Load Splitting

By default in RS2, the entire load on the model due to Field Stress (and / or Body Force, if applicable), is applied in the first stage of the model.

The Load Split option in RS2 allows you to "split" the field stress induced load between any stages of the model, rather than applying the entire load in the first stage. This allows you to gradually apply the field stress load as excavation progresses.

A typical use of Load Splitting, is to simulate the 3D effect of an advancing tunnel face, using a 2D model. This can be used, for example, to simulate the delayed installation of support, at an advancing tunnel face.

NOTE: the Load Split determines how the field stress load (and / or Body Force, if applicable) is applied to the solid elements of the finite element mesh. The Load Split DOES NOT (directly) determine the load which is applied to support elements (i.e. bolt or liner elements). Remember that loading is generated in support elements, due to the deformation of the finite element mesh. Field stress is not applied directly to support elements. Therefore, the Load Split does not DIRECTLY affect the loading of support, but INDIRECTLY, due to the effect on the solid element mesh.

To implement Load Splitting in RS2:

1. First note that the Load Split option is only applicable, and is only enabled if your model is STAGED (i.e. the Number of Stages in the Project Settings option is greater than 1).
2. Select Load Split from the Loading menu.
3. In the Load Split dialog, select the Enable Load Split check box.
4. Enter the Load Split information at each stage (Split Factor and Stress Behaviour) as described below.

Split Factor

A Split Factor may be defined at each stage of the model. The Split Factor is used as follows:

• The Split Factor is simply multiplied by the values of the Field Stress, to obtain the actual Field Stress which will be applied at that stage (see below for example).
• In most cases, a Split Factor will be a number between 0 and 1. However, in the interests of generality, numbers greater than 1 may be entered (this allows you to increase the Field Stress entered in the Field Stress dialog), or even negative numbers may be entered (allowing you to decrease field stress).
• The Field Stress will be applied to the model according to the Stress Behaviour (i.e. Initialize or Add, see below for details).

Stress Behavior

• When the Stress Behaviour = Initialize, the Field Stress at that stage will be INITIALIZED to the value determined by the Split Factor at that stage.
• When the Stress Behaviour = Add, the Field Stress determined by the Split Factor, will be ADDED to the existing stress state of the model, at the indicated stage.

NOTE: by default for all materials, the Stress Behaviour = Initialize at Stage 1, and Stress Behaviour = Add in all subsequent stages. The user cannot change this. However, with Custom Load Splitting (see below), the user may define the Stress Behaviour (Initialize or Add), for any material in the model, at any stage.

EXAMPLE

Consider the following example of load split:

Define "A" as the initial element loading (field stress and/or body force) that would be given to an element of material if no load splitting was used in the model.

Now consider the following load split factors:

Initialize of 0.1 in stage 1

Add of 0.3 in stage 2

Add of 0.4 in stage 4

Add of 0.2 in stage 4

The initial stress in each element, at the beginning of each stage, will be as follows:

Stage 1

The initial stress will be 0.1A

Stage 2

For stage 2 the initial stress will be:

(stress state at the end of stage 1) + 0.3A

Stage 3

For stage 3 the initial stress will be:

(stress state at the end of stage 2) + 0.4A

Stage 4

For stage 4 the initial stress will be:

(stress state at the end of stage 3) + 0.2A

Custom Load Split

To allow the user maximum flexibility in defining a Load Split, the Custom Load Split option is available, which allows you to define Split Factor and Stress Behaviour on a per material basis. To define a Custom Load Split:

1. Select the Advanced button in the Load Split dialog.
2. The dialog will expand, allowing you to define a customized Load Split for any material(s) in the model. Note that the materials in the Load Split dialog, correspond to the materials you have defined in the Define Material Properties dialog.
3. To define a Custom Load Split for a material, select the Custom Load Split check box for the desired material, and enter the Split Factor and Stress Behaviour information for the material.
4. Repeat Step 3, for each material which requires a Custom Load Split.

NOTE: the default Load Split information, in the main (upper) part of the Load Split dialog, will still apply to all materials which have NOT had a Custom Load Split specified.

Typical Use of Load Split

A typical use of Load Splitting is to simulate the delayed installation of support at an advancing tunnel face. For example, in a simple two stage model of an excavation:

• You could set the Split Factor = 0.3 in Stage 1 and Split Factor = 0.7 in Stage 2.
• Install support (e.g. bolts and / or liners) in Stage 2.

When you run the analysis, only 30% of the total Field Stress load will be applied in the first stage. Effectively, this allows some displacement to take place in the first stage, without support, simulating the delayed installation of support at the face of an advancing tunnel, for example. Then, support installed in the second stage can react to the remainder (70%) of the field stress load.

A simple example of the Load Split option can be found in the RS2 Support Tutorial. A discussion on how Load Split factors can be determined is found in the RS2 Axisymmetric Tutorial.

Other uses of the Load Split option are also possible, due to the general formulation of the Load Split / Custom Load Split option in RS2.