## 5 Conclusions  
In order to study the mechanism of the static stress on the initiation of blasting cracks, crater blasting tests on sandstone specimens were conducted without static load, under uniaxial and equal biaxial compressions. The DIC non-contact measurement technique has been used to monitor the evolution of the strain field on the free surface. The evolution law of maximum principal strain under different static stress conditions and the influence of static stress on strain field were analyzed. The maximum tensile strain failure theory was used to explain the mechanism of static stress on crack formation. At the same time, a method to measure the dynamic fracture strain of rock was proposed. The conclusions are as follows:  
1. Static stress controls the pattern of the maximum principal strain field during crater blasting. Without static load and under the equal biaxial compression, an axisymmetric circular tensile strain zone was formed on the free surface. The maximum principal strain was observed at the center of the circle and gradually decreased to the initial static strain with the increase in radius. Under the uniaxial static compression, an elliptical tensile strain field with the long axis parallel to the direction of static stress was formed. The long axis extended with the action time of blasting and the short axis was unchanged during the blasting. In the direction of vertical static stress, the maximum principal strain transitions from tensile strain to compressive strain, forming a concentration zone of compressive strain.
2. Static stress controls the direction of the maximum principal strain field during crater blasting, which in turn affects the formation of cracks. Without static load and under the equal biaxial compression, the direction of the maximum principal strain was perpendicular to the radius. Without static load, the maximum principal strain at the center of blashhole is greater than the dynamic fracture strain of rock, which led to the formation of randomly distributed radial tensile cracks on the free surface. Under the equal biaxial compressive static load and the stress-strength ratio was 0.42, the maximum principal strain at the center of blasthole did not reach the dynamic fracture strain of rock, which restrained the emergence of tensile cracks on the free surface. Under the uniaxial compressive static load, the maximum principal strain was perpendicular to the static loading direction. Under such tensile strain, initially, tensile cracks parallel to the loading direction emerged and propagated. Finally, only one macroscopic tensile crack parallel to the static loading direction was formed on the free surface and the other cracks were restrained.
3. Without static load and under the uniaxial compression, the dynamic tensile fracture strain of the sandstone was \(\varepsilon_{td}\) = 0.00322. This indicated that, under the blasting-induced dynamic loading, the dynamic tensile fracture strain of the rock was independent of the initial static stress state. Therefore, considering the uniqueness of the tensile crack initiation and propagation on the free surface under the uniaxial compression, the proposed method can be used to measure the dynamic tensile fracture strains of various rocks at different loading rates.  
This paper is a result of the collaboration of all co-authors. [PERSON] conceived and designed the study; [PERSON] and [PERSON] conducted the experimental; [PERSON] drafted the manuscript; [PERSON] and [PERSON] revised the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the State Key Research Development Program of China (Grant No. 2017 YFC0602902).  
The authors declare no conflict of interest.