How to calculate effective stress in saturated soil
Total stress is shared between pore-water pressure and the soil skeleton. Effective stress represents the part carried through the soil skeleton in this saturated-soil model.
What the formula is saying
Start from total stress σ and subtract pore-water pressure u: σ′ = σ − u. The prime mark distinguishes effective stress from total stress.
Read the symbols in plain language
- σ
- Total stresskPa
- u
- Pore-water pressurekPa
Sort out the units first
Both values must use the same stress unit. Here both are kPa. Do not subtract a water depth in metres directly from a stress in kPa.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- σ · Total stress
- 150 kPa
- u · Pore-water pressure
- 60 kPa
Identify total stress at the point
Use the total stress component relevant to the question.
(150) = 150 kPaSubtract pore-water pressure
The remainder is the skeleton-carried effective stress.
(150)-(60) = 90 kPa
Does this worked answer make sense?
Add the answer to u: 90 + 60 = 150 kPa. Raising pore pressure at fixed total stress reduces effective stress.
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
Use these new values. Work it out first, then check your answer.
- σ · Total stress
- 200 kPa
- u · Pore-water pressure
- 80 kPa
Find: effective stress in saturated soil
A hint, not the answer
Start from total stress σ and subtract pore-water pressure u: σ′ = σ − u. The prime mark distinguishes effective stress from total stress.
Both values must use the same stress unit. Here both are kPa. Do not subtract a water depth in metres directly from a stress in kPa.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify total stress at the point
Use the total stress component relevant to the question.
(200) = 200 kPaSubtract pore-water pressure
The remainder is the skeleton-carried effective stress.
(200)-(80) = 120 kPa
Avoid the common trap
Adding u instead of subtracting reverses the relationship. A negative computed result needs physical interpretation, not a “safe” label.
When this method applies — and when it does not
Terzaghi effective-stress relation for saturated soil with consistent sign convention. Unsaturated soils need a more specific stress model.
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.
One idea understood. Keep going.
This optional checkmark is saved only in this browser. It is your own progress note, not a certificate.
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.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.