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(OP)
I have run into some spread footing designs for 3-sided precast bridges and arch elements where overburden loads were reduced by multiplying the active soil pressure times the friction coefficient against the column of soil above the footing. In some cases this vitually eliminates the overburden load and significantly reduces footing size. I cannot seem to find any textbook cases to support this method. Is this a valid method and is anyone aware of a supporting reference? Thank you.

I'm not sure that I understand the query, but the only thing that comes to mind is backfilling for pipelines.  When one excavates a trench to place a pipeline and then backfills the trench, if the trench is narrow (compared to the pipe diameter) then some load relief on the pipe is allowed.  Some of the overburden load which would normally act on the pipe is taken in skin friction between the backfill and the sides of the trench.  This relies on arching of the ground within the backfill which I'm not sure that you will get with your problem.

Hope this is of use

Andy Machon

Since the soil you are concerned with is along the side of the structure and not on top of it, think of it in the following terms....

If the structure were not touched by the adjacent soil, there would be no downward load on the structure.  Since it is touched by the soil, the soil inherently has two relevant forces acting on it constantly due to its own weight.  The relevant forces are the vertical force and a lateral force since the soil has properties similar to a liquid under certain conditions (if the soil were a solid ,not granular, object the lateral force would be 0).  The soil acts like a bunch of marbles in a jar...if you have no jar, the marbles will roll laterally until the pile is flat!

Now there are established soil mechanics relationships between the vertical and lateral forces in soil.  These are the active, passive, and at rest pressure coefficients.  There is sufficient treatment of this concept in most soils textbooks.

Once we establish that there is a lateral force exerted by the soil, then another physics relationship is used to determine the "downward or dragging" effect the soil places on the structure.  The total friction force by the soil acting on the structure is the "normal" force multiplied by a coefficient of friction between the soil and the structure.  In this case the "normal" (or perpendicular) force is the lateral load exerted by the soil.

(OP)
Thank you Ginger and Ron. The concept that is being applied is similar to that used for computing loads in a narrow pipe trench installation. However, in that case you have the fill material acting against the undisturbed sides of the trench. Since there are different settlements, the friction does provide a resisting force. Friction is not considered for embankment installations of pipe, which in my opinion, is more like the open excavation used for typical spread footing.

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