# How Bolts are Implemented

Bolts are implemented in a **RocPlane** planar wedge stability analysis as follows:

## Capacity and Orientation

- Bolts affect the Factor of Safety through their
**Capacity**and**Orientation**(**Angle**). - Bolt
**Capacities**and**Orientations**are added vectorially and are included in the Factor of Safety calculation as a single, equivalent force passing through the centroid of the wedge. Either the**Active**or**Passive****Bolt Model**applies (see below). - Multiple bolts that have the same
**Orientation**can therefore be simulated by a single bolt having the same total**Capacity**.

## Length and Location

- If the
**Anchored Length**of a bolt = 0 (i.e., if it does not pass through the wedge), the bolt has NO effect on the model - its effective**Capacity**is zero. - The
**Location**of bolts (on the face of the wedge) has some effect on the Factor of Safety. Even though all forces in the wedge stability analysis are assumed to pass through the centroid of the wedge , the exact location of a bolt can affect the anchor length of the bolt. Where a selected bolt property type utilizes anchor length for its bolt capacity calculations, the Factor of Safety can be affected.

## Bolts vs. External Force

- If the
**Bolt Model**is**Active**, a bolt is exactly equivalent to an External Force with the same magnitude and orientation.

**TIP:** As a suggested exercise, you can verify that a bolt using the Active Bolt Model or an equivalent External Force results in the same Factor of Safety for a given wedge.

- If the
**Bolt Model**is**Passive**, a bolt, and an External Force with the same magnitude and orientation, will NOT be equivalent.

## Active and Passive Bolt Models

In general terms, the Factor of Safety is defined as the ratio of the forces resisting motion to the driving forces. Driving forces include the mass of the wedge accelerated by gravity, seismic forces, and water pressure. Resisting forces arise from the cohesion and frictional strength of the sliding plane (Failure or Discontinuity Plane).

### ACTIVE SUPPORT

**Active** support is included in the **RocPlane** analysis as shown in Equation 1 below:

Eqn. 1

**Active Support** is assumed to act in such a manner as to DECREASE the DRIVING FORCE in the Factor of Safety calculation. Tensioned cables or rockbolts, which exert a force on the wedge before any movement has taken place, are considered **Active** support.

**NOTE:** External Forces are incorporated in the **RocPlane** analysis in the same manner as **Active** support (i.e. according to Equation 1).

### PASSIVE SUPPORT

**Passive Support** is included in the **RocPlane** analysis as shown in Equation. 2.

Eqn. 2

By this definition, **Passive** support is assumed to INCREASE the RESISTING FORCE provided by shear restraint in the Factor of Safety equation. Untensioned dowels or grouted cable bolts, which only develop a resisting force after some movement of the wedge has taken place, are considered **Passive** support.

Since the exact sequence of loading and movement in a rock slope is never known in advance, the choice of **Active** or **Passive Bolt Models** is somewhat arbitrary. The user may decide which of the two models is more appropriate for the wedge being analyzed. In general, **Passive** support always gives a lower Factor of Safety than **Active** support.