Abstract #

This paper revisits the stress update procedure for the Hoek-Brown plasticity model, enhanced by incorporating a Rankine type tension cut-off failure criterion. The study focuses on limiting tensile stresses in weak rock masses with low tensile strength and improving the robustness of the stress return mapping algorithm. The paper thoroughly discusses all potential scenarios within the framework of single- and multi-surface plasticity, detailing the stress return from inadmissible trial stresses where neither the Hoek-Brown yield surface nor its derivative can be evaluated. The procedures were implemented and verified using the GEO5 FEM software.

Technical Relevance #

This document is crucial for geotechnical engineers and researchers working with rock mechanics and advanced numerical methods. The detailed explanation of the stress return mapping scheme enhances the understanding of complex rock behavior under various stress conditions, making it a valuable resource for those using the Hoek-Brown criterion in FEM analysis, particularly when dealing with weak rock masses.

Target Audience #

The document is intended for geotechnical engineers, civil engineers, researchers, and professionals involved in rock mechanics, numerical analysis, and the application of FEM in geotechnical engineering. It is particularly relevant for those specializing in the modeling of rock mass behavior under complex loading conditions.

Software and Methodology #

The study employs the GEO5 FEM software to implement the return mapping scheme. The methodology involves developing a stress update algorithm that incorporates both the Hoek-Brown model and the Rankine criterion to manage scenarios where the trial stresses exceed the tensile strength of the rock mass. The paper details the application of this combined approach in single- and multi-surface plasticity contexts, providing a robust framework for handling inadmissible trial stresses in numerical simulations.

Process Description #

The paper begins with an introduction to the challenges of applying the Hoek-Brown criterion in cases where tensile stresses exceed the rock mass’s tensile strength. It then describes the development of the stress update algorithm, focusing on the integration of the Rankine tension cut-off criterion. The process includes detailed equations governing the Hoek-Brown yield function, plastic potential, and the Rankine yield function. The study also covers the implementation of the return mapping scheme, including single yield surface return strategies and multi-surface plasticity for triaxial stress states.

Main Findings #

The study concludes that incorporating a Rankine type tension cut-off into the Hoek-Brown model significantly improves the robustness of the stress return mapping procedure, particularly in weak rock masses with low tensile strength. The combined approach effectively manages inadmissible trial stresses, ensuring that the stress update process remains stable and accurate. The implementation of this scheme in the GEO5 FEM software has been thoroughly tested, demonstrating its reliability and effectiveness in various geotechnical scenarios.

Practical Applications #

The findings from this study are directly applicable to the numerical modeling of rock masses, particularly in scenarios where tensile failure may occur. Engineers and researchers can use the insights gained to improve the accuracy and stability of their FEM analyses, ensuring that the behavior of rock masses under complex stress conditions is accurately captured. The methodology is especially relevant for projects involving tunneling, mining, and other underground constructions where rock mass behavior is critical to safety and performance.

Limitations and Considerations #

The document acknowledges that while the return mapping scheme improves the robustness of stress update procedures, its accuracy depends on the quality of the input data, particularly the rock mass parameters used in the Hoek-Brown model. Engineers should ensure that they conduct thorough site-specific investigations to obtain reliable data for their simulations. The study also emphasizes the importance of ongoing testing and validation to refine the algorithm and extend its applicability to different rock types and geotechnical conditions.

Conclusions #

The paper concludes that the return mapping scheme for the Hoek-Brown model, enhanced by the Rankine tension cut-off, is an effective tool for managing stress updates in FEM simulations of rock masses. The approach addresses the challenges of modeling weak rock masses with low tensile strength, providing a reliable and stable framework for geotechnical engineers and researchers. The implementation in GEO5 FEM software demonstrates the practicality of the proposed methodology, offering a valuable addition to the tools available for rock mechanics analysis.

Related Resources #

Further reading includes studies on the Hoek-Brown failure criterion, research on the integration of tension cut-off models in FEM, and case studies on the application of these methods in geotechnical engineering. Additional resources on the use of FEM in rock mechanics and the management of tensile failures in weak rock masses can provide deeper insights into optimizing geotechnical simulations.

📥 Download LINK