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Rock fragmentation – Kuz-Ram model

Atualizado: 29 de out. de 2020

You can download O-Pitblast and Wipware article entitled “Pattern Expansion Optimization Model Based on Fragmentation Analysis With Drone Technology” here.

You’ll find other mining/blasting related scientific papers here.

The Basics

In the mining world, rock blasting is one of the main procedures of ore winning process (Hustrulid, 1999). The use of explosives, to break and fragment rock, is the fastest and efficient procedure to make it transportable has become a world-wide used technique. The majority of mines and many civil works recurs to the use of explosives and, since 1627 (the first time explosives were used for rock blasting), lots of blasting techniques were developed (Konya & Walter, 1990).

Overview Mining Process

On one hand, these techniques were established in order to optimize the use of explosive energy and in the other hand, more recently, reduce the overall cost of the operation maintaining blast results’ quality.

Nowadays, with the cost optimization pressure in the majority of mining companies, is compulsory to analyze each mine-to-mill operation and get the best results from it.

Rock Blasting

The three main factors affecting the blast results, depends on explosive selection (and its quality), blast design and the procedures implemented to replicate this design. It’s important to understand the rock characteristics, structures and behaviour when submitted to a certain kind of stress generated by explosives (Bhandari, 1997).

Empirical research and evidences on blasting operations helped to develop a series of blast design formulae in order to propose guidelines for the design process. Is believed, that these important “rules” are meant to be applied with the objective to achieve the desired blast results in an initial stage of any operation (Jimeno, Jimeno, & Carcedo, 1995; p. 200). The results, ground conditions, operation details and geology will be the real decisive kpi’s to define the blast design.

O-Pitblast – Blast Desing Software

As mentioned by Jimeno & Carcedo, 1995, there are a series of authors, mining engineers and researchers that developed empirical formulas, for pattern design, involving relations between:

  • Diameter;

  • Bench high;

  • Hole length;

  • Stemming;

  • Charge length;

  • Rock density;

  • Rock resistance;

  • Rock constants;

  • Rock seismic velocity;

  • Explosive density;

  • Detonation pressure;

  • Burden/Spacing ratio;

  • Explosive energy.

Some of the researchers are Andersen (1952), Pearse (1955), Hino (1959), Allsman (1960), Ash (1963), Langefors (1963), Hansen (1967), Konya (1972) and Lopez Jimeno, E(1980). In Figure 1 are presented some of these parameters on a bench blasting model.

Fragmentation Prediction – Kuz-Ram Model

Humans always tried to understand the future. The same happens with mining engineer trying to predict their blast results. In this case, for fragmentation results and prediction, a world-wide well-known model is presented by Cunningham, 2005– Kuz-Ram Fragmentation model.

Despite several models were developed along the years, the simplicity offered by Kuz-Ram model makes it one of the most used prediction models (Cunningham, 2005). This Model is based in three main equations:

Kuznetsov Equation, presented by Kuznetsov, determines the blast fragments mean particle size based on explosives quantities, blasted volumes, explosive strength and a Rock Factor.

Where = Medium size of fragments (cm); A= Rock factor; K = Powder factor (kg/m3); Q= Explosive per hole (kg); 115 = Relative Weight Strength (RWS) of TNT compared to ANFO; = Relative Weight Strength (RWS) of the used explosive compared to ANFO.

Rosin-Ramler Equation, represents the size distributions of fragmented rock. It is precise on representing particles between 10 and 1000mm (Catasús, 2004; p80).

Where B = Burden (m), S= Spacing (m), d = Drill diameter (mm), W = Standard deviation of drilling precision (m),  = Bottom charge length (m),  = Column charge length (m), L = Charge Length (m), H = Bench height (m).


Vinicius Miranda | Francisco Leite | Thomas Palangio

O-Pitblast & Wipware

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