## 1 Introduction
[36] studied the effect of flaw length on the initiation characteristics of granite samples with cross double flaws by using PFC\({}^{\text{2D}}\), indicating that the crack initiation position was close to the flaw tip and propagated along the principal stress direction, and the initiation cracks were tensile cracks. [PERSON] et al. [37] discussed the influence of flaw width and flaw inclination angle on the crack initiation angle and crack initiation location of samples with the single flaw by using PFC\({}^{\text{2D}}\), and showed that the crack initiation angle decreased with the increase of flaw width. PFC\({}^{\text{2D}}\) can avoid the artificial selection of complex crack initiation criteria to more truly reflect the initiation process of rock-like materials, and it has been developed and extensively used to simulate crack initiation and the propagation of rock-like materials in recent years [38; 39; 40]. Moreover, the failure process of rock or rock-like materials is a process from local failure to global failure, and the essence of failure is the nonlinear instability driven by energy [41; 42]. Therefore, the analysis of energy evolution characteristics is an important method to reveal the failure characteristics of fractured rocks. [PERSON] et al. [43] studied the influence of inclination angle on the energy evolution characteristics of rock samples with a single flaw by using PFC\({}^{\text{2D}}\), and found that the larger the inclination angle was, more energy was absorbed and dissipated, and the higher the failure degree was. [PERSON] et al. [44] carried out uniaxial compression tests of rock with a single flaw under different loading rates by using PFC\({}^{\text{2D}}\), and found that energy evolution and failure modes were closely related to loading rates. Most of the research has focused on the influence of loading conditions [44; 45], and the geometry of single flaws or parallel flaws [46; 47] on the energy evolution characteristics, while studies on the energy evolution characteristics of samples with non-parallel flaws are fewer. At present, scholars have carried out numerous studies on macroscopic and microscopic mechanical characteristics, crack initiation characteristics and crack evolution laws of rock or rock-like materials with single flaws or parallel flaws. Researches on non-parallelflaws, especially non-parallel overlapping flaws, mainly use physical test methods to explore their macroscopic mechanical properties and crack propagation characteristics, while the results on their meso-cracking characteristics and energy dissipation laws are fewer. Therefore, in order to make up for the deficiency of this kind of research, based on the laboratory test of [PERSON] et al. (2020), PFC2D was used to simulate the non-parallel overlapping double flaws of rock-like samples with different inclination angles. From the overall macroscopic mechanical properties, crack initiation stress and deformation field to the local stress field, the crack initiation characteristics of samples with non-parallel overlapping flaws were analyzed, and the failure characteristics are discussed from the aspect of energy evolution.