## 1 Introduction  
As a common geological material, rocks are a feature of many engineering applications such as mining science, underground construction, tunnel excavation, military bunkers, etc. In these geological engineering works, rocks are often subjected to dynamic loads over a wide range of strain rates. Sources of dynamic loads include seismic and earthquake, impact and penetration, explosion and blasting [1]. Therefore, it is significant to study the dynamic fracture characteristics of rock materials. The dynamic properties of materials are often determined by split Hopkins pressure bar (SHPB), which can provide a constant strain rate in the range of \(10^{1}\)-\(10^{4}\) s\({}^{-1}\)[2]. [PERSON] and [PERSON] [3] detailed the development history and principles of the SHPB system. Based on the one-dimensional stress wave theory, the stress-strain curve can be calculated through the strain signals measured by strain gauges on the incident and transmitted bars. Because of the difficulty of the direct test [4], most scholars use indirect testing to determine the tensile strength of rock. As an indirect method, the Brazilian test has been widely used in the laboratory to measure the tensile strength of brittle materials with an apparently low ratio of tensile-to-compressive strengths. [PERSON] and [PERSON] [5] investigated the dynamic tensile properties of granite with the Brazilian test, and this approach has been referenced by many relevant researchers. [PERSON] et al. [2] compared the tensile strength and fracturing of Carrara marble under quasi-static and dynamic Brazilian tests. The influence of different loading conditions on the initiation, enlargement, and coalescence of cracks was observed [6]. [PERSON] et al. [7] used the SHPB system with Brazilian specimens to determine the indirect tensile strength of rock under an intermediate strain rate ranging from 5.2 to 12.9 s\({}^{-1}\). [PERSON] et al. [8] investigated the dynamic tensile characteristics of rock under highly confining stresses through the Brazilian test with a dynamic and static coupled loading SHPB system. In their report, the tensile strength of the granite decreased with the static pre-stress increases. [PERSON] et al. [9] elaborated the dynamic tensile experimental techniques for rock. Three kinds of specimen or fixture configurations for the Brazilian test were presented and compared. The most obvious difference among them was the fracture pattern. For easy preparation of specimens (except flattened Brazilian), a pair of curved anvils between the bar ends and a specimen can prevent the damage or failure caused by local stress concentration when the specimen is directly loaded by bars. Regarding the effects of anvils in dynamic Brazilian tests, [PERSON] et al. [10] discussed its necessity. Two sets of measured tensile strengths of Laurentian granite from the SHPB system with and without curved anvils at the contact end showed a consistency in dynamic tensile strength. The above research indicated the feasibility of using the Brazilian test on an SHPB when determining the dynamic tensile strength of rock materials. In this paper, suggestions from the ISRM test method regarding Brazilian tests on an SHPB system were followed [11]. Generally, the stress level within the material at the fracture moment is defined as the strength, and the rate-dependent effect of the dynamic strength is the research concern. The experimental results of the SHPB are usually presented as the ratio of a measured dynamic strength to a quasi-static strength, i.e., dynamic increase factor (DIF) or normalized dynamic strength. The DIF is usually fitted to be a function of strain rate in logarithm space [1]. Although this approach can simply and intuitively describe the rate-dependent effect of dynamic strength, it ignores the time effect in the dynamic response process. [PERSON] et al. [12] emphasized that the deformation and fracturing processes require time to be mobilized, to develop, and to complete, and the fracture strength depends on strain rates.