Cylindrical cavity expansion in Hoek-Brown rock: analytical Solution with experimental Validation through pressuremeter tests in marls and numerical modeling

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4. Cylindrical cavity expansion in Hoek-Brown rock: analytical Solution with experimental Validation through pressuremeter tests in marls and numerical modeling

The cylindrical cavity expansion problem is an important aspect of geotechnical engineering, with applications in tunneling, geothermal exploration, drilling activities, and underground construction. This study develops a closed-form analytical solution for the expansion of cylindrical cavities in rock masses modeled as elastic-plastic media using the Hoek-Brown (H-B) yield criterion. The solution uses the Lambert W function to express stress distributions, while strains are calculated based on a non-associated plastic flow rule. Key results include predictions for the yielding pressure, plastic zone extent, and stress profiles around the cavity.

To validate the analytical model, pressuremeter tests were conducted in marls, providing experimental data for comparison. Finite element analyses (FEA) were also performed using PLAXIS 2D, with the Hoek-Brown criterion implemented to ensure consistency. Calibration of the numerical model confirmed the accuracy of the simulations for the cavity expansion process.

A comparison of the analytical solution, experimental data, and numerical results shows good agreement, supporting the reliability of the proposed method. While some discrepancies are observed, particularly in the transition between elastic and plastic zones, the analytical approach offers a useful tool for predicting key parameters such as yielding pressure, stress distribution, and plastic zone extent. These results suggest that the analytical method can serve as an efficient alternative to numerical simulations in certain geotechnical applications, particularly when computational efficiency is desired. This study contributes to a deeper understanding of cavity expansion mechanics in rock masses and provides practical insights for the design and analysis of underground structures.

8th International Symposium on Pressuremeters (ISP2025)

Comparative Studies and Correlations