卸荷损伤泥岩应力松弛特征及本构模型研究

Study on the Stress Relaxation Characteristics and Constitutive Model of Unloading Damage Mudstone

软弱岩体开挖卸荷形成的损伤对其支护加固后的应力松弛特性影响不可忽视。以红层泥岩为研究对象,开展了不同卸荷损伤程度泥岩的单轴应力松弛破坏试验,研究了不同应变水平及卸荷损伤程度对泥岩松弛特性的影响规律。结果表明:卸荷损伤泥岩在破坏前后的分级应力松弛试验中应力曲线均表现为不完全松弛,应力松弛曲线主要包含减速及稳定松弛两阶段,且各级应变水平下松弛量和松弛时间均随卸荷损伤程度增加呈线性增大趋势。基于分数阶微积分理论,选取R-L分数阶弹黏性元件(F元件),提出考虑黏滞系数时变特征的弹黏性时变元件(FT元件),然后引入卸荷损伤程度因子,提出考虑卸荷损伤的分数阶弹黏性时变元件(UFT元件),最后将该元件引入传统Burgers模型,建立了基于分数阶的非线性松弛本构模型。基于不同分数阶元件的理论本构模型计算值与试验数据对比表明,基于UFT元件的松弛本构模型具有更高的精确性,且不同应力水平及卸荷损伤程度下的模型理论计算成果与试验数据均较吻合,表明该松弛本构模型能够精确地描述卸荷损伤泥岩松弛特征。

The influence of the damage caused by excavation and unloading of soft rock mass on the stress relaxation characteristics of its support reinforcement cannot be ignored.Taking the red layer mudstone as the research object,the uniaxial stress relaxation failure test of unloading damaged mudstone was carried out,and the influence of different strain levels and unloading damage degrees on the relaxation characteristics of mudstone was studied.The results show that:The stress curves of the graded stress relaxation test of the unloading damaged mudstone before and after failure are all incomplete relaxation,and the stress relaxation curve mainly includes two stages:deceleration and stable relaxation,and the relaxation amount and relaxation time at all levels of strain level show a linear increase trend with the increase of the degree of unloading damage.Based on the fractional calculus theory,the R-L fractional order elastic viscous element(F element)is selected,and an elastic viscous time-varying element(FT element)considering the time-varying characteristics of viscosity coefficient is proposed,and then the unloading damage degree factor is introduced,and a fractional order elastic viscous time-varying element(UFT element)considering the initial unloading damage degree is proposed.Finally,the component is introduced into the traditional Burgers model to establish a nonlinear relaxation constitutive model based on fractional order.The comparison and discussion of the calculation values and experimental data of the theoretical constitutive model based on the three fractional order elements shows that the relaxation constitutive model based on UFT elements has higher accuracy,and the theoretical calculation results of the model under different stress levels and unloading damage degrees are consistent with the experimental data,indicating that the relaxation constitutive model can better and accurately describe the relaxation characteristics of unloading damage mudstone.