周航(1987-), 男, 博士, 副教授, 主要从事桩土相互作用研究, E-mail:
Zhou Hang (1987-), PhD, associate professor, main research interest: pile-soil interaction, E-mail:
载体桩是近年来出现的一种新桩型,其主要利用柱锤对深层土体进行填料夯实,形成桩端扩大载体,从而大大提高桩体竖向承载力。虽然载体桩在实际工程中广泛应用,但目前仍缺乏较为严格的理论分析,特别在关于评价载体的加固范围和载体对土体的挤密效应方面,仍然研究较少,这大大制约了载体桩的推广和发展。针对该问题,将柱锤对填料夯实的过程简化为球孔扩张力学模型,软黏土采用修正剑桥模型的本构关系来模拟,建立球孔扩张偏微分控制方程组,通过相似变换的求解技术将偏微分方程转化为常微分方程组,利用微分方程数值求解技术获得常微分方程组的数值解。开展参数分析,探讨球孔扩张过程中孔周土体强度和刚度的变化、孔周土体挤密区的范围等,从理论角度揭示载体桩载体成形过程中的加固机理,为建立考虑桩端挤密效应的载体桩竖向承载力计算方法提供理论基础。
Carrier pile is newly developed in recent years. It utilizes a column hammer to tamp the filling in the deep soil, which forms an expanded carried at the pile end. This will greatly increase the vertical pile bearing capacity. Although the carrier pile has been widely used in practice, rare theoretical analysis has been conducted to check the size of the reinforced area and the compaction effect. This greatly restricts the popularization and development of the carrier pile. Under this condition, the process of the tamping through a column hammer is simplified as the spherical cavity expansion model. The soft clay is described by the MCC model. Then, a series of partial differential equations (PDEs) for spherical cavity expansion is constructed. Similarity solution technique is used to transform the PDEs to ordinary differential equations (ODEs), which can be numerically solved through the ODE solver. Subsequently, a series of parametric analyses were conducted to investigate the variation of the soil strength and stiffness after spherical cavity expansion and the size of the compaction zone. This reveals the reinforced mechanism of the formation of the carried part of the pile from the theoretical viewpoint and provides a theoretical basis for constructing the theoretical calculation methods for the vertical bearing capacity of the carrier pile considering the compaction effect.
载体桩是近年来发明并得到广泛应用的一种新桩型,该技术通过夯击能量以填料作为介质,挤密加固桩端周围土体,形成桩端扩大载体,从而大大提高单桩竖向承载力[
载体桩的施工工艺(如
载体桩施工过程
Construction process of carrier pile
载体桩技术的核心在于侧限约束下的土体密实形成载体。该技术的研究对象是土体密实理论,也就是研究桩身端以下一定范围内挤密土体和影响土体的物理力学性质的变化。在设计中合理考虑挤密效应至关重要,如果高估了挤密效应,将会给工程带来安全隐患,反之,如果过低估计了载体的作用,将会造成工程造价大大提高。因此,如何从理论角度精确计算桩端挤密效应,成为制约载体桩推广和发展的一个主要因素。目前,关于载体桩的研究主要停留在试验阶段,在理论方面的研究相对较少。王建安等[
扩孔理论作为岩土力学中一种简单有效的力学模型[
如
载体桩载体扩孔成形力学模型
Mechanics model of the cavity expansion formation of carrier pile
式中:
球体的体积
通过数值计算,可以直接获得归一化的球体体积
载体桩球体半径与体积的关系
Relation between the radius of the sphere of carrier pile and the volume
如果已知填料的体积用量,便可以通过式(3)计算出载体扩大头球体的半径,从而利用
对于基于修正剑桥模型的弹塑性球孔扩张问题,孔洞周围将会出现3个区域:临界状态区域、塑性区域以及弹性区。在临界状态区域和塑形区中,应力必须满足平衡方程和修正剑桥模型屈服准则,而在弹性区中,应力需要满足平衡方程和胡克定律。此外,孔扩张的运动学方程则由土体的排水条件、应变-位移关系以及边界条件来控制。在弹塑性分界面(弹性区和塑形区的分界面)上,应力和位移必须保持连续。基于这样的基本原理有以下的推导:
1) 平衡方程
根据Collins等[
式中:
式中:
2) 本构方程
采用Collins等[
根据应变-位移关系,可以知道球坐标下的应变分量可以写成
式中:
定义符号(°)表示土体颗粒的物质导数,可以表达为
式中:
土颗粒的径向和环向应变量可以表示为
将式(12)和式(13)带入到式(7)和式(8)中,可以得到
进一步地,弹性本构关系可以写成
式中:
根据Wood[
将式(17)中的两个应变分量采用式(14)和式(15)中的表达式代替,可以得到
其中:
3) 一致性条件
此外,屈服面需要满足如下的一致性条件
其中:
4) 连续性条件
在球孔扩张过程中,土体需要满足质量守恒条件
其中:
5) 排水条件
由于采用了完全排水的条件,也即在扩孔过程中土体孔隙水压保持不变,因此有
上面5个条件即构成了球孔扩张的控制方程组,采用相似变换技术求解该方程组。采用如下变换方式
式中:
为了求解方程式(33),需要给出初始条件和边界条件,可以利用孔洞和弹塑性边界处的信息来确定。
在弹塑性边界处
在孔口处
结合控制方程和上述边界条件编写Matlab微分方程组数值求解程序,可以获得临界状态区和塑性区的半解析解。
在弹性区,本构关系服从胡克定律,因此有
同时,在弹性区域,应力需要满足平衡方程,将平衡方程写成关于
将式(42)和式(43)代入式(44),可以得到
采用如下的变换
式(45)可以简化为常微分方程
式(47)存在闭合解析解
式中:
此外
因此,球坐标下的应力分量便可以通过式(42)和式(43)获得
式中:
载体桩夯扩过程中土体被挤密,土体的强度和剪切模量会发生变化。根据修正剑桥模型,土体的强度和剪切模量可以表示为
对于排水孔扩张问题,土体的体积比
式中:
不同
Variation of strength coefficient with the radial distance for different
不同
Variation of shear modulus coefficient with the radial distance for different
不同
Variation of strength coefficient with the radial distance for different
不同
Variation of shear modulus coefficient with the radial distance for different
不同
Variation of strength coefficient with the radial distance for different
不同
Variation of shear modulus coefficient with the radial distance for different
不同
Variation of strength coefficient with the radial distance for different
不同
Variation of shear modulus coefficient with the radial distance for different
不同
Variation of strength coefficient with the radialdistance for different
不同
Variation of shear modulus coefficient with the radial distance for different
挤密区半径随着不同参数的变化规律
Variation of the radius of the compaction zone with different parameters
探讨了软黏土中载体桩桩端挤密效应,建立了基于球孔扩张的载体桩桩端夯扩挤密力学模型,分析了桩端挤密效应,可以得到如下的结论:
1) 给出了载体桩桩端夯扩填料体积用量与球孔扩张理论模型中球孔半径关系的闭合解析表达式。
2) 利用相似变换技术求解球孔扩张偏微分控制方程,获得了修正剑桥模型中球孔扩张力学响应的数值解。
3) 采用球孔扩张前后土体强度比和剪切模量比两个物理力学指标来定量分析载体桩桩端夯扩挤密后土体力学性质变化,获得了土体强度比和剪切模量比随着土体参数的变化规律。采用塑性区半径来分析挤密扰动区的大小,获得了挤密扰动区的大小随着土体参数的变化关系。
4) 提出了考虑载体桩桩端挤密效应的理论计算方法,该方法可以较为准确地计算载体桩夯扩过程中周围土体强度和剪切模量的变化以及挤密扰动区的大小,可为建立考虑载体桩桩端挤密效应的承载力计算方法提供理论基础。
王继忠.载体桩技术的诞生与发展[J].建筑结构, 2008, 38(4):118-119.
WANG J Z. Birth and development of carrier pile technology[J]. Building Structure, 2008, 38(4):118-119.(in Chinese)
王建安, 张慧海, 陈琳, 等.载体桩在陕南粉质黏土地区的适用性研究[J].岩土工程技术, 2019, 33(2):109-114.
WANG J A, ZHANG H H, CHEN L, et al. Study on bearing capacity of cast-in-place pile in silty clay area of southern Shaanxi Province[J]. Geotechnical Engineering Technique, 2019, 33(2):109-114.(in Chinese)
于长杰.载体桩对软土地基沉降量控制效果的试验分析[J].四川建筑, 2018, 38(3):101-103.
YU C J. Experimental analysis of control effect of carrier pile on settlement of soft soil foundation[J]. Sichuan Architecture, 2018, 38(3):101-103.(in Chinese)
周斌.高速铁路载体桩复合地基沉降变形规律研究[D].成都: 西南交通大学, 2011.
ZHOU B. Study on settlement regularity of pile with bearing base composite foundation in high-speed railway[D].Chengdu: Southwest Jiaotong University, 2011.
罗浩.高速铁路载体桩复合地基沉降特性现场试验及施工工艺研究[D].成都: 西南交通大学, 2010.
LUO H. Filed research on settlement characters and construction technology of ram-compaction piles with composite bearing base in high-speed railway[D]. Chengdu: Southwest Jiaotong University, 2010.
李建强, 刘洪滨, 张家尊, 等.载体桩复合地基性状数值模拟研究[J].工业建筑, 2018, 48(6):107-110.
LI J Q, LIU H B, ZHANG J Z, et al. Research on the numerical simulation of the carrier pile composite foundation[J]. Industrial Construction, 2018, 48(6):107-110.(in Chinese)
张培成, 孙玉文, 张殿树, 等.基于饱和软土地基大承载力载体桩试验研究[J].河北水利电力学院学报, 2020(1):19-23.
ZHANG P C, SUN Y W, ZHANG D S, et al. Experimental study on piles with ram-compacted bearing sphere for large saturated soft bearing capacity based on soil foundation[J]. Journal of Hebei University of Water Resources and Electric Engineering, 2020(1):19-23.
仇凯斌, 介玉新, 李广信, 等.载体桩承载力性状有限元分析[J].工程勘察, 2009, 37(Sup1):15-20.
QIU K B, JIE Y X, LI G X, et al. Finite element analysis of bearing capacity of carrier pile[J]. Geotechnical Investigation & Surveying, 2009, 37(Sup1):15-20.(in Chinese)
张续萱, 魏殿兴.锚定板挡土结构的实测土压力及其分析研究[J].岩土工程学报, 1994, 16(2):73-79.
ZHANG X X, WEI D X. Measurement and analysis of earth pressure in anchor slab retaining structures[J]. Chinese Journal of Geotechnical Engineering, 1994, 16(2):73-79.(in Chinese)
ZHOU H, KONG G Q, LIU H L, et al. Similarity solution for cavity expansion in thermoplastic soil[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42(2)274-294.
ZHOU H, KONG G Q, LIU H L. A semi-analytical solution for cylindrical cavity expansion in elastic-perfectly plastic soil under biaxialin situ stress field[J]. Géotechnique, 2016, 66(7):584-595.
ZHOU H, LIU H L, ZHA Y H, et al. A general semi-analytical solution for consolidation around an expanded cylindrical and spherical cavity in modified Cam Clay[J]. Computers and Geotechnics, 2017, 91:71-81.
ZHOU H, LIU H L, KONG G Q, et al. Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress[J]. Computers and Geotechnics, 2014, 55:232-239.
ZHOU H, KONG G Q, LI P, et al. Flat cavity expansion:theoretical model and application to the interpretation of the flat dilatometer test[J]. Journal of Engineering Mechanics, 2016, 142(1):04015058.
YU H S. Cavity expansion methods in geomechanics[M]. Springer Science & Business Media, 2013.
CHEN S L, ABOUSLEIMAN Y N. Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified Cam Clay soil[J]. Geotechnique, 2012, 62(5):447-456.
CHEN S, ABOUSLEIMAN Y N. Exact drained solution for cylindrical cavity expansion in modified Cam Clay soil[J]. Geotechnique, 2013, 63(6):510-517.
LI L, LI J P, SUN D A. Anisotropically elasto-plastic solution to undrained cylindrical cavity expansion in K0-consolidated clay[J]. Computers and Geotechnics, 2016, 73:83-90.
COLLINS I F, STIMPSON J R. Similarity solutions for drained a undrained cavity expansions in soils[J]. Geotechnique, 1994, 44(1):21-34.
WOOD D M. Soil behaviour and critical state soil mechanics[M]. Cambridge:Cambridge University Press, 1991.