In the vicinity of a borehole, the least-compressive horizontal stress is _h= -107 Pa, and the most compressive horizontal stress is _H= -2107 Pa. Shear failure of the rock can be described with a Coulomb model, with no cohesion, and with =1. The rock has zero strength in tension. The intermediate principal stress _ii is vertical.

(a) If you were to apply a Coulomb failure model, at what fluid pressure pf might you expect to first create new shear cracks in the borehole wall?

(b) Now you perform a hydrofracture experiment, and you dont see cracks opening up at this pf . Why is Coulomb failure a poor model for a hydrofracturing test in a borehole?

(c) At what value of pf might you first see cracks actually opening up in the borehole wall? Why?

(d) When the pumping pressure reaches the breakdown pressure, the flux of water into the hole increases dramatically, and it is difficult to raise the fluid pressure any further by further pumping. What is the value of the breakdown pressure? Explain in words what is happening in the rock surrounding the hole

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