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5. Comparative verification of hydro-mechanical fracture behavior: Task G of international research project DECOVALEX–2023

Author

Mollaali, Mostafa, Kolditz, Olaf, Hu, Mengsu, Park, Chan–Hee, Park, Jung–Wook, McDermott, Christopher Ian, Chittenden, Neil, Bond, Alexander, Yoon, Jeoung Seok, Zhou, Jian, Pan, Peng–Zhi, Liu, Hejuan, Hou, Wenbo, Lei, Hongwu, Zhang, Liwei, Nagel, Thomas, Barsch, Markus, Wang, Wenqing, Nguyen, Son, Kwon, Saeha, Lee, Changsoo, and Yoshioka, Keita

Subjects
Engineering, Resources Engineering and Extractive Metallurgy, Fracture mechanics, Numerical method, Code comparison, Benchmarking, DECOVALEX-2023, Civil Engineering, Mining & Metallurgy, Civil engineering, Resources engineering and extractive metallurgy
Abstract

Numerical simulations become a necessity when experimental approaches cannot cover the required physical and time scale of interest. One of such area is a simulation of long-term host rock behaviors for nuclear waste disposal and simulation tools involved in the assessment must go through rigorous validation tests. The DECOVALEX project (Development of COupled models and their VAlidation against EXperiments) is dedicated to this purpose by international participants.a This work is part of the ongoing phase DECOVALEX–2023 (D–2023, Task G) particularly aiming to simulate fracture behaviors under various conditions. Here, we cross-verified a variety of numerical methods including continuous and discontinuous approaches against four benchmark exercises with emphasis on numerical accuracy and parameterization of the various numerical approaches. The systematic inter-comparisons of test cases highlight advantages and disadvantages of the different numerical models. Numerical details on discretization effects (e.g. mesh density and orientation) and domain size were investigated in detail for practical applications. It became evident that meticulous attention to mesh resolution and domain size is imperative for achieving accurate numerical simulations, even for static cracks. Moreover, when comparing numerical methods to closed-form solutions for static cracks, all models successfully reproduced the maximum crack opening but encountered challenges near the crack tips. Finally, the paper discusses how to convert between and therefore compare parameters of various numerical approaches. Our benchmark studies reveal that each model necessitates a distinct number of parameters, even in simple scenarios like static crack aperture benchmarks. It is generally more practical to employ fewer parameters to mitigate model over-parameterization and enhance experimental feasibility.

Published
2023

6. Model Analysis

Author

Chaudhry, Aqeel Afzal, Nagel, Thomas, Zhao, Juan, Düsterloh, Uwe, Zhao, Jingbo, Chen, Liang, Wang, Ju, Liu, Yuemiao, Cao, Shengfei, Zhang, Qi, Shao, Haibing, Chen, Chaofan, Yuan, Tao, Lu, Renchao, Fischer, Cornelius, Kolditz, Olaf, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Shao, Haibing, editor, Wang, Ju, editor, Schäfer, Thorsten, editor, Zhang, Chun-Liang, editor, Geckeis, Horst, editor, Nagel, Thomas, editor, and Düsterloh, Uwe, editor

Published
2024
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7. Introduction

Author

Shao, Haibing, Wang, Ju, Schäfer, Thorsten, Zhang, Chun-Liang, Geckeis, Horst, Nagel, Thomas, Düsterloh, Uwe, Kolditz, Olaf, Shao, Hua, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Shao, Haibing, editor, Wang, Ju, editor, Schäfer, Thorsten, editor, Zhang, Chun-Liang, editor, Geckeis, Horst, editor, Nagel, Thomas, editor, and Düsterloh, Uwe, editor

Published
2024
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9. Synthesis and Outlook

Author

Shao, Haibing, Wang, Ju, Schäfer, Thorsten, Zhang, Chun-Liang, Geckeis, Horst, Nagel, Thomas, Düsterloh, Uwe, Kolditz, Olaf, Shao, Hua, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Shao, Haibing, editor, Wang, Ju, editor, Schäfer, Thorsten, editor, Zhang, Chun-Liang, editor, Geckeis, Horst, editor, Nagel, Thomas, editor, and Düsterloh, Uwe, editor

Published
2024
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10. Fazit und Ausblick

Author

Randow, Jakob, Bucher, Anke, Görke, Uwe-Jens, Grimm, Rüdiger, Hastreiter, Nele, Kolditz, Olaf, Lubashevsky, Katrin, Richter, Simon, Rink, Karsten, Schönfelder, Stephan, Shao, Haibing, Vienken, Thomas, Zschoke, H. Konstanze, Bucher, Anke, editor, Shao, Haibing, editor, Grimm, Rüdiger, editor, Schönfelder, Stephan, editor, Randow, Jakob, editor, Vienken, Thomas, editor, Rink, Karsten, editor, and Zschoke, Konstanze, editor

Published
2024
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11. Einführung in das Verbundvorhaben Easyquart

Author

Bucher, Anke, Görke, Uwe-Jens, Grimm, Rüdiger, Hastreiter, Nele, Kolditz, Olaf, Lubashevsky, Katrin, Randow, Jakob, Richter, Simon, Rink, Karsten, Schönfelder, Stephan, Shao, Haibing, Vienken, Thomas, Zschoke, H. Konstanze, Bucher, Anke, editor, Shao, Haibing, editor, Grimm, Rüdiger, editor, Schönfelder, Stephan, editor, Randow, Jakob, editor, Vienken, Thomas, editor, Rink, Karsten, editor, and Zschoke, Konstanze, editor

Published
2024
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12. Orthogonal decomposition of anisotropic constitutive models for the phase field approach to fracture

Author

Ziaei-Rad, Vahid, Mollaali, Mostafa, Nagel, Thomas, Kolditz, Olaf, and Yoshioka, Keita

Subjects
Mathematics - Numerical Analysis
Abstract

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the tension-compression asymmetry. This decomposition follows a variational framework, satisfying the orthogonality condition for anisotropic materials. This implies that the present model can be applied to arbitrary anisotropic elastic behavior in a three-dimensional setting. On this basis, we generalize two existing models for tension-compression asymmetry in isotropic materials, namely the volumetric-deviatoric model and the no-tension model, towards materials with anisotropic nature. Two benchmark problems, single notched tensile shear tests, are used to study the performance of the present model. The results can retain the anisotropic constitutive behavior and the tension-compression asymmetry in the crack response, and are qualitatively in accordance with the expected behavior for orthotropic materials. Furthermore, to study the direction of maximum energy dissipation, we modify the surface integral based energy release computation, $G_\theta$, to account only for the crack-driving energy. The computed energies with our proposed modifications predict the fracture propagation direction correctly compared with the standard G-theta method.

Published
2022
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15. A systematic model- and experimental approach to hydro-mechanical and thermo-mechanical fracture processes in crystalline rocks

Author

Kolditz, Olaf, McDermott, Christopher, Yoon, Jeoung Seok, Mollaali, Mostafa, Wang, Wenqing, Hu, Mengsu, Sasaki, Tsubasa, Rutqvist, Jonny, Birkholzer, Jens, Park, Jung-Wook, Park, Chan-Hee, Liu, Hejuan, Pan, Peng–Zhi, Nagel, Thomas, Nguyen, Son, Kwon, Saeha, Lee, Changsoo, Kim, Kwang-Il, Alexander, Bond, Hadgu, Teklu, Wang, Yifeng, Zhuang, Li, Yoshioka, Keita, Cunha, Gonçalo Benitez, and Fraser-Harris, Andrew

Published
2025
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18. Synthesis and Outlook

Author

Kolditz, Olaf, Cajuhi, Tuanny, Günther, Ralf-Michael, Steeb, Holger, Wuttke, Frank, Yoshioka, Keita, Grunwald, Norbert, Nagel, Thomas, Lohmann, Gerrit, Series Editor, Notholt, Justus, Series Editor, Rabassa, Jorge, Series Editor, Unnithan, Vikram, Series Editor, Kolditz, Olaf, editor, Yoshioka, Keita, editor, Cajuhi, Tuanny, editor, Günther, Ralf-Michael, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2023
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19. Introduction to GeomInt2

Author

Nagel, Thomas, Cajuhi, Tuanny, Günther, Ralf-Michael, Maßmann, Jobst, Wuttke, Frank, Yoshioka, Keita, Kolditz, Olaf, Lohmann, Gerrit, Series Editor, Notholt, Justus, Series Editor, Rabassa, Jorge, Series Editor, Unnithan, Vikram, Series Editor, Kolditz, Olaf, editor, Yoshioka, Keita, editor, Cajuhi, Tuanny, editor, Günther, Ralf-Michael, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2023
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20. Virtual Reality and Computational Efficiency

Author

Rink, Karsten, Graebling, Nico, Bilke, Lars, Buchwald, Jörg, Fischer, Thomas, Lehmann, Christoph, Meisel, Tobias, Naumov, Dmitri, Wang, Wenqing, Yoshioka, Keita, Kolditz, Olaf, Lohmann, Gerrit, Series Editor, Notholt, Justus, Series Editor, Rabassa, Jorge, Series Editor, Unnithan, Vikram, Series Editor, Kolditz, Olaf, editor, Yoshioka, Keita, editor, Cajuhi, Tuanny, editor, Günther, Ralf-Michael, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2023
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28. Artificial intelligence and visual analytics in geographical space and cyberspace: Research opportunities and challenges

Author

Chen, Min, Claramunt, Christophe, Çöltekin, Arzu, Liu, Xintao, Peng, Peng, Robinson, Anthony C., Wang, Dajiang, Strobl, Josef, Wilson, John P., Batty, Michael, Kwan, Mei-Po, Lotfian, Maryam, Golay, François, Joost, Stéphane, Ingensand, Jens, Senousi, Ahmad M., Cheng, Tao, Bandrova, Temenoujka, Konecny, Milan, Torrens, Paul M., Klippel, Alexander, Li, Songnian, Zhang, Fengyuan, He, Li, Wang, Jinfeng, Ratti, Carlo, Kolditz, Olaf, Lin, Hui, and Lü, Guonian

Published
2023
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31. Synthesis and Outlook

Author

Kolditz, Olaf, Görke, Uwe-Jens, Konietzky, Heinz, Maßmann, Jobst, Nest, Mathias, Steeb, Holger, Wuttke, Frank, Nagel, Thomas, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Konietzky, Heinz, editor, Maßmann, Jobst, editor, Nest, Mathias, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2021
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32. Data Management

Author

Helbig, Carolin, Görke, Uwe-Jens, Nest, Mathias, Pötschke, Daniel, Sattari, Amir Shoarian, Schmidt, Patrick, Vowinckel, Bernhard, Yoshioka, Keita, Kolditz, Olaf, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Konietzky, Heinz, editor, Maßmann, Jobst, editor, Nest, Mathias, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2021
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33. Model-Experiment-Exercises (MEX)

Author

Vowinckel, Berhard, Frühwirt, Thomas, Maßmann, Jobst, Nagel, Thomas, Nest, Mathias, Ptschke, Daniel, Rölke, Christopher, Sattari, Amir Shoarian, Schmidt, Patrick, Steeb, Holger, Yoshioka, Keita, Ziefle, Gesa, Kolditz, Olaf, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Konietzky, Heinz, editor, Maßmann, Jobst, editor, Nest, Mathias, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2021
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34. Introduction to GeomInt

Author

Nagel, Thomas, Görke, Uwe-Jens, Konietzky, Heinz, Maßmann, Jobst, Nest, Mathias, Steeb, Holger, Wuttke, Frank, Kolditz, Olaf, Kolditz, Olaf, Series Editor, Shao, Hua, Series Editor, Wang, Wenqing, Series Editor, Görke, Uwe-Jens, Series Editor, Bauer, Sebastian, Series Editor, Konietzky, Heinz, editor, Maßmann, Jobst, editor, Nest, Mathias, editor, Steeb, Holger, editor, Wuttke, Frank, editor, and Nagel, Thomas, editor

Published
2021
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37. DECOVALEX-2015: an international collaboration for advancing the understanding and modeling of coupled thermo-hydro-mechanical-chemical (THMC) processes in geological systems

Author

Birkholzer, Jens T, Bond, Alexander E, Hudson, John A, Jing, Lanru, Tsang, Chin-Fu, Shao, Hua, and Kolditz, Olaf

Subjects
Earth Sciences, Information and Computing Sciences, Geology, Physical Geography and Environmental Geoscience, Civil Engineering, Physical geography and environmental geoscience
Published
2018

38. Digitalisation for nuclear waste management: predisposal and disposal

Author

Kolditz, Olaf, Jacques, Diederik, Claret, Francis, Bertrand, Johan, Churakov, Sergey V., Debayle, Christophe, Diaconu, Daniela, Fuzik, Kateryna, Garcia, David, Graebling, Nico, Grambow, Bernd, Holt, Erika, Idiart, Andrés, Leira, Petter, Montoya, Vanessa, Niederleithinger, Ernst, Olin, Markus, Pfingsten, Wilfried, Prasianakis, Nikolaos I., Rink, Karsten, Samper, Javier, Szöke, István, Szöke, Réka, Theodon, Louise, and Wendling, Jacques

Published
2023
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44. On Advantages of the Kelvin Mapping in Finite Element Implementations of Deformation Processes

Author

Nagel, Thomas, Görke, Uwe-Jens, Moerman, Kevin M., and Kolditz, Olaf

Subjects
Physics - Computational Physics
Abstract

Classical continuum mechanical theories operate on three-dimensional Eu-clidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the relations into a matrix-vector format. This transformation is usually performed using the so-called Voigt mapping. This mapping does not preserve tensor character leaving significant room for error as stress and strain quantities follow from different mappings and thus have to be treated differently in certain mathematical operations. Despite its conceptual and notational difficulties having been pointed out, the Voigt mapping remains the foundation of most current finite element programmes. An alternative is the so-called Kelvin mapping which has recently gained recognition in studies of theoretical mechanics. This article is concerned with benefits of the Kelvin mapping in numerical modelling tools such as finite element software. The decisive difference to the Voigt mapping is that Kelvin's method preserves tensor character, and thus the numerical matrix notation directly corresponds to the original tensor notation. Further benefits in numerical implementations are that tensor norms are calculated identically without distinguishing stress or strain-type quantities and tensor equations can be directly transformed into matrix equations without additional considerations. The only implementational changes are related to a scalar factor in certain finite element matrices and hence, harvesting the mentioned benefits comes at very little cost.

Published
2016
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48. GeomInt-Discontinuities in Geosystems From Lab to Field Scale.

Author

Kolditz, Olaf, Cajuhi, Tuanny, Günther, Ralf-Michael, Kolditz, Olaf, Nagel, Thomas, Steeb, Holger, Wuttke, Frank, and Yoshioka, Keita

Subjects
Earth sciences, Environmental management, Waste management, Benchmarking, Computational Mechanics, Energy Storage, Geoenergies, Radioactive Waste Management, Rock Mechanics Laboratories, Underground Research Laboratories, Virtual Reality
Abstract

Summary: This is an open access book. In view of growing conflicts over strategic georesources, the use of the geological subsurface in the sense of a regional resource is becoming increasingly important. In this context, georeservoirs are playing an important role for the energy transition not only as a source of energy but also as a storage facility and deep geological disposal for energy waste. The success of the energy transition also depends to a large extent on the efficient and safe use of underground resources. This book complements the previous basic book (GeomInt-Integrity of Host Rocks) with a series of application examples in different rock formations, clay, salt, and crystalline. The methodology developed in GeomInt is used, among others, in the Mont Terri underground research laboratory (Opalinus Clay), in the large borehole test in Springen (salt rock) and in the "Reiche Zeche" teaching and research mine (crystalline rock). In addition, new methodological developments are also taken up in experiments and models and embedded in workflows for geotechnical system analyses. The present book summarizes the results of the collaborative project "GeomInt2: Geomechanical integrity of host and barrier rocks - experiment, modeling and analysis of discontinuities" within the program: Geo Research for Sustainability (GEO: N) of the Federal Ministry of Education and Research (BMBF).

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