Effective Stress and Quicksand

Principle of effective stress

A saturated soil is a skeleton of solid particles with water filling the voids. A load on the soil is shared between the two phases.

Effective stress controls compression (settlement), shear strength and permeability changes of soil. Two soils with the same effective stress behave the same regardless of their total stress and pore pressure.

Effective stress is a derived quantity: it cannot be measured directly; total stress and pore pressure are measured or computed.

Stresses in soil at rest (hydrostatic water)

At depth $z$ in a uniform deposit:

• Dry soil: $\sigma ={\gamma }_{d}z$, $u=0$, ${\sigma }^{\prime }={\gamma }_{d}z$.
• Saturated soil with water table at the ground surface: $\sigma ={\gamma }_{sat}z$, $u={\gamma }_{w}z$, ${\sigma }^{\prime }=({\gamma }_{sat}-{\gamma }_w)z={\gamma }^{\prime }z$.
• Water standing above ground (e.g. lake bed with $H$ m of water): $\sigma ={\gamma }_{w}H+{\gamma }_{sat}z$, $u={\gamma }_w(H+z)$ → ${\sigma }^{\prime }={\gamma }^{\prime }z$ — the depth of standing water does not change effective stress in the soil below.

In layered profiles, add layer contributions:

Effect of water table movement

• Lowering the water table (pumping, dewatering, drought): soil that was submerged now contributes moist/bulk weight while pore pressure falls → effective stress increases → consolidation settlement of clays, ground subsidence (e.g. cities over-pumping groundwater).
• Rising water table (flooding, reservoir filling): effective stress decreases → loss of bearing capacity and shear strength; collapse of some unsaturated soils.

Effect of seepage

With vertical seepage over a depth $z$ with gradient $i$:

Upward flow at the critical gradient makes ${\sigma }^{\prime }=0$ — the quick condition (see Seepage Analysis, Flow Nets & Quicksand).

Heads in soil water

At any point in flowing ground water:

• Elevation (position) head $z$ — height above a chosen datum.
• Pressure head $u/{\gamma }_w$ — height to which water would rise in a piezometer.
• Total head $h=z+\frac{u}{{\gamma }_w}$ (velocity head is negligible in soil).

Water flows from higher total head to lower total head. Head loss per unit length is the hydraulic gradient.

Seepage pressure and seepage force

As water flows through soil it loses head by friction with the grains and transfers that energy to the soil skeleton:

• Seepage pressure $=h{\gamma }_w$ over a flow path losing head $h$.
• Seepage force per unit volume $=i{\gamma }_w$, acting in the direction of flow.

Upward flow reduces effective stress (seepage force opposes gravity); downward flow increases it:

Laplace equation

For steady two-dimensional flow in a homogeneous, isotropic, saturated, incompressible soil obeying Darcy's law, continuity gives

Its solution is represented by two families of orthogonal curves — the flow net.

Flow nets

• Flow lines — paths followed by water particles.
• Equipotential lines — lines joining points of equal total head.
• Flow channel — the space between two adjacent flow lines; equipotential drop — head loss between adjacent equipotentials.

Methods of drawing: graphical trial sketching, electrical analogy, sand models, numerical methods.

Uses of a flow net

Uplift pressure on the base of a structure is obtained from the heads at the base points, and must be resisted by the weight of the floor.

Critical hydraulic gradient and quicksand

When water flows upward with a gradient large enough that the seepage force equals the submerged weight of the soil, the effective stress becomes zero:

For typical sands ($G$ ≈ 2.65, $e$ ≈ 0.65), $i_c\approx 1.0$.

At $i=i_c$, a cohesionless soil loses all strength and behaves like a liquid — the quick condition (quicksand). It is a hydraulic condition, not a soil type; it occurs in fine sands and silts (coarse soils need very large flows; clays have cohesion). Examples: excavations below water table with upward seepage, downstream of sheet piles and weirs.