Question

A square rigid footing is to be constructed on a soft clay on land that has an undrained shear strength of 15 kPa and is improved by deep-mixed columns with an area replacement ratio of 30%. The diameter and length of deep-mixed columns are 1 m and 10 m, respectively. They are frictional columns. The field unconfined compressive strength of the column is 750 kPa. The average skin resistance between column and soil is 10 kPa. Calculate the ultimate bearing capacities of the deep-mixed column and the deep-mixed column-reinforced composite foundation.

Answer 1

To calculate the ultimate bearing capacities of the deep-mixed column and the deep-mixed column-reinforced composite foundation, we can use the following formulas:

1. Ultimate bearing capacity of the deep-mixed column (q_c):

q_c = σ_uc * A_c + τ_s * A_s

where:

σ_uc = unconfined compressive strength of the column = 750 kPa

A_c = area of the column base = π * (d/2)^2 (diameter of the column = 1 m)

τ_s = average skin resistance between column and soil = 10 kPa

A_s = surface area of the column = π * d * L (diameter of the column = 1 m, length of the column = 10 m)

Plugging in the values:

q_c = 750 kPa * (π * (1/2)^2) + 10 kPa * (π * 1 * 10)

Calculating q_c will give us the ultimate bearing capacity of the deep-mixed column.

2. Ultimate bearing capacity of the deep-mixed column-reinforced composite foundation (q_f):

q_f = q_c + q_s

where:

q_s = ultimate bearing capacity of the soil = c * N_c

Given that the undrained shear strength of the soil (c) is 15 kPa, and the bearing capacity factor (N_c) is typically taken as 9 for square footings on soft clay.

Plugging in the values:

q_s = 15 kPa * 9

q_f = q_c + q_s

Calculating q_f will give us the ultimate bearing capacity of the deep-mixed column-reinforced composite foundation.

Step-by-step explanation: