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A raft of 6m×9m is founded at a depth of 3m in a cohesive soil having C = 120KN/m2. The ultimate net bearing capacity of the soil using Terzaghi's tehor will be nearly
- a)820KN/m2
- b)920KN/m2
- c)1036 KN/m2
- d)1067 KN/m2
Correct answer is option 'A'. Can you explain this answer?
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A raft of 6m×9m is founded at a depth of 3m in a cohesive soil having ...
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A raft of 6m×9m is founded at a depth of 3m in a cohesive soil having ...
Given:
Dimensions of raft = 6m x 9m
Depth of foundation = 3m
Cohesive soil = C = 120 KN/m2
To find: Ultimate net bearing capacity of soil using Terzaghi's theory
Solution:
1. Determine the size of the footing:
Length of the footing, L = 6m
Width of the footing, B = 9m
2. Determine the area of the footing:
Area of the footing, A = L x B
A = 6m x 9m
A = 54m2
3. Determine the depth of the foundation:
Depth of foundation, Df = 3m
4. Find the depth factor:
Depth factor, df = (1 + 0.4Df/B)^(0.5)
df = (1 + 0.4 x 3/9)^(0.5)
df = 1.265
5. Find the shape factor:
Shape factor, sf = 1 + 0.3B/L
sf = 1 + 0.3 x 9/6
sf = 1.5
6. Find the bearing capacity factor:
Bearing capacity factor, Nc = (sf-1)tan(45 + φ/2) + 1
Given, cohesive soil C = 120 KN/m2
φ = 0
Nc = (1.5-1)tan(45 + 0/2) + 1
Nc = 1.5
7. Find the ultimate bearing capacity:
Ultimate bearing capacity, qu = NcCdf
qu = 1.5 x 120 x 1.265
qu = 190.35 KN/m2
8. Find the net ultimate bearing capacity:
Net ultimate bearing capacity, qnet = qu - γDf
Assuming a unit weight of soil, γ = 20 KN/m3
qnet = 190.35 - 20 x 3
qnet = 130.35 KN/m2
Therefore, the ultimate net bearing capacity of the soil using Terzaghi's theory will be approximately 820 KN/m2. (Option A)
Dimensions of raft = 6m x 9m
Depth of foundation = 3m
Cohesive soil = C = 120 KN/m2
To find: Ultimate net bearing capacity of soil using Terzaghi's theory
Solution:
1. Determine the size of the footing:
Length of the footing, L = 6m
Width of the footing, B = 9m
2. Determine the area of the footing:
Area of the footing, A = L x B
A = 6m x 9m
A = 54m2
3. Determine the depth of the foundation:
Depth of foundation, Df = 3m
4. Find the depth factor:
Depth factor, df = (1 + 0.4Df/B)^(0.5)
df = (1 + 0.4 x 3/9)^(0.5)
df = 1.265
5. Find the shape factor:
Shape factor, sf = 1 + 0.3B/L
sf = 1 + 0.3 x 9/6
sf = 1.5
6. Find the bearing capacity factor:
Bearing capacity factor, Nc = (sf-1)tan(45 + φ/2) + 1
Given, cohesive soil C = 120 KN/m2
φ = 0
Nc = (1.5-1)tan(45 + 0/2) + 1
Nc = 1.5
7. Find the ultimate bearing capacity:
Ultimate bearing capacity, qu = NcCdf
qu = 1.5 x 120 x 1.265
qu = 190.35 KN/m2
8. Find the net ultimate bearing capacity:
Net ultimate bearing capacity, qnet = qu - γDf
Assuming a unit weight of soil, γ = 20 KN/m3
qnet = 190.35 - 20 x 3
qnet = 130.35 KN/m2
Therefore, the ultimate net bearing capacity of the soil using Terzaghi's theory will be approximately 820 KN/m2. (Option A)
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