Stable Feature Behind MSE Wall / Narrow Wall

This will be one of several  posts regarding MSE walls with complex geometry. The main references for this post and the posts to follow will be the research conducted by The Federal Highway Administration (FHWA) and mainly the publications listed below. The methods presented are simplified / preliminary methods. Ultimately a limit equilibrium analysis should be run. However this is beyond the scope… for now.

References

FHWA-NHI-10-024 Design and Construction of MSE walls and Reinforced Soil Slopes

FHWA-NHI-00-043 MSE Walls and Reinforced Soils Slopes Design and Construction Guidelines (Now superseded by publication above)

FHWA-CFL/TD-06-001 Shored MSE Wall Systems (SMSE) Design Guidelines

All of which can be found here on FHWA website.

Overview

I am posting my notes that correlate to the spreadsheet for now and a brief overview. We will elaborate more on the procedure in the near future.

The stable feature prevents external lateral earth pressures from exerting force on the reinforced soil mass. Therefore traditional sliding and overturning are not generally a design concern. For the trial wedge we define the geomtry and solve for the forces in the horizontal and vertical directions. We have two unknowns and two equations of equilibrium which we solve using matrix algebra (in excel) to determine the active force on the wall.

Required checks are as follows:

1. Pullout of geogrid
2. Reinforced soil and stable feature interface failure plane stability
3. Bearing
4. Global / Slope stability

Calculation

Force Diagram – Stable Feature Behind MSE Wall

Calculation assumes that the stable features extends up or very near the top grade surface. The wall face, top grade and stable feature slopes may all be adjusted. Currently the failure angle must be ‘manually’ adjusted to find the maximum active pressure acting on the back of the wall facing units.

Notes

Trial Wedge with Stable Feature Behind Wall Notes HTE

Spreadsheet

Trial Wedge for Stable Feature

As always please use with caution and check for errors!

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Strip Load Surcharge Analysis using Elastic Methods

UPDATED – Problem Solved…

Here we will dig deeper into analyzing strip loads with elastic methods. First to avoid confusion between seeing similar equations which use different reference angles, we will set our own nomenclature.

Strip Load – Elastic Methods RSF Nomenclature

Nomenclature

K = Constant typically between 1 and 2, depending on the stiffness of the wall. It may be appropriate to use K=1 for flexible walls such as cantilevered sheet pile, segmental walls. It may be appropriate to use K=2 for rigid walls. Refer to CivilTech Software manual (http://www.civiltechsoftware.com/downloads/sh_manu.pdf).

Below are (2) common equations which result in the same solution but are shown differently. I will refer to these equations as the integrated method or equations. Most codes and design guides refer to these equations but it seems too differ on who is credited. Some refer to them as Boussinesq as modified by Tang or Spangler, others Mindlin or Terzaghi (although Terzaghi is mostly responsible for modifying point and line load elastic equations).

Note that β is located at half of θ and not half the width of the strip load.

The other

In Joseph Bowles’ “Foundation Analysis and Design” he discuses different methods of analyzing offset surcharges using elastic methods. He discuss the work of Spangler and the factor of two suggested by Mindlin. In summary he suggests that Spangler’s experiments were not accurate and possibly flawed due to the setup geometry. Also the equations derived by Spangler use a Poisson’s ratio of 0.5 which may not be correct for all soils. However Spangler’s equation for the strip load results in the same equation as shown above. Bowles also states that Mindlins reasoning for the factor 2 (Mindlin says that a rigid wall produced a mirror effect) is wrong.
Bowles suggests to only use the original Boussinesq equation.

[EQN – 1]

With these equations one can “discretize” the strip load. Meaning you divide the strip load into a series of concentrated loads. Then apply the Boussinesq equation to each point load. Then the sum the results to find the resulting pressure at a certain elevation on the wall. You then find these resulting pressures at a certain number of elevations on the wall and sum these to find the resulting total force. It should be noted that Poisson’s ratio should be modified so that it represents a plan strain condition.

where represents a triaxial condition
Refer to Excavating Systems, Planning, Design and Safety, 2009 for the following suggested values of
Moist clay soils: 0.4-0.5
Saturated clay soils: 0.45-0.5
Cohesionless, medium dense: 0.3-0.4
Cohesionless, loose to medium: 0.2-0.35

Here are some notes on the discretized method (semi-large file – about 10MB, I will try to shrink later):
Boussinesq Strip Load Discritization Method 2

Now my problem is this – when I compare the “discretized” approach to the integrated I do not get similar values, not even close. I have to think that I am in error somewhere, but I cannot find where. I have compared spreadsheets to other programs to hand calcs. I will continue to search, but for now, I have attached a couple hand calcs showing the discrepancy. I will also attach a spreadsheet comparing techniques.

UPDATE:

I believe I have now solved this problem. Where I went wrong – When integrating for a strip load you would use boundary conditions from +infinity to -infinity. Which is NOT what I was doing. I was taking the load as if it was an AREA surcharge over a one foot length (along the wall). This is not right. I must say though that Bowles does a poor job explaining that part (in my opinion). Therefore if you want to simulate a stip load you MUST enter a large “Y” dimension so that the program realizes the effect of a STRIP load and not an AREA load. This should really be built into the worksheet but is not yet.

Attached is a hand calc comparison between the “integrated” and discretized approach.
Boussinesq Integrated vs Discretized
Elastic Method – Compare Integrated to Discretized

Elastic Methods Nomenclature Notes

Elastic Methods Spangler Derives Integrated Method
Offset Surcharge Strip Load Comparison Spreadsheet

Another problem when using elastic methods is that all equations assume that the load is applied at the same elevation as the top of the wall. How can we handle a slope atop the wall with a load applied at the top of the slope? Well the railroad design manuals (See UPRR Shoring Manual) distribute the load down through the soil at a certain angle (they use a 2V:1H) and find a new uniform load applied at this elevation.

Elastic Methods – Slope Diagram

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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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Just like any other engineering problem it is wise to start with a free body diagram. This will help you get a feel for the loads and what we need to do to resist them. Then next thing is to have an understanding of what assumptions are being made in the analysis. For reference I will use earth retention system and retaining wall interchangeably for most of following articles.

There are many types of earth retention systems but here are some of the basics:

Soldier Pile wall which may also use soil anchors, deadman or whalers.

Soldier Pile and Lagging

Sheet Pile wall which may also use soil anchors, deadman or whalers.

Sheet Piling

Concrete cantilever retaining walls which may be used in some foundations as well.

Concrete Retaining wall

Segmental Retaining Walls which may be made up of large concrete units or reinforced with geogrid.

Tiered Segmental Retaining Walls

These are just some of the basics but the principles of almost all systems are very similar. No matter what system is chosen the retaining wall must be designed to resist soil pressure, hydro-static pressure, surcharges and any other externally applied loads (typical hand rails, guardrails or fences).  Typically there are there areas of stability that should be checked – external, internal and global (or slope stability). External stability typically refers to sliding, overturning and bearing failures of the wall acting as a rigid body. Internal stability is a check of the components which make up the wall to ensure the wall is acting as a rigid body. Overall or global stability is an evaluation of the entire excavation or slope of soil which the wall is bearing on and retaining. This analysis is most commonly preformed by the geotchnical engineer but should be clearly stated on the plans as to whether or not this failure state has been evaluated.

We will now move on to address the lateral earth pressure do to soil and hydrostatic load.

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