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Design of Coal Pillars on Soft Clay Floors ©2012 Dr. B. C. Paul Note – The material presented here relies heavily on notes and support materials compiled by Dr. Paul Chugh for use with his Rock Mechanics course at SIUC. Coal Pillars are Normally Designed Using a Tributary Area Formula Overburden Load SF = Average OB Load/ Coal strength Remaining Coal Pillar After entries mined out. Having that coal pillar mash to Pieces could ruin your whole day! But What If The Failure Comes From the Pillar Punching Into the Floor Such as happens When weak underclays Are present. Factors of Safety • If Pillar Strength Controls – Safety Factor = Uniaxial Compressive Strength (adjusted for pillar size)/ Average Compressive Load on Pillar • If Plastic Floor Failure Controls – Safety Factor = Ultimate Bearing Capacity (adjusted for pillar size) / Average Compressive Load on Pillar • The calculation is essentially the same except that the Ultimate Bearing Capacity of the Floor before plastic failure replaces the crush strength of the coal pillar The Key Ultimate Bearing Capacity • UBC = Nm*Unconfined Shear Strength of the Floor Overburden Load Model is Based on this set-up Coal Pillar Squishy Fireclay Floor Respectable Rock Underneath The Terms of the Equation • The Unconfined Shear Strength can be estimated from plate load tests conducted in a mine – Luck has also be had in estimating Unconfined Shear Strength from the % moisture in the clay • (Hint – this means that getting a fireclay floor wet can cause you to be screwed). • Nm is a bearing constant derived from a mixture plastic failure theory and empirical measurements – Nm is a multi-step pain in the tail section to calculate (unless you can pawn the work off on a spreadsheet) Meet the Soft Clay Floor Spreadsheet (Inspired by the Vesic Method) Soft Floor Pillar Sizing Unconfined Shear Strength Floor (S1) Moisture Cont (MC) Unconfined Shear Strength of Rock below Clay Floor (S2) Angle of Internal Friction (Ø) Weak Layer Thickness (H) Pillar Width (B) Pillar Length (L) Entry Width Cross Cut Width Depth 60 10 500 Speck estimate of S1 S1 (2070 167 * MC ) * .15 0 5 160 160 20 20 450 K 8.333333 β 8 Nq 1 Nc 5.14 Ec 1.194553 Nc* 6.14 Nm 11.36024 681.6145 InSitu psi Stress Ratio Extraction Ratio Floor Stress Safety Factor Safety Factor Safety Factor 495 1.265625 20.98765 626.4844 1.087999 0.924799 0.761599 As typical Yellow fields are for Your input ft ft ft ft ft ft K S2 S1 Green is a calculated Field B*L 2 * ( B L) * H tan( ) Nq e 2 * tan ( ) 4 2 If ( 0)thenNc 5.14elseNc ( Nq 1) * cot( ) Ec 1 Red is answers you Probably want to know B Nq * L Nc Nc* Ec * Nc K * Nc * *( Nc * 1)(( K 1) * Nc* (1 K ) * Nc * 1) 2 Nm UBC 60 ( K * ( K 1) * Nc * K 1)(( Nc * ) * Nc * 1) ( K * Nc * 1)( Nc * 1) UBC Nm * S1 % short term long term wetted safety Factor The Green Fields are Inhabited by Constants Used to Get Nm K 8.333333 β 8 Nq 1 Nc 5.14 Ec 1.194553 Nc* 6.14 K S2 S1 B*L 2 * ( B L) * H tan( ) Nq e 2 * tan ( ) 4 2 If ( 0)thenNc 5.14elseNc ( Nq 1) * cot( ) Ec 1 B Nq * L Nc Nc* Ec * Nc The formulas used to calculate the values in green are shown. You could read papers on how they were developed and what They mean – or your could call Sr. Design an application of Your rock mechanics class and pretend you don’t want to know (or maybe who’s pretending). Your Essential Inputs Unconfined Shear Strength Floor (S1) Moisture Cont (MC) Unconfined Shear Strength of Rock below Clay Floor (S2) Angle of Internal Friction (Ø) Weak Layer Thickness (H) Pillar Width (B) Pillar Length (L) Entry Width Cross Cut Width Depth 60 psi 10 % 500 psi Speck estimate S1 0 5 160 160 20 20 450 ft ft ft ft ft ft Your Rock Mechanics Properties are Unconfined Shear Strengths angles of internal Friction and moisture content Making life more simple – The Angle of Internal Friction for Plastic Clay is usually Treated as 0. Speck developed a respectable correlation of the Unconfined Shear Strength of the Floor with its moisture content The Spreadsheet has Specks Estimator of Shear Strength Right Next to Where You Must Input Shear Strength Speck estimate of S1 60 S1 (2070 167 * MC ) * .15 For this class you can estimate S2 to be 1100 psi and MC to be 12% where the Clay floor has not been wetted. The Rest of the Inputs Come From Your Conditions and Your Pillar Design Unconfined Shear Strength Floor (S1) Moisture Cont (MC) Unconfined Shear Strength of Rock below Clay Floor (S2) Angle of Internal Friction (Ø) Weak Layer Thickness (H) Pillar Width (B) Pillar Length (L) Entry Width Cross Cut Width Depth 60 psi 10 % 1100 psi Speck estima S1 0 5 160 160 20 20 450 ft ft ft ft ft ft You need to enter your Fireclay thickness – assume once thickness goes past 1.3 feet that clay floor designs will take over for pillar sizing. You need to know your Depth The pillar dimensions and entry widths come from your own designs. The Outputs UBC 793.1628 InSitu psi Stress Ratio Extraction Ratio Floor Stress Safety Factor Safety Factor Safety Factor 495 1.2 16.66667 594 1.335291 1.134997 0.934704 UBC Nm * S1 % short term long term wetted safety Factor The Spreadsheet Calculates the Ultimate Bearing Capacity of the Floor It Also Calculates the Extraction Ratio and Stress on the Floor From This the Spreadsheet Estimates Your Factor of Safety UBC 793.1628 InSitu psi Stress Ratio Extraction Ratio Floor Stress Safety Factor Safety Factor Safety Factor 495 1.2 16.66667 594 1.335291 1.134997 0.934704 UBC Nm * S1 % short term long term wetted safety Factor The short term factor of safety is what can be achieved with undegraded floor. For a panel where you will mine in and then abandon a 1.2 short term factor Of safety is acceptable. On a long term basis – such as might be encountered if one wanted to know that Floor failure would not cause subsidence one would consider a long term Safety factor (the floor is assumed to pick up moisture as result of exposure to The air and some minor water incident to mining operations). The reduction is An empirical value based on observations by Dr. Paul Chugh for the Illinois basin. The Last Safety Factor • The Last Safety Factor reduces strength for a clay floor basically getting into constant covered water contact for 24 hours – Again it is based on an average measured by Dr. Paul Chugh • What could cause such wet floor conditions – A mine flood that you failed to pump out in time – Exposing the clay floor to a water bearing formation with significant water present – Exposing a clay floor to bleed water from backfill