Seepage Analysis - Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Seepage Pressure and Seepage Force

Seepage pressure is the pressure exerted by moving water on soil particles due to frictional drag. This drag force always acts in the direction of flow.

The seepage pressure per unit area is related to the head loss producing the flow. Refer to the formula below and the image for the precise expression:

In these expressions, h denotes the head loss producing the flow and γ_w denotes the unit weight of water. Use the standard value γ_w = 9.81 kN/m³ for calculations.

Seepage force on a cross section of area A due to a head loss h is

F_s = h A γ_w

Seepage force per unit volume is

f_s = i γ_w

where i is the hydraulic gradient (= h / z for vertical distance z). Note that P_s, F_s and f_s act in the direction of flow.

Effective Stresses

Pore water pressure (u) is the pressure carried by the water in soil voids (pores). It is sometimes called neutral pressure because it does not resist shear stresses in the soil mass.

The pore pressure at a point below the water surface is given by:

In words: u = γ_w × h_w, where h_w is the pressure head measured from the water free surface to the point considered.

Effective stress is the stress carried by the soil skeleton and is the controlling stress for shear strength and deformation. It is defined by Terzaghi's principle:

For saturated soils, a common form is:

In words: σ' = σ - u, where σ is the total stress and u the pore water pressure. When pore pressure increases (for example due to upward seepage), effective stress reduces and, consequently, shear strength reduces.

Quicksand Condition

Quicksand condition occurs when upward seepage is strong enough to overcome the submerged weight of soil particles and separate them, causing the soil to behave as a fluid. This results in a loss of shear strength and bearing capacity; the soil cannot support external loads.

The condition arises when upward seepage pressure equals or exceeds the downward pressure due to the submerged weight of the soil. The shear strength of cohesionless soil depends on effective stress. The shear strength (for cohesionless soil) may be written as:

The effective stress under upward seepage becomes:

Using typical values G = 2.67 (specific gravity of solids) and e = 0.67 (void ratio), the critical hydraulic gradient obtained from the expression above evaluates to approximately unity. That is, when the hydraulic gradient i = 1, effective stress can become zero and the soil may boil or quicken.

Laplace Equation of Two-Dimensional Flow and Flow Nets

Two-dimensional steady flow in an isotropic, homogeneous porous medium satisfies the Laplace equation for the hydraulic head f(x,y). The general governing equation is:

For isotropic homogeneous soil, this reduces to the standard two-dimensional Laplace equation:

For anisotropic soil, transformations can be used so that the equation takes an equivalent isotropic form; in such approaches f may be written in terms of transformed coordinates (images show typical relations):

Flow nets are constructed from two orthogonal families of curves: flow lines (streamlines) and equipotential lines. Each rectangle formed by their intersections is approximately a channel of equal flow and equal potential drop.

Seepage Discharge (q)

Using a flow net, the discharge per unit length (q) through a porous medium (for the case of flow under a dam or similar) is given by:

The commonly used form is

q = (k h N_f) / N_d

where:

• k = coefficient of permeability,
• h = total head difference between upstream and downstream,
• N_f = total number of flow channels (number of flow paths),
• N_d = total number of equipotential drops (number of potential intervals).

shape factor =

Some useful counting relations used in flow nets (as commonly applied):

• N_f = total number of flow channels.
• N_d = total number of equipotential drops.
• In certain counting conventions, N_f = N_y - 1, where N_y is the number of flow lines counted across a section; apply the chosen convention consistently in a given problem.

Hydrostatic (pore) pressure is

U = h_w γ_w

where h_w is the pressure head and γ_w is the unit weight of water. The term H_w is sometimes used to denote hydrostatic head or potential head in graphical constructions.

Seepage Pressure (alternate notation)

P_s = h' γ_w

Exit Gradient

The exit gradient is the hydraulic gradient at the downstream exit where flow emerges from the soil into the free surface. Exit gradients are important because local hydraulic gradients near the exit can be several times the average gradient and may cause particle detachment (boiling) at the exit face.

For a square exit field of size b × b, the equipotential drop is shown in the figure and may be used in flow-net counting. The equipotential drop expression appears in the image below:

Phreatic Line

The phreatic line is the topmost flow line (streamline) in an earth dam or embankment with seepage beneath it. The phreatic line indicates the free-surface of seepage where pore pressure equals atmospheric pressure (u = 0). Below the phreatic line the pore pressure is hydrostatic.

(a) Phreatic Line with Filter

When a filter or drainage layer is provided downstream, the phreatic line passes through the junction of permeable and impermeable surfaces and can be approximated by a parabola or circular arc depending on geometry. See diagram and related construction:

In the typical construction, the phreatic line (top flow line) follows a base parabola. In the figure:

• CF= radius of circular arc =
  
• C = entry point of base parabola,
• F = junction of permeable and impermeable surface,
• S = distance between focus and directrix (focal length),
• FH = S.

For simple filter designs the discharge per unit length may be taken as:

(i) q = k s

where s is a suitable shape/distance parameter; further relations and formulae for practical shapes are shown in the images below.

® For 2D

® For 3D

(b) Phreatic Line without Filter

When no filter exists and seepage emerges directly into the downstream surface, the phreatic line and discharge depend on the downstream slope angle and geometry. Typical graphical and analytical approximations are shown in the images below.

For the case when the downstream slope angle a < 30°:

For the case when the downstream slope angle a > 30°:

Additional geometric expressions and corrections for neglecting downstream sand flow are available and indicated in the images that follow. The use of a filter or drain is recommended to prevent sand movement and to control exit gradients.

For practical earthworks, filters and drains are designed to intercept seepage and to reduce exit gradients so that particle movement is prevented.

Remember: