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During blasting in engineering construction, the surrounding rock becomes unstable and is damaged under the impacts of multiple low-amplitude stress waves. It is of great practical significance to understand the damage evolution characteristics and the attenuation of the mechanical properties of rocks subjected to multiple stress waves. Single impact and repeated impact tests for sandstone were carried out using a split Hopkinson pressure bar (SHPB) loading system. The single impact test results showed that the sandstone materials were strain-rate-dependent, and the dynamic constitutive curve could be divided into four stages, namely the linear elastic stage, the new crack formation stage, the plastic strengthening stage and the unloading stage. The failure pattern mostly indicated splitting tensile failure, and the impact damage threshold was 45 J. The relationship between the damage and stress wave amplitude was D = 0.0029•exp⁡(5.4127•σ/76.13) − 0.0504. The repeated impact test results showed that the dynamic compressive strength and the dynamic elastic modulus decreased, while the failure strain increased gradually as the number of impacts (n) increased. The sandstone specimen under repeated impacts had only one fracture surface compared with the single impact failure pattern. The cumulative damage presented the development form of ‘rapid rise–steady development–rapid rise’, and the damage evolution law could be expressed by D = 0.265 − 0.328•ln⁡(ln13.989/n). Finally, a set of methods to determine the Holmquist–Johnson–Cook (HJC) model parameters for sandstone was proposed based on a single impact test, repeated impact test, uniaxial compression test and triaxial compression test. The numerical simulation results of the SHPB test showed that the dynamic constitutive curves of sandstone were in good agreement with the experimental results.

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Dynamic mechanical properties of granite were tested by a split Hopkinson pressure bar system at constant strain rates. The experimental results show that granite behaves linearly elastic at the initial loading stage, followed by a significant plastic deformation after yielding, and yield strength, ultimate strength and elastic modulus are all rate dependent. On this basis, the simplified Zhu-Wang-Tang (ZWT) constitutive model is applied in this paper, assuming elastic and high frequency viscoelastic elements only. The damage evaluation equation is introduced to the simplified ZWT model to investigate the effect of damage on the dynamic strength of granite due to impact load. Finally, the proposed model is applied to fit the experimental data. It is known that the fitted stress-strain curves at different strain rates are in agreement with the experimental ones. Compared with experimental data, the error of yield stress, peak stress and corresponding strain obtained by fitting method are all not larger than 10%. This demonstrates that the proposed dynamic constitutive model can accurately describe the dynamic mechanical properties of granite under impact loading.