Effective Stress

Effective Stress

The principle of effective stress, proposed by Terzaghi, is the most important concept in soil mechanics. It states that soil behavior (strength, compressibility) is controlled by the effective stress, not the total stress.

Stress Components

Total Stress ($\sigma$)

The total vertical stress at a depth zz due to the weight of everything above it (soil + water + surcharge). σ=∑γH+q\sigma = \sum \gamma H + q

Pore Water Pressure ($u$)

The neutral stress carried by the water in the pores. u=γwhwu = \gamma_w h_w

  • hwh_w: Depth below the water table (piezometric head).
  • Assumed hydrostatic unless seepage is occurring.

Effective Stress ($\sigma'$)

The stress transmitted through the soil skeleton (particle-to-particle contact). σ′=σ−u\sigma' = \sigma - u

Seepage Effects on Effective Stress

Upward Seepage

Reduces effective stress. σ′=zγ′−izγw\sigma' = z\gamma' - i z \gamma_w If σ′=0\sigma' = 0, a quick condition (boiling) occurs. Critical Hydraulic Gradient (icri_{cr}): icr=γ′γw=Gs−11+ei_{cr} = \frac{\gamma'}{\gamma_w} = \frac{G_s - 1}{1+e}

Downward Seepage

Increases effective stress. σ′=zγ′+izγw\sigma' = z\gamma' + i z \gamma_w

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