Transcript Slide 1
Stress and Deformation: Part I (D&R, 122-126; 226-252) The goal for today is to explore the stress conditions under which rocks fail (e.g., fracture), and the orientation of failure with respect to the principal stress directions. 1. Coulomb law of failure 2. Byerlee's law Experimental studies are fundamental in the study of rock failure Common types of deformation experiments Compressive strength tests: The Goal Compressive strength tests: The Approach #1 #2 #3 Compressive strength tests: The results Linear envelope of failure. The fractures form at angles of 25 to 35 degrees from s1- very consistent! Coulomb's Law of Failure sc = s0 + tanf(sn) sc = critical shear stress required for failure s0 = cohesive strength tanf = coefficient of internal friction (f = 90 - 2q) sN = normal stress Tensile strength tests with no confining pressure Approach: Similar to compressive strength tests Results: (1) Rocks are much weaker in tension than in compression (2) Fracture oriented parallel to s1 (q = 0) Tensile + Compressive strength tests Result: Failure envelope is parabolic 0 < q < 30 Failure envelopes for different rocks: note that slope of envelope is similar for most rocks sc = s0 + tanf(sn) sc = critical shear stress required for failure s0 = cohesive strength tanf = coefficient of internal friction sN = normal stress Example: calculating compressive failure for a limestone The effect of mean stress: The effect of differential stress Byerlee's Law Question: How much shear stress is needed to cause movement along a preexisting fracture surface, subjected to a certain normal stress? Answer: Similar to Coulomb law without cohesion Frictional sliding envelope: sc = tanf(sN), where tanf is the coefficient of sliding friction Preexisting fractures of suitable orientation may fail before a new fracture is formed What about pore fluid pressure? Increasing pore fluid pressure favors failure! -Also may lead to tensile failure deep in crust Effective stress = sn – fluid pressure What is it? What is it? Tensile fracture filled with vein during dilation s1 is parallel to the structure. What does this suggest about very low the magnitude of effective stress? What mechanism may help produce this structure within the deeper crust? high fluid pressure to counteract lithostatic stress What happens at higher confining pressures? Von Mises failure envelope - Failure occurs at 45 degrees from s1 Next Lecture Stress and Deformation II ...A closer look at fault mechanics and rock behavior during deformation ( D&R: pp. 304-319; 126-149) Important terminology/concepts Uniaxial vs. axial states of stress Coulomb law of failure: known how it is determined and equation q values for compression q values for tension Cohesive strength Coefficient of internal friction Byerlee's Law / frictional sliding envelope- know equation Important role of pore fluid pressure