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# FOS for overturning, retaining wall.

## FOS for overturning, retaining wall.

(OP)
I need a second opinion on the method of calculating FOS for a gravity retaining wall. This is a port quay wall structure (water retaining, so high water table).

When calculating the FOS (restoring/overturning), I get significantly different results depending on how I sum the forces.

If I use an effective unit weights, i.e. bulk above water line and bulk minus water weight below, I get very different results as opposed to using full bulk unit weights and a buoyant overturning force to counteract this.

Basically:

EQ1: FOS = effective unit weights / overturning forces with no buoyancy.
EQ2: FOS = bulk unit weights / overturning forces including a buoyancy acting at the base

Hopefully this make sense, what are your thoughts? At the end of the day the differential between overturning and restoring is the same, but because for EQ2, you have higher numbers on top, and on bottom, you get a much smaller FOS.

### RE: FOS for overturning, retaining wall.

Not to criticize,but are you sure about these numbers "bulk minus water weight". Did you use the void ratios and specific gravity in a formula only? You don't subtract anything from the saturated unit weight, although it is roughly OK. I use this formula Sat. unit weight = (G-1)*62.4/(1+e) in lbs/c.f. Where G is specific gravity and e is void ratio.

### RE: FOS for overturning, retaining wall.

Whoops. The formula is for submerged unit weight, not sat. unit wt. Excuses an Old guy please.

### RE: FOS for overturning, retaining wall.

I've had the same conundrum on deadman calcs where the deadman guy was in tension. (For the sliding check, you can subtract the guy uplift from the deadman weight for the base reaction, but doing the same for overturning will increase the factor of safety (as I concluded, artificially)).

I eventually decided that #2 was the rigorously correct way of calculating overturning -- as it better accounts for the external forces acting on your structure -- although I suspect that some engineers may not consider the difference, and that probably eats into the typical 1.5 FS from time to time.

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