考虑淤堵效应的多元排水体复合地基固结解析解

doi:10.3724/1000-6915.jrme.2024.0597

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摘要多元排水体复合地基可结合不同排水体加速地基固结，而固结过程中排水体必然会出现淤堵现象，但目前尚未有考虑淤堵效应的多元排水体复合地基固结解析解答。基于此，引入井阻随时间指数衰减的数学模型和4种桩–板布置形式，建立碎石桩联合塑料排水板的多元排水体复合地基固结模型，考虑地基土内同时存在流向碎石桩与排水板的径向双向渗流与涂抹效应，基于等应变假定，通过分离变量法、傅里叶函数正交性等数学物理方法，分别给出考虑碎石桩淤堵和排水板淤堵的多元排水体复合地基固结解析解答，并通过理论退化与案例对比验证解答的合理性与实用性。对复合地基固结性状进行分析，得到如下结论：考虑淤堵效应会降低复合地基的固结速率，尤其是碎石桩的淤堵效应；若降低最终排水能力或增大渗透系数指数衰减因子，复合地基固结速率将会减慢；最终排水能力对地基固结后期影响大，对固结前期几乎无影响，而指数衰减因子对复合地基固结全周期的影响较为均衡；当碎石桩初始渗透系数较小时，其淤堵效应对地基固结的影响更大，相反排水板初始渗透系数较大时，淤堵效应对地基固结的影响更大；考虑淤堵效应后土体孔压消散速度会变慢，碎石桩淤堵对土体孔压影响较排水板更大。

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	许宝龙1
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	卢萌盟1

关键词 ：地基基础, 复合地基, 固结, 淤堵效应, 碎石桩, 塑料排水板

Abstract：The composite foundation with multiple drains can be combined with different drainage bodies to accelerate the consolidation of foundation，and the multiple drains will clog inevitably during consolidation. However，there is no analytical consolidation theory of composite foundation with multiple drains that can consider the clogging effect. Based on this，the mathematical model with an exponentially decaying well resistance over time and four layout forms are introduced to establish the consolidation model of composite foundation with multiple drains combining stone columns with prefabricated vertical drains(PVDs). Considering the radial two-way seepage to stone columns and PVDs in the foundation soil and smear effect，based on the assumption of equal strain，the consolidation analytical solutions of composite foundation with multiple drains considering stone columns clogging and PVDs clogging are given respectively，using mathematical and physical methods such as the method of separated variables and the orthogonality of Fourier functions. The rationality and practicability of the solutions are verified by theoretical degradation and case comparison. The consolidation behavior is analyzed，and the following conclusions manifest：Considering the clogging effect will slow down the consolidation rate of the composite foundation，especially the clogging effect of the stone columns. If the final drainage capacity is reduced or the exponential attenuation factor of permeability coefficient is increased，the consolidation rate will slow down. The final drainage capacity has a great influence on the later stage of consolidation，with minimal influence on the early stages，while the influence of exponential attenuation factor on the whole stage of consolidation is relatively balanced. When the initial permeability coefficient of stone columns is low，the clogging effect exhibits a greater influence on consolidation，whereas when the initial permeability coefficient of PVDs is large，the clogging effect has a greater impact. Considering the clogging effect，the dissipation of soil pore pressure slows，and the influence of stone columns clogging on soil pore pressure is stronger than that of PVDs.

Key words： foundations composite foundation consolidation clogging effect stone column prefabricated vertical drains(PVDs)

引用本文:

许宝龙1，2，卢萌盟1. 考虑淤堵效应的多元排水体复合地基固结解析解[J]. 岩石力学与工程学报, 2025, 44(4): 1053-1064.
XU Baolong1，2，LU Mengmeng1. Analytical solutions for consolidation of composite foundation with multiple drains considering clogging effect. , 2025, 44(4): 1053-1064.

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https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0597 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I4/1053

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[16]	马昊暄，李传勋，陆向综，等. 考虑变井阻的碎石桩复合地基非线性固结分析[J]. 岩石力学与工程学报，2024，43(4)：1 013- 1 025.(MA Haoxuan，LI Chuanxun，LU Xiangzong，et al. A numerical solution for nonlinear consolidation of stone column composite foundation considering variable well resistance[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(4)：1 013-1 025.(in Chinese))
[17]	卢萌盟，白垚，杨康. 考虑排水板淤堵时空变化的多元复合地基固结性状研究[J]. 岩土工程学报，2023，45(8)：1 564-1 573.(LU Mengmeng，BAI Yao，YANG Kang. Consolidation behaviors of multi-reinforcement composite ground considering time- and depth-dependent clogging effects of prefabricated vertical drains[J]. Chinese Journal of Geotechnical Engineering，2023，45(8)：1 564-1 573.(in Chinese))
[18]	FELLENIUS B H，CASTONGUAY N G. The efficiency of band shaped drains：a full scale laboratory study[R]. Ottawa：National Research Council and the Industrial Research Assistance Program，1985：27-35.
[19]	LU M M，SCOTT W，INDRARATNA S B，et al. A new analytical model for consolidation with multiple vertical drains[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2016，40(11)：1 623-1 640.
[20]	ORLEACH P. Techniques to evaluate the field performance of vertical drains[M. S. Thesis][D]. Cambridge：Massachusetts Institute of Technology，1983.
[21]	卢萌盟，谢康和，王坤，等. 考虑桩体内径向渗流的复合地基固结解[J]. 固体力学学报，2009，30(2)：155-161.(LU Mengmeng，XIE Kanghe，WANG Kun，et al. Analytical solutions for the consolidation of a compound foundation with consideration on the radial flow within the column[J]. Chinese Journal of Solid Mechanics，2009，30(2)：155-161.(in Chinese))
[22]	TAN S A，TJAHYONO S，OO K K. Simplified plane-strain modeling of stone-column reinforced ground[J]. Journal of Geotechnical and Geoenvironmental Engineering，2008，134(2)：185-194.
[23]	陆向综，李传勋. 径竖向渗流下竖井-碎石桩复合地基固结解[J]. 工程力学，2025，待刊.(LU Xiangzong，LI Chuanxun. Consolidation solution for composite foundation with vertical drains-stone columns considering radial and vertical flow in soft soils[J]. Engineering Mechanics，2025，to be pressed.(in Chinese))
[24]	白垚，卢萌盟，杨康，等. 考虑变井阻的多元复合地基固结理论研究[J]. 工程力学，2024，41(6)：44-54.(BAI Yao，LU Mengmeng，YANG Kang，et al. Study on the consolidation behaviors of multi-reinforcement composite foundation considering time-dependent well resistance[J]. Engineering Mechanics，2024，41(6)：44-54.(in Chinese))
[25]	许宝龙，卢萌盟，张鑫岩，等. 基于虚拟桩法的长板-短桩多元排水体复合地基固结模型与解答[J]. 工程科学与技术，2025，待刊.(XU Baolong，LU Mengmeng，ZHANG Xinyan，et al. Analytical models and solutions for consolidation of composite foundation with long prefabricated vertical drains(PVDs) and short stone columns based on virtual pile method[J]. Advanced Engineering Sciences，2025，to be pressed.(in Chinese))