in that the virtual representation corresponds to a mesh with variable resolution (CAD) of the domain under study.

3. The method according to claim 1 or claim 2, CHARACTERIZED in that the boundary Q has a constant thickness δ.

4. The method according to claim 3, CHARACTERIZED in that the thickness δ is 0, generating a transparency boundary to truncate the domain under study.

5. The method according to claim 3, CHARACTERIZED in that the thickness δ is greater than 0, generating a transmission layer to truncate the domain under study.

6. The method according to any one of claims 1 to 5, CHARACTERIZED in that the domain under study is a 2-dimensional domain.

7. The method according to claim 6, CHARACTERIZED in that the limit δ is a geometric or amorphous representation in 2 dimensions.

8. The method according to claim 7, CHARACTERIZED in that the boundary 0 is a circle, square, ellipse or portions and / or combinations thereof.

9. The method according to claim 8, CHARACTERIZED in that the boundary 0 is a circle or a semicircle, the radius of which is at least the maximum distance within the first study space.

10. The method according to any one of claims 1 to 5, CHARACTERIZED in that the domain under study is a 3-dimensional domain.

11. The method according to claim 10, CHARACTERIZED in that the limit 0 is a geometric or amorphous representation in 3 dimensions.

12. The method according to claim 11, CHARACTERIZED in that the boundary δ is a sphere, cube, ellipsoid or portions and / or combinations thereof.

13. The method according to claim 12, CHARACTERIZED in that the limit 0 is a sphere or a hemisphere, the radius of which is at least the maximum distance within the first study space.

14. The method according to any one of the preceding claims, CHARACTERIZED in that the limit Ω is Lipschitz continuous.

15. The method according to any one of the preceding claims, CHARACTERIZED in that a mesh of the plurality of independent meshes may be one of the following: free mesh (only the boundary / base model), mesh with the boundary and at least one complexity to be studied (model that includes boundary with fluid (water pockets, liquid hydrocarbon pockets, underground rivers, underground aquifers, among others), with geological fault, with change of medium, any natural disruption of the earth's crust, or any human activity (tunnels, quarries, explorations, among others) where the natural conformation of the earth's crust is intervened, and combinations of the above), mesh with the boundary and a plurality of complexities to be studied, or mixtures thereof.

16. The method according to claim 15, CHARACTERIZED in that the meshing of the plurality of independent meshes can be discretized / meshed more finely in the vicinity of the boundary.

17. The method according to claim 15 or claim 16, CHARACTERIZED in that the meshing of the plurality of independent meshes can be discretized / meshed more finely in the vicinity of a complexity to be studied.

18. The method according to claim 15 to 17, CHARACTERIZED in that the discretization of the mesh of the plurality of independent meshes increases the mesh pitch as it moves away from the boundary and / or the complexities to be studied.

19. The method according to claim 15 to 18, CHARACTERIZED in that the discretization of the mesh of the plurality of independent meshes corresponds to a mesh of triangles in 2D or a mesh of tetrahedra in 3D.

20. The method according to any one of the preceding claims, CHARACTERIZED in that it further comprises: graphically representing (holographically 2D / 3D), by means of a display screen or graphic interface, the displacements, deformations and / or material / load stresses.

21. The method according to claim 20, CHARACTERIZED in that the representation of material displacements comprises the representation by displacement area and by depth, forming a displacement volume indicative of the depth range and / or effect on the domain under study implied by said displacements caused during a movement of a surface load.

22. The method according to claim 20 or claim 21, CHARACTERIZED in that the representation of material deformations comprises the representation by area of ​​the deformations and by depth, forming a volume of deformations indicative of the depth range and / or effect on the domain under study that these deformations caused during a movement of a surface load imply.

23. The method according to any one of claims 20 to 22, CHARACTERIZED in that the representation of material stresses comprises the representation by area of ​​stresses and by depth, forming a volume of stresses indicative of the depth range and / or effect on the domain under study that these stresses imply when caused during a movement of a surface load.

24. The method according to any one of the preceding claims, CHARACTERIZED in that the domain under study further comprises temporal evolution.

25. The method according to claim 24, CHARACTERIZED in that the temporal evolution is represented as a plurality of states containing the detailed virtual representation of the domain under study for different times.

26. The method according to claim 25, CHARACTERIZED in that the time instants of each state of the plurality of states are separated by at least 1 second.

27. The method according to claim 25 or 26, CHARACTERIZED in that the time instants of each state of the plurality of states are equal.

28. The method according to claim 25 or 26, CHARACTERIZED in that the time instants of each state of the plurality of states are different.

29. The method according to any one of claims 24 to 28, CHARACTERIZED in that the material displacements are described as a function of time, by means of a quasi-static analysis (temporal variation is negligible, and they are considered as individual frames / states per unit of time) of the temporal evolution.

30. The method according to any one of claims 24 to 28, CHARACTERIZED in that the material displacements are described as a function of time, by an adjustment of at least one of: a time-dependent variable or a function dependent on at least one time-dependent variable, in the temporal evolution (where the adjustment can be made, for example, using Green's functions).

31. The method according to any one of claims 24 to 30, CHARACTERIZED in that the material deformations are described as a function of time, by means of a quasi-static analysis (temporal variation is negligible, and they are considered as individual frames / states per unit of time) of the temporal evolution.

32. The method according to any one of claims 24 to 30, CHARACTERIZED in that the material deformations are described as a function of time, by fitting at least one of: a time-dependent variable or a function dependent on at least one time-dependent variable, in the time evolution (where the fitting can be done, for example, by means of Green's functions).

33. The method according to any one of claims 24 to 32, CHARACTERIZED in that the material stresses are described as a function of time, by means of a quasi-static analysis (temporal variation is negligible, and they are considered as individual frames / states per unit of time) of the temporal evolution.

34. The method according to any one of claims 24 to 32, CHARACTERIZED in that the material stresses are described as a function of time, by fitting at least one of: a time-dependent variable or a function dependent on at least one time-dependent variable, in the time evolution (where the fitting can be done, for example, by means of Green's functions).

35. A system for determining the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for making productive and safety decisions with respect to a domain under study, CHARACTERIZED in that it comprises at least one processor and at least one computer-readable storage medium that stores instructions which, when executed by the at least one processor, cause the at least one processor to execute the steps of: to obtain a detailed virtual representation (detailed description) of a domain under study; to identify geomechanical units and geological faults in the domain under study; to define a boundary Ω within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary (representing the edge of the excavated surface or cavity) and complexities to be studied, where the boundary Ω is continuous (and where the space outside said boundary is considered homogeneous and isotropic); to generate a first study space, contained within the interior volume / area such that the boundary is within the first study space;generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are located within said second study space of the plurality of second study spaces; generate a base model, from the first study space (a simplified model eliminating geological faults / singularities / complexities); generate a plurality of secondary models, from the plurality of second study spaces;Generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one feature of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation); process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) - 2D / 3D cases, or mixtures thereof);transform, through at least one processor, the information of each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or; 3D), which also consider boundary conditions at the edges of the Q boundary (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

36. The system according to claim 35, CHARACTERIZED in that the virtual representation corresponds to a mesh with variable resolution (CAD) of the domain under study.

37. The system according to claim 35 or claim 36, CHARACTERIZED in that the boundary Ω has a constant thickness 5.

38. The system according to claim 37, CHARACTERIZED in that the thickness 5 is 0, generating a transparency limit to truncate the domain under study.

39. The system according to claim 37, CHARACTERIZED in that the thickness δ is greater than 0, generating a transmission layer to truncate the domain under study.

40. The system according to any one of claims 35 to 39, CHARACTERIZED in that it further comprises a display screen or graphic interface, for graphically representing (holographically 2D / 3D) the displacements, deformations and / or material / load stresses.

41. The system according to any one of claims 35 to 39, CHARACTERIZED in that it further comprises a computer, smartphone or tablet, to graphically represent (holographically 2D / 3D) the displacements, deformations and / or material / load stresses.

42. The system according to any one of claims 35 to 41, CHARACTERIZED in that the at least one processor further comprises a neural network for learning and iterating the method according to any one of claims 1 to 34.

43. A computer-readable storage medium for determining the mechanical and / or dynamic condition of the rock mass with low error and acquisition time for productive and safety decision-making with respect to a domain under study, CHARACTERIZED in that it contains instructions that, when executed by at least one processor, cause the at least one processor to execute the steps of: obtaining a detailed virtual representation (detailed description) of a domain under study; identifying geomechanical units and geological faults in the domain under study; defining a boundary Ω within the detailed virtual representation of the domain under study (volume / surface) containing an interior volume / area that includes a boundary (representing the edge of the surface or excavated cavity) and complexities to be studied, where the boundary Ω is continuous (and where the space outside said boundary is considered homogeneous and isotropic);generate a first study space, contained within the interior volume / area such that the boundary is located within the first study space; generate a plurality of second study spaces, where each of the plurality of second study spaces is contained within the interior volume / area, such that the boundary and at least one complexity to be studied are located within said second study space of the plurality of second study spaces; generate a base model, from the first study space (a simplified model eliminating geological faults / singularities / complexities); generate a plurality of secondary models, from the plurality of second study spaces;generate a plurality of independent meshes from the base model and at least one of the plurality of secondary models, such that each of the plurality of meshes contains at least one feature of the domain under study, by discretizing the volume / interior area, where each of the plurality of meshes includes physical parameters (modulus of elasticity, Young's modulus, Poisson's ratio and representative density of the solid, forcings), geological parameters (Mohr-Coulomb parameters: cohesion and angle of internal friction, parameters that depend on the morphology / type of geological fault, for example pore density, Darcy percolation); Process, through at least one processor, the plurality of independent meshes according to previously selected options (static (x) / dynamic (x,t) cases - 2D / 3D, or mixtures thereof); transform, through at least one processor, the information of each mesh of the plurality of independent meshes into a plurality of generalized matrices (2D and / or 3D matrices) and a plurality of generalized vectors (2D and / or 3D), which also consider boundary conditions at the edges of the boundary Ω (according to the use of the Steklov-Poincaré operator); and obtain, from at least one processor, a plurality of vectors / matrices (tensors) of displacement, deformations and / or stresses throughout the interior volume / area (static / dynamic case - 2D / 3D), where the plurality of vectors / matrices represents the mechanical / dynamic condition of the rock mass for productive and safety decision-making with respect to the domain under study.

Images