Engineer

Kuz-Ram and other models for fragmentation estimation in blasting

The Kuz-Ram fragmentation model was developed in the early 1980s by A. Kuznetsov and C. Ramstrom. It is a semi-empirical model used to predict the rock fragmentation size distribution resulting from drilling and blasting operations in mining, quarrying, and construction.

The main premise of the model is that the size distribution of fragmented rock is determined by a combination of blasthole parameters (such as diameter, burden, and spacing), explosive energy, and the rock’s inherent properties (e.g., its strength and structure).

The Kuz-Ram model uses the following equation to estimate the mean fragment size (𝑥̅):

𝑥̅ = 𝐴 * (𝑅 * 𝐸)^(1/6) * 𝑏^(5/6) * 𝑠^(1/3)

Where:

  • 𝑥̅ is the mean fragment size
  • 𝐴 is a constant that depends on the rock properties and blast design parameters
  • 𝑅 is the rock factor, which accounts for the influence of rock properties on fragmentation
  • 𝐸 is the specific charge (the amount of explosive energy per unit volume of rock)
  • 𝑏 is the burden (the distance between the blasthole and the free face of the rock)
  • 𝑠 is the spacing (the distance between blastholes)

I draft a calculation tool here for you to calculate the Kuz Ram x50 and other 2 models easily.

Excel to HTML

KUZ RAM MODEL CALCU

Rcok condtion:

UCS(MPa):
Young's module(GPa):
Poisson ratio:
P-wave velocity (m/s):
Rock density:
Mean joint spacing (m):
Joints dip with respect to free face:

Blasting Parameters

Grid Burden:
Grid Spacing:
Bench height(m):
Hole inclination
Stemming(m):
Sub-drilling(m):
hole diameter(mm):
Mean drilling error:
Explosive Type(optional):
Energy(MJ/kg):
Density(g/cm3):
VOD(m/s):
In-row delay(ms):
Scatter of det(ms):

Kuz ram setup:

KZMJPS:
KZMJPA:
KZMC(A):
KZMC(n):

KCO Setup:

KCO Xmax(m):

Output Kuzram:

Charge length(m)
KZMRDI
KZMHF
KZMTmax
KZMAt
KZMQ
KZME
KZMq
KZMRs
KZMRMD
KZMns
KZMA
KZMn
KZMX50 (mm)

CZM Parameters:

PCJ(MPa):
Ph(MPa):
hole radius(m):
rc(m):
Vc(m3):
Fc:
nfines:

CZM:

KCO-b:
The Kuz-Ram model is widely used in the mining industry for blast design and fragmentation prediction. However, it has its limitations and relies on empirical relationships, which may not always hold true for complex geological and blasting conditions. Therefore, it is essential to validate the model with actual field data and adjust the parameters accordingly to improve the accuracy of predictions.

Disclaimer
All tools and knowledge presented on this website stem from my experiences and education at UNIVERSIDAD POLITÉCNICA DE MADRID. I am deeply grateful to my professors, Jose Sanchidrian and Pablo Segarra, for their immense support and guidance throughout my academic journey. With this website, I have compiled the knowledge I gained into tools to share with others, hoping to positively impact their lives.

Please note that the information and tools provided on this website are for reference purposes only. While I have made every effort to ensure accuracy, there may still be errors. Exercise caution when applying this knowledge and these tools, and adjust them based on your specific circumstances.

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