Open Pit Mine Planning and Design, Two Volume Set & CD-ROM Pack, Third Edition, 3rd Edition

CHAPTER 4

Geometrical considerations

4.1 INTRODUCTION

The ore deposits being mined by open pit techniques today vary considerably in size, shape,

orientation and depth below the surface. The initial surface topographies can vary from

mountain tops to valley floors. In spite of this, there are a number of geometry based design

and planning considerations fundamental to them all. These are the focus of this chapter.

By way of introduction consider Figure 4.1 which is a diagrammatic representation of a

volume at the earth’s surface prior to and after the development of an open pit mine.

The orebody is mined from the top down in a series of horizontal layers of uniform

thickness called benches. Mining starts with the top bench and after a sufficient floor area

has been exposed, mining of the next layer can begin. The process continues until the bottom

bench elevation is reached and the final pit outline achieved. To access the different benches

a road or ramp must be created. The width and steepness of this ramp depends upon the type

of equipment to be accommodated. Stable slopes must be created and maintained during the

creation and operation of the pit. Slope angle is an important geometric parameter which

has significant economic impact. Open pit mining is very highly mechanized. Each piece of

mining machinery has an associated geometry both related to its own physical size, but also

with the space it requires to operate efficiently. There is a complementary set of drilling,

loading and hauling equipment which requires a certain amount of working space. This

space requirement is taken into account when dimensioning the so-called working benches.

From both operating and economic viewpoints certain volumes must or should, at least, be

removed before others. These volumes have a certain minimum size and an optimum size.

It is not possible in this short chapter to try and fully cover all of the different geometrical

aspects involved in open pit mine planning and design. However, the general principles

associated with the primary design components will be presented and whenever possible

illustrated by examples.

4.2 BASIC BENCH GEOMETRY

The basic extraction component in an open pit mine is the bench. Bench nomenclature is

shown in Figure 4.2.

290

Geometrical considerations 291

Figure 4.1. Geometry change in pit creation.

Each bench has an upper and lower surface separated by a distance H equal to the bench

height. The exposed subvertical surfaces are called the bench faces. They are described by

the toe, the crest and the face angle α (the average angle the face makes with the horizontal).

The bench face angle can vary considerably with rock characteristics, face orientation and

blasting practices. In most hard rock pits it varies from about 55

◦

to 80

◦

. A typical initial

design value might be 65

◦

. This should be used with care since the bench face angle can

have a major effect on the overall slope angle.

Normally bench faces are mined as steeply as possible. However, due to a varietyof causes

there is a certain amount of back break. This is defined as the distance the actual bench crest

is back of the designed crest. A cumulative frequency distribution plot of measured average

bench face angles is shown in Figure 4.3.

The exposed bench lower surface is called the bench floor. The bench width is the distance

between the crest and the toe measured along the upper surface. The bank width is the

horizontal projection of the bench face.

There are several types of benches. A working bench is one that is in the process of being

mined. The width being extracted from the working bench is called the cut. The width of

the working bench W

B

is defined as the distance from the crest of the bench floor to the new

292 Open pit mine planning and design: Fundamentals

Crest

Bench Width

Toe

Toe

Bench Height

Crest

Bank Width

H

H

∝ (Face Angle)

Figure 4.2. Parts of a bench.

100

80

80

60

60

40

40

20

20

0

Bench Face Angle

(deg.)

Cumulative Percent

(less than)

(85 Data Points)

Figure 4.3. Cumulative frequency distribution of mea-

sured bench face angles (Call, 1986).

toe position after the cut has been extracted (see Fig. 4.4). A detailed calculation of cut and

working bench dimensions is found in Subsection 4.4.5. After the cut has been removed, a

safety bench or catch bench of width S

B

remains.

The purpose of these benches is to:

(a) collect the material which slides down from benches above,

(b) stop the downward progress of boulders.

During primary extraction, a safety bench is generally left on every level. The width varies

with the bench height. Generally the width of the safety bench is of the order of

2

/

3

of the