Term 1: Tensile failure, fracture & fluid flow Flashcards
Hydraulic tensile failure
• 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)
Tensile stress on a Mohr diagram
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°
Tensile failure
- 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
Stress concentrations
- 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.
Stress concentration and crack shape
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»_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)
Griffith’s crack theory
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»_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 )
Griffith’s Crack Theory: Tensile stress field
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
Griffith’s Crack Theory: Compressional stress field
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
Microcracks, process & damage zones
- 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
Griffiths Fracture Criterion
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
Faults and fluids
- 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…
Fracture growth phenomena
- 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
Earthquakes & fluid flow
- 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
Fault valve model
- 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
Shear hydraulic fracture Mohr Circle conditions
Angle: 60
σ1 - σ3 = 8T
F lies on Coulomb Navier line