Abstract
Understanding the time-dependent behavior of rocks is important for ensuring the long-term stability of underground structures. Aspects of such a time-dependent behavior include the loading-rate dependency of Young’s modulus, strength, creep, and relaxation. In particular, the loading-rate dependency of Young’s modulus of rocks has not been fully clarified. In this study, four different types of rocks were tested, and the results were used to analyze the loading-rate dependency of Young’s modulus and explain the underlying mechanism. For all four rocks, Young’s modulus increased linearly with a tenfold increase in the loading rate. The rocks showed the same loading-rate dependency of Young’s modulus. A variable-compliance constitutive equation was proposed for the loading-rate dependency of Young’s modulus, and the calculated results agreed well with measured values. Irrecoverable and recoverable strains were separated by loading-unloading-reloading tests at preset stress levels. The constitutive equations showed that the rate of increase in Young’s modulus increased with the irrecoverable strain and decreased with increasing stress. The increase in the irrecoverable strain was delayed at high loading rates, which was concluded to be the main reason for the increase in Young’s modulus with an increasing loading rate.
Highlights
The strength is known to increase with the loading rate [1,2,3,4], the strain increases under constant stress, and stress decreases under a constant strain [5, 6]
A 15-year creep test was performed on Tage tuff at a stress level of 30% [11]. ese studies showed that understanding the time-dependent behavior of rocks is important for ensuring the long-term stability estimating the lifetime of underground structures [12]. e basic characteristics and theory of relaxation have been used to explain strain hardening and softening [13]
For Tage tuff, Young’s modulus had average values of 4.40, 4.55, and 4.12 GPa at 30%, 50%, and 70%, respectively, of the maximum stress. is corresponds to increases of 1.57%, 1.38%, and 1.92%, respectively, in Young’s modulus for each tenfold increase in the loading rate
Summary
The strength is known to increase with the loading rate (i.e., loading-rate dependency) [1,2,3,4], the strain increases under constant stress (i.e., creep), and stress decreases under a constant strain (i.e., relaxation) [5, 6]. E loading-rate dependency of the strength has been comprehensively studied through uniaxial compression and indirect tensile tests [9] and shear and triaxial compression tests [10]. The loading-rate dependency of Young’s modulus of rocks has not been fully clarified. A few studies have explained the microcrack evolution, associated deformation, and strength properties of rocks with various strain rates [16]. Xu and Dai [17] showed that Young’s and shear moduli exhibited some loading-path
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