考虑二维和三维尺寸效应的基坑抗隆起稳定安全系数

Safety factor of heave-resistant stability considering two-and three-dimensional size effects of foundation pits

大量工程实践均表明,小尺寸基坑具有更好的稳定性,表现出明显的尺寸效应。但现有规范推荐的基坑稳定分析方法均假设基坑宽度和尺寸对安全系数没有影响,造成小尺寸和狭窄基坑围护设计的巨大浪费。目前,还没有采用解析方法计算的安全系数能够合理地考虑基坑的三维尺寸效应。为解决基坑稳定性的三维尺寸效应问题,提出了一个新的基坑安全系数W K,把基坑底隆起失稳问题简化为弹性半空间上在坑底施加一个负载所引起的塑性区扩展问题。基坑开挖形成的负载绝对值为1H。围护墙的存在导致基坑达到失稳极限状态时的塑性区向下扩展延伸,当塑性区的破裂面通过围护墙底时达到负载的极限状态。采用弹性力学解析解可计算出负载引起的附加应力,与地应力场叠加可计算出极限负载u p的大小,考虑坑外超载q后,定义W u 1K p/(H q)。利用这个新的安全系数不但可以分析长条形基坑宽度和矩形基坑大小对围护结构稳定性的影响,还可以针对基坑不同位置计算安全系数。本文方法为利用基坑的二维和三维尺寸和空间效应缩短围护结构入土深度提供了一个有力的理论工具,有极高的推广应用价值。

A large number of project practices show that small-size foundation pits are more stable, which display obvious size effects. However, the methods recommended by the existing codes all assume that the excavation width and size do not affect the safety factor, resulting in a great waste of enclosure structure of small-size and narrow foundation pits. Currently, the safety factor calculated by the analytical method cannot scientifically and reasonably consider the three-dimensional size effect of foundation pits. In order to solve the problem, a new safety factor Kw is proposed, by which the problem of excavation bottom uplifting and instability is reduced to that of the expansion of the plastic zone due to unloading in the elastic half-space. The absolute value of the load caused by excavation is γ1H. The enclosure structure of foundation pits leads to the extension of the plastic zone under the pit bottom downward when they fail. The ultimate state of the load will be reached when the fracture surface of the plastic zone passes through the toe of the enclosure structure, The additional stress caused by unloading can be calculated by the analytical solution of the elasticity. The limit load can be obtained by the additional stress plus the ground stress. Considering the overload q outside the foundation pits, Kw is equal to po/（γ1H ＋ q） The new safety factor Kw can be adopted to analyze the impact of the excavation width on the stability of strip pits and the impact of the excavation size on the stability of rectangular pits and to calculate the safety factor at the different positions for the same foundation pit. An important method is proposed to decrease the embedded depth of enclosure structure taking the advantages of two-and three-dimensional size effects and spatial effect of foundation pits so that the new safety factor can be widely applied.