Shear Rheological Characteristics and Nonlinear Constitutive Model of Serrate Structure Surface
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摘要: 为了对岩体结构面的蠕变和松弛特性进行比较分析，用水泥砂浆浇筑成不同角度的结构面试样，在岩石双轴流变试验机上对同一应力起点的规则齿形结构面进行剪切应蠕变试验和松弛试验.首先分析了的蠕变与松弛特性，其次对参数非线性流变本构模型的建立和求解进行探讨，最后采用参数非线性流变方程对试验曲线进行拟合. 试验结果表明：结构面剪切蠕变曲线和松弛曲线都可以分为瞬时、衰减和稳定3个阶段；基于能量理论分析蠕变和松弛过程，显示蠕变是能量的注入与耗散过程，而松弛主要是能量的耗散过程；建立非线性流变模型时，应采用流变力学模型理论推导其本构方程；积分法与Laplace变换法求解蠕变方程或松弛方程时，相应的初始条件不相同；考虑黏性系数是与时间相关的非定常参数，提出了参数非线性Maxwell模型的蠕变方程和松弛方程，与试验曲线拟合结果比较理想；蠕变方程和松弛方程的拟合参数值不同，表明蠕变与松弛不等价且不能相互置换.Abstract: In order to investigate the creep and stress relaxation characteristics of rock mass discontinuity with different slope ratios, the creep and stress relaxation tests of dentate discontinuity poured by cement mortar on the condition of shear stress are carried out by using a biaxial creep machine. First, the comparison of creep and relaxation was made. Secondly, the establishment and solution of nonlinear rheological constitutive model were discussed. Final, nonlinear rheological equation was used to fit the test curve. According to the test results, both creep curves and relaxation curves can be divided into three stages: the instantaneous stage, attenuation stage, and stable stage. From the energy perspective, creep is the process of energy accumulation and dissipation, and stress relaxation is the process of energy dissipation. The constitutive equation of nonlinear rheological model should be deduced by using rheological theory. The initial condition of creep is different to that of relaxation when the finite integration method and Laplace transformation is used to solve equations. The creep equation and relaxation equation of the nonlinear-parameters Maxwell model are obtained by determining the relation between the viscosity coefficient and time, and the equation curves agree with the test results. The parameter values of the creep equation is different to that of relaxation equation, which reveal that the creep properties are not equivalent to the relaxation properties and creep and relaxation cannot be mutual conversion.
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Key words:
- structure surface /
- creep /
- relaxation /
- nonlinear rheological model /
- creep and relaxation equation /
- equivalent
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图 4 不同角度蠕变速率和应力松弛速率曲线
Figure 4. Creep rate and relaxation rate curves of structure surface
图 7 10°结构面高应力下蠕变速率曲线
Figure 7. Creep rate curve of 10° discontinuities under high stress
图 8 应力松弛速率图
Figure 8. Variation curves of stress relaxation rate for red silty mudstone with time
表 1 正确与错误推导方法的结果比较
Table 1. Comparison between correct and wrong methods
流变方程 常参数方程 非线性本构方程 模型参数 $\eta (t)$ 正确 错误 蠕变方程 \setlength{\voffset}{0pt}$\varepsilon \left( t \right) = {\sigma_0}\left({\displaystyle\frac{1}{E} + \displaystyle\frac{t}{\eta }} \right)$ \setlength{\voffset}{0pt}$\displaystyle\frac{\sigma }{{\eta \left( t \right)}} + \displaystyle\frac{{\dot \sigma }}{E} = \dot \varepsilon $ \setlength{\voffset}{0pt}$A + Bt$ \setlength{\voffset}{0pt}$\varepsilon \left( t \right) = \displaystyle\frac{{{\sigma _0}}}{E} + \displaystyle\frac{{{\sigma _0}}}{B}\ln \left( {1 + \displaystyle\frac{{Bt}}{A}} \right)$ \setlength{\voffset}{0pt}$\varepsilon \left( t \right) = {\sigma _0}\left( {\displaystyle\frac{1}{E} + \displaystyle\frac{t}{{A + Bt}}} \right)$ 松弛方程 \setlength{\voffset}{0pt}$\sigma \left( t \right) = {\sigma _0}{{\rm{e}}^{-\textstyle\frac{E}{\eta }t}}$ \setlength{\voffset}{0pt}$\displaystyle\frac{\sigma }{{\eta \left( t \right)}} + \displaystyle\frac{{\dot \sigma }}{E} = \dot \varepsilon $ \setlength{\voffset}{0pt}$A + Bt$ \setlength{\voffset}{0pt}$\sigma (t) = {\sigma _0}{{\rm{e}}^{\textstyle{\frac{E}{B}\ln \left(\frac{A}{{A + Bt}}\right)}}}$ \setlength{\voffset}{0pt}$\sigma \left( t \right) = {\sigma _0}{{\rm{e}}^{ - {\textstyle\frac{E}{{A + Bt}}t}}}$ 
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表 2 非线性Maxwell模型参数
Table 2. Parameter values for nonlinear Maxwell models
试验类型 角度/（°） \setlength{\voffset}{0pt}$\displaystyle\frac{{{\tau _0}}}{{{\tau _{{\max}}}}}$ G/GPa A/（GPa•h） B/GPa 相关系数R 蠕变 10 0.4 0.520 0.808 52.98 0.975 4 蠕变 45 0.4 0.685 1.125 114.08 0.975 6 松弛 10 0.4 0.302 0.091 6.48 0.981 2 松弛 45 0.4 0.772 0.086 19.46 0.987 8
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