the shear stress (τ) is smaller than the frictional strength, which can be represented by this expression: μ(σ – ρ). The term (σ – ρ) is called the effective stress. The symbol μ represents the friction coefficient, a parameter that varies only in a narrow range, typically between 0.6 and 0.8 for most rock types. This condition for triggering slip, known as the Coulomb criterion, is discussed in more detail in Box 2.1 and Appendix G (see also Jaeger et al., 2007; Scholz, 2002).
The key parameters controlling the initiation of slip are therefore the normal and shear stresses acting on the fault as well as the pore fluid pressure (hereafter simply referred to as “pore pressure”). The normal and shear stresses on the fault depend on the orientation of the fault and on the state of stress in the rock. Due to the weight of the overlying rock and other processes in the Earth’s crust, rocks are usually under compression. The compressive normal stress acting on a rock at depth varies with direction; this variation of the normal stress with direction is linked to the shear stresses that are responsible for slip along a fault if the frictional resistance of the fault is overcome. In contrast, for a fluid at rest, the state of stress is hydrostatic: the normal stress is the same in all directions, and it cannot transmit any shear stresses.
The state of effective stress at a point in the Earth involves both the stress tensor and the pore pressure. The stress tensor is described by the vertical stress (σv) and the minimum and maximum horizontal stresses (σh and σH) that act in two orthogonal directions. The direction of σH, as well as the relative values of σv, σh, and σH, control the orientation of the fault most likely to slip; three different fault regimes are defined depending on the relative magnitude of σv, σh, and σH (Box 2.2). Once the most critical fault orientation has been identified, the normal and shear stresses acting on the fault can in principle be computed from the state of effective stress.
Determination of the in situ state of stresses in the subsurface is complex and often expensive. Consequently, the information on the in situ stress in the Earth is usually too fragmentary to allow confident estimates of the actual stresses acting on a fault. In most cases the only reliable information available is the magnitude of the vertical stress, as it can simply be estimated from the average density of the overlying rock and the depth. Estimating the general fault types and configurations as well as the broad orientation of the maximum and minimum horizontal stresses at a scale of tens or hundreds of kilometers is also sometimes possible, based on a variety of stress indicators (see also Figure 4 in Box 2.2).
In contrast to the difficulty of determining the maximum and minimum horizontal stresses and their orientations, the undisturbed initial pressure of the fluid permeating the rock and the fractures or faults can usually be reliably estimated from the depth of the rocks, under normally pressurized conditions. Techniques also exist for direct measurement of the pore pressure from a well.
Although the conditions for initiating slip on a preexisting fault are well understood, the difficulty remains to make reliable estimates of the various quantities in the Coulomb