Kiyohiko Okumura

Time-dependent closure of a fracture with rough surfaces under constant normal stress

Abstract Time-dependent closure of a fracture with rough surfaces subjected to stepwise normal stress was considered theoretically by viscoelastic modeling of rock. A formula for the relationship between constant normal stress and time-dependent closure as a function of time was derived based on the aperture distributions of a fracture and the relaxation modulus YE′(t) of rock. Theoretical consideration showed that the ultimate closure of a fracture under constant normal stress can be estimated from the normal stress–elastic closure curve by using the values of the relaxation modulus at t=0 and ∞, and that the ultimate time-dependent closure is independent of the normal stress if the elastic closure is linear with the logarithm of the normal stress. Experiments and a Monte Carlo simulation on time-dependent closure under constant normal stress were conducted for a hydraulic fracture created in granite in the laboratory to provide the verification of the theory. The results obtained in the experiments showed that the ultimate time-dependent closure of a hydraulic fracture was almost independent of the normal stress when the elastic closure was linear with the logarithm of the normal stress. A Monte Carlo simulation on time-dependent closure of a fracture under constant normal stress showed that time-dependent closure of a fracture for which the elastic closure is linear with the logarithm of the normal stress does not depend on the normal stress because the increase in contact area during time-dependent closure increases with the normal stress.

The effects of driving pressure and traverse rate on the depth of cut for slot cutting in rocks with high-speed waterjets. A study on the slot cutting in rocks with high-speed waterjets both in air and in water (1st Report).

In order to evaluate the applicability of high-speed waterjets technology to slot cutting in rocks from economic point of view, it is necessary to predict the depth of cut of an objective rock for various cutting conditions. The depth of cut is influenced by the cutting parameters such as driving pressure, traverse rate, standoff distance and nozzle diameter in addition to the mechanical properties of the rock.In this paper systematic experiments were carried out both in air and in water for five rocks including mortar to know the effects of both driving pressure up to 98.1 MPa and traverse rate up to 198mm/min.Main results obtained in this study are summarized as follows:1) There exists a critical-driving pressure below which no cutting occurrs for both in air and in water.2) The depth of cut in water is often greater than that in air when driving pressure is sufficiently large and traverse rate is small enough except granite. This is due to the cavitation errosion in water.3) The depth of cut h can be expressed by the following equation as a function of driving pressure p and traverse rate V for both in air and in water.h=A1V-n (p-pc)where Pc is a critical pressure, A1 and n are coefficients.4) The critical pressure is less dependent on the traverse rate in the range of this study and increases almost linearly with tensile strength of rocks.5) The coefficient n is almost independent of the mechanical properties of rocks but depends mainly on the environmental medium.