# Swellex / Split Set

The **Swellex / Split Set** bolt model (also called Frictional bolts or Shear bolts) in **RS2** 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 **RS2** 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 **RS2**, 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 **RS2**.

## Tensile Capacity

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

- The Tensile Capacity option is only enabled, if the Bolt Model = Plastic (see below). If the Bolt Model = Elastic, then by definition the bolt behaves in an elastic manner only, and tensile (and shear) capacity (strength) is not considered, and is not applicable.
- Tensile Capacity is equal to the (Yield Stress of the steel) * ( Tributary Area)

## Residual Tensile Capacity

The *Residual Tensile Capacity* option will only be enabled if the *Bolt Model* = *Plastic*. (It is not applicable if the *Bolt Model* = *Elastic*). See below for information about the *Bolt Model*.

If the axial load in a bolt reaches the (peak) *Tensile Capacity*, then the axial capacity of the bolt will thereafter be determined by the *Residual Tensile Capacity*.

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. Note:

- The
*Bond Strength*option is only enabled, if the Bolt Model = Plastic (see below). If the Bolt Model = Elastic, then by definition the bolt behaves in an elastic manner only, and shear (and tensile) capacity (strength) is not considered, and is not applicable. *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 *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.

## Material Dependent Bolt Properties

When the **Material Dependent check box is ON**, the following properties must be defined:

- Bond Strength Coefficient
- Bond Shear Stiffness Coefficient

When the **Material Dependent check box is OFF**, the following properties must be defined:

- Bond Shear Stiffness (MN/m)
- Residual Bond Strength (MN/m)
- Bond Strength (MN/m)

### THEORY

The Bond Strength will be calculated based on Morh Coulomb criteria:

*T = (C + signmaN * tan (alpha))* shear strength coefficient*

If the shear stiffness Coefficient is used then it will calculate the young's modulus for the material and multiple by the shear stiffness Coefficient.

*C* and *Tan(alpha)* are calculated from the material surrounding the bolt similar to how we do the SSR. Please note that only the following material will be used with bolt material dependent:

- Morh-Coulomb
- Hoek Brown
- Any soil models that have C and Phi in their formulation

*SigmaN* is the stress perpendicular to the bolt direction of the rock/soil material around the bolt. The residual bond strength of the bolts was also calculated based on the residual strength of the surrounding materials.

## Out-of-Plane Spacing

This is the spacing between bolts in the out-of-plane direction (i.e. normal to the analysis plane).

## Bolt Model

__Elastic__

If the Bolt Model = Elastic, the bolt will behave in an elastic manner only, and the forces in the bolt will be determined by the Axial and Shear Stiffness. The tensile capacity and bond strength (shear) capacity of the bolt is not considered, and the Tensile Capacity and *Bond Strength* options will be disabled.

__Plastic__

If the *Bolt Model* = *Plastic*, then the tensile capacity and bond strength (shear) capacity of the bolt is considered. The Tensile Capacity, *Residual* Tensile Capacity and *Bond Strength* options will be enabled. If the *Tensile Capacity* of the 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. If the *Bond Strength* of the bolt is reached, then the shear force on the bolt will not vary with further shear displacement.

## Face Plates

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

- If the Face Plates check box 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 check box 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 Bolt Option and Face Plates__

If you are using the Add Bolt option to add individual bolts to a model, and the bolts have face plates, it is important to note that the face plate is always added to the FIRST vertex of the bolt, when you add bolts to the model.

## Add Pull Out Force

The Add Pull Out Force option allows the user 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 check box, 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)].