圆形隧道弹塑性分析的强度理论效应研究

Effect of strength theory in elastic-plastic analysis of a circular tunnel

合理的强度准则对隧道围岩的弹塑性分析十分重要,首先归纳建立了平面应变条件下8种岩土常用强度准则的统一线性方程,进而考虑围岩剪胀特性和塑性区不同弹性应变情况,推导了理想弹塑性围岩应力和位移的新解,并对所得新解进行可比性分析,最后探讨了围岩弹塑性分析的强度理论效应与塑性区位移的参数影响特性。研究结果表明：本文统一线性方程应用简洁灵活,便于探讨强度理论效应;围岩弹塑性新解可退化为众多已有解答,具有广泛的适用性;隧道围岩的强度理论效应明显,应优先选用广义Matsuoka-Nakai准则、统一强度理论（b=1/2）、Mogi-Coulomb准则和广义Lade-Duncan准则,谨慎采用统一强度理论（b=1）、外接圆Drucker-Prager准则,不鼓励使用内切圆Drucker-Prager准则和Mohr-Coulomb准则;围岩塑性区位移受剪胀特性、塑性区弹性应变的影响显著,且不同强度准则下二者的影响程度不同,应综合考虑3种因素的共同影响。

A reasonable strength criterion is very critical in elastic-plastic analysis of rock tunnel. Under the plane strain condition, a unified linear equation is first established inductively for eight commonly used strength criteria in geotechnical engineering. Then, with considerations of dilatancy and different elastic strains in the plastic zone, new solutions for stress and displacement of elastic-perfectly plastic rock are deduced. Furthermore, the feasibility analysis of the obtained solutions is carried out. Finally, both the effect of strength theory and parametric studies about the plastic displacement of tunnel are investigated. It is found that the unified linear equation is concise and flexible, which is convenient to discuss the effect of strength theory. The new solutions of elastic-perfectly plastic rock can be degraded into many existing solutions and have broad applicability. The effect of strength theory in elastic-plastic analysis of a circular rock tunnel is remarkable, therefore the generalized Matsuoka-Nakai criterion, the unified strength theory with parameter b=1/2, the Mogi-Coulomb criterion and the generalized Lade-Duncan criterion are recommended to be adopted. The application of the unified strength theory with parameter b=1 and the circumscribed Drucker-Prager criterion should be adopted cautiously. The inscribed Drucker-Prager criterion and the Mohr-Coulomb criterion are not encouraged. The dilatancy and the elastic strains in the plastic zone affect the plastic displacement of tunnel significantly, and the influencing extent of these two factors obviously varies with different strength criteria. The effects of the dilatancy, elastic strains in the plastic zone and strength theory should be comprehensively considered.