Mecanica De Rocas

4

Shear strength of discontinuities
4.1

Introduction

All rock masses contain discontinuities such as bedding planes, joints, shear zones and
faults. At shallow depth, where stresses are low, failure of the intact rock material is
minimal and the behaviour of the rock mass is controlled by sliding on the
discontinuities. In order to analyse the stability of this system of individualrock blocks,
it is necessary to understand the factors that control the shear strength of the
discontinuities which separate the blocks. These questions are addressed in the discussion
that follows.
4.2

Shear strength of planar surfaces

Suppose that a number of samples of a rock are obtained for shear testing. Each sample
contains a through-going bedding plane that is cemented; in otherwords, a tensile force
would have to be applied to the two halves of the specimen in order to separate them. The
bedding plane is absolutely planar, having no surface irregularities or undulations. As
illustrated in Figure 4.1, in a shear test each specimen is subjected to a stress σn normal to
the bedding plane, and the shear stress τ, required to cause a displacement δ, is measured.
Theshear stress will increase rapidly until the peak strength is reached. This
corresponds to the sum of the strength of the cementing material bonding the two halves
of the bedding plane together and the frictional resistance of the matching surfaces. As
the displacement continues, the shear stress will fall to some residual value that will then
remain constant, even for large shear displacements.Plotting the peak and residual shear strengths for different normal stresses results in
the two lines illustrated in Figure 4.1. For planar discontinuity surfaces the experimental
points will generally fall along straight lines. The peak strength line has a slope of φ and
an intercept of c on the shear strength axis. The residual strength line has a slope of φr.
The relationship between thepeak shear strength τp and the normal stress σn can be
represented by the Mohr-Coulomb equation:
τ p = c + σ n tan φ
where

c is the cohesive strength of the cemented surface and
φ is the angle of friction.

(4.1)

Shear strength of planar surfaces

61

Figure 4.1: Shear testing of discontinuities

In the case of the residual strength, the cohesion c has dropped to zero and therelationship between φr and σn can be represented by:

τ r = σ n tan φr
where

(4.2)

φr is the residual angle of friction.

This example has been discussed in order to illustrate the physical meaning of the term
cohesion, a soil mechanics term, which has been adopted by the rock mechanics
community. In shear tests on soils, the stress levels are generally an order of magnitude
lowerthan those involved in rock testing and the cohesive strength of a soil is a result of
the adhesion of the soil particles. In rock mechanics, true cohesion occurs when cemented
surfaces are sheared. However, in many practical applications, the term cohesion is used
for convenience and it refers to a mathematical quantity related to surface roughness, as
discussed in a later section. Cohesion issimply the intercept on the τ axis at zero normal
stress.
The basic friction angle φb is a quantity that is fundamental to the understanding of the
shear strength of discontinuity surfaces. This is approximately equal to the residual
friction angle φr but it is generally measured by testing sawn or ground rock surfaces.
These tests, which can be carried out on surfaces as small as 50 mm × 50mm, will
produce a straight line plot defined by the equation :

τ r = σ n tan φb

(4.3)

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Chapter 4: Shear strength of discontinuities

Figure 4.2: Diagrammatic section through shear machine used by Hencher and Richards (1982).

Figure 4.3: Shear machine of the type used by Hencher and Richards (1982) for
measurement of the shear strength of sheet joints in Hong Kong granite....