One-dimensional flow through soils [Lecture 13]

Filter design

earth embankment dam for water storage (w eroded sandy layer)

• sandy layer is permeable → water drains out safely instead of under the dam

Internal erosion (piping)

Soil particles moved freely to an escape exit leading to structure degradation/collapse

Slope stability (drains)

• natural earth cofferdam slope stabilised with built-in drainage layers

• changes in environmental conditions may alter the degree of saturation and strength of soil

Design of road drainage systems

• proper drainage systems collect and transport water to safer locations within the structure

Pavement degradation

• poor drainage can cause pumping/water bleeding leading to structure degradation

Flow around a sheet pile (homogeneous soil)

downwards flow → positive effect on effective stress (increases)

upwards flow → negative effect on effective stress (reduces)

Dewatering systems

• sheet piles susceptible to floods

• place two borehole pumps + external dewatering wells

1D flow of water through soil

• water flows from zones of high mechanical energy to zones of low mechanical energy (per unit mass/weight)

Bernoulli’s theorem:

Total head h

Elevation head h_z = z (with reference to datum)

Pressure head = h_p = u/𝝲_w (height of column in piezometer)

Velocity head (negligible for soils)

Hydraulic gradient

i=Δh/l (loss per unit length)

Example downward seepage

Static liquefaction σ’=0

σ’=z𝝲’-iz𝝲_w=0

i_cr=𝝲’/𝝲_w

~ 1 for most soils (since 𝝲’ ~ 9 to 10kN/m3)

Discharge & seepage velocities

q=v*A=v_s*A_v [L³/T]

q = flow rate

v = discharge velocity (average velocity)

v_s = seepage velocity

A=A_v+A_s

Darcy’s law

v proportional to k*i

for most soils:

k*i=q/A=Q/(tA)=k*Δh/l

k = hydraulic conductivity (or coefficient or permeability)

Q = flow volume [L³] (for mass conservation Q_in=Q_out)

Permeability

• soil property that varies significantly

(range of 10 billion times)

Permeability lab evaluation

a) Constant-head test (coarse-grained soils)

b) Falling-head test (fine-grained soils)

Constant head test

k = hydraulic conductivity [L/T]

Q = flow volume or outflow [L³]

t = test duration [T]

h = constant head [L], (=Dh)

A = specimen area [L ]

L = specimen length [L]

Falling-head test

k = 2.303*(aL)/(At)*log₁₀*(h₁/h₂)

k = hydraulic conductivity [L/T]

t = test duration [T], (=t1-t2)

A = specimen area [L²]

a = standpipe area [L²]

L = specimen length [L]

Permeability preliminary assessment only