A constitutive model for load-displacement performance of modified cable bolts

Abstract

Cable bolts are extensively used in mining and civil structures as one of the most important support systems for ground control. In order to design an effective support system, understanding the performance of cable bolts under the conditions other than those tested in the laboratory is essential. Thus, this paper outlines the development of a constitutive model that can predict the full load-displacement performance of the modified cable bolts at different confining pressures. The model includes the nonlinear dilation equation and the peak axial load envelope as the governing laws. The governing equations for the failure mechanisms at the cable to grout interface and grout annulus are coupled using advanced partial differential equations. The full load-displacement behaviour of modified cable bolts with a smooth transition from initial elastic behaviour to progressive failure is simulated using continuous yielding method. The model is then calibrated against the experimental data reported in the literature. It has been demonstrated that there is a good agreement between the model simulations and the experimental results confirming the suitability of the proposed constitutive model for performance prediction of the modified cable bolts at different confining pressures.

Introduction

Fully grouted cable bolts are extensively used as one of the most reliable support systems in surface and underground rock structures (Li et al., 2017). Their performance includes the transition of the load from the unstable rock zone to relatively stable rocks far from the excavation (Ghadimi et al., 2015). Despite the substantial improvement in the design and performance of cable bolts over the past few decades, there is still some likelihood of ground failure within the reinforced area using cable bolts. It has been reported that cable bolt failure generally occurs at the bolt to grout interface if strand rupture has not occurred (Goris, 1991, Hutchinson and Diederichs, 1996, Hyett et al., 1992a, Hyett et al., 1992b, Yazici and Kaiser, 1992). Therefore, to better understand such a problem, the focus on the mechanical performance of the strand steel to grout interface is important.

To date, two types of cable bolts have been used in the mining industry including conventional and modified cable bolts. The former is made of several plain steel strands such as plain strand cable bolt while the latter consists of bulbed, nutcase and birdcaged cable bolts that exhibit some form of deformed structure. Extensive experimental investigations have focused on the performance of conventional cable bolts under axial loading over the past few decades (Benmokrane et al., 1995, Blanco Martín et al., 2013, Farah and Aref, 1986, Goris et al., 1993, Hassani and Rajaie, 1990, Hyett et al., 1995, Macsporran, 1993, Reichert et al., 1991, Stillborg, 1984) though there have been very limited studies assessing its behaviour from an analytical viewpoint (Blanco Martin, 2012, Chen et al., 2015, Hyett et al., 1995).

Yazici and Kaiser (1992) introduced a bond strength model (BSM) using thick wall cylinder theory to determine the load carrying capacity. The modified cable bolts were developed to improve the load carrying capacity under axial loading condition. Hyett et al., 1994, Moosavi et al., 1996, Moosavi et al., 2002 assessed the performance of the modified cable bolts (nutcase and Garford bulbed) under both constant confining pressure and constant radial stiffness conditions. Thomas (2012) evaluated the performance of bulbed and nutcaged cable bolts under constant radial stiffness. Moosavi (1997) developed an analytical model for load-displacement behaviour of modified cable bolts based on linear dilation assumption.

It has been well accepted that the failure mechanism of conventional and modified cable bolts can differ during a pull-out test. Hyett et al. (1995) stated three types of failure mechanisms for bond failure of conventional cable bolts including dilation slip, unscrewing and shear failure of the cement flutes. The dilation slip failure mechanism is applicable to modified cable bolt and dominates the bond failure. Hyett et al. (1995) reported that the unscrewing and shear failure of the cement flutes have negligible effects on the failure mechanism of modified cable bolts.

Several parameters are important in the performance of modified cable bolts under axial loading including elastic properties of the grout, the design and fabrication of the cable bolt and the boundary conditions that is applied to outside the grout annulus. Thus, this study was undertaken with the aim to combine these parameters in a meaningful way resulting in the development of a constitutive model for prediction of the load-displacement performance of the modified cable bolts at different confining pressures. The important feature of this model is the inclusion of nonlinear dilation for the grout at the cable bolt to grout interface during the pull-out test. This is the significant distinction between this study and that conducted by Moosavi (1997).