422-2013-Lec04 Subsidence.jnt

MinE 422: Subsidence
Resources:
Blodgett and Kuipers, 2002. Underground Hard-Rock mining: Subsidence
and hydrologic environmental impacts
Bauer. 2008. Planned Coal mine Subsidence in Illinois
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Cause of Subsidence
Effects
Modeling, monitoring and mitigation
Examples
Background: Locations Affected
• Anywhere there is underground mining!
– United kingdom, China, South Africa, Australia, United States
• Most research done on coal mining
– Specifically longwall and room and pillar mining
• Thinking is that underground mining has less environmental impact,
but subsidence effects the land above and the water below
Subsidence feature from collapse of one of the deeper
lead and zinc mines in Cherokee County.
Subsidence due to block caving at the Ridgeway Mine, South Carolina
What causes subsidence
• Compaction of natural sediments/weak rock
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Ground water dewatering
Withdrawal of petroleum and geothermal fluids
Mining of coal/limestone/salt
Melting of permafrost
Crustal deformation
Mining of metallic ores
• “subsidence is an
inevitable consequence
of underground mining
– it may be small and
localized or extend over
large areas, it may be
immediate or delayed for
many years (SME, 1992).
Drilling rid being retrieved from
collapsed mineshaft, Glasgow, 1995
Physical hazards identified by the AGS
• Including subsidence from underground coal mining
(Cardiff just north of Edmonton)
Definition of Subsidence
• Two general types of subsidence:
– Continuous and Discontinuous
• Continuous or trough type subsidence is associated with extraction
of thin, flat-dipping orebodies overlain by weak sedimentary strata
Surface

Subsidence
Profile
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Continuous
• Fairly easy to predict
– Happens almost immediately
• Angle of draw
– Depends on geology
– Seam depth
• Rate of drop
– Entire mass of rock moves downward as a single block, rather
than gradually
– Some bending and flexing as bedding surfaces shift
Subsidence
Mechanics
Width of Subsidence
• Usually predicted empirically
• Subcritical width
– Panel is narrow, causes less than the maximum level of subsidence
• Critical width
– Pannel is wider, only the center has the maximum level of subsidence
• Supercritical width
– Maximum level of
subsidence has a flat
profile in center of the
surface trough
– Angle of draw remains
the same, width
increases
Discontinuous
• Discontinuous type subsidence is associated with
different mining methods and geological features.
+ crown hole
+ plug subsidence
+ chimney caving
+ solution cavities, block caving
Hard rock mining
• Most (nearly all) research on coal mining
• Some hardrock mines are bedded (sedimentary) but most
in igneous or metamorphic rock
– Different (more complex) geology
– Faults/folds/hydrothermally altered rocks complicate
subsidence prediction
From,
Anatomy of a mine:
From Prospect to Production
Planned Subsidence
• Longwall mining or block caving
– Subsidence occurs almost immediately
– In Illinoi, horizontal distance to subsidence is
about 50% of the mine depth (eastern United
States, about 100% of the mine depth)
– Some residual subsidence (say about 5% of
mine height) occurs years (~1-3) after mining
– Initial subsidence is higher
• Room/pillar or stope, etc
– May occur over 10-100 years
– Difficult to predict
– Land use issues
Floor Failure
• Coal mining in Illinois (room and pillar)
• Hanging wall very stable
• Floor made up of weak claystone
Some factors that affect subsidence
• After Blodgett and Kuipers (2002)
Somewhat related, uplift
• What about the opposite effect
• Uplift is more recent, mining/subsidence has been
happening for years, but fluid injection for only a few
decades (~50 years)
• SAGD or EOR
• Increase pressure and the surface bulges, eventual decline
and subsequent subsidence
• Magnitude:
– Up to tens of centimeters over a few months
• Eventually subsidence will occur as pressure normalizes
after extraction (unless you inject more water than you
removed oil/water)
Uplift
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Passive seismic and surface monitoring of geomechanical deformation
associated with steam injection
S.C. MAXWELL, J. DU, and J. SHEMETA, Pinnacle Technologies, Calgary,
Canada
surface uplift …
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Total overpresurized reservoir, 125m by 75m area affected
Shallow operation (<100m depth)
Stopped production in some nearby wells
More info: http://www.ercb.ca/docs/Documents/reports/ERCB_StaffReport_JoslynSteamRelease_2010-02.pdf
Prediction
Prediction Methods
• Trough subsidence fairly straightforward
• Methods include
– Empirical, profile functions, influence functions and numerical
– United kingdom national coal board graphical method
• Figure 16.18 (p. 458) gives maximum (central) subsidence, S, as a
fraction of the extraction thickness, m, for a given depth, h, and
panel width, W.
• The subsidence profile can next be determined using Figure 16.20.
• Need to modify for you location, i.e. use in Wyoming
overestimates subsidence
Prediction Methods
• Different subsidence profiles
Prediction
method
• Influence Functions
– Still need to calibrate the coefficients
– Can do some theoretically
Prediction method
• Numerical models
– Physical simulation, program of interest would be “FLAC”
– Finite element, boundary element and distinct element methods
– Need geo-mechanical parameters above mine area
• Modulus of elasticity and Poisson’s Ratio (could use geostatistics …)
– Often assume only elastic behavior (not very realistic)
Prediction method
• Summary
– Empirical methods are very localized and difficult to
extrapolate in new areas
• i.e. tried to use the UK system in the US and double the
subsidence was predicted.
– Empirical methods focused on coal mining and specific to a
particular geology
– Profile functions work best in rectangular situations
– Influence functions and numerical methods difficult to infer
the necessary parameterization
• Faults, bedding, rock type profiles, soil/rock parameters etc.
– Accurately predicting geology (faults/layers/rock strength, etc)
for numerical models is difficult
Subsidence monitoring
• Space based imagery (InSAR technology)
• Interferometric Synthetic Aperture Radar
• Ground survey
Subsidence monitoring
• Interferometric Synthetic Aperture Radar (InSAR)
• Subsidence still occurring over abandoned coal mines
– Bellevue shut down in 1961
Deformation pattern of the lower
part of Frank Slide. The white stripes
indicate underground coal mines; the
red line outlines the Frank Slide
boundary, and the black rectangle is
the reference area.
Figure 4. Crowsnest Pass. In conjunction with studies being
undertaken by the Alberta Geological Survey (AGS) on
unstable slopes on Turtle Mountain, site of the Frank Slide,
InSAR technology was utilized to map subsidence of the ground
overlying the abandoned coal mine workings. By utilizing
Radarsat-1 Fine beam data from fall 2004 to summer 2006,
many thousands of coherent targets were identified above
the mines and a map was produced showing the rates and
patterns of deformations
Example1
• Fairmont West Virginia
– Shallow, ~30m depth
– Room and pillar (then
pillars removed)
Coal Seam
Subsidence damage
• Mining in the 1800’s, subsidence started in 1980’s,
companies are long gone
Example 2:
Retsof Salt Mine
• Roof Failure, 1994
Example 3: Mississippi Delta
• ~4000km2 of land lost since 1930
Mitigation
Techniques
• Post-mining stabilization
– Backfilling, grouting
(~$300k/acre), blasting
• Alteration in the mining
techniques
– Partial mining (leave area
supported by pillars)
– Backfilling with waste rock or
milled tailings
– Only reduces the amount of
subsidence
• Bridge the area on surface
Negative effects of subsidence
• Damage to structures/people above
– Some construction modifications can be implemented with
little success, i.e:
• trenches filled with compressible material around building
foundations
• reinforced foundations
• Foundations resting on compacted sand
– Caused by the tensile and compressive forces at edges of
subsidence, not by the vertical movement of land (horizontal)
– Dr. D. Apel: worked on mining without tensile/compressive
forces, balance them out …
• Destruction of natural vegetation or farm land
– Surface land use can be dramatically altered
– Changes ground slope, surface drainage, disruption of ground
water hydrology, pot holes, etc.
Negative effects of subsidence
• Hydrologic impacts
– Surface water
• Subsidence can cause open fractures which allows for surface
water to flow into lower strata or open mine workings
– Ground water
• Fracturing can increase the capacity of an aquifer, ground water
level drops as water fills lower void space
• Water quality can be affected if ground water is brought in contact
with minerals surrounding the mine or the mine workings
• Vertical flow rate increased through new pathways/fractures
– Water is drained from the surrounding aquifer into the mine
cavity, similar to surface mining
– Water flow patterns (shallow, intermediate and deep) are
altered (increased or decreased) by subsidence
• Utilities – need to install flexible piping
Negative effects of subsidence
• Roads, not
usually too
difficult to repair
Regulations
• United states, Surface Mining Control and Reclamation act
– Prevent subsidence from causing material damage to the
extent technologically and economically feasible
– Maximize mine stability
– Maintain the value and reasonably foreseeable use of such
surface lands, except in those instances where the mining
technology used requires planned subsidence in a predictable
and controlled manner.
– Each state has their own regulations
• Canada, MINES AND MINERALS ACT
– Coal mining leases section: Without compensation of any nature
whatsoever the lessee shall, at all times during the term of a lease of a
road allowance and any renewal of it, perform, observe and comply
with the orders and directions of the Minister of Infrastructure
affecting underground operations and, without restricting the
generality of the foregoing, those orders or directions may require any
measures that that Minister considers necessary to prevent any
subsidence.
Review
• Subsidence is inevitable when underground mining
• Dewatering contributes as well
• Greater depths of overburden do not, generally, prevent
subsidence, but may delay timeline
• Direct relationship between mine extraction height and
magnitude of subsidence
• Many ‘factors’ influence magnitude of subsidence
• Varied effects on water level/ quality/ flow rate/etc
• Some mitigation strategies, but none eliminate subsidence
• Uplift can also temporarily occur if we are injecting…
– Subsidence is likely to follow
Subsidence
Let’s do an example problem.
Given: seam thickness, m= 4 m
depth, h = 250 m
width, W = 200 m
Fig. 16.18 gives S/m = 0.77
Thus S = 0.77 (4 m) = 3.1 m
Subsidence
Now assume that the face has advanced
far enough for full subsidence to occur.
Now using Fig. 16.20, noting that
w/h = 200 m/250 m = 0.8
Subsidence
Using each “S curve,” go to w/h = 0.8 and then read off the
value for d/h.
Subsidence in
terms of S
Distance from panel center
in terms of depth, d/h
1.00 = 3.10 m
0.95 = 2.95
0.80 = 2.48
0.70 = 2.17
0.60 = 1.86
0.50 = 1.55
0.40 = 1.24
0.20 = 0.62
0.10 = 0.31
0 = 0
0
0.08
0.17
0.21
0.25
0.28
0.33
0.43
0.53
1.10
=
=
=
=
=
=
=
=
=
=
center panel
20.0 m
42.5
52.5
62.5
70.0
82.5
107.5
132.5
275.0
Subsidence
The following subsidence profile results:
Distance from panel center, m
0
25
50
75
1.0
2.0
3.0
Subsidence
100 125
150 175
200 225 250
MinE 422: Erosion
Resources:
Horst. 2007. Landforming : an environmental approach to hillside development,
mine reclamation and watershed restoration. 354p.
2005, Morgan, Soil Erosion and Conservation
Johnson, 2003 Design of Erosion Protection for Long-Term Stabilization
http://pbadupws.nrc.gov/docs/ML0225/ML022530043.pdf
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Cause of Erosion
Effects
Modeling
Mitigation
Dust …
Definition of
Erosion
“Dislodgement and transportation of soil
materials through the action of water
and wind” Spitz (quote and image)
•Can occur in a number of ways:
1.Impact of raindrop dislodges soil particles, splash erosion
(~6m/s, 0.6m movement vertically of soil particles)
2.Movement of water over surface dislodges and transports
soil, Sheet, Rill, Gully, channel
Erosion Details
The basic process at a point in the landscape is simple.
Rainfall is partitioned into infiltration and run-off.
Infiltration is the rate at which the soil absorbs water
(mm/hr). Basic Infiltration rate (saturated), initial (dry)
Excess water is run-off: schematically it can be
represented as:
Detaches soil particles
Rainfall
Run-off
Carries soil
downhill
Infiltration
Erosion Processes and Measurements
The basic process can be graphically represented below.
Each factor is subject to significant spatial and temporal variability.
Rate
Soil’s infiltration rate
(soil’s characteristic)
Varies with soil type,
characteristic and location
Rainfall
rate
Varies with time,
space, season
Leads to variable
energy of impact
detaching soil
particles –
= rainfall
erosivity
Run-off
Time
to runoff
Time
Rate of soil detachment is
affected by the energy
(erosivity) of rain and run-off
Detached soil particles are then transported downhill by
water or rainsplash
Rate and velocity
are affected by
inf rate, slope,
surface
roughness,
surface cover –
all affected by
management
Run-off energy
contributes to
soil detachment
Point processes need to be
integrated over time and space
so that soil loss can be
quantified for a defined area
(generally at the bottom).
Erosion Processes and Measurement
Effect of soil structure & texture
Rate
Soil’s infiltration rate
Rainfall
rate
Run-off
Well structured,
Sandy soils =
High infiltration rate,
low run off rates,
low total run off
Infiltration
Initially moist soil
Further reduces curve
Time to
run-off
Time
Degraded soil,
high silt/clay =
Low infiltration rate,
high run off rates,
high total run off
Other factors that affect curves
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Surface roughness
Slope
Length
Type of flow
Vegetation
Effects of Erosion
• Reduce slope stability, causing failure
• Reduce capacity of soil to support organic material
• Potential desertification
Different models for predicting
erosion
• USLE: Universal Soil Loss Equation
– Most common (not necessarily the best) method of prediction
– http://www.iwr.msu.edu/rusle/soil_loss.htm
or
– Can be found on the USDA website
– Windows program
http://www.ars.usda.gov/Research/docs.htm?docid=6038
or
– By hand …
– http://www.techtransfer.osmre.gov/nttmainsite/Library/hbmanual/rusle/fro
ntmatter.pdf
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11,000 plot years of data, 47 locations 24 states (1930s-1950s)
1965 completed USLE
RUSLE (revised) (~1998)
RUSLE2 (revised revised) (~2003)
(R)USLE explained
• Empirical formula stemming from many soil tests in the US
• Used world wide now (maybe inappropriate)
Soil Loss=R K L S C P
R=rainfall-runoff erosivity factor
K=soil erodibility factor
(particle size and plasticity)
L and S = topographic factors
slope length and gradient
C=ground management, veg cover
P=soil conservation practices
Limitations of the RUSLE
• Assumes linear relationship
• Does not consider physical processes (empirical)
• Does not consider gully/channel erosion, only sheet and rill
– Often we have gully/channel erosion (think spoil piles)
– Remember Highvale?
• May be hard to accurately infer parameters for new locations
• Much tradecraft involved
• Based on tests carried out in US, may not be portable
Process based models
• To name a few
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GUEST (most friendly?)
WEPP
EUROSEM
LISEM
• Most use some model of transport of material:
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A=mean annual value (kg/yr)
N=number of years
Mi in kg is the mass of individual runoff events
c(t) suspended sediment concentration (kg/m3)
Q(t) runoff rate in m3/s
Ti time duration in s
• Models differ in how these values are simulated
– Need different inputs for different models
– Soil properties, rainfall behavior (type of erosion), etc.
Process based models
• Benefits
– More likely to be applicable outside initial application (i.e.
USLE)
– Inputs may be more inferable as they are related to soil
qualities not abstracts
– Lower long term experimentation cost (if model is accurate),
USLE was very expensive
• Drawbacks
– CPU time
– Complex set up/programs
– inputs
Comparison of modeling techniques
From Yu. 2005, Process-based erosion modeling: Promises and progress. In Forests, Water and People in the
Humid Tropics: Past, Present and Future Hydrological Research for Integrated Land and Water Management. 944p.
Entering Channels/Streams
• Material transported by
– Suspension
– Bed load-particles bounce along the bottom of the stream
• Einstein (2004)
• Y is an empirical coefficient that depends on the size and
shape of the sediment particles
• T0 is the shear at the streambed
• Tc is the magnitude of the shear at which transport begins
• w is the specific weight of waters
• Maybe more useful …
Mitigation/prevention strategies
• Under the Surface Mining Law ALL surface water flowing
off disturbed areas of the mine must be routed through
sediment ponds. The ponds are designed to slow the flow
of water
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Other practices include:
– Riprap:
– Jute matting
– Concrete drainage channels
– Rock lined drain
– Erosion control structures
Mitigation/prevention strategies
• Two categories
– Sustain soil cover, prevent erosion (erosion controls)
• Reduce tendency of particles to become dislodged/suspended
– Reduce suspended particles in water (sediment controls)
• Once particles have been suspended, reduce velocity of water so
particles settle
• Goal is to
1.
2.
3.
4.
5.
Minimize ground disturbance
Manage run-on to critical areas
Manage drainage within critical areas
Manage ground cover
Manage runoff and sediment exiting system
1.Minimize ground disturbance
• -prevent removal of natural vegetation (remember the C
factor in USLE)
• Vegetative buffer strip dissipates runoff energy and
reduces soil tendency to become detached:
• Only takes one trip with dozer to destroy, plan for areas to
be undisturbed
2.Manage run-on to critical areas
• Diversion ditch around disturbed areas, reduce suspended
solids
• Prevent gullies from forming
3.Manage drainage within critical
areas
• Blanket/mulch/covering to protect important areas
• Eliminate/reduce sheet/splash erosion
– Thus no gullies
• Water should not flow under covering
• Trying to minimize quantity of flow area and reduce flow
velocity
4.Manage ground cover
• Keep natural vegetation if possible or re-vegetate (even if
temporary)
• remember the C factor in USLE
5.Manage runoff and sediment
exiting system
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Fence (perpendicular to flow or parallel to contour)
Sediment builds up on fence, requires removal
Sediment filter
Reduce flow velocity
• Settling Ponds
• Includes rip-rap, etc (previous)
• Last line of defense, material is already
suspended, need to keep on site
6.Increase infiltration
• If more water infiltrates there is less opportunity for erosion
• Add layer of rocks. Water seeps into crevasse between and
stays there until infiltration
• Infiltration trench
Reclaimed Slopes
• Predicting erosion is critical
• Prevent contamination of site water with waste material
– Depends on the composition of the material
– Changing the slope changes the flora/fauna that will inhabit the area
• Traditional:
Reclaimed Slopes
• Why not be more innovative
– We have fast computers for design
– We know how fluvial systems work
– We have GPS equipment
• Natural landforms to
– Minimize runoff on upper slopes
– Complex slopes, steep where there is little water
Traditional
• Long slopes without channels, rill/gully erosion
– Need artificial lined conduits for flow
• Turbid water quality
• Minimal diversity for flora/fauna
• Does not look good/blend with nature
GeoFluv Design
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Complex slopes with modeled water flow
Less turbid water run-off
Natural slope for wildlife and vegetation
Looks good / blends in
More info
– http://www.landforma.com/images/downloads/LF004_Natural%
20Approach%20to%20Mined%20Land%20Rehabilitation.pdf
La Plata mine, New Mexico, Coal
• After a 1 in a 100yr storm, no erosion…
Wind Erosion
• Similar mitigation strategies
• Will discuss when we talk about modeling dust
Review
• Erosion
• Overland flow:
– Sheet, rill gully erosion
– What ever water does not infiltrate (infiltration capacity of soil
important) flows on surface
• Modeling
– USLE
– Process based
• Mitigation techniques
• Natural landforms
MinE 422
Acid Rock Drainage
Online ‘Gard Guide is a great source of information
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Definition
Chemistry
Factors
Mitigation
Terminology
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acid rock drainage (ARD)
saline drainage (SD)
acid mine or acid and metalliferous drainage (AMD)
mining influenced water (MIW)
neutral mine drainage (NMD).
Terminology
• All types of drainage caused by oxidation of sulphide
minerals
• Above pH ~6 is NMD and SD
• Sulphate concentration greater than 1000 mg/L is
considered saline drainage
• MIW includes ARD, NMD and SD
• A final term is metal leaching (ML) as these waters often
have high levels of metals
Occurrence
• Can occur naturally
• Weathering (oxidization) of pyrite
• Mining accelerates the process because
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Increase movement of air and water over the sensitive areas
Exposes large volumes of material
Increases the surface area of the reactive component
Creates opportunities for the colonization of the area by
microorganisms that catalyze the process
History
• First occurrence believed to be ~3000BC in the Iberian
Pyrite Belt
– Effects included heavy metal pollution in rivers, increased
erosion and deforestation
– Similar effects in Ireland, Great Britain and Austria
• Iron age and medieval times saw an increase in mining
activity
– Effects of ARD very clear by 1556 (Georgius Agricola)
• Industrial revolution required vast quantities of coal
– Increased ARD
• Modern times require even more minerals, but we are now
aware of the harmful effects of ARD and can
mitigate/prevent it
Acid Generation
• The occurrence of ARD, NMD or SD depends on the source,
the pathway for transportation and the environment
• Most common ore sources for ARD are
– Volcanogenic massive sulphide deposits (VMS), High
sulphidation epithermal deposits, Porphyry copper deposits,
Skarn deposits, Coal deposits
• Most common ore sources for SD are
– Low-sulphide gold-quartz veins and clean skarns
• Characteristics and relative abundance of sulphides and
neutralizing minerals determine the type of drainage
Ficklin Diagram
• ARD comparison between various mines
• Metals selected on y-axis better diagnostic in differentiating
type of drainage
Ficklin Diagram
Sulphur
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Sulphur is key for AMD, NMD and SD generation
Chemistry require is mostly REDOX (reduction oxidation)
Sulphides of interest include:
Global cycle (before looking at specifics):
Acid rain
Pyrrhotite
Fe1‐xS
Bornite
Arsenopyrite
Cu5FeS4
FeAsS
Enargite/famatinite
Tennantite/tetrahed
rite
Realgar
Cu3AsS4/Cu3SbS4
(Cu,Fe,Zn)12As4S13/
(Cu,Fe,Zn)12Sb4S13
AsS
Orpiment
As2S3
Stibnite
Sb2S3
Biogeochemical Sulphur cycle
The Chemistry 1
• Note, the composition of the drainage (and sulphur content)
can vary depending on a large number of factors and can
change over the mine life or location of mining:
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Ore deposit
Mine waste
Spatial location (could be isolated or disseminated)
Mining type (surface or
underground)
– Processing methodology (heap
leaching, tailings) often
concentrates sulphur
• Main point: things can change
• Overall
FeS2 + 7/2O2 + H2O = Fe2+ + 2SO42- + 2H+ [1]
The Chemistry 2
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The general reaction
FeS2 + 7/2O2 + H2O = Fe2+ + 2SO42- + 2H+ [1]
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Aqueous ferric iron can oxidize pyrite as well, this is 2 or 3 orders
of magnitude faster and produces more acid
Requires disolved iron (pH < 4.5)
FeS2 + 14Fe3+ + 8H2O = 15Fe2+ + 2SO42- + 16H+ [2]
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Reaction [1] occurs first, lowers the pH then reaction [2] takes
over.
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A final reaction of importance is what happens to the ferrous iron
from [1]:
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Fe2+ + ¼O2 + 2½H2O = Fe(OH)3+ 2H+ [4]
Combining [1] and [4], which usually occurs when ph<4.5, twice
the acid from [1] is produced
All metal sulpides can produce acid, but some do not when
oxygen is the oxidant, pyrite (and some other) do
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The Chemistry 3
• Microorganisms act as a catalyst
• Cause these reactions to occur orders of magnitude faster
• Also, causes some reactions to occur that violate
thermodynamic expectations
• All metal sulphides produce acid with aqueous ferric iron
as the oxidant
The Chemistry 4
• Effect of temperature
The Chemistry 4
• Potential products from the aforementioned reactions
include
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Acid
Sulphur species
Total dissolved solids
Metals
• Which reactions are generated and the environment (recall
previous slide) determines if ARD, NMD, or SD occur
– Ability of the environment to neutralize acid or dilute other
compounds/metals
– The oxidizer is very important (oxygen or dissolved iron)
The Chemistry 5
• Stage 1 may last for years, may give false results if
monitoring at the start of mine life
• Acid generation increases rapidly after stage 1.
Factors
• Factors that affect the rate of sulphur oxidation
• Factors that affect the composition of the drainage
• Factors that affect the composition of the drainage after the
mine
Rate of Oxidation can vary …
– Sulphide mineral:
• Type of mineral
• Surface area
• Encapsulation
• Crystallinity
• Morphology
• Assemblage
– Ambient environment:
• pH (low ph allows for increased bacteria activity)
• Oxidation-reduction (redox) potential
• Temperature
• Source of water
– Oxidant:
• Type of oxidant (remember ferric iron increases by 2-3 orders)
• Oxygen (often limits the reaction rate)
• Ferric iron
• Availability of oxidants
– Bacteria
Drainage modifiers
• The drainage must travel from the mine to the environment
• Along which, the composition of the drainage can be
modified
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Runoff
Overland flow
Discharge into surface waters
Transport via surface water
Infiltration
Movement of mine waters by mine water management
• Factors (chemical/physical)
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pH
Redox conditions
Chemical composition of drainage
Secondary mineral formation
Sorption
Neutralization reactions
•Climate conditions
•Precipitation events
•Water movement
•Temperature
Receiving Environment
• Natural neutralization
• Sensitivity of the area to the mine release
• Dilution
• Buffering ability
Regulations
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How to keep that ‘social license to mine’
Have to meet the regulations of the country within which you operate
Have to meet the regulations of your own company
Should meet the regulations of your ‘home country’
Should consider post-closure management
– Note that contamination can occur years afterward if the ‘buffer’ was not
reached during mining (unlikely but possible)
• Some voluntary standards you could use
– International Council on Mining and Metals Principles (ICMM, 2003)
– International Cyanide Management Code (International Cyanide
Management Institute [ICMI], 2006)
– Kimberley Process (Kimberley Process Certification Scheme [KPCS], 2008)
– Guidelines For Metal Leaching and Acid Rock Drainage at Mine Sites in
British Columbia (Price, 1997)
– Minerals Council of Australia – Enduring Value (MCA, 2006)
– Mining Association of Canada – Towards Sustainable Mining (MAC, 2007)
– International network for acid prevention
Regulations
• Likely a part of your EIA
• Need a long term plan for closure
• Some legislation you may want to consider
– Mine Environment Neutral Drainage (MEND) initiative
– Guidelines for Metal Leaching and Acid Rock Drainage at Mine
Sites in British Columbia (Price and Errington, 1998)
– Federal Metal Mining Effluent Regulations (MMER)
– Guidelines for ARD Prediction in the North (Department of
Indian and Northern Development, 1992)
Summary
• AMD is a large environmental issue in mining (if not the
largest)
– Can contribute to acid rain
• The chemistry is fairly simple
• Reaction rates depend on a large number of factors and my
be difficult to predict
– Source
– Pathway
– Receiving environment
• pH and temperature are major factors
• Volume of material and capacity of environment to buffer
are also major factors
• Must meet regulations
Part 2: Characterization of ARD
• What information do we need to collect? Multi-disciplinary
Predicting ARD
• Difficult:
– Lab conditions are different
– Scale in field is different
– Both physical and chemical nature important (perm, access to
air, transport mechanism) …
Types of data of interest
Before Mining:
• Geostatistical resource map of total sulphur
– Build a potential/risk map of ARD
• Remote sensing data …
• Exploration drill holes provide valuable hydrogeological data
– Depth to water
– Quantity of water
– Flow conditions, permeability (harder)
• Surface sampling for baselines
• Surface sampling for H2O transport mechanisms
– Rivers
– Lakes
– Runoff (topography) – easy now, satellite info very available
• Static tests (testing smaller samples) and kinetic tests (long term
leach testing)
Types of data of interest
During mining
• Identify/confirm ARD sources
• Identify environmental impact
• Water quality measurement to assess need for treatment
• Regulatory guidelines important
After mining
• Decommission water treatment facilities (if possible)
• (long term) monitoring of water quality still important
Characterization of the Source
Sources of ARD
• Potential (common) sources of ARD are
–
–
–
–
Ore stockpiles
Heap leach piles
Waste rock facilities
Tailings storage facilities
Sources of ARD: Surface Mining
• Avoid high ARD areas
• Predict effect on groundwater
• Surrounding rock properties control seepage into groundwater
Berkeley pit
Berkeley pit
• Berkeley pit Superfund site, Montana
Sources of ARD: Underground
Mining
• Caving may cause fractures above
Sources of ARD: Waste Piles
Sources of ARD: Tailings
• Sources: runoff and seepage
• Composition of tailings and dyke materials important for
discharge composition
• Permeability of dyke usually low (for good reason), reduces
ARD, but seepage a concern
Heap Leach Piles, coal and uranium
Heap Leach Piles
• Sulphuric acid (copper) or sodium cyanide (gold) heap
leach piles are common
• Improper lining, leakage or overruns with excessive runoff
can cause acidic solutions to enter the surrounding
environments
Coal
• Sulphur in coal and (pyrite) in surrounding rock (above and
below)
• Underground maybe more of an issue (surface is often strip
mining and all of coal is often removed, consider
stockpiles)
Uranium
• Leaching sometimes used
• Sulphides sometimes present in waste rock
Characterization of the Pathway
Pathway
• Almost always water
• Delineate the watershed boundary
– Topographical maps
– Which watershed(s) contain the potential to be affected
• Assess the groundwater as well (porosity/permeability for flow
characterization)
• Climate (yes there is a reason for your chapter 1 from 402)
– How much rainfall
– Temperature
– Assess seasonal water influences
• Hydrologic characterization
– Streams, rivers, lakes, points of discharge (lakes/oceans)
• Information needed to assess ARD release, fate and
transportation mechanisms
•
Baseline water quality and quantity important to assess the effect of
mining (often high metal content before mining due to mineralization)
Characterization of the watershed
• Aka the receiving environment
The Receiving Environment
• Sensitivity of the ecosystem to a change in pH and metal
content
– Vegetation, aquatic life, terrestrial life, livestock, drinking
water/human habitations
• Buffering capacity (base minerals)
• Dilution capacity (volume of water)
Prediction of water quality
• The main point of the previous information gathering and
site modeling/characterization is to predict water/drainage
chemistry
• Qualitative methods usually sufficient for drainage that is
certainly acid generating or certainly not
• Quantitative may be required if unsure
• Quantitative may be required to refine mitigation strategies
– Test leach properties of samples in the lab
– Test leach properties of material under field conditions
– Geological, hydrological, chemical and mineralogical
characterization of waste materials
– Geochemical modeling
Pre-mining Phase Prediction
• Full geochemical composition of samples is usually
sufficient to identify potential ARD issues from:
– A single rock type
– A particular zone of the deposit
– The waste (may require information on ore processing)
• Make sure you sample for ARD generating minerals, not
just the commodity of interest
• Usually sufficient, don’t really need a quantitative ‘amount’
of ARD, just need to be aware of the potential to plan for
mitigation/prevention strategies
Prefeasibility and feasibility
• Now have a mine plan
• Can plan for prevention strategies using:
– watershed information
– Waste stockpile information
– Water management plans
• May want to initiate some field scale kinetic tests
• Start thinking of material balance equations
– Estimate impact of environment and strategies
• Start thinking of monitoring program
– Iterate mitigation strategies
Summary
• Purpose of site characterization/prediction is
–
–
–
–
–
Water treatment requirements
Mitigation methods
Assessment of water quality
Assessment of impact of drainage on surrounding ecosystem
Determination of reclamation bond amounts
• Mitigation strategies to come …
• Need 4 components to have ARD (exposed sulfides, air,
water, bacteria)
• ARD occurs if acid production > acid neutralization
• ARD causes dissolution of metals
• Dissolved Fe is a stronger oxidizing agent than air
Extra
• Ontario: 20/100 abandoned mines have ARD issues (830 ha)
• Quebec: 21/107 abandoned mines have ARD issues (4500 ha)
Mitigation, Handling Methods
• Goal is to control physical properties (i.e. hydraulic conductivity,
surface area, etc) to minimize ARD, some examples include…
• Remining
–
–
–
–
–
Excavate UG mines or dumps, often hard to deal with after the fact
Apply more appropriate mitigation strategy
Cover existing waste pile with benign material
Rehandle waste to new storage facility
Not always economical
• Segregation of potentially acid generating (PAG) material
– Keep subaqueous or minimize surface area exposed and water/air
infiltration
• Coal Mines, typical strategy consists of
– Compacting and treating with alkaline materials
– Cap with low perm material (i.e. clay)
– Cover with non acid generating (NAG) material and topsoil to decrease
air/water movement
Mitigation, Handling Methods
• Compaction
– Decreases porosity and
permeability
• Blending
– Mix PAG with neutralizing
material
– Requires cheap local alkaline material
– Need to consider possible flow pathways through material
– The degree of mixing is important, heterogeneous material
could cause localized ‘hot spots’
– Often use limestone or ash
• Permafrost/freezing
– Decrease chemical reaction rate to acceptable levels such
that environment can absorb pH
– i.e. Nanisivik Mine, Nunavut
Mitigation, Water Management methods
• Diversion of site surface drainage and groundwater
• Almost always sufficient H2O to react, goal is to stop or
intercept transportation of acid before reaching the
environment
• Divert flow to treatment/storage areas using
ditches/channel, very topography dependent
Mitigation, Water Management methods
• Divert flow around low perm tailings, water flows around PAG material
• Dewatering around affected areas
• Flooding
– Most effective method, oxygen levels of
water 30 times less in water
– Risk of partial flooding a serious concern
– Seasonal H2O levels change
– Must seal mine openings (UG)
– Need sufficient depth to prevent wave action
Liners and Dry Covers
• Dry covers
–
–
–
–
Earthen
Organic
Synthetic
Reduce air and water
flow through PAG
– Will not go into depth,
see MEND…
Summary
Costs
Summary
• Chemistry fairly well understood
• For your site need to understand
– ARD source
– Pathway to surrounding environment
– Receiving environment
• Apply mitigation strategy appropriate to the above three
MinE 422:Prediction of air contaminates
from a point source
Dispersion of contaminates
• Assumptions
• Calculations
•
Impact analysis involves:
• Impact Prediction:
 To forecast the nature, magnitude, extent,
and duration of the main impacts.
• Impact Evaluation (significance testing):
 To determine the significance of residual
impacts i.e. after taking into account how
mitigation will reduce predicted impact.
2
Dispersion of a Contaminant from
an Elevated Point Source
Plume
centerline
Z
(X, Y, Z)
h
Ug (Z, stability class)
X
(X, 0, 0)
(X, Y, 0)
H
h
Y
ug (z, stability class)
= wind velocity (m/sec)
H = effective height of stack (m)
h = physical height of stack (m)
h = plume rise (m)
Gaussian Dispersion Model
2
2





Q
1
y
1
z
H

C( x,y,z ) 
exp     
 
2u g y  z
2  z  
 2  y 


where,
C(x,y,z) = concentration of contaminant i at
location x, y, and z relative to source
Q
= source strength of contaminant i
ug
= wind speed at physical height of
stack (h)
y = standard deviation of the plume’s
probability distribution function along the
y axis, also referred to as the plume’s
dispersion coefficient along the y axis
z = standard deviation of the plume’s
probability distribution function along the
z axis, also referred to as the plume’s
dispersion coefficient along the z axis
H = effective height of plume
ug,2
 Z2 
 ug,1 
 Z1 
P
where,
ug,2 = wind speed at height Z2
ug,1 = wind speed at height Z1, which is
typically at Z1 = 10 m
P = function of atmospheric stability and
surface roughness
Value of Exponent P
Stability
Category
A
Rural
exponent
0.07
Urban
Exponent
0.15
B
0.07
0.15
C
0.10
0.20
D
0.15
0.25
E
0.35
0.30
F
0.55
0.30
Determination of Atmospheric Stability Classes
Wind speed,
u
(m/sec)a
<2
2–3
3–5
5–6
>6
Day
Solar Radiation
Strongb
Moderatec Slightd
B
A
A - Bf
f
B
C
A-B
f
C
B
B-C
f
D
C
C-D
C
D
D
Night
Cloudinesse
> 4/8 Cloud
< 3/8 Cloud
E
F
D
E
D
D
D
D
aSurface
wind speed is measured at 10 m above the ground
to clear summer day with sun higher than 60 above the horizon
cCorresponds to a summer day with a few broken clouds, or a clear day with
sun 35-60 above the horizon
dCorresponds to a fall afternoon, a cloudy summer day, or a clear summer day
with the sun 15-35 above the horizon
eCloudiness is defined as the fraction of sky covered by clouds
f For A-B, B-C, or C-D conditions, average the values obtained for each
bCorresponds
Note: A: very unstable; B: moderately unstable; C: slightly unstable; D:
neutral; E: slightly stable; F: stable. Regardless of wind speed, class D
should be assumed for overcast condition, day or night
Pasquill-Gifford Curves: Dependence of y and z on
Stability, Surface Type, and Distance Downwind
y
z
Empirical Constants Used to Determine
Values for y and z for Rural Environment
 y  axb
where, b = 0.894
z  cx d  f
Stability
A
B
C
D
E
F
a
213
156
104
68
50.5
34
c
440.8
106.6
61.0
33.2
22.8
14.35
x  1 km
d
1.941
1.149
0.911
0.725
0.678
0.740
f
9.27
3.3
0
-1.7
-1.3
-0.35
c
459.7
108.2
61.0
44.5
55.4
62.6
x  1 km
d
2.094
1.098
0.911
0.516
0.305
0.180
SOURCE: D.O. Martin, J. Air Pollu. Control Assoc. 26, no. 2 (1976):145.
Note: X is in km, y and z are in m.
f
-9.6
2.0
0
-13.0
-34.0
-48.6
Example 1
Nitric oxide (NO) is emitted at 110 g/s from a stack with
effective height of 100 m. The wind speed at the
physical stack height is 5 m/s on an overcast morning.
Assume rural environment.
a) calculate the ground level centerline concentration 1.0
km from the stack.
b) Calculate the concentration at 100 m off the centerline
at the same x distance.
Class D stability should be used for overcast conditions.
for x = 1km, rural environment, and Stability class D, y ,z
=?
From Pasquill-Gifford curves, y = 69 m and
z = 32m
 1 y
Q
C
exp   
2  ug  y  z
 2   y




2

 1  z  H 2 
 exp   
 

 2   z  

 1  0 2 
 1  0  100 2 
110(106 )
C
exp - 
  exp   2  32  
2(5)(69)(32)
2
69
 

 
 

 1  100 2 
 1586(1)exp   
   1586(0.0076)
2
32

 

C  12g / m3
 1 y
Q
C
exp   
2  ug  y  z
 2   y




2

 1  z  H 2 
 exp   
 

 2   z  

b) At y = 100m, everything else being the same,
 1  100 2 
C  12exp - 
 
2
69

 

C  12(0.34)
g
C  4.2 3
m
Example 2
Nitric oxide (NO) is emitted at 110 g/s from a stack with
effective height of 100 m. The wind speed at the
physical stack height is 5 m/s on an overcast morning.
Assume rural environment.
a) calculate the ground level centerline concentration 2.0
km from the stack.
b) Calculate the concentration at 100 m off the centerline
at the same x distance.
Class D stability should be used for overcast conditions.
b = 0.894,
for x = 2km and Stability class D, a = 68, c= 44.5, d =
0.516, f =-13
y ,z =?
 y  axb  68(20.894 )  126m
 z  cxd  f  44.5(20.516 )  (13)  51m
z > H/2.15  Reflection on earth surface must be considered
2
 


Q
1 y
1zH

C
exp     
2 ug  y  z   2   y  2   z
 



 1  y 2 1  z  H
 exp -    
 2   y  2   z

2







2

 


 1  y 2 
C
exp    
2 ug  y  z
 2   y  


  1  z  H  2 
 1  z  H  2  
  
   exp  
 exp  
 2   z   
  2   z  
Q
 1  0 2 
110(106 )
C
exp - 
 
2 (5)(126)(51)
 2  126  
  1  0  100  2 
 1  0  100  2  
 exp  
 
   exp  
2
51
2
51

  


 


 1  100  2 
 545(1)(2)exp  
   545(0.293)
2
51
 


C  159 g / m 3
b) At y = 100m, everything else being the same,
 1  100  2 
C  159 exp - 
 
2
126
 
 
C  159(0.73)
g
C  116 3
m
(18 pts) A coal-fired power plant is proposed to be established in an urban
area. The proposed power plant will have a stack with a physical height of
40m. When the plant is operated, it is expected that it will emit SO2 at a
rate of 12 kg/min. For a clear summer day, at noon (sun about 90o above
horizon), a 10m high meteorological tower adjacent to the proposed power
plant reports an average temperature of 25oC, wind speed of 4 m/sec, and
atmospheric pressure of 1 atm. At these meteorological conditions, the
plume rise will be 10 m, the wind speed at the physical stack height will be
4.9 m/s, the wind speed at the effective stack height will be 5.1 m/s.
Answer the following questions and show how you were able to answer
each question.
 (10 pts) Determine the ground-level centerline concentration of SO2 at
2,000 m downwind of the power plant in mg/m3.
 (5 pts) Determine the ground-level centerline concentration of SO2 at
150 m downwind of the power plant in mg/m3.
 (3 pts) What is the value (in mg/m3) and location (in m) of the local
maximum ground level concentration of SO2 downwind of the facility?
Maximum Ground-level Concentration
•Graphical and analytical methods are available to determine
the maximum ground-level concentrations of contaminants
that are emitted from elevated point sources.
• The max location exists at ground level along the centerline
of the plume (y = z = 0).
•graphical technique requires, atmospheric stability class,
effective stack height (H), wind speed (ug), and source
strength (Q)
•Given that information, the distance downwind (xmax) where
the maximum concentration occurs and the parameter
(Cug/Q)max can be determined
• The maximum ground-level concentration of the
contaminant (C) can then be determined knowing ug and Q.
Maximum Ground-Level Concentration
and its Location
This maximum concentration can also be
determined analytically:

 C ug 


 exp a  b (In (H))  c (In (H))2  d (In (H))3
 Q max
where,
H
= effective stack height (m)
 C ug 

 = (m-2)
 Q max
a,b,c,d = empirical constants
Values of Constants Used to Calculate
 C ug 


 Q max
Stability
Class
A
B
C
D
E
F
a
-1.0563
-1.8060
-1.9748
-2.5302
-1.4496
-1.0488
Coefficients
b
c
d
-2.7153 0.1261
0
-2.1912 0.0389
0
-1.9980
0
0
-1.5610 -0.0934
0
-2.5910 0.2181 -0.0343
-3.2252 0.4977 -0.0765

Summary
•Effect of pollution from a stationary point
source can be determined
•Concentrations often measured at point
source, need to infer downstream
•Impact prediction important for regulatory
guidelines
• many assumptions imbedded in this
model, but it is a reasonable starting point
•Could use your VBA skills to generate a
3D model with this equation …
25
MinE 422: Modeling Environmental
Variables
Resources:
-Some slides modified from Andrew W. Moore, Carnegie Mellon
-Many geostatistics/environment books out there
•
•
•
•
Applications of Geostatistics
What is different about environmental variables
Some techniques from machine learning
Examples
Types of variables of interest
•
•
•
•
•
•
Contaminants/pollution
Radiation
Precipitation
Temperature
Illness rates (cancer, infection, highly contagious diseases, …)
Etc ..
• What is different about most of these variables when compared
to grade?
Physical Setting
1.
Underground
– Contaminates transported following flow in
porous media relationships
– Need to infer/measure input contaminate rate
– Need to infer rock properties (geostatistics)
– Need to model contaminate dispersion
2.
Surface
– Contaminates in spoil/tailings/surroundings
– Similar to modeling common in mining
3.
Air
– Similar to underground water flow
4.
Water, streams
– Euclidian distance is wrong, shortest path
between two locations is not a straight line
5.
Water, open bodies
– Complex contaminate diffusion issues
1) Underground Flow in Porous
media
• A dissolving non-aqueous-phase-liquid (NAPL) contamination
scenario:
•
•
•
Uncertainty in permeability, source geometry, dissolution rate, decay rate
forward modeling to simulate uncertainty in source geometry
inverse modeling to simulate uncertainty in flow/transport parameters
Single phase flow equation:

xi

h 
h
 θki
  qsr  S s
xi 
t

Dissolved mass transport equation:
θCs  

xi
t


 θDij Cs    θvi Cs   θ  R NAPL  θCs

x j  xi



R NAPL  max 0, k NAPL C seq  C s
where, ki, h, qsr, C, Dij, vi, kdis, Ceq, and lambda represent hydraulic conductivity, hydraulic head, dispersion coefficient,
seepage velocity, NAPL dissolution rate constant, equilibrium concentration, and first-order biodegradation rate constant

Flow in Porous media
• Flow simulate to predict plume movement
2,3) Surface and air
Surface
• Estimating variables measured at surface
– Contaminate concentrations in soil
– Buildup over time, cumulative effects
• Identical to estimating grades, etc.
Air
• Identical to estimating flow underground but physics
(equations) are different.
• Predicting wind patterns becomes important
4) Water in streams
• How to estimate along a (virtually) 1D stream
• Could straighten the stream
• Could calculate distance along stream
5) Open water spills
• Similar mechanics to predicting underground/air flow but
with different physics again
– (think BP oil spill)
– http://www2.ucar.edu/news/ocean-currents-likely-to-carry-oil-spillalong-atlantic-coast
Spatial data
• Use some type of interpolator
– Poor in extrapolation mode
– Often do not have many samples (almost always in 2D from
the surface)
n
Z (u)   i  Z (u i )
*
i 1
n
  C(u , u )  C(u, u ) ,
j1
j
i
j
i
i  1,..., n
1
c  d iw
i 
1
n
 i 1 c  d w
i
Interpolation Technique
• Inverse distance
– Select a power
• Kriging
– Select a variogram and some
search parameters
• Trends are a significant aspect
of all resource estimation, but
can be very important in
environmental data
Radioactivity around Chernobyl
Some important details
• Trends
• Debiasing
• Temporal effects
Trends
•
The full cokriging approach (you may have taken in MinE 310) is
impractical in most cases:
–
–
–
•
Different approximations are considered depending on:
–
–
–
–
•
K(K+1)/2 direct and cross variograms in multiple directions
LMC is difficult to fit
Full cokriging is not completely implemented in most software
Source of secondary data (trends, measurements,…)
Scale of the secondary data
Number of variables being considered (interested in a few or many)
Spacing of the secondary data (exhaustive, isotopic,…)
Some methods:
1.
2.
3.
4.
5.
6.
7.
LVM
ED
CCK
BU
SW
CT
PF
locally varying mean
external drift
collocated cokriging
Bayesian updating
stepwise transformation
cloud transform
p-field simulation
Trends: Locally Varying Mean
• LVM:
– The local mean of the primary variable is created as a trend
model and used in simulation
– Two different implementations:
np
y  u   m  u       y ( u )  m( u ) 
*
 1
np


y  u      y (u )  1    m  u 
 1
  1 
*
np
– The mean gets a large influence in the first approach
– Affect of the mean is mitigated in the second approach
– Appropriate for geological trends and smooth secondary data
Debiasing
• Monitoring stations are expensive, where would be put
them?
• Need to correct in areas we know are low …
Debiasing
• Calibrate to some (potentially made up) secondary
Modeling Time series data
• Simple univariate time series (at a single spatial location)
Major Issues
• Trends (same as with spatial data)
– Consider a well log (same in mining) and a temporal variable
• Need to remove the trend from the data
– Fit a line and subtract the value
– Model residual and add trend back in
Major Issues
• Seasonal effects
– Fit a periodic function (i.e. sine wave) and subtract value like a
trend
Some interesting machine learning algorithms
that are becoming more common
•
•
•
•
•
Neural Networks
Support vector machines
Genetic algorithms
Simulated annealing
Clustering
• OK a bit of a stretch for the course, but you should know
about these …
Optimization
Artificial Neural Networks (ANN’s)
• A data structure to emulate (our current understanding) the
mechanism of biological neurons.
• Applications in geostats:
– Modeling functions (variograms)
– Classification of facies/soil/waste/anything
– Seismic inversion
A Neuron Model
• Weights represent signal
strength
• Multiple signals (inputs) are
combined
– Sum, product, or other
• We change the neuron function
by adjusting the weights –
learning
Biological
http://www.utexas.edu
Numerical
 k

output  f   wi xi 
 i 1

Humans versus Computers
• Humans:
– Highly parallel: 100 billion (1010) neurons and up to 104
connections per neuron
– One neuron passes information (fires) in 10-3 seconds
• Computers:
– Networks composed of <10 to 100’s of nodes
– Operate in 10-9 seconds
– Can parallelize
Types
• Feed-forward
–
–
–
–
Back-propagation (most common)
Bidirectional associating memory
Adaline
Self-organizing
• Feedback or recurrent
– Elman (finite state machine)
– Hopfield (form of associative memory)
– Others
Basic Network Architecture
• Layers
– Inputs
– Hidden (multiple layers)
– Output
• Fully or partially connected
• Activation Functions
– Differentiable
– Twice-differentiable
– f(x) [0,1] or [-1,1]
Sigmoid
1.5
1.0
0.5
0.0
-5
-4
-3
-2
-1
0
1
2
3
4
5
-0.5
Training the network
• Basic process:
– Randomly initialize
network weights
– Evaluate error using
training data
– Calculate
gradient/Hessian for all
weights
E E  2 E  2 E
2E
,
,
,
,
wij w jk wij 2 w jk 2 wij w jk
– Update using gradient
descent or Newton
method
 h
 n

yˆ k  f   w jk  g   wij  xi  
 i 1

 j 1
m
1
2
E    yˆ k  yk 
m k 1
Neural Networks Example
• neural network model for typhoon-rainfall forecasting
Support vector machines
• Support vector machines
– Just a linear classifier
denotes +1
w x + b>0
f(x,w,b) = sign(w x + b)
denotes -1
How would you
classify this data?
w x + b<0
Support vector machines
• Support vector machines
– Just a linear classifier
f(x,w,b) = sign(w x + b)
denotes +1
denotes -1
How would you
classify this data?
Support vector machines
• Support vector machines
– Just a linear classifier
f(x,w,b) = sign(w x + b)
denotes +1
denotes -1
How would you
classify this data?
Support vector machines
• Support vector machines
– Just a linear classifier
f(x,w,b) = sign(w x + b)
denotes +1
denotes -1
How would you
classify this data?
Support vector machines
• Classifier Margin
denotes +1
denotes -1
f(x,w,b) = sign(w x + b)
Define the margin
of a linear
classifier as the
width that the
boundary could be
increased by
before hitting a
datapoint.
Support vector machines
• Maximum Margin
denotes +1
denotes -1
Support Vectors
are those
datapoints that
the margin
pushes up
against
1. Maximizing the margin is good
accordingf(x,w,b)
to intuition
= sign(w x + b)
2. Implies that only support vectors are
important; other The
training
examples
maximum
are ignorable.
margin linear
3. Empirically it works
well
classifier
is the
linear classifier
with the, um,
maximum margin.
Linear SVM
This is the
simplest kind of
SVM (Called an
LSVM)
Support vector machines
• How to get the actual line:
– Simple optimization problem
• Can fit in a high dimension, then boundary is nonlinear in
low dimension
• Can use kernels to weight misclassified data values or to
consider soft boundaries:
denotes +1
denotes -1
What are the mining/environmental applications
Example
• Soil type classification and estimation of soil properties
using support vector machine
• Area near Serbia
• Need to classify soil for land use issues
Review
• General issues in modeling environmental variables
– Dealing with spatial-temporal issues
– Dealing with complex contaminate transportation mechanics
– Trends and debasing
• Machine learning techniques