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Memo to Russ Means 2 November 14, 2007 <br />Bulkhead Cost Estimate File No. M-2007-044 <br />where: H =hydrostatic head (feet) <br />~„ =water density (62.4 pounds per squaze foot) <br />p =pressure head (psi) <br />Potential for HvdrofracinQ at the Proposed Main Bulkhead <br />The bulkhead must by constructed at a depth below ground surface that will provide sufficient overburden <br />pressure to prevent hydrostatic pressure from the impounded water hydrofracing the rock surrounding the <br />bulkhead. The hydrostatic pressure at which hydrofracing will occur is the formation breakdown pressure. <br />Intentional hydrofracing of rock from within drill holes is frequently undertaken by the petroleum industry <br />for the purpose of stimulating oil well production, and as a result has been intensively studied and is well <br />understood. In oil field applications, formation breakdown pressure (BP) is a function of (1) the tensile <br />strength of the rock immediately adjacent to the drill hole, (2) the in situ stress field in the plane <br />perpendicular to the drill hole, and (3) the pore pressure present in the formation. Bredehoeft, et al (1973) <br />presented the following equation for breakdown pressure: <br />Bo = T, + (3 x S„o„) - 5,,,,x - Pf <br />where: Bp =breakdown pressure <br />TS =tensile strength <br />Sm;,, =minimum stress normal to the drill hole <br />S,„~ =maximum stress normal to the drill hole <br />Pf=formation pore pressure <br />all terms in psi <br />The equation can be simplified for the case of hydraulic pressure on a mine bulkhead. The tensile strength <br />can be assumed to be zero because the adit wall rock is jointed and is fractured by blasting, and the pore <br />pressure in and near adit wall rock must be low and can be assumed to be zero. A simple assumption is that <br />hydrostatic stress conditions are equal to the overburden stress. This assumption is generally conservative <br />since the overburden stress must be present and the more general stress state measured is for the horizontal <br />stresses to equal or exceed the overburden stress. Normal formation breakdown pressures encountered in <br />oil field work range from 1.4 to 2.8 times the overburden stress, indicating that the hydrostatic stress <br />assumption where the breakdown pressure equals two times the overburden stress is not unreasonable. This <br />analysis yields the following simplified breakdown equation: <br />B <br />Sob 2 <br />where: S°a =overburden stress in psi <br />