Time-dependent performance of damaged marble and corresponding fractional order creep constitutive model
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ORIGINAL PAPER
Time-dependent performance of damaged marble and corresponding fractional order creep constitutive model Jing Chen 1 & Quan Jiang 2
&
Yanran Hu 1 & Weimin Qin 2 & Shaojun Li 2 & Jun Xiong 3
Received: 5 November 2019 / Accepted: 6 October 2020 # Saudi Society for Geosciences 2020
Abstract The time-dependent behaviour of a rock mass is crucial to the long-term stability of underground engineering projects, such as large tunnels, caverns and roadways. This paper focused on the experimental and theoretical studies of marble creep behaviour considering its initial damage due to excavation damage. Based on the onsite investigation of the creep performance of Jinping marble, detailed creep tests were carried out on damaged marble under different confining stresses, which indicated that damaged marble exhibited more notable creep properties than the intact marble. A new time-dependent creep constitutive model was proposed to characterize the time-dependent mechanical behaviour of damaged marble in terms of fractional derivatives and damage variables by replacing the Newtonian dashpot with the Abel dashpot. Furthermore, this one-dimensional creep equation was extended to a three-dimensional numerical model for analyzing the long-term deformation of hydraulic caverns. The simulation results indicated that the proposed model provided a precise description for the full creep process of marble containing initial damage. Keywords Initial damage . Creep test . Fractional derivatives . Damage variables . Creep model
Introduction As Scheidegger (1970) stated, “The problem of the longterm behaviour of rocks is an important issue in connection with the construction of tunnels, dams and similar structures”. The creep behaviour of the surrounding rock, as one of the important mechanical characteristics of rock over time, plays a key role in the stability of underground structures. In the early 1970s, it had been found that the hard and intact granite of a traffic tunnel in Switzerland had flaked 2 years after completion (Liu 2011). Due to the
Responsible Editor: Zeynal Abiddin Erguler * Quan Jiang [email protected] 1
School of Architectural Engineering, Tongling University, Tongling 244061, Anhui, People’s Republic of China
2
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
3
Department of Civil and Environmental Engineering, University of Alberta, Edmonton T6G 2W2, Canada
relatively weak quartzite and high geostress, many underground roadways in South African gold mines eventually experienced long-term deformation, which resulted in serious stability challenges (Malan 2002). Similarly, reinforcement was imposed on the surrounding rock of the Jinping I and Laxiwa hydropower stations due to the time-dependent deformation and breakage under high stress (Lu et al. 2010; Jiang et al. 2020a). Many research works related to time-dependent deformation and failure have been carried out mainly from three aspects:
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