The Mechanics of Rock Failure Due to Water Jet Impingement
Authors: Forman S.E. , Secor G.A. 
Published: December 2007

Abstract
The initiation of fracture in a rock mass subjected to the impingement of a continuous water jet has been studied. The jet is assumed to place a quasistatic pressure loading on the surface of the rock, which is treated as a saturated, porous-elastic, isotropic, and homogeneous half-space. While this pressure loading is held constant, the impinging water flows through the rock according to Darcy's law and pressurizes the fluid in the pores. The pore pressure distribution couples with the stress field due to the surface loading to produce an effective stress field, which can start tensile fracturing directly under the load. At various time intervals after initial impingement, the effective-stress field is computed using finite element methods and the results, together with the Griffith criterion for tensile failure, produce the loci of the zones of fracture initiation. The behavior of these zones is displayed as a function of the two jet parameters - pressure and nozzle diameter - and the five rock properties: Young's modulus, Poisson's ratio, tensile strength, porosity and permeability, and time. To experimentally verify that pore pressure plays an important role in the mechanism of rock fracture due to jet impingement, thin sheets of copper (0.001 to 0.005 in.) were placed between a continuous jet (up to 20,000 psi) and the surface of a block of Indiana limestone. The purpose of the copper sheet was to allow the pressure of the jet to be transmitted to the rock, but to prevent water from entering the pore structure. Using pressure substantially greater than the threshold pressure of pressure substantially greater than the threshold pressure of limestone (3,500 psi) where penetration always occurred in the absence of the copper sheet, placement of the sheet was sufficient to prevent any visible damage from occurring to the rock surface, provided the jet did not penetrate the copper first. provided the jet did not penetrate the copper first

Introduction
The method by which a water jet penetrates and fractures a rock mass is highly complicated and poorly understood. This is mainly because the rock is subjected during the impact to several separate processes, each of which can cause failure. Failure can result from the effects of dynamic stress waves, static pressure loading and erosion. The degree of failure caused by each mechanism is, of course, dependent on the rock properties and jet parameters. parameters. In the first few microseconds of impingement, a subsonic jet pressure on the rock surface reaches the so-called "water hammer" pressure on the rock surface reaches the so-called "water hammer" pressure of pvv(c) and then drops to the nozzle stagnation pressure pressure of pvv(c) and then drops to the nozzle stagnation pressure of approximately 1/2 pv2. (p = fluid density, v = jet velocity, and v(c) = velocity of compression waves in the liquid.) During this initial period of impact, large-amplitude compressive waves are caused to emanate from the point of impingement. Upon reflection off a free surface, these waves become tensile and can cause spalling failures. This mode of failure is usually important with pulsed jet impingement. For continuous jets the spalling effects are small and will be neglected for this study. During the impingement process, the water of the jet flows into the accessible pore space of the rock mass. Since in a continuous jetting process the jet applies a quasi-static pressure loading to the rock surface, the water in the pores is pressurized while the surrounding rock mass is simultaneously stressed. The intent of this paper is to describe the role played by this static pressure loading coupled with the pore-pressure distribution, or pressure loading coupled with the pore-pressure distribution, or the "effective stress," in the first moments of penetration. In studying the process, we will take into account the influence of jet parameters and rock properties. In the course of the impingement process, the jet pressure loading is constantly being redistributed over the crater as it is formed. During this progressive removal of material, erosion is also contributing. The process of erosion is in itself highly complex, so no attempt will be made to characterize it here.

EFFECTS OF STATIC PRESSURE DISTRIBUTION-ZERO PORE PRESSURE
It has been shown by Leach and Walker that a water jet emanating from the nozzle depicted in Fig. 1 applies a quasi-scatic pressure loading to the surface upon which it is impinging.
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