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# Boussinesq Equation - factor 2 or 14

## 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.

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

Skip the argument about Boussinesq and use one of the methods described in CIRIA 760 (Georgiadis and Anagnostopoulos (1998) or Pappin et all (1986).

### RE: Boussinesq Equation - factor 2 or 1

In the referred article, I don't quite follow the author's discussion on Figure 3, for which he says:

"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

I haven't looked at the referenced article, however, the difference is likely related to the stiffness of the wall. If you wall is stiff, then I would use the 2x factor. If your wall is very flexible, then I would use the 1x factor. If you do not have control of the wall stiffness, then I would use the 2x factor.

Mike Lambert

### RE: Boussinesq Equation - factor 2 or 1

(OP)
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

Maybe an alternative thought experiment to the mirror load is this:

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

(OP)
Thanks steveh49, that's an interesting way of looking at it.
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

steveh49 - I was thinking that looked just like CIRIA 760 and then I realized it's from the previous version (CIRIA 580).

Absolutely brilliant manual

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