1 ROCK MECHANIC 21

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ROCK MECHANICS IN PETROLEUM ENGINEERING
TOPIC: THERMO-MECHANICAL ROCK FRACTURE PREDICTION VIA THE MOHR-COULOMB
FAILURE CRITERION
NAME
KOUDJOU DONATIN DAVID-JOS
ID
202427000006
SCHOOL
PETROLEUM ENGINEERING
SCHOOL
MAJOR
Field Development Engineering oil and
gas
ADVISOR
Dr Hao Yu
Date: 2025.06.13

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Table of Contents
Abstract ........................................................................................................................................................ 3
Introducon .................................................................................................................................................. 4
I. Literature Review ....................................................................................................................................... 5
1. Previous studies .................................................................................................................................................. 5
2. Recent Studies and the purpose of this study ...................................................................................................... 6
II. Methodology ............................................................................................................................................ 7
1. Theorecal Framework ....................................................................................................................................... 7
2. Algorithm Design and Implementaon .............................................................................................................. 11
III. Case Study Applicaon ........................................................................................................................... 14
1. Mathemacal model of the rock to be studied ................................................................................................. 14
2. Random Generaon of stress values for Geomechanical Analysis ...................................................................... 14
3. Generaon of 150 Mohr circles with fracture predicons and export them to an Excel le with Python code .... 14
4. Concise overview of each major step in the code .............................................................................................. 15
IV. Results Analysis ...................................................................................................................................... 16
1. Graphical Analysis (Mohr Circles) ...................................................................................................................... 16
2. Hyperparameter Opmizaon (GridSearchCV) .................................................................................................. 16
3. Performance of the Best Model......................................................................................................................... 17
4. Learning and Validaon Curves ......................................................................................................................... 17
5. Predicons on Test Examples ............................................................................................................................ 17
V. Discussion of Results ............................................................................................................................... 19
1. Interpretaon of Mohr Circles and Observed Trends ......................................................................................... 19
2. Impact of Hyperparameter Opmizaon and Model Reliability ......................................................................... 19
3. Model Predicon Accuracy and Limitaons ....................................................................................................... 19
VI. Study limitaons .................................................................................................................................... 20
VII. Applicaons .......................................................................................................................................... 20
CONCLUSION .............................................................................................................................................. 21
REFERENCES ............................................................................................................................................... 22
APPENDIX ................................................................................................................................................... 23
Generaon of 150 Mohr circles with fracture predicons and export them to an Excel le with Python code ........ 23
PYTHON CODE FOR THE DATA OF THE 150 CIRCLES CONSTRUCTION (open this le in Microso Excel) .................. 27
PYTHON CODE EXECUTED IN THIS STUDY .............................................................................................................. 32

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Abstract
Understanding the thermo-mechanical behavior of low-porosity rocks is crucial for predicting fracture
development in various geological settings. This study examines how temperature variations impact the
mechanical properties of limestones and Senonian formations. The Mohr-Coulomb failure criterion provides
a theoretical framework for modeling rock stability under combined thermal and mechanical stress. To
enhance prediction accuracy, machine learning algorithms analyze complex interactions between stress states,
cohesion, and thermal effects. The study incorporates experimental and numerical simulations to validate the
proposed model. The results of some studies show that rock cohesion significantly decreases beyond 500°C,
leading to an increased likelihood of fracture. A dataset of 150 Mohr circles was generated, demonstrating that
fractures occur in approximately 16.7% of cases under thermal stress. The optimized machine learning model
achieves 94.44% prediction accuracy, effectively identifying intact and fractured conditions. However,
fracture recall is 73%, indicating some misclassifications in high-temperature scenarios. These findings
contribute to refining geo-mechanical models for engineering applications particularly in rock mechanics in
petroleum engineering, including geothermal energy, deep mining, and underground storage. Future research
will focus on experimental validation and expanding the dataset to include additional rock types. Integrating
thermal effects into predictive frameworks enhances infrastructure safety and improves decision-making in
high-risk geological environments.
Keywords: Thermo-mechanical behavior, rock fracture prediction, Mohr-Coulomb criterion, machine learning,
geomechanics, rock mechanic in petroleum engineering, stability assessment.

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Introduction
Understanding the thermo-mechanical behavior of low-porosity rocks, such as limestones and Senonian
formations, is essential for various geological and particularly in rock mechanics in petroleum engineering.
These rocks, characterized by their low porosity and dense structure, respond specifically to temperature
variations and mechanical stresses. The Mohr-Coulomb failure criterion provides a robust framework for
analyzing their behavior under combined thermo-mechanical loading. However, the influence of temperature
on the strength and deformation of these materials requires further investigation to enhance predictive model
accuracy. That is why we title our topic:” Thermo-Mechanical Rock Fracture Prediction via the Mohr-
Coulomb Failure Criterion”. This study aims to refine the prediction of fracture behavior in low-porosity
rocks by integrating thermo-mechanical effects and validating the results using machine learning. The specific
objectives include firstly investigating the influence of temperature on the mechanical properties of limestones
and Senonian formations. Secondly, developing an advanced model that incorporates thermal and mechanical
stresses within the Mohr-Coulomb framework. Finally, validating the proposed model through experimental
and numerical simulations, as well as machine learning algorithms, to improve prediction accuracy. By
integrating thermal effects and machine learning validation into the Mohr-Coulomb failure criterion, the
findings provide valuable insights for industries relying on these rock formations. The proposed approach
aims to enhance the safety, efficiency, and reliability of engineering projects involving thermo-mechanical
interactions while leveraging machine learning capabilities to optimize predictive models and better
understand the fracture mechanisms of dense and low-porosity rocks.

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I. Literature Review
1. Previous studies
1. Tian, H., Ziegler, M., Kempka, T., & Xu, N.-X. (2012). A modified Mohr-Coulomb failure criterion for intact
granites exposed to high temperature. Rock Engineering and Technology for Sustainable Underground
Construction: Proceedings of the ISRM International Symposium (EUROCK 2012), Stockholm, Sweden, May
28–30, 1–12.
Rock engineering in high-temperature environments is a major challenge for scientists and engineers. Rocks
can experience extreme temperatures in various contexts, such as nuclear waste storage, geothermal heat
extraction, geological CO₂ storage, and deep mining. These high temperatures alter the mechanical properties
of rocks, making conventional failure criteria insufficient to describe their behavior. This study proposes a
modification to the Mohr-Coulomb failure criterion to better represent thermo-mechanical effects on the
strength of granites exposed to high temperatures. The model accounts for thermal damage and confinement
conditions, enabling a more reliable prediction of rock strength in extreme environments. The authors
reviewed experimental studies on the mechanical properties of granites subjected to high temperatures. The
experimental results show that elasticity, compressive strength, and cohesion decrease as temperature
increases, particularly beyond 500-600°C, where mechanical strength can drop to less than 50% of its ambient
temperature value. The proposed model modifies the Mohr-Coulomb criterion by introducing a tension cut-
off, correcting the overestimation of tensile strength in the classical model. This new criterion incorporates
temperature-dependent parameters, such as cohesion and internal friction angle, providing a more accurate
representation of granite behavior under high temperatures. The study demonstrates that the modified Mohr-
Coulomb criterion offers better predictions of granite strength under extreme thermal conditions. The model
is also applicable to other types of rocks exposed to high temperatures. Numerical analysis indicates that the
failure zone predicted by the modified model is larger than that calculated with the classical model, validating
the need to integrate a thermo-mechanical failure criterion in rock stability studies.
2. Rene Houpert;Francoise Homand-Etienne, Influence of Temperature on the Mechanical Behavior of
rocks, Paper presented at the 4th ISRM Congress, Montreux, Switzerland, September 1979. Paper
Number: ISRM-4CONGRESS-1979-025. Published: September 02 1979. Onepetro.com
R. Houpert & F. Homand-Etienne (1979) studied the temperature effects on rock mechanical behavior at the
4th ISRM Congress, Montreux (Paper ISRM-4CONGRESS-1979-025). This article in French version presents
an experimental study on the mechanical behavior of rocks as a function of temperature, under low
confinement (0 to 20 MPa), which is relevant for underground storage or in situ gasification projects. The
mechanical behavior of rocks varies depending on temperature. This study explores the impact of thermal
variations on material microcracking and its consequences on the propagation of elastic waves, stress-strain
curves, and compressive strength. The tests were conducted on two granites (Senones and Remiremont) and
one marble (Carrara), with temperatures ranging from 180°C to 600°C. Crystalline rocks develop microcracks
under the effect of thermal variations due to differential expansion of mineral grains. This microcracking,
mainly intergranular, alters the cohesion and mechanical strength of the material. The granites of Senones and
Remiremont show a linear reduction in the velocity of elastic waves up to 500°C, followed by a sharp drop
beyond this point. The marble from Carrara, composed exclusively of calcite crystals, undergoes similar
variations due to the thermal anisotropy of calcite. Following compression tests at different temperatures,