## An equvivalent lateral force due to a square footing

## An equvivalent lateral force due to a square footing

(OP)

Good morning

We have a 20 m high retaining wall with a 4x4 m footing seating right beside the edge of the retaining wall. How can I estimate an equivalent lateral force (and its location) on the wall caused by the footing? I've been thinking of two approaches so far but I am not sure if are they appropriate.

I was thinking of using a simplified 2:1 (slope) load distribution approach to estimate vertical pressure at any given depth and to convert this vertical pressure into lateral one by multiplying it by K

The problem is the higher the wall the higher the equivalent lateral force. At certain wall height the equivalent lateral force becomes bigger than the original vertical force on the footing which I guess does not really sound logical.

The second approach I was thinking of is the one suggested by Bowles (1992) to use theory of elasticity (The Boussinesq Equation for point load) to estimate the lateral pressure. Bowles suggested to divide a square load into many point loads and to calculate a lateral contribution of each at the certain depth. So theoretically I can calculate a lateral force distribution with the depth. The problem is again this lateral distribution (similar to stress bulbs) won't be constant everywhere but will keep changing along the edge of the footing (and away from it).

So I have to do some sort of integration on all these lateral distributions. This makes it very hard to come up with an equivalent lateral force.

My other option would probably be using one of these 3D FE programs.

Am I out of options or missing something?

Would appreciate your advice.

Thank you

We have a 20 m high retaining wall with a 4x4 m footing seating right beside the edge of the retaining wall. How can I estimate an equivalent lateral force (and its location) on the wall caused by the footing? I've been thinking of two approaches so far but I am not sure if are they appropriate.

I was thinking of using a simplified 2:1 (slope) load distribution approach to estimate vertical pressure at any given depth and to convert this vertical pressure into lateral one by multiplying it by K

_{a}.The problem is the higher the wall the higher the equivalent lateral force. At certain wall height the equivalent lateral force becomes bigger than the original vertical force on the footing which I guess does not really sound logical.

The second approach I was thinking of is the one suggested by Bowles (1992) to use theory of elasticity (The Boussinesq Equation for point load) to estimate the lateral pressure. Bowles suggested to divide a square load into many point loads and to calculate a lateral contribution of each at the certain depth. So theoretically I can calculate a lateral force distribution with the depth. The problem is again this lateral distribution (similar to stress bulbs) won't be constant everywhere but will keep changing along the edge of the footing (and away from it).

So I have to do some sort of integration on all these lateral distributions. This makes it very hard to come up with an equivalent lateral force.

My other option would probably be using one of these 3D FE programs.

Am I out of options or missing something?

Would appreciate your advice.

Thank you

## RE: An equvivalent lateral force due to a square footing

DaveAtkins

## RE: An equvivalent lateral force due to a square footing

The only problem with what you suggested is that this would be correct for the (infinite) line load along the wall. In my case, I have a finite loaded area.

## RE: An equvivalent lateral force due to a square footing

## RE: An equvivalent lateral force due to a square footing

DaveAtkins

## RE: An equvivalent lateral force due to a square footing

A caution: Spangler assumed an unyielding wall, which receives a pressure twice as high as the pressure on a plane with soil on both sides. If your wall is somewhat yielding, this result will be conservative. If your wall is very stiff, as I suspect, your Boussinesq approach will give too low a result.

## RE: An equvivalent lateral force due to a square footing

Pressure variation along the length of the wall is treated just as though you had a setback from your wall.

A full integral is a pain, but you should be able to create a reasonable distribution of stresses at discrete increments that will be accurate enough.

## RE: An equvivalent lateral force due to a square footing