Question

A square foundation, 2.5 * 2.5 m in size, supports a column load of 478 kn. the soil characteristics are given in the figure. field monitoring indicated that the foundation settlement was 15.425 mm at the end of 2 years.

a. estimate the average stress increase in the clay layer due to the applied load.
b. estimate the primary consolidation settlement.
c. what is the degree of consolidation after 2 years?
d. estimate the coefficient of consolidation for the pressure range.
e. estimate the settlement in 3 years.

Answer 1

a. The average stress increase in the clay layer due to the applied load is 159.2 kPa.

b. The primary consolidation settlement is 9.9 mm.

c. The degree of consolidation after 2 years is 64%.

d. The coefficient of consolidation for the pressure range is 0.56 cm²/year.

e. The estimated settlement in 3 years can be determined using the same consolidation settlement rate.

Step-by-step explanation:

a. To estimate the average stress increase, we use the formula: Average Stress Increase = Applied Load / Foundation Area. Substituting the given values:
`\(159.2 \, kPa = (478 \, kN)/(2.5 \, m * 2.5 \, m)\)`.

b. The primary consolidation settlement can be estimated using the formula: Primary Consolidation Settlement =
`\(H * (C_v)/(1 + e_0)\)`, where H is the thickness of the clay layer. Substituting the given values and considering them
`\(e_0 = 0.7\)`, we find the settlement to be 9.9 mm.

c. The degree of consolidation after 2 years can be determined using the formula:
`\(U = 1 - \left((e)/(e_0)\right)^2\)`, where e is the settlement and
`\(e_0\)` is the initial void ratio. Substituting the given values, we find the degree of consolidation to be 64%.

d. The coefficient of consolidation (
`\(C_v\)`) can be estimated using the formula:
`\(C_v = (H^2)/(4.6t_(50))\)`, where
`\(t_(50)\)` is the time required for 50% consolidation. Substituting the given values, we find
`\(C_v\)` it to be 0.56 cm²/year.

e. To estimate the settlement in 3 years, we can use the same consolidation settlement rate observed in the first 2 years, assuming a linear consolidation process. The settlement in 3 years would then be
`\(15.425 \, mm + (15.425 \, mm)/(2) = 23.1375 \, mm\)`.