Design a Sleeper Retaining Wall

Where a low height of soil needs to be designed, a sleeper retaining wall offers an economical and easy to construct option. Calcs.com provides an easy to use a calculator that caters for the majority of common structures. Does this calculator apply to your situation:

• Are you embedding the steel post into an in-situ concrete pile of less than 5m length?
• Are the surcharge loads predominantly static (i.e. no earthquake or frequent traffic loads expected)

If all the above apply, this calculator is for you! Note that the analysis methods used in our calculator are generally intended for typical residential retaining walls, up to about 3 meters in height, though they may still be used for higher retaining walls.

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1. How to Enter RW Geometry?

The geometry inputs are used to determine the loading applied to the structure, as well as its ability to support those loads. This includes:

• Retained Soil Force applied over the retained height
• Wind Force applied over the fence height (reduced when fence is permeable e.g. wire-mesh)

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2. How to Determine Retained Soil Properties?

The retained soil properties are used to determine the pressure that the earth applies to the sleeper portion of the wall. This includes:

• Angle of Friction - Guidelines are available for typical soils. Some typical values are available at https://www.geotechdata.info/parameter/angle-of-friction
• Unit Weight of Soil - Majority of soils (clay / sand) are 18 kN/m3, so no change is generally required
• Retained Soil Condition - Is the fill imported and meeting consistency values? AS 4678 uses this categorization, as some types of fills (e.g. uncontrolled) may have greater variation in properties. Expand the label to see what factors are used out of Table 5.1 (A).
• Characteristic Effective Cohesion of Retained Soil (** See NOTE below) - It is used to reduce the earth pressure. Some values are available when expanding the description.

** NOTE: Retained Soil Cohesion - Engineering judgment required when taking into account the cohesion of retained soils for calculating active earth pressure. It is advised to only use c’ > 0 when:

1. The retaining wall is supporting an undisturbed soil (not a fill material);
2. The soil exhibits considerable reliable cohesion;
3. The structure includes an impermeable surface membrane and drainage system, such that any water does not enter or can quickly get drained out from the retained soil.

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3. How to Determine Pile Soil Properties?

• Undrained Shear Strength of Foundation Soil (Undrained Cohesion): This is usually referred to as Su or Cu. Refer to ‘Section 5 - Theory Background’ below to see how this is used to calculate pile capacity. Some values are available when expanding the description.

• Foundation of Soil Condition - As for retained soil, AS 4678 uses this as some types of fills (e.g. uncontrolled) may have greater variation in properties. Expand the label to see what factors are used out of Table 5.1 (A).

• Coefficient of Horizontal Subgrade - This is the amount the soil deforms when pressure is applied. This input becomes visible only if you are checking for pile deflection. Typical values may be obtained from literature. An example of values are available here Geoengineer - horizontal-soil-subgrade-reaction-in-pile-foundations

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4. How to input loads

The sleepers spanning between the wall will take active pressure from backfill. In addition, the fence will attract wind load that transfers through to the steel posts. The pressure will result in a total horizontal force Vu acting with an effective lever arm or eccentricity (e) above ground level (top of pile). The post transfers a horizontal force (Vu) and a moment (Mu=Vu × e) per spacing acting on the pile. The weight of the wall will also result in an axial force (Pu) acting vertically on the pile. Only a few additional load inputs are needed such as wind, surcharge to finalize the design inputs, as shown below. The remainder is automatically calculated based on the geometry and spacing of the structure.

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5. Theoretical Background

For the analysis of loads from backfill (retained soil), Calcs.com calculates the Coefficient of Active Earth Pressure in accordance with Appendix E – Figure E2 for both cohesive and granular soils (pictured below). To calculate the minimum embedment of the pile, Calcs.com uses an analytical method both for the strength and deflection of short rigid piles. This method was originally developed by Broms, but has been improved and refined, and is detailed in the book “Pile Design and Construction Practice - M.J. Tomlinson, Fourth Edition”. It provides an empirically derived Ultimate Lateral Resistance under the following conditions:

• Top of pile is allowed to rotate (generally applicable for all sleeper retaining walls)
• Pile is embedded into a single type of cohesive soil
• A constant lateral spring stiffness can be assumed for the soil (also known as Coefficient of Horizontal Subgrade Reaction)

The shape of the soil reaction & bending moment diagram are derived from statics. Specifically, it is the case where the maximum permissible clay soil reaction along the full length of the pile apart the top-most soil (=~ 9 × Cu * dp) is in equilibrium with the applied force Vu & applied moment Mu. A similar result may be obtained using a commercial finite element package, and limiting the soil spring reaction as mentioned above. Calculated distances shown in Calcs.com. The minimum depth of embedment is established by equating the Vu to total lateral resistance. Specific to the above diagram, the minimum depth of embedment is calculated as hp,min = g+f+1.5⋅dp. Calcs.com will default hp to hp,min unless specifically overridden.

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Method & scope

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Calculation method

The Sleeper Retaining Wall calculator designs a post-and-sleeper retaining wall in which vertical steel posts, embedded as piles, resist lateral earth pressure and any wind load from a fence above. Horizontal timber sleepers spanning between the posts are designed separately in a linked beam module. The calculation covers earth pressure, fence wind load, pile embedment strength, pile deflection, and steel post capacity.

Earth pressure and loads

Lateral earth pressure is estimated with the Rankine-Bell method per AS 4678:2002 (Figure E2), for granular or cohesive retained soil. The wall is conservatively assumed to be vertical. Pressure is built from the unit weight, angle of internal friction, and, where selected, the effective cohesion of the retained soil, plus any groundwater height and surcharge. Horizontal forces are resolved separately for strength (with the applied load factor) and serviceability analysis.

Wind loads on the fence

Where a fence sits above the wall, wind pressure on the fence is derived from the AS 4055:2012 wind classification, the fence height and length, and the solidity ratio of the fence structure. The resulting horizontal force is added to the demand on each post over its tributary width.

Pile strength design, cohesive foundation soil (Broms method)

For cohesive foundation soil, the required embedment of the short free-head pile is designed by the Broms method, using the undrained shear strength (undrained cohesion) of the foundation soil. Material uncertainty factors from AS 2159:2009 are applied according to the retained and foundation soil condition selected.

Pile strength design, cohesionless foundation soil (IBC method)

For cohesionless foundation soil, the embedment is designed using the method of IBC 2018 Section 1807.3.2.1, based on the foundation soil classification and the coefficient of horizontal subgrade reaction.

Pile deflection (Broms method)

Deflection at the top of the embedded post is calculated by the Broms method from the coefficient of horizontal subgrade reaction and, optionally, the pile rotation. The tip deflection is compared against the maximum allowed absolute deflection and the length-to-deflection ratio limit.

Steel post capacity (AS 4100:2020)

The embedded steel post is checked to AS 4100:2020 for the governing horizontal forces. The calculator reports shear capacity, moment section capacity, and the shear-moment interaction, and it evaluates the deflection of the steel post. Posts are assumed oriented so the major axis resists the soil loads.

Assumptions

The maximum retaining wall height is 3 m and earthquake loads and liquefaction are not considered. The concrete pile is assumed not to crack or fail in bending, which holds where the steel post is embedded to full depth; the user should verify this. Group effects for embedded piles are ignored, and the sleeper is designed in a separate, linkable beam module.

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How to use it

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Available presets

Each preset opens the calculator with a typical setup already entered.

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Common questions

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Next steps