Subsidence Monitoring with a Survey Network:
Analysis of Network Layout
Presented to:
National Associate of Abandoned Mine Lands Program
Co-authored by:
Jeffrey Riedel P.E. (Pioneer Technical Services, Inc)
Claire Rasmussen M.S. (Pika Statistical Consulting)
9/26/2016
Introduction
• Origin of Work
• Part of Red Lodge Subsidence
Investigation
• Objective – Determine whether
historic underground coal mines
have any potential for causing (or
have caused) ground subsidence.
• In response to concerns from
several citizens
• Abandoned Mines Lands Section,
Montana Department of
Environmental QualityRemediation Division.
• P.M. Bill Snoddy (AML DEQ)
• P.M. Tim Ranf (Pioneer Technical
Services)
Project Background
• Red Lodge, Montana
Geology and Mining
• Tongue River Member of Ft. Union
Formation
• Red Lodge Coal Field
• 1882 thru 1932
• Room and Pillar
• 32 square miles
• Number of seams and thickness
•
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No 1
No. 1 ½
No 2
No 3
No 4
No 4 ½
No 5
No 6
No 7
No 8
No 9
11 Feet
5 Feet
8 feet
10 Feet
10 Feet
5 Feet
8 Feet
6 Feet
2 Feet
25 Feet
10 Feet
Geology and Mining
• Red_Lodge_Coal_Workings_highdef.mp4
Analysis Findings
• Seams beneath Red Lodge
• Mine depths range from 100 to 600 feet below ground surface
• Up to four seams mined in study area
• Existing openings range between 6 feet in height and
collapsed, average opening is 2 feet.
Analysis Findings
• Trough Subsidence
Estimates
3 – 7 inches
• Maximum vertical
settlement is estimated
between 3-7 inches
• Subsidence may
accumulate over the next
50 – 100 years
• Potential subsidence
rates of 0.003 - 0.012 feet
per year.
• Structural Damage may
be slight to appreciable
over this time frame
(Provide reference)
JOB TITLE : Y-Displacement Contours
(*10^3)
5.800
FLAC (Version 7.00)
LEGEND
5.600
22-Sep-16 11:02
step 117911
-5.556E+02 <x< 5.556E+02
4.714E+03 <y< 5.825E+03
Y-displacement contours
-1.20E+00
-1.05E+00
-9.00E-01
-7.50E-01
-6.00E-01
-4.50E-01
-3.00E-01
-1.50E-01
0.00E+00
1.50E-01
5.400
5.200
5.000
Contour interval= 1.50E-01
4.800
Pioneer Technical Services
Bozeman, JJR
-4.000
-2.000
0.000
(*10^2)
2.000
4.000
Big Picture
• Is the ground is subsiding?
• Survey 63 points in study area
once every 6 months for 2
years
• Crux: Can’t just look at points
and say definitively if there is
subsidence
• Measurement error is on the
order as the subsidence rate we
are trying to detect
• Using leveling networks and
linear regression will help
address this problem
Big Picture
• Use leveling network to
minimize error for each round of
the survey
• Repeat network measurement
on a semi-annual basis
• Use linear regression to
estimate movement rate at each
monitoring point.
• Use regression results to make
statistical inference about
whether each monitoring point
is subsiding
Survey Design and Accuracy of Estimation
• Building more
redundancy into the
survey design results in
more accurate
estimates
• When using the leveling
network method we
get:
• An elevation estimate
for each point in the
survey
• A Standard Error
associated with each
elevation estimate
Survey Design
• The Standard Error is a measure of how variable the
elevation estimate is
• A small SE means we would likely get a similar estimate if we
were to immediately repeat the survey
• How do we ensure our survey will produce estimates
accurate enough to be useful?
• We can use computer simulations to
analyze the SEs of our survey points
before actually performing the survey
• We can compare different surveys to
help decide where to include
redundancies
Survey Design
Example
Monitoring Point
Elevation
1
Elevation 2
Elevation 3
Elevation 4
1
5580.723
5580.454
5580.448
5580.219
2
5581.224
5581.223
5581.219
5581.223
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Example - Continued
• H0: True Slope = 0 vs. HA: True Slope < 0
• Can make a decision using the p-value from a t-test
• Can estimate a confidence interval for the true slope
Example - Continued
• p-value = 0.025
• This means there is
approximately a 2.5%
chance of observing a
random sample of survey
elevations that produce a
slope as or more negative
than this one, if this point is
not actually subsiding
• Slope estimate = -0.152
• Associated 95% confidence
interval
-∞
-0.024
0
• We are 95% confident that the true rate of subsidence of
monitoring point 1 is greater than or equal to 0.024 feet per
6-month period
Example - Continued
• p-value = 0.296
• This means there is
approximately a 29.6%
chance of observing a
random sample of survey
elevations that produce a
slope as or more negative
than this one, if this point
is not actually subsiding
• Associated 95% confidence
interval
0 0.003
-∞
• We are 95% confident that the true rate of subsidence of
monitoring point 2 is less than or equal to -0.003 feet per 6month period
Summary
• Red Lodge Subsidence Investigation
• Possible subsidence on the order of 3 - 7 inches over the next
50 - 100 years
• Is subsidence occurring?
• Crux:
• Estimated subsidence rate is small relative to measurement error
• Solution:
• Use leveling network to minimize survey error
• Simulate network to ensure selected survey provides estimates
with small enough error to be useful
• Obtain confidence interval for subsidence rate at each monitoring
point.
• Confidence interval
• Contains 0, no statistical evidence of subsidence
• Negative, statistical evidence of subsidence
• LONG STORY LONG: Accurate Survey and Quantified Answer
Question or Comments?
• Thank You