Rock creep behaviour is a key aspect of many engineering projects, such as deep tunnels in which squeezing problems could occur. Many theories have been published in the literature to reproduce rock creep behaviour; however, most of them are not able to capture the last phase of creep (i.e., tertiary creep, or the accelerating strains that occur prior to failure). In this work, the Distinct-Element Method (DEM) approach is employed, in conjunction with Rate Process Theory (RPT), to simulate the effect of rock creep in deep tunnels. To do that, the DEM models are constructed using particles, whose interactions are simulated with a hybrid mixture of the Flat Joint Contact Model (FJCM) and the Linear Model (LM) contact models; the RPT is implemented into DEM models using a Visual C++ function. Results show that the DEM plus RPT combination can suitably reproduce the tunnel convergences due to rock creep.
The time-dependent (creep) behaviour of rocks is a key aspect on the stability and performance of deep tunnels; in particular, in deep tunnels excavated in soft rocks [1][2]. Creep is a progressive deformation with time that occurs in rocks (or other materials) subjected to a constant stress level [3]. Figure 1 presents an idealized creep behaviour under a stress increase that is kept constant afterwards; it consists of an instantaneous elastic strain due to the applied stress (1→2); then, if such stress is keep constant with time (and it is high enough to lead the full process to develop), the following 3-stages can occur: (i) Primary creep, where strains increase with a decreasing strain rate (2→3), (ii) Secondary creep, with a quasi-constant strain rate (3→4), and (iii) Tertiary creep, with a non-linear strain acceleration until rock failure is observed (4→5).
Several theories have been developed in the literature to analyze creep behaviour observed in rock laboratory tests [5], and to predict creep tunnel convergences [2][6]. For instance, the Burger model has been used to simulate the creep behaviour of intact siltstone samples [7]; however, such approach cannot reproduce the rock failure due to tertiary creep. As an alternative, recent works have demonstrated that the Rate Process Theory (RPT) proposed by Eyring [8] could be successfully employed to simulate all stages of creep in soils [3] or in rocks [4]. The aim of this paper is to examine the applicability of RPT, and its implementation through the Distinct-Element Method (DEM), to simulate rock creep convergences in deep tunnels.