Overview Page:

• Introduction
• Map3D Versions
• Overview
• Applications
• Model Building
• Boundary Element Formulation
• Documentation and course notes

Introduction

Map3D is a fully integrated three-dimensional layout (CAD), visualization (GIS) andstability analysis package (BEM stress analysis). Various program modules can be used to construct models, analyze and display stresses, strains, displacements, strength factors and probability of failure contours. Map3D is suitable for building and modelling rock and soil engineering design problems involving both irregular 3D massive excavations, tunnels and tabular shapes.

Models can include underground excavations, rock slopes, open pits, tunnels, fractures and surface infrastructure loads. The stress analysis models can simulate yielding (non-linear) zones of different moduli (e.g. stiff dykes or soft ore zones) and loads due to steady state thermal/fluid flow. Excavations can be intersected by multiple discrete faults (non-planar and gouge filled) that slip and open. Map3D can simulate ground support elements such as arches, steel sets, props, thick liners, chalks, backfill etc.

The program is designed for fast, easy building and visualization of 3D models:

• Self-contained 3D CAD system for model construction
• Integrated GIS for storing, analyzing and displaying geographical reference information
• Advanced boundary element (BEM) stress analysis

Map3D Versions

Map3D Modeller - 3D CAD and GIS visual database.

Display of these items can be filtered in various ways. The location of each point can be displayed as colour shaded spheres with size and colour scaled according to various combinations of parameters. Point magnitude density can be contoured on a plane according to user defined density functions. Contour planes can be user defined of fitted using automated linear-regression.

Map3D Results Viewer - viewing and analysis of stress analysis results.

Includes the GIS visual database but not the CAD system. 

• views stress analysis results generated by Map3D stress analysis codes
• displays contours on cutting planes, along lines and at specific points
• user defined contouring functions
• direct export to Excel for plotting x-y graphs
• display of 3D trajectories
• display of all stress, strain, displacement and strength parameters including principal components and resultant values on user defined planes and lines
• export in dxf and pnt format for compatibility with other CAD and display systems
• probability of failure contours
• safety factor contours
• light source shaded models
• topographical contours

Map3D Fault-Slip - elastic rock mass and fully plastic fault-slip stress analysis.

This module is used for conducting stress analysis of 3D models. This software is used for civil, geological and mining projects.

Includes the 3D CAD modeller, the results viewer and the GIS visual database.

The stress analysis utilizes the BEM (boundary element method) and has many features:

• the ability to analyze very large problem sizes (one million degrees of freedom)
• full 3D complex excavation shapes
• multiple elastic zones with different moduli (stiff dykes or soft ore)
• zones with different pre-mining stress states
• tabular mining with yielding pillars
• discrete non-planar fault planes that slip and dilate elasto-visco-plastically (including creep)
• cracks and fractures can be readily simulated including energy release rate and stress intensity calculations
• multiple mining steps are required to consider effects such as backfill placement or crack propagation
• automatic Boolean intersections allows for excavations, faults and fractures to cross and overlap
• automated discretization

A demonstration version of Map3D Fault-Slip is available at no charge. All features are available except the user is only permitted to run small size problems. This version is extremely useful for teaching the fundamentals of modelling, visualization and 3D CAD.

Map3Di Integrated Seismicity - superimpose external field loading effects into the stress analysis.

Includes all capabilities from Map3D Fault-Slip and adds field loading effects. The field loading effects can be imported from any database of thermal heating, fluid pressure, non-linear behaviour and deformations indicated by seismicity. These effects can be used to characterize 2D and 3D geologic features, accommodate changing lithology and incorporate seismic loading effects into the stress analysis.

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Overview

Map3D has the ability to simulate everything from simple tunnels and tabular shapes to detailed 3D excavation shapes and large scale mine wide problems. The difficulty users will encounter in model construction and interpretation depend on the amount of complexity required for the simulation at hand. While simple tabular models or single tunnels are fast and easy to construct in Map3D, complex three-dimensional problems are more difficult to work with and interpret.

Map3D has a completely self-contained CAD facility. One of the keys to the ease of use is model construction using either conventional surface elements or the built-in solid modelling technology. This permits users to build models using a series of three-dimensional building blocks. These blocks, which can be any desired shape or size, are used to construct excavations and accesses, as well as to define large or irregular shaped non-homogeneous zones (ore zones, dykes and yielding zones). All of the material outside the model boundary is assumed to be a solid host material.

The program automatically builds intersections between excavations, faults and multiple material zones. By coupling this capability with the built-in Boolean operations, complex multi-step mining sequences can be constructed with ease.

Special features have been implemented to allow fast construction of tabular mining shapes. The user need only specify the perimeter of each mining step and Map3D automatically builds the required elements. The perimeter does not necessarily have to be planar. In fact any bounding polyhedron of three-dimensional points are acceptable. Complex, multi-reef, non-tabular (rolling or offset) mining is readily simulated. Intersecting faults or three-dimensional dykes can be simulated.

The tabular mining can be extruded into 3D blocks then back into tabular mining if desired. This allows construction of detailed development to be completed very quickly. Also different parts of the model can be simulated using the tabular approximation while details can be obtained in areas of interest by using true 3D shapes.

Wireframe mine plan outlines and excavation geometries can be digitized from within Map3D or imported from several sources including AutoCAD-DXF and a universal ASCII PNT format. The user can interactively build a model comprising 3D blocks and planes using the built-in CAD capabilities of Map3D. Based on the geometric outlines or free-hand drawing, the user picks corners of blocks and planes to complete construction of the model. All of this is done graphically using the comprehensive set of tools available in the CAD interface.

A model comprises one or more connected or unconnected blocks and/or planes that can be mined and filled in a specified sequence. Surfaces of blocks and planes are subsequently discretized into a number of boundary elements by the program. Extensive error checking assists the user in identifying whether the geometry is topographically valid or not. The same input data can be used for elastic, thermal/fluid flow or non-linear analysis.

Analysis results can be contoured on element surfaces or on a series of used defined field point grid planes. These later planes can be positioned at any desired location and allow contouring of stresses, strains, displacements, strength factors or any desired combination of these components. Line contours and/or colour filled contours can be generated with options for labels, trajectories, transparency, grid lines and more.

Results can be exported in many formats including raster screen dumps, vector screen dumps or selected grid or surface locations with user configurable format.

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Applications

Map3D is suitable for building and display of any three-dimension geometric shape. Optional stress capabilities are designed for rock engineering problems involving both large tabular ore bodies and irregular 3D massive excavations.

The program is designed to be very versatile in its application. It has the ability to simulate everything from simple tabular shapes to detailed 3D excavation shapes and large scale mine wide problems. Models can include tunnels, large irregular shaped excavations, ore zones, massive and tabular excavations, open pits, faults, fractures and more. It is possible for excavations to the intersected by multiple faults or discontinuities that are allowed to slip or open. Problem size and complexity are only limited by the amount of detail the user wants to incorporate.

Map3D can simulate ground support elements such as arches, steel sets, props, thick liners, chalks, strong backfill etc. When simulating stiff support systems such as arches, steel sets, props, thick liners, chalks, strong backfill etc., it is necessary to model the ground movement up to the point of support placement, then insert the support elements either in a stress/strain free state, or with a prescribed pre-stressing. This feature is particularly useful for simulation of structural support elements and can accommodate placement, modification of properties and subsequent removal if desired. This option has been enabled for use with 3D FF blocks and DD planes.

To enable this feature you must first excavate the desired support element (either a 3D FF block or DD plane) to the desired pre-stressed state, then in a subsequent mining step insert the support material. Map3D conducts the necessary calculations to place support elements in a stress/strain free state or with a prescribed pre-stressing at the current mining step. The action of excavation to a zero or prescribed stress state followed by insertion of an alternate material signals Map3D to conduct the required calculations.

Map3D can be applied to the analysis of underground layout and mining sequence problems, as well as the assessment of pillar designs, stope span stability and fault stability. Depending on the version being used, non-linear material behaviour can be used when modelling pillars, seams and abutments.

There is also a facility to visualize point data. Points can be displayed as light source shaded spheres with diameter and/or colour varying as magnitude. Each point can be tagged with a series of numeric values (e.g. colour, magnitude, orientation etc.) keywords, text messages and file associations. Upon clicking on a point, the location, magnitude and text message are displayed. This feature can be used to display a database of useful geologic information such as grade, rock mass quality etc.

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Model Building

Map3D stress analysis is based on the Boundary Element formulation. With this method, one starts with an infinite homogeneous elastic medium (rock mass). The process of model building consists of making excavations and superimposing non-homogeneous zones (dykes, ore zones or yielding zones) and any faults or joints upon which slip may occur. Since one starts with an infinite medium, far field boundaries are automatically accommodated.

This is unlike domain formulations such as the Finite Element or Finite Difference methods, where one starts with empty space. For these latter methods, model building consists of assembling the entire rock mass and all its components. Elements must be assembled out to some far field boundary many diameters away from the excavations.

These fundamental differences make the boundary element method much more suitable and economic (in terms of analysis time) for rock mass problems.

There are several types of boundary elements available in Map3D:

• Fictitious force (FF) elements are used to specify the location of excavation surfaces and boundaries between regions with differing material properties.
• Displacement discontinuity (DD) elements are used to specify the location of joints, faults, fractures, pit walls and ground surface. These elements can intersect excavations at any location, since Map3D builds edge intersections internally.
• Inactive elements are used to construct excavation surfaces that can be displayed, but are not used in the stress analysis.
• Special proprietary boundary elements are incorporated for the thermal and non-linear analysis versions.

The objective of model building is to create a series of surface patches that when taken together, form a seamless, non-overlapping, continuous skin which describes the location of excavations, boundaries of regions with different moduli, faults etc. These surfaces must be further subdivided into smaller boundary elements where the actual influence functions are evaluated and solved. This approach is called surface modelling.

The user is free to construct surface models and supply this basic input data to Map3D. While this approach is ideal for describing ore outlines or as-built models, it has been found to be tedious and error prone when constructing mine layouts. In order to simplify model building, the program has a powerful pre-processor built into it that can accept and manipulate higher order three-dimensional entities. This approach is called solid modelling.

Solid modelling permits users to build models using a series of three-dimensional building blocks. These blocks, which can be any desired shape or size, are used to construct excavations and accesses, as well as to define non-homogeneous zones (ore zones, dykes and yielding zones).

The program automatically builds intersections between excavations, faults and multiple material zones. By coupling this capability with the built-in Boolean operations, complex multi-step mining sequences can be constructed with ease. Map3D creates the required surface description and automatically discretizes these surfaces into elements for the boundary element stress analysis.

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Boundary Element Formulation

Numerical modelling is an attempt to mathematically simulate the way the rock mass responds to mining. This is done by accommodating the effects of:

• Loading conditions - Prior to mining the rock mass is loaded by overburden and tectonic forces.
• Structural support elements - There may also be loads do to mechanical ground support, backfill, heating, etc.
• Geometry - When you make excavations, these pre-existing loads are redistributed around the excavations, concentrating in abutments and pillars. Stiff dykes and soft ore zones will also influence the response.
• Elasticity - At locations where the stresses do not exceed the strength, the rock deforms in a more or less elastic manner. This simply means that the deformations are relatively small in magnitude and are mostly recoverable.
• Non-linearity - At locations where the stresses are concentrated to the point where they exceed the strength, the rock will yield to these loads and deform. This means that the deformations can be relatively large in magnitude and are mostly non-recoverable. This can include the effects of fault slip, cracking and generalized 3D non-linear yielding.

How does numerical modelling work?

Numerical modelling achieves this simulation by using certain physical constraints on how the rock mass can respond:

• Equilibrium – Applied forces must always balance one another at all locations in the model. If you cut out a small cube of material and examine the stresses acting on this cube these stresses must be in equilibrium.
• Continuity – In the rock mass continuum, the mass of material must be maintained. You cannot have material disappearing or being created.
• Elasticity - At locations where the stresses do not exceed the strength, the rock deforms in a linear elastic manner: stresses varying in direct proportion to the elastic strains.
• Non-linearity - At locations where the stresses are concentrated to the point where they exceed the strength, the rock will yield to these loads and deform. Deformations are all allowed to proceed until the stresses relax down to the strength. This may be accompanied by some dilation. This can include the effects of fault slip, cracking and generalized 3D non-linear yielding.

Note that the equations of equilibrium and continuity are expressed as differential equations. What we need to do to solve these is to integrate them over the rock mass volume such that the appropriate boundary conditions are satisfied. There are many ways of accomplishing this. Boundary Element Methods integrate the equations analytically, and then use a numerical approximation to satisfy the boundary conditions. Finite Element Methods and Finite Difference Methods use a numerical integration scheme to integrate the differential equations. No matter which method is used, in the end they all use some sort of numerical approximation and you end up with a large set of equations that describes how various parts of the rock mass interact upon one another. In BEM the resulting equations appear as

s_surface = s_{far_field} + M P

where M is the set of simultaneous equations and P represents the loads or deformations that need to be applied to cause the stresses at the excavation surfaces to be zero. This constitutes a mathematical description of how the rock mass responds. All numerical models use some variation on this approach. These equations need to be solved simultaneously such the boundary conditions are satisfied. By solving these equations throughout the rock mass, along with the loading conditions and geometry, you conduct a "stress analysis".

Map3D is based on a very efficient Indirect Boundary Element Method (Banerjee and Butterfield, 1981), and incorporates simultaneous use of both fictitious force and displacement discontinuity elements. Special proprietary boundary elements are incorporated for the thermal and non-linear analysis versions. This Boundary Element formulation offers many advantages over other stress analysis techniques. Direct Boundary Element formulations require approximately twice the computational effort to assemble and solve the boundary element matrix, compared to the indirect method used in Map3D. Matrix lumping techniques are used to reduce the matrix size, and as a result, very large problems (more than 333333 elements - 1,000,000 degrees of freedom) can be accommodated on PC platforms. Without lumping, a 333333 element problem would take almost 4000 GB of disk space. With lumping, this can be reduced down to a few GB. This permits users to specify existing mining geometry in detail, and add new mining as required. This greatly reduces the effort required to set up and run analyses and permits the whole mine to be considered when necessary.

With the Boundary Element formulation, one starts with an infinite homogeneous elastic medium (rock mass). The process of model building consists of making excavations and superimposing non-homogeneous zones (dykes, ore zones or yielding zones) and any faults or joints upon which slip may occur. Since one starts with an infinite medium, far field boundaries are automatically accommodated. This is unlike domain formulations such as the Finite Element or Finite Difference methods, where one starts with empty space. For these latter methods, model building consists of assembling the entire rock mass and all its components. Elements must be assembled out to some far field boundary many diameters away from the excavations. While Finite Element and Finite Difference formulations are very well developed for non-linear problems such as plasticity, transient heat and fluid flow, and dynamic simulations, there are also very difficult to use and require very long run times. The difficulty in use comes from the large amount of information required to discretize the host rock mass. While this can be minimized by use of mesh generators and powerful front-end graphics, the cost and effort to learn the interface outweighs the simplicity with which the Map3D Boundary Element analyses can be conducted.

These fundamental differences make the boundary element method much more suitable and economic (in terms of analysis time) for rock mass problems.

Many of the supposed limitations of the boundary element method have been overcome in Map3D. The program can accommodate multi-step mining sequences and multiple material zones with different material properties and stress states. These zones are permitted to behave non-linearly. Multiple intersecting fault planes can slip and open according to user specified shear strength. Steady state thermal/fluid stress analysis can be simulated. The built-in solid modelling technology makes model construction very straightforward by building complex intersections internally. The discretization routines built into Map3D relieve the user of the burden of attempting to optimize the use of elements by automatically concentrating them only where results are requested. The internal lumping procedures reduce both matrix size and computational effort to a nearly linear dependence on problem size.

Documentation and course notes

Map3D is integrated with online context sensitive help. Help is available for all menu functions and toolbar buttons simply by right clicking on the item of interest. A complete description of each function along with a simple example is provided. Over 500 pages are devoted to this section. This is included with all versions of Map3D including the demo version.

A complete application manual is also included. This describes the fundamentals of how to setup and use Map3D, and includes several tutorials on model building. Over 100 pages are devoted to this section. This is included with all versions of Map3D.

Course notes are available that describe how to apply Map3D and interpret modelling results. This includes a thorough discussion of basic and advanced rock mechanics topics. This includes over 600 pages.