Elastic Foundation Settlement Example

Problem Statement

Estimate the immediate elastic settlement of a shallow footing using:

• Net service pressure $q_{\mathrm{net}}=150\ \mathrm{kPa}$.
• Footing width $B=2.5\ \mathrm{m}$.
• Representative soil modulus $E_s=30{,}000\ \mathrm{kPa}$.
• Poisson ratio $\nu=0.30$.
• Combined influence factor $I_s=1.12$.

The influence factor is assumed to represent the selected method's shape, rigidity, embedment, and evaluation-point corrections. The example does not calculate consolidation or secondary settlement.

Step 1: State The Model

Use the simplified elastic expression:

Pressure and modulus use the same units, so their ratio is dimensionless. Multiplication by footing width gives settlement in metres.

Step 2: Poisson-Ratio Term

Step 3: Pressure-Modulus Ratio

The calculation assumes the selected modulus represents the footing's stress and strain range and the relevant depth of influence.

Step 4: Calculate Settlement

Convert to millimetres:

The estimated immediate settlement is approximately $12.7\ \mathrm{mm}$.

Step 5: Sensitivity To Modulus

If the representative modulus were $20{,}000\ \mathrm{kPa}$ rather than $30{,}000\ \mathrm{kPa}$:

If it were $45{,}000\ \mathrm{kPa}$:

This range shows why modulus selection deserves more attention than extra decimal places in the final calculation.

Engineering Interpretation

The computed $12.7\ \mathrm{mm}$ is one settlement component at one representative point. Acceptance requires comparison with project-specific total and differential movement criteria.

Before using the result, verify:

• The net pressure and excavation-stress convention.
• Whether the modulus is drained or undrained as appropriate.
• Whether it represents the full influence depth or only a near-surface test zone.
• Whether layered-soil integration is needed.
• Whether consolidation, creep, collapse, or heave adds movement.
• Whether adjacent footing interaction changes the stress field.
• Whether the structural system can tolerate the predicted settlement pattern.

Limits Of The Example

The calculation idealizes the soil as homogeneous, isotropic, and elastic. Real soil stiffness is nonlinear and often increases with confining stress. Construction disturbance, groundwater, anisotropy, and stress history can change the response.

For a mat or strongly layered deposit, an integrated or numerical analysis may be more appropriate. A sophisticated model still requires defensible stiffness parameters and construction stages.

References And Further Reading

• USACE EM 1110-1-1904, Settlement Analysis.
• FHWA GEC 6, Shallow Foundations.
• Project-specific field and laboratory stiffness data.

FAQ

Why use net pressure?

Settlement is driven by stress change relative to the preconstruction condition. Net pressure can represent that change when excavation, replacement, groundwater, and load history are modeled consistently.

Is 12.7 millimetres acceptable?

The number cannot be judged without structure-specific total and differential movement criteria and comparison with other supports.

Can the default influence factor be used for every footing?

No. Select the factor from the calculation method being used and confirm which shape, rigidity, embedment, and location corrections it represents.