pillar strength equation
Pillars Factor of Safety (FOS) calculation method:
CMRI formula
CMRI developed a formula for pillar strength taking into account the pillar w/h ratio, the uniaxial compressive strength of the pillar, the height of seam and depth of cover S = Pillar strength (MPa) σc = Uniaxial compressive strength (UCS) (MPa) h = Working height or seam height (in m)
H = Depth of cover (in m) w = Pillar width (in m)
Obert-Duvall/Wang Formula (Obert and Duvall, 1967)
It was derived from laboratory tests on hard rock and elasticity considerations the same relationship as did Bunting in 1911. Greenwald et al. (1939) mention that this form of an expression for pillar strength was proposed in 1900 for anthracite after laboratory tests made for the Scranton Engineers Club. This formula is given as Where σp is pillar strength, σ1 is uniaxial compressive strength of a cubical specimen (w/h = 1), and w and h are pillar dimensions. According to Obert and Duvall, this equation is valid for w/h ratios of 0.25 to 4.0, assuming gravity-loading conditions. Through back calculations from mining case histories and utilization of laboratory rock properties, safety factors of 2 to 4 were derived for short- and long-term pillar stability, respectively. Essentially, this safety factor accounts for strength scaling from laboratory (or rock-material) strength to in situ (or rock-mass) strength for hard rock.
Holland - Gaddy Formula
Holland & Gaddy, Holland (1964) extended the work by Gaddy (1956) and proposed the following formula: Where, k is the Gaddy factor, w and h is pillar dimensions in., and σp is pillar strength in psi. Holland specified a safety factor between 1.8 and 2.2 for the design of coal pillars, with a recommended value of 2.0. The width-to height ratio, for which the Holland formula is valid, ranges from 2 to 8. Although popular in the 1970s, the
CMRI formula
CMRI developed a formula for pillar strength taking into account the pillar w/h ratio, the uniaxial compressive strength of the pillar, the height of seam and depth of cover S = Pillar strength (MPa) σc = Uniaxial compressive strength (UCS) (MPa) h = Working height or seam height (in m)
H = Depth of cover (in m) w = Pillar width (in m)
Obert-Duvall/Wang Formula (Obert and Duvall, 1967)
It was derived from laboratory tests on hard rock and elasticity considerations the same relationship as did Bunting in 1911. Greenwald et al. (1939) mention that this form of an expression for pillar strength was proposed in 1900 for anthracite after laboratory tests made for the Scranton Engineers Club. This formula is given as Where σp is pillar strength, σ1 is uniaxial compressive strength of a cubical specimen (w/h = 1), and w and h are pillar dimensions. According to Obert and Duvall, this equation is valid for w/h ratios of 0.25 to 4.0, assuming gravity-loading conditions. Through back calculations from mining case histories and utilization of laboratory rock properties, safety factors of 2 to 4 were derived for short- and long-term pillar stability, respectively. Essentially, this safety factor accounts for strength scaling from laboratory (or rock-material) strength to in situ (or rock-mass) strength for hard rock.
Holland - Gaddy Formula
Holland & Gaddy, Holland (1964) extended the work by Gaddy (1956) and proposed the following formula: Where, k is the Gaddy factor, w and h is pillar dimensions in., and σp is pillar strength in psi. Holland specified a safety factor between 1.8 and 2.2 for the design of coal pillars, with a recommended value of 2.0. The width-to height ratio, for which the Holland formula is valid, ranges from 2 to 8. Although popular in the 1970s, the