Misoriented fault reactivation: A comparison with theoretical principles

While a detailed deliberation of the mechanics of fault reactivation is beyond the scope of this thesis, having been examined in depth elsewhere [Jaeger, 1959; Sibson, 1985,

137

1990b; Hill and Thatcher, 1992; Jaeger et al., 2007], the following overview provides context for the discussion.

In the brittle regime, potential for fault reactivation, as opposed to fault initiation, can be assessed, to a first order, by comparing the parameters of cohesion and coefficient of friction between the fault zone and surrounding rock mass. Within the intact rock samples, conditions of failure can be defined by:

𝜏𝑓 =𝐶+𝜇𝜎𝑛′ = 𝐶+𝜇(𝜎𝑛− 𝑃𝑓) 1

where 𝜏_𝑓 is the critical shear strength, 𝐶 is the cohesive strength of the rock, 𝜇 is the coefficient of internal friction and 𝜎_𝑛′ is effective normal stress given by (𝜎_𝑛− 𝑃_𝑓), where is 𝜎_𝑛 is normal stress and 𝑃_𝑓 is the pore fluid pressure, where present [Hubbert and Rubey, 1959]. In the case of re-shear along an existing cohesionless fault, failure strength is broadly defined by Amontons’ law:

𝜏 =𝜇𝑠𝜎𝑛′ = 𝜇𝑠(𝜎𝑛− 𝑃𝑓) 2

where 𝜇_𝑠 is the coefficient of static friction. These equations have been used to define a failure envelope for both the intact Fontainebleau sandstone and the pre-ground sliding surfaces (Fig. 25). A coefficient of internal friction of 1.17 is estimated for the intact rock failure of Fontainebleau sandstone; this value falls outside the typical range for most intact rocks (0.5 < µ < 1) [Hoek, 1965; Jaeger et al., 2007]. The cohesive strength of the intact rock is estimated to be ~81MPa based on the intersection point of the shear failure envelope with the y-axis. However, it is likely that, as confining pressure is reduced, the failure criterion deviates from the linear Coulomb relationship (see Appendix 5). Under laboratory conditions, maximum cohesive strength values for sandstones and granites have been estimated to between 20-30MPa [Handin et al., 1963; Jaeger et al., 2007] and possibly represent a more realistic strength approximation. A decrease in the cohesive strength of ~9MPa is observed for new faults forming after frictional lock-up. For the pre-ground sliding surfaces, the estimated coefficient of static friction is 0.54, assuming that these faults are cohesionless at the time slip. This value is lower than the experimentally-determined friction coefficients of Byerlee [1978] that indicate friction coefficients of sliding surfaces usually lie within the range 0.6 < μs < 0.85. However, the coefficient of static friction is consistent with

Reactivation of Misoriented Faults

138

If it is assumed, for the current suite of experiments, that the existing fault plane contains the σ2 axis, stress conditions for the reactivation of faults oriented at varying

angles to the maximum principal stress, can be defined in terms of the ratio of the effective principal stresses as [Sibson, 1985]:

𝑅 = 𝜎_𝜎1′

3′=

(1 +𝜇𝑠𝑐𝑐𝜕𝜃𝑟)

(1− 𝜇𝑠𝜕𝑡𝑡𝜃𝑟)

3

where R is the effective stress ratio, 𝜃_𝑟 is reactivation angle defined as the angle of the fault relative to the orientation of the maximum principal stress. A fault can be defined as being optimally-oriented for reactivation (𝜃_𝑜𝑎𝑡) when R has a minimum positive value and is calculated by:

𝜃𝑜𝑎𝑡 = 0.5𝜕𝑡𝑡−1(1⁄𝜇𝑠) 4

[Sibson, 1974]. As θr increases or decreases away from θopt the effective stress ratio

increases (Fig. 26), ultimately approaching infinity and causing lock-up at 2θopt. In order

to achieve fault reactivation under such conditions, either 𝜎₁′ → ∞ or 𝜎₃′ →0, as

𝑃𝑓 → 𝜎3. Where θopt < θr < 2θopt, faults are referred to as ‘misoriented’, whereas faults

with orientations greater than 2θopt is regarded as ‘severely-misoriented’. For θr > 2θopt

reactivation can only be achieved if the effective minimum principal stress is tensile (Pf

> σ3) [Sibson, 1985, 1990a]. This analysis indicates that the optimal angle for fault

reactivation for the current suite of experiments is ~31°, and that frictional lock-up should occur at ~62°. These estimates are consistent with the experimental observations that fault reactivation occurs for θr up to 60°, and that failure on a new optimally-

oriented fault occurs for θr = 65°.

The current suite of experiments highlights the point that there can be major differences in the shear strength during intact rock failure and reactivation of an existing optimally- oriented fault. Although part of this difference is related to the high cohesive strength (~81MPa) of intact rock, an important result is that the coefficient of internal friction (~1.17) is substantially higher than the coefficient of static friction (~0.54) associated with fault reactivation. The resulting differences in shear strengths have a significant impact on the relative ease of reaction of misoriented faults versus nucleation of new intact rock failure.

139

Figure 25: Failure envelopes and theoretical analysis of the mechanical results.

(A) Failure and reactivation envelopes for stress-driven deformation events. Data points represent shear and normal stress values at failure or fault reactivation. The slope of the associated failure/reactivation envelope (assuming a Mohr-Coulomb relationship) represents either the coefficient of internal friction for rock failure (1.17) or the coefficient of static friction for fault reactivation (0.54). The intercept of the envelope with the y-axis provides an indication of the cohesive strength of the sample. A second failure envelope is also shown for the data generated upon failure of the new optimally-oriented fault after lock up of the existing fault (indicated by the purple line). Normal stress and shear stress values of two severely misoriented (frictionally locked) faults are plotted in green. These points lie very close to the estimated failure envelope for intact rock. (B) Shear stress and normal stress data from the fluid-driven failure and fault reactivation experiments are plotted alongside the failure envelopes defined by the stress- driven failure/reactivation data. Note the good fit with the existing envelopes.

Reactivation of Misoriented Faults

140 Figure 26: Conditions for the reactivation of existing faults.

The effective stress ratio for the reactivation of cohesionless faults plotted as function of the reactivation angle [after Sibson, 1985], for experimental sliding surfaces where μs = 0.54. The low frictional value of

the experimental faults (compared with the typical range for experimental faults [Byerlee, 1978] increases

the range of fault orientations that can theoretically be reactivated prior to frictional lock-up, encompassing experimental faults inclined from θr = 25-60º to the cylinder axis. The orientation of θopt is

shown for both fault reactivation (solid line) and intact rock failure (dashed line). Schematic sample

cross-sections show the orientation of the formation of new faults in intact rock where μ = 1.17 and the

optimal and lock-up angles of faults where μs = 0.54.