This post is an extension of a previous post https://howtoengineer.com/retaining-wall-lateral-earth-pressure/

The spreadsheet will use the nomeclature found in NCMA’s Design Manual for Segmental Retaining Walls and Coulomb Theory.

See here:
Lateral Earth Pressure – Soil Basic 1 Geometry Sketch

Also here is a ‘fun’ spreadsheet where you can enter values in green columns. There are a bunch of graphs to show you how ka (the horizontal earth pressure coefficient will change with different values for backslope, effective friction angle, wall batter, and friction between wall and soil.

Earth pressure spreadsheet: Lateral Earth Pressure – Coulomb

Attached are a couple of TEDDS calcs that show the analysis of active and passive pressures based on Coulomb Theory. I am working on incorporating a berm distance into the passive equations and will probably present this in a seperate post. Using Coulomb equations for Toe slopes and backslopes should be used with caution and these conditions may warrant a Global (or slope) Stability Analysis!

Soil Evaluation NAVDAC DM – 7.2

Soil Evaluation – NCMA

Equivalent Slope

Another note: When there is a toe slope that passive pressure will be reduced a good reference for this condition is CALTRAN Trenching and Shoring Manual 2011 and NAVDAC DM 7.2 page 7.2-65 Figure 4 .

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This is a short post in which I will elaborte on at some point in the future.

I am attaching a pdf of a TEDDS calculation that is based on the 1990 California Trenching and Shoring.  The design concept is similiar to Cantilevered Soldier Pile Wall Design.

Attachment: Soldier Pile Design w-Anchor Cali TnS 1990

Here is the link to the manual: http://www.vulcanhammer.net/geotechnical/TrenchingandShoring.pdf

And new 2011 manual which is also very helpful:

http://www.dot.ca.gov/hq/esc/construction/manuals/

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Cantilevered Solider Pile Retaining Wall Design

I have attached a pdf showing the basics of designing a cantilevered solider pile retaining wall. It is largely based on the California Trenching and Shoring manual. The California trenching and shoring manual is a great design reference for earth retention. However I found some parts to be slightly confusing so I tried to make it easier to understand.

PDF: Soldier Pile and Lagging Caltan 1990

Also a TEDDS calc example: Soldier Pile and Lagging Caltan 1990 Tedds Calc Note that I need to update the nomenclature and I haven’t incorporated the surcharge how I show in the hand calc, but it should be conservative.

For an Anchored wall see Anchored Soldier Pile Design

Design Concept

The design method is very similar to sheet pile design. Instead of multiplying the soil pressure that is above the excavation line and acting on the pile by the spacing of the piles a reduction factor ‘f’ is used. This factor reduces the passive pressure resistance. This factor also considers that the passive pressure will act over a greater width than just the pile width. Therefore and effective pile width is used (based on the soil friction angle with a maximum value of 3). Therefore you must remember that after you determine the maximum moment on the pile you should multiply it by the pile spacing to get the total moment. Also you can see that if you set ‘f’ = 1.0 you can use this design methodology for sheet pile design as well.

A general ‘net’ earth pressure diagram is assumed. Essentially the portion of the soldier pile that is above the excavation line (bottom grade) is subject to active pressure. Then below the excavation line passive pressure is exerted on the pile until a point of no translation or a pivot point per se. This is the point where the pile is assumed to pivot about. Because of this rotation there is now passive pressure on the back (high) side of the pile. More than one soil stratum may be used however the active and passive pressure diagrams would need to be adjusted accordingly. From there it is simple statics. The pile must be in equilibrium, so sum your forces and moments to find the distance of these inflection points. It should be noted that the embedment depth of the pile should be increased 20-40 percent after ‘D’ (the depth below the excavation line) is found in the design example. Alternatively a factor of safety may be applied to the passive pressure. Any type of lateral pressure resulting from a surcharge may be superimposed on the soil pressure diagram and an example can be found in the California Trenching and Shoring Manual.

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Retaining Wall – Lateral Earth Pressure

Update: For spreadsheets and more examples of calculating active and passive pressures see Lateral Earth Pressure II

We will briefly discuss lateral earth pressure caused by soil weight and ground water effects. I’m not going to go through all the derivations just the results and how they are typically used in practice. More of the ‘I don’t want to hear about the labor just show me the baby’ technique.

See this post for a broader overview of earth retention design:

General Earth Retention Design

Rankine and Coulomb Methods

The most common theories for determining lateral pressure due to soil are Rankine and Coulomb methods. Both methods use an idealized failure plane where the soil ‘shears’ itself and causes the soil mass to move toward the wall. The Rankine method assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical, the failure surface on which the soil moves is planar, and the resultant force is angled parallel to the backfill surface. The Coulomb method accounts for friction between the wall and the soil and also a a non-vertical soil-wall interface (battered wall). Earth pressures may also be found in geotechnical reports as Equivalent Fluid (or Lateral) Pressures (EFP or ELP). Which are given in units of lbs per sq ft. per ft of depth or pcf. All this represents is a lateral earth coefficient already multiplied by the soil density. So if you find your active pressure coefficient using one of the formulas below say Ka=0.33 and multiply this by the soil density say 120 pcf you get about 40pcf. Because earth loads are applied as uniformly increasing loads (triangular distribution against the back of wall). The equivalent lateral pressure is 40psf / ft of depth.

Basic Geometry Sketches

Lateral Earth Pressure – Soil Basic 1

Lateral Earth Pressure – Soil Basic 1 Geometry Sketch

Rankine equations for Active and Passive pressure (more on that below):

φ = (phi, html format looks slightly different than image) effective friction angle of the soil

β = Angle of backslope from the horizontal

For the case where β is 0, the above equations simplify to

 Coulomb equations:

φ = (phi, html format looks slightly different than image) effective friction angle of the soil

β = Angle of backslope from the horizontal

δ = effective friction angle between the two planes being evaluated. Usually between wall and soil with typical values being 2/3*φ or between two soil surfaces (i.e. for segmental retaining walls – reinforced zone soil and retained soil)

θ  = batter or angle of wall from the horizontal (you may see some coulomb eqns which use values from the horizontal so don’t be confused)

To account for wall batter the hoizonatal and vertical component of the active pressure are:

Kah=cos(δ+θ)

Kav=sin(δ+θ)

The Active state referes to pressures where the soil is sliding toward the wall or the wall is giving. The Passive state refers to soil pressures where the soil is being compressed such as soil at the low side of a sheet pile wall. Passive pressures will be higher than active as you can imagine that the soil will ‘push back’ when it is being pushed. The soil may also be ‘at-rest’. You may wish to use at rest pressures when designing concrete basement walls which do not allow much movement or other type retaining walls where minimal movement is wanted.

At rest pressure coeffcient:

K0= 1 − sin
(φ)

References

Reference for wall movement under to ‘engage’ active pressure:

In Winterkorn and Fang, “Foundation Engineering Handbook” Table 12.1
Sand:
Active Pressure: Parallel to Wall .001H
Active Pressure: Rotation About Base .001H
Passive Pressure: Parallel to Wall .05H
Passive Pressure: Rotation About Base >.1H
Clay:
Active Pressure: Parallel to Wall .004H
Active Pressure: Rotation About Base .001H
Passive (No values given) however NAVDAC DM2.2 states that the required strain or wall movement required to mobilize the passive soil is about 2x the movement required for active pressure.
A great reference, but I’m sure it’s been out of print for a while.  My copy is dated 1975.

Water Pressure

Water pressure can be greatly reduced by providing drainage aggregate and drain pipe directly behind the wall. The density of water is much less than most soils (64 pcf) however its lateral pressure coeffcient is = 1.0 so the Equivalent Fluid or Lateral pressure is 64.5 psf/ft which is higher than most soils in an active pressure case. Therefore water pressure can have a serious impact on the lateral load applied to wall and should be given proper attention if the water is not given a relief source as mentioned above.

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