Page 279 - Physical Principles of Sedimentary Basin Analysis

8.2 Friction 261

hanging wall
hanging wall
footwall
footwall
(a) strike-slip fault (b) normal fault (c) reverse (thrust) fault
Figure 8.1. Three types of faults.

τ f
σ n

σ
n
τ f
Figure 8.2. The friction stress τ f acts in the fault plane as a result of the (compressive) normal stress
σ n when the fault blocks slide against each other.

N

F = −R
R

Figure 8.3. The friction force R that resists sliding is proportional to the normal force N, with a
coefficient that does not depend on the area between the block and the surface.

where μ is the coefficient of friction. This relationship is Amontons’ law.Itisthesame
law as for the friction of a block sliding along a surface, which says that the friction is
proportional to the normal force (the weight of the block), see Figure 8.3. The coefficient
of proportionality between the friction force and the normal force does not depend on the
area of contact, because both forces relate to the same area. Dividing the forces by the area
of contact then gives Amontons’ law.
Byerlee (1977, 1978) found that the crust is characterized by a coefficient of fric-
tion μ ≈ 0.85 for normal stress less than 200 MPa. At larger depths the friction stress
is estimated as τ f ≈ 0.6σ n + 60 MPa. This specific version of Amontons’ law

0.85σ n σ n ≤ 200 MPa
τ f = (8.2)
0.60σ n + 60 MPa σ n > 200 MPa
is called Byerlee’s law, and it applies to a wide range of rocks.