## Boussinesq Equation - factor 2 or 1

## Boussinesq Equation - factor 2 or 1

(OP)

I'm using the Boussinesq Equation for surcharge loads and have come across the factor of 2 which some use.

Initially based on experiments a while ago.

Bowles gives recommendations in Section 11-13 (see attached).

This website has an article: http://www.ejge.com/iGEM/Articles/FactorOf2/FactorOf2.htm

I don't have enough understanding and experience to feel comfortable either way, whether to use 2 or 1.

What are your thoughts.

Have you come across a definitive journal article which you think makes the correct recommendation.

https://files.engineering.com/getfile.aspx?folder=...

Initially based on experiments a while ago.

Bowles gives recommendations in Section 11-13 (see attached).

This website has an article: http://www.ejge.com/iGEM/Articles/FactorOf2/FactorOf2.htm

I don't have enough understanding and experience to feel comfortable either way, whether to use 2 or 1.

What are your thoughts.

Have you come across a definitive journal article which you think makes the correct recommendation.

https://files.engineering.com/getfile.aspx?folder=...

## RE: Boussinesq Equation - factor 2 or 1

## RE: Boussinesq Equation - factor 2 or 1

"This means that if the two forces were acting together, solutions could be superposed leading to a condition where the displacements would cancel each other, while

the stresses would double. Therefore, if the two loads were acting together, our plane A-A would not move. It means that if we were to remove all the material from the right side of the plane A-A, while still maintaining its position, the material on the other side of the plane would not even "know" about it. To maintain the A-A plane in position though, we would have to provide the support equal to twice the stresses due to Q alone. So this represents a rigid boundary simulating a rigid retaining wall.Is that where the factor of 2 came from? I think the stress has doubled since the load has doubled too, Q+Q'.

## RE: Boussinesq Equation - factor 2 or 1

Mike Lambert

## RE: Boussinesq Equation - factor 2 or 1

As well as the stiffness being a variable GoePaveTraffic.

I don't think I can comfortably lean either way without having to spend more time looking into it. The experiments in the article: I couldn't find anything online. The experiments mentioned by Bowles: 0.15m thick wall, 1.8m high. I wouldn't know whether this would be classed as "stiff" but the results leaned towards are factor of 2 ... but it has been decades since and it looks like there is still debate. I don't know if there are other experimental results.

geotechguy1, I could not find CIRIA by Georgiadis and Anagnostopoulos. Would the method be such that you could compare with Boussinesq?

## RE: Boussinesq Equation - factor 2 or 1

1. Apply the load to the elastic half-space. The ground moves under the load.

2. Insert the wall into the model. The stress on the wall is that from Boussinesq.

3. Excavate the far side of the wall. Assume the wall doesn't deflect, but the ground movement from stage 1 is still there.

4. To return the ground to its original position, as though a rigid wall had been there from before the load was applied, you need to push the wall back towards the retained ground. This increases the force on the wall.

## RE: Boussinesq Equation - factor 2 or 1

## RE: Boussinesq Equation - factor 2 or 1

The alternative methods are helpful and I will try all methods for comparison. The method which includes the angle of friction to the wall will be interesting, as typically the soil retained has a strip of coarser material which apparently reduces the stresses.

## RE: Boussinesq Equation - factor 2 or 1

Absolutely brilliant manual