Structural modelling tools

4.4.1 Solid modelling

Three-dimensional solid modelling of the structural geology using a commercially available modelling system such as Vulcan™, DataMine™, Gemcom™ or MineSite™

has become routine at most mine sites and design offices.

Like the geological model, the first step is to compile the entire field mapping and core drilling structural data (sections 2.2 and 2.4) into a geological plan of the pit. The plan is then incorporated into a 3D solid geological model using one of the modelling systems mentioned above.

Mapped data from Autocad are usually imported as DXF files so that the geologist can connect the structural or other geological boundary traces and build on those traces in 3D to make modelled shapes or triangulations. Once the triangulations are made it is easy to cut them to pit shells or into sections.

Figures 4.22 and 4.23 illustrate typical steps in this process. Figure 4.22 shows a sequence of normal faults intersecting a mapped ore body from the east (near side) to the west (far side) inside the proposed ultimate pit shell and above planned underground workings. Figure 4.23 shows major structures mapped from available drill hole and pit mapping data intersecting a proposed ultimate shell.

4.4.2 Stereographic projection

4.4.2.1 General guidelines

Structural modelling is an exercise in 3D geometry requiring the application of descriptive geometry or

Figure 4.22: 3D solid model of an ore body (dark red) intersected by a sequence of normal faults Source: Courtesy Argyle Diamonds

trigonometry. A number of tabular and graphical aids can help construct these solutions (Badgley 1959), but they are often difficult to manipulate in three

dimensions. The stereographic projection method provides the neatest solution to this difficulty.

Historically the method was used mainly by

crystallographers and mineralogists, but it was brought into prominence in structural geology during the 1950s by Phillips (1960). Although out of print, the Phillips publication remains the definitive stereographic projection textbook. A comprehensive outline of stereographic solutions is also given in Ragan (1985) and more recently in Lisle and Leyshon (2004). A number of basic techniques for use in slope stability engineering problems are presented in Wyllie and Mah (2004). It is vital to remember that in geotechnical engineering applications of the stereographic projection, the lower half of the hemisphere is used.

The main attraction of the stereographic projection is that it is easy to use. It can quickly provide solutions to complex geometric problems in the field or the office, and is an ideal tool for plotting and contouring sets of

structural data. Because of its power and flexibility, it is recommended as the basic tool for all open pit structural modelling analyses. It is easily adapted to computer

solutions and has been incorporated into a number of commercial software packages. Probably the best-known of these and certainly the most widely used in the open pit mining industry is the Rocscience Inc. program DIPS™

(Rocscience 2003), which is used illustratively in a number of figures in sections 4.2 and 4.5.

4.4.2.2 Blind zones

As outlined in section 2.4.9.6 the occurrence of structures that have low angles of intersection (a) with the drill hole raises the issue of blind zones.

All too frequently the occurrence and effect of blind zones are ignored or unrecognised when the structures in an open pit are being modelled. Most commonly they are created when the investigation drill holes along one side of the pit are angled back into the wall. Terzaghi (1965) noted that the only way to overcome their effect is to drill a sufficient number of drill holes so oriented that no structural pole can lie in or near the blind zone of each hole. An appropriate layout for a single cluster of three holes was for each hole to plunge at 45°, with the

orientation of the trace of each hole differing by 120° from that of the other two. A structure of any orientation would be intersected by at least one of these holes at an angle (a) equal to or greater than about 31°.

Figure 4.23: Major structures intersecting a proposed ultimate pit shell Source: Courtesy BHP Billiton, Nickel West

4.4.2.3 Terzaghi correction for joint spacing When the spacing of joints are measured from drill hole core (or along an outcrop scanline), the number of observations of joints of any one set is a function of the angle of intersection (inclination) between that set and the axis of the drill hole. Specifically, the number of

intersection with a drill hole of given length decreases as the angle of inclination decreases such that:

Na= Lsind a (eqn 4.1) where

a = inclination of the joints to the drill hole d = the spacing between the joints

L = the length of the drill hole

Na = the number of joints intersected by the drill hole.

Hence, in a vertical drill hole, Na ranges between L/d for horizontal joints, of which a is 90°, and zero for vertical joints, of which a is zero (Terzaghi 1965).

No adequate correction can be made for joints with low angles of a. If a group of variously oriented drill holes is available, Terzaghi (1965) suggested that:

■ it is generally advisable to disregard the poles of joints with an angle of inclination (a) of less than 20–30°

because joints of the same set, if abundant, will be intersected at a higher angle by one or more of the other holes;

■ data from the group of holes will provide a better basis for estimating the spacing of such joints.

4.4.2.4 Terzaghi weighting

The Terzaghi correction can also be used to establish an indication of the relative proportions of structures where a single drill hole or scan line orientation creates a bias in the structural orientation data. In this case, the relative proportions or weighting of the individual structures intersected in the scanline/hole(s) can be assessed through the equations:

R´ (true density of joint population) = 1/d =

1/d´ sina = d´ coseca (eqn 4.1)

W (weighting applied to individual pole for

the density calculation = (1) coseca (eqn 4.2) where:

a = angle between plane and the drill hole or scan line

d = the true spacing of the fractures

d´ = apparent spacing along the drill hole or scan line

Since the weighting function tends to infinity as alpha (a) approaches zero, a maximum limit for this weighting must be set to prevent unreasonable results. This maximum limit corresponds to a minimum angle, which is typically set between 5° to 25°, and normally 15°.

Because the effect of applying the Terzaghi weighting to some data distributions can be quite marked, it is important to understand the weighting procedure before applying it.

4.4.3 Discrete fracture network modelling

Discrete fracture network (DFN) modelling explicitly represents how the faults and joints recognised by the structural model are spatially distributed within the rock mass. This feature has made it an important tool in helping to visualise how the rock mass deforms and slope failure mechanisms develop, particularly when the failure involves sliding along the major structures and fracture across the intact blocks of rock (rock bridges) left between these structures. Other important uses include estimating block size distributions for fragmentation analyses and determining flow conditions in hard rock masses.

The DFN modelling packages most commonly referred to in the literature include:

■ FracMan (Golder Associates Inc. 2007);

■ JointStats (Brown 2007);

■ 3FLO (Billaux et al. 2006);

■ SIMBLOC (Hamdi & du Mouza 2004).

The FracMan suite of DFN modelling tools was developed and released by Golder Associates Inc. in 1986.

It was initially developed for mining and civil engineering applications and has been widely used in oil and gas and environmental projects, including radioactive waste management. More recently it has been applied to slope stability and tunnelling problems, in situ fragmentation prediction and groundwater management.

JointStats software was developed by the Julius

Kruttschnitt Mineral Research Centre (JKMRC), University of Queensland, as part of the International Caving Study research and technology transfer program (Brown 2007).

The original software accepts standard structural data from a face mapping or drill hole scanline but as part of the LOP project it has been enhanced to deliver a structural and a rock mass material properties database that enables data uncertainty to be assessed and confidence limits

determined for specified data and/or attributes from within a single geotechnical domain. Milestones in this program included expanding the existing JointStats database to include quantitative measures of rock mass parameters and structural data collected using digital techniques.

3FLO was developed by Itasca Consultants S.A.

(France) primarily for the hydrogeological analysis of fractured media. The code is capable of generating its own DFN and has many features similar to the standard Itasca codes, including the built-in programming language FISH.

FracMan, JointStats and 3FLO base their modelling on the random disc model where the size of the circular discontinuities is defined by the discontinuity radius and the locations are determined by a stochastic process,

usually the Poisson process (Brown 2007). In SIMBLOC, the discontinuities are assimilated to flat discs. Each set is simulated independently of the others and the disc centres are generated in space using a uniform distribution law.

The orientation of the discs is simulated following the mean and standard deviations of the distribution law that fits the actual field measurements. The radius of the disc is estimated from the trace length distribution. The joint intensity is calculated on the basis of the mean linear frequency and the radius distribution. Known applications of this code have been related mainly to block size distribution.