On Some Simplified Approaches to Coal Mine Seal Design

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On Some Simplified Approaches to Coal Mine Seal
Design

• Murali M. Gadde
• David A. Beerbower
• John A. Rusnak
• Peabody Energy, St Louis, MO

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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

3
MSHAs 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

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The Past Design Approach

• Physical explosion tests at LLEM
• 20 psig peak overpressure
• Air leakage tests
• Blanket approval
• No clear criteria on field conditions

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The result

• No available engineering methods to address the
  seal design problem

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Mine Seal Design

• Two key tasks
• Estimate the explosion load
• Study the structural response of the seal

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Final Rule Explosion Loading Criteria

• MSHAs final rule published in April 2008
  provides three tired strength ratings for seals
• 50 psi
• 120 psi
• Greater than 120 psi

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Structural Response...
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What is the Correct Approach?

• Dynamic stress analysis models
• Should be used if the rise-time of a
  non-periodic 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

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What is Considered in a Dynamic Model?

• Loads are time-dependent
• Solve the complete equation of motion

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How to Solve the Equation of Motion?

• Simple analytical
• Complex Numerical

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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.

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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

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When to use a SDOF model?

• Must know the expected mode of deformation in
  advance
• Multiple dominant modes of failure should not
  exist

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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

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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

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Applicability of SDOF models for seal design
Simply supported
Fixed
Supported by steel rods
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Strengths

• Simple and easy to use
• Validated by Military tests for certain boundary
  conditions
• Do not require lot of expertise

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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

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Equivalent Dynamic Models

• Plug-design equation or static numerical modeling
• Uses a dynamic load factor (DLF)
• DLF normally estimated from elastic SDOF models

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Equivalent dynamic models
Rectangular pulse Dynamic model
Static model DLF 2.0
Peak Pressure 40 psi in both cases
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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

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Numerical Models

• Parts-to-Whole approach
• Solves the basic equation of motion
• Complicated geometries, material behavior and
  boundary conditions
• Any type of explosion loading

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Numerical Models

• Good understanding of the failure mechanism
• Contacts can be incorporated
• Mining loads can be included

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Limitations of Numerical Models

• Computing resources may limit the element sizes
• Large number of inputs
• Longer solution times
• Expertise of the user

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An MSHA Approved (ETS) Seal Design Example

• Cementitious foam type seal
• Longwall mine gob isolation seals
• Variable mining height
• Convergence induced loads

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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

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Results
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Results

• Seal deformation

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Results(9ft x 20ft)
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Results(14ft x 22ft)
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Peabodys Analytical Mine Seal Design Process
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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

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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

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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

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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

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