Effective Stress

The Principle of Effective Stress, first proposed by Karl Terzaghi in 1923, is the most fundamental concept in soil mechanics. It states that the strength and deformation characteristics of a soil are governed by the effective stress (σ′\sigma'), not the total stress (σ\sigma).

Stress Components

In a saturated soil mass, the total stress at any point is distributed between the soil skeleton and the pore water.

Total Stress (σ\sigma)

The total vertical stress at a depth zz due to the weight of everything above it (soil + water + surcharge).

Total Stress

Vertical stress at a given depth due to the total weight of all overlying soil layers and any surface surcharge.

σ=∑γH+q\sigma = \sum \gamma H + q

Variables

SymbolDescriptionUnit
σ\sigmaTotal vertical stress-
γ\gammaUnit weight of soil layer-
HHThickness of soil layer-
qqUniform surcharge at the surface-

Pore Water Pressure (uu)

The neutral stress carried by the water in the voids. It acts equally in all directions (hydrostatic).

Pore Water Pressure

Hydrostatic water pressure at a given depth below the groundwater table under static (no-flow) conditions.

u=γwhwu = \gamma_w h_w

Variables

SymbolDescriptionUnit
uuPore water pressure-
γw\gamma_wUnit weight of water9.81 kN/m³
hwh_wDepth below the groundwater table (piezometric head)-
  • Assumption: Hydrostatic conditions (no seepage).

Effective Stress (σ′\sigma')

The stress transmitted through the soil skeleton (particle-to-particle contact points).

Effective Stress

The intergranular stress carried by the soil skeleton; the fundamental driver of strength, compressibility, and volume change in soils.

σ′=σ−u\sigma' = \sigma - u

Variables

SymbolDescriptionUnit
σ′\sigma'Effective stress-
σ\sigmaTotal stress-
uuPore water pressure-
  • Effective stress cannot be measured directly; it is always calculated.
  • An increase in effective stress leads to compression (settlement) and increased shear strength.

Interactive Stress Profile

Visualize how the total stress, pore water pressure, and effective stress vary with depth and water table position.

Effective Stress Profile

Parameters

Water Table Depth (m)5.0
Layer 1 Unit Weight (kN/m³)16.0
Layer 2 Unit Weight (kN/m³)19.0

Layer 1: 0-4m (Sand)
Layer 2: 4-10m (Clay)
Observe how raising the water table increases pore pressure (uu) and decreases effective stress (sigma′\\sigma').

0m1m2m3m4m5m6m7m8m9m10m03978117157196Stress (kPa)Layer 1 / Layer 2 Interface▼ Water TableTotal Stress (σ)Pore Pressure (u)Effective Stress (σ')

Seepage Effects

When water flows through soil, the seepage force alters the effective stress.

Upward Seepage

Water flowing upward exerts a drag force on soil particles, opposing gravity. This reduces the effective stress.

Effective Stress with Upward Seepage

Effective stress in a soil layer experiencing upward seepage; the drag force of water reduces the effective stress, potentially causing a quick condition.

σ′=zγ′−izγw\sigma' = z\gamma' - i z \gamma_w

Variables

SymbolDescriptionUnit
σ′\sigma'Effective stress-
zzDepth-
γ′\gamma'Effective (submerged) unit weight of soil-
iiHydraulic gradient (h/L)-
γw\gamma_wUnit weight of water-

Quick Condition (Boiling): Occurs when the upward seepage force equals the effective weight of the soil, reducing effective stress to zero (σ′=0\sigma' = 0). The soil loses all strength and behaves like a fluid.

Critical Hydraulic Gradient (icri_{cr}):

Critical Hydraulic Gradient

The upward hydraulic gradient at which upward seepage forces exactly balance the submerged weight of the soil, causing a quick (boiling) condition.

icr=γ′γw=Gs−11+ei_{cr} = \frac{\gamma'}{\gamma_w} = \frac{G_s - 1}{1+e}

Variables

SymbolDescriptionUnit
icri_{cr}Critical hydraulic gradient-
γ′\gamma'Effective unit weight-
γw\gamma_wUnit weight of water-
GsG_sSpecific gravity of soil solids-
eeVoid ratio-
  • Typically icr≈1.0i_{cr} \approx 1.0.

Downward Seepage

Water flowing downward exerts a drag force in the direction of gravity. This increases the effective stress.

Effective Stress with Downward Seepage

Effective stress in a soil layer experiencing downward seepage; the drag force of water increases the effective stress, enhancing stability.

σ′=zγ′+izγw\sigma' = z\gamma' + i z \gamma_w

Variables

SymbolDescriptionUnit
σ′\sigma'Effective stress-
zzDepth-
γ′\gamma'Effective (submerged) unit weight of soil-
iiHydraulic gradient (h/L)-
γw\gamma_wUnit weight of water-

Capillary Rise and Frost Heave

Above the water table, pore water interactions can cause complex, detrimental phenomena.

Capillary Zone

In fine-grained soils (silts and clays) above the water table, surface tension pulls water upward into the voids.

  • Pore water pressure is negative (suction) in the capillary zone: u=−γwhcu = -\gamma_w h_c.
  • This increases effective stress: σ′=σ−(−u)=σ+u\sigma' = \sigma - (-u) = \sigma + u.
  • This phenomenon provides "apparent cohesion" to moist sands and silts (e.g., building sandcastles).

Frost Heave

In cold climates, the freezing of pore water can cause devastating upward expansion of the soil surface.

  • Mechanism: As frost penetrates the ground, it draws capillary water upward from the unfrozen soil below to form continuous ice lenses.
  • Because water expands 9% by volume when it freezes, and continuous ice lenses draw massive amounts of water, the soil physically heaves upward, cracking pavements and foundations.
  • Conditions Required: Three things must exist simultaneously for frost heave:
    1. Freezing temperatures penetrating the soil.
    2. A source of groundwater (high water table).
    3. A frost-susceptible soil. Clean sands are not susceptible (pores too large for capillarity). Dense clays are not susceptible (permeability too low for water to feed the ice lens). Silts are the most dangerously frost-susceptible soils because they have high capillarity combined with high enough permeability.
Key Takeaways
  • Effective Stress (σ′\sigma') controls the mechanical behavior of soil (strength and compression).
  • Total Stress (σ\sigma) is the weight of everything above a point; Pore Pressure (uu) is the hydrostatic pressure.
  • σ′=σ−u\sigma' = \sigma - u is the defining equation.
  • Upward seepage reduces effective stress and can lead to a Quick Condition (boiling) if i≥icri \ge i_{cr}.
  • Capillarity causes negative pore pressure (suction) above the water table, increasing effective stress.
  • Frost Heave requires freezing temperatures, groundwater, and a frost-susceptible soil (primarily silts), resulting in the formation of destructive ice lenses.
PreviousFlow Nets and Seepage Analysis - Examples & Applications
NextEffective Stress - Examples & Applications