The axial direction of a roadway often forms a certain spatial angle with the in-situ stress field.Variations in the spatial angles can lead to differences in the stress environment in which the roadway is exposed.Different forms of failure characteristics occur in the roadway.In order to study the failure mechanism with different spatial characteristics,rock-like material specimens with holes in 9 different horizontal and vertical angles were designed.The true triaxial test system was used to carry out the test with the same loading path.The results show that the horizontal angle a and vertical angle β have a significant effect on the specimen strength,specimen rupture angle,and the form of spalling failure in the hole.The spatial angle leads to the formation of asymmetric heterotype V-notches in both sides within the hole.The asymmetry is evident in both the depth and extent of spalling.The strength of the specimen increases and then decreases with increasing vertical angle β.The rupture angle increases and then decreases with increasing horizontal angle a and increases with the increase of the vertical angle β.The stress analytical model of the specimen under three-dimensional compression was established.The distribution of principal stresses around the holes was theoretically analyzed.It is found that the presence of spatial angle changes the distribution of principal stresses around the hole from symmetric to asymmetric distribution.The shift of the principal stresses is responsible for the change from a V-notch to a heterotype V-notch.

financiallysupportedbytheNSFCprojects(Nos.52225404,42321002,and4204100030)；BeijingOutstandingYoungScientistProgram(No.BJJWZYJH01201911413037)；theExcellentYouthTeamoftheCentralUniversitiesofChina(No.2023YQTD01)；

1. Introduction
2. Test procedure
2.1.Sample preparation
2.2.Test equipment
2.3.Stress path
3. Result analysis
3.1.Analysis of mechanical properties
3.2.Failure characteristics
3.2.1.Failure mode of heterotype V-notch
3.2.2.Overall failure characteristics
3.3.Rupture angle
4. Discussion
4.1.Horizontal and vertical angle effects
4.2.Laboratory comparison and engineering comparison
4.3.Mechanism analysis of heterotype V-notch
5. Conclusions

[1]Ma Z ,Zuo J .Failure mechanisms of roadways with non-coplanar axial direction and stress space: True triaxial test and mechanical analysis[J].International Journal of Mining Science and Technology,2024,34(12):1711-1725.