NUMERICAL SIMULATION OF THE STRAIN LOCALIZATION OF A CIRCULAR TUNNEL AT DIFFERENT ELASTIC MODULI
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摘要: 利用基于运动方程求解的FLAC程序模拟了不同弹性模量时圆形巷道的应变局部化过程。在计算中, 采用了"先加载, 后挖洞"方式。模拟结果表明, 在弹性模量中等或较小的条件下, 由于开挖卸荷而产生的围岩向空腔内部的"涌入"(运动)现象比较明显, 进而围岩中诱发了较多的破坏、V形坑或短剪切带式破坏。在上述条件下, 基于静力平衡的解析及数值方法不再适用, 而且是偏于不安全的。弹性模量越小, 开挖之后, 围岩维持其均匀周向(或环向)变形的能力越差, 这种轴对称变形越容易被打破, 也被打破得越早。尽管随着弹性模量的增加, 破坏单元数的变化并不是单调的, 但是在总体上, 随着弹性模量的增加, 破坏单元数目降低, 最大剪切应变增量急剧单调下降。Abstract: Strain localization processes of a circular tunnel at different elastic moduli are modeled by use of FLAC where the solution is based on equations of motion. In the present calculation, the tunnel is excavated after the model is loaded to reach a static equilibrium state. The numerical results show that at low and moderate elastic moduli, the movement of the surrounding rock toward the center of the tunnel is apparent once the tunnel is excavated, generating many fracture bands, V-shaped notches and shorter shear bands. The analyses and numerical simulations based on static equilibrium, which may yield unsafe solutions, cannot be applied to these cases. When the elastic modulus is lower, the capacity of the surrounding rock maintaining uniform circumferential or loop deformation is worse, and the axially-symmetrical deformation mode is easier to be broken and broken earlier. Although the failed number of elements is not monotonic with an increase of the elastic modulus, in general, as the elastic modulus is increased, the failed number of elements decreases, and the maximum shear strain increment is decreased monotonically and rapidly.
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Key words:
- circular tunnel /
- strain localization /
- shear band /
- elastic modulus /
- shear strain /
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图 1 模型的几何特征及边界条件
(a)巷道开挖之前; (b)巷道开挖之后
Figure 1. Model geometry and boundary conditions
图 2 各方案围岩的破坏样式(时步= 60000)
(a)方案1; (b)方案2; (c)方案3; (d)方案4; (e)方案5; (f)方案6; (g)方案7; (h)方案8; (i)方案9; (j)方案10; (k)方案11; (l)方案12; (m)方案13; (n)方案14
Figure 2. Failure modes in schemes 1 to 14 (step = 60000)
图 3 方案1的破坏过程(a-h)及最大失衡力-时步曲线(i)
Figure 3. The failure process (a-h) of Scheme 1 and the maximum unbalanced force-timestep curve (i)
图 4 方案8的破坏过程(a-d)及最大失衡力-时步曲线(e)
Figure 4. The failure process (a-d) of Scheme 8 and the maximum unbalanced force-timestep curve (e)
图 5 方案12的破坏过程(a-g)及最大失衡力-时步曲线(h)
Figure 5. The failure process (a-g) of Scheme 12 and the maximum unbalanced force-timestep curve (h)
图 6 不同方案的破坏单元数及最大剪切应变增量
Figure 6. The numbers of failed elements and the maximum shear strain increments in different schemes
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