Page 140 - Reservoir Geomechanics

123 Rock failure in compression, tension and shear

a small amount. Once the Mode I fracture starts to grow, the strength of the rock in
tension is irrelevant.
Unlike compressional strength, tensile strength does not seem to be dependent on
simple effective stress, especially in low-porosity/low-permeability rocks. Schmitt and
Zoback (1992) demonstrated in the laboratory with granitic rocks that pore pressure act-
ing in rocks had less of an effect on reducing the tensile stress at which failure would be
expected. They attributed this effect to dilatancy hardening –asfailure was approached
the creation of micro-cracks in the incipient failure zone causes pore pressure to locally
drop, thereby negating its effect on strength. It is not known how significant this effect
is in higher-porosity rocks.

Shear failure and the frictional strength of rocks

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
= µ (4.39)
σ n
where τ is the shear stress resolved onto the sliding plane. The role of pore pressure
of frictional sliding is introduced via σ n , the effective normal stress, defined as (S n −
P p ), where S n 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 friction µ i , 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, that µ in equation (4.39) describes slip on a pre-existing fault
whereas µ i 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.