Practice Question: Lateral Pressure on a Sheet Pile
NCEES Civil PE Specification Soil Mechanics: Lateral earth pressure, Effective and total stresses
Problem
A sheet pile wall is used to support soil in a vertical trench, as shown in the figure. The dredge side is located 15 feet below ground level and water table is at 10 ft from the ground level. The overall length of the sheet pile wall is 25 feet. The total lateral pressure (lb/ft) on the wall due to the active soil is most nearly:
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Solution
The active earth pressure coefficient is given by:
\(K_a=\frac{1-sin{\varphi' }}{1+sin{\varphi' }}\)
\(K_a=\frac{1-sin30}{1+sin30}=0.33\)
At a depth of 10 feet, the effective vertical pressure is \(125×10 = 1,250\ psf\).
The effective horizontal pressure is then calculated as \(0.33 × 1,250 = 412.5\ psf\) and total horizontal pressure is \(412.5 + 0 = 412.5\ psf\) (since we are still above the water table)
At a depth of 25 feet, the effective vertical pressure is \(125 × 10 + (125 – 62.4) × 15 = 2,189\ psf\).
The effective horizontal pressure is \(0.33 × 2,189 = 722.37\ psf\)and the total horizontal pressure \(= 733.37 + 62.4 × 15 = 1,658.37\ psf\).
Therefore, the total horizontal earth pressure diagram increases from zero at the surface to 412.5 psf at a depth of 10 feet and then to 1,658.37 psf at a depth of 25 feet.
This diagram can be divided into a triangle from depth = 0 to depth = 10, a rectangle from depth =10 to depth = 25, and a triangle from depth = 10 to depth =25.
The resultants of these pressure diagrams are successively calculated as follows:
