A time-dependent creep model for rock based on damage mechanics
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ORIGINAL ARTICLE
A time‑dependent creep model for rock based on damage mechanics Shuqi Ma1,2 · Marte Gutierrez2 Received: 2 December 2019 / Accepted: 12 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A creep model based on the damage mechanics is proposed in this study to describe the three-stage creep deformation of rocks under conventional triaxial loading conditions. The proposed model has a simple form as it is based on the mechanism which assumes that the time-dependent creep behavior of rocks is solely described by the damage evolution. Verification of the proposed model against the creep tests shows that the model can reflect the three-stage creep behavior under higher stress levels as well as the elastic behavior under lower stress levels using the same model equations. The features of the proposed model include: (1) Simple mathematical form as it contains only one strain component without strain partitioning, and one set of equations to predict the creep deformation for all stress levels; and (2) The model requires only four parameters. All these features make the proposed model simple to use and easy to implement. Keywords Creep strain · Damage mechanics · Three-phase · Strain partitioning
Introduction Creep refers to the increase in deformation with time of geomaterials which are subjected to a constant stress smaller than the failure stress. In addition, geomaterials respond differently at different strain rates. Better understanding of the creep behavior of rocks is important to predict the long-term deformation of geological structures, such as landslides, tunnels, dams, and foundations, which are subjected to a longterm loading. Experimentally observed creep behavior of materials typically exhibits three stages (Fig. 1): (1) Primary creep, (2) Secondary creep, and (3) Tertiary creep, followed by failure (Lockner 1993; Main 2000; Wang 2004; Amitrano and Helmstetter 2006; Heap et al. 2009). The creep strain rate during the primary creep stage decays gradually with time. During secondary creep, the strain rate remains nearly constant. The strain rate during tertiary creep increases exponentially before rupture.
* Shuqi Ma [email protected] 1
Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China
Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401, USA
2
Various approaches have been proposed to model the time-dependent deformation of rocks. The existing constitutive models can be classified into two groups: (1) Classical creep models based on a network of many components of springs, dashpots and sliders which interact by sharing the applied load (Nishihara 1952; Boukharov et al. 1995; Davy et al. 1995; Ranalli 1995; Zhou et al. 2011; Jiang et al. 2013; Yang et al. 2014), and (2) Empirical damage models in forms of power laws or exponential laws which are able to describe the experimentally obtained strain–time behavior (Zhang et al. 1999, 2004; Ma
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