Tractive Stress (aka Tractive Force, Shear Stress) Calculations and Design

Introduction

When conduits and channels have sufficient tractive stress they are essentially self-cleaning in that particles will either not settle or they will be re-suspended if they do. To determine if there is sufficient tractive stress in a gravity conduit or channel, it is necessary to compare the actual tractive stress calculated by the model with a target tractive stress required to move particles. The tractive stress does not need to continuously exceed the target tractive stress to be self-cleaning but should exceed the target at least some time during each day.

Related PowerPoint presentation available for download here:

Tractive Force.pptx

Solvers

Conduit tractive shear stress is now calculated when using the following solvers (versions 10.00.00.40 and later).

• GVF-Convex
• Explicit
• Implicit (Dynamic Wave)

Note: Previously (versions 08.11.xx.xx), tractive stress was only supported by the GVF-Convex solver.

Tractive Stress Calculations

Tractive stress is computed using the equation:

τ = ρgRS

Where

τ = tractive shear stress, Pa
ρ = fluid density, kg/m3
g = acceleration due to gravity, m/s2
R = hydraulic radius, m
S = slope of energy grade line

Reference: Wastewater Collection System Modeling and Design, chapter 2.9

Tractive Stress Fields

The target tractive stress required to have self-cleaning conduits can be specified globally in the calculation option field "Tractive Stress (Global Minimum)".

Local minimums can also be specified on a per-pipe basis and will override the global target. To do this, set the conduit/channel property "Use Local Minimum Stress (Local Minimum)" to True and enter the target value for that individual element into the field "Tractive Stress (Local Minimum)".

The following results are provided. The model calculates that available tractive stress for each link element and reports if the target value is exceeded for the current time step or at any time step.

The flow used by the tractive force calculation is capped at the full flow capacity of the pipe. So if the calculated flow in the conduit is higher than the capacity (i.e., if the pipe is above capacity), the tractive force will be based on the full flow capacity. If the flow is less than the full flow capacity, the tractive force will be based on the actual flow results.

Using Tractive Stress as Design Criteria

Starting with the release of CONNECT Edition (version 10.00.00.40 and later) tractive stress be included in constraint based design.

The tractive stress constraint will not be met if there is a conflict with either the maximum Cover or maximum Velocity constraints.
Similar to other design constraints, there will be warnings if the new tractive stress constraint is not met, these warnings are only shown if the tractive stress design is included in the design process (the "Include Tractive Stress Design" check box is checked).

Note: Tractive Stress is also referred to as Tractive Force and Shear Stress. While the term “Tractive Force” is commonly used, the quantity of interest is actually tractive stress which has units of force per unit area parallel to the direction of flow.

Viewing Results with Color Coding

You can also color code by "tractive stress target exceeded" or "tractive stress target ever exceeded" to visualize:

Troubleshooting

Solutions to problems related to Tractive Stress are documented here.

Tractive stress is negative for a conduit with adverse slope

Due to the negative pipe slope, the calculated tractive stress for a conduit with an uphill (adverse) slope will show as negative. This issue was reported as of version 10.03.04.53. This issue is planned to be addressed in a future version - reference # 1002119.

See Also

Help Article "Tractive Force Design"