# Bolt Orientation Efficiency

Bolts that intersect a wedge in **RocPlane** can deform in a number of different ways, as shown in the figure below. As a result, the mechanism of failure of a bolt can be quite complicated. In order to simplify the behavior for the purpose of including support in a limit equilibrium wedge analysis program such as **RocPlane**, an empirical reinforcement efficiency factor can be used.

Possible bolt deformation modes [Windsor, 1996]

The theoretical **Tensile Capacity** of a bolt at any point along its length is determined from the Bolt Force Diagram and the point at which a wedge plane intersects the bolt. This assumes that a bolt is in pure tension. However, pure tension occurs only if the bolt orientation is aligned exactly with the sliding direction or direction of movement of the wedge (see **b: Pure Tension** in the figure above).

If a bolt is not in pure tension but also shear, the effective **Tensile Capacity** of the bolt is reduced. The amount of reduction is given by the Bolt Orientation Efficiency factor, which may range between zero and one.

- If the
**Bolt Orientation Efficiency**factor is zero, the bolt has no effect and zero force is placed into the equilibrium equations of the wedge. - Conversely, if the
**Bolt Orientation Efficiency**factor is one, the bolt is in pure tension and the entire capacity is added as a force in the direction of the bolt in the equilibrium equations of the wedge.

**NOTE:** The **Bolt Orientation Efficiency** factor, if used, is ONLY applied to the **Tensile Capacity** of a bolt as determined from the Bolt Force Diagram. It is NOT applied to the **Shear Capacity** of a bolt, if the Use Shear Strength option is being used. For an overall summary of the bolt support force implementation in RocPlane, see Bolt Support Force in RocPlane.

## Calculation of Bolt Orientation Efficiency Factor

The **Bolt Orientation Efficiency** factor is calculated by relating the direction of sliding or movement of the wedge to the orientation of the bolt. In **RocPlane**, there are two different calculation methods.

### COSINE TENSION / SHEAR

This is the default method in **RocPlane**. With reference to the figure below, the efficiency is calculated as:

**NOTE;** This applies to bolt deformation modes A, B, C, D (see the figure above). For bolt deformation modes E (pure shear) or F (compression and shear), the **Bolt Orientation Efficiency** factor = 0.

Bolt orientation and sliding direction used for Bolt Efficiency calculation

### LINEAR TENSION / SHEAR

With the **Linear Tension / Shear** method, the efficiency is calculated as:

**NOTE:** This applies to bolt deformation modes A, B, C, D (see the first figure above). For bolt deformation modes E (pure shear) or F (compression and shear), the **Bolt Orientation Efficiency** factor = 0.

## Bolt Orientation Efficiency Off

The **Bolt Orientation Efficiency** option can be turned off. To turn off the option, deselect the **Use Bolt Orientation Efficiency** check box in the **Bolt Properties** dialog.

If **Bolt Orientation Efficiency** is OFF, then the **Bolt Orientation Efficiency** factor = 1, regardless of the bolt deformation mode (A,B,C,D,E,F in the first figure above).

## Bolt Efficiency and Shear Strength

Finally, note that **Bolt Orientation Efficiency** is NOT used in conjunction with the Bolt Shear Strength option. If you have selected the **Use Bolt Shear Strength** option and the bolt deformation mode is D, E or F so that the **Bolt Shear Strength** is applied, the **Bolt Orientation Efficiency** factor DOES NOT multiply the **Shear Strength**. **Bolt Orientation Efficiency** is only used as a factor for the **Tensile Capacity** determined from the Bolt Force Diagram.