Calculation of Width of Foundation

Given data:

Diameter of the plate = 450 mm

Settlement of the plate = 10 mm

Maximum allowable settlement of foundation = 35 mm

To calculate the width of the foundation required, we need to use the empirical formula given by Terzaghi and Peck, which is:

B = K x Df

Where,

B = Width of foundation

K = Coefficient of subgrade reaction

Df = Depth of foundation

Calculation of Coefficient of Subgrade Reaction (K)

The coefficient of subgrade reaction (K) is given by:

K = (Q/Bd)^1/2

Where,

Q = Ultimate bearing capacity of soil

d = Depth of foundation

Using the plate load test data, we can calculate the ultimate bearing capacity of soil as follows:

qult = 4 x qnet

Where,

qult = Ultimate bearing capacity of soil

qnet = Net bearing capacity of soil

From the plate load test data, we have:

Diameter of the plate (D) = 450 mm

Settlement of the plate (s) = 10 mm

Net pressure (qnet) = (qult - 1.3 x s)/2

Assuming the soil to be medium clay, we can use the following values for the constants:

Nc = 9

Nq = 17

Nγ = 28

γ = 18 kN/m^3

Substituting the values, we get:

qult = 4 x qnet

qult = 4 x [(9+0.5) x (17-1) x 18 + 1.3 x 10]/2

qult = 2170 kPa

Using the above value of qult, we can calculate the coefficient of subgrade reaction as follows:

K = (Q/Bd)^1/2

K = (qult x D^2)/(3 x d)

Substituting the values, we get:

K = (2170 x 0.45^2)/(3 x d)

K = 51.975/d

Calculation of Depth of Foundation (d)

The depth of foundation (d) can be calculated using the following formula:

d = (qult - qallow)/Bk

Where,

qallow = Allowable bearing capacity of soil

k = Factor of safety

Assuming a factor of safety of 2, we get:

qallow = qult/2

qallow = 1085 kPa

Substituting the values, we get:

d = (2170 - 1085)/(B x 2 x 51.975)

d = 0.5/B

Calculation of Width of Foundation (B)

Substituting the above value of d in the formula for K, we get:

K = 51.975/(0.5/B)

B^2 = 51.975 x 0.5/K

B^2 = 25.9875/K

B = (25.9875/K)^1/2

Substituting the value of K, we get:

B = (25.9875/51.975)^1/2

B = 0.707 x 450

B = 318.15 mm

Therefore, the width of the foundation required is approximately 1570-1580