Groundwater Flashcards
How can you apply Bernoulli’s equation to flow through soil? h=?
h= u / gamma + z
u is pore pressure
gamma is unit weight of water 9.81
z is elevation head.
What causes water to flow?
it is when groundwater is non-hydrostatic.
Caused by different total heads.
What is Darcy’s equation?
q = A * k * i q = volumetric flow rate (m^3/s) A= cross-sectional area (m^2) i= hydraulic gradient (no unit) k= Coefficient of permeability (m/s)
What is Darcy’s Velocity? Vd=?
But what is the true velocity?
and why is it different?
Vd= k * i
Vt= (Vd * (1 + e)) / e or Vd/n
because flow only travels through interconnected voids so the path is actually ‘tortuous’ (not straight).
What does k depend on?
and how does it affect it?
Soil type & particle size & shape:
- larger grains larger k
- more rounded, smoother grains higher k
- uniform clean sand k=D10^2/100
Void ratio e:
- higher e, higher k
- approx k=x * e^2. (x is constant)
Pore fluid type (e.g. viscosity and density)
homogeneity, layering and fissuring:
- fissures- any gaps in the soil. (higher k)
- layers- a thin impermeable layer can act as a barrier to the flow.
Saturated/ Unsaturated zones:
-air bubbles significantly reduce permeability due to surface tension effects.
What are the two types of lab experiments to find k?
- Constant head permeameter (course material)
2. Falling-head parameter (fine material)
Describe the constant head test.
How is k found?
A constant head of water feeds water to a soil sample with a C-S of A below through a porous stone. There are two piezometers connected to the soil sample at a distance L apart from each other. They have a difference in head of /\h. The water then flows out of the soil sample at the bottom through another porous stone. Finally, the water flows into a measuring cylinder via a constant head overflow.
k = q / /\h * L / A
Describe the falling head test.
How is k found?
A thin tube (tube 2, area A2) feeds the soil sample in tube 1 (area A1) and the water head drops over time. Tube 1 has a height of L and the water flows through the soil and out the bottom. Finally, the water flows out a constant head overflow. The head is measured from the top of the constant overflow and you measure the height of the water surface (h) in tube 2 over time (t).
k= A2 / A1 * L / t * ln( h2 / h1 )
What are the issues with measuring k in the lab?
- Can easily lose fine particles when sampling, resulting in an over-exaggeration of k
- Soil structure isn’t accounted for. (e.g. fissures)
- Clay swelling in sample tubes. (underestimate of k)
- Large scale features inhomogeneity may not be picked up.
Field measurements of k; describe what happens in a pump test.
What are the two ways of finding GW level?
- Water is pumped out of a well.
- Fall in groundwater level is recorded at points away from the well.
- Horizontal flow is assumed.
- Observation wells; open throughout depth via slotted pipe and screen. Measure head over full depth.
- Sandpipe piezometers; open only at the base. Measure head at a point. (better for heterogeneous/ layered soils that observation wells.
How to find k in an unconfined and confined aquifer?
unconfined:
k= ( q * ln( r2/ r1 ) ) / ( pi * ( h2^2 - h1^2) )
r= distance from pumped out well
h= height from datam
Confined:
k= ( q * ln( r2/ r1 ) ) / ( 2 * pi * D * ( h2^2 - h1^2) )
D= thickness of confined aquifer.
What are laminated or layered soils?
When soil is laid down in layers of coarser and finer material. This results in a “cross-anisotropic” permeability (different k in the vertical direction) compared with the two other directions (horizontal).
How do you calculate kh and kv with n layers?
kh = ( d1*k1 + .... + dn*kn ) / ( d1 + .... + dn) d= thickness of soil layer
kv = ( d1 + …. + dn) / ( d1/k1 + …. + dn/kn )
