Slip on faults is important in a number of geomechanical contexts. Slip on faults can shear well casings and it is well known that fluid injection associated with water flooding operations can induce earthquakes, for reasons explained below. As will be discussed in Chapter 12, some stress paths associated with reservoir depletion can induce normal faulting. Chapter 11 discusses fluid flow along active shear faults at a variety of scales.
In this chapter we discuss the frictional strength of faults in order to provide constraints on the magnitudes of principal stresses at depth.
Friction experiments were first carried out by Leonardo da Vinci, whose work was later translated and expanded upon by Amontons. Da Vinci found that frictional sliding on a plane will occur when the ratio of shear to normal stress reaches a material property of the material,µ, the coefficient of friction. This is known as Amontons’
law τ σn
=µ (4.39)
whereτ is the shear stress resolved onto the sliding plane. The role of pore pressure of frictional sliding is introduced viaσn, the effective normal stress, defined as (Sn − Pp), where Sn is the normal stress resolved onto the sliding plane. Thus, raising the pore pressure on a fault (through fluid injection, for example) could cause fault slip by reducing the effective normal stress (Hubbert and Rubey 1959). The coefficient of friction,µ, is not to be confused with the coefficient of internal frictionµi, defined above in the context of the linearized Mohr–Coulomb criterion. In fact, equation (4.39) appears to be the same as equation (4.3), with the cohesion set to zero. It is important to remember, however, thatµin equation (4.39) describes slip on a pre-existing fault whereasµi is defined to describe the increase in strength of intact rock with pressure (i.e. the slope of the failure line on a Mohr diagram) in the context of failure of an initially intact rock mass using the linearized Mohr–Coulomb failure criterion.
Because of his extensive research on friction (Coulomb 1773), equation (4.39) is sometimes referred to as the Coulomb criterion. One can define the Coulomb failure function (CFF) as
CFF=τ−µσn (4.40)
When the Coulomb failure function is negative, a fault is stable as the shear stress is insufficient to overcome the resistance to sliding,µσn. However, as CFF approaches zero, frictional sliding will occur on a pre-existing fault plane as there is sufficient shear stress to overcome the effective normal stress on the fault plane. Again, the CFF in this manner presupposes that the cohesive strength of a fault is very small compared to the shear and normal stresses acting upon it. As will be illustrated below, this assumption appears to be quite reasonable.
As mentioned above, equation (4.39) predicts that raising pore pressure would tend to de-stabilize faults and encourage slip to take place by raising the ratio of shear to normal stress on any pre-existing fault. While there have been many examples of seis- micity apparently induced by fluid injection in oil fields (see the review by Grasso 1992), two experiments in the 1960s and 1970s in Colorado first drew attention to this phenomenon (Figure 4.22) and provided implicit support for the applicability of Amon- tons’ law/Coulomb failure to crustal faulting. A consulting geologist in Denver named David Evans pointed out an apparent correlation between the number of earthquakes occurring at the Rocky Mountain Arsenal and the volume of waste fluid being injected into the fractured basement rocks at 3.7 km depth. Subsequently, Healy, Rubey et al.
(1968) showed there to be a close correlation between the downhole pressure during injection and the number of earthquakes (Figure 4.22a). The focal mechanisms of the earthquakes were later shown to be normal faulting events. This enabled Zoback and Healy (1984) to demonstrate that the magnitudes of the vertical stress, least principal stress and pore pressure during injection were such that equation (4.39) was satisfied and induced seismicity was to be expected for a coefficient of friction of about 0.6 (see below). A similar study was carried out only a few years later at Rangeley, Colorado (Figure 4.22b) where water was being injected at high pressure in an attempt to improve production from the extremely low permeability Weber sandstone (Raleigh, Healy et al. 1976). In this case, it could be seen that a downhole pressure of 3700 psi (25.5 MPa) was required to induce slip on pre-existing faults in the area, as predicted by equation (4.39) (Zoback and Healy 1984).
As mentioned above, friction is a material property of a fault and Byerlee (1978) summarized numerous laboratory experiments on a wide variety of faults in different types of rock. He considered natural faults in rock, faults induced in triaxial compression tests and artificial faults (i.e. sawcuts in rock) of different roughness. His work (and that of many others) is summarized in Figure 4.23 (modified from Byerlee 1978). Note that for an extremely wide variety of rock types, Byerlee showed that at elevated effective normal stress (≥ ∼10 MPa), friction on faults is independent of surface roughness,
Average monthly pressure at bottom of arsenal well (in bars) 320 330 340 350 360 370 380 390 400 410
60
40
20
1962 1963 1964 1965 1966 1967 1968
Number of Denver earthquakes, per month, of magnitude 1.5 or greater Pressure
Quak es
ONDJFMAMJJ ASONDJFMAMJ JASONDJFMAMJ JASONDJ FMAMJJASONDJFMAM
0 50 100 150 200
Number of earthquakes Monthly downhole pressure, psi
1000 2000 3000 4000 5000
1969 1970 1971 1972 1973 1974
Fluid injection
Fluid withdrawal
Fluid injection
a.
b.
Figure 4.22. (a) Correlation between downhole pressure and earthquake occurrence during periods of fluid injection and seismicity at the Rocky Mountain Arsenal. Modified from Healy, Rubey et al.
(1968). (b) Correlation between downhole pressure and earthquake occurrence triggered by fluid injection at the Rangely oil field in Colorado. After Raleigh, Healy et al. (1976).
0 20 40 60 80 100
Shear stress, t (MPa)
Maximum friction
SLO PE = 1.0
t = 0.85 sN
SLOPE
= 0.6 E X P L A N TAT I O N
10 30 50 70 90
0 20 40 60 80 100
Normal stress, sN (MPa)
10 30 50 70 90
Figure 4.23. Rock mechanics tests on wide range of rocks (and plaster in a rock joint)
demonstrating that the coefficient of friction (the ratio of shear to effective normal stress) ranges between 0.6 and 1.0 at effective confining pressures of interest here. Modified after Byerlee (1978).
normal stress, rate of slip, etc. such that the coefficient of friction is found to be within a relatively small range:
0.6≤µ≤1.0 (4.41)
This relation is sometimes known as Byerlee’s law. In fact, John Jaeger, perhaps the leading figure in rock mechanics of the twentieth century, once said: There are only two things you need to know about friction. It is always 0.6, and it will always make a monkey out of you.