Study on the Prediction Method of Pile Foundation Bearing Capacity Based on Finite Medium Cavity Expansion Theory
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摘要: 挤土桩在沉桩过程中的挤土效应对其承载力有明显的提高作用，基于有限介质弹塑性小孔扩张理论提出一种新的挤土桩承载力的计算方法。通过Mohr-Coulomb屈服准则推导了有限介质球形孔和柱形孔扩张的统一解析解，分析了打桩过程中的贯入挤土作用，并建立了桩基承载力的计算模型。结果表明：小孔扩张过程中具有明显尺寸效应，对于柱形孔扩张，当外内径比大于110时，有限土体扩张的内壁孔压和塑性区范围与无限土体扩张的大致相同；球形孔土体外内径比大于25时与无限土体扩张曲线一致；将桩端部分简化为球形孔扩张模型，桩侧部分假设为柱形孔扩张模型，求解得到了沉桩施工中桩周土体的应力场变化及成桩后桩基承载力值。桩基承载力计算结果与现有理论解、规范计算值和工程现场实测值进行对比，验证了本文方法的可靠性，为挤土桩的承载力预测提供了一种新的计算方法。Abstract: Installation of displacement pile could significantly increase the bearing capacity of pile foundation, and a new analytical method for bearing capacity prediction of displacement pile is proposed based on the elastic-plastic cavity expansion solution in finite soil medium. Mohr-Coulomb yield criterion is used to derive the unified analytical solution for both cylindrical and spherical cavities, assuming the pressure is remained constant at the outer boundary. The solutions are then adopted to analyze the penetration of precast pile, and a mechanical model for pile bearing capacity is constructed. The results show that scale effect is important for cavity expansion. For cylindrical cavities, the cavity pressure and the plastic zone of a finite medium with outer/inner radius ratio greater than 110 is similar to that of infinite medium, whereas the soil expansion curve is comparable for spherical scenarios with outer/inner radius ratio larger than 25. The mechanical model assumes the spherical cavity expansion at the pile end, and pile shaft is taken as cylindrical cavity expansion, which provides the changes of stress field during displacement pile installation and the bearing capacity. The magnitude of pile bearing capacity is compared with existing solution, standard design value, and measured data from field test, validating the proposed novel cavity-expansion based method.
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表 2 试验土层的物理力学性质指标[19]
层序 土层分类 层厚$ /\mathrm{m} $ 重度$ \gamma /(\mathrm{k}\mathrm{N}\cdot {\mathrm{m}}^{-3}) $ 三轴(UU) 三轴(CD) 压缩模量$ {E}_{\mathrm{s}}/\mathrm{M}\mathrm{P}\mathrm{a} $ 弹性模量$ E/\mathrm{M}\mathrm{P}\mathrm{a} $ 黏聚力$ {c}_{\mathrm{u}}/\mathrm{k}\mathrm{P}\mathrm{a} $ 内摩擦角${\varphi }'$/(°) 1 耕植土 0.5 17.8 19.0 2 粉质黏土 0.9 18.5 19.0 13.2 4.69 3.48 3 淤泥质粉质黏土 3.0 18.0 16.4 10.1 3.63 2.70 4 淤泥质粉质黏土夹粉土 3.8 18.4 22.6 15.4 3.78 2.81 5 淤泥质粉质黏土 3.1 17.8 8.9 12.4 2.73 2.03 6 粉质黏土夹粉土 12.3 18.0 15.2 19.5 5.11 3.80 7 淤泥质粉质黏土 6.0 18.1 13.0 12.6 3.56 2.64 
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