Lateral Pressure due to Point Load Equation Discrepancies

[Alex_1]

I am using two equations that give completely different solutions for lateral pressure due to point load.

Equation 1 is based on Boussinesq's solution from Foundation Engineering Handbook edited by Hsai-Yang Fang 1991.

Equation 2 is from NAVFAQ and Caltrans Trenching and Shoring Manual 2011.

I have attached the equations below along with a graph comparing the two from my excel calculations. The scenario is for point load= 3300 lbs, distance from excavation edge to point load of 3 ft, poisson ratio of 0.25, excavation depth of 22 ft. As you can see the solution from Hsai-Yang Fang 1991 is much larger than Navfaq/Caltrans solution.

Does anyone know which equation is correct to use ? Should the solutions be similar ?

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1525891337/tips/quation_comparison_bay2jx.pdf[/url]

https://files.engineering.com/getfi...818-44c1-b8c3-54078552ccaf&file=equations.pdf

 

[JAE]

I would not think that they would be significantly different.

Without knowing your retained height, type of soil, Poisson's ratio of soil, location and magnitude of load, we can't do our own check on it.

The Fang method requires the use of a Poisson's ratio while the other does not as far as I can see.
Also - Fang states that the wall does not move...i.e. a rigid wall perhaps attracting more pressure vs. an active wall?

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[Alex_1]

Please see my revised post with parameters included for my scenario.

 

[Doctormo]

Please provide the example you are modeling. What is Q load and and Q offset distance from the wall that is represented by the curves. If you are using Poisson's ratio, what is the value? Most simplified equations assume 0.50 in the general Boussinesq so that the term (1 - 2u) goes to zero and eliminates that part. This creates some issues as discussed in Bowles.

 

[RFreund]

It's been a while since this has been brought up and something I used to post about frequently. However, just quickly looking at this, my inclination is your input might off. Are you using a spreadsheet?

EIT

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[Doctormo]

Sorry, I see you did provide some data in the original post.

The H.Y. Fang plot is the most correct based on the lateral loading being 2X the calculated load as noted in the Fang text. The other plot is incorrect and not representative of the point loading and Boussinesq distribution.

There is also justification for the load without doubling (±50psf peak). This is a never ending discussion that may be a function of stiffness of the wall structure and other associated items, see Bowles. Equations with and without the 2X factor can be found in various texts.

 

[BridgeSmith]

"Also - Fang states that the wall does not move...i.e. a rigid wall perhaps attracting more pressure vs. an active wall?"

I think that is the key to the discrepancy. For retaining wall design, the "at-rest" pressure coefficient (ko) for a wall that cannot move and engage the interlock of the soil particles, is typically on the order of twice the "active" pressure coefficient (ka) for a wall the can move and engage soil particle interlock. Without movement to engage the interlock, the angle of internal friction essentially goes to zero and the lateral pressure approaches "fluid pressure" reactions.