Last reviewed 16 Sept 2026 · 6 min read
Heads in soil water
At any point in flowing ground water:
- Elevation (position) head — height above a chosen datum.
- Pressure head — height to which water would rise in a piezometer.
- Total head (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 over a flow path losing head .
- Seepage force per unit volume , 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.
- Flow lines and equipotential lines intersect at right angles.
- The fields formed are (curvilinear) squares — their mean width equals mean length.
- The quantity of flow is the same in every flow channel.
- The head drop is the same between successive equipotential lines.
- Flow lines cannot cross each other; nor can equipotential lines.
- The flow net depends only on the boundary conditions, not on the permeability (for a homogeneous soil).
- Smaller squares mean higher gradient and velocity.
Methods of drawing: graphical trial sketching, electrical analogy, sand models, numerical methods.
Uses of a flow net
Discharge per unit length:
= total head loss; = number of flow channels; = number of equipotential drops. is the shape factor.
Pore pressure at a point after drops from the upstream side: total head , then .
Exit gradient in the last square at the downstream exit (, = length of that square).
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 ( ≈ 2.65, ≈ 0.65), .
At , 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.