**4.2. Modelling the bolt**

The steel bar, which resists axial and shear loads during loading, due to rock movement, is the main element within the rock bolt system,. The steel bar was modelled appropriately, particularly with regard to the type of element designed and bolt behaviour, in the linear and non-linear region. 3D solid elements, solid 95 with 20 nodes, was used to model the steel bar, with each node having three translation degree of freedom. The approach adopted is to reveal that the experimentally verified shear resistance of fully grouted bolt can be investigated by numerical design. Elastic behaviour of the elements was defined by Young's Modulus and Poisson's ratio of various materials. The stress, strain relationship of steel is assumed as the bi-linear kinematic hardening model and the modulus of elasticity of strain hardening after yielding, is accounted as a hundredth of the original one, *Cha et al.* (2003),

*Hong et al*. (2003) and *Abedi et al*. (2003). Figure 7 displays the solid 95 elements and FE mesh for bolt.

Numerical Simulation of Fully Grouted Rock Bolts 613

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**Figure 5.** (a) 3D Solid 65 elements; (b) Concrete mesh

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**Figure 6.** FE mesh for grout

**Figure 4.** The process of FE simulation (Dof = degrees of freedom)

**Figure 5.** (a) 3D Solid 65 elements; (b) Concrete mesh

**Figure 6.** FE mesh for grout

**Figure 4.** The process of FE simulation (Dof = degrees of freedom)

for bolt.

*Hong et al*. (2003) and *Abedi et al*. (2003). Figure 7 displays the solid 95 elements and FE mesh

Numerical Simulation of Fully Grouted Rock Bolts 615

mediums for an accurate load transfer. *Nietzsche and Hass* (1976) proposed a model for bolt, grout-rock that assumed a linear elastic behaviour for all materials, and perfect bonding for all contact interfaces (bolt- grout and grout- rock). It has to be noted that perfect bonding, particularly between the bolt-grout interface could not be considered to be the right behaviour, because there is no cohesion strong enough between them. In addition, there are large stresses and strains concentrated near the shear joints, which restrict perfect bonding. The interface between the grout and concrete was considered as standard behaviour where normal pressure changes to zero when separation occurs. As found from laboratory results, a low cohesion (150 kPa) was adopted for the contact interface, which was determined from

3D surface-to-surface contact element (contact 174) was used to represent contact between the target surfaces (steel-grout and rock - grout). This element is applicable to 3D structural contact analysis and is located on the surfaces of 3D solid elements with mid-side nodes. This contact element is used to represent contact and sliding between 3-D "target" surfaces (Target 170) and a deformable surface, is defined by this element. The element is applicable to three-dimensional structural and coupled thermal structural contact analysis. This element is also located on the surfaces of 3-D solid or shell elements with mid-side nodes. It has the same geometric characteristics as the solid or shell element face to which it is connected. Contact occurs when the element surface penetrates one of the target segment elements on a specified target surface. The contact elements themselves overlay the solid elements describing the boundary of a deformable body and are potentially in contact with the target surface. This target surface is discritised by a set of target segment elements (Target 170) and is paired with its associated contact surface via a shared real constant set.

An actual 3D geometrical model was created to simulate the rock-bolt- grout behaviour and their interactions. The model bolt core diameter ( D ) of 22 mm and the grouted cylinder ( <sup>b</sup> D ) of 27 mm diameter had the same dimensions <sup>h</sup> as those used in the laboratory test. Due to the symmetry of the problem, only one fourth of the system was considered. Figure 9

A numerical representation model for a fully grouted reinforcement bolt was developed and its validity assessed with laboratory data conducted in a variety of rock strengths and pretension loadings. A comparison of experimental results with numerical simulations showed that the model can predict the interaction between bolt, grout, and concrete, and how the interfaces behave. The consistency of the experimental observations with a numerically design model is presented by typical shear load, shear displacement curves shown in Figure 10. It is clear that when the strength of the concrete was doubled there was a twofold

the test results under constant normal conditions.

Figure 8 displays the target 170 geometry.

shows the geometry of the FE model with mesh generation.

**4.4. 3D geometrical model** 

**5. Verification of the model** 

reduction in shear displacement.

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**Figure 7.** (a) 3D Solid 95 elements (b) FE mesh for bolt
