Name: Lab 3 -The Mohr Circle Pore Pressure, and Rock Strength PROBLEM 4-BARRE GR
ID: 287372 • Letter: N
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Name: Lab 3 -The Mohr Circle Pore Pressure, and Rock Strength PROBLEM 4-BARRE GRANITE In this exercise, we wish to demonstrate that Coulomb-Mohr analysis can be used to determine which fracture orientation is most favorable for slip. To do so, we create an experimental rock cylinder of Barre Granite with three fractures (saw cuts that have been slightly polished, Fig. 2). Fractures make angles of 45, 60 and 75" to respectively. We place the rock in a triaxial load machine, set the confining pressure at 150 MPa, and gradually increase the axial load until failure by sliding on a fracture occurs. -45 The granite sample fails by sliding on one of the fractures when the value the sample is jacketed, we cannot of o reaches a sufficiently high value. Because determine which fracture slipped until we remove the sample from the machine and strip off its jacket. In order to prove that the Coulomb-Mohr analysis correctly predicts steps of interpretation (Le, predict us Figure 4: Three pre- existing fractures in a cylinder of Barre Granite, the orientation of the slipped fracture, we first complete the following the differential stress at failure and predictall intersecting along a line which fracture failed first). that is perpendicular to the cylinder axis First, we attempt to predict the differential stress at the time of failure. We know that o, is 150 MPa, so we guess that the mean stress is at least 300 MPa. If this guess is correct, we can use the general friction equation (Equation 1: .-50 + 0.6 × .) to define the failure envelope for frictional sliding. 1. 1.a. According to the friction equation, what is the coefficient of friction ()? /0.5 1.b. Based on your previous answer, what is the slope of the frictional sliding envelope (p)1 " /05] 1.c According to the friction equation, what is the cohesive strength (C) of the Barre Granite? I /0.5 2. Construct a Mohr diagram showing this frictional sliding envelope. GEOL 314 Fall 2017 10/12Explanation / Answer
The friction equation gives the relation between shear stress (s) and normal stress (n):
s = C + tan * n
where C is the cohesive strength, which defines the inter-particle bonding in the rock mass (in this case, the Barre Granite)
is the slope of frictional sliding envelope
tan is the coefficient of friction (since, by equating the forces: µmgcos = mgsin, we get µ = tan)
The friction equation given in the question is s = 50 + 0.6 * n
Answer 1.a. The coefficient of friction, according to the given equation, is µ = tan = 0.6
Answer 1.b. The slope of frictional sliding envelope is = tan-1 (0.6) = 30.9
Answer 1.c. The cohesive strength of the Barre Granite is C = 50 MPa
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