Term 1: Tensile failure, fracture & fluid flow

Question 1

Hydraulic tensile failure

Answer 1

• To initiate a tensile fracture (horizontal in this case, represented by the pink surface), the pore fluid pressure needs to overcome:
– Tensile strength of the rock (i.e. “break the bonds”)
– Minimum principal stress (σ3)

Question 2

Tensile stress on a Mohr diagram

Answer 2

Tensile normal stresses are negative in geology

Can represent the tensile strength (T) on the negative, normal stress axis of a Mohr diagram

Concept of Effective normal stress: σ_n^’=σ_n-pfp

Tensile failure occurs at 2θ = 180°

Question 3

Tensile failure

Answer 3

• Tensile strengths vary for different materials
• Can calculate theoretical value for T based on atomic bond strengths
• But theoretical values are up to two orders of magnitude higher than observed T values

Question 4

Stress concentrations

Answer 4

• A key question is how and why does the stress field (i.e. magnitude & orientation of the principal stresses) vary within a volume of rock?
• Key issue here is that all natural materials are far from perfect: they contain large numbers of microdefects or flaws
• These fundamentally change their strength and the way in which stress concentrations occur – especially during tensile failure.

Question 5

Stress concentration and crack shape

Answer 5

For a circular crack in an ideal elastic material with an applied remote tensile stress (σ_r), the crack tip stress (σ_t) = 3σ_r

For a 3:1 elliptical crack (σ_t) = 7σ_r

More realistic shaped cracks are 100:1 (a&raquo_space; c) where (σ_t) > 200σ_r

The relationship between remote stress & crack shape/length is described by stress intensity factor (Ki)

The resistance of a pre-existing fracture to growth given by a critical threshold value Kic: fracture toughness (or critical stress intensity factor)

Question 6

Griffith’s crack theory

Answer 6

In order to explain observed weakness of solids, A.A.

Griffiths hypothesised that all solids contain millions of randomly-oriented cracks

Cracks are elliptical in cross-section (a&raquo_space; c) and generate large tensile stress in crack tip (σ_t)

So crack shape/length is important, but so is orientation of cracks relative to principle stresses (angle )

Question 7

Griffith’s Crack Theory: Tensile stress field

Answer 7

Griffiths cracks are open
For cracks normal to σ_3^’ ( = 90), σ_tis parallel to σ_3and has maximum value
Unstable tensile (Mode I) fractures propagate rapidly
Materials are very weak in tension

Question 8

Griffith’s Crack Theory: Compressional stress field

Answer 8

Griffiths cracks are closed
Cracks experience a shear stress
Tensile “wing cracks” are generated when θ > 45°
Wing cracks propagate slowly because σ_3^’ is compressional
Materials are stronger in compression than tension

Question 9

Microcracks, process & damage zones

Answer 9

• Griffith’s cracks exist: microcracks
• Develop in elliptical process zones ahead of a propagating fracture tips
• Leave behind a damage zone in rock volume surrounding fracture
• Fracture development can be associated with widespread dilantancy
• Major implications for the interactions between fracturing and fluid flow processes in the Earth

Question 10

Griffiths Fracture Criterion

Answer 10

Griffith’s crack theory predicts a parabolic failure envelope
Note scales and intercepts on σ_n and τ axes!
Cohesion S = 2T

Parabolic envelope makes accurate prediction for low & negative σ_n^’ values
Slope is too shallow in compression
Coulomb-Navier criterion gives better prediction for shear failure
Combine to give composite failure envelope

Question 11

Faults and fluids

Answer 11

• If faults were planar, fluid transport properties would be pretty uniform
• But natural faults are complex, segmented and linked due to the ways they grow & interact with other structures, some of them pre-existing
• Where would you expect fluid flow processes to be focussed in the example below?
• Fluid transport properties vary both in space
• Fluid transport properties also vary in time…

Question 12

Fracture growth phenomena

Answer 12

• Shear fractures cannot grow in their own plane & so develop tensile wing cracks along both Mode II and Mode III edges
• Focus fluid flow & mineralization here see as vein arrays
• Other termination & interaction features:
• Splays
• Horsetail splays
• Antithetic shears
• Jogs and relays

Question 13

Earthquakes & fluid flow

Answer 13

• It is well known that major hydrological changes follow modern earthquakes
• Associated with a whole range of large-scale geological phenomena such as:
• Liquefaction
• Formation of new springs
• Increased stream discharge
• Change in groundwater levels
• And we know that mineralization is widely associated with ancient fault zones
• So is fluid flow driven by active faulting or are faults driven by fluid pressures (or both)?
• Earthquake sequences are cyclic – stick-slip behaviour
• Therefore likely that pore fluid pressure and fluid flow events will also be cyclic – and correlated in time/space

Question 14

Fault valve model

Answer 14

• Periodic build-ups in fluid pressure trigger earthquakes
• Requires
• High pfp gradients (>10MPa/km)
• Focussed fluid source
• Local or regional impermeable barrier
• Once breached, fault must be an effective fluid channel way
• Fall in pfp leads to resealing

Question 15

Shear hydraulic fracture Mohr Circle conditions

Answer 15

Angle: 60
σ1 - σ3 = 8T
F lies on Coulomb Navier line

Question 16

Hybrid hydraulic Fracture Mohr Circle conditions

Answer 16

Angle between 60-90
F on latter end of parabolic failure envelope
σ1 - σ3 between 4 and 8 T

Question 17

Tensile hydraulic fracture Mohr Circle conditions

Answer 17

Angle: 90 degrees
σ1-σ3 = less than or equal to 4T
Curve lies on end of parabolic failure envelope