## 1 Introduction  
Drilling and blasting technology has been widely used in mining and tunneling as an economical and efficient approach for rock breaking [1, 2]. In hard rock mining practice, the immediate release of explosive energy in the blast hole can break the surrounding rock material [3]. However, to date, the results of blasting in projects such as rock excavation have not been satisfactory [4]. The empirical design of blast operation results in low energy efficiency, which may lead to mineral loss, high ground vibration, explosive wastage, and even safety accidents [5, 6, 7, 8, 9]. To optimize blasting design and make rock blasting more efficient, improvement in the understanding of rock fragmentation induced by blast loading is essential. Research on rock fragmentation mechanisms has been conducted for decades. In the early studies, there were two views on the rock fragmentation mechanism. One view was that rock fragmentation was mainly caused by stress waves [10; 11]. Another view was that explosive gas played the dominant role in rock fragmentation [12; 13]. Since the 1970s, a more acceptable view of the rock fragmentation mechanism has been found, i.e., the combined effect of stress waves and explosive gas dominates rock fragmentation [14; 15; 16; 17]. According to the fracture characteristics around a blast hole under blast loading, the damaged area around the blast hole is usually divided into the borehole expansion zone, crushed zone, fracture zone, and vibration zone from near to far [6; 18; 19]. After the explosive column in the blast hole is detonated, radial and circumferential cracks are generated around the blast hole under the influence of the stress wave and gas pressure [20]. When the stress wave propagates to the free surface, the reflected tensile wave will induce the fracturing of the surface rock. [PERSON] [21] studied crack propagation using granite specimens. The study showed that radial cracks initiated from the surface and propagated inward, that spalling cracks formed near the free surface, and that other radial cracks propagated from the blast hole. As the cracks develop and intersect within the rock, the rock is broken into fragments that can be moved under the effect of expanding gases [22]. For a long time, optimizing blasting design to obtain better fragmentation has been a hot study topic for researchers and engineers. The emergence of electronic detonators has allowed for more precise control of detonation time, which has led to more attention being given to study of the effect of delayed initiation on rock damage and fragmentation, especially the influence of stress wave interaction on fragmentation. [PERSON] [23; 24] used Lagrange diagrams to analyze the stress wave superposition in two adjacent boreholes with different detonation times. He concluded that stress wave superposition positively affects rock fragmentation and that using a short delay time between two boreholes is beneficial in achieving uniform rock fragmentation. Influenced by the study of [PERSON], [PERSON] and [PERSON] [25] performed field tests using short delays between blast holes. Their field test results indicated a dramatic improvement in rock fragmentation using short delay times compared to long delay times, with a 45.6% improvement in median size. [PERSON] [26] concluded, according to image analysis of blast fragments and statistics of fragment sizes, that the delay time needs to be sufficiently short to allow for the interaction of stress waves between adjacent boreholes. However, as more relevant studies were conducted, the view that the stress wave superposition is not the dominant factor in improving rock fragmentation appeared. [PERSON] and [PERSON] [27] conducted blasting tests using concrete bench specimens to investigate the influence of stress wave interactions on fragmentation. Their study showed there is not enough experimental evidence suggesting that short delays with shock wave interactions can obtain better fragmentation than long delays. [PERSON] et al.