Semester 1

Question 1

How can you apply the Bernoulli equation to water flow through soil

Answer 1

H = u/γ(w) + V^2/2g + Z
by assuming water flow through soil is small …
H = u/γ(w) + Z

Question 2

Using two standpipe piezometers in the ground, how can you tell if there will be water flow or not?

Answer 2

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

Question 3

Define Darcy’s Law for flow through a soil

Answer 3

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)

Question 4

How do you calculate ‘Darcy’s velocity’ or ‘superficial seepage velocity’?

Answer 4

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.

Question 5

How do you calculate ‘true’ or ‘tortuous’ velocity?

Answer 5

V(t) = V(d)/n = V(d)*(1+e)/e

Question 6

How do you calculate permeability in a falling head test?

Answer 6

k = A1/A2 * L/t * ln(h1/h2)

page 1-12

Question 7

list some issues with measuring permeability in a lab

Answer 7

• 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.

Question 8

Describe how the pumping test can be used to find the permeability of a soil in the field.

Answer 8

-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.

Question 9

How do you calculate permeability during a pump test?

Answer 9

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

Question 10

How do you calculate horizontal and vertical permeability in flow parallel and perpendicular to soil laminations?

Answer 10

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.

Question 11

How do you calculate the ‘constrained’ or ‘1-D’ modulus?

Answer 11

E0’ = Δσv’ / Δεv’ = 1/Mv

Mv is the modulus of compressibility

Question 12

How do you calculate initial specific volume from the final moisture content?

Answer 12

Vi = hi/hf * (1 + wf * Gs)

page 2-11

Question 13

How do you calculate the compression index (Cc) and the swelling index (Cs)?

Answer 13

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)

Question 14

What is the over consolidation ratio (OCR)?

Answer 14

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.

Question 15

How do you calculate the ultimate settlement of a soil?

Answer 15

ρult = Δσv’ * H / E0’

Question 16

How do you calculate the rate/ coefficient of consolidation?

Answer 16

Cv = E0’ * k / γ(w) = k / Mv *γ(w)

Cv is constant for any stress range.

Question 17

How do you calculate the consolidation time factor?

Answer 17

Tv = Cv * t / d^2

• dimensionless
• t is the time for ρult to occur

Question 18

How do you calculate the consolidation ratio?

Answer 18

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

Question 19

How do you calculate the secondary compression index?

Answer 19

Taking gradient of secondary flat line on the Casagrande graph …
Cαe = Δe / Δlog(t)

Question 20

How can you speed up soil consolidation?

Answer 20

• 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.

Question 21

What are strip footings and pad footings?

Answer 21

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.

Question 22

How do you calculate volumetric strain?

Answer 22

εvol = εx + εy + εz

Question 23

How do you calculate youngs modulus, shear modulus, bulk (volumetric) modulus and poisson’s ratio?

Answer 23

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

Question 24

Define: equipotential line, flow line, flownet, seepage stress.

Answer 24

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.

Question 25

What is the Laplace equation used to calculate dimensional and planar flow through a soil?

Answer 25

3-D: ∂^2h/∂x^2 + ∂^2h/∂y^2 + ∂^2h/∂z^2 = 0

2-D: ∂^2h/∂x^2 + ∂^2h/∂z^2 = 0

Question 26

How do you calculate total flow quantity through multiple elements?

Answer 26

qT = k * H * NF/NH
NF- number of flow tubes (spaces between flow lines)
NH- number of equipotential drops
page 5-5

Question 27

What is the Laplace equation used to calculate flow through an anisotropic soil?

Answer 27

kx * ∂^2h/∂x^2 + ky * ∂^2h/∂y^2 + kz * ∂^2h/∂z^2 = 0

kx * ∂^2h/∂x^2 + kz * ∂^2h/∂z^2 = 0

Question 28

How do you calculate the factor of safety against slope failure?

Answer 28

F = tan(Φ’) / tan(β’)

page 5-18