空洞上方浅基础地基破坏模式与极限承载力分析

利用极限分析上限法求解地基极限承载力问题的关键在于构造合适的破坏模式。当地基下方存在空洞时，地基的破坏模式变得相当复杂。通过分析空洞存在时地基的受力特点及破坏形态，将地基破坏范围划分成为不同的刚性区和过渡区，构造了空洞上方条形基础地基的破坏模式。利用上限法，建立与破坏模式对应的速度场，推导了破坏模式不同区域内的耗散功率和外力功率，得到地基极限承载力的目标函数，并采用数学优化方法进行求解，获得了极限承载力的上限解。通过算例分析，讨论了空洞顶板厚度、空洞大小与地基极限承载力的关系，并与无空洞条件下地基极限承载力进行对比分析。结果表明，随着空洞顶板厚度增加，地基极限承载力增加，破坏模式也由地基与空洞之间扩散到地基两侧；空洞顶板厚度存在临界值，当超过此临界值时，空洞对地基极限承载力的影响可忽略。

Failure mechanism and ultimate bearing capacity of strip footing above void

The most important step of solving ultimate bearing capacity problem by using upper bound limit analysis is to form a suitable failure mechanism. The failure mechanism becomes complex when there is a void beneath the footing. By analyzing the mechanic properties and failure shape of strip footing above void, its failure mechanism was formed and the failure range was divided by various rigid and transition area. Upon upper bound method, the velocity field corresponding to failure mechanism was built, and the energy caused by external force and energy dissipation under limit state was deduced. Thus the object function of ultimate bearing capacity can be obtained and solved by mathematic optimization. Finally, the influence factors of ultimate bearing capacity, such as void roof thickness and size, were analyzed by using calculating example. The obtained results were also compared with the case which no void contains. It shows that ultimate bearing capacity is increased with the increase of void roof thickness and the range of failure mechanism is therefore diffusing from area beneath the footing to both sides of footing. And there also exists a critical void roof thickness beyond which, the influence of void can be neglect..