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EPS116 Chapter Summary 2011

Adam Casias and Tyler Seaman

Edited by: James Dabalos 2013

8.1 Experimental fracturing of Rocks

Failure: sample is unable to support an increase in stress without permanent deformation

Brittle failure: occurs with the formation of a brittle fracture, surface or zone across which material loses cohesion

Ductile failure: occurs when material deforms permanently without losing cohesion

Pore fluid pressure: confined isostatic pressure of water in the pore spaces of rocks causing internal stress on the material

Extension fractures: the fracture plane is perpendicular to the minimum principal stress σ3 and parallel to the maximum principal stress σ18.2 A Fracture Criterion for Tension Fractures

Tensile strength (To): the amount of stress in the extensional direction where thematerial fractures

Tension fracture envelope: (σn* = T0)on a Mohr diagram, the boundary between stable and unstable states of tensile stress

Fracture plane angle (αf): angle b/n the max principal stress σ1 and the fracture

Fracture angle (θf): angle b/n the max principal stress σ1 and the normal to the fracture plane

8.3 Coulomb Fracture Criterion for confined compression

Coulomb fracture criterion: the critical shear stress |σ*s| is equal to a constant c (cohesion) plus the tangent of the slope angle  of the line times the normal stress σn

|σ*s| = c + µσn where µ = tan

Cohesion(c): resistance to shear fracture on a plane across which the normal stress is zero

µ: Coefficient of internal friction :angle of internal friction

Riedel shears: (secondary shears) are “synthetic”, having the same sense as the imposed shear and are oriented about 15 degrees from the plane of imposed shear. The shears are not parallel to the imposed direction of shearing.

8.4 Effects of confining pressure on fracturing and frictional sliding

*Coulumb fracture criterion does not apply in the tensile part of the Mohr diagram

von Mises criterion: on a Mohr diagram, it consists of a pair of parallel lines of constant shear stress symmetric about the normal stress axis; implies that ductile deformation begins at a critical shear stress

Amontons’ second law of friction: the critical shear stress for frictional sliding is proportional to the normal stress

Stable sliding: at low confining pressure, frictional sliding occurs as a smooth, continuous motion

Stick-slip behavior: compressive stress across the sliding surface increases with increasing confining pressure. Characterized by “stick” intervals of no motion alternating with “slip” intervals of sliding

8.5 Effects of pore fluid pressure on fracturing and frictional sliding

where

Hydrostatic pore fluid pressure (pf) and vertical lithostatic normal stress (σv) are found at depth

Pf = ρwgh and σv = ρrgh

Where density of water = 10^3 kg/m^3 and that of sediment is 2.3 * 10^3 kg/m^3

8.6 Effects on fracturing of anisotropy, the intermediate principal stress, temperature and scale

Mechanically isotropic: rocks have the same mechanical properties in all directions

Mechanically anisotropic: strength is different in different directions

Increased temperature causes increased ductility of material.

Larger the scale, more heterogeneous your system. There are flaws such as joints and faults.

8.7 Limitations of the coulomb fracture criterion

This is only a two dimensional version of a more general criterion, it is missing the third dimension of stress.

8.8 Griffith theory of fracture

Griffith cracks: All solids contain a myriad of microscopic to sub-microscopic randomly oriented cracks

References & Resources

Robert J. Twiss, Eldridge M. Moores, Structural Geology 2nd edition, (W. H. Freeman), p. 209-230, 2006

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EPS116 Chapter Summary 2011

Adam Casias and Tyler Seaman

Edited by: James Dabalos 2013