Rectangular uniform surface loading on semi-infinite area 1

[tipsabc]

I am doing an elastic stress analysis for a rectangular uniform surface loading on semi-infinite area. The formulus are on P54 of "Elastic Solution for Soil and Rock Mechanics" by H. G. Poulos and E. H. Davis (1973). The normal stresses of Eqns 3.18a~c are not dependent on Poisson's Ratio (They are only the function of pressure p and geometry). However, the normal stresses of Eqns 3.19b~c become dependent on Poisson's Ratio. Why? Which should we use? Thank you very much.

 

[jdonville]

tipsabc,

I'd like to help, but it's practically impossible to get a copy of that book nowadays. (I knew I should have photocopied it when a previous employer had a copy in their library...)

Jeff


Jeffrey T. Donville, PE
TTL Associates, Inc.

http://www.ttlassoc.com

 

[BigH]

You might have to go back to Holl's original 1940 work to find out if he assumed a specific poisson's ratio - if so, then his formulations would be solely for that particular ratio; though he does give the shear stresses as well to go along with the normal stresses. Not 100% positive, but perhaps this covers the effect of the poisson's ratio - when you find that the "normal stresses" no longer lie in the x-y-z directions.

Giroud (1970) obviously derived an expression that would permit a deviation in the poisson ratio - the tables of page 55 would be developed accordingly. He gives no shear stresses. So his computed stresses would be the normal ones in the x-y-z directions but the maximum stresses might/would? be in an skewed axis to the normal directions.

This is one of the weak points of the Polous and Davis book - it is shy on some of the underlying principals. But, all in all, it is a great book to have in your library and I wouldn't be without it.

 

[DRC1]

I am going to take a guess that the first set of equations are for an undrained conditon. In that case pore water controls lateral pressure and poisons ratio is 1.0. The second , again, I am guessing, is for drained material, where the material itself contols the lateral pressure and is signifcantly less than 1. Again I am not familar with the book, but not letting that slow me down, so value my free advise at the price you paid!

 

[BigH]

Don't think that the undrained condition for poisson's ratio is 1. Are you sure of that? I've never seen the max taken more than 0.5 which means an incompressible soil (elastic). Conduto: "The magnitude of v [sic., poisson's ratio] in elastic materials varies from 0 to 0.5. Those with v = 0.5 are said to be incompressible because the compression in the direction of the load is exactly matched by the expansion in the two perpendicular direction, resulting in no net volume change."

 

[DRC1]

Big H:
I thought I was, but went back and checked and you are right - the maximum value for v is .5
Sorry!

 

[tipsabc]

Thank you for your comments. Does anyone know any other reference papers or books to give the tools or the formulus to do the stress analysis calculation with poisson's ratio effect instead of Eqn 3.19a~c in the book by Poulos & Davis? I checked the paper by Giroud (1970). But I cannot find any further information. Thanks again.