为探究深埋不等直径圆形隧道围岩塑性区的应力状态和发展规律,本文在前人研究的基础上,基于Hoek-Brown屈服准则描述塑性区围岩,采用复变函数中的保角映射方法描述弹塑性边界,通过在弹塑性边界联立方程,推导了倾斜布置深埋不等圆隧道围岩塑性区边界解析解。随后基于边界的应力连续性条件验证了求解结果的可靠性,并将计算结果与数值模拟计算结果及Mohr-Coulomb屈服准则计算结果进行了对比,最后分析了解析解方法在不同屈服准则下的适用性。结果表明,本文解析解塑性区计算结果对数值模拟结果进行拟合时具有很好的一致性;与Mohr-Coulomb屈服准则的计算结果相比,本文解析解对2个塑性区边界相邻“尖角”处的拟合效果更好。本研究可为不等圆隧道围岩塑性区的分析提供新思路。
In order to investigate the stress state and development law of the plastic zone in the surrounding rock of deep buried unequal circular tunnel, this paper, on the basis of previous research, adopted the angle-preserving mapping method in the complex function to characterize the elastic-plastic boundary. The Hoek-Brown yield criterion was used to characterize the surrounding rock in the plastic zone. Following this, the stress equations were established at the elastic-plastic boundary. Through these equations, the analytical solution of the boundary analysis of the plastic zone of the surrounding rock of a deeply buried unequal circular tunnel with inclined arrangement can then be deduced. Subsequently, the reliability of the solution results is verified based on the stress continuity condition of the boundary, and the results of this paper are compared with those of numerical simulation and Mohr-Coulomb yield criterion calculations. Finally, the applicability of the analytical solution method under different yield criteria is analyzed. The results show that the results of the analytical solution of the plastic zone in this paper are in good agreement with the numerical simulation results. Compared with the results of the Mohr-Coulomb yield criterion, the analytical solution in this paper is more effective in fitting the two plastic zone boundaries adjacent to the “sharp corners”. The results of the study can provide new ideas for the analysis of the plastic zone of the surrounding rock in unequal circular tunnels in engineering.
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