Immediate Settlement Calculator

Find the elastic (immediate) settlement of a shallow foundation on elastic soil from applied pressure, width, Poisson's ratio, soil modulus, and foundation shape.

🏗️ Immediate Settlement Calculator
Net applied foundation pressure (q)150 kPa
kPa
10500
Foundation width (B)2 m
m
0.510
Soil Poisson's ratio (ν)0.30
—
0.10.49
Soil elastic modulus (Es)20 MPa
MPa
2150
Immediate settlement (Se)
—
Settlement in meters
—
Influence factor (If)
—
Step-by-step working

🏗️ What is Immediate Settlement?

Immediate settlement, also called elastic settlement, is the downward movement of a shallow foundation that occurs essentially as soon as a load is applied, caused by elastic deformation of the soil beneath and around the loaded area. It is calculated using elastic theory for a foundation resting on a semi-infinite elastic soil mass, treating the soil as a continuous elastic material characterized by its elastic modulus Es and Poisson's ratio nu, rather than modeling the slow, time-dependent squeezing-out of pore water that governs consolidation settlement in saturated clay.

Geotechnical and structural engineers check immediate settlement whenever a shallow foundation, a spread footing, mat, or strip footing, will bear on sand, gravel, or unsaturated or partially drained clay, where most of the total settlement happens quickly rather than over years. A structural engineer sizing a footing on sandy soil checks the predicted immediate settlement against the structure's tolerance for movement before finalizing the footing dimensions. A geotechnical consultant comparing candidate foundation widths for the same applied load uses the settlement-versus-width relationship to find a width that keeps settlement within an acceptable limit. A bridge engineer designing an abutment footing checks immediate settlement alongside bearing capacity, since a foundation can satisfy strength requirements while still settling more than the structure can tolerate.

A common misconception is that this formula gives the complete settlement of every foundation. In reality, it captures only the immediate, elastic component. Saturated clay layers also undergo consolidation settlement, a separate, slower process driven by pore water dissipation and calculated with a different formula (see the Consolidation Settlement Calculator on this site). For a foundation on sand or gravel, immediate settlement is usually the dominant or only significant component, but for a foundation partly bearing on clay, both components should be checked and, where appropriate, added together.

This calculator takes the net applied foundation pressure, foundation width, soil Poisson's ratio, soil elastic modulus, and a foundation shape (circular, square, or strip), and returns the immediate settlement in both millimeters and meters, along with a chart showing how settlement changes as foundation width varies for the same soil and pressure.

📐 Formula

Se  =  q × B × (1 − ν²) × If / Es
q = net applied foundation pressure (kPa)
B = foundation width (m)
ν = soil Poisson's ratio (dimensionless, typically 0.3 to 0.45)
If = influence factor, flexible-center value: circular ≈ 1.00, square ≈ 1.12, strip (L/B ≥ 10) ≈ 2.00
Es = soil elastic modulus (MPa, converted to kPa by multiplying by 1000 before use)
These If values are center-of-flexible-foundation values, a commonly used simplification for a quick estimate. A rigid foundation settles slightly less and more uniformly than this formula predicts.
Example: q = 150 kPa, B = 2 m, ν = 0.3, Es = 20 MPa, square footing (If = 1.12) → Se ≈ 0.0153 m ≈ 15.29 mm.

📖 How to Use This Calculator

Steps

1
Choose the foundation shape. Select circular, square, or strip footing to set the influence factor If.
2
Enter the applied pressure and foundation width. Type the net applied foundation pressure q and the foundation width B.
3
Enter the soil properties. Type the soil's Poisson's ratio and elastic modulus Es.
4
Read the settlement result. See the immediate settlement Se and a chart of settlement versus foundation width.

💡 Example Calculations

Example 1 — Square Footing on Medium-Dense Sand

q = 150 kPa, B = 2 m, ν = 0.3, Es = 20 MPa, square footing

1
Square footing → If = 1.12
2
Se = 150 × 2 × (1 − 0.3²) × 1.12 / (20 × 1000) = 150 × 2 × 0.91 × 1.12 / 20000 = 0.01529 m = 15.29 mm
Se = 15.29 mm
Try this example →

Example 2 — Circular Tank Foundation on Stiff Clay

q = 200 kPa, B = 3 m, ν = 0.35, Es = 15 MPa, circular footing

1
Circular footing → If = 1.00
2
Se = 200 × 3 × (1 − 0.35²) × 1.00 / (15 × 1000) = 200 × 3 × 0.8775 × 1.00 / 15000 = 0.0351 m = 35.10 mm
Se = 35.10 mm, larger than Example 1 despite a smaller pressure-width product, because the softer clay (lower Es) dominates the result
Try this example →

Example 3 — Strip Footing on Loose Sand

q = 100 kPa, B = 1.5 m, ν = 0.3, Es = 10 MPa, strip footing

1
Strip footing (L/B ≥ 10) → If = 2.00
2
Se = 100 × 1.5 × (1 − 0.3²) × 2.00 / (10 × 1000) = 100 × 1.5 × 0.91 × 2.00 / 10000 = 0.0273 m = 27.30 mm
Se = 27.30 mm, almost double a circular footing of the same width would give under the same pressure, illustrating how strongly shape affects settlement
Try this example →

❓ Frequently Asked Questions

What is immediate settlement in geotechnical engineering?+
Immediate (elastic) settlement is the portion of a foundation's total settlement that occurs essentially as soon as a load is applied, caused by elastic (recoverable, non-time-dependent) deformation of the soil beneath it. It is calculated separately from the slower, time-dependent consolidation settlement that saturated clay layers undergo as pore water is squeezed out.
How do you calculate immediate settlement of a shallow foundation?+
Se = q times B times (1 minus nu squared) times If divided by Es, where q is the net applied foundation pressure, B is the foundation width, nu is the soil's Poisson's ratio, If is a dimensionless influence factor that depends on foundation shape, and Es is the soil's elastic modulus, converted to the same pressure units as q before dividing.
What influence factor If should I use for a square footing?+
This calculator uses an If of approximately 1.12 for a square footing, 1.00 for a circular footing, and 2.00 for a strip or long rectangular footing with a length-to-width ratio of 10 or more, all standard published flexible-center values for a foundation resting on a semi-infinite elastic soil mass.
What is the difference between a flexible and a rigid foundation for this calculation?+
A flexible foundation bends freely under load, so its center settles more than its edges, this is the case the influence factors on this page assume. A rigid foundation is stiff enough to force uniform settlement across its full width, giving a somewhat lower average settlement than the flexible-center formula predicts, roughly 7 to 20% less depending on shape, a difference this quick-estimate tool does not separately model.
What Poisson's ratio should I use for my soil?+
Typical values range from about 0.3 for dense, well-drained sand or gravel up to 0.45 to 0.5 for soft saturated clay under short-term (undrained) loading. When in doubt, laboratory triaxial testing gives the most reliable value, a mid-range estimate of 0.3 to 0.35 is a reasonable default for many soils absent test data.
Where does the soil elastic modulus Es come from?+
Es is typically obtained from a plate load test, a pressuremeter test, or an empirical correlation with standard penetration test (SPT) N-values or cone penetration test (CPT) resistance. It can range enormously, from under 10 MPa for soft clay to well over 100 MPa for dense sand or stiff clay, so a site-specific value is strongly preferred over a generic assumption.
How does immediate settlement differ from consolidation settlement?+
Immediate settlement occurs essentially as soon as load is applied and is calculated with elastic theory using Es, nu, and an influence factor. Consolidation settlement, relevant mainly for saturated clay, develops slowly over months to years as excess pore water pressure dissipates, and is calculated with an entirely different formula based on the compression index Cc and void ratio e0, see the Consolidation Settlement Calculator (Terzaghi) on this site.
Why does a wider foundation settle more for the same applied pressure?+
Settlement is directly proportional to foundation width B in this formula, so a wider footing carrying the same net pressure q settles proportionally more. Physically, a wider loaded area stresses a larger, deeper volume of soil beneath it, so more soil mass compresses elastically even though the pressure at the surface is unchanged.
Does foundation shape really change the settlement result?+
Yes, significantly. For the same pressure, width, Poisson's ratio, and modulus, a strip footing (If approximately 2.00) settles almost twice as much as a circular footing (If approximately 1.00), because a long strip loads a larger volume of soil along its length compared to a compact circular or square footprint of the same width.
Is this formula valid for deep foundations like piles?+
No, this elastic settlement formula applies specifically to shallow foundations resting on or near the ground surface. Deep foundations like driven or bored piles settle through a different combination of end bearing and skin friction load transfer, use the Pile Capacity Calculator on this site for pile-specific analysis.
What units does the elastic modulus Es need to be entered in?+
Enter Es in megapascals (MPa). The calculator internally converts it to kilopascals (multiplying by 1000) to match the units of the applied pressure q, so the final settlement comes out correctly in meters (then converted to millimeters for display).
Tags: Immediate Settlement Calculator Elastic Settlement Calculator Shallow Foundation Settlement Calculator Influence Factor Settlement Calculator Foundation Settlement Calculator Calculator Formula Free Online

🔗 Related Calculators

🪨
Consolidation Settlement Calculator (Terzaghi)
Engineering - Structural
🏢
Foundation Bearing Capacity Calculator (Terzaghi)
Engineering - Structural
🔩
Pile Capacity Calculator
Engineering - Structural
🧱
Retaining Wall Stability Calculator
Engineering - Structural
📊
Slenderness Ratio Calculator
Engineering - Structural

What is immediate settlement in geotechnical engineering?

Immediate (elastic) settlement is the portion of a foundation's total settlement that occurs essentially as soon as a load is applied, caused by elastic (recoverable, non-time-dependent) deformation of the soil beneath it. It is calculated separately from the slower, time-dependent consolidation settlement that saturated clay layers undergo as pore water is squeezed out.

How do you calculate immediate settlement of a shallow foundation?

Se = q times B times (1 minus nu squared) times If divided by Es, where q is the net applied foundation pressure, B is the foundation width, nu is the soil's Poisson's ratio, If is a dimensionless influence factor that depends on foundation shape, and Es is the soil's elastic modulus, converted to the same pressure units as q before dividing.

What influence factor If should I use for a square footing?

This calculator uses an If of approximately 1.12 for a square footing, 1.00 for a circular footing, and 2.00 for a strip or long rectangular footing with a length-to-width ratio of 10 or more, all standard published flexible-center values for a foundation resting on a semi-infinite elastic soil mass.

What is the difference between a flexible and a rigid foundation for this calculation?

A flexible foundation bends freely under load, so its center settles more than its edges, this is the case the influence factors on this page assume. A rigid foundation is stiff enough to force uniform settlement across its full width, giving a somewhat lower average settlement than the flexible-center formula predicts, roughly 7 to 20% less depending on shape, a difference this quick-estimate tool does not separately model.

What Poisson's ratio should I use for my soil?

Typical values range from about 0.3 for dense, well-drained sand or gravel up to 0.45 to 0.5 for soft saturated clay under short-term (undrained) loading. When in doubt, laboratory triaxial testing gives the most reliable value, a mid-range estimate of 0.3 to 0.35 is a reasonable default for many soils absent test data.

Where does the soil elastic modulus Es come from?

Es is typically obtained from a plate load test, a pressuremeter test, or an empirical correlation with standard penetration test (SPT) N-values or cone penetration test (CPT) resistance. It can range enormously, from under 10 MPa for soft clay to well over 100 MPa for dense sand or stiff clay, so a site-specific value is strongly preferred over a generic assumption.

How does immediate settlement differ from consolidation settlement?

Immediate settlement occurs essentially as soon as load is applied and is calculated with elastic theory using Es, nu, and an influence factor. Consolidation settlement, relevant mainly for saturated clay, develops slowly over months to years as excess pore water pressure dissipates, and is calculated with an entirely different formula based on the compression index Cc and void ratio e0, see the Consolidation Settlement Calculator (Terzaghi) on this site.

Why does a wider foundation settle more for the same applied pressure?

Settlement is directly proportional to foundation width B in this formula, so a wider footing carrying the same net pressure q settles proportionally more. Physically, a wider loaded area stresses a larger, deeper volume of soil beneath it, so more soil mass compresses elastically even though the pressure at the surface is unchanged.

Does foundation shape really change the settlement result?

Yes, significantly. For the same pressure, width, Poisson's ratio, and modulus, a strip footing (If approximately 2.00) settles almost twice as much as a circular footing (If approximately 1.00), because a long strip loads a larger volume of soil along its length compared to a compact circular or square footprint of the same width.

Is this formula valid for deep foundations like piles?

No, this elastic settlement formula applies specifically to shallow foundations resting on or near the ground surface. Deep foundations like driven or bored piles settle through a different combination of end bearing and skin friction load transfer, use the Pile Capacity Calculator on this site for pile-specific analysis.

What units does the elastic modulus Es need to be entered in?

Enter Es in megapascals (MPa). The calculator internally converts it to kilopascals (multiplying by 1000) to match the units of the applied pressure q, so the final settlement comes out correctly in meters (then converted to millimeters for display).

📌 Quick Tips

💡This calculator reports only immediate (elastic) settlement, the portion of total settlement that occurs essentially as soon as the load is applied. It does not include the time-dependent consolidation settlement that a saturated clay layer undergoes separately, covered by the Consolidation Settlement Calculator (Terzaghi) on this site.
💡The influence factor If used here is the flexible-center value, a commonly used simplification for a quick estimate. A rigid foundation (one stiff enough not to bend under load) settles slightly less at its center and slightly more at its edges than a flexible one, giving a more uniform but generally smaller average settlement than the flexible-center formula predicts.
💡Settlement scales directly with foundation width B for a fixed pressure q, so doubling the footing width roughly doubles the immediate settlement even though the total load carried also doubles. This is one reason wider footings are not always the answer to a bearing capacity problem, they can trade a bearing capacity issue for a settlement issue.
💡Poisson's ratio for soil typically ranges from about 0.3 for stiffer, well-drained sands and gravels to 0.45 or higher for soft saturated clays under short-term (undrained) loading, where volume change is restricted. A higher Poisson's ratio reduces predicted settlement for the same pressure, width, and modulus.
💡The soil elastic modulus Es is usually the least certain input in this formula, typical values range from under 10 MPa for soft clay to over 100 MPa for dense sand or stiff clay, and it is best obtained from a plate load test, pressuremeter test, or correlation with SPT/CPT results rather than assumed.