不同应变率下煤岩破坏特征及其本构模型

利用直径50 mm的分离式霍普金森压杆，对煤岩展开20～100 s?1动态应变率下的单轴冲击压缩试验，结合高速摄影分析其变形破坏特征，并建立基于Weibull统计分布和Drucker-Prager破坏准则的煤岩动态强度型统计损伤本构模型。试验结果表明:（1）煤岩动态应力-应变曲线存在明显的非线性特征，随应变率升高，动态抗压强度与弹性模量均呈线性增长且增幅显著，破坏形态由低应变率下的轴向劈裂破坏向高应变率下的压碎破坏过渡；（2）在动态应变率20～100 s?1下，煤岩破坏后碎块具有明显的分形特性，破碎块度分维值为1.9～2.2，且随着应变率的升高，煤岩破碎程度增大，碎块块度减小；（3）基于Weibull分布参数F₀、m和应变率的关系，修正煤岩的本构模型，并与试验结果进行对比，验证该模型的合理性。

Failure characteristics and constitutive model of coal rockat different strain rates

With the increasing demand for coal resources, safe and efficient coal mining has attracted the attention of all sectors of society. In order to study the dynamic failure characteristics and constitutive relation of coal rock under different strain rates, uniaxial impact compression tests of coal rock were carried out over a strain rate range from 20 s?1 to 100 s?1 under nine air pressures by using a split Hopkinson pressure bar (SHPB) with a diameter of 50 mm, and a high-speed camera was used to monitor the whole process of coal rock failure. Based on the dynamic mechanical properties and fracture fractal dimension characteristics of coal rock under different strain rates, the dynamic failure characteristics of coal rock were deeply analyzed, and a dynamic strength statistical damage constitutive model was established based on Weibull statistical distribution and Drucker-Prager failure criterion. The results show that the dynamic stress-strain curves of coal rock under different strain rates exhibit obvious nonlinear characteristics, which can be roughly divided into linear elastic stage, plastic yield stage, peak stress stage and post-peak softening stage. As strain rate increases, dynamic uniaxial compressive strength and elastic modulus both show a significant linear growth. The failure mode of coal rock changes from axial cleaving failure at low strain rate to crushing failure at high strain rate. Coal rock fragments after dynamic failure are sieved and found to have obvious fractal characteristics. At the strain rates of 20?100 s?1, average fragmentation of coal rock samples is concentrated in 30?40 mm, and fractal dimension ranges from 1.9 to 2.2. With the increase of strain rate, the degree of fragmentation increases and fractal dimension increases, indicating that the proportion of large-scale coal rock fragments to the total mass gradually decreases. Based on the relationship between the Weibull distribution parameters F₀, m and strain rate, the dynamic constitutive model of coal rock is modified. Comparing the model results with test results, it is found that the model can fully reflect the relationship between stress, strain and strain rate, and the rationality of this model is also verified.