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The single cleavage drilled compression specimens of sandstone were impacted by the large-diameter split Hopkinson pressure bar, during which the whole model-I dynamical fracture process was successfully observed. A crack propagation gauge is used to monitor the key time moment of dynamic initiation, propagation, arrest and re-initiation, respectively. The fractal crack extension model is used to analysis the propagation speed of the tortuous crack, and with further combination of the experimental–numerical-analytical method, to determine the dynamic initiation toughness, dynamic propagation toughness, dynamic arrest toughness, and dynamic re-initiation toughness of sandstone. The results show that in the process of crack propagation, the crack propagation path is torturous; and for this curved path, the value of the universal function, which is characterized by the crack's velocity, is smaller than that with a straight path. The dynamic propagation toughness thus obtained is closer to its real value by using the fractal model. Sandstone's dynamic initiation toughness is greater than the dynamic arrest toughness, and the dynamic initiation toughness is slightly bigger than the dynamic re-initiation toughness. [ABSTRACT FROM AUTHOR]