Transcript No Slide Title

On Some Simplified Approaches
to Coal Mine Seal Design
Murali M. Gadde
David A. Beerbower
John A. Rusnak
Peabody Energy, St Louis, MO
Backdrop
•Gas explosions in 2006 brought
coal mine seals into intense
scrutiny and prompted several
regulatory changes
•Lot of criticism on the 20 psig
design criteria
MSHA’s Response
•Moratorium on seals built with
alternative materials in June,
2006
•New guidelines via PIB P06-16
in July 2006 (50 psi seals)
•ETS in May 2007
•Final Rule April 2008
The Past Design Approach
•Physical explosion tests at LLEM
•20 psig peak overpressure
•Air leakage tests
•Blanket approval
•No clear criteria on field
conditions
The result…
•No available engineering
methods to address the seal
design problem
Mine Seal Design
•Two key tasks
– Estimate the explosion load
– Study the structural response of
the seal
Final Rule Explosion Loading Criteria
•MSHA’s final rule published in
April 2008 provides three tired
strength ratings for seals:
•50 psi
•120 psi
•Greater than 120 psi
What is the Correct Approach?
• Dynamic stress analysis models
– Should be used if the “rise-time” of a nonperiodic load is much smaller than the
natural time period or if the time period of a
periodic load is comparable to the natural
period of a structure
• Static stress analysis models
– For situations not mentioned above
What is Considered in a Dynamic Model?
•Loads are time-dependent
•Solve the complete equation of
motion:
  C U  K U  F (t )
MU
How to Solve the Equation of Motion?
•Simple analytical
•Complex Numerical
Simple Models
• Single-degree-of-freedom (SDOF) models
• “Equivalent” to dynamic (ED) models
• The dynamic load factors (DLF) used in the later
models are also based on SDOF models
– DLF indicates by how many times the peak
overpressure be multiplied to provide the same
structural response from a static stress analysis as from
a dynamic solution.
SDOF Models
• Seeks response at a
single point in the
structure (normally
the midpoint)
• Estimate equivalent
mass, stiffness and
damping
• Derive proper
resistance function
• Corp of Engineers’
WAC and SBEDS
programs
When to use a SDOF model?
•Must know the expected mode of
deformation in advance
•Multiple dominant modes of
failure should not exist
Applicability of SDOF models
for seal design
•Multiple modes of failure are
possible for non-hitched coal
mine seals
•Both bending and contact-shear
modes of failure possible
•One must choose only one of the
two dominant failure modes
Applicability of SDOF models
for seal design
• The most problematic assumption is
related to the seal-rock boundary
conditions
• Lack of proper verification of the
boundary conditions for the SDOF
models force the designer to make
conservative assumptions resulting in
expensive seal designs
Applicability of SDOF models
for seal design
Simply supported
Fixed
Supported by steel rods
Strengths
•Simple and easy to use
•Validated by Military tests for
certain boundary conditions
•Do not require lot of expertise
Limitations
•Requires many simplifying
assumptions, which may not be
valid for coal mine seals
•Contacts can not be simulated
•Failure mechanism is not
reproduced
•Validated mainly for unconfined
detonations
“Equivalent” Dynamic Models
• Plug-design equation or static
numerical modeling
• Uses a dynamic load factor (DLF)
• DLF normally estimated from elastic
SDOF models
“Equivalent” dynamic models
Rectangular pulse:
Dynamic model
Static model:
DLF = 2.0
Peak Pressure = 40 psi in both cases
Issues with ED models
•SDOF model based DLF may or
may not be conservative
•No work has been done so far to
show the equivalency of the
simplified approach with a full
dynamic model
Numerical Models
•‘Parts-to-Whole’ approach
•Solves the basic equation of
motion
•Complicated geometries,
material behavior and boundary
conditions
•Any type of explosion loading
Numerical Models
•Good understanding of the failure
mechanism
•Contacts can be incorporated
•Mining loads can be included
Limitations of Numerical Models
•Computing resources may limit
the element sizes
•Large number of inputs
•Longer solution times
•Expertise of the user
An MSHA Approved (ETS) Seal Design
Example
•Cementitious foam type seal
•Longwall mine gob isolation seals
•Variable mining height
•Convergence induced loads
Recent Seal Design Exercise
•Rock testing
•Lab testing for seal material
properties
•Field Instrumentation to obtain
model inputs
•3D numerical models with
contacts between seal and rock
Results
Seal
Results
• Seal deformation
Results
(9ft x 20ft)
Results
(14ft x 22ft)
Peabody’s Analytical Mine Seal
Design Process
Conclusions
•Recent events have changed
the way mine seals are
designed in US coal mines
•Mine seals can be designed
with simple analytical or
complex 3D dynamic
modeling approaches
Conclusions
•At this juncture, no extensive
validation studies have been
conducted on any of the seal
design approaches
•Based on the solution
methodology and the
fundamentals involved, 3D
numerical modeling appears
to the best available
technique for seal designs
Conclusions
•Without extensive validation
studies, any method of seal
design could be questioned for its
suitability
•A well informed designer with a
clear understanding of the
dynamic structural design theory
could obtain acceptable designs
with any of the approaches
discussed in this paper
Conclusions
•Extreme care is necessary in
selecting the inputs for seal
design
•If the explosion loading is
prescribed (e.g. as in the final
rule), then the structural analysis
must be made with the best tool
available