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 2450 psf
- Pore pressure (psf) 624
- Effective vertical stress sigma'_v 1826 psf
- Buoyant unit weight below the table 62.6 pcf
Details, formula, and sources
Total 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.
z_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.
Terzaghi'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.
The effective-stress principle is a public first-principles result; gamma_w = 62.4 pcf is a physical constant already used across this module.
Estimate. AHJ and licensed professional govern.
Field names used by the API: gamma_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