# Settlement of Bored Pile Foundations | Worked Example

#### This article explores estimation of settlement in piled foundation, highlighting the various methods of deriving the settlement of pile foundations and illustrating the process through a worked example.

The settlement of foundations is a critical factor in the design of any structure. For piled foundations, particularly bored piles, understanding and accurately calculating settlement is essential. Settlement affects the stability, durability, and serviceability of a structure. Therefore, engineers must ensure that the settlement remains within acceptable limits to prevent structural failure or excessive deformation.

Settlement calculations are vital because they determine how a foundation will behave under various loads. If settlements are underestimated, it can lead to uneven settling, causing cracks or even collapse of the structure. Overestimation, on the other hand, could result in unnecessarily expensive foundation designs. Thus, an accurate settlement analysis helps achieve a balance between safety and cost-effectiveness.

This article explores the subject of settlement calculations, by explaining in detail the various methods by which the settlement of piled foundation may be assessed, thereafter a worked example is provided to illustrate the process.

### Estimation of Settlement of Foundations to Eurocode 7

There are several methods for estimating the settlement of piled foundations. The main methods include empirical correlations, analytical approaches, and numerical methods. Each method has its own set of assumptions, limitations, and applicable conditions, making it crucial for engineers to select the appropriate method based on the specific project requirements.

#### Empirical Methods

Empirical methods rely on correlations derived from field observations and experimental data. These methods are quick and suitable for preliminary design stages. Engineers often use empirical methods to estimate settlement when they have limited soil data or when detailed analysis is not required.

One popular empirical method is the Schmertmann method, which is based on cone penetration test (CPT) data. Schmertmann’s method estimates settlement by calculating the compression of soil layers beneath the pile. This method considers factors such as soil type, pile geometry, and applied loads. Engineers use the results from CPTs to predict soil behavior under loading, which helps them estimate settlement. The Schmertmann method is particularly useful for sands and silts, where immediate settlement is a significant concern.

Another empirical approach is the use of pile load test results to predict settlement behavior under working loads. Engineers conduct these tests on-site by applying loads to a test pile and measuring the resulting settlement. The test results provide a direct measure of the soil’s response to loading, which can be used to estimate settlement for other piles in similar soil conditions. While empirical methods provide a quick way to estimate settlement, they are generally less accurate and should be used cautiously, especially for critical structures.

#### Analytical Methods

Analytical methods use mathematical models to estimate settlement based on soil properties, pile geometry, and loading conditions. These methods provide more accurate settlement estimates than empirical methods, especially when detailed soil data is available. Analytical methods often assume the soil behaves elastically, which simplifies the calculations.

One well-known analytical method is presented by Bowles (1997) in his book “Foundation Analysis and Design.” This method calculates immediate settlement based on the elastic deformation of the soil and the pile. The formula considers factors such as the pile’s length, cross-sectional area, and the modulus of elasticity of the soil and pile material. The equation for estimating immediate settlement is as follows:

S_p=\frac{QL}{A_pE_p}+q_pD(\frac{1-\mu^2}{E_s}).I_sF

where: Sp​ = total pile settlement (mm); Q = applied load on the pile (kN); L = pile length (m); D= pile diameter (m) Ap = cross-sectional area of the pile (m²) Ep​ = modulus of elasticity of the pile material (MPa); qb​ = bearing pressure at the pile toe (kPa) μ = Poisson’s ratio of the soil; Es = modulus of elasticity of the soil; (MPa); Is​ = shape factor for settlement; and F = embedment factor.

The first term in the equation represents the axial settlement of the pile due to its compression. The second term accounts for the settlement of the soil beneath the pile toe. This approach assumes an end-bearing pile, where the primary resistance is provided by the pile tip bearing on a strong stratum.

The method outlined by Bowles is particularly useful for bored piles in cohesive soils. It allows engineers to estimate settlement by considering soil properties and pile characteristics, providing a more accurate assessment than empirical methods. This method is suitable for projects where the soil profile is well understood, and detailed analysis is required.

#### Numerical Methods

Numerical methods, such as the finite element method (FEM), are used for complex projects requiring high precision. These methods involve creating a numerical model of the soil-pile system and solving the governing equations to estimate settlement. Numerical methods are highly accurate but require significant computational resources and expertise, making them more suitable for detailed design stages.

One popular numerical method is the Plaxis 3D Foundation package, which uses the finite element method to simulate the behavior of soil and pile foundations. Engineers use Plaxis to create a detailed model of the soil-pile system, including soil layers, pile geometry, and loading conditions. The software then calculates the settlement by solving the governing equations for the soil and pile interactions. Plaxis can model complex soil behavior, such as nonlinear stress-strain relationships and soil-pile interaction effects.

Numerical methods are particularly useful for projects with complex soil conditions, such as layered soils or soil with varying properties. They allow engineers to account for factors that are difficult to capture with empirical or analytical methods, such as soil-pile interaction and soil heterogeneity. Numerical methods also enable engineers to perform sensitivity analyses, which helps them understand how changes in soil properties or loading conditions affect settlement.

Numerical methods, such as FEM, are essential for designing piled foundations in challenging soil conditions. They provide a high level of accuracy and can model complex soil behavior, making them indispensable for detailed design stages. However, due to their complexity and resource requirements, numerical methods are typically used for final design validation rather than preliminary design.

### Worked Example: Settlement Calculation for a Bored Piled Foundation

To illustrate the calculation of immediate settlement using the analytical method, consider a bored pile foundation with the following site conditions and pile characteristics

#### Project Details:

• A single bored end bearing pile with a diameter of 0.8 meters and a length of 20 meters is installed in a clayey soil.
• The pile is subjected to a service load of 2400 kN.
• Modulus of elasticity of pile material Ep = 32,000Mpa
• Bearing pressure at pile toe qb = 3000kpa
• Soil properties:
• Modulus of elasticity of soil Es=100 MPa
• Poisson’s ratio of soil μ = 0.3
• Shape factor Is= 1.0
• Embedment factor F =0.5

According to Boyle’s (1997), the total settlement can be assessed as the sum of the axial and the point settlement. Thus:

S_p=\frac{QL}{A_pE_p}+q_pD(\frac{1-\mu^2}{E_s}).I_sF

#### Area of Pile:

A=\frac{\pi d^2}{4}=\frac{\pi(0.8)^2}{4}=0.45m^2

Substituting the values into the equation:

\frac{2400\times20}{0.45 \times 32000}+3000\times0.8(\frac{1-0.3^2}{100})\times1.0\times0.5
S_p= 3.33+10.9=14.23mm

### Conclusion

The total immediate settlement for the bored pile foundation, calculated using Bowles’ analytical method, is approximately 14.23 mm. This value reflects the combined effect of axial compression of the pile and the compression of the soil beneath the pile toe. Engineers must ensure that the total settlement is within acceptable limits for the specific structure and soil conditions. For this structure, foundation settlement should not be more than 2% of pile diameter = 16mm for 800mm diameter. Therefore, the settlement is within the acceptable limits

### Sources & Citations

• Bowles, J. E. (1997). Foundation Analysis and Design. 5th ed. McGraw-Hill. ISBN 0-07-912247-7.
• Schmertmann, J. H. (1978). “Guidelines for Cone Penetration Test, Performance, and Design.” U.S. Department of Transportation, Report No. FHWA-TS-78-209, Washington, D.C.
• Eurocode 7: Geotechnical design – Part 1: General rules (EN 1997-1:2004). European Committee for Standardization, Brussels, 2004.
• Gabrielaitis, L., Papinigis, V., & Žaržojus, G. (2013). “Estimation of Settlements of Bored Piles Foundation.” Procedia Engineering, 57, 287-293. DOI: