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

Time-dependent closure of a fracture with rough surfaces subjected to stepw ise normal stress was considered theoretically by viscoelastic modeling of rock. A formula for the relationship between constant normal stress and tim e-dependent closure as a function of time was derived based on the aperture distributions of a fracture and the relaxation modulus Y-E'(t) of rock. Th eoretical consideration showed that the ultimate closure of a fracture unde r constant normal stress can be estimated from the normal stress-elastic cl osure curve by using the values of the relaxation modulus at t = 0 and infi nity, and that the ultimate time-dependent closure is independent of the no rmal stress if the elastic closure is linear with the logarithm of the norm al stress. Experiments and a Monte Carlo simulation on time-dependent closu re under constant normal stress were conducted for a hydraulic fracture cre ated in granite in the laboratory to provide the verification of the theory . The results obtained in the experiments showed that the ultimate time-dep endent closure of a hydraulic fracture was almost independent of the normal stress when the elastic closure was linear with the logarithm of the norma l stress. A Monte Carlo simulation on time-dependent closure of a fracture under constant normal stress showed that time-dependent closure of a fractu re 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 contac t area during time-dependent closure increases with the normal stress. (C) 2001 Elsevier Science Ltd. All rights reserved.