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## Brittle deformation

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**Earth 238-20**Brittle deformation • *See chapter 6 of the Book “Earth Structure” http://www.uib.no/people/nglhe/Brittle%20deformation%2002.swf**Earth 238-20**Brittle deformation-definition • *Brittle deformation is nonrecoverable (the deformation • remains when the stress is removed). • -Brittle deformation= breaking, fracture. • -This is a permanent change in solid material due to the • growth of fracture and/or sliding on fracture surfaces. • At microscopic scale, brittle deformation corresponds to the • breaking of bonds between atoms or moleculs • *Brittle deformation mechanisms • Located in the first 10-15km of the crust • At the grain scale: • -Granular flow • -Cataclasis • -Frictionnal sliding**Earth 238-20**What is a fracture? • Fault • Relative movement parallel to the fracture surface • Fissure • Opening or aperture • Movement normal to the fracture surface • Joints • Fracture without visible offset • Parallel or perpendicular to the fracture offset**Earth 238-20**Experimental apparatus • Used to explore shear fracture development • Used to explore the tensile crack development**Earth 238-20**Tensile cracking (mode I) K1 is stress intensity factor st is far-field tensile stress Y is geometry of crack (dimensionless) c is half the length of the crack K1 = stY(p c)1/2 • *Favoured by low confining pressure • *Develop perpendicular to the strain axis • s3 and parallel to the s1 • *Can be formed by fluid overpressure s3 s3**Earth 238-20**Tensile cracking (mode I) Csr sr 3sr • *Strength paradox: remote stress gets concentrated at the side of • flaws inside the material.**Earth 238-20**Tensile cracking (mode I) C = 2a/c + 1 C: amount of stress concentration (parameter without dimension) a: long axis of the ellipse c: short axis of the ellipse • *The larger axial ratio is, the greater the stress concentration will be. • *Cracks or discontinuities (Griffith cracks) with high axial ratio will propagate first under stress.**Earth 238-20**Tensile cracking (mode I)**Earth 238-20**Shear fracture (Fault)**Earth 238-20**Shear fractures (mode II and mode III) • * Mode II fracture develop at 20 to 30° to the s1**Earth 238-20**Shear fractures (mode II and mode III) Experimentally determined by triaxial compression test. • In triaxial stress, the surrounding pressuresnis added. Ifsn is uniform (say the pressure of a gas or liquid), then the normal stresss = s1 - sn • sis referred to as differential stress or deviatoric stress s1 sn= s2= s3**Earth 238-20**Shear fractures (mode II and mode III)**Earth 238-20**Failure criteria • *Anderson theory of failure • -Related to Mode I and II fractures • -consequences: • relation between the geometry of fault and the associated stress • conditions. This is an angular relationship between shear fractures and • principal stress axis.**Earth 238-20**Failure criteria • *Coulomb’s failure criterion s = critical shear stress for failure to occur C = critical shear stress required to initiate slip along a plane oriented so that the normal stress that acts on that plane is zero (cohesion) n = normal stress across shear zone at instant of failure Ф = angle of internal friction ss = C + sntgФ ss = C + sntgФ**Earth 238-20**Failure criteria Failure envelope separates fields of “stable” and “unstable” stress state s s s n n n no failure (stable) Failure (brittle failure) impossible (unstable) • Failure envelops=straight lines which slope is μ=tgФ and C • is the intercept with the vertical axis • When s1-s3 (differential stress) is great enough to reach the failure envelops, the failure occurs.**Earth 238-20**Failure criteria Constructing failure envelopes -Experimentally determined by triaxial compression test with variable confining pressure by increasing the differential stress. -the shape of failure envelopes is dependant of the type of rocks**Earth 238-20**Failure criteria -further work by Otto Mohr on shear-fracture criteria showed that the straight line for Coulomb criterion is valid only for limited range of confining pressures… at lower confining pressures: curves to steeper slope at higher confining pressures: curves to shallower slope**Earth 238-20**Failure criteria For high confining pressures: plastic deformation begins • cannot have “failure” envelope…implies brittle • can approximate “yield” envelope…sample yields plastically two parallel lines that parallel n axis. known as Von Mises criterion which is independent of differential stress. s n**Earth 238-20**Failure criteria**Earth 238-20**Brittle deformation**Earth 238-20**Failure criteria • *Griffith’s failure criterion • -based on the assertion that a rock is never homogeneous. • In other words, rocks display always defects as pore or lattice • discontinuity. ss2 = 4T0sn-4(T0)2=0 T0: Uniaxial tensile strength of the rock • -Micro-discontinuities oriented parallel to the direction of maximum shear stress will grow faster than randomly oriented fractures. s n T0**Earth 238-20**Failure criteria**Earth 238-20**Failure criteria**Earth 238-20**Failure criteria *Frictional sliding criterion Because of friction, certain critical shear stress is required before sliding initiates on preexisting fracture Experimental data show that failure criterion for frictional sliding is largely independent of rock type s / n = constant Byerlee’s law s = 0.85 n s = 50 MPa + 0.6 n for n < 200 MPa: s = 0.85 n for 200 MPa < n < 2000 MPa: s = 50 MPa + 0.6 n**Earth 238-20**Role of fluids in fracturing What happens when fluid are present in the pores of a rock ? Hydrostatic pressure: Pf= ρ.g.h ρ : Density of water**Earth 238-20**Role of fluids in fracturing Compressive field Tensile field ss = C + (sn-pf)tgФ -s*n =sn-pf, called effective pressure -Increase in pore pressure moves the Mohr circle to the left. -When the circle reaches the envelop failure, the fracture occurs -Fluid pressure is equal in all the directions. The radius of Mohr Circle does not change.