Question

The figure below shows a flexible rectangular raft foundation that is proposed for one of the industrial buildings at the site. The foundation is 10 feet X 20 feet and applies an uniform pressure of 3000 psf to the underlying soil.

a. Using the influence factor method to calculate the stress below a rectangular area, find the vertical stress increase ( $\Delta \sigma$ ) at 6 feet below points A, B, and C.

b. Assume that this foundation (thickness = 1.25 feet, E_f = 3.3 x 10⁸ psf) is installed with the base of the foundation at a depth of 5 feet below the ground surface and the soil profile consists of 85 feet of sand ( $\mu$ _s = 0.4, E₀ = 4.1 x 10⁵ psf, k = 10,500 lb/ft²/ft) overlying bedrock. Use the improved equation for elastic settlement in granular soils (Mayne and Poulos, 1999) to determine the elastic settlement of the sand layer under the center of the foundation.

Answer 1

Given data: The Foundation apphes = 10ft times 20 ft uniform pressure = 3000 pst Depth of the stress point (z) (pi) = 6ft Let rightarrow L = 20ft B = 10ft m = L/2 rightarrow (1) = 20/6 = 3.33 n = B/z rightarrow (2) = 10/6 = 1.67 \r\n Out of the point A.B.C point A lies labour a colney and B.C lie below area Vertical stress below the corner [A]: - rightarrow we know that: z = q I_N rightarrow (3) where I_N = 1/2H [mn/ squareroot m^2 + n^2 + 1 times m^2 + n^2 + 2/m^2 + n^2 + m^2 n^2 + 1 + (sin^-1 mn squareroot m^2 + n^2 + m^2 n^2 + 1)] Newmarks influence coefficient rightarrow substituting values of m and n from (1) &(2) = 1/2 pi[3.33 times 1.67/(3.33^2 + 1.67^2 times 1)^1/2 times 3.33^2 + 1.67^2 + 2/3.33^2 + 1.67^2 + 3.33^2 + 1.67^2 + 1 + sin^-1(3.33 times 1.67/3.33^2 + 1.67^2 + 3.33^2 + 1.67^2 + 1)^1/2)]