TY - JOUR

T1 - Time-dependent closure of a fracture with rough surfaces under constant normal stress

AU - Matsuki, K.

AU - Wang, E. Q.

AU - Sakaguchi, Kiyotoshi

AU - Okumura, K.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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.

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U2 - 10.1016/S1365-1609(01)00022-3

DO - 10.1016/S1365-1609(01)00022-3

M3 - Article

AN - SCOPUS:0035386396

VL - 38

SP - 607

EP - 619

JO - International Journal of Rock Mechanics and Minings Sciences

JF - International Journal of Rock Mechanics and Minings Sciences

SN - 1365-1609

IS - 5

ER -