A numerical model based on time-dependent degradation law was applied in the paper to simulate thetime-dependentdamageand deformationofrock materialsunderconstantstresslevels. An empiricalrelationbetweendegradationofmaterialpropertiesandappliedstressisusedto simulatethe mechanical behavior of each elementoffinite element model. The time-dependent degradationlawofmaterialisusedatthescaleofeachelementtosimulateitsdamage. In modeling, an element is damaged by decreasing its Young's modulus or strength to simulate the effectoflocaldamageatmicroscopicscales. Elasticinteractionsbetweenelementsand heterogeneity of material properties lead to the emergence of a complex macroscopic behavior. In particular, the primary and tertiary creep regimes associated respectively with a degradation and increase of the rate of strain, damage event and energy release were observed in the simulations. Damage localization emerges at the transition between primary and tertiary creep, when damage rate starts accelerating. This model can reproduce the three creep regimes and associated damage evolutionofrock,whichisofgreathelptoinvestigatetime-dependentinstabilityfailure mechanisms of rock mass and to prevent associated rock hazards in rock engineering.


The time-dependent behavior of rock material is one of fundamental mechanical properties of the rocks, which is important in designing the underground mines, as well as predicting the long-term stability for rock engineering structures such as nuclear waste repository. The study of the deformation and fracture of rocks under creepis one of the main problems in rock mechanics.

Threeregimesareusuallyobservedduringcreep experiments: primary creep or transient creep (decreasing strainrate),secondarycreeporsteady-statecreep (constant strain rate), and, for large enough stress, tertiary creeporacceleratingcreep(increasingstrainrate), endingbyfailure(Lockner,1993a;Boukharovetal., 1995; Chen et al, 1997). During primary creep, the strain rateusuallydecreasesasapowerlawofthetimesince thestresschange. Thisexperimentallawwasfirst observedfor metalsandthenfor manyother materials, suchasrocks(Lockner,1993b). Thestrainrateduring secondary creep is nearly constant, and strongly depends on the applied stress. A power law acceleration of strain ratehasbeenrevealedduringtertiarycreep(Voight, 1989). Thethreeregimesdevelopinparallelandtoa certain extent independently.

Laboratory tests and in-situ rheological observations are the major methods employed to study time-dependent behavioranddeformationrulesofrockmaterials.

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