# Research on Fracture Mechanism and Stability of Slope with Tensile Cracks
###### Abstract  
Tensile cracks at the crest of slope will attenuate the stability of slope. The aim of this paper is to investigate the computation of safety factors acting on a clay slope when the slip surface consists of tensile crack and shear surface. Based on the theory of limit equilibrium, an analytical solution for safety factors containing three types of failure mechanisms is presented. The optimal crack depth was obtained by using the principle of minimum safety factor. In the solution, effects of parameters such as crack depth, slope angle, height, cohesion, and internal friction angle on slope stability were discussed. By comparing with the results of previous studies, the rationality of the proposed approach was verified. Results show that consideration of tensile cracks lead to a significant reduction in slope stability, and the safety factor decreases by about 10% compared with the slope without cracks. The law of safety factor varying with crack depth indicates that it first decreases as the crack depth is increased and then increases as the crack depth is further increased. Through the parametric analysis, it is found that the safety factor increases with an increase in cohesion and internal friction angle but decreases with the slope angle and height increase. It is important to note that the optimal crack depth does not exceed one-third of the slope height. Moreover, a highway landslide that occurred in the road running across the Yunnan and Tibet Province was investigated to verify the practicality of the present method. type:stability; tensile crack; optimal crack depth; analytical calculation; safety factor +
Footnote †: journal: Medical Engineering  
[PERSON] earth pressure theory and considered that the depth of tension cracks is not more than half of the slope height. This viewpoint is echoed by some researchers, such as [PERSON], [PERSON], and [PERSON] et al., who believed that existence of cracks is already dangerously for the stability of slope [10; 11; 12]. [PERSON] et al. [13] proposed a simple formula estimating the depth of tensile cracks at the slope tailing edge with arbitrary inclination, but the depth is independent of slope shape. Compared with previous studies, [PERSON] [14] considered the influence of slope geometry on the depth of tensile crack by searching for the most dangerous pure shear slip surface. [PERSON] [15] employed the limit analysis method to investigate the stability of slope with open cracks, based on three types of conditions regarding the presences of cracks, and the same conclusion was also obtained--that the existence of cracks could result in a considerable reduction in stability factors. [PERSON] [16] also studied the stability assessment of slopes with cracks which contains two types of cracks, including an open crack that existed prior to slope failure and a formation crack that formed contemporaneously with slope failure by using the limit analysis approach, similarly demonstrating the adverse effects of the different types of cracks. [PERSON] et al. [17] proposed that the mechanisms of cracks formation can be considered part of the internal dissipation process in the limit analysis method, and the stability number obtained by using the limit analysis method was consistent with the conclusion of [PERSON]. Moreover, the results also indicated that neglecting the effect of cracks formation could lead to an erroneous judgement in the stability of slope. For the sake of the accuracy of slope stability evaluation, the influence of tensile crack must be considered. Hence, the mechanisms of cracks and stability analysis has gradually become a research hotspot in slope fields in the future, especially combined with the method of determined cracks value, which is also exactly what this study discusses. So far, the analysis methods of slope stability mainly include limit equilibrium method, limit analysis method, and numerical simulation method [1; 2; 9].