Figure G-35b is a map showing the Johnson Valley Fault in southern California. This is a right-lateral strike-slip fault that lies a short distance to the north of the San Andreas Fault zone. On June 28, 1992, one of the largest earthquakes in recent decades occurred on the Johnson Valley Fault, a magnitude 7.5 event named the ‘‘Landers earthquake’’. This large earthquake presumably released shear stress that had accumulated over a long period of time on the Johnson Valley Fault.

Some geologists have suggested that such an accumulation of shear stress on faults can be prevented by injecting water into the fault zone. By increasing the pore pressure, blocks on opposite sides of the fault are permitted to slip continuously past one another, rather than lurching episodically.

Determine the pore pressure required for a fault slip to occur on the Johnson Valley Fault. Regional σ₁ in this area is oriented 007°, and estimated to be 10 MPa; μ is 0.4 (Stein et al., 1992). Assume σ₃ to be 6 MPa. (Because the rocks are already fractured, draw your failure envelope with straight lines that meet at the origin of the graph, as in Fig. 13.14.)

Figure G-35b

Os -20 MPa -10 -10 -20 10 = 0.81 = 39 State of stress Ion fault 20 30 40 Failure envelope for Weber Sandstone with pre-existing fractures 50 On 60MPa Mohr circle at zero pore pressure 20 b 10 Os 20 MPa +10 +10 -20 10 20 30 Mohr circle of effective stress 40 50 On 60MPa Fig. 13.14 Mohr circles and failure envelope for Weber Sandstone at Rangely, Colorado. (a) Assuming zero pore pressure. (b) Mohr circle of effective stress after the injection of 27 MPa of fluid pressure, which triggered a series of earthquakes. The earthquakes ceased when the Mohr circle of effective stress was moved 3.5 MPa to the right.