BLASTING FRAGMENTATION

MANAGEMENT USING

COMPLEXITY ANALYSIS Jacopo Seccatore

Landscape, Environment and Geotechnologies Engineering Department,

Polytechnic of Torino, Italy

Giorgio De Tomi

Mining & Petroleum Engineering Department, Polytechnic School,

University of São Paulo, Brazil

Mauricio Dompieri

Ontonix-Brasil;

Mining & Petroleum Engineering Department, Polytechnic School,

University of São Paulo, Brazil

Alvaro Rezende

Sociedade Extrativa Dolomia Ltda – Taubaté, Brazil

Politecnico di Torino Escola Politécnica

da Universidade de São Paulo

Gutta cavat lapidem

but, due to time issues, we use dynamite

SECONDARY

BREAKING

TRANSPORT

LOADING

BLOCKS HAULING

CRUSHING & MILLING

THE COSTS OF ROCK BLASTING

Mc Kenzie, 1967

THE COSTS OF ROCK BLASTING

Generally:

costs

Fragmentation

Loading&CrushingDrill&Blast

optimum optimumoptimum

1. Where is OPTIMUM?

2. Is OPTIMUM the appropriate answer?

Geology 1

Geology 2

Geology 3

PROBLEMS

• Geological conditions give this kind of working a high level

of uncertainty

• Optimum conditions vary from bench to bench

• Some blast design must be performed at the beginning of

operations, and cannot vary greatly from blast to blast

APPROACH TO SOLUTION

Rather than optimum, it results more efficient to look for

ROBUSTNESS, granting constancy of results under varying

conditions

Optimized solution Robust solution

COMPLEXITY ANALYSIS

Structure(How information

flows within a

given system,

how many variables

are involved)

Entropy(How noisy the

interactions are)

COMPLEXITY

Complexity is a function of the structure and the internal entropy

of a system

COMPLEXITY ANALYSIS:

how it works

Critical complexity

Complexity

Lower complexity

CRITICAL COMPLEXITY: In its proximity the system becomes chaotic and

vulnerable.

ROBUSTNESS is proportional to the margin Ccritical – C. This measure quantifies the

system’s ability to preserve its functionality.

Critical complexity

Complexity

Lower complexity

COMPLEXITY x UNCERTAINTY = FRAGILITY

Cdesign x (Umanufacturing + Uenvironment) = Fproduct

Blast design Drilling &

Charging

operations

GeologyFragmentation

CONTROLLABLE PARTIALLY

CONTROLLABLE

NOT

CONTROLLABLE

UNCERTAINTY IN THE ENVIRONMENT CANNOT BE AVOIDED

WE NEED TO MANAGE COMPLEXITY

Fragility is the property of a system to behave unexpectedly with undesired

results without signs of breaking

COMPLEXITY ANALYSIS:

how it works

OntoSpace™ analyses multi-dimensional maps

images plotting xi Vs xj ∀ 𝑖,𝑗∈variables of the

system, with i≠j.

Each map is divided into cells. On each cell an

IMAGE ANALYSIS is performed. Through this

image analysis technology, multi-dimensional data

are transformed into Process Maps.

The result of a process map is a graph of nodes

(variables) and arcs (interconnections).

COMPLEXITY ANALYSIS:

how it works

The reliability (credibility) of a model is the percentage of fitting of its results

with reality or test results

A measurement of the reliability (credibility) of a model can be given by the

Model Credibility Index (Marczyk, 2008).

test

eltest

C

CCMCI

mod

When the MCI is low, the model and the test data have a good structural accordance

1. Drilling Geometry

2. Charging

3. Initiation

4. Rock Structure

Groups of variables:

INPUT

SOUTPUT

SYSTEM

here lies complexity

Application to BLASTING OPERATIONS

Application to BLASTING OPERATIONS

To achieve this analysis three stages have been analyzed:

• The empirical dimensioning model used by Dolomia mine

direction

• The analytical dimensioning model proposed by Berta (1985)

• The field data of drilling pattern and charging used in

Dolomia mine during blasting operations in the month of

March 2010

MINE MANAGEMENT´S MODEL

Monomial formula

• 𝑄=𝑃𝐹∙𝐻∙𝐸∙𝑉

Empirical thumb rules

• Burden 𝑉=33÷39 ∅𝑓

• Spacing 𝐸=1,15÷1,30 V

• Stemming 𝐵=0.7 𝑉• Underdrilling 𝑈=0.3 𝑉

Empirical determination of Specific Charge

• 𝑃.𝐹.=150÷200𝑔/𝑡 (𝑚𝑎𝑠𝑠𝑖𝑣𝑒 𝑟𝑜𝑐𝑘)

• 𝑃.𝐹.=80÷100𝑔/𝑡 (𝑤𝑒𝑎𝑡h𝑒𝑟𝑒𝑑 𝑟𝑜𝑐𝑘)

MINE MANAGEMENT´S MODEL

•high degree of empiricism

•no correlations between the

geometrical characteristics of the

pattern and the charging parameters

•this kind of modelling cannot be

based on theoretical proceedings

without calibrating the specific

charge with tests

Level of contribution to

Complexity

Parameter Percentage of

contribution to

complexity [%]

1st Stemming 25.03

2nd Burden 25.01

3rd Underdrilling 24.81

4th Spacing 24.77

MINE MANAGEMENT´S MODEL

Since the drilling parameters have no

connection with the others, they can be

deleted to consider a simplified datasheet

that takes into account only the height of

the bench and the P.F. (as input) and the

charge per hole as a result

BERTA’S MODEL

Acoustic transfer efficiency

Acoustic transfer efficiency

Acoustic transfer efficiency

η3 = 0,15

Specific Charge

s desired degree of

fragmentation

εss rock specific surface

energy

ε explosive specific energy

Charge per Hole

𝑄=𝑃𝐹∙𝐻∙𝐸∙𝑉

BURDEN

BERTA’S MODEL

•High degree of inter-

correlation

•Increased functionality,

taking into consideration

additional parameters.

•Redundant connections

•Fragile model. Might

generate fuzzy results

•Generates noise, has a low

level of confidence.

Level of contribution to

Complexity

Parameter Percentage of contribution to

complexity [%]

1st Burden 16.95

2nd Mine Volume 16.83

3rd Rock Density 15.26

4th Explosive Specific Energy 11.07

5th Specific Charge 9.26

MINE IN-SITU DATA

•The large dimension of

the bench to be blasted (number of rows x total length of

the blast) largely contribute

to the complexity of the

operations

•The number of rows

influences the charging

parameters, confirming what is

suggested by many authors (e.g.

Mancini & Cardu, 2001) to vary

the P.F. for the holes of the rows

after the first one

•The degree of complexity

of this kind of working

appears to be very low

and far away from its

criticality

Burden

n# of

rows

Bench

Length

Number

of holes

Bench

Height

Bench

Volume

Qespl

(hole)

Volume

of single

mine

P.F.

(single

mine)

L n. rows C Furos P m3 Eforo Vcomp Pfforo

Level of contribution to

Complexity

Parameter Percentage of

contribution to

complexity [%]

1st Charge per hole 10.80

2nd Length of the Bench 10.80

3rd Number of rows 8.22

PARAMETERS

THAT HAVE

BEEN

CONSIDERED

COMPARISON OF RESULTS

Comparison of the models

•The analytical approach appears more affected by complexity.

•Its parameter that mostly contributes to complexity appears to be much

more critical for the system than the one in the empirical model.

Empirical Model

(Dolomia Mine

Direction)

Analytical Model

(Berta)

Complexity Level C 6.39 8.50

Critical Complexity CCR 8.16 9.74

Robustness 73.9 56.7

Maximum Contribution to

complexity of the most

critical parameter

16.95% 25.03%

COMPARISON OF RESULTS

Applied model Vs In-Situ Data

•The complexity of the whole model is much higher than the complexity of the field data

•Simplifying the datasheet to its essential variables, the degree of complexity appears very

close to the one of the field data

• The model misses some links between geometrical and charging parameters that are

visible in the map of real data.

•This kind of empirical model needs calibration

Dolomia Model Dolomia In-Situ Data

Dolomia Model

simplified datasheet

Complexity Level C 6.39 1.98 2.12

Critical Complexity CCR 8.16 2.892.56

Robustness 73.9 86.8 70.3

Model Credibility IndexM.C.I. = 2.22

M.C.I. = 0.07

CONCLUSIONS

• In the approach to the blasting problem, searching for the optimum, appears to be

inefficient. The geological environment is characterized by too many uncertainties to

have an optimum valid for many applications. Researching for robustness in blast

design results in much more efficiency.

• Complexity Analysis allows a clear understanding of the correlations between the

variables in blasting systems and helps to manage their robustness

• Robustness and complexity levels can be used to compare different models and to

measure the fitting of models with field data

• Complexity Analysis allows the understanding of the behaviour of critical variables that

can generate instability in the system thus leading to unexpected results.

FUTURE STEPS OF THE RESEARCH

The continuation of this research project is expected to produce results

related to:

• Identification of the most critical parameters of the blast

fragmentation process through complexity analysis

• Selection of the most robust model that can grant a more controlled

variability in the results, even at the cost of greater precision, under

variable operative conditions through topological robustness

management

Thank you for your attention

May you have a blasting day...

CONTACTS

Jacopo Seccatore

jacopo.seccatore@gmail.com

Mauricio Dompieri

mauricio@ontonix-brasil.com

mdompieri@usp.br