Some Thoughts on Calibrating LaModel

Transcription

1 Some Thoughts on Calibrating LaModel Dr. Keith A. Heasley Professor Department of Mining Engineering West Virginia University

2 Introduction Recent mine collapses and pillar failures have highlighted hli ht the need for a standard accurate calibration process for the LaModel progam

3 Introduction Numerical modeling has become a powerful tool for analyzing mine design Modern models can simulate very complex material behavior: rock failure, discontinuities, strainhardening/ softening, etc.

4 Introduction Unfortunately, simulation capabilities have often outstripped our abilities for obtaining accurate input parameters Models are often Databound where sufficiently accurate input parameters to make use of the complex numerical simulations are not available

5 Introduction Given a Databound situation, what is the best way to calibrate a realistic LaModel analysis?

6 Calibration When calibrating LaModel, there can be Two different approaches to calibration. Relative Calibration Absolute Calibration

7 Relative Calibration In a Relative Calibration: LaModel is used to analyze a previous mining situation and the derived stresses and safety factors are compared with underground observations Then the LaModel analysis of future mining is used to determine the Relative Stability by comparing the LaModel results to past experience.

8 Relative Calibration

9 Absolute Calibration In an Absolute Calibration: The LaModel input is determined using the best available input information either: Empirical Observed Measured With the goal of obtaining the most realistic output values

10 Absolute Calibration In an absolute calibration, the accuracy of the LaModel results depends entirely on the accuracy of the input parameters

11 Absolute Calibration 25 Left 24Left Vertical Stress (psi) Left Left Left Harris #1 Mine

12 Absolute Calibration 25 Left Safety Factor Left Left 22 Left Left Harris #1 Mine

13 Absolute Calibration In an Absolute Calibration: The most critical input parameters are: Rock Mass Stiffness Gob Stiffness Coal Strength

14 Rock Mass Stiffness Primarily determines: Extent of abutment stress Convergence over gob areas Multiple-seam stress transfer

15 Rock Mass Stiffness In LaModel, the rock mass stiffness is primarily determined by two parameters: Rock Mass Modulus Lamination Thickness

16 Rock Mass Stiffness In the fundamental differential equation for the laminated overburden, the Rock Mass Modulus and Lamination Thickness are multiplied together.

17 Rock Mass Stiffness PRACTICAL ASPECTS: Changing either the Elastic Modulus (E) or the Lamination Thickness (t) will have the same effect!!! I recommend only changing the Lamination Thickness! Poisson s Ratio has very little practical effect!!!

18 Rock Mass Modulus 1) Use a thickness-weighted average 2) Use an average or default value 3) Since the rock mass discontinuities (bedding planes) are naturally incorporated into the model, laboratory values of elastic moduli can often be directly used

19 Lamination Thickness PRACTICAL ASPECTS: Use an average value for the Lamination Thickness Use a thickness relative to the Slip Planes in question Large thickness for abutment stresses Small thickness for subsidence & multiple-seam stresses LaModel does not simulate the vertical joints, so there is still a trade-off between a realistic abutment extent and realistic convergence values

20 Lamination Thickness Most critical rock mass parameter For good Stress Calculations, I recommend calibrating to the extent of the abutment zone: 1) Measured 2) Observed 3) Average Empirical Data

21 Empirical Abutment Extent For ALPS and ARMPS, the extend of the abutment zone is: Where: D = the Extent of the Abutment Zone H = the Depth of Cover

22 Empirical Abutment Extent 90% of the abutment load occurs within the distance: Where: D.9 = the Extent of the Abutment Zone for 90% of load H = the Depth of Cover

23 Empirical Abutment Extent For ALPS and ARMPS, the curve for the abutment stress (σ a ) is: Where: L s = the Total Abutment Load D = the Extent of the Abutment Zone x = the Distance from the Panel Edge

24 LaModel Abutment Distribution

25 Abutment Stress 14,000 12,000 Stress (psi) 10,000 8,000 6,000 4,000 Lam Stress (psi) ALPS Stress (psi) 2, Distance from Edge of Panel (ft)

26 LaModel Abutment Integrate the stress equation to get the load within a given distance Solve for the Lamination Thickness

27 Lamination Thickness Where: E s = the Elastic Modulus of the Seam h = the Seam Thickness D n = the Extent of the Abutment Zone n = the Percentage of the Abutment Load

28 Adjustments Cannot solve for 100% of the load with the laminated model Laminated stress profile assumes elastic seam material, but typically, there is a yield zone

29 Lamination Thickness Where: E s = the Elastic Modulus of the Seam h = the Seam Thickness d = the Extent of the Yield Zone

30 Yield Zone Stress Gradient Where: S i = the Coal Strength h = the Seam Thickness x = the Distance into the Pillar

31 Yield Zone Distance 16,000 14,000 Stress (psi i) 12,000 10,000 8,000 6,000 4,000 Lam Stress (psi) Coal Strength (psi) 2, Distance from Edge of Panel (ft)

32 Lamination Thickness Where: E s = the Elastic Modulus of the Seam h = the Seam Thickness d = the Extent of the Yield Zone

33 Lamination Thickness Wizard

34 Calibrating LaModel Rock Mass Stiffness Gob Stiffness Coal Strength

35 Gob Stiffness Primarily determines: Overburden load on the gob Abutment load on the adjacent coal

36 Gob Stiffness The gob behavior is critical to accurately determining the pillar stresses and safety factors. Unfortunately, our understanding of insitu gob properties and stresses is very poor.

37 Lab Test of Gob Material

38 Gob Behavior

39 Material Models A 1 E Linear Elastic C Elastic-Plastic E i E B ( p, p ) ( r, r ) Elastic modulus E p Strain-Softening D 1 ( p, p) E 1 u E f Bi-Linear Hardening F ( o, o ) 1 E h E E f E h E i E p o p r o p r u KEY Final modulus H ard ening mod u lus Initial m odulus Plastic modulus Offset strain Peak strain Residual strain Offset stress Peak stress Residual stress Ultim ate stress

40 Gob Stiffness In LaModel, the Strain Hardening gob model is specified by 5 parameters: Initial Modulus (100 psi) Final Modulus (start at psi) Ultimate Vertical Stress (4000 psi) Gob Height Factor (1) Gob Poisson s Ratio (0.35)

41 Gob Stiffness In LaModel, it is highly recommended that the user calibrate the Gob Stiffness by only adjusting the: Final Gob Modulus

42 Final Gob Modulus Most critical gob parameter I recommend calibrating to the expected gob/abutment load: 1) Measured 2) Observed 3) Average Empirical data

43 Gob Stiffness To determine the Gob Loading for Calibrating the Gob Stiffness, the Abutment Angle Concept provides a good starting point.

44 Abutment Angle Concept

45 Gob Stiffness First, determine if the gob width is supercritical or not: Where: P = the Panel Width H = the Depth of Cover β = the Abutment Angle

46 Average Gob Loading (Supercritical) Where: H = the Depth of the Seam δ = the Density of the Overburden P = the Width of the Panel β = the Abutment Angle

47 Average Gob Loading (Subcritical) Where: δ = the Density of the Overburden P = the Width of the Panel β = the Abutment Angle

48 Deep Cover Gob Loading ARMPS Stabili ity Factor Successful Case Unsuccessful Case Design Line Depth of Cover (ft)

49 Gob Loading At this point, interactively use LaM2D to determine the final gob modulus to get the desired gob stress. Also, check the extent of the Abutment Zone and the Yield Zone

50 Gob Loading For Crandall Canyon: 2000 ft of cover D=416 ft, D.9 = 224 ft 8 ft thick seam Yield zone = 40 ft Lam. Thickness = 533 ft, (use 500)

51 Calculated Gob Load Vertical Stres ss (psi) Vertical Stress Distance from Panel Edge (ft)

52 Gob Loading Modeled in LaM2D with 500 ft lam: D.9 = 205 ft Yield zone = 35 ft Average Gob Stress = 574 psi

53 Calculated Gob Load Average Gob Str ress (psi) ft Laminations 500 ft Laminations 600 ft Laminations 0 100, , , , , , , ,000 Final Gob Modulus (psi)

54 Abutment Stress 8,000 7,000 Stress (ps si) 6,000 5,000 4,000 3,000 2,000 1,000 Lam Stress (psi) ALPS Stress (psi) Distance from Edge of Panel (ft)

55 Gob Wizard

56 Calibrating LaModel Rock Mass Stiffness Gob Stiffness Coal Strength

57 Coal Strength Primarily determines: Pillar Yielding Pillar Safety Factors

58 Coal Strength Most critical seam parameter I strongly recommend using empirical coal strengths (900 psi, Mark-Bieniawski) Or Back-Analysis

59 Coal Strength Why not Laboratory Tests?: Difficult to get a representative sample Scaling to insitu values is very imprecise Why not traditional Failure Criteria?: Difficult to obtain accurate input parameters Standard failure criteria do not fit coal behavior very well.

60 Back Analysis In LaModel, an Accurate Back Analysis of the coal strength from actual pillar failure is an excellent technique to determine a site specific coal strength. However, the back analysis and subsequent LaModel analyses must be consistent. And any coal strength values that vary considerably from the default 900 psi should be viewed very critically.

61 Observed Pillar Failure

62 Calculated Pillar Failure

63 Summary Calibrate the lamination thickness using the expected abutment load extent Calibrate the final gob modulus using the expected gob/abutment loading Use a 900 psi coal strength or back-analyze field failure. I have recommended some calibration techniques Starting point for improvement in the future LaModel users should be aware of: abutment extent, gob/abutment loading, pillar failure strength

64 Questions?

65

66 Calibrating the LaModel Program for Deep Cover Pillar Retreat Coal Mining Dr. Keith A. Heasley Christian Calderon-Arteaga Larry Jimison Morgan Sears Ihsan Berk Berk Tulu Phyllip Worley LaModel Workshops, 2010

67 Objective Utilize the ARMPS and LaModel programs to analyze the deep-cover retreat mining conditions at field sites and develop calibrated models Develop a standardized and VERIFIED calibration process for LaModel Implement Document

68 Progress Develop Case History Database 55 Potential Case Histories 55 ARMPS Analysis 35 Idealized LaModel 47 Full LaModel Present Work Document Present Case Histories Add Multiple-Seam Analysis where necessary

69 Progress LaModel Development New Pillar Safety Factor Calculation New Energy Release Rate Calculation New Lamination Thickness Wizard Improved Grid Editor New Gob Wizard

70 Stress Based Safety Factors Pillar Stress-Strain Curve 1.6 Stress s (psi) Peak Stress, 3343 Safety Factor, 0.55 Average Element Safety Factor Stress Safety Factor Pillar Sa afety Factor Strain

71 Deep-Cover, Pillar Retreat Database 47 Case Studies (11 Mines) Idealized Model Analysis Full LaModel Analysis Grid from Mine Map Topography from Mine Map Multiple-Seam (if necessary)

72 Database Overview: Mines: 4 Western, 7 Central App. Depth: Avg= , Min=750, Max=2200 Thickness: Avg= , 69 Min=3.6, 36 Max= No. of Entries: Avg=6.2, Min=3, Max=13 Pillar Width: Avg=78 78, Min=50, Max=100 CC Len: Avg= , Min=80, Max=150 Panel Wid: Avg= , Min=160, Max=940 Stab Fac: Avg= , Min=0.85, Max=2.14

73 Distribution of Successes and Failures ARMPS Stability Factor Failures Middling Success Design Line Depth (ft)

74 Results 10% Average Change with adding Topography (max = 40% change). Good Correlation between ARMPS and LaModel Safety Factors 30% Less Load on AMZ Difference Increases with Depth Difference Decreases with Panel Width

75 ARMPS Vs. LaModel SF LaModel Safe ety Factor y = x R² = y = x R² = Idealized Stability Factor Detailed Stability Factor ARMPS Stability Factor

76 Loading Comparison ARMPS - Development LaModel - Development

77 Loading Comparison ARMPS Adjacent Gob LaModel Adjacent Gob

78 Loading Comparison ARMPS Active Gob LaModel Active Gob

79 Loading Comparison ARMPS Slab Cut LaModel Slab Cut

80 LaModel Results LaModel Safe ety Factor Failures Middling Success Design Line Even Split Depth (ft)

81 Logistic Regression Depth is Not Statistically Significant Idealized LaModel SF: SF = 1.16 (even split) Success: 86%, Failures: 44%, Total: 70% SF = 1.39 Success: 64%, Failures: 62%, Total: 63% LROC = 0.746

82 LaModel Results 2.50 LaModel Safe ety Factor Failures Middling Success Even Split Design Line Depth (ft)

83 Logistic Regression Detailed LaModel SF SF = 1.16 (even split) Success: 79%, Failures: 50%, Total: 69% SF > 1.30 Success: 69%, Failures: 75%, Total: 72% LROC = SF > 1.40 = 10% Chance of Failure SF > 1.50 = 0% Chance of Failures

84 Present Work Finalizing Upgrades to LamPre Documentation Comprehensive Help System/User s Manual Multi Multi-Media Media Training Modules Further Analyze Gob and Abutment Loading Expand Database to All Mines

85

86 Adjusted Gob Loading (Subcritical) Where: H = the Depth of the Seam δ = the Density of the Overburden P = the Width of the Panel β = the Abutment Angle

87 Gob Loading (LaModel) Where: H = the Depth of the Seam δ = the Density of the Overburden H c = the Width of a Critical Panel

88 ARMPS Vs. LaModel SF 2.00 Detailed SF Ratio Stress Safety Fa actor Ratio y = x R² = Depth (ft)

89 ARMPS Vs. LaModel SF 2.00 Stress Safety Factor Ratio Detailed SF Ratio y = x R² = Panel Width (ft)

90 Gob Loading For a 2000 ft deep, 800 ft wide panel: Subcritical gob bl loading = 586 psi Adj. Subcritical loading = 1362 psi LaModel Approximation = 1125 psi