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

The post Surcharge Analysis – Elastic Methods – Strip Load appeared first on How To Engineer.

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 .

The post Lateral Earth Pressure II appeared first on How To Engineer.

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.

The post Retaining Wall – Lateral Earth Pressure appeared first on How To Engineer.