The document presents a neural tree model for estimating the uniaxial compressive strength (UCS) of rock materials from index test parameters. It develops and compares models using fuzzy inference systems, adaptive neuro-fuzzy inference systems, multi-layer perceptrons, and heterogeneous flexible neural trees. The best performing and lightest weight model was a multiobjective heterogeneous flexible neural tree, which estimated UCS with the lowest error and highest correlation. Among the different index test parameters, the point load strength test was found to be the most significant in estimating UCS.

1. Neural Tree for Estimating the
Uniaxial Compressive Strength
of Rock Materials
Varun Kumar Ojha
ETH Zurich, Switzerland
Deepak Amban Mishra
Indian Institute of Petroleum & Energy, Visakhapatnam, India
Conference: Hybrid Computational Intelligence (HIS 2017)
Paper title:
Authors:

2. Uniaxial Compressive Strength (UCS)
• USC indicate strength of a rock
material
• UCS is used to test failing behavior of
rock material
• In laboratory a instrument
compresses a rock material and
checked when it crack (fail)
• UCS is important test to avoid
unintended event
Image source: Siratovich et al. Article, Physical property relationships of the Rotokawa Andesite,
a significant geothermal reservoir rock in the Taupo Volcanic Zone, New Zealand
July 2014 Geothermal Energy 1(2):10

3. UCS Index test parameters
• Block punch index (BPI),
• Point load strength (Is-50),
• Schmidt rebound hardness (SRH),
• Ultrasonic P-wave velocity (𝑉𝑝)
• Porosity (𝜂 𝑒)
• Density (𝜌)
Rock: before failing
Rock: after failing
Image source: Mohd Ashraf Mohamad Ismail, Laboratory and in-situ rock testing,
Advanced Geotechnical Engineering

4. Rock samples
Figure: Core sample photographs of (a) granite, (b) schistand (c) sandstone, and
corresponding photomicrographs (d, e, and f).
Collected from
Malanjkhand Copper
Project, Malanjkhand,
India; UCIL mine at
Jaduguda, India;
and SCCL,
Kothagudem, India
respectively.

5. Dataset
: : : : : : : :
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: : : : : : : :
Total samples: 60
Total input features: 5
Total output feature(s): 1
Training set: 40 randomly
selected samples)
Test set: 20 randomly
selected samples)

6. Computational Intelligence:
Fuzzy Inference System (FIS): Adaptive Neuro-Fuzzy Inference System (ANFIS):
Multi-layer Perceptron (MLP): Heterogeneous Flexible Neural Tree (HFNT):

7. Model Evaluation Criteria and Results
• Root mean squared error (𝑒)
• Correlation coefficient (𝑟)
• Squared of correlation coefficient (𝑟2)
• Number of parameters in the developed model (𝜒)
[1] Mishra DA, Srigyan M, Basu A, Rokade PJ (2015) Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests. Int J Rock Mech Min Sci 80:418{424

8. Model Evaluation Criteria and Results
• Root mean squared error (𝑒)
• Correlation coefficient (𝑟)
• Squared of correlation coefficient (𝑟2)
• Number of parameters in the developed model (𝜒)
[1] Mishra DA, Srigyan M, Basu A, Rokade PJ (2015) Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests. Int J Rock Mech Min Sci 80:418{424
The
Best
Model

9. Model Evaluation Criteria and Results
• Root mean squared error (𝑒)
• Correlation coefficient (𝑟)
• Squared of correlation coefficient (𝑟2)
• Number of parameters in the developed model (𝜒)
[1] Mishra DA, Srigyan M, Basu A, Rokade PJ (2015) Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests. Int J Rock Mech Min Sci 80:418{424
Best 𝑒, 𝑟,
𝑟2, and 𝜒

10. Light-weight efficient model (HFNTM)
HFNTM: Ojha et al. (2016) Ensemble of heterogeneous flexible neural trees using multiobjective genetic programming, Applied Soft Computing

11. Feature Selection

12. Feature Selection
Is-50 is the most
significate index
test

13. Conclusion
• UCS from the index tests was best estimated by a light weight a
multiobjective heterogeneous flexible neural tree (HFNTM)
• Among the different types of index tests—destructive indices, non-
destructive indices, and physical properties—the destructive
mechanical rock indices BPI and Is-50 are found to be the best index
tests to estimate the UCS.

14. Thankyou
Varun Ojha
vkojha@ieee.org
Deepak Mishra
deepakamban@gmail.com