Void ratio is a crucial concept in soil mechanics that describes the relationship between the volume of voids (spaces) and the volume of solid particles in a given soil sample. It is a dimensionless quantity, represented by the symbol “e.” It provides valuable insights into the soil’s behavior, strength, and compressibility.

Void ratio (e) is the volume of voids divided by the volume of solids in a soil mass. The void ratio formula is e = V_v / V_s. It is dimensionless, it can be greater than 1, and it relates to porosity by e = n / (1 − n).

Void Ratio Definition and Meaning

Let me start with the basics. Soil isn’t a solid block. It’s made of solid particles with gaps between them.

Those gaps are called voids. They’re filled with air, water, or both. Voids in soil control how the soil compresses, drains, and carries load.

Void Ratio Meaning in Soil

It is a measure of the soil’s porosity and compactness. It indicates the proportion of voids within the soil structure. A higher void ratio means more voids and a looser soil structure, while a lower void ratio indicates fewer voids and a denser soil structure. Understanding the void ratio helps engineers assess the soil’s behavior under loading conditions and design appropriate foundation systems.

Significance in Soil

It plays a significant role in understanding soil behavior. A higher void ratio indicates a looser soil structure with more voids, while a lower void ratio suggests a denser soil with fewer voids.

It directly influences soil properties such as permeability, shear strength, and compressibility. Soils with higher void ratios tend to be more compressible and have lower shear strength compared to soils with lower . It plays a crucial role in soil classification, ground improvement, foundation design, and soil-structure interaction.

Soil Compressibility: Soils with higher value are more compressible, meaning they undergo greater volume change when subjected to loading. This is because the presence of more voids allows for easier rearrangement and compression of soil particles. Conversely, soils with lower are less compressible and more resistant to volume change.

Shear Strength: Soils with lower ratios tend to have higher shear strength due to the increased contact and interlocking between soil particles. As the void ratio decreases, the soil becomes denser, resulting in improved shear resistance. This is particularly important when designing foundations, slopes, and retaining structures, as soil shear strength plays a crucial role in their stability.

Permeability: This is the ability of water to flow through the soil pores. Soils with higher ratios generally have higher permeability because the presence of more voids allows for easier water movement. On the other hand, soils with lower ratios have reduced permeability, as the smaller and fewer voids restrict water flow.

Soil Classification: The void ratio, along with other properties like particle size distribution and Atterberg limits, helps in categorizing soils into different groups based on their engineering behavior. This classification aids in understanding the soil’s suitability for various construction purposes and helps in selecting appropriate design parameters.

Soil Improvement: Ground improvement methods like compaction, grouting, and vibro-compaction aim to reduce the void ratio of soil, thereby increasing its density, strength, and bearing capacity.

Soil-Structure Interaction: Soils with lower ratios provide better support to foundations, while soils with higher ones may lead to excessive settlement and stability issues.

Soil Volume Change: As the ratio changes due to loading or moisture variations, the soil undergoes corresponding volume changes. Understanding the relationship between void ratio and volume change is essential for predicting and managing soil behavior in various geotechnical applications, such as foundation settlement analysis and expansive soil mitigation.

Void Ratio Calculation in Soil Mechanics

To calculate you need to determine the volume of voids (Vv) and the volume of solid particles (Vs) in a soil sample. The void ratio is then calculated using the following formula:

e = Vv / Vs

It’s important to note that the void ratio is different from porosity, which is the ratio of the volume of voids to the total volume of the soil sample.

Void Ratio Formula

The formula can be expressed in terms of other soil properties, such as the specific gravity of soil solids (Gs), water content (w), and unit weight of water (γw). The formula is as follows:

e = (Gs * γw / γd) – 1

where γd is the dry unit weight of the soil.

How to Calculate

To calculate, follow these steps:

• Determine the volume of voids (Vv) and the volume of solid particles (Vs) in the soil sample.
• Use the void ratio formula: e = Vv / Vs.
• Alternatively, if you have the specific gravity of soil solids (Gs), water content (w), and dry unit weight (γd), you can use the formula: e = (Gs * γw / γd) – 1.

Calculation Example
Let’s consider an example to understand the calculation. Suppose a soil sample has a volume of voids (Vv) of 150 cm³ and a volume of solid particles (Vs) of 350 cm³. Using the formula:

e = Vv / Vs
e = 150 cm³ / 350 cm³
e = 0.43

In this example, the void ratio of the soil sample is 0.43

Void Ratio Test for Soil

Several laboratory tests can be conducted to measure or calculate , here are some commonly used tests :

• Specific Gravity Test (ASTM D854): The specific gravity test is a fundamental test used to determine the specific gravity of soil solids, which is the ratio of the density of soil solids to the density of water. The test involves measuring the weight of a known volume of soil solids and calculating the specific gravity. The void ratio can then be calculated using the formula, which relates the specific gravity, water content, and unit weight of the soil.

• Moisture Content Test (ASTM D2216): The moisture content test is used to determine the amount of water present in a soil sample. It involves weighing the soil sample before and after oven-drying to remove the water. The moisture content is calculated as the ratio of the weight of water to the weight of dry soil solids. The moisture content is an essential parameter in calculating the void ratio, as it is used in the formula along with the specific gravity and unit weight of the soil.

• Dry Density Test: The dry density test is used to determine the dry unit weight of soil, which is the weight of dry soil solids per unit volume. There are different methods to measure the dry density, such as the sand cone test (ASTM D1556), rubber balloon test (ASTM D2167), and nuclear density gauge test (ASTM D6938). The dry density is required to calculate the void ratio of the soil.

• Direct Measurement Test: In some cases, the void ratio can be directly measured using specialized equipment. One such method is the mercury intrusion porosimetry (MIP) test, where mercury is forced into the soil pores under increasing pressure. By measuring the volume of mercury intruded at each pressure increment, the pore size distribution and void ratio can be determined. However, this test is less common and requires specialized equipment.

• Computed Tomography (CT) Scanning: Advanced imaging techniques like computed tomography (CT) scanning can be used to visualize and quantify the void space within a soil sample. CT scanning provides high-resolution 3D images of the soil structure, allowing for the measurement of void ratio and other pore-related properties. However, this method is more sophisticated and requires access to CT scanning facilities.

• Consolidation Test (ASTM D2435): Although not a direct test, the consolidation test can provide information related to void ratio changes in fine-grained soils. During a consolidation test, a soil sample is subjected to incremental loading, and the resulting deformation is measured. void ratio can be calculated at each load increment based on the change in sample height and the initial value. This test helps in understanding the compressibility and void ratio-stress relationship of fine-grained soils.

It’s important to note that the choice of test depends on the soil type, project requirements, and available resources. The specific gravity test and moisture content test are the most commonly used tests, as they are relatively simple and provide the necessary parameters for void ratio calculation.

When conducting tests, it’s crucial to follow standard procedures, ensure proper sample preparation, and maintain quality control measures to obtain reliable results. The test results should be interpreted by qualified geotechnical engineers who can analyze the data and provide recommendations based on the soil’s void ratio and related properties.

Many students and site engineers get stuck on one small question in soil mechanics: is it porosity or void ratio? And which volume goes in the denominator? I made this mistake in my first soil lab, and my whole consolidation calculation went wrong.

The void ratio formula looks simple, but it feeds into settlement, compaction, permeability, and strength calculations. If the void ratio is wrong, the foundation settlement estimate is wrong too. Even a homeowner reading a soil report before building should understand this number.

In this guide, I’ll explain what void ratio means, the basic formula, and how it relates to porosity. I’ll also show the formula using specific gravity and water content. Then I’ll cover air voids, critical void ratio, typical values for sand, gravel, and clay, and lab methods. Every formula has a solved example, so you can calculate void ratio confidently for exams, lab reports, or real projects.

Define Void Ratio

To define void ratio: it’s the ratio of the volume of voids to the volume of soil solids.

That’s the standard void ratio definition. So the void ratio meaning is simple: how much empty space the soil has for every unit of solid material.

Definition of Void Ratio in Simple Words

Here’s the definition of void ratio I give beginners. Imagine 1 m³ of soil particles. If the gaps between them add up to 0.6 m³, the void ratio is 0.6.

What Is Void Ratio in Soil Mechanics?

What is void ratio in soil mechanics? It’s one of the basic index properties of soil, along with water content, porosity, degree of saturation, and unit weight.

What is void ratio of soil? It’s the same property measured on a specific soil sample. What is void ratio? Short answer: voids divided by solids.

Void Ratio Adalah (For Indonesian Readers)

Many Indonesian students search void ratio adalah, which means “void ratio is.” The answer is the same: angka pori (void ratio) is the volume of voids divided by the volume of solids.

People also type void ration, a common typo. Older textbooks use void index for the same property.

Void Ratio Formula

Here’s the core void ratio formula:

Where:

• e = void ratio
• V_v = volume of voids (air + water)
• V_s = volume of soil solids

This is the basic formula of void ratio, also called the formula for void ratio, void ratio equation, equation for void ratio, voids ratio formula, or simply the void formula.

Ratio of Volume of Voids and Volume of Soil Solids

Remember this line for exams. Void ratio is the ratio of volume of voids and volume of soil solids.

Students often confuse it with the ratio of volume of voids and volume of soil. If “volume of soil” means the total volume, that ratio is porosity, not void ratio.

My tip: void ratio uses solids in the denominator, and porosity uses total volume. Write that on your formula sheet.

Void Ratio Symbol and Unit

• Void ratio symbol: e
• Void ratio unit: none. It’s dimensionless because it’s volume divided by volume.

We usually write void ratio as a decimal, like 0.65. Porosity is more often written as a percentage.

Three-Phase Diagram of Soil (Diagrammatic View)

Many readers search what does it actually look like, diagramatic, show in images, image, or give me a picture like this. Here’s the phase diagram I sketch on every lab sheet:

        Volume                    Weight
   ┌───────────────┐
   │      AIR      │  Va          Wa ≈ 0
   ├───────────────┤
   │     WATER     │  Vw          Ww
   ├───────────────┤
   │    SOLIDS     │  Vs          Ws
   └───────────────┘
   Vv = Va + Vw
   V  = Vs + Vv

In a real soil, the particles and gaps are mixed together. The diagram simply stacks them so the volumes are easy to see.

Practical tip: if you’re publishing this topic, add a clean labeled phase diagram image with alt text such as “three-phase diagram showing void ratio.” It helps readers and image search.

Volume of Voids Formula

The volume of voids formula is:

The volume of void (or volume of voids) is everything that isn’t solid particle.

How to Calculate Void Volume

How to calculate void volume:

1. Find the total volume V of the sample.
2. Find the volume of solids: V_s = W_s / (G γ_w).
3. Subtract: V_v = V − V_s.

That’s the void volume formula for soil. The void volume depends directly on how loose or dense the soil is.

How to Calculate Volume of Voids in Soil (Example)

Say a sample has V = 1000 cm³, dry mass = 1650 g, and G = 2.65.

This is the full void volume calculation for one soil sample.

Porosity: The Partner of Void Ratio

Porosity (n) is the ratio of the volume of voids to the total volume:

Porosity is always less than 1, or less than 100%. It can’t be more than the total volume.

Define Void Ratio and Porosity

To define void ratio and porosity together:

• Void ratio: voids ÷ solids
• Porosity: voids ÷ total volume

Relationship Between Void Ratio and Porosity

This is the most searched part of the topic. Let’s derive it properly.

Assume V_s = 1. Then V_v = e, and the total volume is V = 1 + e.

Rearranging:

This is the relationship between void ratio and porosity. You’ll also see it called the relation between void ratio and porosity, the relationship between porosity and void ratio, the relation between porosity and void ratio, the void ratio and porosity relation, the porosity and void ratio relation, the porosity and void ratio relationship, the void ratio and porosity relationship, the void ratio porosity relationship, and the porosity void ratio relation.

Porosity and Void Ratio Are Related By

A common exam question asks: porosity and void ratio are related by which equation? The answer is:

Void Ratio and Porosity Formula

This table covers the void ratio and porosity formula, the porosity and void ratio formula, and the porosity void ratio formula.

Porosity to Void Ratio: Solved Example

Porosity to void ratio: if n = 0.40:

Going the other way, if e = 0.60:

Void Ratio vs Porosity

That’s the difference between void ratio and porosity. For void ratio vs porosity or porosity vs void ratio questions, focus on the denominator.

Why Engineers Prefer Void Ratio

From my experience, void ratio is much easier to use in settlement work. When soil compresses, V_s stays the same, but the total volume changes.

So a change in void ratio directly shows how much the voids have shrunk. Porosity changes both its top and bottom numbers, which makes the calculation messier.

The topics void ratio and porosity, porosity and void ratio, void ratio porosity, and porosity void ratio always come back to this point.

Void Ratio Formula With Specific Gravity

You can’t measure the volume of voids directly on site. So in practice, we use specific gravity, water content, and unit weights.

Using Dry Unit Weight

This is the most useful void ratio formula with specific gravity.

Example: G = 2.68, γ_d = 16.5 kN/m³, γ_w = 9.81 kN/m³.

Using Bulk Unit Weight and Water Content

Use this when you know the field (bulk) unit weight from a core cutter or sand replacement test.

Using Degree of Saturation: Se = wG

For a fully saturated soil (S = 1), e = w G.

Example: a saturated clay with w = 25% and G = 2.70:

My tip: I use e = w G as a quick check on every saturated sample. If it doesn’t match the void ratio from unit weight, something is wrong with the lab data.

All Void Ratio Equations at a Glance

These void ratio formulas, also called void ratio equations, cover almost every exam and lab case. Use any of them as a void ratio formula for soil.

How to Calculate Void Ratio of Soil

How to calculate void ratio step by step:

1. Find the specific gravity G with a pycnometer test.
2. Find the water content w by oven drying.
3. Find the bulk unit weight γ with a core cutter or sand replacement test.
4. Calculate γ_d = γ / (1 + w).
5. Apply e = G γ_w / γ_d − 1.

This is how to calculate void ratio and how to calculate void ratio of soil in a real project.

How to Find Void Ratio: Worked Example

How to find void ratio for a field sample:

• γ = 19.0 kN/m³
• w = 15%
• G = 2.65

That’s a complete void ratio calculation, or void calculation, in five lines.

Void Ratio Calculator (Spreadsheet Method)

You don’t need an app. Build your own void ratio calculator in Excel or Google Sheets:

I keep a sheet like this for every lab batch. It saves time and avoids calculator slips.

Void Ratio of Soil Formula: Initial and Change in Void Ratio

Initial Void Ratio

The initial void ratio (e₀) is the void ratio before loading, for example at the start of an oedometer test.

The initial void ratio formula using the height of solids is:

Where H₀ is the initial sample height and A is the sample area. For saturated samples, check it with e₀ = w₀ G.

Change in Void Ratio Formula

The change in void ratio formula from consolidation is:

Example: H₀ = 20 mm, ΔH = 1.2 mm, e₀ = 0.90:

The new void ratio is 0.90 − 0.114 = 0.786.

Why Initial Void Ratio Matters for Your Building

Consolidation settlement uses e₀ directly:

If e₀ is wrong, the settlement estimate for your house or office building is wrong too. This is where the theory meets real cracks in real walls.

Air Voids and Air Content

Air Void Ratio

The air void ratio is sometimes defined as the volume of air divided by the volume of solids:

That’s the air void ratio formula. Many textbooks use air content and percentage air voids instead, so check which definition your syllabus uses.

Percentage Air in the Voids (Air Content)

The percentage air in the voids, or air content a_c, is:

Percentage of Air Voids Formula

The percentage of air voids formula is:

In terms of dry unit weight:

This is the percentage of air voids formula in soil mechanics that’s used to draw air-void lines on compaction curves. It’s also called the air voids formula.

Example: n = 0.40, S = 0.60:

Site tip: well-compacted fills usually have a low percentage of air voids. A high value tells me the roller needs more passes or the moisture content is off.

Void Ratio Range and Typical Values

Can Void Ratio Be Greater Than 1?

Can void ratio be greater than 1? Yes. If the voids take up more volume than the solids, e > 1. Soft clays and organic soils often do.

That’s why the classic MCQ says “the void ratio of soil mass can be greater than unity.” Porosity, on the other hand, can never reach 1.

Typical Void Ratio of Soils

These are the typical void ratio of soils values I use for quick sense checks. Treat them as a rough guide, not design values.

Void Ratio of Sand

The void ratio of sand (sand void ratio) depends on grading and packing. Uniform loose sand sits near 0.8, and dense well-graded sand can drop below 0.45.

Void Ratio of Gravel

The void ratio of gravel (gravel void ratio) is usually low because well-graded gravels pack tightly. Uniform gravel can still have a high void ratio.

Void Ratio of Clay

The void ratio of clay varies the most. Stiff clays may be around 0.6. Soft marine clays and organic clays can exceed 2.

Range of Void Ratio

The void ratio range (range of void ratio) for natural soils runs from about 0.3 for dense, well-graded soils to above 3 for very soft organic clays.

Maximum Void Ratio of Soil and Relative Density

The maximum void ratio of soil (e_max) is its loosest state. The minimum (e_min) is its densest. Together they give relative density:

Example: e_max = 0.85, e_min = 0.45, e = 0.60:

This tells you the sand is medium dense to dense.

Critical Void Ratio

The critical void ratio is the void ratio at which sand shears without any change in volume. Arthur Casagrande introduced this idea.

• Above the critical void ratio, loose sand contracts when sheared. When it’s saturated, pore pressure rises, which can lead to liquefaction.
• Below it, dense sand dilates (expands) when sheared.

Why it matters: loose saturated sands above the critical void ratio are at risk of liquefaction during earthquakes. I always flag them in site reports.

Void Ratio Soil Lab Methods

Here are the common lab methods I use to find soil void ratio and the void ratio in soil:

In India, follow the IS 2720 series. In the US, follow ASTM D854 for specific gravity and ASTM D4253/D4254 for maximum and minimum density.

Lab tip: most errors I’ve seen come from specific gravity. A wrong G shifts every void ratio you calculate.

Void Ratio Beyond Soil: Related Terms People Search

Some searches use “void” in other fields. Here are quick answers so you don’t mix them up with soil voids.

Void Percentage in Aggregates

Void percentage in coarse aggregate (ASTM C29) is:

This helps in concrete mix design and drainage layer design.

Air Content & Void System Analysis (Concrete)

Air content & void system analysis refers to the microscopic test on hardened concrete (ASTM C457). It measures air content, specific surface, and the spacing factor of entrained air bubbles.

A small spacing factor means better freeze-thaw resistance. This is a concrete test, not a soil test.

Void Volume in HPLC and Dead Volume

Void volume in HPLC is the volume of mobile phase inside the column. Dead volume is the extra volume outside the column, in the tubing, injector, and detector.

How to calculate void volume in HPLC:

Where F is the flow rate and t₀ is the retention time of an unretained peak.

A quick void volume calculation formula in HPLC is V₀ ≈ 0.5 × L × d², with L and d in mm, which gives the volume in µL. A 150 × 4.6 mm column gives about 1.6 mL.

What Is a Positive Void Coefficient?

What is positive void coefficient? Or what is a positive void coefficient? It’s a nuclear reactor term. It means reactor power increases when steam bubbles (voids) form in the coolant.

It’s unrelated to soil, but students land here searching “void.” The RBMK reactor at Chernobyl had a positive void coefficient.

Common Mistakes I See in Void Ratio Problems

• Using total volume instead of solids volume in e.
• Writing void ratio as a percentage.
• Forgetting to convert water content from percent to decimal.
• Using e = w G for partly saturated soil.
• Using bulk unit weight in the dry unit weight formula.
• Assuming void ratio can’t exceed 1.

Frequently Asked Questions

What is the void ratio formula?

e = V_v / V_s, the volume of voids divided by the volume of solids.

What is the relation between void ratio and porosity?

n = e / (1 + e) and e = n / (1 − n).

Can void ratio be greater than 1?

Yes, especially in soft clays and organic soils.

What is the unit of void ratio?

It has no unit. It’s dimensionless.

What is the void ratio formula with specific gravity?

e = G γ_w / γ_d − 1, or e = w G / S.

Conclusion

The void ratio formula is short, but it shows up across all of soil mechanics. Get it right, and settlement, compaction, and strength calculations become much easier.

Key takeaways:

• Void ratio is e = V_v/V_s, and porosity is n = V_v/V.
• Convert between them with n = e/(1+e) and e = n/(1-n).
• In practice, use e = G\gamma_w/\gamma_d - 1 or Se = wG.
• Void ratio can exceed 1, but porosity can’t.
• The initial void ratio controls consolidation settlement.

My advice: take one soil report or lab sheet today and work out the void ratio yourself with these formulas. If you’re a homeowner or facility manager, check e_0 in your soil investigation report. Ask your engineer how it affects expected settlement before construction begins.