Kuz Ram Model

Dr Hyongdoo Tom Jang Kuz-ram model

Rosin-Rammlar equation (relations of fragmentation distribution and mean particle size): 𝑅𝑅 = 𝑒𝑒 −(𝑋𝑋⁄𝑋𝑋𝑐𝑐 )

𝑛𝑛

R is proportion of material retained on the screen. n is the uniformity index xc is the characteristic size (a scale factor) x is the fragment size (screen size).

Conditions: 𝑋𝑋 = 𝑋𝑋𝑚𝑚 then R=0.5

Kuz-Ram model: 𝑋𝑋𝑐𝑐 =

𝑋𝑋𝑚𝑚 (0.693)1⁄𝑛𝑛

𝑋𝑋𝑚𝑚 = 𝐴𝐴 ∙ (𝑉𝑉𝑜𝑜 ⁄𝑄𝑄𝑇𝑇 )0.8 ∙ 𝑄𝑄0.167 𝑇𝑇 Xm is the mean fragment size (cm) A is the rock factor (7: medium, 10: hard, hardly fissured rock, 13: hard, weakly fissured rock. VO is the rock volume fragmented per blasthole (m3) QT is the mass of TNT containing the energy equivalent of the explosive charge in each blast hole (kg).

Kuznetsov equation (Modified by Cunningham for ANFO based explosives in 1987):

Since the Kuznetsov formula gives the screen size Xm for 50% of the passing materials

𝑋𝑋𝑚𝑚

Kuznetsov equation (1973):

𝑋𝑋𝑚𝑚 = 𝐴𝐴 ∙ 𝐾𝐾 −0.8 ∙ (𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ⁄115)−0.633 ∙ 𝑄𝑄𝑒𝑒0.167 K is the powder factor (kg/m3) SANFO is the weight strength of the explosive relative to ANFO 115: relative weight strength of TNT compared to anfo (100) Qe is the mass explosive being used in each-hole (kg) A (Cunningham’s A factor) is the blastability index, originally proposed by Lilly 𝐴𝐴 = 0.06 ∙ (𝑅𝑅𝑅𝑅𝑅𝑅 + 𝐽𝐽𝐽𝐽 + 𝑅𝑅𝑅𝑅𝑅𝑅 + 𝐻𝐻𝐻𝐻)

A is the rock factor RMD the rock mass description JF the joint factor RDI the rock density index HF the hardness factor.

We also can calculate Required 𝑲𝑲 to yeield the desired 𝑿𝑿𝒎𝒎 with the function.

Uniformity coefficient: (Cunningham): 𝑛𝑛

𝐵𝐵 1 + (𝑆𝑆⁄𝐵𝐵 ) � 𝑛𝑛 = �2.2 − 14 � �� � 2 𝐷𝐷

0.5

�1 −

𝑊𝑊 𝐿𝐿 �� � 𝐵𝐵 𝐻𝐻

B is the blasting burden (m) S is the blast hole spacing (m) (B and S are in drilling layout but not timing layout) D is the blast hole diameter (mm) W is the standard deviation of drilling accuracy (m) L is the total charge length (m) H is the bench height (m) Cunningham notes that the uniformity coefficient ‘n’ usually varies between 0.8 and 1.5

Western Australian School of Mines