不同长径比煤样动力学特征及本构模型

为研究冲击荷载下不同长径比煤样的动力学性能，借助改进的霍普金森压杆实验装置(?75 mm),开展6个冲击等级(4.18～8.03 m/s)、4种长径比(0.33～1.33)下的冲击压缩实验，并结合灰色关联理论分析动力学参数与长径比之间的关联性，建立基于力学机制、Weibull分布、D-P准则的4参数单轴煤岩强度型统计损伤模型。研究表明：(1)煤样长径比与应变率、动抗压强度、耗散能均呈二次函数关系，且耗散能随长径比增加而降低；与电磁能呈一次函数关系，且保持正相关。(2)煤样长径比对动力学参数的影响排序为：电磁能(0.88)>动抗压强度(0.84)>耗散能(0.81)>应变率(0.78)。(3)基于Weibull分布、D-P准则构建初始本构模型，并借助动抗压强度σ_max与应变率、长径比n的关系修正，进而对比实验应力-应变曲线，验证模型可靠性(R²>0.91)。

Dynamic characteristics and constitutive model of coal samples with different length diameter ratio

In order to study the dynamic performance of coal samples with different length diameter ratio under impact load, this paper used an improved Hopkinson compression bar experimental device (?75 mm), and carried out the impact compression experiments under 6 impact grades (4.18~8.03 m/s)and 4 aspect ratios(0.33~1.33).It analyzed the correlation between the dynamic parameters and the aspect ratio in combination with the gray correlation theory, and this study then established a 4-parameter uniaxial strength type statistical damage model of coal and rock based on the mechanical mechanism, Weibull distribution and D-P failure criterion.Results show that: ① The length diameter ratio of coal samples has a quadratic function relationship with the strain rate and dynamic compressive strength; The relationship between the dissipation energy and the aspect ratio is a quadratic function, and the dissipation energy decreases with the increase of the aspect ratio; The relationship between the electromagnetic energy and the aspect ratio is a linear function and keeps a positive correlation. ② According to the grey correlation theory, this study obtained the influence order of length diameter ratio of coal sample on dynamic parameters: electromagnetic energy(0.88)>dynamic compressive strength(0.84)>dissipation energy(0.81)>strain rate(0.78).③ The initial constitutive model is constructed based on Weibull distribution and D-P criterion, and the dynamic compressive strength σ_max and strain rate、the relationship between length to diameter ratio n was corrected, and then the experimental stress-strain curves were compared to verify the reliability of the model(R2>0.91).