1Fracturing and Brittle FailureGeol341/342Outline•Review• 3D Mohr Circles• States of Stress• Stress and deformation• Brittle failure envelope• Fluid Pressure and fracturing• Modes of FracturingStress Ellipsoidσ1 > σ2 > σ3Stress componentsMagnitude of Normal and Shear Stressesσ1σ3NormalShear2General Stress Equationsσn= ½ (σ1 + σ3) + ½(σ1- σ3) cos 2Θ(eq. 3.7)σs= ½(σ1- σ3) sin 2Θ (eq. 3.10)Θ= angle between plane and σ3 or between normal to the plane and σ1+ counterclockwise, - clockwiseMohr Circle of Stressσn= ½ (σ1 + σ3) + ½(σ1- σ3)cos2Θσs= ½(σ1- σ3) sin 2ΘMean StressDeviatoric StressCommon States of StressTriaxial StressUniaxial Stress σ2= σ3= 0Biaxial Stress σ3=0Hydrostatic PressureIsotropic StressAnisotropicStressStrain is caused by deviatoric stressStress TrajectoriesStress Measurements• Earthquakes• Fault sets• Hydraulic fracturing of wells– Borehole break outs– Drilling-induced fractures3World Stress MapOvercoring in minesDrillholeStrain GageStrain GageBrittle DeformationCh. 6• How rock breaks• Fractures, cracks, faults, veins, joints, etc• Dominant deformation near the Earth’s surface (top ~15 km)• EarthquakesOnce a fracture exists deformation continues by frictional sliding or cataclastic flowFailure= rupture of atomic bonds4Role of HolesStress Concentration around holesC=2(b/a)+1Stress field around a holeσ3σ1Microscopic flaws control the macro strengthFormation of Shear Fracturesσ3σ15Role of Fluid