砂岩单轴压缩黏弹塑性分数阶蠕变模型研究

Study on the viscoelastic-plastic fractional creep model ofsandstone in uniaxial compression

为建立参数少、计算简便、蠕变过程描述准确的蠕变模型,基于岩石力学及分数阶理论,引入分数阶软体元件,将其与弹性、塑性、黏性元件相结合,得到了创新的黏弹塑性蠕变模型,推导蠕变模型的本构方程,并对砂岩单轴压缩蠕变试验数据进行参数辨识、曲线拟合和对比分析,进而对蠕变模型进行验证。结果表明:引入的分数阶软体元件应变随时间呈幂函数趋势增长,可表征非线性蠕变阶段,详细地分析了弹性元件、塑性元件、黏性元件及分数阶软体元件在蠕变过程中不同阶段发挥的作用;推导得到模型在ε·(t→∞)=0(σ<σ_(s))、ε·(t→∞)>0(σ<σ_(s))、ε·(t→∞)>0(σ≥σ_(s))情况下的本构方程,以及计算简便的参数辨识方法,试验数据拟合曲线的拟合度均在0.9以上,验证了蠕变模型的合理性和科学性;所建立的六参数黏弹塑性分数阶模型能全面地描述蠕变的整个过程,并且与其他模型对比模型参数更少、计算量更小。

In order to establish a creep model with few parameters,simple calculation and accurate description of the creep process,based on rock mechanics and fractional order theory,fractional-order soft components were introduced and combined with elastic,plastic and viscous components,and an innovative viscous model was obtained.The elastic-plastic creep model was used to derive the constitutive equation of the creep model,and the parameter identification and curve fitting and comparative analysis were performed on the sandstone uniaxial compression creep test data,and then the model was verified.The results showed that the strain of the introduced fractional-order soft element increases with time as a power function,which can characterize the nonlinear creep stage.The creep process of elastic element,plastic element,viscous element and fractional-order soft element was analyzed in detail.The constitutive equations of the model under three different conditionsε·(t→∞)=0(σ<σ_(s)),ε·(t→∞)>0(σ<σ_(s)),ε·(t→∞)>0(σ≥σ_(s))and the parameter identification method with simple calculation were derived,and the fitting degree of the fitting curve of the test data was above 0.9.The rationality and scientificity of the creep model were verified.The established six-parameter viscoelastic-plastic fractional order model could comprehensively describe the whole process of creep,and compared with other models,the model required fewer parameters and less computation.