Active Pressure Combined with Water Pressure

[structurebeton]

Can someone show me an example of calculation of equivalent fluid pressure when a retaining wall is designed to support the soil + water the full height?

Thanks.

 

[PEinc]

This is a very basic question. Any soils book or foundation engineering book will address this.

You really did not provide enough information to get an accurate answer. However, Earth Pressure = Depth Below Top of Wall x Equivalent Fluid Pressure.

Water Pressure = Depth below Water x Unit Weight of Water.

Don't forget to include lateral pressures from any surcharges behind the wall.

 

[structurebeton]

Say Ka=0.333
Say soil density = 115 pcf
Say H=10 ft
Water table is at top of wall

Can we say Total Equivalent Fluid pressure = 62.4 psf + (115-62.4)*0.333 = 80 psf?

 

[dgillette]

I think it is much better to think of it as separate active force and hydrostatic force, rather than equivalent fluid pressure. The numbers come out the same if and only if the water table is at the ground surface, the wall is frictionless and vertical, the ground is horizontal, and there are no surcharges. Just get out a Coulomb chart and use that with total unit weight above the water table and bouyant unit weight below (plus 1/2*62.4*h^2).

DRG

 

[hokie66]

structurebeton,

Your calculation is correct.

 

[PEinc]

Basically, yes. (62.4 x 1.0 x D) + [(115-62.4) x 0.333 x D] = 80 PSF per vertical foot of wall.

You did not say what type of wall you have. The earth pressure distribution and magnitude could be different depending on the type of wall and compaction of backfill, if any, behind the wall.

Braced and tiedback walls do not usually have triangular earth pressure distributions behind the walls. Rigid walls may not use Ka. Compacted earth pressures may not be triangular or active.

The actual earth pressure depends on several different factors.

 

[DRC1]

The Bouyant Weight may not be the 115-62.4. Generally quoted unit weights are moist unit weights as oppsed to saturated unit weights, which are slightly higher. Bouyant unit wt is typically around 65 psf for granular soils

 

[structurebeton]

The type of wall would be a reinforced concrete pit, with a floor slab on top. So, for the purpose of backfill it will be like a cantilever retaining wall, with the slab on top, it will act more as a restrained wall.

Interior pit dimensions are 8'-0" X 8'-0" x Depth 10'-6".

I would consider a triangular shaped pressure on the wall, with maximum at the base, using the fully calculated equivalent fluid pressure of 80 psf. Thus, the pressure at the base would be 80psf x 10.5' =840 lb/ft, and total horizontal force would be at 1/3 from the base = 840 x 10.5' x 1/2 = 4410 lb/ft of wall.

This the way I have always calculated retaining walls.

 

[BigH]

http://www.dot.ca.gov/hq/esc/techpu...ridge-design-specifications/page/section5.pdf

 

[hokie66]

Since this is not a cantilevered wall, the k will be greater, as there will not be enough movement to consider the force as active. Probably at rest condition, with k about .5, but you should consult with your geotech.

 

[PEinc]

DRC1 is correct about the saturated soil weight but that's the weight we were quoted.

hokie66, the pit walls will deflect when they are being backfilled, before the concrete slab is installed. The slab will not support the walls until after the soil load is supported by the cantilevered walls. Therefore, the earth design pressure is, at best, debatable.

 

[hokie66]

PEinc,

My comment was based on the pit being a box which will span horizontally. As it is only 8' square, there will be negligible deflection. The lid doesn't matter in this case. Structurebeton said it would act like a cantilever when it is backfilled, but he is mistaken.

 

[PEinc]

If the pit is only 8' x 8' with granular soils, we could also consider earth pressure reduction due to arching.

 

[structurebeton]

You are correct, in reality, the design should consider horizontal span rather than cantilevering action because width is smaller than height. However, how can the foundation strength be taken into consideration (because it is acting as a beam) at the base, where the pressure is maximum? At what point the foundation-beam action is no longer an influence for the design of the horizontal wall design?

 

[hokie66]

Structurebeton,

As a structural engineer rather than a geotech, I would always consider the pressure on a box like yours as resulting from the at rest condition. I would design the walls horizontally spanning based on the pressure perhaps three feet above the base. The vertical reinforcement would take care of fixity at the base. As to arching action as PEinc suggested, sure it is there, but I wouldn't use it. With this type structure, the labor is the major item. A bit more reinforcement would be insignificant in the cost.

 

[dgillette]

Expanding a little on what PEinc wrote on 23 May 08 17:08:

If fill is compacted against a stiff wall, the lateral pressure near the top can actually be higher than the simple Ko condition. (Search earlier threads. For explanation, see paper by Duncan and friends in December 1991 ASCE JGE + errata in March 1992 + discussion in July 1993.) This can have the double whammy of moving the centroid of the force higher, in addition to increasing the total force. The equivalent fluid-pressure model can't capture this (or having the water table below the ground surface).

Of course, for an 8'x8' box, you might just want to throw in some extra steel and call it good.