中文摘要：

为了可以合理地描述岩石的体积变形行为,从分数阶微积分出发,基于分数阶常黏性和变黏性系数Abel黏壶元件,提出了环向-轴向应变分数阶黏壶,构建了岩石在单三轴压缩,松弛及蠕变条件下的分数阶体积应变-轴向应变关系,得到了模型的解析解,新模型可为求解岩石的体积应变提供一种新方法。在完整砂岩、泥岩试样及单裂隙砂岩试样的单三轴压缩、松弛及裂隙花岗岩蠕变试验数据的基础上,通过拟合分析确定了分数阶导数体积-轴向应变关系模型的参数,并进行了参数敏感性分析,揭示了围压、单裂隙倾角、微分阶数及模型参数对体积应变的影响规律。结果表明,利用该黏壶构建的体积-轴向应变关系模型,不仅可以更好地描述岩石体积变形的剪缩、剪胀特性,还能够反映岩石的松弛及蠕变变形特性。

英文摘要：

To provide better description for the volume deformation of rock, a lateral-axial strain fractional dashpot is presented on the basis of the Abel dashpot with a constant viscosity coefficient and a variable viscosity coefficient. A new model of volume-axial strain relationship is proposed based on fractional order calculus. The analytical solution for the model of volume-axial strain relationship is given theoretically. The new models have the advantages of solving volumetric strain of rock. Moreover, a multifunctional material testing setup is employed to measure volume-axial strain of various rock samples under the condition of triaxial compression, stress relaxation and uniaxial creep compression. The parameters of the volume-axial strain model are determined by regressing the experimental results of volume-axial strain of rock. In addition, a sensitivity study of the analytical solution of the volume-axial strain model is carried out, which shows the effects of confining pressure, fracture angle, fractional derivative order and model coefficient on volumetric strain of rock samples. It is found that the new models can describe not only the volumetric strain phenomenon of negative and positive dilatancy but also the stress relaxation and creep deformation characteristics in rock.