# 矿山围岩蠕变破坏过程数值模拟Numerical Simulation of Creep Failure Process of Mine Surrounding Rock

DOI: 10.12677/ME.2019.72027, PDF, HTML, XML, 下载: 437  浏览: 1,391

Abstract: Creep property of rock mass has a significant impact on the stability of underground constructions. On the basis of classical power-law creep model, the time-dependent creep behavior of rock is in-vestigated based on damage mechanics principle, in which the damage evolution is considered as a key factor dominating the accelerating creep and a damage-based constitutive law for tertiary creep is proposed. The maximum tensile strain criterion and the Mohr-Coulomb criterion are utilized as two damage thresholds to control the rock damage. Then the damage-based creep model is implemented using finite element method by MATLAB programming, a powerful PDE-based multiphysics modeling environment. The model is firstly validated by comparing the numerical results with the previously published experimental observation and then used to simulate the rock creep under uniaxial and biaxial compression. The model accurately reproduces the classic tri-modal behaviour (primary, secondary and tertiary creep) seen in laboratory creep (constant stress) experiments. So the fact shows that the rheological model is appropriate to predict the nonlinear creep failure of rocks, and the complex macroscopic time-dependent behavior can be mechanically explained by the material degradation (damage) at the mesoscale.

1. 引言

2. 蠕变损伤模型建立

2.1. 蠕变本构模型

$\epsilon ={\epsilon }_{\text{e}}+{\epsilon }_{\text{c}}$ (1)

(2)

B是比例因子， $\Delta H$ 是活化能，R是普适气体常数，T是温度。

${\stackrel{˙}{\epsilon }}_{\text{c}}=A{\sigma }^{\beta }\alpha {t}^{\alpha -1}$ (3)

(4)

${\sigma }_{\text{e}}=\left(\frac{1}{\sqrt{2}}\right){\left[{\left({\sigma }_{11}-{\sigma }_{22}\right)}^{2}+{\left({\sigma }_{33}-{\sigma }_{22}\right)}^{2}+{\left({\sigma }_{11}-{\sigma }_{33}\right)}^{2}+6\left({\sigma }_{12}^{2}+{\sigma }_{23}^{2}+{\sigma }_{13}^{2}\right)\right]}^{\frac{1}{2}}$ (5)

2.2. 损伤演化方程

${F}_{1}\equiv -{\sigma }_{3}-{f}_{t0}=0$${F}_{2}\equiv {\sigma }_{1}-{\sigma }_{3}\frac{1+\mathrm{sin}\theta }{1-\mathrm{sin}\theta }-{f}_{c0}=0$ (6)

Figure 1. Elastic damage constitutive law of element under uniaxial tensile and compressive stress

$E=\left(1-D\right){E}_{0}$ (7)

$D=\left\{\begin{array}{l}0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{F}_{1}<0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{F}_{2}<0\\ 1-{|\frac{{\epsilon }_{t0}}{{\epsilon }_{1}}|}^{n}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{F}_{1}=0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}d{F}_{1}>0\\ 1-{|\frac{{\epsilon }_{c0}}{{\epsilon }_{3}}|}^{n}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{F}_{2}=0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}d{F}_{2}>0\end{array}$ (8)

3. 数值模拟

3.1. 数值模型验证

Figure 2. Model boundary condition

(a) 邱贤德的蠕变试验结果 (b) 杨春和的蠕变试验结果

Figure 3. Comparison between simulated creep curve and experimental creep curve

3.2. 蠕变特性数值模拟

Figure 4. Calculation model

Table 1. Physico-mechanical parameters of model specimens

Figure 5. Numerically obtained creep deformation curves under uniaxial compression creep

Figure 6. Failure process of rock specimen under uniaxial compression creep

Figure 7. Numerically obtained creep deformation curves under biaxial compression creep

4. 结论

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