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Rock Mass Homogenization and Numerical Classification

By Michel Chalhoub

CRC Press – 2015 – 200 pages

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    January 1st 2015
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In the modelling or design phase of many mining or civil projects conducted in rock masses, the designer is confronted with a set of questions that is not always easy to answer. This is mainly due to the anisotropy and heterogeneity of the fractured medium, and to the complexity of the fractures’ geometry and their mechanical parameters. In this work, a practical tool is provided for the purpose of numerical homogeneization and modelling of fractured mediums, using the finite elements method. Through this, this book intends to give an answer to, amongst others:

  • the estimation of elastoplastic properties of rock;
  • the estimation of discontinuities by means of elementary tests;
  • the most appropriate model to approach the rock’s mechanical behaviour;
  • the possibility of replacing fractured medium by a homogeneous equivalent one;
  • size estimation of the mechanical representative elementary volume (REV);
  • selecting the most suitable type of loading for numerical large-scale stress-strain tests;
  • the calculation of homogenized elastoplastic properties of a rock mass or a fractured medium with the finite element method.

Besides dealing with a considerable number of practical questions, in a more fundamental way, this guide presents a new numerical classification of some typical rock masses. With only a few mechanical and geometrical parameters of rock and discontinuities, the designer can refer to the classification tables to derive the elastic properties of a rock mass.

This volume is intended for professionals, researchers and advances students in civil, geological and mining engineering and earth sciences working on rock mass and masonry structures.


1. Structure and behavior of rock masses

1. Geometrical structure of rock masses

1.1 Geological aspect

1.2 Geometrical parameters of discontinuities

1.3 Geometrical model of discontinuities

2. Rocks

2.1 Geological classification of rocks

2.2 Mechanical behavior of rocks

3. Discontinuities

3.1 Morphology of a discontinuity

3.2 Mechanical behavior of a discontinuity

3.2.1 Behavior under a normal stress Empirical tests and observations Normal stress-strain model

3.2.2 Behavior under a shear stress Mechanical test and strength criteria Filling material Shear stress-strain model

3.3 Practical determination of a discontinuity’s mechanical parameters

4. Conclusion

2.Existing rock mass classifications

1. Geomechanical classifications

1.1 Types and interests of existing rock mass classifications

1.2 The Rock Mass Rating RMR

1.3 The Q-system

1.4 The Geological Strength Index (GSI)

1.5 Comments on a variety of rock mass classification systems

2. Identification of compliance and strength parameters

2.1 Empirical approaches

2.1.1 Mechanical properties according to RMR and Q-system

2.1.2 Mechanical properties according to GSI

2.2 Analytical approaches

3. Conclusion

3.Numerical homogenization of fractured mediums

1. The theory of homogenization applied to fractured mediums

2. Interpretation of numerical homogenized results in elasticity

2.1 Hook’s law

2.2 Theory of elasticity applied to rock masses in 2D

2.3 Homogenization problems in 2D

2.4 Numerical modeling

2.4.1 Descritized form of homogenized stress and strain

2.4.2 A new loading pattern independent of nodes’ coordinates of the REV contour Differences between numerical loading types Numerical calculation of the compliance tensor

2.4.3 A traditional loading depending on the nodes’ coordinates of the REV contour

2.5 Ellipsoidal adjustment of Saint-Venant

2.5.1 Principles and interests of the ellipsoidal elasticity theory for rock masses

2.5.2 Ellipsoidal adjustment of homogenized results

3. Interpretation of numerical homogenized results in plasticity

3.1 Selection of the numerical loading pattern

3.2 Homogenized strength’s calculation

4. Conclusion

4. Finite Elements numerical modeling method

1. Modeling of the fractured rock mass mechanical behavior

1.1 Models in stability

1.2 Models in deformation

1.3 Mechanical behavior model of rock and joints

1.4 Mathematical formulation of the “joint” finite element

2. Procedure of numerical modeling and homogenization

2.1 Fractures’ sets generation

2.1.1 Generation of disks in a 3D finite volume size

2.1.2 Research of fractures’ trace in a plan

2.2 The REV geometrical size’s calculation

2.2.1 Criteria of a mechanical REV calculation

2.2.2 Geometrical REV: mean spacing calculation

2.3 Some useful techniques to avoid difficulties in mesh generation and nodes’ duplication

2.4 Numerical loading and homogenized compliance tensor

2.4.1 Selection of the adequate numerical loading pattern

2.4.2 Calculation of the homogenized compliance tensor

3. Numerical homogenization tool: HELEN

3.1 Pre-processing modules

3.1 Post-processing modules

4. A case study: Granitic rock mass

4.1 Vienne rock mass

4.2 Numerical procedure and results

4.2.1 Geometrical REV

4.2.2 Mechanical REV and elastoplastic homogenized properties

5. Conclusion

5. Numerical rock mass classification of some typical rock masses

1. Selection and presentation of the studied rock masses

2. The REV size

2.1 fractures’ sets generation

2.2 Calculation of the REV size

2.3 Analytical formulation of the REV size

3. Illustration of mesh generation and rock mass deformation

4. Numerical classification results

4.1 Results’ verifications

4.2 Results’ analysis

4.2.1 General remarks

4.2.2 Results of one set of fractures

4.2.3 Results of two sets of fractures

5. Analytical formulation of numerical results

5.1 Adjustment procedure

5.2 Adjustment results

5.2.1 Adjustment of Young Modulus (one set of fractures)

5.2.2 Adjustment of Shear Modulus (one set of fractures)

5.2.3 Adjustment of Young Modulus (Two sets of fractures)

5.2.4 Adjustment of Shear Modulus (Two sets of fractures)

6. A case study: sedimentary rock mass

6.1 Kousba rock mass

6.2 Geometrical and mechanical properties of rock and fractures 182

6.3 Calculation of the homogenized properties using the numerical classification tables

7. Conclusion


Appendix 1 : Geomechanical classifications

Appendix 2 : Homogenization theory for fractured mediums

Appendix 3 : Geometry of the analyzed sets of fractures

Appendix 4 : Numerical rock mass classification

Appendix 5 : Numerical tool HELEN

Author Bio

Dr Michel Chalhoub obtained his PhD degree from the Ecole des Mines (Mines ParisTech) in Paris. As a structural engineer and an Assistant Professor at a number of Lebanese universities, he currently combines his consulting engineering firm with his academic work, and conducts researches on numerical modeling and homogenization of fractured mediums, such as rock masses and masonry structures. For his studies of rock mass, Dr Chalhoub was nominated a finalist for the 'Rocha Medal', the highest achievement award in Rock Mechanics, awarded by the International Society for Rock Mechanics (ISRM).

Name: Rock Mass Homogenization and Numerical Classification (Hardback)CRC Press 
Description: By Michel Chalhoub. In the modelling or design phase of many mining or civil projects conducted in rock masses, the designer is confronted with a set of questions that is not always easy to answer. This is mainly due to the anisotropy and heterogeneity of the fractured...
Categories: Rock Mechanics, Civil, Environmental and Geotechnical Engineering, Mining, Mineral & Petroleum Engineering