Also in: Disaster Response and Recovery
Soil Vertical Total and Effective Stress (Terzaghi)
The vertical effective stress at a depth, from the soil profile and the water table.
Example
You enter
- Moist unit weight above water table (pcf) 120
- Saturated unit weight below water table (pcf) 125
- Depth of interest (ft) 20
- Depth to water table (ft, >= depth = dry) 10
You get
- Total vertical stress sigma_v 2,450 psf
- Pore pressure (psf) 624
- Effective vertical stress sigma'_v 1,826 psf
- Buoyant unit weight below the table 62.6 pcf
Checked against published worked examples from: FHWA.
Details, formula, and sources
ScopeTotal stress is everything stacked above the point (surcharge, then moist soil to the water table, then saturated soil below); pore pressure below the table is hydrostatic u = 62.4 x depth below it; and Terzaghi's sigma' = sigma - u is what the soil skeleton actually carries. At 20 ft in a 120/125 pcf profile with the table at 10 ft: 2,450 psf total, 624 psf pore, 1,826 psf effective. Below the table that equals stacking the BUOYANT unit weight (125 - 62.4 = 62.6 pcf), which is why submerged soil weighs about half and why moving a water table shifts settlement and bearing capacity with no load change at all. A surcharge raises total and effective equally since it adds no pore pressure. Feed the results straight into a liquefaction screen or a consolidation settlement. Hydrostatic, level ground, uniform layers. A design aid; the geotechnical engineer of record governs.
Formula or tablez_dry = min(z, z_wt); z_sub = max(0, z - z_wt); sigma_v = q + gamma_moist x z_dry + gamma_sat x z_sub; u = gamma_w x z_sub (gamma_w = 62.4 pcf); sigma'_v = sigma_v - u. Below the table this equals q + gamma_moist x z_wt + (gamma_sat - gamma_w) x z_sub.
Source and editionTerzaghi's effective-stress principle and the hydrostatic vertical stress profile, as compiled in Das, Principles of Foundation Engineering, and NAVFAC DM-7.01 (Soil Mechanics), by name.
Free accessThe effective-stress principle is a public first-principles result; gamma_w = 62.4 pcf is a physical constant already used across this module.
What governsEstimate. AHJ and licensed professional govern.
API field namesgamma_moist_pcf, gamma_sat_pcf, depth_ft, water_table_depth_ft, total_stress_psf, pore_pressure_psf, effective_stress_psf, gamma_buoy_pcf
- Effective-stress principle sigma' = sigma - u; the skeleton carries what the water does notTerzaghi 1925
- Hydrostatic pore pressure u = 62.4 x depth below the water table; no seepage gradient or artesian headDas / NAVFAC DM-7.01
- Buoyant equivalence below the table, sigma' accumulates at (gamma_sat - gamma_w)first-principles algebra
- Surcharge a surface surcharge raises total and effective stress equally, adding no pore pressurefirst principles