Transcript Document
Movement of Water
Through Soils
Hydraulic Conductivity
Laboratory Tests
Empirical Relations
Field Tests
Flow Nets
Capillary Rise
Hydraulic Conductivity
Bernoulli’s Equation
Total Head is calculated as a
summation of pressure, velocity, and
elevation heads
h = (u/gw) + (v2/2g) + Z
Velocity head (v2/2g) typically
neglected
Water Flow Through Soils
Dh=ha-hb
i = Dh/L
Fig 5.1 in Text
Water Flow Through Soils
Fig 5.2 in Text
Darcy’s Law
Assumes laminar flow
Discharge velocity is directly related
to the product of hydraulic
conductivity times hydraulic gradient
v=ki
Discharge vs Seepage
Velocity
Discharge Velocity,v – Factitious
velocity of flow through gross crosssectional area of soil (v = ki)
Seepage Velocity,vs – Factitious
velocity of flow through void spaces
in soil (vs = v/n)
Discharge vs Seepage
Velocity
Fig 5.3 in Text
Hydraulic Conductivity
Hydraulic conductivity of soils
related to several soil factors:
Fluid viscosity
Grain-size distribution
Pore-size distribution
Void ratio
Degree of saturation
Hydraulic Conductivity
Table 5.1 (p 96) Typical Values
Clean Gravel – 100 to 102 cm/sec
Coarse Sand – 10-2 to 100 cm/sec
Fine Sand – 10-3 to 10-2 cm/sec
Silty Sand – 10-5 to 10-3 cm/sec
Clays - < 10-6 cm/sec
Laboratory Measures
Constant Head Test
Suitable for clean sands and gravels
with relatively high hydraulic
conductivities
Falling Head Test
Suitable for dirty sands and fine
grained silts and clays with appreciably
lower hydraulic conductivity
Constant Head Test
Fig 5.4 in Text
Constant Head Test
q = Q/t = k i A
Q = captured volume of water (cc)
T = time of capture (sec)
k = hydraulic conductivity (cm/sec)
i = hydraulic gradient (cm/cm)
A = cross-sectional area of flow (cm2)
Constant Head Test
k=QL/Aht
Tests can be conducted at varying
hydraulic gradients to assess impact
of head differential on flow regime
Falling Head Test
Fig 5.5 in Text
Falling Head Test
k = (aL/At) ln (h1/h2)
k = 2.303 (aL/At) log (h1/h2)
Empirical Relations
Hazen’s equation – developed for
loose, clean filter sands with fairly
uniform gradation (Cu -> 1)
k (cm/sec) = D102 (mm)
Casagrande – developed for fine to
medium clean sands
k = 1.4 e2 k0.85
Empirical Relations
Equations 5.19 to 5.24 in Text
Be careful whenever using empirical
relationships – examine basis for
relationship and limits of
observations used
interpolations/extrapolations
Tavenas, et al., 1983
US Dept of Navy, 1971