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The toppling failure of anti-dip rock slopes is significantly affected by crack propagation from non-persistent cross-joints (NPCJs). In this study, a strength-based localized maximum stress (SLMS) criterion is adopted to model the toppling failure process caused by crack propagation in anti-dip rock slopes containing a set of NPCJs via the finite element method. The crack initiation sequence from NPCJs and the toppling evolution of anti-dip slopes under different stratum dips and slope angles, as well as the influences of stratum dips and slope angles on toppling evolution, are investigated. Variations in the displacements during the toppling of the slope and the influence of toppling on the displacements are analyzed. Additionally, variations in the magnitude and distribution area of interlayer friction between rock layers during the toppling evolution process and the effects of toppling on the evolution of interlayer friction are examined. The results indicate that the toppling process of the anti-dip slope containing NPCJs involves three stages: crack initiation and propagation from the NPCJs, the development of interlayer tensile and shear cracks, and toppling failure of the rock layers. The stability of anti-dip slopes containing NPCJs is greatly affected by the stratum dip and slope angle. The horizontal displacements and interlayer crack aperture increase nonlinearly with the development of toppling evolution, and the magnitude of the increase gradually increases. Moreover, the magnitude and distribution area of interlayer friction vary with the development of toppling evolution. The maximum interlayer friction gradually increases, but the distribution area of friction decreases. • Slope angle affects slope stability more significantly than does the stratum dip. • Horizontal displacements increase nonlinearly with toppling evolution. • Crack apertures of interlayer shear cracks appear like a triangle. • Distribution areas of interlayer friction decrease with toppling evolution. • Locations of final fracture in rock layers affect interlayer friction distribution. [ABSTRACT FROM AUTHOR]

• The failure mode of rock bridges gradually changes from shear to tensile with increasing rock bridge inclination. • Flaws located in the middle of the slope have a significant effect on the failure mode and the depth of the sliding surface at this location. • Micro-failure monitoring methods can achieve early warning of landslides when displacement monitoring cannot be performed effectively. • The contact status of crack surfaces gradually changes from sticking or sliding to opening during the formation of the sliding surface. In this study, we adopt the proposed strength-based local maximum stress (SLMS) criterion to calculate the crack propagation of tensile and shear cracks in a plate with two parallel closed flaws at different rock bridge inclinations (β) under compression. The effect of β on the failure mode of rock bridges was investigated. Then, we modeled the three-section landslides caused by crack propagation under different friction coefficients to validate the effectiveness of SLMS in modeling crack propagation in slopes. Finally, the formation of sliding surfaces in four specific rock slopes with multi-flaws was modeled to investigate the effect of flaw distribution on the depth and shape of sliding surfaces of slopes. Results indicate that flaws located in the middle of the slope have a significant effect on the failure mode and the depth of the sliding surface at this location. Due to the small increments of displacement during the failure process of the slope, which are difficult to monitor, displacement monitoring methods are ineffective for landslide early warning. The instability of the rock slope is caused by the initiation, propagation, and coalescence of cracks, therefore, real-time monitoring of the micro-failure accumulation in the slope is beneficial for early warning of landslides. Moreover, the variation of contact status of crack surfaces during the formation of slope sliding surfaces was analyzed, and the effect of sliding surface formation on contact sliding distance and contact gap distance of crack surfaces was investigated. [ABSTRACT FROM AUTHOR]

• Positive and negative oscillations of K II under compression are the reason for zigzag crack propagation paths modeled by the traditional fracture criterion. • GMTS criterion considering T -stress can effectively eliminate K II oscillations but requires complicated parameter calculations. • SLMS criterion proposed in this study can conveniently and efficiently model the propagation of both tensile and shear cracks. • The effects of flaw inclination, friction coefficient, loading level, and flaw surface contact status on the crack propagation paths were studied. The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (K II) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of K II can be effectively eliminated when the non-singular stress (T -stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T -stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions. [ABSTRACT FROM AUTHOR]