lateral soil pressure

[ajk1]

How do you determine the lateral soil pressure on a proposed caisson shoring wall, that is caused by the existing building spread footings? There are formulae given in the Canadian Foundation Engineering Manual and other soil mechanics texts for the effect of a "point" load and for a "line" load, but not for a spread footing load.

For example, there is a row of 2 m square spread footings at about 9 m centres, the bottom of the footing being near the top of the proposed excavation, and the row of spread footings being located about 2 m away from the proposed caisson wall.

 

[ishvaaag]

If you have the adequate formula for a point load, you can do it by integration; you divide your footing in areas and identify the loads they are sustaining at their respective center of gravity; then calculate the outwards pressure at the point of interest for each of these loads and sum. This would also show shearing vertical stresses, to compound. Then, horizontal (friction at the footing interface) may also be present, so better you start with the effects of an inclined loads at any point in the elastic half-space.

I have not presently the particular case in Mathcad but have the formula in cartesian I think; it is just a matter of building the integration for the loaded areas and the points of interest.

See attachment. If you are ready to substitute the loading for just the resultant in planes orthogonal to your wall and the footings are reasonably away then just the use of the worksheet may identify the local maximums since the effects of far away footings quite likely can be dismissed to this purpose.

All above as if a cut in the elastic halfspace would represent the status in the wall. Other "hybrid" view is just to get the vertical stress (or maybe better the "total" vertical stress, that compounds the vertically shearing forces) and multiply by a K factor.

Other way to readily get the status in the elastic half-space is to make a solid model with a cube of the elastic half-space in FEM and subject it to the footing loads, then inspect the stresses at the vertical plane of your wall.

 

[ishvaaag]

The Mathcad 2000 Professional worksheet originating the above printout (well maybe I made it before since I started working with Mathcad at the 7 release, but it functions well in 2000 and most surely later versions).

 

[Ron]

ajk1...draw a truncated pyramid from the bottom of your spread footing. Its intersection with the wall is the line of action. Force is computed from formulae for stress reduction below footing with depth, based on depth equal to twice the footing width (B). Interpolate from that, assuming your wall will intercept above a depth of 2B.

 

[ishvaaag]

To use the hybrid method of using a K on the added effective vertical pressure you need the vertical pressure exerted by the footing in the elastic subspace; this is the Steinbrenner's method. Attached a chart for the Influence factor for stress for a rectangular loaded area in the surface at a point at some depth.

Equate your footings to rectangular areas of plastified soil stress response, placed in plan. Then use the chart to obtain the vertical stress, and then a K factor.

 

[ishvaaag]

How to proceed for points inside and outside the plan of the loaded area.

 

[ishvaaag]

The horizontal pressure in a wall directly given based in elastic solutions, use in same way that Steinbrenner's method.

Reference is

Earth Pressures and Earth Retaining Structures, 2nd ed.
Clayton, Milititsky and Woods
Blackie Academic and Professional - Chapman and Hall Imprint 1993

 

[Lion06]

Bowles Foundation Design text uses the Bousinesq equation. This is the method I would typically use.

 

[RFreund]

Ishvaaag - that is a pretty solid mathcad routine there, is there a reference it is based from.

FWIW I would typically use the same as Lion suggests.

EIT

 

[ishvaaag]

Yes, I quote it in the body of the worksheet,

"We have used as reference

Elasticidad, 4th ed.
Eduardo Torroja
Dossat, Madrid, 1967, page- 245"

See atachment.

Eduardo Torroja was a well known civil engineer ("Ingeniero de Caminos, Canales y Puertos" of fame even in the XX century thirties' for his works in shells and other written engineering works. Today the main Institute in Spain related with concrete bears his name.

So if someone finds something in error, quite likely it would be mine or some errata.

 

[cap4000]

If you can get a copy of the 4th edition Soil Engineering book by Spangler and Handy. You have a finite area load conditon. I believe Ram Advanse can do this also. What is the column footing bearing pressure? If the caisson wall is assumed as rigid the lateral pressure will 2x the typical elastic equations.

 

[ishvaaag]

The worksheet given is for a planar case and so verily not greatly adequate for a 3D problem like yours. Integration of the stress effects of a (preferably inclined) point load in the surface in any point within the soil, as Lion06 suggests, is the way to go from classical elastic solutions. Quite likely if one does not have such thing made but knows how to use a 3D solid elements program, the FEM method of finding such stresses within the soil will be the more expeditive.

 

[ishvaaag]

You then can fix one side of the cube soil besides the footing loads to replicate the rigid wall support cap4000 refers to.

 

[ishvaaag]

... well, not "fixed", laterally indesplaceable.

 

[ishvaaag]

See in attachment the simplified conversion of footing loads to strip footing loads to the purpose of push on walls.

From

CIRIA C580
Embedded Retaining Walls - guidance for economic design
London 2003

 

[ajk1]

Thanks everyone. I will have to study all of this.Converting to an equivalent line load looks simple and interesting. I will try it. I suspect all these different approaches give different answers to varying degrees.

 

[ishvaaag]

Yes, there must be likely also statements for the loads in

AASHTO
USACE/NAVFAC
FHWA on walls
Geotechnical Circular

and of course some of the many general texts ... one never ends finding resources in one protracted search; I have not yet searched those above.

Attached, just the case for strip load in the CIRIA C580 publication.

 

[FixedEarth]

There are several crucial aspects that have not been mentioned which leads me to say you need an experienced shoring design firm.