Flow through Soils (ch7)

Energies Kinetic E (velocity) Strain E (fluid pressure) Potential E (elevation) Head: convert each form of energy into the equivalent potential energy and express it as the corresponding height. units of LENGTH

Heads hv = velocity head (KE) hp = pressure head (SE) he = elevation head (PE) h = total head = hv + hp + he (Bernoulli) units of LENGTH

Heads in a tank of water… B

Head loss l head loss = Dh = h1 – h2 Fluid flows from point of high total head to point of low total head h2 1 2 l head loss = Dh = h1 – h2

Hydraulic gradient Rate at which the total head changes along a length

Heads in soils Since velocity is slow through soils, we neglect the velocity head. Thus,

Soil piezometer The “pore water pressure” at A is Pressure head at A. hp Pressure head at A. A The “pore water pressure” at A is

Pore water pressures uhydrostatic = uh = due to hydrostatic condition only uexcess = ue = due to additional processes

Hydrostatic pore water pressure Depth, z zw zw1 zw2

One dimensional flow SOIL Flow is in one direction Flow vectors: parallel of equal magnitude SOIL Flow is in one direction

Flowrate through soil SOIL Flowrate = Q [m3/sec] What is the flowrate through a soil? Concrete dam Flowrate = Q [m3/sec] SOIL

Darcy’s Law Assumptions: flow is laminar soil properties do not D with time Cross-sectional area to flow Hydraulic conductivity “permeability” [cm/s] Hydraulic gradient

Finding k Dh A L Measure Q Figure 7.11 (text)

k fluid soil Measure of a soil-fluid system’s resistance to flow depends on soil fluid Void size Fabric (structure) Void continuity Specific surface (drag) Viscosity Mass density

k Units are in cm/sec but k = velocity

k SOIL TYPICAL VALUES [cm/s] gravel 101 – 102 sands 10-3 – 100 silts 10-8 – 10-3 clays 10-10 – 10-6 Probably soil’s most varying parameter (largest numerical range)

Lab testing sand clay “seam” k1 = 10-2 k2 = 10-6 Soil specimens sand clay “seam” k1 = 10-2 k2 = 10-6 k – precision is on the order of +/- 50% or more! Report values to one decimal place.

Lab testing (constant head test) Dh A L Measure Q Figure 7.11 (text)

In-situ testing Slug test Pumping test

Hazen’s Correlation k a pore size ~ (pore diameter)2 (pore diameter) ~ D10 For loose clean sands with 0.1mm < D10 < 3mm and Cu < 5 USE THESE UNITS! k = [cm/sec] C = Hazen’s coefficient = 0.8 – 1.2 (typical = 1) D10 = [mm]

Example Compute seepage loss (Q) through the sand seam el. = 167.3m clay el. = 165m sand seam 256 m 3.2 m Given: ksand = 4x10-2 cm/sec reservoir length (into board) = 1000 m Compute seepage loss (Q) through the sand seam

Solution Q = kiA k = 4x10-2 cm/sec i = Dh/L = (167.3m – 165m) / 256m = 0.009 A = (3.2 m) (1000 m) = 3200 m2 Q = kiA = 0.0115 m3/sec = 41.5 m3/hr