Settlement Tilt and Horizontal displacement of Footing

Hi,

Eccentrically obliquely loaded footings settle down as shown in the figure. Let Se & Sm be the settlements of the points under the load and edge of the footing.
Let 't' be the tilt of the footing,

Sm = Se + (B/2-e).Sin.t

After carrying out a number of tests Agarwal(1986) & Agarwal and Saran(1991), gave the following relationship:

Se/S' = A' + A1(e/B) + A2(e/B)^2

Sm/S' = B' + B1(e/B).

Where, A' = 1- 0.56(i/phi) - 0.82(i/phi)^2  
            A1 = -3.51 + 1.47(i/phi) + 5.67 (i/phi)^2
            A2 = 4.74 - 1.38(i/phi) - 12.45(i/phi)^2
             B' = 1- 0.48.(i/phi) - 0.82(i/phi)^2
            B1 = -1.80 + 0.94(i/phi) + 1.63(i/phi)^2
 here, phi = angle of friction
           i = e/B

Generalized correlation:

Hd/B = 0.121(i/phi) - 0.682(i/phi)^2 + 1.99(i/phi)^3 + 2.01(i/phi)^4

Here, Hd = Horizontal Displacement of the footing.


Settlement of Footing on Slope:

Sud(1985) gave the following relationship

Ss/S' = 0.00385.s + (1-0.00125.s) De/B

Here, Ss= Settlement on slopes
          s= slope with the horizontal
           De = Distance of edge of footing from the top of the slope.


Thanks for your kind visit!