Advanced Geotechnical Engineering
ES4D8
Contaminated Land (Lecture 7)
Mohaddeseh Mousavi-Nezhad
Room: D211
Email:m.mousavi-nezhad@warwick.ac.uk
31/05/2016
The University of Warwick
1
Runge-Kutta - Example
A lake has been polluted with initial concentration of
pollutant at 106 parts/m3. Addition of fresh water
lowers the concentration of the pollutant, this is
governed by the equation:
dC/dt + 0.1C = 0
with C(0) = 106, time in days
Using the Runge-Kutta 4th order method find the
concentration after 10 days using a step size of 5 days.
Runge-Kutta - Example
dC/dt + 0.1C = 0
dy /dx
= f(x,y)
dC/dt = -0.1C
f(t,C) = -0.1C
h = step size = 5 days
Cn+1 = Cn + 1/6 (k1 + 2k2 + 2k3 + k4)h
Runge-Kutta - Example
Cn+1 = Cn + 1/6 (k1 + 2k2 + 2k3 + k4)h
f(t,C) = -0.1C
Step 1
n= 0
t0 = 0
C0 = 106
k1 = (f(t0, C0)) = f(0,106) = -0.1(106) = -105
k2 = f( (t0 + ½ h) , (C0 + ½ h k1) )=
k3 = f( (t0 + ½ h) , (C0 + ½ h k2) )=
k4 = f( (t0 + h) , (C0 + h k3) )
C1 =
Runge-Kutta - Example
Step 2
n= 1
t1 = 5
C1 =
k1 = (f(t1, C1)) =
k2 = f( (t1 + ½ h) , (C1 + ½ h k1) )=
k3 = f( (t1 + ½ h) , (C1 + ½ h k2) )=
k4 = f( (t1 + h) , (C1 + h k3) )=
C2 =
The approximate concentration of pollutant after 10 days is
368171 parts/m3
Runge-Kutta - Example
In this example we know the exact solution is given by
C(t) = 106 e(-0.1t). Below is a plot of the exact and
estimated solutions.
1200000
dC/dt + 0.1C = 0
1000000
800000
Exact values
600000
Runge-Kutta approximation
400000
200000
0
0
2
4
6
8
10
Protection and Remediation
RemediationPurpose of
Purpose:
A- Hydraulic control of contaminated ground
water
Prevent contamination from spreading to
uncontaminated area
B- Treatment of contaminated groundwater
Reduce concentrations in ground water to
below cleanup standards
Landfill operation &
construction
Landfill Cell Construction
MSW Landfill Cell Construction
Waste cell is typically 3 to 5
meters high
Slope of working face
controls area to volume of
landfill and compaction of
waste
Best compaction at 10:1 (horizontal: vertical)
Usual slope is 3:1 to reduce landfill surface area
MSW Landfill Cell Construction
• “Working face” = area of
active waste placement
• Approximately 60-cm (2-ft)
thickness of waste placed on
slope
• Compacted by 2 to 5 passes
of steel-wheel compactor
• (Compacting is lighter at bottom, near liner, to avoid
puncture)
• Multiple lifts placed to complete a cell
• Cell is covered by 15 cm (6 inches) of daily cover
MSW Landfill Cell Construction
Residential waste at curbside
After compaction in garbage
truck
In landfill after compaction
Typical soil (for comparison)
150 kg/m3
300 kg/m3
3
(range: 180 to 415 kg/m )
590 to 830 kg/m3
1,800 kg/m3
(1.5 tons/yd3)
MSW Daily Cover
Materials:
Usually soil
Sometimes:
shredded vegetation
chipped wood
compost
spray-on proprietary mixes
Cover-to-waste ratio is typically 1 to 4 for soil
→Substantial volume of landfill goes to daily
cover!
Purposes of daily cover
Reduce moisture entering waste
Most moisture enters waste during filling
Control litter
Reduce odors
Limit access to rodents and birds
Reduce fire risk
Provide vehicle access to active face
Improve aesthetics
Liner systems
Alternative liner materials
1. Soil liner
Also called compacted clay liner (CCL)
2. Flexible membrane liner (FML)
Also called geomembrane
3. Geosynthetic clay liner (GCL)
4. Composite liners
Soil Liner
Advantages:
Clay can attenuate pollutants
Thickness provides redundancy, resistance to
penetration
Long-lived, self-healing
Inexpensive if locally available
Soil Liner
Disadvantages:
Construction is difficult – requires heavy equipment
Thickness reduces volume for waste
Subject to freeze/thaw and desiccation cracking
Low tensile and shear strength – may shear or crack
due to settlement
May be degraded by chemicals
Expensive if not available locally
Liner materials – geomembranes
Advantages:
Easily installed – needs only light equipment
Very low leakage rates if free of holes
Has high tensile and shear strength, flexibility –
accommodates settlement
Thin – leaves volume for waste
Liner materials – geomembranes
Disadvantages:
Slopes on geomembranes may be unstable
High leakage if punctured or poorly seamed
Some chemicals may be incompatible, permeable
Thin – subject to puncturing
No sorptive capacity
Unknown lifetime
Liner materials – geosynthetic clay
Manufactured composite of bentonite and
geotextile
Advantages:
http://liufangzi.en.alibaba.com/product/9701905
35203642060/Geosynthetic_Clay_Liner_for_landfills
.html
Easily installed
Self sealing
Some sorptive capacity
Low leakage rates
Liner materials – geosynthetic clay
Disadvantages:
Thin – easily punctured
Liner materials – composite liners
Composite liner ≠ double liner
Composite liner = two or more materials
Usually clay and geomembrane
Combines desirable properties of two materials
Liner materials – composite liners
Hydraulic properties
Physical properties
Endurance properties
Geomembrane
Decreases leakage
Thin: can be torn or
punctured
May crack under stress or
strain
Subject to aging
Not self-healing
Chemically resistant
Clay
Delays travel time
Thick: cannot be torn
or punctured
May crack under stress
or strain
Does not age
Self-healing
May be affected by
chemicals
Liner materials – composite liners
Advantages:
Low leakage rates
Low contaminant mass flux
Provides sorptive capacity
Acceptable loss of waste storage space
Acceptable ground-water protection
Liner materials – composite liners
Disadvantages:
Difficult to construct
Expensive
Liner failure modes
Tension failure
Liner slippage
Liner uplift by water pressure
Liner uplift by wind
At pipes, access ways, other structural details
Tensile failure
Flexible membrane liners (FMLs) have finite tensile
strength
Measured in laboratory by increasing stress on sample
and measuring strain
Typical FML yield stress = 1000 to 5000 psi
Manufacturers provide tensile strength data for
their products
Forces on FML due to its own weight
W = weight of FML (per unit width) ;
d = depth of landfill
;
d
F = force of friction (per unit width)
Β = angle of landfill side slope
W
β
Weight of liner, W
W = g ρL t (d / sin β)
t = liner thickness
ρL = density of liner = 0.92 to 1.4 g/cm
Forces on FML due to its own weight
d
F
W
β
Forces on FML due to its own weight
d
W sin β
F
W cos β
W
Friction force on liner
Normal force N = W cosβ
F = N tanφ = W cosβ Tan φ
β
Forces on FML due to its own weight
d
W sin β
F
W cos β
W
Tensile force on liner: T = W sin β – F
β
Forces on FML due to its own weight
d
W sin β
F
W cos β
W
β
Tensile force on liner: T = W sin β – F = W sin β – W cos β tan φ
Tensile stress on liner =
tensile force
=σ
X-section area
σ < σy to avoid liner failure!
For unit liner width, σ = T/t
Liner slippage
Liner slippage
Net force on liner at top of slope =
W sin β – F = W sin β – W cos β tan φ
W sin β
F
d
β
Friction force on liner
Normal force N = W cos β
Liner slips unless:
F = N tan φ = W cos β tan φ > W sin β
tan φ > W sin β / W cos β = tan β
Liner slippage
Typical values of φ:
Soil to FML
Soil to geotextile
FML to geotextile
Friction angle, φ
17 to 27°
23 to 30°
6 to 23°
Typical design is 3:1 = 19.5°
Horizontal:vertical
3.3:1 to 2:1
2.3:1 to 1.7:1
9.5:1 to 2.4:1
Liner slippage
Factor of safety for liner slippage:
FS =
tan φ
tan β
= 1.25 to 1.5
A higher factor of safety is needed when
outcome endangers public or environment!
Anchorage to resist liner slippage
FB is the net force on the liner at the top of the slope
= W sin β – W cos β tan φ
FB is resisted by FA, the anchorage force
b
LA
FB
h
FML
d
β
Soil of unit
density ρS
Anchorage design
FA = g ρS h b tan φ + g ρL t LA tan φ
Friction due to
anchorage
b
LA
FA
Friction of extra
liner with length
of LA
h
g ρS h b
g ρ L t LA
All formulas are in unit liner width.
Anchorage design
Anchorage force, FA , resists pull by liner, FB
b
LA
FA
FB
h
Virtual
pulley
Factor of safety = FSA = FA/FB should be 1.2 to 1.5
Standpipe structural elements
Standpipe structural elements
Standpipes are installed to
provide access to leachate
collection system
Consolidating waste exerts
downward pull on standpipe
Frictional pull can punch
standpipe through liner if forces
get too great
Remedy is to cover standpipe with
liner or other low-friction material
to reduce pull of waste, and to
strengthen below standpipe
Leachate pipes
• If leachate pipe is firmly fixed to liner, then if the pipe
gets hit by a vehicle or similar, liner can tear.
• Need instead to construct flexible penetrations, to avoid
damage.
Wind forces on liner
Requires analysis of potential maximum wind, uplift
associated with that wind
Design needs to determine spacing of sand bags to
weigh down empty liner