Engineering Rock Mechanics

30 Stress

the subject of Chapter 4. The in situ stress field usually governs the
boundary conditions for the rock mechanics problem. A knowledge of
how the in situ stress field is then perturbed by changes in geometry (e.g.
excavating a tunnel) or direct loading (e.g. the foundations of a dam) is
crucial for engineering design. Understanding the fundamental nature
of rock stress is an essential prerequisite, and so the questions in this
chapter concentrate on this fundamental understanding.

3.2 Questions and answers: stress

43.1 Show how the stress state in a solid can be described via

the stress components (normal and shear) on an elemental cube

of rock. Also, show how these components are listed in the stress

matrix. What do the components in a row of the stress matrix have in

common? What do the components in a column of the stress matrix

have in common?

A3. 1 The components on an elemental cube are shown below.

Normal stress

Shear stress

L

7 0, -

4

z (middle finger)

Y (forefinger)

x (thumb)

Right-handed

co-ordinate

system

/

OYY

The components are listed in the stress matrix as follows:

I

I

I

Cxx % Txz __ The components in a row are the components acting

on a plane; for the first row, the plane on which a,,

I

The components in a column are the components acting in one

direction; for the first column, the x direction.

Note: There are several conventions for expressing the stress components. We have

used the most common notation in engineering rock mechanics, with u for normal stress

components and 5 for shear stress components, and with compressive stress positive. The

most important aspect is to understand the concept and manipulation of stress: these are

independent of the symbol convention used. With this understanding, any convention

can be used with equal facility. Similarly, if necessary one can learn to use the SI units

(Pa) and Imperial or 'British' units (lbf/in2) with equal facility: 1 MPa * 145 psi.