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# Tieback

The Tieback bolt model in RS2 allows you to model grouted tieback support. Bolts may be pre-tensioned and grouted with a user-defined bonded length. In terms of its implementation in the RS2 analysis engine, a tieback uses the same formulation as the Swellex/Split Set bolt model, with allowance for an unbonded length.

For more information regarding the bolt models and their numerical implementation in RS2, see the Bolt Formulation document in the Theory section.

The following properties define a Tieback bolt in RS2.

## Bolt Diameter

The diameter of the tieback bolt.

## Bolt Modulus

The Young’s Modulus of the bolt steel.

## Tensile Capacity

The peak tensile capacity of the bolt steel.

## Residual Tensile Capacity

The residual tensile capacity of the bolt steel.

## Out-of-Plane Spacing

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

## 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)
• 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.

## Bond Strength

This is the maximum shear force capacity along the Bond Length of the tieback. This should be the lesser of the bolt/grout interface strength or the grout/(rock or soil) interface strength. The Bond Strength is expressed as a Force per unit Bond Length.

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

## Bond Shear Stiffness

This is the shear stiffness of the bolt/(rock or soil) 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.

## Borehole Diameter

The borehole diameter is only used if:

• the Joint Shear option is turned on, and
• the unbonded length of a tieback crosses a joint.

In this case, the borehole diameter (minus the tieback diameter) determines how much joint movement can take place before the joint movement impinges on the tieback. The borehole diameter has no effect on the interaction of joints with the bonded length of the tieback.

## Bolt Model

See the Swellex/Split Set topic for information.

## Bond Length

The bonded (grouted) length of the tieback, measured from the embedded end of the tieback. The Bond Length can be defined as:

• a percentage of the total tieback length
• an absolute length

by selecting one of the two options in the dialog and entering a value.

## Secondary Bond Length

The Secondary Bond Length allows you to define an additional bond length after the initial installation of the tieback. The secondary bond length is added to the initial (primary) bond length. For example, if the initial bond length is 40% and the secondary bond length is 60%, the tieback would be fully bonded.

To define a secondary bond length:

1. Select the Secondary Bond Length check box and select the Define button.
2. You will see a dialog which allows you to define the secondary bond length as a percentage of the total bolt length, as an absolute length or as fully bonded (100% bond length). You must also choose the installation stage for the secondary bond length, with respect to the installation stage of the bolt.

NOTE: the properties of the secondary bond length are assumed to be the same as the properties of the initial (primary) bond length (i.e. bond stiffness and bond strength). It is not possible to specify different properties for the primary and secondary bond length.

## Pre-Tensioning Force

See the Pre-Tensioning topic for information.

## Joint Shear

See the Joint Shear topic for information.