Constitutive model of coal considering temperature under cyclic loading and unloading conditions
ZHOU Hongwei;HOU Wei;ZHANG Longdan;XIE Senlin;JIA Wenhao;SHI Beibei
随着煤炭资源深部开采趋于“常态化”,深入了解处于高地应力和高地温环境中深部煤体在扰动条件下的力学性质及其损伤演化规律,对煤矿深部开采具有重要意义。选取平煤十二矿己16-17-17200工作面的煤体为研究对象,开展了在不同温度条件下三轴循环加卸载试验,分析了温度对试件峰值强度、变形模量、泊松比等基本力学参数的影响。将不同加卸载速率相关的应力−应变问题转化为时间−应力−应变问题,同时引入分数阶导数理论和连续介质损伤理论,提出了一个考虑了热−力耦合作用的分数阶粘弹塑性本构方程,通过试验数据验证了其有效性。结果表明:煤体变形模量随着循环次数的增加呈出现线性减小的趋势,而煤体泊松比减速上升,在峰值应力处达到极值,然后降低,表明循环加卸载作用对煤体基本力学性能有劣化作用。随着温度的升高,煤体峰值强度非线性减小,损伤累积变缓,对应的应变逐渐增大,表明升温能增强煤体延性变形能力,加速煤体损伤的发展。在循环加卸载过程中,输入能密度、弹性能密度和耗散能密度在煤体破坏失稳阶段随温度升高呈现出明显的衰减现象,说明高温加剧了煤体内部的损伤,降低了煤体强度,使得破坏所需外界输入能量减少。考虑温度影响的分数阶粘弹塑性模型可以较好地描述深部煤体在循环加卸载条件下的力学行为。模型适用于热力耦合下深部煤体的复杂应力状态。
As the deep coal mining tends to be “normal”, it is of great significance to understand the mechanical properties and damage evolution of coal under high ground stress and high ground temperature environment in deep coal mining. The coal body of the Ji16-17-31030 working face in the Pingmei 12th Coal Mine was selected as the research object. The triaxial cyclic loading and unloading tests on the coal samples were carried out under different temperature conditions to examine the impact of temperature on their fundamental mechanical parameters, including peak strength, deformation modulus, and Poisson’s ratio. The stress-strain problems associated with different loading and unloading rates were reformulated into time-stress-strain problems, and a fractional viscoelastic-plastic constitutive equation considering the coupling effect of thermal and force was proposed by introducing the fractional derivative theory and the continuum damage theory. The results show that the deformation modulus of coal decreases linearly with the increase of cycle times, while the Poisson ratio of coal shows a deceleration increase, reaches the extreme value at the peak stress, and then decreases, indicating that the cyclic loading and unloading has a deterioration effect on the basic mechanical properties of the coal. With the increase of temperature, the peak strength of coal decreases nonlinearly, the damage accumulation slows down, and the corresponding strain increases gradually, which indicates that heating could enhance the ductile deformation ability of coal and accelerate the development of coal damage. In the process of cyclic loading and unloading, the input energy density, elastic energy density and dissipated energy density decay obviously decay with the increase of temperature in the stage of coal failure and instability, indicating that high temperature intensifies the damage inside the coal, reduces the coal strength, and reduces the external input energy required for failure. The fractional viscoelastic-plastic model considering the effect of temperature can better describe the mechanical behavior of deep coal body under cyclic loading and unloading conditions. The model is suitable for the complex stress state of deep coal body under a thermal-mechanical coupling, and provides an important reference for the research on the deformation and stability of deep coal body.
deep coal;fractional derivative;cyclic loading and unloading;temperature effect;thermo-mechanical coupling
主办单位:煤炭科学研究总院有限公司 中国煤炭学会学术期刊工作委员会