**4.3. Contact interface model**

The main difficulties with numerically simulating a reinforced shear joint are the bolt- grout and grout-rock interfaces. An important parameter controlling the load transfer from the bolt to the rock through resin is bond behaviour between the interfaces. If they are not designed properly it is difficult to understand their behaviour, when and where de-bonding occurs, how a gap is created between the interfaces, and how the load is transferred. Thus the contact interfaces were designed to act realistically. To study the stress, strain generation through numerical modelling, it is very important to model the interfaces accurately, *Pal et al.* (1999). *Ostreberge* (1973) also emphasised the bond strength between two adjacent 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 the test results under constant normal conditions.

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. Figure 8 displays the target 170 geometry.

#### **4.4. 3D geometrical model**

614 Numerical Simulation – From Theory to Industry

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

The main difficulties with numerically simulating a reinforced shear joint are the bolt- grout and grout-rock interfaces. An important parameter controlling the load transfer from the bolt to the rock through resin is bond behaviour between the interfaces. If they are not designed properly it is difficult to understand their behaviour, when and where de-bonding occurs, how a gap is created between the interfaces, and how the load is transferred. Thus the contact interfaces were designed to act realistically. To study the stress, strain generation through numerical modelling, it is very important to model the interfaces accurately, *Pal et al.* (1999). *Ostreberge* (1973) also emphasised the bond strength between two adjacent

(b)

(a)

**4.3. Contact interface model** 

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 shows the geometry of the FE model with mesh generation.

## **5. Verification of the model**

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 reduction in shear displacement.

Numerical Simulation of Fully Grouted Rock Bolts 617

15 cm

Laboratory Numeric

**Figure 9.** Geometry of the model and mesh generation

7.5cm

**Shear load**

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100

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200

Shear load (kN) .

250

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15

**Bolt** 

**Grout** 

**Concrete** 

**Figure 10.** Load-deflection in 80 kN pretension bolt load and 40 MPa concrete

0 5 10 15 20

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C

**Shear joint**

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T

C

Shear displacement (mm)

**Figure 8.** Target 170 geometry (Ansys 2012)
