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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。
The key to solve the ultimate bearing capacity of foundation by using the upper bound method of limit analysis is to construct a suitable failure mode. When there is a hole below the foundation, the failure mode of the foundation becomes quite complicated. By analyzing the stress characteristics and failure modes of the foundation in the presence of empty cavities, the failure area of the foundation is divided into different rigidities and transitional regions, and the failure mode of the foundation above the hollow is established. The upper bound method is used to establish the velocity field corresponding to the failure mode and the dissipative power and external force in different regions of the failure mode are derived to obtain the objective function of the ultimate bearing capacity of the foundation. Mathematical optimization is used to solve the velocity field. The ultimate bearing capacity The upper solution. Through the case study, the relationship between the thickness of the roof, the size of the cavity and the ultimate bearing capacity of the foundation is discussed, and the ultimate bearing capacity of the foundation under the condition of no void is compared. The results show that with the increase of the thickness of the roof, the ultimate bearing capacity of the foundation increases, and the failure mode also spreads from the foundation and the cavity to both sides of the foundation. The thickness of the cavity roof has a critical value. When the critical value is exceeded, The effect of force can be neglected.