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A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be?
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A plate load test was conducted in sand on a 300 mm diameter plate. If...
Solution:
Given, Diameter of the plate, D = 300 mm
Pressure, P = 100 kPa
Settlement of the plate, s = 5 mm
To find the settlement of a rectangular footing of size 5 m x 8 m, we need to use the concept of the consolidation settlement of a footing.
Consolidation settlement of a footing can be calculated using the following formula:
s = (1 + e0) × (q/Bc) × (Df/1 + e0) × (log(2z/Df) + 0.5)
where,
s = settlement of the footing
e0 = initial void ratio of the soil
q = pressure applied on the footing
Bc = coefficient of consolidation of the soil
Df = depth of the footing
z = depth of the layer of soil in which consolidation is taking place
Let us assume that the soil under the footing is homogeneous and the same as that under the plate.
Therefore, the coefficient of consolidation, Bc, and the initial void ratio, e0, will be the same.
Let us assume that the depth of the layer of soil in which consolidation is taking place, z, is also the same as that under the plate.
Now, we need to find the depth of the footing, Df.
Let us assume that the footing is placed at a depth of 2D below the ground surface.
Therefore, Df = 2D + thickness of the footing.
Let us assume that the thickness of the footing, t, is 500 mm.
Therefore, Df = 2 x 300 mm + 500 mm = 1100 mm
Substituting the given values in the formula, we get:
s = (1 + e0) × (q/Bc) × (Df/1 + e0) × (log(2z/Df) + 0.5)
s = (1 + e0) × (100 kPa/Bc) × (1100 mm/1 + e0) × (log(2z/1100 mm) + 0.5)
Now, we need to find the value of Bc.
For the given sand, we can use the following empirical formula to find Bc:
Bc = 5.36 × (t50)^2 / (Cc × H)
where,
t50 = median particle size of the soil
Cc = compression index of the soil
H = height of the layer of soil above the water table
Let us assume that the median particle size of the sand, t50, is 0.3 mm.
For sand, Cc can be assumed to be 0.2.
Let us assume that the height of the layer of sand above the water table, H, is 3 m.
Therefore, Bc = 5.36 × (0.3 mm)^2 / (0.2 × 3 m) = 0.01512 m^2/year
Substituting the value of Bc in the previous equation, we get:
s = (1 + e0) × (100 kPa/0.01512 m^2/year) × (1100 mm/1 + e0) × (log(2z/1100 mm) + 0.5)
Let us assume that the initial void ratio of the sand, e0,
Given, Diameter of the plate, D = 300 mm
Pressure, P = 100 kPa
Settlement of the plate, s = 5 mm
To find the settlement of a rectangular footing of size 5 m x 8 m, we need to use the concept of the consolidation settlement of a footing.
Consolidation settlement of a footing can be calculated using the following formula:
s = (1 + e0) × (q/Bc) × (Df/1 + e0) × (log(2z/Df) + 0.5)
where,
s = settlement of the footing
e0 = initial void ratio of the soil
q = pressure applied on the footing
Bc = coefficient of consolidation of the soil
Df = depth of the footing
z = depth of the layer of soil in which consolidation is taking place
Let us assume that the soil under the footing is homogeneous and the same as that under the plate.
Therefore, the coefficient of consolidation, Bc, and the initial void ratio, e0, will be the same.
Let us assume that the depth of the layer of soil in which consolidation is taking place, z, is also the same as that under the plate.
Now, we need to find the depth of the footing, Df.
Let us assume that the footing is placed at a depth of 2D below the ground surface.
Therefore, Df = 2D + thickness of the footing.
Let us assume that the thickness of the footing, t, is 500 mm.
Therefore, Df = 2 x 300 mm + 500 mm = 1100 mm
Substituting the given values in the formula, we get:
s = (1 + e0) × (q/Bc) × (Df/1 + e0) × (log(2z/Df) + 0.5)
s = (1 + e0) × (100 kPa/Bc) × (1100 mm/1 + e0) × (log(2z/1100 mm) + 0.5)
Now, we need to find the value of Bc.
For the given sand, we can use the following empirical formula to find Bc:
Bc = 5.36 × (t50)^2 / (Cc × H)
where,
t50 = median particle size of the soil
Cc = compression index of the soil
H = height of the layer of soil above the water table
Let us assume that the median particle size of the sand, t50, is 0.3 mm.
For sand, Cc can be assumed to be 0.2.
Let us assume that the height of the layer of sand above the water table, H, is 3 m.
Therefore, Bc = 5.36 × (0.3 mm)^2 / (0.2 × 3 m) = 0.01512 m^2/year
Substituting the value of Bc in the previous equation, we get:
s = (1 + e0) × (100 kPa/0.01512 m^2/year) × (1100 mm/1 + e0) × (log(2z/1100 mm) + 0.5)
Let us assume that the initial void ratio of the sand, e0,
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A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be?
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A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be?.
A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5 mx 8 m rectangular footing at the same pressure will be?.
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