**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.

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