In order to understand the mechanical properties and energy dissipation law of frozen sandstone under impact loading, the cretaceous water-rich red sandstone was selected as the research object to conduct impact tests at different freezing temperatures (0°C, −10°C, −20°C, and −30°C). The test results suggested the following: (1) the peak stress and peak strain of frozen sandstone are positively correlated with strain rate and freezing temperature, and the strain rate strengthening effect and the low-temperature hardening effect are obvious. (2) The strain rate sensitivity of dynamic stress increase factor (DIF) is negatively correlated with temperature. Water-ice phase change and the difference in the cold shrinkage rate of rock matrix under strong impact loading will degrade the performance of rock together, so DIF is less than 1. (3) In the negative temperature range from −10°C to −30°C, DEIF is always greater than 1. The energy dissipation rate of red sandstone specimens fluctuated between 10% and 25% under the impact loading, and the data are discrete, showing obvious strain rate independence. The failure form changes from tensile failure to shear and particle crushing failure. (4) Combined with the micromechanism analysis, the difference in dynamic mechanical properties of red sandstone at different temperatures is caused by the water-ice phase change and the different cold shrinkage rates of the frozen rock medium. When the temperature drops from 0°C to −2°C, water migrates to the free space of the pore of frozen rock and freezes into ice crystal, resulting in frozen shrinkage. At −30°C, the expansion of ice dominates and the migration of water will stop, leading to frost heave.

To obtain the dynamic mechanical properties of frozen sandstone at different temperatures (i.e., 20°C, −10°C, −20°C, and −30°C), dynamic uniaxial compression tests of saturated sandstone are conducted using a split-Hopkinson pressure bar. The experimental results demonstrated that the brittleness of the saturated sandstone increased and its plasticity weakened with a decrease in temperature. The peak strength and dynamic elastic modulus of the sandstone were positively correlated with its strain rate. The peak stress was most sensitive to the strain rate at −10°C, and the elastic modulus was most sensitive to the strain rate at −30°C. According to the evident segmentation characteristics of the obtained stress-strain curve, a viscoelastic dynamic constitutive model considering the strain rate effect and temperature effect is developed; this model combines a nonlinear (or linear) body and a Maxwell body in parallel with a damage body. The applicability of the constitutive model is also verified using experimental data. The fitting results were demonstrated to be in good agreement with the experimental results. Furthermore, the fitting results serve as reference for the study of the constitutive model of weakly cemented soft rock and the construction of roadway freezing methods.

To obtain the impact mechanical response and establish the dynamic damage constitutive relationship of frozen sandstone at low temperature conditions, the impact test of Cretaceous red sandstone under different temperatures was conducted using a split Hopkinson pressure bar (SHPB) device. According to the characteristics of the stress-strain curves obtained by the test, a constitutive model considering the damage effect, temperature effect, and strain rate effect was established, which was improved by Zhu–Wang–Tang (Z–W–T) constitutive model. It was proved that the fitting curves of constitutive equation were in good agreement with the test curves. The fluctuation amplitude of fitting error was controlled within ±4 MPa. The physical meaning of each parameter of the constitutive model is clear, and most of them are fixed values. The selection range of variable parameters and the related change rules are confirmed, which improves the practicability of constitutive model. The constitutive equation can well describe the nonlinear features of this kind of frozen sandstone under impact loading. It was also found that the constitutive equation was applicable to express the dynamic mechanical properties of rock-like materials such as hard rock, soft rock, frozen soil, raw coal, and concrete. It can be referred to the parameter determination method in this paper to study and determine the parameters, reduce the difficulty of parameter selection, and improve the practicability of the constitutive model and parameters, so as to guide the engineering practice better.

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