土体内球形空穴扩张及挤土桩沉桩机理研究
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摘要
本文主要研究土体内球形空穴扩张问题，静压挤土桩沉桩机理以及它们在工
程中的应用。
在前人工作的基础上，根据土塑性力学的基本原理，假定土体为均质、各向
同性的理想弹塑性体，考虑到土体具有不同于其他材料的剪胀特性，引入了土性参
数剪胀角，采用摩尔-库仑屈服函数和不相适应的流动法则首次获得了考虑土体剪
胀性的球形扩张问题的解析解，包括球形空穴扩张后周围塑性区范围的大小、空穴
扩张总体积变化、总塑性体积变化、总弹性体积变化、塑性区内平均体积应变、塑
性体积变化和弹性体积变化，空穴扩张到任一直径时的极限内压力及其周围土体中
的应力和位移分布。分析了土性参数、流动法则及排水条件变化对解的影响，并得
出了一些规律性的结论。
对挤土桩沉桩机理的研究方面，假定桩身沉入时桩尖处各点均按球形空穴扩
张，创造性地提出利用源-源的影像法和Boussinesq解解决用无限体内球形扩张的
解答来模拟半无限体中沉桩的问题，同时还考虑了沉桩时桩侧摩阻的影响，获得了
挤土桩沉桩后在周围土体内产生的应力场、位移场、孔隙水压力场和土体强度变化
规律的分析方法，并和其它方法进行了比较。研究了土性参数和桩参数变化对应力
场和位移场的影响。分析了六个工程实例，分别计算了静力压桩压桩力、静力触探
端阻力、单桩和群桩贯入后产生周围土体的水平位移、强度变化规律，理论计算结
果与实测值基本一致，说明本文方法的合理性和可靠性，并得出了一系列具有工程
实用价值的结论。
在工程应用方面，根据上述理论，本文提出直接利用土性基本参数求得沉桩压
力的方法，可有效地选择沉桩或桩基设备并较准确地预估桩基承载力。在此基础上
本文进一步推得了用球形空穴扩张时塑性区半径的大小来确定桩基进入持力层的
“临界深度”或离软弱下卧层“最小厚度”及其相应端阻的计算公式。分析证明了
许多学者从现场实测上得到的关于“临界深度”、“最小厚度”及其相应端阻的一
系列结论，回答了工程上经常碰到的三个问题：（1）对于有软弱下卧层的桩基持力
层，桩尖离下卧层顶面应留的“最小厚度”；（2）桩尖进入持力层的“临界深
度”；（3）不同的上下土层或土层组合对“最小厚度”或“临界深度”的影响。对
现行的《建筑桩基技术规范》关于桩基进入持力层深度及离软弱下卧层距离大小进
行了讨论，并提出了自己的见解。根据本文推得的计算方法和现场实测，初步探讨
了群桩施工迎桩面和背桩面挤土问题的遮帘效应。
文章最后提出了还有待解决的问题和进一步研究工作的建议。
Spheric cavity expansion, static piling in subsoils and its application have been studied in this paper.
Soil is assumed to be a homogeneous, isotropic and elastic-perfectly plastic material, and a dilational angle is used to consider soil dilatancy. By using the principle of the elasto-plastic theory, the analytical solution of the spherical cavity expansion including the ultimate pressure, the stress field and displacement field, plastic scope, the total volumetric increase, plastic and elastic volumetric increase was obtained. The effect of flow rule, the variations of the soil parameters and the drainage conditions of subsoils on the calculated results have been discussed and several conclusions are presented.
On the study of the mechanism of static piling, a model of spherical cavity expansion at the pile toe while piling is introduced. The problem of static piling in half-space medium has been creatively solved by a source-source imaging technique and Boussinesq's solution. The solutions of a stress field, a displacement field, a pore pressure field and the variation of soil strength for pile installing have also been proposed. The resistance, displacement field, variation of soil strength caused by pile installation and the end bearing of static sounding have been calculated for six cases. It has been founded that the calculated results are approached to those of the observation in site.
In practical application, the analytical solutions can be used to assess the resistance while piling and to select efficiently the piling equipment. Moreover, the formulas of calculating the "Critical Depth" and the "Minimal Thickness" are proposed. Several qualitative conclusions proposed by other scholars with in-site measurement results are theoretically confirmed. Three problems encountered in engineering have been solved: (1) the minimal thickness which the pile toe has to keep from the interface between the bearing stratum and the soft substratum; (2) the critical depth in which the pile toe thrusts in bearing stratum; (3) the variation of the critical depth and the minimal
thickness for two different soil stratum. The critical depth and the minimal thickness determined by current pile code are compared with the presented results. A case of pile installation are analyzed, the effect of group piling on lateral displacement has been discussed and compared with in-site measurement results. Some suggestions have been proposed in this paper.
程中的应用。
在前人工作的基础上，根据土塑性力学的基本原理，假定土体为均质、各向
同性的理想弹塑性体，考虑到土体具有不同于其他材料的剪胀特性，引入了土性参
数剪胀角，采用摩尔-库仑屈服函数和不相适应的流动法则首次获得了考虑土体剪
胀性的球形扩张问题的解析解，包括球形空穴扩张后周围塑性区范围的大小、空穴
扩张总体积变化、总塑性体积变化、总弹性体积变化、塑性区内平均体积应变、塑
性体积变化和弹性体积变化，空穴扩张到任一直径时的极限内压力及其周围土体中
的应力和位移分布。分析了土性参数、流动法则及排水条件变化对解的影响，并得
出了一些规律性的结论。
对挤土桩沉桩机理的研究方面，假定桩身沉入时桩尖处各点均按球形空穴扩
张，创造性地提出利用源-源的影像法和Boussinesq解解决用无限体内球形扩张的
解答来模拟半无限体中沉桩的问题，同时还考虑了沉桩时桩侧摩阻的影响，获得了
挤土桩沉桩后在周围土体内产生的应力场、位移场、孔隙水压力场和土体强度变化
规律的分析方法，并和其它方法进行了比较。研究了土性参数和桩参数变化对应力
场和位移场的影响。分析了六个工程实例，分别计算了静力压桩压桩力、静力触探
端阻力、单桩和群桩贯入后产生周围土体的水平位移、强度变化规律，理论计算结
果与实测值基本一致，说明本文方法的合理性和可靠性，并得出了一系列具有工程
实用价值的结论。
在工程应用方面，根据上述理论，本文提出直接利用土性基本参数求得沉桩压
力的方法，可有效地选择沉桩或桩基设备并较准确地预估桩基承载力。在此基础上
本文进一步推得了用球形空穴扩张时塑性区半径的大小来确定桩基进入持力层的
“临界深度”或离软弱下卧层“最小厚度”及其相应端阻的计算公式。分析证明了
许多学者从现场实测上得到的关于“临界深度”、“最小厚度”及其相应端阻的一
系列结论，回答了工程上经常碰到的三个问题：（1）对于有软弱下卧层的桩基持力
层，桩尖离下卧层顶面应留的“最小厚度”；（2）桩尖进入持力层的“临界深
度”；（3）不同的上下土层或土层组合对“最小厚度”或“临界深度”的影响。对
现行的《建筑桩基技术规范》关于桩基进入持力层深度及离软弱下卧层距离大小进
行了讨论，并提出了自己的见解。根据本文推得的计算方法和现场实测，初步探讨
了群桩施工迎桩面和背桩面挤土问题的遮帘效应。
文章最后提出了还有待解决的问题和进一步研究工作的建议。
Spheric cavity expansion, static piling in subsoils and its application have been studied in this paper.
Soil is assumed to be a homogeneous, isotropic and elastic-perfectly plastic material, and a dilational angle is used to consider soil dilatancy. By using the principle of the elasto-plastic theory, the analytical solution of the spherical cavity expansion including the ultimate pressure, the stress field and displacement field, plastic scope, the total volumetric increase, plastic and elastic volumetric increase was obtained. The effect of flow rule, the variations of the soil parameters and the drainage conditions of subsoils on the calculated results have been discussed and several conclusions are presented.
On the study of the mechanism of static piling, a model of spherical cavity expansion at the pile toe while piling is introduced. The problem of static piling in half-space medium has been creatively solved by a source-source imaging technique and Boussinesq's solution. The solutions of a stress field, a displacement field, a pore pressure field and the variation of soil strength for pile installing have also been proposed. The resistance, displacement field, variation of soil strength caused by pile installation and the end bearing of static sounding have been calculated for six cases. It has been founded that the calculated results are approached to those of the observation in site.
In practical application, the analytical solutions can be used to assess the resistance while piling and to select efficiently the piling equipment. Moreover, the formulas of calculating the "Critical Depth" and the "Minimal Thickness" are proposed. Several qualitative conclusions proposed by other scholars with in-site measurement results are theoretically confirmed. Three problems encountered in engineering have been solved: (1) the minimal thickness which the pile toe has to keep from the interface between the bearing stratum and the soft substratum; (2) the critical depth in which the pile toe thrusts in bearing stratum; (3) the variation of the critical depth and the minimal
thickness for two different soil stratum. The critical depth and the minimal thickness determined by current pile code are compared with the presented results. A case of pile installation are analyzed, the effect of group piling on lateral displacement has been discussed and compared with in-site measurement results. Some suggestions have been proposed in this paper.
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《桩基工程手册》编写委员会，《桩基工程手册》，中国建筑工业出版社。
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王启铜，龚晓南，曾国熙(1992)，考虑土体拉、压模量不同时静压桩的沉桩过程，浙江大学学报，Vol．6,No．26。
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Yang, N. C.(1970), Relaxation of piles in sand and inorganic silt, J. Soil. Mech. And Found. Div, ASCE, Vol.96,SM2.
Yu, H. S. & Houisby, G. T.(1991), Finite cavity expansion in dilatant soils: loading analysis, Geotechnique 41, No. 2, 173-183.
郑钢(1994)，预估静力压桩沉桩阻力，浙江省第六届土力学及基础工程学术会议论文集，绍兴，杭州：浙江大学出版社。
《桩基工程手册》编写委员会，《桩基工程手册》，中国建筑工业出版社。