Fadum's chart 1

[billsumner]

Has anyone got equations that can be used to represent Fadum's chart for influence values to determine settlement?

Fadum R E Influence values for vertical stresses in a semi-infinite solid due to surface loads - School of engineering Harvard university (1941).

 

[BigH]

Normally, I would say Poulos and Davis' book of Elastic Solutions for Soil and Rock Mechanics without looking - but I looked it up this time and they only give the chart. However, they give formulas by Holl (1940), Giroud (1970) - although they do not give the individual formulas of a number of 'constants' required - and Harr (1966) which does give the formulations for vertical displacement at depth z under the corner of a rectangle (Section 3.4 of Poulos and Davis, pp 54 to 58. Giroud (1969) also gives values for horizontal displacements.
Poulos and Davis is the "bible" for elastic solutions.

 

[billsumner]

Thanks for your help BigH. Page 54 of Poulos gives the formulae as you say:
I[σ]_z = 1/(2[π])*[arctan(m*n/sqrt(m²+n²+1)) + {m*n/sqrt(m²+n²+1)}*{1/(1+m²) + 1/(1+n²)}]
where I[σ]_z = influence coefficient
m = B/z
n = L/z
B = half breadth of foundation
L = half length of foundation
z = depth
We use half breadth and length because we work from the centreline in both directions and then multiply by four to model the four quadrants of the foundation.

My old book assumed that we would work from charts etc rather than work it all out.