Semester 1 Flashcards
How can you apply the Bernoulli equation to water flow through soil
H = u/γ(w) + V^2/2g + Z
by assuming water flow through soil is small …
H = u/γ(w) + Z
Using two standpipe piezometers in the ground, how can you tell if there will be water flow or not?
If h1 = h2 and u1 =/ u2 then hydrostatic
If h1 =/ h2 and u1 =/ us then non-hydrostatic
Flow is caused by the difference in head
page 1-4
Define Darcy’s Law for flow through a soil
q = A * K * i q-volumetric flowrate A-cross-sectional area k-coefficient of permeability i-hydraulic gradient (decrease in total head/distance x along flowline)
How do you calculate ‘Darcy’s velocity’ or ‘superficial seepage velocity’?
V(d) = q/A = K * i
V(d) is an average velocity across the whole cross-section of flow, but flow in soil flow occurs through voids - path is tortuous.
How do you calculate ‘true’ or ‘tortuous’ velocity?
V(t) = V(d)/n = V(d)*(1+e)/e
How do you calculate permeability in a falling head test?
k = A1/A2 * L/t * ln(h1/h2)
page 1-12
list some issues with measuring permeability in a lab
- can easily lose fine particles when sampling, resulting in an over estimation for k.
- soil structure can be disturbed by sampling.
- clay smearing in sampling tubes results in. underestimation of k.
- large scale features of inhomogeneity may not be picked up.
Describe how the pumping test can be used to find the permeability of a soil in the field.
-water is pumped from a well
-fall of GWL is recorded at points away from the well
-horizontal flow towards the well is assumed
equipment used: pump, observation wells or standpipe piezometers.
How do you calculate permeability during a pump test?
Unconfined aquifer: k = q*ln(r2/r1) / pi*(h2^2-h1^2) Confined aquifer: k = q*ln(r2/r1) / 2*pi*D*(h2-h1) An aquifer is confined if top and bottom strata have very low or no permeability. page 1-14
How do you calculate horizontal and vertical permeability in flow parallel and perpendicular to soil laminations?
k(h) = sum d*k / sum d
horizontal hydraulic gradient is same in all layers.
k(v) = sum d / sum (d/k)
vertical flowrate is same in all layers.
How do you calculate the ‘constrained’ or ‘1-D’ modulus?
E0’ = Δσv’ / Δεv’ = 1/Mv
Mv is the modulus of compressibility
How do you calculate initial specific volume from the final moisture content?
Vi = hi/hf * (1 + wf * Gs)
page 2-11
How do you calculate the compression index (Cc) and the swelling index (Cs)?
On the NCL (normal compression line)
Cc = -Δe / Δlog(σv’) = -e1 -e0 / log(σv’1/σv’0)
On the URL (unload-reload line)
Cs = -Δe / Δlog(σv’) = -e1 -e0 / log(σv’1/σv’0)
What is the over consolidation ratio (OCR)?
OCR = σv’(prev.max) / σv’(current) = σc’ / σv’(current)
OCR indicates the stress state of the soil. If OCR = 1, the soil is normally consolidated. If σc’ > σv’(current) then soil is overconsolidated.
How do you calculate the ultimate settlement of a soil?
ρult = Δσv’ * H / E0’
How do you calculate the rate/ coefficient of consolidation?
Cv = E0’ * k / γ(w) = k / Mv *γ(w)
Cv is constant for any stress range.
How do you calculate the consolidation time factor?
Tv = Cv * t / d^2
- dimensionless
- t is the time for ρult to occur
How do you calculate the consolidation ratio?
U = current settlement of all layers / ultimate settlement of all layers
for U < 63% U is approx. 2 * (Tv)^0.5 / (pi)^0.5
Usually just use graphs on page 3-10
How do you calculate the secondary compression index?
Taking gradient of secondary flat line on the Casagrande graph …
Cαe = Δe / Δlog(t)
How can you speed up soil consolidation?
- Sand drains, bore holes filled with sand to reduce drainage path length and accelerate consolidation.
- Geotextile drains, alternative to sand drain
- Preloading, loaded with surcharge fill until settlement equals max settlement under building pressure.
What are strip footings and pad footings?
Strip footing: 2-D, long compared to its width. Used to support masonry walls, usually in the form of a trench.
Pad footings: used to support isolated loads such as columns or support slabs. Often recommended forms of foundation generally constructed 3m below ground.
How do you calculate volumetric strain?
εvol = εx + εy + εz
How do you calculate youngs modulus, shear modulus, bulk (volumetric) modulus and poisson’s ratio?
E = direct stress / direct strain = σ / ε G = shear stress / shear strain = τ / γ K = isotropic (mean) stress / volumetric strain = ρ / εvol ν = lateral strain / direct strain = εx / εy
Define: equipotential line, flow line, flownet, seepage stress.
Equipotential line- line representing constant head.
Flow line- flow path of a particle of water.
Flownet- graphical representation of a flow field.
Seepage stress- stress imposed on a soil as water flows through it.
What is the Laplace equation used to calculate dimensional and planar flow through a soil?
3-D: ∂^2h/∂x^2 + ∂^2h/∂y^2 + ∂^2h/∂z^2 = 0
2-D: ∂^2h/∂x^2 + ∂^2h/∂z^2 = 0
How do you calculate total flow quantity through multiple elements?
qT = k * H * NF/NH
NF- number of flow tubes (spaces between flow lines)
NH- number of equipotential drops
page 5-5
What is the Laplace equation used to calculate flow through an anisotropic soil?
kx * ∂^2h/∂x^2 + ky * ∂^2h/∂y^2 + kz * ∂^2h/∂z^2 = 0
kx * ∂^2h/∂x^2 + kz * ∂^2h/∂z^2 = 0
How do you calculate the factor of safety against slope failure?
F = tan(Φ’) / tan(β’)
page 5-18
