journal article·2025-09-18Open access

Lode Angle-Dependent Fracture Mechanisms in Brittle Rock Under 3D Stress Conditions

Jie Huang, Zhenlong Song, Cheng Huang, Qinming Liang

Applied Sciences· Volume 15· Issue 18

Abstract

The fracture evolution of brittle rock under 3D stress states remains poorly understood, particularly the role of deviatoric stress symmetry as characterized by the Lode angle (θσ). To address this knowledge gap, we systematically investigated sandstone using a true triaxial loading apparatus under a constant mean stress (100 MPa) while varying θσ from −30° to +30°, integrated with real-time acoustic emission (AE) monitoring and post-failure X-ray computed tomography. Our results demonstrate a critical linear reduction in peak strength with increasing θσ. This strength reduction is accompanied by a corresponding transition in failure mechanism, from a progressive mode dominated by dilation to an abrupt mode characterized by shear localization. Innovatively, we introduce a novel AE-based parameter (C), derived from the coupled evolution of AE energy and hit rates, which quantifies fracturing intensity in real-time without pre-defined lithological and monitoring scale. Furthermore, digital reconstruction reveals that consistent X-shaped polymodal fault networks are governed by sequential tensile–shear interactions. This key mechanistic insight prompts us to propose a new “deflected shear–tensile hybrid kinked fracture” classification, which more accurately captures the topological complexity of fractures under 3D stresses than conventional monomodal schemes. This study provides fundamental insights into 3D rock fracture mechanics and practical tools for enhancing safety and efficiency in deep geo-engineering.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Rock Mechanics and Modeling · Geotechnical and Geomechanical Engineering · Landslides and related hazards

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Institute of Future Civil Engineering Science and Technology, Chongqing Jiaotong University, Chongqing 400074, China

High Performance Computing Department, National Supercomputing Center in Shenzhen, Shenzhen 518055, China

State Key Laboratory of Coal Mine Disaster Dynamics and Control, School of Resources and Safety Engineering, Chongqing University, Chongqing 400044, China

China Coal Technology and Engineering Group, Chongqing Research Institute, Chongqing 400037, China

Funding

National Natural Science Foundation of China · Brain-Gain Plan of New Chongqing—Young Elite Program · Postdoctoral Fellowship Program of CPSF · 75th China Postdoctoral Science Foundation Funded Project · Open Funding of State Key Laboratory of Coal Mine Disaster Prevention and Control · Chongqing Special Project for Technological Innovation and Application Development

References (51)

Show source-provided references
1. Experimental investigation on the failure mechanism of water-bearing sedimentary rocks under true-triaxial stress10.1016/j.engfailanal.2025.109605 ↗
2. Study on the influence of true triaxial principal stress loading and unloading on gas permeability characteristics of coal seams containing gangue10.1016/j.rineng.2025.105667 ↗
3. Stress-induced borehole deformation mechanism of self-rotating waterjets drilling under true triaxial stress conditions10.1016/j.geoen.2025.214021 ↗
4. Directional development mechanism of hard rock fracture under true triaxial stress: Insights from macroscopic and microscopic fracture perspectives10.1016/j.engfracmech.2025.111000 ↗
5. Development of experimental system for rock anisotropic seepage under true triaxial stress10.1016/j.gete.2025.100677 ↗
6. Influence of lithological contrast on elastic anisotropy of shales under true-triaxial stress and thermal conditions10.1016/j.ijrmms.2025.106100 ↗
7. Wellbore stability in high-temperature granite under true triaxial stress10.1016/j.geothermics.2021.102334 ↗
8. Dynamic damage mechanism of coal with high true triaxial stress level subject to water jets10.1016/j.powtec.2024.119583 ↗
9. True triaxial stresses mobilizing dilatant fracturing and engineering failure of hard rocks10.1016/j.engfailanal.2023.107652 ↗
10. Acoustic characterization of crack damage evolution in sandstone deformed under conventional and true triaxial loading10.1002/2016JB013646 ↗
11. DEM simulation on the damage of sandstone with a three-dimensional embedded rough fracture with different width and inclination angle under true-triaxial stress conditions10.1016/j.tafmec.2024.104528 ↗
12. Progressive failure characteristics and energy accumulation of granite with a pre-fabricated fracture during conventional triaxial loading10.1016/j.tafmec.2021.103219 ↗
13. A damage evolution model of red sandstone under uniaxial compressive loading with different loading rates based on infrared thermography10.1016/j.infrared.2024.105664 ↗
14. A true triaxial geomechanical model test apparatus for studying the precursory information of water inrush from impermeable rock mass failure10.1016/j.tust.2019.103078 ↗
15. A rigid true triaxial apparatus for analyses of deformation and failure features of deep weak rock under excavation stress paths10.1016/j.jrmge.2022.08.009 ↗
16. Experimental study on the influence of hydrostatic stress on the Lode angle effect of porous rock10.1016/j.ijmst.2022.02.007 ↗
17. Dependence of rock properties on the Lode angle: Experimental data, constitutive model, and bifurcation analysis10.1016/j.jmps.2016.08.004 ↗
18. Three-dimensional strength criterion for rocks: A review10.1016/j.enrev.2024.100102 ↗
19. A three-dimensional elastoplastic constitutive model incorporating Lode angle dependence10.1016/j.gete.2024.100567 ↗
20. New void growth-based ductile fracture models incorporating interaction effects of stress triaxiality and Lode angle parameter10.1016/j.tafmec.2025.105204 ↗
21. Revisiting the normal stiffness–permeability relations for shale fractures under true triaxial stress10.1016/j.jrmge.2025.01.007 ↗
22. Evolution of the hydraulic wetting path in fractured coal under true triaxial stress and the influence mechanism of fracture orientation10.1016/j.jhydrol.2024.131692 ↗
23. Chen, J., Gui, Z., Rui, Y.C., Zhao, X., Pan, X., Wang, Q., Pu, Y., Li, Z., and Liu, M. (2025). A dual attention-based deep learning model for lithology identification while drilling. J. Rock Mech. Geotech. Eng., S1674775525002562.10.1016/j.jrmge.2025.03.051 ↗
24. Influences of initial damage on the saturated granite failure characteristics under true triaxial stress with a free face: Insights into the rockburst prevention and control10.1016/j.engfracmech.2025.111263 ↗
25. Tunnel rockburst with a single set of joints under true-triaxial stress condition10.1016/j.jrmge.2024.11.048 ↗
26. A Novel True Triaxial Apparatus to Study the Geomechanical and Fluid Flow Aspects of Energy Exploitations in Geological Formations10.1007/s00603-016-1060-7 ↗
27. Influence of the intermediate principal stress on sandstone failure10.1007/s00603-019-01756-1 ↗
28. A method for monitoring acoustic emissions in geological media under coupled 3-D stress and fluid flow10.1016/j.petrol.2022.110227 ↗
29. 3-D transport and acoustic properties of Fontainebleau sandstone during true-triaxial deformation experiments10.1016/j.ijrmms.2014.02.014 ↗
30. Multi-surface Cyclic Plasticity Sand Model with Lode Angle Effect10.1007/s10706-007-9170-3 ↗
31. In-situ stresses, abnormal pore pressures and their impacts on the Triassic Xujiahe reservoirs in tectonically active western Sichuan basin10.1016/j.marpetgeo.2020.104708 ↗
32. Confining stress effect on the elastoplastic ground reaction considering the Lode angle dependence10.1016/j.ijmst.2020.04.002 ↗
33. An Alternative Approach for Representing the Data Provided by the Acoustic Emission Technique10.1007/s00603-018-1494-1 ↗
34. Temporal dominant frequency evolution characteristics during the fracture process of flawed red sandstone10.1016/j.tafmec.2020.102838 ↗
35. New insights into the development of brittle shear fractures from a 3-D numerical model of microcrack interaction10.1016/j.epsl.2006.06.041 ↗
36. Polymodal faulting: Time for a new angle on shear failure10.1016/j.jsg.2015.08.013 ↗
37. A super-critical stress model for polymodal faulting of rocks10.1016/j.jog.2019.06.003 ↗
38. Hydraulic fracture morphology and conductivity of continental shale under the true-triaxial stress conditions10.1016/j.fuel.2023.129056 ↗
39. 3D morphology and formation mechanism of fractures developed by true triaxial stress10.1016/j.ijmst.2022.09.002 ↗
40. Experimental study on acoustic emission (AE) characteristics and crack classification during rock fracture in several basic lab tests10.1016/j.ijrmms.2020.104411 ↗
41. Effect of the Intermediate principal stress on pre-peak damage propagation in hard rock under true triaxial compression10.1007/s00603-022-02981-x ↗
42. Racine, J.S. (2019). Conditional Probability Density and Cumulative Distribution Functions, Cambridge University Press.
43. Failure analysis of Nehbandan granite under various stress states and strain rates using a calibrated Riedel-Hiermaier-Thoma constitutive model10.1007/s40948-024-00876-5 ↗
44. Pradhan, S., Stroisz, A.M., Fjær, E., Stenebråten, J., Lund, H.K., Sønstebø, E.F., and Roy, S. (2015). Fracturing tests on reservoir rocks: Analysis of AE events and radial strain evolution. arXiv.
45. Simulation of Fracture Coalescence in Granite via the Combined Finite-Discrete Element Method10.1007/s00603-019-01773-0 ↗
46. Double-phase-field formulation for mixed-mode fracture in rocks10.1016/j.cma.2020.113655 ↗
47. An efficient phase-field model of shear fractures using deviatoric stress split10.1007/s00466-023-02348-1 ↗
48. Experimental and numerical investigation on the deformation and failure behavior in the Taylor test10.1016/j.matdes.2011.01.016 ↗
49. The Emerging of Stress Triaxiality and Lode Angle in Both Solid and Damage Mechanics: A Review10.3103/S0025654421050058 ↗
50. Optimizing microseismic sensor networks in underground space using Cramér–Rao Lower Bound and improved genetic encoding10.1016/j.undsp.2025.02.009 ↗
51. An innovative analytical solution of AE/MS source location with singular value decomposition and weight estimation10.1016/j.measurement.2025.117652 ↗