# Swellex / Split Sets

The **Swellex / Split Set** bolt model (also called Frictional bolts or Shear bolts) in *RS3* works as follows:

- The entire bolt behaves as a single element. For purposes of the algorithm, the bolt is discretized according to the intersections with the finite elements, however, the behaviour of each segment of the bolt has a direct effect on adjacent segments.
- The stiffness of the bolt / rock interface is taken into account.
- Unlike the Plain Strand Cable model, the confining stress level in the rock does NOT affect the shear strength or stiffness of the bolt.

## Failure Mechanisms

A Swellex / Split Set bolt in *RS3* can fail in two modes:

- In tension, if the Tensile Capacity is exceeded.
- In shear, if the Bond Strength is exceeded.

For more information regarding the bolt models and their numerical implementation in *RS3*, see the Bolt Formulation document in the Theory section.

For guidelines on typical property values of Swellex and Split Set bolts see the references at the end of this topic.

The following properties define a **Swellex / Split Set** bolt in *RS3*.

## Tensile Capacity

This is the maximum tensile (axial) force which the bolt is capable of sustaining. NOTE:

**Tensile Capacity**is equal to the (Yield Stress of the steel) * (Tributary Area)

## Residual Tensile Capacity

If the Tensile Capacity of a bolt is reached, then the **Residual Tensile Capacity** of the bolt will be in effect. The bolt will thereafter behave in a perfectly plastic manner, and the axial force in the bolt will not vary with further axial displacement.

The Residual Tensile Capacity can vary between zero and the peak Tensile Capacity.

## Tributary Area

Swellex / Split Set bolts are hollow. The **Tributary Area** is the effective cross-sectional area of the bolt (i.e. the cross-sectional area of the annulus of steel which makes up the bolt). It is NOT the total cross-sectional area of the bolt (i.e. it does NOT include the hollow area of the bolt). The Tributary Area is used to calculate the axial stiffness of the bolt (see below).

## Bolt Modulus

The **Bolt Modulus** is the Young’s Modulus of the bolt steel. NOTE:

- The Bolt Modulus, Tributary Area and bolt length determine the axial stiffness of a bolt, i.e.
- Axial Stiffness = (Bolt Modulus) * (Tributary Area) / (bolt length)

## Bond Strength

This is the maximum shear force capacity of the bolt / rock interface. The **Bond Strength** is expressed as a FORCE per unit BOLT LENGTH. If the Bond Strength of a bolt is reached, then the shear force on the bolt will not vary with further shear displacement. Note:

- Bond Strength can be determined from empirical methods such as pull-out tests.

NOTE: see below for typical values of Bond Strength and Bond Stiffness for Swellex bolts.

## Bond Shear Stiffness

This is the shear stiffness of the bolt / rock interface. Note that the units of **Bond Shear Stiffness** are FORCE / LENGTH / LENGTH. The Shear Stiffness can be thought of as follows:

- On a shear force vs. shear displacement graph, the Shear Stiffness is equal to the slope of the ELASTIC portion of the graph. Remember shear force is expressed as a FORCE / LENGTH therefore the units of the Shear Stiffness are FORCE / LENGTH / LENGTH.

NOTE: see below for typical values of Bond Strength and Bond Stiffness for Swellex bolts.

## Face Plates

The **Face Plates** option allows you to simulate the effect of face plates used on bolts.

- If the Face Plates checkbox is selected, then the first vertex of each bolt will be "fixed" to the rock mass, allowing the bolt to develop load starting at the face plate.
- If the Face Plates checkbox is NOT selected, then the load at the beginning of the bolt will be zero.

Face Plate Drawing

Bolts with face plates are drawn with a small rectangular icon at the beginning of the bolt, to indicate the presence of the face plate.

## Add Pull Out Force

The **Add Pull Out Force** option allows you to simulate the effect of a pull-out test on a bolt, by applying a tensile force to the beginning of the bolt. To use this option, select the Add Pull Out Force checkbox, and enter the desired value of pull out force. The force will be applied as a tensile load to the first vertex of the bolt.

## Pre-Tensioning Force

See the Pre-Tensioning topic for information.

## Joint Shear

See the Joint Shear topic for information.

## Typical Values for Swellex Bond Strength and Bond Shear Stiffness

The following parameters come from a review of many lab and field tests done throughout different organizations worldwide [Atlas Copco (2006)], and are considered the most representative parameters characterizing bond strength and bond shear stiffness of Swellex bolts.

In hard rock:

Swellex Bolt Type | Bond Strength (MN/m) | Bond shear stiffness (MN/m/m) |

Mn12 / Pm12 | 0.17 | 100 |

Mn24 / Pm24 | 0.3 | 200 |

In weak rock with a low Young's Modulus, reduce the values to:

Swellex Bolt Type | Bond Strength (MN/m) | Bond shear stiffness (MN/m/m) |

Mn12 / Pm12 | 0.12 | 75 |

Mn24 / Pm24 | 0.2 | 150 |

## Typical Values for Split Set Bolt Properties

For a discussion of factors influencing split set bolt properties see the following document:

Factors Influencing the Effectiveness of Split Set Friction Stabilizer Bolts [Tomory (1997)].