下伏空洞地基极限承载力与破坏模式上限有限元法

Upper bound finite element method for ultimate bearing capacity and failure mechanism of subgrade above void

地基极限承载力的确定对于下伏空洞地区基础设计和施工具有重要意义。采用上限有限元法对地基破坏时的极限状态进行数值模拟。首先,简要介绍上限有限元法的基本原理与计算过程;进而提出合理的计算假定,建立可考虑多种影响因素的计算模型;其次,利用上限有限元法计算出多种工况下的地基极限承载力上限解,按Tergaghi建议的地基承载力公式,得到承载力系数N_c、N_q、N_g,并对其影响因素进行分析;最后,根据大量的能量耗散图及速度场图提出3类典型的破坏模式,并对其影响因素进行分析。研究表明:随着内摩擦角j的增大,N_c和N_q均增大,而当j较大时,N_g才出现正数,且随着j增大而增大;随着空洞顶板厚度与基础宽度之比H/B的增大,N_c和N_q均增大。而当j较小时,N_g随着H/B的增大而减少;当j较大时,N_g随着H/B的增加而增加。N_c、N_q和N_g均随着D/B的增大而减少。下伏空洞地基存在3种典型的破坏模式:冲切破坏模式、冲切剪压破坏模式和Prandtl破坏模式。

Determining ultimate bearing capacity problem is of great importance in design and construction of the subgrade above void. The limit damage state of subgrade is numerically simulated by using upper bound finite element method. Firstly, the basic principles and calculation process of the upper bound finite element method are briefly introduced. Secondly, reasonable calculation assumption is proposed; and then a numerical model that can take various factors into consideration is established. Thirdly, the upper-limit solutions of ultimate bearing capacity under various conditions are calculated by using upper bound finite element method; and the bearing capacity coefficients Nc, Nq, Nγ are computed by using the formula of ultimate bearing capacity, as Tergaghi suggested; and then their influencing factors are analyzed. Finally, based on the large amount of energy dissipation and velocity field pattern analysis, three typical failure modes are presented and their influencing factors are analyzed. It is shown that Nc and Nq increase with the increasing of internal friction angle of φ, and when φ is larger, Nr is positive number, and increases with the increasing of φ; Both Ne and Nq increase with the increasing of the ratio of viod roof thickness and footing width H/B; and when φ is smaller, Nr decreases with the increase of H/B. When φ is larger, Nγ increases with the increasing of H/B; and Nc, Nq and Nγ both decrease with the increase of D/B. The subgrade above void has three typical failure mechanisms： punching failure mode, punching shear press failure mode and Prandtl failure mode.