soil physics 2010 outline where were we? hysteresis constitutive relationships
TRANSCRIPT
Soil Physics 2010
Outline
• Where were we?
• Hysteresis
• Constitutive relationships
Soil Physics 2010
Where were we? Wet region
h
Wet
Pore only drains if:
Big enough
Not isolated
Air can get to it
g hr
aw
cos2
Air entryAir accessStructural pores
A model porous medium being drained
Drainage allowed:
Poreradius:
Big
Small
Soil Physics 2010
Poreradius:
Big
Small
Drainage allowed:
Soil Physics 2010
A model porous medium being drained
Poreradius:
Big
Small
Drainage allowed:
Soil Physics 2010
A model porous medium being drained
Poreradius:
Big
Small
Drainage allowed:
Soil Physics 2010
A model porous medium being drained
Poreradius:
Big
Small
Drainage allowed:
Soil Physics 2010
A model porous medium being drained
Soil Physics 2010
Middle region
h
Middle
Air and water are both continuous
Best conditions for life
Reasonable reflection of pore size distribution
Mixed textural & structural pores at wetter part
Textural pores at drier part
Hysteresis
Soil Physics 2010
Dry region
h
Dry
Most water is in films sorbed to solid surface
Water retention mostly determined by surface area
Little or no hysteresis (if at equilibrium)
Water flow in films is very slow
→ 0 as h → ∞ (for example, drying at
105° for 24 hrs)
Soil Physics 2010
Hysteresis
• Thermostats
• Wind turbine
• Domain concept
• “Ink bottle” pores
• Individual pores
• Pore regions
Sir James Albert Ewing:The macroscopic, continuous hysteresis that we see is the result of many microscopic hysteretic events, each of which is abrupt rather than smooth.
Soil Physics 2010
Ink-bottle pores
h
Confuses
individual pore with whole soil
Soil Physics 2010
Converging & diverging
Draining
g hr
aw
cos2
Soil Physics 2010
Wetting
Converging & diverging 2
g hr
aw
cos2
h → r
Soil Physics 2010
Ink-bottle pore
h → r
Soil Physics 2010
Ink-bottle pore
r is too big for h!
Jump started where pore radius increases –
where r too big for h
Soil Physics 2010
Ink-bottle pore
r is too big for h!
Jump started where pore radius decreases – where
r is too small for h
Soil Physics 2010
Ink-bottle pore hysteresis
h
draining
wetting
1 pore:
Soil Physics 2010
Ink-bottle pores
A cluster of larger pores surrounded by smaller pores
Soil Physics 2010
Hysteresis
h
draining
wetting
Soil Physics 2010
2 kinds of equations
• Physically-based and/or derived equations• Darcy’s law• Capillary rise• Newton’s laws• Terzaghi’s effective stress equation
• Empirical, phenomenological, and/or statistical equations• Topp’s equation (relating to r for TDR)• van Genuchten -h relationship 32
rrr dcba
m
nrs
r
h
1
1
Soil Physics 2010
Empirical & phenomenological equations
Brooks & Corey:
s at saturation
r at 1.5 MPa (“residual”)
hb bubbling pressure
fitting (“pore size distribution index”)
log
log
h
log
h
hb: Lowest
pressure at which air can flow through the soil
otherwise
for 1
h
h
hh
b
b
rs
r
hb
Soil Physics 2010
Empirical & phenomenological equations
m
nrs
r
h
1
1
s at saturation
r at 1.5 MPa
1/hb
n, m fitting. Often, m ≡ 1-(1/n)
van Genuchten:
s
hb
r
h
Soil Physics 2010
3 kinds of equations
• Physically-based and/or derived equations• Darcy’s law• Capillary rise• Newton’s laws
• Empirical, phenomenological, and/or statistical equations• Topp’s equation (relating to r for TDR)• van Genuchten -h relationship
• Physico-empirical equations• Brooks & Corey?
Soil Physics 2010
Competition for pores
h
draining
wetting
When both water and air are present (middle range):
• Water is in the smaller pores
• Air is in the larger pores