考虑时效损伤的岩石分数阶蠕变本构模型

为准确描述岩石蠕变变形破坏全过程,引入连续损伤和分数阶微积分理论建立全面、简练的蠕变本构模型。首先基于弹性模量随时间衰减规律,根据能量损伤的方式定义损伤变量,构建考虑时效损伤的弹性体,并验证该损伤演化方式的可行性。采用Riemann-Liouville型分数阶微积分算子理论,构建具有非线性特征的分数阶软体元件,利用该软体元件作为分数阶黏滞体描述岩石黏弹性应变,在该软体元件的基础上进行损伤演化,得到考虑时效损伤的分数阶黏塑性体。联合分数阶黏滞体、考虑时效损伤的弹性体和分数阶黏塑性体,建立一个新的考虑时效损伤的分数阶蠕变本构模型。给出参数解析方法,利用泥质板岩蠕变数据验证模型合理性和优越性。分析损伤发展过程,判断模型参数敏感度,并通过红砂岩、千枚岩单轴压缩各向异性蠕变特性试验研究蠕变试验数据验证模型适用性。研究成果为岩石蠕变全过程辨识及岩体工程长期稳定性研究提供一定参考。

Fractional Creep Constitutive Model of Rock in Consideration of Aging Damage

To accurately describe the whole process of creep deformation and failure of rock, a comprehensive and concise creep constitutive model is established by introducing continuous damage and fractional calculus theory. First of all, damage variable is defined according to the energy damage mode, and the elastic body in consideration of aging damage is constructed based on the attenuation law of elastic modulus with time, and the feasibility of the damage evolution mode is verified. The fractional order software components with nonlinear characteristics are constructe based on the Riemann-Liouville type fractional calculus operator theory, and the viscoelastic strain of rock is described with the aforementioned software components as a fractional viscous body. On such basis, the fractional order viscoplastic body in consideration of aging damage is obtained via damage evolution. Hence, a new fractional creep constitutive model in consideration of aging damage is established. The parameter analysis method is given, and the rationality and superiority of the model are verified by the creep data of argillaceous slate. Moreover, the damage development process is analyzed to determine the sensitivity of the model parameters, and the applicability of the model is verified by creep test data of red sandstone and phyllite. The research results offer reference for identifying the whole creep process and the long-term stability of rock mass.