Terzaghi Lateral Load due to Surcharge

[cancmm]

In the 1954 Terzaghi formula for lateral loads due to a point load surcharge, there is a reference to a variable "H". In a sheet pile design, would H be the length of the sheet or simply the excavation depth? From the figures I've seen, the excavation depth seems to be the right answer, however this would imply that the surcharge is negligible/zero below the excavation depth. Any idea which is right?

Thanks.

 

[FixedEarth]

The point load does not automatically dissapear at the bottom of the excavation. It depends on magnitude of the load and proximity to the sheetpile wall.

Try "Foundations and Earth Retaining Structures" book by Budhu for clarification. These formulas are tedious in that one equation would only gve you the lateral earth pressure at one point, say 10 ft below top of excavation.

Lately I have been using SoilStructure's Lateral Stress Software.

 

[wmta]

Based on my experience the surcharge load is usually cut off at the bottom of the excavation due to the fact that the passive resistance of the soil below grade is an order of magnitude greater than the active load.

 

[fattdad]

Here's the general equation for Poisson's Ratio of 0.5:

delta qh= (3Q/pi)*(r^2*Z/R^5) where,

Q= point load
R= line of sight distance to the wall point of interest (using pythagorean theorem with r and Z)
r= horizontal distance to the wall point of interest
Z= depth to the wall point of interest

I've explained the variables as such because you may want to look at wall stresses in other planes (i.e., not just perpendicular to the wall where the point load is applied).

Please note that this equation assumes a non-yielding wall. Please note also that the Bousinessq equation would give you half the value of the equation that I've typed. I've removed the "2" from the denominator because when you are up against the wall, the "free field" stress conditon does not exist. Field measurements by Spangler (1930's) show that the actual wall stresses are about 1.5 to 2 times the calculated values from free field analysis.

Hope this helps.

f-d

¡papá gordo ain’t no madre flaca!