Study on the crack propagation mechanism of single cracks in red sandstone based on stress field evolution characteristics

To elucidate the influence of fracture dip angle on the mechanical response of red sandstone and the mechanism of crack evolution, this study employs the discrete element software PFC2D to construct a single-fracture sandstone model. Numerical uniaxial compression tests are conducted under varying fracture dip angles α. By integrating the ‘stress field–microcrack’ coupling criterion with fracture initiation displacement field characteristics, the study quantitatively derives the segmented enhancement patterns of peak strength and fracture initiation stress, systematically elucidating the mechanisms of microcrack initiation and propagation. Results indicate that as α increases, the normal clamping effect of the fracture surface intensifies, making it more difficult for the vicinity of the fracture surface to first reach the damage threshold. Microcrack activity gradually shifts from “preferential growth in the middle section of the fracture surface” to “easier triggering at the fracture tip,” driving the macrocrack path from local control at low inclination angles to synchronous evolution with high-stress zones at high inclination angles (This consistency becomes more pronounced at larger inclinations). The mechanical response manifests as an overall increase in both initiation stress and peak strength with inclination angle, exhibiting a more pronounced enhancement trend within the larger inclination range. Additionally, the strain value required for the first AE signal increases, the strain range where AE events occur narrows, and the peak ringing count rises.The crack initiation stress increased from 11.5 MPa (α = 0°) to 25.0 MPa (α = 90°), representing an approximately 117% increase; the peak stress rose from 24.2 MPa to 33.6 MPa, an increase of approximately 39%. Microcrack counts exhibited exponential growth with accumulated strain, dominated by tensile cracks, indicating a tensile-dominated brittle failure mechanism in the rock specimens.The research findings provide an interpretive framework based on stress thresholds for identifying failure modes under controlled joint dip angles and for engineering stability assessments.