A mat foundation has dimensions of 40 m x 20 m. The live load and dead load on the mat are 250 MN. The mat is placed over a layer of soft clay that has a unit weight of 19 kN/m³. Find Dr for a fully compensated foundation.
Answer (1)
To find the required depth (Dr) for a fully compensated foundation, you must ensure that the weight of the excavated soil is equal to the weight of the new structure placed on the foundation. This is also known as a weight equilibrium condition.
Given:
Dimensions of mat foundation : 40 m x 20 m
Live Load and Dead Load on the mat : 250 MN
Unit weight of the clay : 19 kN/m³
Step-by-Step Solution:
Calculate the total weight of the structure (W_s):
The total load on the mat includes both the live and dead loads which amount to 250 MN (or 250,000 kN).
Calculate the volume of soil to be excavated (V):
To find the depth of excavation, we first assume a certain depth Dr where the volume of soil removed equals the volume that adds up to the weight of the structure.
Relating the weights:
The problem involves balancing the total weight of the structure with the weight of soil displaced,
W s = γ so i l × A × D r Where:
γ so i l = Unit weight of soil = 19 kN/m³
A = Area of the mat = 40 m x 20 m = 800 m²
Solve for Dr:
Using the above formula, substitute the known values:
250 , 000 = 19 × 800 × D r
Rearrange the equation to solve for D r :
D r = 19 × 800 250 , 000
Calculate D r :
D r = 15 , 200 250 , 000 ≈ 16.45 meters
Conclusion:
The depth D r required for a fully compensated mat foundation, where the weight of the excavated soil equals the weight of the structure, is approximately 16.45 meters. This ensures that the foundation is balanced and effectively supported by the soil characteristics provided.
