Learn: Saturation relationship Sr·e = w·Gs
When direct phase volumes are unavailable, degree of saturation can be found from water content, solids specific gravity and void ratio. The identity links a mass-based measurement to how full the void space is with water.
What the formula is saying
The phase relation is Sr e = w Gs when Sr is a decimal fraction. Divide w Gs by e, then multiply by 100 for percent saturation.
Read the symbols in plain language
- w
- Water content as decimal
Mass of water divided by dry solid mass: 15% is 0.15 in the ratio option. It is not water volume divided by total volume.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Gs
- Specific gravity of solids
Specific gravity of solids. Specific gravity connects the water-to-solids mass ratio to the corresponding volume relationship.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- e
- Void ratio
Void volume divided by solid volume, not total volume. This ratio may exceed one.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Sr
- Result to find
Saturation relationship Sr·e = w·Gs. Multiply the physical fraction by one hundred, without capping inconsistent data.
%
Sort out the units first
w is water mass divided by dry solids mass and must be a decimal ratio. Gs and e are dimensionless. The output is percent; 15% water content is entered as 0.15 unless percent units are selected.
Assumptions before calculating
Use representative volumes or masses from the same soil sample and the same state. Treat solids, water and air as distinct phases; the stated phase relationship does not determine soil strength or suitability for construction.
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 Sr and explain the result in the stated output unit.
- w · Water content as decimal
- 0.15
- Gs · Specific gravity of solids
- 2.65
- e · Void ratio
- 0.7
Convert water content to a phase-volume ratio
Specific gravity connects the water-to-solids mass ratio to the corresponding volume relationship.
(0.15) × (2.65) = 0.3975Find the fraction of voids filled with water
Divide by the void-to-solids volume ratio to isolate saturation.
(0.3975) ÷ (0.7) ≈ 0.5678571429Express saturation as percent
Multiply the physical fraction by one hundred, without capping inconsistent data.
(0.5678571429) × 100 ≈ 56.78571429 %
Does this worked answer make sense?
At full saturation wGs equals e. Increasing water content at fixed void ratio and solids properties raises saturation until the physical limit is reached.
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.
- w · Water content as decimal
- 0.2
- Gs · Specific gravity of solids
- 2.65
- e · Void ratio
- 0.65
Convert water content to a phase-volume ratio
Specific gravity connects the water-to-solids mass ratio to the corresponding volume relationship.
(0.2) × (2.65) = 0.53Find the fraction of voids filled with water
Divide by the void-to-solids volume ratio to isolate saturation.
(0.53) ÷ (0.65) ≈ 0.8153846154Express saturation as percent
Multiply the physical fraction by one hundred, without capping inconsistent data.
(0.8153846154) × 100 ≈ 81.53846154 %
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.
- w · Water content as decimal
- 0.18
- Gs · Specific gravity of solids
- 2.7
- e · Void ratio
- 0.6
Find: Learn: Saturation relationship Sr·e = w·Gs
A hint, not the answer
The phase relation is Sr e = w Gs when Sr is a decimal fraction. Divide w Gs by e, then multiply by 100 for percent saturation.
w is water mass divided by dry solids mass and must be a decimal ratio. Gs and e are dimensionless. The output is percent; 15% water content is entered as 0.15 unless percent units are selected.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Convert water content to a phase-volume ratio
Specific gravity connects the water-to-solids mass ratio to the corresponding volume relationship.
(0.18) × (2.7) = 0.486Find the fraction of voids filled with water
Divide by the void-to-solids volume ratio to isolate saturation.
(0.486) ÷ (0.6) = 0.81Express saturation as percent
Multiply the physical fraction by one hundred, without capping inconsistent data.
(0.81) × 100 = 81 %
Avoid the common trap
Do not enter wet-basis water fraction in place of dry-basis w. Do not use porosity n in place of void ratio e, or confuse solids specific gravity with bulk density.
When this method applies — and when it does not
Require e > 0, Gs > 0 and w ≥ 0, with wGs ≤ e so saturation does not exceed 100%. Inconsistent measurements are rejected rather than silently capped.
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: Saturation relationship Sr·e = w·Gs. 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.