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Geotechnical Engineering


Interstate Technical Group on Abandoned Underground Mines
Fourth Biennial Abandoned Underground Mine Workshop

Numerical Modeling Simulation of Old Works Stability New Technologies and Practical Considerations


Matthew J. DeMarco, Geotechnical Engineer
Central Federal Lands Highway Division - FHWA
Lakewood, CO

In recent years, a variety of numerical modeling procedures have been developed to assist the engineer in determining design requirements and stability conditions of planned and/or existing subsurface excavations. These methods include both 2-D and 3-D applications of finite-, distinct-, discrete-, and boundary-element codes, hosting a wide array of hybrid modeling options (slip elements, non-elastic solutions, dynamic analyses, massive deformation solutions, dynamic "material point" solutions, etc.). Of these technologies, "quasi" 3-D boundary-element codes have emerged as being extremely applicable to both in- and off-seam stress-deformation-failure analyses for tabular deposits - particularly suitable for underground coal mine settings. Boundary-element solutions can be readily generated for existing and planned mining conditions, and can account for many mine-specific parameters not generally considered in more traditional empirical design analyses. For example, such things as multiple seam interaction, changing topography, variable seam extraction sequences and mining heights, developing gob zones (full-retreat sections), off-seam deformations (including surface subsidence), and cascading pillar failure can all be readily modeled using the boundary-element approach.

The figure shows four horizontal slices through the earth at a mined location.  The top slice shows stresses in the overburden in color.  The next slice shows stresses in the mined seam.  The next slice shows stresses in the strata between the upper and lower seams.  And the bottom slice shows the stresses in lower mined seam.
Boundary-element modeling is especially useful in assessing multi-seam mining conditions subject to rapidly changing topography settings.

Two such modeling methods in particular are commonly used in the coal industry today: MULSIM/NL, a non-linear multi-seam boundary-element code developed in the early 90's by the now-defunct U.S. Bureau of Mines, and LAMODEL, a hybrid of the MULSIM technology for generating off-seam deformations in overburden units developed in the late 90's by the National Institute for Occupational Safety and Health. Both methods are relatively easy to use and can provide excellent correlation with measured and observed structure stability at active and abandoned coal properties. The models are generally characterized by the following:

  • Rapid Model Development: Both of these codes allow the user to develop detailed models of extremely complex excavations in a relatively short amount of time. CAD-based interfacing during pre-processing allows for actual mine maps to be readily incorporated into the model development, providing for a level of design analysis not available in traditional empirical methods.

  • Rapid Model Calculation: MULSIM/NL allows a mesh size of 150 x 150 "elements" per model (within the seam). Element size is defined by the user to accommodate the problem at hand, but generally falls in the range of 5- to 10-ft square. This allows for high model resolution over moderately large mine areas, with typical MULSIM/NL models usually requiring only a few minutes to run once compiled. If high resolution is desired over a large area, several overlapping models can be run and then "stitched" together to eliminate edge effects. In contrast, the LAMODEL is not constrained by mesh size; however, large mesh sizes can require long run times (for example, a whole day may be required for large areal extent models, as opposed to a few minutes for smaller mesh sizes).

    Figure of pillar yielding characterization. See text.
  • Pillar Yielding Characterization: The boundary element method allows for "confined-core" analyses of coal pillars employing a nonlinear Mohr failure criterion - a field-proven, accurate mechanical representation of how coal pillars actually load and eventually fail. Pre- and post-yield conditions are developed for each element as a function of location within the pillar. For instance, elements close to the pillar ribline are defined by a low yield strength and very low residual strength (no confinement), whereas elements toward the pillar center have higher pre- and post-yield strength due to triaxial confinement. The added confining effects of roof and floor stiffness are also accounted for in the models.

  • Multiple Seam Analyses: Currently, up to six seams can be modeled simultaneously. This allows complex stress interactions to be mapped as mining and/or progressive failure of old works occurs within any given seam, thereby redistributing loads within the seam and transferring load concentrations to adjacent seams. In some cases, sudden, rapid failure in one seam may result in stress levels in adjacent seams exceeding the load carrying capacity of the supporting structures - resulting in widespread mine system failure.

  • Stepped Mining Sequence Analyses: Active mining or sequential changes in mining condition (e.g., staged flooding of old workings) can be rapidly modeled, showing the changes in mine loading, stability, and ground deformation to be anticipated. This approach can be used for active day-to-day mining, or can be used to assess the effects of years of slow mine degradation.

    The figure shows retreat pillar splitting and floor mining resulting in cascading pillar failure.  See text.
  • Cascading Pillar Failure Analyses: The potential for cascading pillar failures (or "domino" failures) in active and old workings can be readily evaluated by parametrically changing coal strengths and bounding strata stiffnesses. This type of failure occurs in moderately deep workings where high extraction ratios are present, and results in sudden, catastrophic surface subsidence.

  • User-Friendly "Yield Condition" Mapping: Simple to understand, color-coded graphical representations of mine stability conditions simplify analysis interpretation. The more readily the results are understood, the more likely they will be implemented in the project.

  • Off-Seam Vertical Displacement Determination: LAMODEL has the added capability to determine vertical deformations within a plane or surface defined above or below the coal seam. This "surface" could be another mining horizon or the surface of the earth - allowing surface and subsurface subsidence conditions to be estimated.

MULSIM/NL and LAMODEL have been used on hundreds of mining-related projects worldwide, and have proven to be effective tools for characterizing underground structure stability in the ever-changing mining environment. Applications have included not only active and abandoned coal mines, but other forms of tabular deposits as well; including limestone, lead-zinc, trona, potash, and phosphate operations. Although most cases have involved mine design planning and optimization evaluations, recent developments in boundary element modeling technology (LAMODEL) are providing for applications related to surface and subsurface subsidence issues as well.

To better understand the power of the boundary-element numerical modeling method, the following examples are provided for (1) long-term subsidence estimation over recently abandoned coal workings, and (2) subsidence due to cascading pillar failure at a post-mining slurry injection operation.

Example 1: Potential Pipeline Subsidence, Ute Water District

As part of a geotechnical assessment for a water pipeline replacement project near Grand Junction, CO, an evaluation of long-term subsidence potential along the pipeline alignment was conducted for a critical segment overlying recently abandoned coal mine workings. The Ute Water District replacement pipeline (24-inch diameter concrete) transports water from the top of the Grand Mesa to a water treatment facility near Grand Junction. The new pipeline alignment generally follows that of the existing pipeline constructed in the early 1960's, and lies partially above the abandoned room-and-pillar workings of the Roadside Mine. The study area lies primarily on a gently rolling alluvial terrace east of the Colorado River, with cover depths ranging from less than 100 ft to more than 1,200 ft.

Mining at the Roadside property has been underway at various times since the 1940's, with a majority of the coal extracted over the past 20 years. Working in a fairly consistent 6.5-ft seam height, mining has involved various forms of full-extraction retreat, partial-extraction, and single-pass mining methods. Barrier pillars have been used in to isolate production panels, mains, and submains from one another, but have commonly been partially extracted as the operation pulled out of the section or mining district. As a result of this wide variation in mining schemes, this operation has developed many high-extraction panels containing small remnant pillars and pillar fender/stump structures over a relatively large area. These structures are susceptible to failure in the near-term as time and environmental conditions slowly degrade the coal seam.

To evaluate the potential for subsidence along the proposed pipeline alignment, and determine the magnitude of strains imposed, LAMODEL was used to simulate current and future stability of the operation. The following general steps were undertaken in the analysis:

(1) Model Calibration to Past Subsidence Events: In 1982, the operation experienced a catastrophic pillar collapse in a recently abandoned section of the mine. Pillar splitting and slabbing operations in this area of the mine left behind pillar remnants too large to yield controllably, allowing slow caving of the overburden rock mass, and yet too small to resist overburden gravity loads indefinitely. Time-dependent fatigue failure within one or two pillars eventually initiated a cascading pillar run across the panel section, with complete panel failure propagating to the surface in just a few minutes. This panel failure and subsequent surface subsidence zone, coupled with evaluations of more controlled subsidence zones elsewhere on the property, provided a basis to "calibrate" model behavior to actual conditions.

(2) Model Current Mine Stability: Following calibration of the model, an assessment of the current stability condition of the mine was undertaken. This analysis provided a baseline from which to alter the model for estimation of time-dependent failure, and allowed a check of model performance against what was currently known about mine stability.

(3) Model Maximum Subsidence Potential: The final step was to determine what the worst-case subsidence profile might look like along the planned pipeline alignment. To arrive at this condition, model seam strength parameters were systematically reduced to encourage yielding in the remnant pillars. Empirical assessments, past in-mine geotechnical studies, and experience were used to determine appropriate upper-end ranges for yielding (maximum pillar sizes likely to yield over time). This approach eventually led to a Long-Term Yield Condition Map for the operation, from which surface deformations were then determined.

Previous modeling illustrations show the types of panel-to-panel graphical outputs obtained for this operation (actually many models were stitched together to cover the large area in detail). The following illustrations show the results of the calculated surface deformations:

Figure pipeline alignment relative to mine for example 1.

Example 2: Cascading Mine Failure Due to Slurry Injection Operations

Slurry injection into abandoned mines or completed panels in active mines is an attractive alternative for the disposal of coal preparation plant fines. However, in areas where surface subsidence cannot be tolerated, either by law or necessity to protect surface structures or aquifers, special consideration must be given to the effect of slurry injection on mine stability. It is imperative that these operations evaluate the potential for production coal pillar failure and subsequent surface subsidence before initiating injection operations.

Recently, unplanned subsidence related to slurry injection occurred at an Indiana room-and-pillar coal mine experiencing weak floor conditions. A combination bearing-capacity failure in the saturated weak underclay and ensuing pillar failure resulted in sudden, catastrophic failure of the injection panel. Panel failure occurred in just a few minutes, resulting in approximately 2-ft of surface subsidence propagation directly over the injection panel - an intolerable deformation in the farmland states of the central U.S.

To ensure this type of failure did not occur within future injection panels at the property, a MULSIM/NL evaluation of required stable pillar dimensions was undertaken, including the following general steps:

(1) Modeling of Current Failure Conditions: MULSIM/NL (directed by empirical analyses) was used to model the initial stable conditions of the panel before slurry injection. Reasonable factors of safety were assumed based on in-mine observations of pillar and entry conditions following panel completion. Model floor and seam strength parameters were then degraded until cascading failure occurred throughout the panel, matching the extent of the failed zone expressed on the surface. This approach "calibrated" the model parameters for future evaluations.

(2) Determining Future Injection Panel Design Requirements: The calibrated MULSIM/NL model was then used to determine minimum pillar sizes and panel dimensions for various cover depths to ensure catastrophic subsidence would not occur during injection.

(3) Bearing Capacity Estimation: Finally, a check was completed on the bearing capacity of the underclay floor strata for the proposed pillar/panel systems to ensure that floor failures would not occur independent of pillar failures.

Figure shows that 30X40 ft. pillars would fail (top). Figure shows that 40X40 ft pillars would not fail. (bottom)

This example shows how MULSIM/NL (or LAMODEL) can be used to design future developments to avoid problems related to surface subsidence, as opposed to the previous example where the goal was to determine what damage might be imminent.

Boundary-element modeling techniques provide the highway engineer with the means to determine potential impacts of both abandoned and active mining operations on surface constructions in a timely, cost-effective, and quantitative manner. The methodology is constantly evolving as well. Future developments, sponsored by the FHWA, will include assessments of both trough-type and sinkhole-type subsidence occurrences, horizontal surface and subsurface strains, and easier Windows-based manipulation of model input/output.

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Updated: 04/07/2011

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