Blasting Fragmentation Management Using Complexity Analysis
Transcript of Blasting Fragmentation Management Using Complexity Analysis
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...