Foundation Design: Bearing Capacity and Settlement Calculations

Foundation Design: Bearing Capacity and Settlement Calculations

The foundation is arguably the most critical part of any building as it transfers the building load onto the soil. Therefore, proper foundation design requires an understanding and computation of both the bearing capacity and settlement that would occur. In this section, we shall detail these two crucial aspects, including example calculations.

1. Introduction to Foundation Design
When designing a foundation, it should so be that soil carries the load without failure and that settlement is within acceptable limits. A foundation must:

• Not experience shearing failure of the soil.
• Should have no excessive settlement of the structure.

Two parameters to be taken on board are:

• Bearing Capacity: The maximum pressure that soil can carry safely.
• Settlement: The amount of vertical displacement which will occur as a result of soil compression by the applied loads.

2. Definition of Bearing Capacity

Ultimate Bearing Capacity (qₐ)
This is the peak pressure that soil can take before failure or shearing at its ultimate limit. This may give way to foundation collapse or extreme tilting of structure.

Allowable Bearing Capacity (q_a)
To ensure safety, we calculate the foundation based on the allowable bearing capacity rather than the ultimate bearing capacity. This is further multiplied by a Factor of Safety (FOS). The formula is:

q_a = q_u / FOS

Where:
q_u = ultimate bearing capacity
FOS = factor of safety, typically between 2.5 and 3.

3. Calculating Bearing Capacity
The most commonly used way to calculate bearing capacity for shallow foundations is the Terzaghi's Bearing Capacity Equation:

qₐ = cN_c + qN_q + 0.5γBN_γ

Where:
qₐ = ultimate bearing capacity (kN/m²)
c = cohesion of the soil (kN/m²)
q = overburden pressure (kN/m²), calculated as q = γ × D where D is the foundation depth.
γ = unit weight of soil (kN/m³)
B = width of the foundation (m)
N_c, N_q, N_γ = bearing capacity factors, dependent on the soil's friction angle (ϕ).

Bearing Capacity Example Calculation
Let us assume the following conditions for our problem on a shallow foundation:

• Cohesion, c = 25 kN/m²
• Unit weight of soil, γ = 18 kN/m³
• Foundation width, B = 3 m
• Foundation depth, D = 1.5 m
• Internal friction angle, ϕ = 30°

From ϕ = 30°, the bearing capacity factors are as follows:

• N_c = 30.14
• N_q = 18.4
• N_γ = 15.7

Now the overburden pressure is calculated as follows:

q = γ × D = 18 × 1.5 = 27 kN/m²

Substitute the values into the Terzaghi's equation:

qₐ = (25 × 30.14) + (27 × 18.4) + (0.5 × 18 × 3 × 15.7)

qₐ = 753.5 + 496.8 + 423.9 = 1674.2 kN/m²

With a Factor of Safety (FOS) of 3, the allowable bearing capacity is:

q_a = qₐ / FOS = 1674.2 / 3 = 558.07 kN/m²

So the allowable bearing capacity is about 558 kN/m².

4. Settlement Understanding

What is settlement?
Settlement is the vertical movement of the ground due to applied load by the structure. Proper settlement estimation is required to prevent excessive displacement that may further cause damage to the structure.

Settlement is classified into two types:

• Immediate Settlement: It occurs right after the applied load; primarily it takes place in sandy soils.
• Consolidation Settlement: It occurs over time, mainly in clayey soils when the soil dries out as moisture in the soil escapes out.

5. Settlement Computation
The formula for settlement computation is the following for immediate settlement:

S = (q × B × (1 – v²)) / E

Where:

S = settlement in m
q = applied pressure in kN/m²
B = width of the foundation in m
v = Poisson's ratio (usually in range 0.3-0.5)
E = modulus of elasticity of soil in kN/m²

Example Settlement Computation
Given that:

• Applied pressure (q) = 250 kN/m²
• Width of foundation (B) = 3 m
• Poisson's ratio (v) = 0.35
• Modulus of elasticity (E) = 25,000 kN/m²

From the formula of settlement:

S = (250 × 3 × (1 - 0.35²)) / 25,000

S = (750 × 0.8775) / 25,000 = 26.325 / 25,000 = 0.00105 m = 1.05 mm

Thus, the calculated settlement is 1.05 mm.

6. Factors Affecting Bearing Capacity and Settlement
There are various factors which affect the bearing capacity of soil besides affecting the settlement of the structure.

Factors Affecting Bearing Capacity:

• Soil Type: Load-carrying capability varies in clay, sand, and gravel.
• Water Table: Higher the water table will weaken the soil, which subsequently lowers its bearing capacity.
• Foundation Width and Depth: Wider foundations can carry loads better; hence, their bearing capacity increases.
• Soil Density: Dense soils have more resistance to shear failure.

Factors Affecting Settlement:

• Soil Compressibility: The clayey soils are also more compressible than the sand soils, so more settlement takes place due to it.
• Foundation Size: The bigger the size, it means greater dispersal of loads and lesser settlement.
• Applied Load: The more extensive structure, the more settlement. Calculations ought to comprise absolute loads.
• Time: Consolidation settlement for clay might take months and years about the permeability of the soil.

7. Conclusion
Founding means more than the bearing capacity of soils. The amount of settlement necessary to ensure that the foundations fail or move too much is required in designing foundations. Being aware of these concepts will result in safe and lasting structures.

Civil engineers consider the type of soil on which the structure is erected, the load applied by the structure, and how the soil will behave under that load over a period of time while designing. In other words, careful calculations and proper safety factors ensure a stable foundation.