Soil Flashcards
How to characterise soils? *
- particle die distribution curves
- atterberg limits
- moisture
- colour
- fabric
- strength
- compressibility
What is a particle size distribution curves?
Percentage passing through sives vs. Particle size (mm). Silt -> Sand -> Gravel
What is an Atterberg limits Casagrande chart?
Plasticity vs. Liquid limit. A line across with clays at the top left and silts bottom right.
What is the problem if silt and sand partings in rock?
When you dig a hole you relieve stress from the blocks which means that they will move along the silt and sand partings where water is.
Vv
Volume of liquid
Vs
Volume of solids
V
Volume
Fabric
Spatial and geometric configuration of all the elements that make up a rock
M
Overall mass of soil sample
Vs= Ms/ (Gs*ρw)
Solid volume = solid mass / specific gravity * water density
ν = V/ Vs
Specific volume = total volume/ solid volume
e= Vv/ Vs
Void ratio = liquid volume/ solid volume
n= Vv/ V
Porosity = liquid volume/ total volume
ν = 1 + e
Specific volume = 1 + void ratio
e= n/ (1-n)
void ratio = porosity/ (1-porosity)
Saturated soil?
All voids completely fill with water
Partly saturated soil (unsaturated soil)?
Some voids contain water
γ = ρg
Unit weight (kN/m^3) = density * gravitational acceleration
γw =
9.81 Kn/m^3
σa= F/A
Axial stress = force / area
E= σa / εa
Young’s modulus = stress/ strain
εa = δL/ L
Strain = change in length / original length
Principal stress?
Total force on a soil point
Effective principal stress?
Total force - pore pressure
Pore pressure?
(u) stress caused by the water acting in every direction with equal intensity
Suction?
Negative pore water pressure
S= ua - uw
Suction = pore air pressure - pore water pressure
What is pore water pressure at the water table or phreatic surface?
Zero
Perched water table?
Water lies on a stratum of low permeability above the level of the normal water table
Artesian conditions?
Water is confined by an overlying layer of low permeability and fed from a distant source where the water table is at a higher elevation
Seepage?
Flow through a soil
During steady state seepage what happens to pore pressure?
Pore pressures remain constant and no soil deformations occur
What controls the flow in seepage?
The hydraulic driving head and in particular its gradient
h= u/γw + z + v^2/2*g
h= total head (potential head)
u= pore water pressure
γ= bulk unit weight
z= elevation above a chosen datum
v= flow/seepage velocity
g= gravitational acceleration
q= Aki or. v=q/A = ki (Darcy’s law)
q= volume of water flowing per unit time (m^3/s)
A= cross- sectional area of soil corresponding to flow q (m^2)
k= coeff of permeability (m/s)
i= hydraulic gradient
v= discharge velocity (m/s)
What is the relationship between coefficient of permeability and particle size of soil.
The larger the particle size the larger the coefficient of permeability
Hydraulic gradient (i)?
The rate of change of total head with distance in the direction of flow
i= -dh/ds
i= hydraulic gradient
dh= change in total head
ds= the distance between the flow line between the two points being compared
u=p γw (finding pore pressure using standpipe)
pore pressure = height of water in the standpipe * bulk unit weight of water
Quick condition?
The upward water pressure gradient and water flow reduce the effective stress
icrit - critical hydraulic gradient?
The hydraulic gradient when quick conditions occur
icrit= (γs/ γw) - 1
icrit = critical hydraulic gradient
γs = bulk unit weight of soil
γw= water unit weight
Assumptions for Darcy’s law (3)?
- homogeneous, porous, saturated, constant volume medium
- fluid homogeneous and incompressible
- flow is steady and continuous (steady state)
(dh^2dx^2) + (dh^2/dy^2) = 0
Laplace equation
dh= change in total head
dx= change in x direction
dy= change in y direction
How can you show flow lines and total head lines?
You can draw flow lines as orthogonal trajectories against equal total head lines.
EP lines?
Equipotential lines. These represent lines of equal total head
FL lines?
Flow lines enclose flow ‘channels’ within which flow is constant
H= Nd Δh (orthogonal trajectory flow lines)?
Δh= head drop between adjacent EP lines
H= total head drop across system
Nd= number of potential drops (6?)
Stages in flow net construction?*
- identify boundary condition relating to flow lines and equipotentials e.g. impermeable boundary usually coincides with a flow line; open water surface constitutes an equipotential
- sketch trial flow lines remembering that flow ‘channels’ are like tubes within which flow occurs. Flow lines do not cross one another, nor do they converge completely
- sketch trial equipotential lines such they are perpendicular to the flow lines and so that the enclosed areas between flow lines and equipotential lines form ‘curvilinear squares’
- it is convenient if EPs drawn with equal head losses between adjacent EPs
Δq = kH / Nd (flow through incremental channel)
Δq = change in vol of water flowing per unit time
K= coeff of permeability
H= total head across system
Nd= number of potential drops
q = kH Nf / Nd (flow through system)
q= vol of water flowing per unit time
k= coeff of permeability
H= total head drop across system
Nf= number of flow channels
Nd= number of potential drops
What is the impact on the change in total head over distance as EPs are closer of that given distance?
The closed the EPs are over a given distance, the greater the change in total head over that distance and hence the greater the hydraulic gradient
(Gs + S*e) * γw = γ
—————
(1+e)
Gs= specific gravity
S= saturation
e= void ratio
γw = unit weight of water
γ= unit weight of soil
e* S = w* Gs
e= void ratio
S= saturation
w= water content
Gs= specific gravity
γdry = (Gs) * γw
——
(1+e)
γdry = unit weight of dry soil
Gs= specific gravity
e= void ratio
γw = unit weight of water
w= Mw/ Ms
Water content = water mass / solid mass
Sr = Vw/ Vv
Saturated = water volume / liquid volume
Gs= ρs/ ρw
Specific gravity = density solid / water density
When soil is not isotopic with respect to permeability, can FL and EP lines be orthogonal?
No
Kx?
Coefficient of permeability in the x direction
What happens when you change principal stress in granular soil?
Δ σ=Δσ´ drained condition
What happens when you change principle stress for fine grained soil?
Δ σ = Δu undrained condition
Consolidation?
When effective stress increases in fine-grained soil, the pore water pressure will increase. The increase in pore water pressure Δu is termed an excess pore pressure which induces a pressure gradient, resulting in a transient flow towards free- drowning boundaries of the soil layer. Flow continues until the excess pore water pressure have dissipated. In the long term when t=tinf and the excess pore water pressure have dissipated, the increment of total stress is carried entirely by the soil skeleton Δ σ = Δσ´ and is once again drained conditions. As drainage takes place the particles re orientated themselves and the soil compresses as inter-particle forces increase and there is a reduction in volume
Oedometer test?
Measured compression and time on consolidation of settlement
ΔH/ H0 = Δe/ (1+e)
Change in height/ original height = change in void ratio/ 1+ void ratio
What do you plot from oedometer data to understand consolidation?
e vs σv’
How does compression change in over consolidated and normally consolidated clays?
The settlement/ compression of over- consolidated clays is much less than normally consolidated clays. Therefore beware of exceeding pre consolidation pressure in over consolidated clays
Over consolidated?
Clays that have been loaded up in the past to effective stresses greater than those acting at present
3 causes of unloading?
- melting of ice sheets
- erosion of upper layers
- rise in ground water table (affecting u rather than σv)
mv = 1/(1+e0) (Δe/ Δ σ´)
Mv = coeff of volume compressibility
e0= original void ratio
e1= new void ratio
σ1´= new effective stress
σ2´= old effective stress
mv= 1/H0 * (ΔH/Δσ´)
Μv= coeff of volume compressibility
H0= original height
H1= new height
σ´1= new effective stress
σ0´= original effective stress
Assumptions of theory of one-dimensional consolidation?
- soil is homogeneous
- soil is fully saturated
- solid particles & water are incompressible
- compression and flow are one- dimensional
- strains are small
- Darcy’s law valid at all hydraulic gradients
- the coefficient of permeability, k, and the coefficient of volume compressibility, mv, remain constant throughout the process
- there is a unique relationship, independent of time, between void ratio and effective stress
Cv= d2u/dx2 = du/dt
Cv= coeff of consolidation
du= change in pore water pressure
dz= change in distance along z
dt= change in time
uz = Σ (2ui/M) * (sin(Mz/H))e^(-M^2Tv)
limits= m=inf and m=0
uz= value of the excess pore water pressure at depth z at time t
ui = initial excess pore water pressure, uniform over depth z
M= 0.5π(2m+1) where m= positive integer varying from 0 to infinity
Tv= dimensionless time factor
H= length of drainage path
Tv= Cv * t / H^2
Tv= dimensionless time factor
Cv= coeff of consolidation
H= length of drainage path
t= time
What is the length drainage path for 2 way drainage - permeable of both sides?
H/2
What is the length drainage path of a 1 way drainage system - flow is one direction with one permeable side.
H
Where in a shape of soil does consolidation immediately occur?
Top and bottom of shape
U= (ui-ue)/ui = 1-ue/ui
U= average degree of consolidation
ui= initial excess pore water pressure, uniform over depth z
ue= value of the excess pore water pressure when σ´ is acting within the soil
