1. Introduction

Currently, rock/cable bolts and steel mesh are widely used as temporary and permanent support element in tunnelling, underground excavations, and the surface slope stability. A combination of the rock/cable bolts and steel mesh can provide a robust system, which is known as a combined or yielding support. A combined support can transfer the applied external load from the damaged exterior to the confined interior of a rock mass. The load transferring mechanism between the unstable exterior and interior of a rock mass by means of the combined support system is still of the grey areas in designing the support systems. The understanding the load transferring mechanism between the engaged elements in a rock mass will

be more complicated when it comes to designing effective elements against rock/ coal burst. Ref. [1] defined ground support as a combination of surface support and reinforcement systems. Ref. [1] also mentioned that the words support and reinforcement are usually used interchangeably. Another concept to recall the support system as a membrane system is determined by [2]. Ref. [2] classified the surface support or containment support as the application of the reaction of the forces at the face of the excavation where it can include the techniques and smart devices to establish both local and global supports. These techniques and devices included fill, timber, steel sets, shotcrete, and the steel mesh. Ref. [3] defined rock reinforcement as an enhancement of the overall rock mass properties within the rock mass, and contain all techniques and devices that perform within the rock mass, including rock bolts, cable bolts, and ground anchors. Dynamic support is defined as ground support systems in which it would be available to resist against sudden energy release and dynamic loading so as to uphold the strength of an underground excavation. A number of researchers including [4–8] focused on studying the shear behaviour of rock bolts when it comes to the high stress and jointed rock mass condition. Ref. [9] classified the procedure for rock mass damage mechanisms by including the sudden volume expansion or bulking of the rock due to fracturing of the rock mass around an excavation. Rock mass bulking is a major cause of damage to support burst-prone condition.

## 2. Overview of research on yielding support

Ansell [10] carried out further tests on another type of energy-absorbing rock bolt made of soft steel. The aim of the test was to determine the strain rate effects on the yield stress and ultimate strength of the steel bars under dynamic loading conditions. The results demonstrated that the strain rate has a pronounced influence on the yield stress of steel bars. Ansell [10] concluded that the yield stress, the ultimate strength, and the energy absorbing capacity increased with the increasing loading rate, and the soft steel bars had a delayed plastic yielding when subjected to the dynamic loading. The impact was plastic during the retardation of the movable components of the testing machine; it was large at the beginning but dropped dramatically as an exponential curve. Ansell [10] also proposed that a rock bolt used under dynamic loading should have high dynamic-yield capacity so that it can resist high peak forces when experiencing impact loading. There are two methods commonly used to test energy absorption capacity of rock bolts under dynamic loading: free fall of a mass and momentum transfer. Plouffe et al. [11] performed the free fall method in the laboratory, where dynamic loading was simulated by dropping a mass over a certain distance onto the impact plate attached to the lower tube. The load and the displacement at the split were recorded by a load cell under the plate and a differential extensometer, respectively. The performance of bolts under dynamic loading was then analysed in terms of loads, displacements, and energy dissipated. The results showed that the potential and kinetic energies were almost equal to each other, and not all the energy was transferred to the support elements. The dissipated energy results in noise and permanent deformation of the domed plate. An experiment was carried out by [12] to estimate the energy absorption capacity of a new rock bolt, named D bolt, which has a large capacity for load bearing and deformation. Both static pull tests and dynamic drop tests were performed to evaluate the characteristics of the D bolt. For dynamic tests, boreholes were simulated by a split steel tube, which was placed in a jig to align it with a drill. During the test, a mass was dropped from a certain height onto a plate connected to the D bolt, and the impact load and the plate load were then measured during the

#### A New Concept to Numerically Evaluate the Performance of Yielding Support under Impulsive… DOI: http://dx.doi.org/10.5772/intechopen.79643

dropping process. The results indicated that the D bolt's impact peak load capacity was slightly larger than the static tensile strength of the bolt. The D bolt absorbed a large amount of energy along its entire length. The bolt was equally loaded in each deformable section which worked alone to stop rock expansion. Ghadimi et al. [13] developed an analytical model to calculate shear stress in a fully grouted rock bolt in jointed rock mass. The model considered the bolt profile and jump plane under pull test conditions. The results demonstrated that shear stress from the bolt to the rock decreased in an exponential rate. This decrease in shear stress is determined by bolt profiles such as the height, width and spacing of rib, resin thickness, material, and jointed properties. Jiang et al. [14] proposed another analytical model of the grouted rock bolt. The coupling behaviour of the rock bolt and rock mass was discussed from the point of displacement. Based on the analysis, the initial force in rock mass was controlled by its displacement. Another finding was that each bolt has at least one neutral point whose position is influenced by the displacement in the rock mass around the tunnel. The axial force of a rock bolt and the shear stress at the interface between the bolt and rock mass were affected by the length of the rock bolt, the internal radius of the tunnel, and the characteristics of the rock mass. A similar analytical model was also proposed by [15], in which the stress of distribution and variation of fully grouted rock bolts in surrounding rock mass were investigated and analysed. Based on the stress equilibrium in a tiny area of a rock bolt and the shear stress transfer mechanism of the interface between the rock bolt and rock mass, the axial displacement differential equation of the rock bolt was developed. Aziz et al. [16] researched the load transfer capacity of fully grouted rock bolts under an elastoplastic rock mass condition and proposed an analytical solution to determine the axial load along the rock bolts. In this model, the rock bolts were assumed to be elastic material and the surrounding rock mass was considered as an elastoplastic material. According to the model analysis, the load transfer capacity of a fully grouted rock bolt can be expressed as a function of various parameters of the surface condition, including bolt length, shear stiffness of the interfaces, in situ stress, and rock displacement along the bolt. Rock bolts are part of the reinforcement support system in underground excavations. It is important to evaluate and understand the performance of bolts under varying loads. Laboratory testing methods, especially the double shear test, can be used to determine the mechanical properties of rock bolts under static loading. Tests for rock bolts under dynamic loading are used to determine the energy absorption capacity, which is an important parameter for describing the dynamic performance of a rock bolt. Numerical modelling by using simulation software and theoretical analysis can also be used to analyse the behaviour of rock bolts in a jointed rock mass. Since experimental investigation of cable bolts under dynamic loading is very complicated and requires sophisticated facilities, numerical modelling can be used as a reliable method.

### 3. Numerical procedure

The proposed three-dimensional Finite Element model is developed using the commercial software ABAQUS, due to its ability to deal with complex contact problems. In fact, one of the main difficulties in the modelling of steel and concrete members with ABAQUS is in the convergence issues which need to be addressed due to the extensive number of contacts required to be implemented between the cable bolt and the concrete boxes. The proposed numerical model is developed to predict the structural response of the cable bolts using solid elements for all components. For this purpose, the 8-node linear brick element (C3D8R) with a reduced integration and hourglass control is adopted, which is the element with three transitional degrees of freedom (Figure 1).

One of the main difficulties in the modelling of steel and concrete members with ABAQUS is in the convergence issues which need to be addressed due to the extensive number of contacts required to be implemented between the cable bolt and the concrete blocks. The proposed numerical model is developed to simulate the structural response of the cable bolts using solid elements for all components. For this purpose, the 8-node linear brick element (C3D8R) with a reduced integration and hourglass control is adopted, which is the element with three transitional degrees of freedom. The base model in this chapter is similar to the author's previous work [17], where preliminary numerical modelling and analytical study were conducted to examine cable behaviour. This study provides further parametric analysis on bolts behaviour under different conditions. The adequacy and stability of a Finite Element model to describe the behaviour of a cable bolt is strongly influenced by the definition of adequate contact properties between the concrete and steel components, as suggested by [17]. The presence of a large number of contact regions, especially when dealing with cable bolt models, significantly increases the complexity of the analysis due to the nonlinear and discontinuous nature of cable bolts. For this reason, the Finite Element simulations carried out as part of this study are implemented with ABAQUS/Explicit, to avoid convergence difficulties. The interface behaviour between the concrete box and the cable bolt is modelled using the surface-to-surface interaction available in ABAQUS. In particular, a HARD contact property is adopted in the direction normal to the interface plane. For the tangential behaviour, the PENALTY option is used with a friction coefficient of 0.5 between the cable bolts and the grout. The behaviour of the cable bolts is described using a linear elastic relationship up to yielding, followed by a strain-hardening behaviour. The concrete in compression is described with an initial linear elastic range up to 40% of its compressive strength after which it is represented by the Concrete Damage Plasticity model available in ABAQUS. Its

Figure 1. An example of 3-D finite element models under static and dynamic loading.

tensile behaviour is initially linear elastic followed by a softening response after cracking is initiated.
