### 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 Y_{E}'(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.

Original language | English |
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Pages (from-to) | 607-619 |

Number of pages | 13 |

Journal | International Journal of Rock Mechanics and Mining Sciences |

Volume | 38 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

### ASJC Scopus subject areas

- Geotechnical Engineering and Engineering Geology

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## Cite this

*International Journal of Rock Mechanics and Mining Sciences*,

*38*(5), 607-619. https://doi.org/10.1016/S1365-1609(01)00022-3