# Features

- Full three-dimensional and tabular stress analysis
- Elastic, plastic, non-linear, creep and thermal/fluid flow options
- Fault slip, fracture analysis and large displacement block movements
- Simulation of stiff dykes, weak schist zones, structural support and backfill
- Completely self-contained CAD including DXF import and export
- Practically unlimited problem sizes
- Boolean intersection solid model building
- GIS graphics database - Seismic display and analysis
- Fast OpenGL graphics

## Full three-dimensional and tabular stress analysis

- Map3D is a fully three-dimensional boundary element program allowing for simultaneous use of both FF (fictitious force) and DD (displacement discontinuity) element types.
- FF elements are used to define the location of excavation surfaces and the boundaries of alternate material zones.
- 3D alternate material zones can include materials with differing material properties (stress state, stiffness and strength parameters) and are thus useful for simulation of soft "schist" zones, stiff dykes and backfilled zones.
- Map3D Non-Linear has the capability to simulate non-linear yielding of these 3D zones.
- Map3D Visco-Plastic has the capability to simulate plastic yielding of these 3D zones.
- DD elements are used to simulate fractures, fault slip surfaces and tabular mining.
- DD elements can be filled with alternate materials making them useful for simulation of fault gouge, non-linear fault slip, yielding tabular pillars and backfilled (hyperbolic model is included) tabular zones.
- Map3D Fault-Slip has the capability to simulate non-linear yielding of these DD zones.
- Multi-step analysis allows for simulation of progressive mining including backfill and structural support placement.
- Since FF and DD elements can be used simultaneously, complex fault slip interactions with 3D excavations can be analyzed. This capability is also useful for studying the interaction of fractures around boreholes or other excavation shapes.

## Elastic, plastic, non-linear, creep and thermal/fluid flow options

- Map3D is based on the assumption of an infinite homogeneous elastic host rockmass. Non-homogeneous features are readily added to this.
- 3D alternate material zones are added by defining the surface of such zones using FF elements.
- Within each zone the material can be assigned differing elastic properties, initial stress state, and strength properties.
- In Map3D Non-Linear and Map3D Visco-Plastic, these zones are permitted to yield. This yielding is controlled by use of a Bingham flow model which allows for simulation of creep and relaxation.
- Explicit time stepping is simulated by use of the multi-step analysis feature. This is useful for simulation of yielding pillars, abutments, structural supports and backfilled zones.
- Fractures and slip planes are added by defining such zones using DD elements.
- These zones are permitted to crack, slip and yield.
- As above, each zone can be assigned differing elastic properties, initial stress state, and strength properties with yielding controlled by use of a Bingham flow model. This is useful for simulation of fault slip and wedge failures.
- Map3D Thermal-Fluid Flow has the added capability to simultaneously solve the coupled steady state thermal or fluid flow problem. The complete flow and temperature or head distribution is solved. This can be directly coupled to the stress analysis through a coefficient of thermal expansion or effective stress in the case of fluid flow.

## Fault slip, fracture analysis and large displacement block movements

- The DD (displacement discontinuity) elements used in Map3D are fully capable of simulating discrete slip and crack opening.
- Faults are permitted to intersect excavations and other faults enabling simulation of jointed rock masses with a limited number of discrete structures.
- DD elements can be used to describe any desired shape thus allowing one to model non-planar fractures, bending or waving fault planes and the intersection with other similar features.
- Filling the DD elements with alternate materials allows for simulation of fault gouge and non-linear fault slip with complete closure control. Multi-step analysis allows for simulation of progressive mining and fracture propagation.
- Since DD elements satisfy rigid body motion requirements, large displacement block movements can also be considered. This includes the simulation of blocks sliding on planes under external or gravity loading and is useful for simulation of wedge failures along convoluted 3D slip surfaces.
- Since FF and DD elements can be used simultaneously, complex interactions with 3D excavations can also be analyzed.

## Simulation of stiff dykes, weak schist zones, structural support and backfill

- Alternate material zones can be defined as either 3D or planar features. By specifying the material in these zones to be stiffer, softer, weaker etc., a variety of problems including stiff dykes and weak schist zones can be modelled. Map3D Fault-Slip can simulate non-linear yielding in planar zones. Map3D Non-Linear has the capability to simulate non-linear yielding of these 3D zones.
- The multi-step mining feature in Map3D permits excavation and placement of materials at any desired time in the mining sequence. 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 capability of Map3D is particularly useful for simulation of structural support elements and backfill, 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.

## Completely self-contained CAD including DXF import and export

- Map3D has a completely self-contained CAD facility (Map3D Modeller). 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.
- Special features have been implemented to allow fast construction of tabular (CAD > Build > DDLoop) and three-dimensional (CAD > Build > FFLoop) 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.
- Multiple floor plans or sections can be traced then automatically linked together into 3D zones to represent excavations or alternate material zones.
- 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.
- The same input data can be used for elastic, thermal/fluid flow or non-linear analysis.

## Practically unlimited problem sizes

- One of the features that sets Map3D apart from other stress analysis programs is its ability to handle very large problem sizes. For small problems involving only a few excavations and perhaps a single intersecting fault, models limited to 10000 nodes can provide results with reasonable accuracy. However, it is not uncommon to encounter problems with many thousands, or even hundreds of thousands of components (including excavation surfaces, alternate material zone boundaries and intersecting faults). For such models, accurate results can only be obtained for model sizes approaching 1,000,000 nodes or more.
- Map3D is currently set up to accommodate problems with a maximum of 8,000,000 nodes, i.e. 24,000,000 degrees of freedom (it can be configured for larger models if required). This is accomplished by use of matrix lumping. Through analysis of the geometric relationships between various parts of the model, sections of the coefficient matrix are lumped together thus reducing the matrix size. In physical terms this means that finely discretized zones that are far apart do not need to be represented in detail and hence are candidates for lumping. The amount of lumping that is permitted is controlled by user specified parameters thus easily allowing this feature to be limited or completely disabled if desired.
- In a typical boundary element model with n nodes, a coefficient matrix is generated with 3 degrees of freedom per node. Since all elements influence one another, the coefficient matrix is of size 3n x 3n = 9n² coefficients. Allowing 4 bytes for each coefficient, problems with 1,000,000 nodes would require many tera-bytes of storage without matrix lumping. Even if you had this storage capacity, it would take too long to solve such a matrix.
- The matrix lumping procedures in Map3D can reduce storage requirements by 100 fold or more for large problems bringing our 1,000,000 node problem down to a much more reasonable size on the order of Gigabytes, a readily solvable size. In addition, discretization can be optimized by setting a few control parameters to automatically concentrate elements at locations of interest. These capabilities give Map3D the unique ability to solve realistic size problems on a desktop computer.

## Boolean intersection solid model building

- 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.
- Map3D 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. Intersecting faults or three-dimensional dykes can be simulated.

## GIS graphics database - Seismic display and analysis

- This option (Map3D Modeller) enables visualization of 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.) and a text message. Upon clicking on a point, the location, magnitude and text message are displayed on the status bar. This feature can be used to display a database of useful geologic information such as grade, rockmass quality etc.
- Point data can be contoured on a plane to display density etc. A linear regression routine is included for plane fitting to the data.

## Fast OpenGL graphics

- Map3D features fast, accurate graphics display through the implementation of OpenGL.
- For optimal performance you will need a graphics adapter that supports 3D T&L (translation and lighting) with on board hardware. An OpenGL driver must be installed. Users should see approximately 100 fold display rate increase over non-hardware assisted displays.
- For users without T&L graphics hardware, Windows can emulate OpenGL functionality through software emulation. Even though there will be no increase in display rate, the graphics display will be more accurate due to z-buffer hidden surface removal.

#### Map3D International Ltd

Rock Mechanics and Stress Analysis for the Mining, Civil and Geomechanics Industries.

#### Why Use Map3D

Map3D has been developed specifically for mining applications from the ground up. The program is designed to allow you to get high accuracy answers quickly, in order that you can get on with the engineering instead of the modelling. Large complex problems can be built easily either with Map3D’s own CAD interface or outside the program then imported in a variety of different formats.

No other program can handle the analyses that Map3D can in the time (run pre & post processing time), cost (may times cheaper) and ease (Map3D can be used on site for routine analyses).

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