Term 1 - Mohr circles, frictional sliding, pore fluid pressure, effective stress & hydraulic fracture

Question 1

Fractures

Answer 1

• Two main groups recognized in nature & laboratory experiments with predictable relationships to principle stresses
• Shear fractures (faults)
• Extension or tensile fractures (joints, fissures, veins, dykes..)

Question 2

“Andersonian” faults shear fractures

Answer 2

• Total angular offset of shear fractures from planes of τmax = φ = ‘angle of internal friction’

Question 3

Slip on a pre-existing fault

Answer 3

τf=S+μσn
Coulomb-Navier failure criterion describes the shear stress required to initiate a fault in previously intact rock
What about the state of stress required to initiate slip on a pre-existing fault?
Frictional sliding

• Frictional sliding on pre-existing fractures
  • Fault surfaces observed in outcrops commonly appear to be smooth / polished…but…
  • In reality, fault surfaces are characterised on all scales by interlocking asperities, which give rise to frictional resistance

Question 4

Experimental version: Byerlee’s Law

Answer 4

Expts show that at shallow depths (< approx. 10km), shear stress for frictional sliding on pre-existing faults is given by:

τ_f=0.85σ_n

At greater depths
τ_f=0.5+0.6σ_n

Holds for a wide range of rock compositions except those that contain water-rich clays
Note that once again prediction is that faults get stronger with depth

μs = 0.6-0.85

Question 5

Stick-slip vs. stable sliding

Answer 5

• At low confining pressures (<10km) there are two modes of frictional sliding behaviour:

Aseismic stable sliding, ideally at a constant rate with no further increase in stress
• In reality, often see a steady slip hardening due to slip zone damage, so increasing amounts of stress required
• Tends to be most common in uppermost parts of crust (<3km) where σn is lowest and/or in clay-rich fault zone gouges

Seismogenic stick-slip where slip happens during sudden slip events separated by periods of no slip where elastic strain energy builds up
• Release of this energy as frictional strength of fault is exceeded is what causes an earthquake.
• Magnitude of earthquake is related to the size of the associated stress drop
• Dominant at depths below 3km

Question 6

Earthquake occurance

Answer 6

• A 6.5-6.9 magnitude earthquake along a 15-20km long fault only produces ~1m of offset
• Largest quakes generate offsets of 10-15m
•  faults with km-scale offsets require v. large number of earthquakes
• Throw rates from large active faults are typically in the range 1-10mm/yr
• Different patches seem to slip during different events - complex accumulation of displacement over time despite simple overall displacement profile

Question 7

Cataclasites

Answer 7

• Indicative of faulting at the greatest depths within the brittle crust
• Distributed brittle deformation: ‘ductile’

Question 8

Pore fluids

Answer 8

pore spaces within crustal rocks are typically filled with fluids: water, hydrocarbons, magma
• The presence of such fluids can have a profound influence on the fracturing behaviour of rocks
• Under equilibrium conditions in a sedimentary basin, hydrostatic pressure = ρwatergh
• Lithostatic pressure = ρrockgh
• Pfp = 0.4 x lithostatic pressure assuming free fluid movement

Question 9

Overpressure

Answer 9

• Fluids can become overpressured, e.g. oil well data
• Two ways to induce overpressure:
– Restrict fluid movement, e.g. compaction of sediments
– Input new fluid, e.g. diagenesis/ metamorphism; migration of hydrocarbon or magma

Question 10

Drained vs. undrained triaxial experiments

Answer 10

• Triaxial compression tests
• Samples of clay saturated with pore fluid

Experiment 1: drained (pore fluid can escape)
• As pconf rises, σn rises and, as the fluids are able to leak off, the pfp remains constant: results are the same as for dry clay – ultimate strength rises with increasing depth

Experiment 2: undrained (pore fluid cannot escape)
• As pconf rises, σn rises, but as fluids are not able to leak off, pfp rises by an equal & opposite amount so the ultimate strength remains constant and μ = 0

Key point: it is the fluid pressure, not simply the presence of fluids, that influences the mechanical behaviour of rocks

Question 11

Concept of effective stress

Answer 11

Terzaghi (1923) introduced the concept of effective (normal) stress, σ_n’, where:
σ_n^’=σ_n-pfp

Pore fluids pressures effectively counteract σ_n

hus we can modify the Coulomb-Navier failure criterion to account for pfp
τ_f=S+μσ_n’

Question 12

Hydraulic fracturing of ‘fresh’ rock

Answer 12

• Pore fluid pressure counteracts the normal stresses

* The apparent reduction in normal stress results in failure

Question 13

Ancient hydraulically-induced fractures

Answer 13

• Dykes/sills

* Veins

Question 14

Modern hydraulically-induced frictional sliding

Answer 14

• Landslides

Question 15

“Fracking”

Answer 15

Hydraulic fracture stimulation (“fracking”) of shale gas reservoirs works on the same principle!
τ_f=0.85σ_n’ where
σ_n^’=σ_n-pfp