Learn: Immediate elastic settlement
A loaded foundation compresses the supporting ground even when bearing failure is not reached. This elastic estimate combines contact pressure, foundation width, soil stiffness, Poisson’s ratio and an influence factor.
What the formula is saying
The ratio q/Es is a strain-like scale. Multiplying by width B converts it to a displacement scale; (1 − ν²) and Is adjust that scale for the stated elastic geometry model.
Read the symbols in plain language
- q
- Net foundation pressure
Net foundation pressure. Matching stress units cancel and produce the elastic strain scale.
kPaOne kilopascal equals one kN/m² and 1000 Pa.
- B
- Footing width
Footing width. Multiplying the strain scale by width and influence converts it into displacement.
mMetres measure length; 1 m = 1000 mm.
- ν
- Soil Poisson ratio
The negative transverse-to-axial strain ratio of the isotropic material; this describes lateral contraction or expansion.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Is
- Influence factor
Influence factor. Poisson’s ratio and the supplied influence coefficient modify the simple width-based estimate.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Es
- Soil modulus
Elastic stiffness: the stress change needed for a unit strain in the stated material model. It is not a strength limit.
kPaOne kilopascal equals one kN/m² and 1000 Pa.
- s
- Result to find
Immediate elastic settlement. Multiplying the strain scale by width and influence converts it into displacement.
m
Sort out the units first
Use q and Es in the same stress unit, here kPa, and B in m. The result is m. Is and ν are dimensionless; Es is a soil modulus appropriate to the strain and drainage condition, not concrete stiffness.
Assumptions before calculating
This is an idealized study model with supplied soil parameters and loading. Ground investigation, drainage condition, groundwater, geometry and the governing design approach must be established by the responsible geotechnical design process.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find s and explain the result in the stated output unit.
- q · Net foundation pressure
- 150 kPa
- B · Footing width
- 2 m
- ν · Soil Poisson ratio
- 0.3
- Is · Influence factor
- 1
- Es · Soil modulus
- 30000 kPa
Compare applied pressure with soil stiffness
Matching stress units cancel and produce the elastic strain scale.
(150) ÷ (30000) = 0.005Combine the elastic influence factors
Poisson’s ratio and the supplied influence coefficient modify the simple width-based estimate.
(1-(0.3)^2) × (1) = 0.91Estimate elastic settlement
Multiplying the strain scale by width and influence converts it into displacement.
(0.005) × (2) × (0.91) = 0.0091 m
Does this worked answer make sense?
Doubling Es halves the estimate. Doubling q doubles it in this linear model, and the result should be converted to mm before comparing with a millimetre-based study limit.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- q · Net foundation pressure
- 200 kPa
- B · Footing width
- 2.5 m
- ν · Soil Poisson ratio
- 0.3
- Is · Influence factor
- 1.1
- Es · Soil modulus
- 40000 kPa
Compare applied pressure with soil stiffness
Matching stress units cancel and produce the elastic strain scale.
(200) ÷ (40000) = 0.005Combine the elastic influence factors
Poisson’s ratio and the supplied influence coefficient modify the simple width-based estimate.
(1-(0.3)^2) × (1.1) = 1.001Estimate elastic settlement
Multiplying the strain scale by width and influence converts it into displacement.
(0.005) × (2.5) × (1.001) = 0.0125125 m
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- q · Net foundation pressure
- 120 kPa
- B · Footing width
- 1.8 m
- ν · Soil Poisson ratio
- 0.25
- Is · Influence factor
- 1
- Es · Soil modulus
- 25000 kPa
Find: Learn: Immediate elastic settlement
A hint, not the answer
The ratio q/Es is a strain-like scale. Multiplying by width B converts it to a displacement scale; (1 − ν²) and Is adjust that scale for the stated elastic geometry model.
Use q and Es in the same stress unit, here kPa, and B in m. The result is m. Is and ν are dimensionless; Es is a soil modulus appropriate to the strain and drainage condition, not concrete stiffness.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Compare applied pressure with soil stiffness
Matching stress units cancel and produce the elastic strain scale.
(120) ÷ (25000) = 0.0048Combine the elastic influence factors
Poisson’s ratio and the supplied influence coefficient modify the simple width-based estimate.
(1-(0.25)^2) × (1) = 0.9375Estimate elastic settlement
Multiplying the strain scale by width and influence converts it into displacement.
(0.0048) × (1.8) × (0.9375) = 0.0081 m
Avoid the common trap
Do not mix Es in MPa with q in kPa. Do not treat Is as a universal constant or interpret this immediate elastic estimate as total long-term settlement.
When this method applies — and when it does not
Assume a compatible homogeneous elastic-soil and footing influence-factor model. Layering, stress-dependent stiffness, consolidation, creep, footing rigidity and differential settlement are not automatically resolved. Require −1 < ν < 0.5 for this elastic material model.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Immediate elastic settlement. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.