基于Hoke-Brown准则的深埋圆形透水隧洞弹塑性分析

针对深埋圆形隧洞轴对称问题,将Hoke-Brown准则方程代入考虑渗透体积力影响的平衡微分方程进行求解,得到关于塑性区洞周应力的隐式方程,通过求解超越方程得到塑性区洞周应力数值解;再考虑应力重分布影响,利用塑性区半径处应力连续条件得到弹性区岩体应力数值解。将该解答与基于Mohr-Coulomb准则的解答进行了比较。结果表明,两种准则条件下岩体应力分布规律相似。采用Hoke-Brown准则计算时,塑性区较小,径向应力绝对值较大,塑性区环向应力也较大;采用Mohr-Coulomb准则准则计算时,塑性区较大,径向应力绝对值较小,塑性区环向应力也较小。在内外水头比值较小时,按Mohr-Coulomb准则求得的峰值应力较按Hoke-Brown准则求得值大,当水头比较大时则相反。

Elastio-plastic Analysis on Deep Buried Circle Tunnel Considering Seepage Effect Based on Hoke-Brown Criterion

For the deeply buried circle tunnel under the condition of axial symmetry, the equilibrium differential equation considering the body force of seepage is resolved by using the Hoke-Brown criterion, the implicit equation about the stress of tunnel in the plastic zone is obtained, and the numerical solution of the stress in the plastic zone is obtained by solving the transcendental equation. Considering the influence of stress redistribution, the numerical solution of stress in the elastic zone is obtained by using the stress continuous condition at the radius of the plastic zone. An example is analyzed by two methods based on the Hoke-Brown criterion and the Mohr-Coulomb criterion. The research shows that stress distribution characteristic is similar to the two criteria. The plastic zone is smaller, the radial stress is larger, the circumferential stress in the plastic zone is larger under the Hoke-Brown criterion. The plastic zone is larger, the radial stress is smaller, the circumferential stress in the plastic zone is smaller under the Mohr-Coulomb criterion. When the inner water head of the tunnel is smaller, the maximum stress based on the Hoke-Brown failure criterion is larger than the one based on the Mohr-Coulomb failure criterion, and the opposite result appears when the inner water head is large.