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What is Atterberg Limits in Geotechnical Engineering?

In 1900s, Engr. Albert Atterberg developed a method to classify the consistency of fine-grained soils based on their moisture content, which led to the identification of the Atterberg Limits, a key indicator of soil behavior in different states.

Atterberg Limits are water content boundaries that define the behavioral states of fine-grained soils.

They include:

Shrinkage Limit
Plastic Limit
Liquidity Limit

The Key States are:

Solid States: No change in volume, no moisture.
Semi-Solid States: Cracks were present when molded due to a little bit of moisture.
Plastic State: Soil can be molded without cracking.
Liquid State: Soil flows like a liquid.

1. Liquid Limit (LL)

What is liquid limit and why is it important?

Water content where soil starts behaving like a liquid.

2. Plastic Limit (PL)

What is plastic limit and why is it important?

Soil at this consistency is starting become plastic, flexible and moldable.

How it’s tested:

Take a small amount of moist soil.
Air dry to reduce water content.
Roll it into 3 mm diameter threads on a glass plate.
When threads cracks at exactly 3 mm diameter, determine its water content.

3. Shrinkage Limit (SL)

What is shrinkage limit and why is it important?

Shrinkage limit is the water content below which additional drying does not result in a decrease in soil volume.

Overview of the Formulas

Plasticity Index (PI)

How do you calculate Plasticity Index and what does it mean?

PI is the range between the Liquid and Plastic Limits, basically, how much room there is for soil to behave plastically.

To calculate Plasticity Index, use the formula:

$PI = LL - PL$

According to Burmister (1949), this is how he classified plasticity index.

PI	Description
0	Nonplastic
1 – 5	Slightly Plastic
5 – 10	Low Plasticity
10 – 20	Medium Plasticity
20 – 40	High Plasticity
> 40	Very High Plasticity

Example

If LL is 50% and PL is 25%, then PI = 25.

This means that the soil is highly plastic, and likely to expand or shrink significantly.

Engineering Significance

Higer PI indicates that it has more volume clay content. With greater volume change potential, the higher its compressibility.

Shrinkage Index

What is shrinkage index and how do you calculate it?

It measures the volume change potential of clay soils during drying. It also indicates the natural consistency of clay soil relative to its plastic range.

To calculate this, use the formula:

$SI = PL - SL$

Liquidity Index

What is liquidity index and how to calculate it?

LI is the flip side (not reciprocal) of CI. It shows how liquid the soil is based on its moisture content.

$LI = \frac{w-PL}{LL-PL}$

Example

LI = (35 – 25) / 25 = 0.4

Then based from the table, the soil still sits in the plastic range.

LI Value	Soil State
LI < 0	Solid
LI = 0	At Plastic Limit
LI = 1	At Liquid Limit
LI > 1	Very soft/liquid-like

Consistency Index (CI)

What is constency index and how to calculate it?

CI shows how close the current water content is to the soil’s plastic and liquid limits.

$CI = \frac{LL-w}{LL-PL}] </div> </div>     <figure class="wp-block-table is-style-stripes"><table class="has-fixed-layout"><thead><tr><th class="has-text-align-center" data-align="center"><strong>CI Value</strong></th><th class="has-text-align-center" data-align="center"><strong>Soil State</strong></th></tr></thead><tbody><tr><td class="has-text-align-center" data-align="center">CI > 1</td><td class="has-text-align-center" data-align="center">Semi-solid</td></tr><tr><td class="has-text-align-center" data-align="center">CI = 1</td><td class="has-text-align-center" data-align="center">At Plastic Limit</td></tr><tr><td class="has-text-align-center" data-align="center">CI = 0</td><td class="has-text-align-center" data-align="center">At Liquid Limit</td></tr><tr><td class="has-text-align-center" data-align="center">CI < 0</td><td class="has-text-align-center" data-align="center">Liquid-like</td></tr></tbody></table></figure>   <strong>Example:</strong>   LL = 50, PL = 25, w = 35   PI = 25, CI = (50 - 35) / 25 = 0.6   <em>The soil is in the plastic range but neither too wet nor too dry.</em>     <h2 class="wp-block-heading has-large-font-size" id="flow-index">Flow Index</h2>   <blockquote class="wp-block-quote"> Flow index is the slope of the curve and this can be expressed as: </blockquote>   <div class="wp-block-columns has-border-color has-palette-color-4-color has-palette-color-6-background-color has-text-color has-background has-link-color" style="border-color:#4adede;border-width:2px;border-radius:20px;margin-top:0;margin-bottom:0;padding-top:17px;padding-right:20px;padding-bottom:17px;padding-left:20px"> <div class="wp-block-column"> \[FI= \frac{w_1-w_2}{log(N_2/N_1)}$

where:
$w_1$ = moisture content corresponding to number of blows of $N_1$
$w_2$ = moisture content corresponding to number of blows of $N_2$

Other Formulas:

Shrinkage Limit Test

Shrinkage Limit can be calculated using this formula

$SL= \frac{m_1-m_2}{m_2}-\frac{(V_1-V_2)\rho_w}{m_2}$

where:
$m_1$ = mass of wet soil
$m_2$ = mass of oven-dried soil
$V_1$ = volume of wet
$V_2$ = volume of oven-dried soil

Shrinkage Ratio

$SR=\frac{m_2}{V_2\rho_w}$

Specific Gravity of Solids

$G = \frac{1}{\frac{1}{SR}-\frac{SL}{100}}$

References:

‌Das, B. M. (2013). Fundamentals of geotechnical engineering. Cengage Learning.

Geo Engineer. (2020). Atterberg Limits. Www.geoengineer.org. https://www.geoengineer.org/education/laboratory-testing/atterberg-limits

(2025). Youtu.be. https://youtu.be/CL-Rxg8bE6M?si=bo3Wcdee6Ssz1CuB

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CH 1: SOIL PROPERTIES

Index	Engineering Behaviour	Formula
Plasticity	Clay Content Indicator	$PI= LL-PL$
Shrinkage	Volume Change	$SI=PL-SL$
Liquidity	Natural Consistency	$LI=\frac{w-PL}{LL-PL}$
Consistency	Stiffness	$CI=\frac{LL-w}{LL-PL}$
Flow	Moisture Sensitivity	$FI= \frac{w_1-w_2}{log(N_2/N_1)}$
Toughness	Clay Toughness	$TI=\frac{PI}{FI}$

What is Atterberg Limits in geotechnical Engineering