Checking sheet pile for quick condition

[usuallycivil]

I am just completing a sheet pile design for shoring an excavation. I am quite satisfied with the design, except for analyzing the potential for a quick condition at the toe. In practical terms I have dealt with the issue by requiring dewatering to a depth that I am comfortable will prevent failure at the toe. (Meaning dewatering depth outside the excavation. Inside the excavation will be dewatered to the dredge line). Still it bothers me not to be able to analyze it numerically. I have reviewed the literature, and most authors seem to take me 90% there and leave me hanging. Most derive the equation for critical hydraulic gradient ic=(SG-1)/(1+e). Now what do I do with the result? The USS manual has a simple formula (reduction in submerged unit weight)=20*Hu/D. Now this I can use in my wall analysis to find the max Hu (unbalance head) that will still leave an acceptable FS. But after giving this simple formula, USS goes on to confuse me with a bunch of criptic nomographs. Can anybody shed some light on this subject? The basics of my design problem: braced wall, 18' dredge depth, 11' penetration, med.-dense fine sand, existing water table 2.5' below grade. Thanks!

 

[fattdad]

Draw a flow net and look at the exit gradient at the toe. If the exit gradient is greater then the critical gradient, you must lengthen the penetration (or lower the dewatering depth).

f-d

¡papá gordo ain’t no madre flaca!

 

[oldestguy]

Typically that critical gradient is 1.0 ft. head loss for one foot of flow. We like to spec. 1.0 ft. head loss for two feet of flow. We still got problems when artesian water was present below the tips.

 

[fattdad]

The critical gradient is the ratio of the bouyant unit weight divided by the unit weight of water - typically that's close to unity (confirming oldestguy). I'd agree with a safety factor of 2 also!

f-d

¡papá gordo ain’t no madre flaca!

 

[usuallycivil]

Thanks for your input... but what I really need is something much more specific... short of drawing a flownet, is there a formula I can use? How to calculate the head loss per foot of flow? And what about the USS formula I mentioned, is anyone familiar with it? Thanks in advance.

 

[fattdad]

How to calculate the head loss per foot of flow?

From a flow net (or a numerical model, which is MUCH more complicated). A suitable flow net (especially for confined flow) should not take more than a half-hour or an hour to complete. Once done, you can then take your ruler (knowing the scale) and measure the flow length at the exit square and divide it by the head drop between the equipotential lines. It's really not that hard.

f-d

¡papá gordo ain’t no madre flaca!

 

[PEinc]

The 1987 Pile Buck Steel Sheet Piling Design Manual (and the older 1970 US Steel Sheet Pile Design manual) has a section and chart for checking the depth of sheet pile needed to prevent piping or a quick condition. The chart is on page 125 of the 1987 Pile Buck manual. There supposedly a newer version of the manual which most likely also has the same chart. The US Steel manual has the same chart on page 65.

Based on the width of the cofferdam and the unbalanced hydrostastic head, the chart gives you the embedment required for safety factors of either 1.0, 1.5, or 2.0 in both loose sand and dense sand. The chart also considers that there is all soil below the sheets or an impervious layer at some distance below the tip of the sheets.

Do an internet search for "Pile Buck Steel Sheet Piling Design Manual." It is a must reference for those designing sheet pile walls.

 

[oldestguy]

Short of drawing a flow net and making the equipotential lines at spacing depending on the hydraulic conductivities, here is at least a quick check.

Assume all the soil is the same. Then the difference in elevation between the outside water table and the bottom of the excavation is your head differential.

The flow path is the length of flow from that outside top of water table, down around the tips snd back up to the inside of the excavation.

It really is very simple I wonder why the question.

Divide that head differential, by the flow path to get the gradient. The inverse of that is your safety factor.

Thus the tip embedment below the bottom of excavation should be one half of the head difference.

 

[usuallycivil]

Finally, oldestguy, after reading your last post, a light went on and now I realize what was the mental block that prevented me from "getting it". I understood calculating the critical gradient and applying a FS, but I did not understand how to calculate the actual gradient. Designing storm sewers all the time, hydraulic gradient in my thinking equates to the slope of the hydraulic grade line, and for some reason I could not conceptualize it in the vertical direction. But it's fundamentally the same. Duh!

"It really is very simple I wonder why the question."

Its simple if you understand the words! I just needed someone to 'splain it to me, and you've done that; thanks!

 

[vulcanhammer]

PEInc: Since I co-authored the new Sheet Pile Design by Pile Buck, I can confirm that the charts are in there. But I also expanded the whole topic of water flow in soil and around sheet pile walls. Obviously flow netting is possible, but you can also use finite element software to estimate the gradient. Pile Buck continues to offer this book.

http://www.vulcanhammer.net

http://www.vulcanhammer.info