基于等幅周期荷载下软岩Bingham本构模型的研究

Study on Bingham constitutive model for soft rock under constant amplitude periodic load

为建立一种描述等幅周期荷载下软岩应变特性的本构模型,将Bingham模型中的常值黏壶元件替换成与循环次数相关的变系数黏壶元件,常值弹性元件替换为随周期荷载循环次数的增大而衰减的非定值弹性元件,即可得到反映周期荷载下软岩各种应变规律的Bingham本构模型。当循环荷载应力上限值σmax大于岩石的临界强度σs时,模型为可反映软岩3个应变阶段的改进4参数Bingam模型;反之则为反映软岩前两个应变阶段的非常值2参数Hook模型。将周期荷载分解为一个定值荷载和一个平均应力值为零的周期荷载,基于流变力学理论给出了定值荷载作用下基于该模型的本构方程式,再根据黏弹性力学理论,给出了平均应力值为零的周期荷载下基于该模型的本构方程式,最后将已获得的本构方程式叠加即得到周期荷载下软岩本构方程式。结果表明:所建立的本构方程式可较好描述周期荷载下不同软岩各类应变特征,对各类软岩的应变曲线拟合的相关系数均在0.868以上,且同一种岩石模型中弹性元件系数初始值随周期荷载的动应力幅值的增大而减小,岩石加速应变速率参数随动应力幅值的增大而增大。

In order to develope a constitutive model to describe the strain characteristics of soft rock under constant amplitude cyclic loading,the constant-value dashpot element in Bingham model is replaced by the cycle-number-related variable coefficient dashpot element,while the constant-value elastic element is replaced by the non-constant-value elastic element that is attenuated along with the increase of the cycle-number of the cyclic loading,thus the Bingham constitutive model for reflecting all the strain laws of the soft rock under cyclic loading can be obtained. When the upper limit of cyclic load stress σmaxis larger than the critical strength σs of rock,the model is an improved four-parameter Bingam model that can reflect the three strain stages of the soft rock. contrarily,it is a non-constant-value two-parameter Hook model that can reflect the first two strain stages of the soft rock. By decomposing cyclic loading into a constant-value load and a periodic load with the mean stress value of zero,this model-based constitutive equation under the constant-value load is given out in accordance with the theory of rheological mechanics,and then this model-based constitutive equation under the periodic load with the mean stress value of zero is given out as well,finally,the constitutive equation under the periodic load can be acquired through superimposing the obtained constitutive equations. Finally,the constitutive equation under the cyclic loading can be acquired through superimposing the obtained constitutive equations. The result shows that the established constitutive equation can better describe all kinds of the strain characteristics of various soft rocks under cyclic loading,of which all the correlation coefficients for the fittings of the strain curves for all kinds of soft rocks are over 0. 868; moreover,the initial value of the elastic element in the model for the same kind of rock decreases along with the increase of the value of the dynamic stress amplitude,while the parameter of the accelerated strain rate increases along with the increase of the value of the dynamic stress amplitude.