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