A simplified model to study the behavior of pre-tensioned fully grouted bolts around tunnels and to analyze the more important influencing parameters

Abstract

This paper develops an analytical method to obtain distribution of the axial force in the pretensioned fully grouted rockbolts around a circular tunnel. For his purpose, the axial force along the bolt is calculated by the assumption of rigid connection between the bolt and rock mass. To include the effect of relative shear displacement, the condition of end boundaries of bolt is focused on i.e. the reduction of the force on the bolt head is calculated through modeling of the flexibilities of its component (washer, plate …) and tunnel surface. Then, this force is simulated by applying a fictitious compressive force on the bolt head. The distribution of this fictitious force along the bolt is obtained to subtract from that of rigid connection. According to a case study, the theoretical prediction of axial force in the passive cases is comparable to the in-situ measured data. The magnitude of pre-tensioning force, delay in installing of bolts, stiffness of bolt head, and rockbolt density are considered as parameters to perform the sensitive analysis. INTRODUCTIONThe axial force is one of the most fundamental factors to adjust a rockbolt design [1,2]. Different parameters such as the shear stiffness and the end boundaries condition can influence on the distribution of the force along the bolt [3,4]. However, the end boundaries condition seems to have more effect on the efficiency of the pre-tensioned grouted bolts. This is because, this parameter controls the magnitude of the force transferred to tunnel surface.The near end stiffness includes the consideration of conditions such as bedding in the components of nut and washer on the plate, seating the plate on rock mass, and compressing of rock mass. The more flexibility of near bolt head, the less resulted force on the tunnel surface [5,6]. The far end condition of bolt is another important issue which is particularly more addressed in the pre-tensioned bolt [7].In regard to obtain the axial force, Oreste and Peila [5] presented an analytical approach by focusing on modeling the influence of different boundary conditions at near bolt head. Lee and Stillborg [8] developed another solution to simulate the shear stress along the bolt-rock interface for the coupling and decoupling behavior, and obtained the axial force by integrating the simulated shear stress. However; the force applying on the tunnel wall was not predicted for the coupling condition, and was assumed to be zero. Cai et al. [9] acquired a solution to get the axial force through considering the bolt and the rock mass consistent displacement in which the calculation of shear 1 The article is published in the original. 534 RANJBARNIA et al. JOURNAL OF MINING SCIENCE Vol. 50 No. 3 2014stiffness between bolt and rock mass was focused on. To solve the equation, it was assumed the bolt does not apply the force on tunnel wall for both coupling and decoupling mechanisms i.e. the bolt was considered without the end pale (a plate with great flexibility). Oreste [6] presented an analytical model based on the princ...

New Analytical Approaches for Evaluating the Performance of Systematic Pre-Tensioned Fully Grouted Rockbolts in Tunnel Stabilization

“…As the bolts are installed systematically (Figs 2a and 2b), it is assumed, each bolt increases radial pressure within the influence domain of itself. Therefore (Ranjbarnia et al, 2014a(Ranjbarnia et al, , 2015 …”

“…It is assumed that the pre-tensioned force provides equivalent radial stress in domain zone of each bolt (Fig. 3) (Ranjbarnia et al, 2014a(Ranjbarnia et al, , 2015. After installing the bolts, as tunnel face is again advancing within the influence limit of the working face, the fictitious constrained radial stress will be further reduced and will be ultimately diminished.…”

“…When the rockbolts are installed, it is assumed, a certain convergence of tunnel has already been occurred and an initial plastic zone of radius re will develop around the tunnel ( Fig. 1) (Ranjbarnia et al, 2014a). In this condition, there is a radial pressure on tunnel periphery supplied by proximity of the face, and its value is a percentage of field stress p 0 ( p i = β · p 0 ), 0 < β < 1).…”

“…The pre-tensioned grouted rockbolt installation consists of placing a grouted anchor, tensioning the rockbolt and tying end of the bolt by nut and plate to the tunnel surface, and then grouting the reminder of the bolt length as (Fig. 2a) (Ranjbarnia et al, 2014a(Ranjbarnia et al, , 2015. The pre-tensioned force applied by the bolt plate to tunnel surface develops the radial pressure extending within circumferential space between bolts (redrawn by Ranjbarnia et al (2015)) (b) longitudinal spacing between bolts the rock mass in the radial direction.…”

“…A number of analytical methods of varying degrees of accuracy, efficiency, and sophistication have been developed. Among these works, in a group of approaches, it has been attempted to obtain the engineering properties of reinforced rock mass as an improved composite material (Ranjbarnia et al, 2014a(Ranjbarnia et al, , 2015. However, in another group of approaches, the grouted bolt have been considered as an individual element which its contribution to rock mass is in the form of a radial load inducing the radial pressure within the influence domain of itself (Ranjbarnia et al, 2014a(Ranjbarnia et al, , 2015.…”