基于随机介质理论的基坑开挖地层变形计算
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TU91

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国家重点研发计划课题(2023YFC3707803);中铁建交运集团有限公司科研计划课题(2024-03)


Calculation of Strata Deformation Induced by Foundation Pit Excavation based on Stochastic Medium Theory
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    摘要:

    基坑开挖不可避免地引起周边地层的变形,进而影响周围建筑的安全,为建立一种基坑开挖引起地层变形的计算方法。将基坑开挖引起地层变形的发生和发展视为三个独立的过程,并据此将变形分解为地层损失、墙背摩擦和坑底开挖卸荷三部分;随后基于随机介质理论和Mindlin解,分别推导了各部分引起的地层三维变形,并在小变形假设下,基于叠加原理得到了基坑开挖引起的地层变形三维解;进一步考虑到实际工程中基坑形状的多样性,建立了一种基坑支护结构与地层间接触面的标定及分组方法,该方法仅需几个特定的向量即可实现对基坑形状及尺寸的精确描述,极大的简化了基坑开挖引起地层变形的计算过程;同时实现了整个计算过程的程序化,在实际应用中仅需修改输入参数即可进行基坑开挖引起的地层变形分析,便于工程人员的广泛应用。最后以实际工程为例,对所建立的地层变形计算方法进行了工程应用和对比分析,结果表明该方法得到的地层变形解析结果与现场实测间的误差在合理范围,解析结果符合基坑开挖引起的地层变形规律,验证了方法的可靠性。为实现变形控制,实际工程中应尽可能地减小地层损失、开展坑底堆载。该方法理论依据明确、程序化较高、应用简单,能够为实际工程中基坑开挖引起的地层变形分析及控制提供参考。

    Abstract:

    Deformation of the surrounding strata is inevitably induced by foundation pit excavation, which in turn affects the safety of nearby buildings. In this study, a calculation method for analyzing the deformation of surrounding strata induced by foundation pit excavation is proposed. The occurrence and evolution of strata deformation are regarded as three independent processes, and the deformation is decomposed into three components: ground loss, wall friction, and excavation unloading. Based on stochastic medium theory and the Mindlin solution, the three-dimensional strata deformation induced by each component is derived separately. Under the small-deformation assumption, a three-dimensional solution of strata deformation induced by foundation pit excavation is obtained based on the superposition principle. Considering the variability of foundation pit shapes in engineering practice, a method for calibrating and categorizing the contact surface between the foundation pit support structure and the strata is proposed. With this method, the shape and size of the foundation pit can be accurately described using only a few specific vectors, thereby greatly simplifying the calculation of surrounding strata deformation induced by foundation pit excavation. Moreover, the entire calculation process has been implemented in a program, and in practical applications, only the input parameters need to be adjusted to assess the strata deformation induced by foundation pit excavation, facilitating its broader application in engineering practice. Finally, using an actual project as a case study, the proposed method was applied and compared with field measurements. The results indicated that the discrepancy between the analytical and measured values remained within acceptable ranges, and the analytical results exhibited good agreement with the observed patterns of strata deformation induced by foundation pit excavation, thereby verifying the reliability of the method. To achieve effective deformation control, measures are recommended to be taken to minimize ground loss and apply pit-bottom loading. The proposed method has a clear theoretical basis, is highly programmable and readily applicable, and provides a practical reference for analyzing and controlling strata deformation induced by foundation pit excavation.

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吴可嘉,赵佳乐,刘洋,等. 基于随机介质理论的基坑开挖地层变形计算[J]. 科学技术与工程, 2026, 26(27): 11872-11883.
Wu Kejia, Zhao Jiale, Liu Yang, et al. Calculation of Strata Deformation Induced by Foundation Pit Excavation based on Stochastic Medium Theory[J]. Science Technology and Engineering,2026,26(27):11872-11883.

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  • 收稿日期:2025-10-23
  • 最后修改日期:2026-09-15
  • 录用日期:2026-02-06
  • 在线发布日期: 2026-09-30
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