Permeability and Seepage N. Sivakugan Duration = 17 minutes

What is permeability? A measure of how easily a fluid (e.g., water) can pass through a porous medium (e.g., soils) water Loose soil - easy to flow - high permeability Dense soil - difficult to flow - low permeability

Bernoulli’s Equation 1. Kinetic energy 2. Strain energy The energy of a fluid particle is made of: 1. Kinetic energy fluid particle z - due to velocity 2. Strain energy - due to pressure datum 3. Potential energy - due to elevation (z) with respect to a datum

Bernoulli’s Equation Velocity head + Total head = Pressure head + Expressing energy in unit of length: datum z fluid particle Velocity head + Total head = Pressure head + Elevation head

Bernoulli’s Equation Velocity head + Total head = Pressure head + For flow through soils, velocity (and thus velocity head) is very small. Therefore, datum z fluid particle Velocity head + Total head = Pressure head + Elevation head Total head = Pressure head + Elevation head

Some Notes If flow is from A to B, total head is higher at A than at B. water A B Energy is dissipated in overcoming the soil resistance and hence is the head loss.

Some Notes At any point within the flow regime: Pressure head = pore water pressure/w Elevation head = height above the selected datum

Some Notes Hydraulic gradient (i) between A and B is the total head loss per unit length. water A B length AB, along the stream line

Darcy’s Law Velocity (v) of flow is proportional to the hydraulic gradient (i) – Darcy (1856) v = k i Permeability or hydraulic conductivity unit of velocity (cm/s)

Large Earth Dam crest filter free board riprap SHELL SHELL blanket CORE SHELL SHELL blanket FOUNDATION cutoff

Permeability Values (cm/s) 10-3 10-6 100 clays gravels sands silts Coarse Fines For coarse grain soils, k = f(e or D10)

Stresses due to Flow v = whw + satz u = w (hw + z) v ' = ' z Static Situation (No flow) X soil hw L z At X, v = whw + satz u = w (hw + z) v ' = ' z

Stresses due to Flow v = whw + satz v ' = ' z + wiz u = w hw Downward Flow At X, v = whw + satz hw L flow X soil z … as for static case hL u = w hw w hw + w(L-hL)(z/L) u = = w hw + w(z-iz) = w (hw+z) - wiz Reduction due to flow u = w (hw+L-hL) v ' = ' z + wiz Increase due to flow

Stresses due to Flow v = whw + satz u = w hw u = w (hw+L+hL) Upward Flow At X, flow v = whw + satz hw L X soil z hL … as for static case u = w hw w hw + w(L+hL)(z/L) u = = w hw + w(z+iz) = w (hw+z) + wiz Increase due to flow u = w (hw+L+hL) v ' = ' z - wiz Reduction due to flow

Quick Condition in Granular Soils During upward flow, at X: flow hw L X soil z hL v ' = ' z - wiz Critical hydraulic gradient (ic) If i > ic, the effective stresses is negative. i.e., no inter-granular contact & thus failure. - Quick condition

Seepage Terminology Stream line is simply the path of a water molecule. From upstream to downstream, total head steadily decreases along the stream line. concrete dam impervious strata soil hL datum TH = hL TH = 0

Seepage Terminology Equipotential line is simply a contour of constant total head. concrete dam impervious strata soil datum hL TH = 0 TH = hL TH=0.8 hL

Flownet A network of selected stream lines and equipotential lines. concrete dam impervious strata soil curvilinear square 90º

Quantity of Seepage (Q) # of flow channels ….per unit length normal to the plane head loss from upstream to downstream # of equipotential drops impervious strata concrete dam hL

Heads at a Point X Total head = hL - # of drops from upstream x h Elevation head = -z Pressure head = Total head – Elevation head impervious strata concrete dam hL datum TH = hL TH = 0 z h X

Piping in Granular Soils At the downstream, near the dam, the exit hydraulic gradient datum concrete dam impervious strata soil hL l h = total head drop

Piping in Granular Soils If iexit exceeds the critical hydraulic gradient (ic), firstly the soil grains at exit get washed away. This phenomenon progresses towards the upstream, forming a free passage of water (“pipe”). datum concrete dam impervious strata soil hL no soil; all water

Piping in Granular Soils Piping is a very serious problem. It leads to downstream flooding which can result in loss of lives. Therefore, provide adequate safety factor against piping. concrete dam impervious strata soil typically 5-6

Piping Failures Baldwin Hills Dam after it failed by piping in 1963. The failure occurred when a concentrated leak developed along a crack in the embankment, eroding the embankment fill and forming this crevasse. An alarm was raised about four hours before the failure and thousands of people were evacuated from the area below the dam. The flood that resulted when the dam failed and the reservoir was released caused several millions of dollars in damage.

Piping Failures Fontenelle Dam, USA (1965)

Filters Used for: facilitating drainage preventing fines from being washed away Used in: Filter Materials: earth dams granular soils retaining walls geotextiless

Granular Filter Design Two major criteria: granular filter (a) Retention Criteria - to prevent washing out of fines  Filter grains must not be too coarse (b) Permeability Criteria - to facilitate drainage and thus avoid build-up of pore pressures  Filter grains must not be too fine

Granular Filter Design Retention criteria: Permeability criteria: D15, filter < 5 D85, soil D15, filter > 4 D15, soil average filter pore size - after Terzaghi & Peck (1967) D15, filter < 20 D15, soil - after US Navy (1971) D50, filter < 25 D50, soil GSD Curves for the soil and filter must be parallel

Drainage Provisions in Retaining Walls weep hole geosynthetics granular soil drain pipe