**7. Bolt modelling under axial loading**

632 Numerical Simulation – From Theory to Industry

While shearing takes place, strains are induced through the grout near the shear joint and reaction zones. The strain in the grout was around ten times greater than the linear region at critical zones. This means that the grout in those areas had broken off the sides that were in tension. The rate of induced strain along the grout in an axial direction is shown in Figure

A comparison of the strain along the joint interface in the grout showed that it decreased between 3% and 5% in the compression and tension zones with increasing pre-tension to 80 kN, which is due to higher shear resistance and lower lateral displacement. It was also found that the grout layer at the bolt - joint intersection will start to crush after slight

Tensile zone

**Figure 35.** The rate of induced strain along the grout layer without pre-tension in an axial direction

induced stresses along the bolt - grout interface.

exponential relationship till the end of the load stepping process.

In high strength concrete induced stress was reduced slightly and pre-tension reduces

From the results at contact pressure in the bolt-grout-concrete it was found that there is an exponential relationship between contact pressure and loading process at the bolt - grout interface, which started after around 15% of the loading process. However, the contact pressure trend in the concrete - grout interface was formed by 2 parts. From the beginning to around 15% of the loading, there is an approximate linear relation followed by an

movement along the joint, which causes plastic strain in the grout layer.

Compression zone

Distance from centre to end (mm)

*6.3.2. Strain in grout* 

35.

Strain along the grout

A numerical model was developed to investigate the contact interface behaviour during shearing under pull and push tests. The same 3D solid elements and surface-to-surface contact elements were used to simulate grout and steel. The numerical simulation of the cross section of the bolt and its ribs was complicated, and is almost impossible with the range of software available in the market today. However an attempt was made to model the bolt profile configurations by taking into account the realistic behaviour of the rock - grout and grout - bolt interfaces based on laboratory observations. To achieve this end, the coordinates of all nodes for all materials were defined then all these co-ordinates were inter-connected to form elements, which were extruded in several directions to obtain the real shape of the bolt.

Figure 36 shows the FE mesh. Figure 37 shows the bolt under pull test. Two main fractures were produced as a result of shearing the bolt from the resin. The first one begins at the top of the rib at an angle of about 530 running almost parallel to the rib, and the second one has an angle of less than 400 from the axis of the bolt. When these fractures intersect they cause the resin to chip away from the main body because it is overwhelmed by the surface roughness of the rib while shearing. Internal pressure produced by the profile irregularities of the bolt induces tangential stress in the grout. The grout fractures and shears when the induced stress exceeds the shearing strength, allowing the bolt to slide easily along the sheared and slikenside fractures in the grout interface.

**Figure 36. FE** mesh: a quarter of the model
