Library / Civil / CIV-47
Civil
Vertical effective stress below a water table
Vertical effective stress at depth beneath a surface surcharge q, through a moist layer of thickness zm and unit weight γm above the water table and a saturated layer of thickness zs and unit weight γsat below it.
- Ref
- CIV-47
- Rev
- v1
- Field
- Civil
- Result
- σ′v [Pa]
Effective stress is total stress minus pore water pressure, and it is what controls soil strength and compression. Above the water table the soil has its moist unit weight γm. Below it, the soil is saturated, the water supports γw per metre, and the soil skeleton carries γsat − γw. Adding the surcharge, the vertical effective stress at depth zm + zs is q + γm zm + (γsat − γw) zs.
Vertical effective stress at depth beneath a surface surcharge q, through a moist layer of thickness zm and unit weight γm above the water table and a saturated layer of thickness zs and unit weight γsat below it. Below the table the buoyant unit weight γsat − γw applies. Hydrostatic water and negligible suction above the table.
Calculator
- Total vertical stress, q + γmzm + γsat·zs106,000 Pa
- Pore water pressure, γw·zs29,430 Pa
- Buoyant unit weight, γsat − γw10,190 N/m³
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The effective stress is 76.57 kPa, while the total stress is 106 kPa; the difference is the 29.43 kPa of pore pressure.
- If the water table rose to the surface the effective stress would fall, which is why flooding and dewatering change settlement and strength.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Pa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| zm Thickness above the water table | 0 to 20 m | 40,570 | 400,600 | 360,000 | +10% | +4.7 % |
| zs Saturated thickness | 0 to 20 m | 46,000 | 249,800 | 203,800 | +10% | +3.99 % |
| q Surface surcharge | 0 to 100,000 Pa | 66,570 | 166,600 | 100,000 | +10% | +1.31 % |
| γsat Saturated unit weight | 10,000 to 25,000 N/m³ | 46,570 | 91,570 | 45,000 | +10% | +7.84 % |
| γm Moist unit weight | 10,000 to 25,000 N/m³ | 60,570 | 90,570 | 30,000 | +10% | +4.7 % |
| γw Unit weight of water | 9,000 to 10,500 N/m³ | 74,500 | 79,000 | 4,500 | +10% | −3.84 % |
Sweep of Saturated thickness
| Saturated thickness (m) | Vertical effective stress (Pa) |
|---|---|
| 0 | 46,000 |
| 2.5 | 71,480 |
| 5 | 96,950 |
| 7.5 | 122,400 |
| 10 | 147,900 |
| 12.5 | 173,400 |
| 15 | 198,900 |
| 17.5 | 224,300 |
| 20 | 249,800 |
Sweep one variable
Variables and how each one contributes
Vertical effective stress
What the equation gives you. Everything else feeds it.
Surface surcharge
The uniform surcharge at the surface, in Pa. Adds to the stress at every depth in direct proportion. Raising it by 10 % (to 11,000) moves the result by +1.31 %, from 76,570 to 77,570 Pa.
Moist unit weight
The moist unit weight above the water table, in N/m³. Raises the stress in proportion to the thickness zm. Raising it by 10 % (to 19,800) moves the result by +4.7 %, from 76,570 to 80,170 Pa.
Thickness above the water table
The thickness of soil above the water table, in m. Raises the stress at γm per metre. Raising it by 10 % (to 2.2) moves the result by +4.7 %, from 76,570 to 80,170 Pa.
Saturated unit weight
The saturated unit weight below the water table, in N/m³. Raises the buoyant weight in proportion to zs. Raising it by 10 % (to 22,000) moves the result by +7.84 %, from 76,570 to 82,570 Pa.
Unit weight of water
The unit weight of water, in N/m³ (about 9810). Lowers the effective stress below the table, because of buoyancy. Raising it by 10 % (to 10,790) moves the result by −3.84 %, from 76,570 to 73,630 Pa.
Saturated thickness
The thickness of saturated soil, in m. Raises the stress at only γsat − γw per metre, much less than above the table. Raising it by 10 % (to 3.3) moves the result by +3.99 %, from 76,570 to 79,630 Pa.
Worked example with the values above
- Above the table: q + γm zm = 10,000 + 18,000 × 2 = 46,000 Pa.
- Below the table: (γsat − γw) zs = 10,190 × 3 = 30,570 Pa.
- σ′v = 46,000 + 30,570 = 76,570 Pa.
Assumptions and limits
- A vertical smooth wall, level drained cohesionless backfill, and enough wall movement to mobilise the active or passive state.
- Effective stresses for soil strength, with water pressure computed separately.
Common mistakes
- Using total instead of effective stress below the water table.
- Using the active coefficient where the wall cannot move, when at-rest pressure applies.
- Entering the friction angle in degrees where the page needs radians.
Statistics and uncertainty
Earth pressure is among the most uncertain quantities in structural design. The effective friction angle is rarely known to better than ±2° to 3°, which alone changes Ka by 10 % to 15 %, and the wall movement needed to reach the active state is rarely checked. Treat the numbers as estimates with generous margins.
Where it is used
- Designing retaining walls, basement walls and sheet piles.
- Finding overturning moments and sliding forces on walls.
Maths you need
- Effective stress: total stress minus pore water pressure
- Friction angle: the angle whose tangent is the shear to normal stress ratio at failure
- Active and passive states: minimum and maximum lateral stress at limiting equilibrium