Liner Type: Reinforced Concrete

The Reinforced Concrete liner type greatly simplifies the task of modeling composite two-component liner systems such as reinforced concrete, or steel sets and shotcrete.

• The reinforcement component is typically steel (e.g. rebar, I-beam, lattice girder)
• The "concrete" component may represent concrete, shotcrete or other material

The properties of the reinforcement and the concrete are defined separately in the input dialog. For analysis purposes, RS2 uses this input data to determine a homogeneous beam cross-section which has properties equivalent to the actual reinforced liner. After the analysis, the forces within the reinforcement and concrete components are then back-calculated from the overall results and displayed on support capacity plots in the RS2 Interpret program.

The Reinforced Concrete liner type in RS2 was designed to be used as an Elastic support material in conjunction with the support capacity plots in the Interpret program. Although a Plastic material option is provided, in most cases you should use the Elastic option, as discussed below.

Like a Standard Beam liner, a Reinforced Concrete liner is made up of beam elements which respond to flexural, axial (compressive or tensile) and shear loads. In fact the RS2 analysis engine does not distinguish between a Standard Beam liner and a Reinforced Concrete liner, given equivalent properties. The primary difference between the two liner types is the input data and the output of results.

NOTE: see the Standard Beam versus Reinforced Concrete topic for a discussion of the differences between these two liner types in RS2.

To define the properties of a Reinforced Concrete liner:

1. Select Define Liners from the toolbar or the Properties menu.
2. Select Liner Type = Reinforced Concrete.
3. Enter the reinforcement and/or concrete properties described below.
4. You can turn OFF either the reinforcement or the concrete component of the liner by clearing the desired check box. This allows you to use the Reinforced Concrete liner option to model support which only uses one component.

Initial Conditions

For a Reinforced Concrete liner, the initial conditions include the Unit Weight and Initial Temperature. For Standard Beam and Reinforced Concrete liner types, the Include Weight in Stress Analysis option controls whether the liner unit weight will be accounted for in the stress analysis.

Unit Weight

The Unit Weight will be included in the stress analysis if the Include Weight Stress Analysis option is ON. The Unit Weight will be included in the thermal analysis if the Thermal Analysis = Steady Thermal FEA or Transient Thermal FEA in the Project Settings menu, and the Activate Thermal option is ON in this dialog.

Include Weight in Stress Analysis

See the Standard Beam topic as the definition of Include Weight in Analysis is the same for both Reinforced Concrete and Standard Beam liner types.

NOTE: for Reinforced Concrete the unit weight of reinforcement and concrete are defined separately. Reinforcement weight is defined per linear unit of reinforcement.

Initial Temperature

The Initial Temperature option is only available when Thermal Analysis is enabled in the Project Settings menu AND the Activate Thermal checkbox is selected in this dialog.

Concrete Properties

First of all, note that the "concrete" component of a Reinforced Concrete liner does not necessarily have to be concrete. It may represent shotcrete or other material which surrounds the reinforcement. The name concrete was chosen for convenience as a typical matrix material for the reinforced liner.

The required Concrete properties are:

• Thickness
• Young's Modulus
• Poisson's Ratio
• Compressive Strength
• Tensile Strength

NOTE: you can turn OFF the concrete component of the liner by clearing the Concrete check box. This allows you to use the Reinforced Concrete option to model a "reinforcement only" liner (e.g. steel sets without shotcrete).

Reinforcement Properties

The reinforcement component of a Reinforced Concrete liner is typically steel (e.g. rebar, I-beam, lattice girder), but could be any material as long as the reinforcement configuration can be defined by the available input parameters.

The required Reinforcement properties are:

• Spacing
• Section Depth
• Area
• Moment of Inertia
• Young's Modulus
• Poisson's Ratio
• Compressive Strength
• Tensile Strength

NOTE:

• For assistance with entering the Reinforcement properties, you can select the Common Types button. This will display a dialog which includes a database of hundreds of common reinforcement types. See the Reinforcement Database topic for details.
• You can turn OFF the reinforcement component of the liner by clearing the Reinforcement check box. This allows you to use the Reinforced Concrete option to model a homogeneous concrete or shotcrete liner, for example.

Advanced Properties

For a Reinforced Concrete liner, its advanced properties include the Material Type, Sliding Gap, Beam Element Formulation, and Axial Strain. Each is described below.

Material Type

Material Type: Elastic

The Reinforced Concrete liner type in RS2 was designed to be used as an Elastic support material. This allows the calculation of liner safety factors and visualization of the liner data on support capacity plots. In most cases you should use the Elastic material type for a Reinforced Concrete liner.

When the Material Type = Elastic, the liner will only respond elastically to loading, and there will be no upper limit to the loads which can be sustained by the liner (i.e. the liner can carry loads greater than the strength of the liner material). The strength properties of the liner are used to compute the safety factor of the liner elements and to generate support capacity envelopes which are viewed in the RS2 Interpret program.

Material Type: Plastic

In general, the use of the Plastic material type option is NOT recommended for the Reinforced Concrete liner type in RS2. The Plastic option should only be used if you specifically wish to define your liner input properties using the Reinforced Concrete liner type, and you wish to model liner yielding. However, in this case you must be aware of the following issues:

• The safety factors and support capacity plots in the RS2 Interpret program will NOT BE VALID for liner elements which have yielded, and should NOT be used for design purposes.
• The plasticity calculation for Reinforced Concrete liners involves several simplifying assumptions, which are described below.

Assumptions for Plastic Liner

1. Yielding is computed for the equivalent homogeneous cross-section, using the layering method described for the Standard Beam liner type. Actual failure mechanisms of the composite two-component Reinforced Concrete liner are NOT considered.
2. The tensile and compressive strengths of the composite liner are computed by weighting the strengths of the reinforcement and concrete according to their area. For example:

   
   sigcp = r_sigcp*Ar/(Ar+Ac) + c_sigcp*Ac/(Ar+Ac)

   where:

   sigcp = peak composite compressive strength

   r_sigcp = peak reinforcement compressive strength

   c_sigcp = peak concrete compressive strength

   Ar = Area of reinforcement per unit length of excavation

   Ac = Area of concrete per unit length of excavation

3. Both the tensile and compressive strength of the reinforcement are assumed to be perfectly plastic. This means that the residual tensile strength is equal to the peak tensile strength and the residual compressive strength is equal to the peak compressive strength.
4. For concrete, the residual tensile strength is zero and the residual compressive strength is 20% of the peak.

Sliding Gap

See the Standard Beam topic as the definition of Sliding Gap is the same for both Reinforced Concrete and Standard Beam liner types.

Beam Element Formulation

See the Standard Beam topic as the definition of Beam Element Formulation is the same for both Reinforced Concrete and Standard Beam liner types.

Axial Strain

This option allows users to assign axial strain to simulate liner contraction/expansion. In terms of the sign convention, negative input parameter (-) indicates contraction, and positive (+) represents expansion. The liner axial strain can be staged, using the Stage Concrete Properties option in the dialog.

Thermal

This section is only available if the Thermal Analysis is enabled in the Project Settings menu.

You can select the checkbox for Activate Thermal to include thermal properties for liners. Available parameters depend on the involved thermal method, as described below.

Thermal Method: Static Temperature

If thermal method = Static Temperature, available properties include the Static Temperature, Thermal Expansion, and Initial Temperature (under Initial Conditions section).

The Static Temperature parameter can be defined either as a Constant value or a Grid (temperature girds can be entered in Temperature Grid from the Thermal menu).

Thermal Method: Steady Thermal FEA

If thermal method = Steady Thermal FEA, available properties include the Thermal Conductivity, Thermal Expansion, Initial Temperature, and Unit Weight (under Initial Conditions section).

Thermal Method: Transient Thermal FEA

If thermal method = Transient Thermal FEA, available properties include the Thermal Conductivity, Specific Heat Capacity, Thermal Expansion, Initial Temperature, and Unit Weight (under Initial Conditions section).

Stage Concrete Properties

Concrete properties of a Reinforced Concrete liner can be modified at different stages of a multi-stage model, by using the Stage Concrete Properties option in the Define Liner Properties dialog. This could be used, for example, to model the increase in strength and stiffness of shotcrete or concrete after initial placement.

See the Stage Liner Properties topic for details about staging concrete properties.

NOTE: reinforcement properties of a Reinforced Concrete liner CANNOT be staged, only the Concrete properties can be staged.