Geotechnical Immediate Settlement

What Is Immediate Settlement?

In geotechnical engineering, total settlement of a foundation is usually made up of three parts:

1. Immediate (elastic) settlement – happens almost instantly as the load is applied.
2. Primary consolidation settlement – time-dependent settlement in saturated clays as pore water is squeezed out.
3. Secondary settlement (creep) – long-term, slow deformation after primary consolidation.

Immediate settlement is:

• Fast (seconds to days)
• Mainly due to elastic deformation of soil
• Dominant in granular soils like sand and gravel
• Also important in stiff clays and silts under lightly loaded foundations

Your Geotechnical Immediate Settlement Calculator focuses on this elastic, short-term component.

Think of it as:

“How much will the foundation sink right away when I place the load?”

Why Immediate Settlement Matters

Even if a building does not collapse, excessive or uneven settlement can cause:

• Cracks in walls and slabs
• Tilting of columns or towers
• Malfunction of doors, windows and machinery
• Leakage in pipelines and tanks
• Serviceability problems and expensive repairs

Most codes and design practices set allowable limits for settlement, such as:

• Total settlement ≤ 1–2 inches (25–50 mm) for many buildings
• Differential settlement limited to avoid distortion and cracking
• Settlement ratio (S/B) checked to understand how settlement compares with footing size

Your calculator directly computes:

• Immediate Settlement, Sᵢ (inches)
• Settlement Ratio, S/B (%)
• Settlement Classification – Very Small, Small, Moderate, Large, Excessive

So you can quickly judge if the predicted settlement is within acceptable limits.

How Immediate Settlement Is Estimated (Conceptual)

In elastic theory, immediate settlement under a loaded footing is often calculated using a form of this basic idea:

Settlement ∝ (Applied pressure × Footing width × Influence factor × Shape/Depth factors) ÷ Soil modulus

Your calculator uses a refined form of this concept and includes:

• Elastic soil modulus (Eₛ)
• Poisson’s ratio (μ)
• Influence factor (Iₛ) – depends on footing size, shape and layer thickness
• Shape factor (I_f) – accounts for square, rectangular, strip, mat, circular foundations
• Depth factor (I_d) – accounts for foundation depth below ground surface
• Rigidity factor (I_r) / correction factor – accounts for rigid vs flexible footing behavior
• Water table factor – accounts for effect of groundwater on stiffness

All of this is done behind the scenes in the script you shared, but we can break down each part in plain language.

Input Parameters in Your Immediate Settlement Calculator

Let’s go through each input and what it represents.

Foundation Type

You can choose:

• Square Footing
• Rectangular Footing
• Circular Footing
• Strip Footing
• Mat Foundation

Each foundation type comes with:

• A shape factor (I_f)
• A rigidity factor (I_r)

These adjust the settlement based on the geometry and stiffness pattern of the foundation. For example:

• Strip footings behave differently than isolated square footings.
• Mats spread loads over large areas, influencing settlement patterns.

The shape factor adjusts how load spreads in the soil, while rigidity accounts for how a rigid vs flexible foundation distributes contact pressure.

Soil Type

You can select from:

• Dense, medium and loose sand
• Stiff, medium and soft clay
• Silt
• Gravel
• Rock

Each soil type has:

• A typical soil modulus, Eₛ (psf)
• A typical Poisson’s ratio, μ

Your calculator lets you either:

• Use these default values, or
• Enter custom values for soil modulus and Poisson’s ratio if you have lab-test data or reliable correlations.

Soil modulus (Eₛ) represents how stiff or compressible the soil is:

• Higher Eₛ → stiffer soil → less settlement
• Lower Eₛ → softer soil → more settlement

Poisson’s ratio (μ) reflects how soil deforms laterally when compressed vertically. It slightly adjusts the settlement through the term (1 − μ²).

Foundation Width (B), Length (L) and Depth (Dₓ)

• Foundation width, B – main dimension used in settlement calculation.
• Foundation length, L – forms the aspect ratio (L/B), which affects influence factor.
• Foundation depth, Dₓ – distance from ground surface to foundation base.

These geometric inputs do several things:

• Wider footings usually produce more immediate settlement (because load spreads deeper).
• Length-to-width ratio changes how load is distributed in the soil mass.
• Deeper foundations may experience slightly different stiffness due to confinement and stress distribution (captured through the depth factor, I_d).

Applied Pressure, q (psf)

This is the net contact pressure beneath the footing, usually:

q = (Total load on footing / footing area) − overburden relief (if any)

Higher q means:

• More stress in the soil
• Greater immediate settlement

So, settlement is roughly proportional to the applied pressure.

Soil Modulus (Eₛ) and Poisson’s Ratio (μ)

These are key elastic parameters:

• If you enter custom values, the calculator uses those.
• If you leave them at 0 (or not relevant), the calculator uses the default values from soil type.

Important concept:

As Eₛ increases → settlement decreases
As soil becomes more compressible (lower Eₛ) → settlement increases

Poisson’s ratio is used in the term (1 − μ²). A higher μ (more lateral expansion) slightly modifies the settlement result.

Layer Thickness, H

• Represents the thickness of the compressible soil layer beneath the foundation that significantly contributes to settlement.
• If the soil layer is very thick relative to footing width (H/B ≥ 10), the calculator treats it like a semi-infinite medium.
• If the layer is finite, the influence factor is adjusted to capture that.

This is important because a thin stiff layer over softer soil behaves differently from a thick uniform layer.

Water Table Depth

• Depth from the ground surface to the water table.
• When the water table is close to the foundation base, effective stress decreases and soil stiffness may reduce.
• The calculator uses a water table factor to adjust settlement:
  • Water table well below foundation influence zone → factor ≈ 1.0
  • Water table at or near foundation depth → factor reduces settlement capacity (i.e., more settlement).

Water is a key player in geotechnical behavior, and this factor captures its immediate effect in a simplified way.

Depth Correction Factor

You can choose:

• 0.85 – Flexible foundation
• 0.90 – Semi-rigid
• 0.95 – Rigid foundation
• 1.00 – No correction

This factor fine-tunes the settlement prediction based on:

• The rigidity of the footing and
• The way stress distributes with depth.

Rigid foundations distribute load differently than flexible ones, affecting how soil strains and settles.

Behind-the-Scenes: How the Calculator Computes Immediate Settlement

Your calculator essentially does these steps:

1. Read all inputs:
   • Foundation type, soil type, geometry, loads, soil modulus, Poisson’s ratio, layer thickness, water table depth, depth correction.
2. Determine effective soil parameters:
   • If custom Eₛ and μ are provided and > 0 → use them.
   • Otherwise → use default values from selected soil type.
3. Calculate influence factor, Iₛ:
   • Computes aspect ratio m = L/B and depth ratio n = H/B.
   • If H/B ≥ 10 → uses an infinite-layer influence formula.
   • If H/B < 10 → uses a finite-layer influence formula, involving logs, arctan functions and μ.
   • This influence factor represents how the stress from the footing spreads and causes strain in the soil mass.
4. Calculate depth factor, I_d:
   • Based on D/B ratio.
   • Shallow footings may have a factor close to 1.0.
   • Deeper foundations get a correction for depth effect.
5. Calculate water table factor:
   • Checks relative position of water table to foundation depth and width.
   • Reduces effective stiffness when water table is high.
6. Combine all factors in settlement equation: In conceptual terms: [
   S_i \propto \frac{q \times B \times (1 - \mu^2) \times I_s \times I_f \times I_d \times W_{factor} \times C_{depth}}{E_s}
   ] where:
   • ( q ) = applied pressure
   • ( B ) = foundation width
   • ( I_s ) = influence factor
   • ( I_f ) = shape factor
   • ( I_d ) = depth factor
   • ( W_{factor} ) = water table factor
   • ( C_{depth} ) = depth correction factor
   • ( E_s ) = soil modulus
7. Convert settlement into inches:
   • Settlement is first in feet (or equivalent), then multiplied by 12 → Sᵢ in inches.
8. Compute settlement ratio S/B (%):
   • ( S/B = (settlement;in;inches / B) \times 100 )
9. Classify settlement:
   • Uses settlement value to assign labels such as:
     • VERY SMALL
     • SMALL
     • MODERATE
     • LARGE
     • EXCESSIVE
10. Color-code the result:
    • Settlement ≤ 0.5 in → Very small (often green zone)
    • Up to 1.0 in → usually acceptable for many buildings
    • 1–2 in → moderate, may be acceptable depending on structure
    • 2 in → large or excessive, needs careful check
    • 4 in → often considered severe or critical for most buildings

The calculator then displays:

• Immediate Settlement, Sᵢ (inches)
• Influence Factor, Iₛ
• Shape Factor, I_f
• Depth Factor, I_d
• Rigidity Factor, I_r
• Settlement Ratio, S/B (%)
• Settlement Classification

All in a clean, easy-to-understand results panel.

How to Use an Immediate Settlement Calculator in Practice

Here’s a simple, practical workflow:

1. Define the foundation
   • Choose type (square, rectangular, strip, mat, circular).
   • Enter B, L and Dₓ (Width, Length, Depth).
2. Describe the soil
   • Select soil type (dense sand, stiff clay, etc.).
   • Use default Eₛ and μ or override with site-specific values from lab tests.
3. Enter load and stress
   • Input applied pressure, q (psf), based on structural design.
4. Specify soil layer and groundwater
   • Enter compressible layer thickness, H.
   • Enter water table depth.
5. Set correction/rigidity factor
   • Choose flexible, semi-rigid or rigid based on foundation behavior.
6. Calculate settlement
   • Click “Calculate Settlement”.
   • Review the displayed settlement value and classification.
7. Evaluate acceptability
   • Compare settlement value with project-specific allowable limits.
   • Check S/B ratio and classification.
   • Decide if changes are necessary.
8. Adjust design if needed
   • Reduce applied pressure (increase footing size or use lighter structure).
   • Improve soil (compaction, replacement, ground improvement).
   • Use a deeper or stiffer foundation system (piles, rafts with soil improvement).
   • Lower water table where feasible.

Limitations and Good Engineering Practice

While your Immediate Settlement Calculator is powerful and handy, it is still a simplified elastic model.

It does not fully capture:

• Long-term consolidation settlement in soft clays
• Highly non-linear soil behavior at high stress levels
• 3D effects around complex structures
• Differential settlement between adjacent foundations
• Effects of layered soils with very different stiffnesses at different depths (beyond the chosen H)

Therefore:

• Use this tool for preliminary design, quick checks, and education.
• For final design, especially in soft soils, highly loaded structures, or sensitive buildings, always:
  • Perform a full geotechnical investigation
  • Use appropriate design methods or advanced software
  • Consult a licensed geotechnical engineer