悬浮长芯劲性搅拌桩复合地基固结解析解

杨涛; 戴基彤; 王恒栋

doi:10.11779/CJGE202002005

悬浮长芯劲性搅拌桩复合地基固结解析解 English Version

1.
上海理工大学土木系,上海　200093
2.
上海市政工程设计研究总院(集团)　有限公司,上海　200092

基金项目:

国家重点研究发展计划项目 2016YFC0802405

详细信息

作者简介:
杨涛（1962— ）,男,博士,教授,从事地基加固技术与复合地基理论研究工作。E-mail：shyangtao@163.com

中图分类号: TU473
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出版历程
- 收稿日期: 2019-05-07
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-01-31

Analytical solutions for consolidation of a composite ground with floating stiffened deep cement mixing columns with long core piles

1.
Department of Civil Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., Shanghai 200092, China

摘要

摘要: 推导出瞬时加荷情况下悬浮长芯劲性搅拌桩复合地基的固结方程和相应的定解条件,利用三层地基一维固结理论,建立了相应的固结解析解,包括桩间土和下卧层土中超静孔隙水压力解答和复合地基整体平均固结度解答。通过固结速率解析解与有限元数值解的比较,证明了解析解的合理性。利用解析解进行复合地基固结速率影响因素分析,研究了悬浮长芯劲性搅拌桩复合地基的固结性状。结果表明：悬浮长芯劲性搅拌桩复合地基的固结速率主要受桩的贯入比和下卧层刚度的影响。复合地基的固结速率随桩的贯入比和下卧层土压缩模量的增加而增大。搅拌桩壳长度、厚度和刚度以及芯桩截面含心率的变化对复合地基固结速率没有影响。增加芯桩的压缩模量只会使固结前期复合地基的固结速率略微减小,不会影响固结后期复合地基的固结速率。
- 长芯劲性搅拌桩 /
- 复合地基 /
- 固结 /
- 解析解 /
- 含芯率
Abstract: The consolidation equations and the corresponding solution conditions of the composite ground with floating stiffened deep cement mixing (SDCM) columns with long core piles are derived under an instant loading. On the basis of one-dimensional consolidation theory of a third-layer soil ground, the corresponding analytical consolidation solutions are developed, including the average excess pore water pressures within the surrounding soil and underlying soil and the overall average degree of consolidation of the composite ground. The correctness and accuracy of the proposed analytical solutions are verified by comparison of the consolidation rates by the proposed analytical solution and the FEM. Some main factors are analyzed to investigate the consolidation behavior of this type of composite ground using the proposed analytical solution. The results show that the consolidation rate of the composite ground depends mainly on the penetration ratio of the SDCM columns with long core piles and the stiffness of the underlying soil. It increases with increasing penetration ratio of the pile and the constrained modulus of the underlying soil. The variations in the length, thickness and stiffness of the deep cement mixing (DCM) column sockets as well as the area core ratio of the concrete core piles have little effect on the consolidation rate of the composite ground. An increase in the modulus of the core pile decreases slightly the consolidation rate of the composite ground at the early stage of consolidation process, and it affects insignificantly the consolidation rate at the later stage of consolidation.
- SDCM column with long core pile /
- composite ground /
- consolidation /
- analytical solution /
- area core ratio

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0. 引言

劲性水泥搅拌桩（SDCM column）也称“混凝土芯搅拌桩”,是一种由水泥搅拌桩(DCM column)壳和中心处较小面积预制混凝土芯桩组成的复合材料桩。按照芯桩与DCM桩壳二者长度间的相对关系,SDCM桩分为3种类型：芯桩长度小于DCM桩壳长度的短芯SDCM桩、芯桩长度等于DCM桩壳长度的等芯SDCM桩和芯桩长度大于DCM桩壳长度的长芯SDCM桩。较之传统的DCM桩,SDCM桩的竖向和水平向承载力高,沉降控制效果好。它既可作为桩基础,也可作为复合地基的竖向增强体,在国内外都得到了大量应用^[1-2]。

很多学者通过室内外试验和数值模拟等方法,从承载力、荷载传递机制和控沉效果等方面对短芯SDCM桩和短芯SDCM桩复合地基进行了较为系统的研究。凌光荣等^[3]、董平等^[4]和吴迈等^[5]通过现场单桩载荷试验研究了SDCM桩的轴向承载特性。试验发现,芯桩的插入使搅拌桩桩侧摩阻力充分发挥,SDCM桩的竖向承载力可高于混凝土灌注桩。Voottipruex等^[6]采用三维有限元法研究了芯桩长度和截面积等因素对SDCM桩竖向和水平向承载力、芯桩轴力和弯矩分布的影响。吴迈等^[7]、丁永君等^[8]和顾士坦等^[9]采用理论分析和现场实测芯桩桩身应力的方法研究了SDCM桩的荷载传递特性。Wonglert等^[10-11]基于室内模型试验成果,提出短芯SDCM桩有土体破坏、芯桩底部破坏和搅拌桩壳顶部破坏3种破坏模式,研究了芯桩长度和搅拌桩壳强度对悬浮SDCM桩竖向承载力和破坏模式的影响。Wang等^[12]通过现场荷载板试验,比较了刚性基础下SDCM桩复合地基与DCM桩复合地基的竖向承载力。Voottipruex等^[13]和Wang等^[14]进行了路堤下SDCM桩复合地基现场试验,比较了柔性基础下SDCM桩复合地基与DCM桩复合地基的沉降控制效果。叶观宝等^[15-16]提出了悬浮SDCM桩复合地基桩-土应力比和沉降的计算方法。杨涛等^[17]建立了端承短芯SDCM桩复合地基的固结计算模型。

近年来,随着长芯SDCM桩在中国的逐渐应用,其承载机理和设计理论的研究开始受到学术界的关注。陈华顺等^[18]和程博华^[19]分别提出了长芯SDCM桩桩侧摩阻力和竖向承载力的计算方法。杨涛等^[20]给出了端承长芯SDCM桩复合地基固结解析解,但该解答无法用于分析悬浮长芯SDCM桩复合地基的固结问题。有鉴于此,本文研究悬浮长芯SDCM桩复合地基的固结计算方法,分析悬浮长芯SDCM桩复合地基的固结特性,进一步完善SDCM桩复合地基的固结计算理论。

1. 固结模型与基本假定

1.1 轴对称固结模型

图1给出悬浮长芯SDCM桩复合地基轴对称固结模型,r和z分别是径向和竖向坐标。r_e为一根SDCM桩的影响区半径,可由桩的间距和布桩方式计算得到。水泥搅拌桩壳外半径和长度分别为r_p和L_p=H₁,上部SDCM桩的置换率为m（m=(r_p/r_e)²）,压缩模量为E_p。芯桩打穿水泥搅拌桩壳,其半径和长度分别为r_sp和L_sp（L_sp=H₁+H₂）,压缩模量为E_sp。芯桩的截面含芯率为ρ（ρ=(r_sp/r_p)²）。根据水泥搅拌桩壳和芯桩的长度将复合地基加固区分为Ⅰ和Ⅱ二部分,加固区Ⅰ内桩间土的厚度、渗透系数、固结系数和压缩模量分别为H₁,k_v1,c_v1,E_s1,加固区Ⅱ内桩间土的厚度、渗透系数、固结系数和压缩模量分别为H₂,k_v2,c_v2,E_s2。下卧层土厚度、渗透系数、固结系数和压缩模量分别为H₃,k_v3,c_v3,E_s3。复合地基总厚度H= H₁+H₂+H₃。

图 1 复合地基固结模型

Figure 1. Consolidation model for composite ground

下载: 全尺寸图片幻灯片

1.2 基本假定

本文公式推导采用如下假定：①地基土完全饱和,水的流动符合Darcy定律；②搅拌桩壳不排水；③芯桩桩端以下的下卧层土和搅拌桩壳以下芯桩桩端以上的土仅发生径向渗流；④芯桩与搅拌桩壳间无相对滑移,加固区中任意深度处的桩和土的竖向应变相等；⑤大面积均布荷载p瞬时施加,在待加固地基中引起的竖向附加应力沿深度均布；⑥土的渗透系数和压缩模量不随固结而变化。

2. 固结方程与定解条件

2.1 固结方程

基于前述基本假定,参考杨涛等^[20-21]的研究,可得到荷载p瞬时施加情况下悬浮长芯SDCM桩复合地基得固结方程如下：

${\begin{cases} \frac{\partial {\bar{u}}_{s 1}}{\partial t} = c_{v 1 e} \frac{\partial^{2} {\bar{u}}_{s 1}}{\partial z^{2}} \begin{matrix} \end{matrix} (0 \leq z < H_{1}), \\ \frac{\partial {\bar{u}}_{s 2}}{\partial t} = c_{v 2 e} \frac{\partial^{2} {\bar{u}}_{s 2}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} \leq z < H_{1} + H_{2}), \\ \frac{\partial {\bar{u}}_{s 3}}{\partial t} = c_{v 3 e} \frac{\partial^{2} {\bar{u}}_{s 3}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} + H_{2} \leq z \leq H) 。 \end{cases}$

(1)

$c_{v 1 e} = (1 + \frac{m [ρ E_{s p} + (1 - ρ) E_{p}]}{(1 - m) E_{s 1}}) c_{v 1}$ ,

(2)

$c_{v 2 e} = (1 + \frac{m ρ E_{s p}}{(1 - m ρ) E_{s 2}}) (\frac{1 - m}{1 - m ρ}) c_{v 2}$ ,

(3)

$c_{v 3 e} = (1 - m ρ) c_{v3} 。$

(4)

式中 ${\bar{u}}_{s 1}$ , ${\bar{u}}_{s 2}$ , ${\bar{u}}_{s 3}$ 分别为加固区Ⅰ、Ⅱ中桩间土和下卧层土中任意深度z处的平均超静孔隙水压力；c_v1e,c_v2e,c_v3e分别为考虑劲性桩和芯桩影响的加固区Ⅰ、Ⅱ中桩间土和下卧层土的等效竖向固结系数。

2.2 定解条件

（1）边界条件

考虑复合地基上边界排水、下边界不排水的单面排水情况,边界条件如下：

$z = 0, {\bar{u}}_{s 1} = 0$ ,

(5)

$z = H, \frac{\partial {\bar{u}}_{s 3}}{\partial z} = 0$ 。

(6)

（2）孔压和水流连续性条件

考虑到 $(1 - m) {\bar{u}}_{s 1}$ 和 $(1 - m ρ) {\bar{u}}_{s 2}$ 分别为加固区Ⅰ和加固区Ⅱ内任意深度处的平均孔压,可得加固区Ⅰ与加固区Ⅱ分界面处、加固区Ⅱ与下卧层分界面处孔压和水流连续性条件如下：

z=H₁时,

$(1 - m) {\bar{u}}_{s 1} = (1 - m ρ) {\bar{u}}_{s 2}$ ,

(7)

$(1 - m) k_{v 1} \frac{\partial {\bar{u}}_{s 1}}{\partial z} = (1 - m ρ) k_{v 2} \frac{\partial {\bar{u}}_{s 2}}{\partial z}$ 。

(8)

z=H₁+H₂时,

$(1 - m ρ) {\bar{u}}_{s 2} = {\bar{u}}_{s 3}$ ,

(9)

$(1 - m ρ) k_{v 2} \frac{\partial {\bar{u}}_{s 2}}{\partial z} = k_{v 3} \frac{\partial {\bar{u}}_{s 3}}{\partial z}$ 。

(10)

（3）初始条件

荷载施加的瞬时,桩间土和下卧层土中没有竖向变形。参照杨涛等^[20-21]的研究,容易写出如下初始条件：

${\bar{u}}_{s 1} (z, 0) = \frac{p}{1 - m}$ ,

(11)

${\bar{u}}_{s 2} (z, 0) = \frac{p}{1 - m ρ}$ ,

(12)

${\bar{u}}_{s 3} (z, 0) = p$ 。

(13)

3. 固结解析解

3.1 方程与定解条件的函数变换

为便于求解,进行如下函数变换：

${\begin{cases} {\hat{u}}_{s 1} = (1 - m) {\bar{u}}_{s 1}, \\ {\hat{u}}_{s 2} = (1 - m ρ) {\bar{u}}_{s 2}, \\ {\hat{u}}_{s 3} = {\bar{u}}_{s 3} 。 \end{cases}$

(14)

显然, ${\hat{u}}_{s 1}$ 和 ${\hat{u}}_{s 2}$ 分别是复合地基上、下加固区任意深度处的平均超静孔隙水压力。将式（14）代入固结控制方程式（1）和定解条件式（5）～（13）,则变换后的复合地基固结控制方程和求解条件如下：

${\begin{cases} \frac{\partial {\hat{u}}_{s 1}}{\partial t} = c_{v 1 e} \frac{\partial^{2} {\hat{u}}_{s 1}}{\partial z^{2}} \begin{matrix} \end{matrix} (0 \leq z < H_{1}), \\ \frac{\partial {\hat{u}}_{s 2}}{\partial t} = c_{v 2 e} \frac{\partial^{2} {\hat{u}}_{s 2}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} \leq z < H_{1} + H_{2}), \\ \frac{\partial {\hat{u}}_{s 3}}{\partial t} = c_{v 3 e} \frac{\partial^{2} {\hat{u}}_{s 3}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} + H_{2} \leq z \leq H) 。 \end{cases}$

(15)

$z = 0 ： {\hat{u}}_{s 1} = 0$ ,

(16)

$z = H ： \frac{\partial {\hat{u}}_{s 3}}{\partial z} = 0$ ,

(17)

z=H₁,

${\begin{cases} {\hat{u}}_{s 1} = {\hat{u}}_{s 2} \\ k_{v 1} \frac{\partial {\hat{u}}_{s 1}}{\partial z} = k_{v 2} \frac{\partial {\hat{u}}_{s 2}}{\partial z} \end{cases}$ ,

(18)

z=H₁+H₂,

${\begin{cases} {\hat{u}}_{s 2} = {\hat{u}}_{s 3} \\ k_{v 2} \frac{\partial {\hat{u}}_{s 2}}{\partial z} = k_{v 3} \frac{\partial {\hat{u}}_{s 3}}{\partial z} \end{cases}$ ,

(19)

${\hat{u}}_{s 1} (z, 0) = {\hat{u}}_{s 2} (z, 0) = {\hat{u}}_{s 3} (z, 0) = p$ 。

(20)

3.2 固结解析解

显然,式（15）,（16）～（20）分别是瞬时荷载p作用在由复合地基上、下加固区复合土和下卧层土组成的三层土系统固结问题的固结方程和定解条件。与瞬时荷载p作用下的三层天然地基固结问题相比,只是各层天然地基土的固结系数c_v1,c_v2和c_v3分别被c_v1e,c_v2e和c_v3e代替而已。设三层土系统中土层i的渗透系数为k_vi(i=1,2,3),则其压缩模量为E_sie=c_vier_w/k_vi (i=1,2,3）。

为使计算公式得以简化,定义5个无量纲参数：

$\begin{array}{l} a_{i} = \frac{k_{v i}}{k_{v 1}}; b_{i} = \frac{E_{s 1 e}}{E_{s i e}}; c_{i} = \frac{H_{i}}{H_{1}}; μ_{i} = \sqrt{\frac{b_{i}}{a_{i}}} (i = 1, 2, 3) ； \\ d_{i} = \sqrt{\frac{a_{i - 1} b_{i - 1}}{a_{i} b_{i}}} \begin{matrix} \end{matrix} (i = 2, 3) 。 \end{array}}$

(21)

根据谢康和^[22]的研究,容易得到：

（1）各加固区和下卧层的平均超静孔压

${\begin{cases} {\hat{u}}_{s 1} (z, t) = p \sum_{m = 1}^{\infty} C_{m} s i n (λ_{m} \frac{z}{H_{1}}) e^{- λ_{m}^{2} T_{v1e}}, \\ {\hat{u}}_{s 2} (z, t) = p \sum_{m = 1}^{\infty} C_{m} [s i n (λ_{m}) c o s (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}}) + \\ d_{2} c o s (λ_{m}) s i n (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}})] e^{- λ_{m}^{2} T_{v1e}}, \\ {\hat{u}}_{s 3} (z, t) = p \sum_{m = 1}^{\infty} \frac{C_{m} A_{m}}{c o s (μ_{3} c_{3} λ_{m})} c o s (μ_{3} λ_{m} \frac{H - z}{H_{1}}) e^{- λ_{m}^{2} T_{v1e}}, \end{cases}$

(22)

$T_{v1e} = c_{v1e} t / H_{1}^{2}$ 。

(23)

（2）桩间土和下卧层土的平均孔压

将式（14）代入式（22）,可得悬浮长芯SDCM桩复合地基上、下部加固区中桩间土和下卧层土平均超静孔隙水压力：

${\begin{cases} {\bar{u}}_{s 1} (z, t) = \frac{p}{1 - m} \sum_{m = 1}^{\infty} C_{m} s i n (λ_{m} \frac{z}{H_{1}}) e^{- λ_{m}^{2} T_{v 1 e}}, \\ {\bar{u}}_{s 2} (z, t) = \frac{p}{1 - m ρ} \sum_{m = 1}^{\infty} C_{m} [s i n (λ_{m}) c o s (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}}) + \\ d_{2} c o s (λ_{m}) s i n (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}})] e^{- λ_{m}^{2} T_{v1e}}, \\ {\bar{u}}_{s 3} (z, t) = p \sum_{m = 1}^{\infty} \frac{C_{m} A_{m}}{c o s (μ_{3} c_{3} λ_{m})} c o s (μ_{3} λ_{m} \frac{H - z}{H_{1}}) e^{- λ_{m}^{2} T_{v1e}}, \end{cases}$

(24)

$C_{m} = \frac{2 d_{2} s i n (2 μ_{3} c_{3} λ_{m})}{λ_{m} [s i n (2 μ_{3} c_{3} λ_{m}) (d_{2} + μ_{2} c_{2} F_{m}) - μ_{3} c_{3} D_{m}]}$ ,

(25)

$A_{m} = s i n (λ_{m}) c o s (μ_{2} c_{2} λ_{m}) + d_{2} c o s (λ_{m}) s i n (μ_{2} c_{2} λ_{m})$ ,

(26)

$D_{m} = s i n (2 μ_{2} c_{2} λ_{m}) E_{m} - d_{2} s i n (2 λ_{m}) c o s (μ_{2} c_{2} λ_{m})$ ,

(27)

$E_{m} = s i n^{2} (λ_{m}) - d_{2}^{2} c o s^{2} (λ_{m})$ ,

(28)

$F_{m} = s i n^{2} (λ_{m}) + d_{2}^{2} c o s^{2} (λ_{m})$ 。

(29)

按下面方程求解出特征值 $λ_{m}$ ：

$A_{m} + d_{3} c o t (μ_{3} c_{3} λ_{m}) B_{m} = 0$ ,

(30)

$B_{m} = s i n (λ_{m}) s i n (μ_{2} c_{2} λ_{m}) - d_{2} c o s (λ_{m}) c o s (μ_{2} c_{2} λ_{m})$ 。

(31)

（3）复合地基整体平均固结度

参考谢康和^[22]的研究,容易得到悬浮长芯SDCM桩复合地基按沉降定义和按孔压定义的整体平均固结度U_s和U_p的计算公式：

$U_{s} = 1 - \sum_{m = 1}^{\infty} \frac{C_{m}}{λ_{m} (1 + b_{2} c_{2} + b_{3} c_{3})} e^{- λ_{m}^{2} T_{v1e}}$ ,

(32)

$\begin{matrix} U_{p} = 1 - \sum_{m = 1}^{\infty} \frac{\sqrt{a_{2} b_{2}} B_{m} (b_{3} - b_{2}) + b_{2} b_{3} + (b_{3} - b_{2} b_{3}) c o s (λ_{m})}{λ_{m}^{} b_{2} c_{3} (1 + c_{2} + c_{3})} \cdot \\ C_{m} e^{- λ_{m}^{2} T_{v1e}} 。 \end{matrix}$

(33)

4. 算例验证

算例中,H=20 m,r_e=1.1 m；芯桩：r_sp=0.175 m,L_sp= H₁+ H₂=12 m,E_sp=20 GPa,泊松比μ_sp=0.17。搅拌桩壳：r_p=0.35 m,L_p=H₁=8 m,E_p=150 MPa,泊松比μ_p=0.25。地基土：H₃=8 m,E_s1=E_s2=3 MPa,E_s3=9 MPa,k_v1=k_v2=k_v3=10^-8 m/s,泊松比μ_s=0.35。为了在数值计算中近似模拟等应变条件,在复合地基表面铺设0.5 m厚的混凝土板,板上荷载p=68 kPa瞬时施加。混凝土板压缩模量和泊松比与芯桩相同。地基土、芯桩、搅拌桩壳和混凝土板均采用线弹性模型。在各材料的弹性模量E和压缩模量E₁之间按E= (1+ μ)(1-2μ)E₁/(1-μ)近似换算,μ为泊松比。图2为悬浮长芯SDCM桩复合地基轴对称有限元模型。模型左、右侧边界上约束径向位移,不排水。模型底边界上径向和竖向均约束,不排水。复合地基表面自由,排水。

图 2 有限元模型

Figure 2. FEM model

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采用ABAQUS有限元软件进行算例固结分析。混凝土板、芯桩和搅拌桩壳采用4结点四边形单元（CAX4）剖分,桩间土采用应力-孔压耦合4结点四边形单元（CAX4P）剖分。芯桩-土交界处设置摩擦接触对,摩擦系数取0.42。模型共剖分2466个单元,结点总数2742个。

图3给出本文解析解计算的悬浮长芯SDCM桩复合地基整体平均固结度（U_s）曲线与有限元计算结果的比较,时间轴采用无量纲时间因数T_u=c_v1t/H²。图3表明,本文解析解与有限元计算结果较为接近,解析解数值略大于数值解,二者差值最大不超过3.0%。计算表明,解析解有较高的计算精度。

图 3 解析解和有限元解的比较

Figure 3. Comparison between analytical results and FEM results

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5. 复合地基结性状分析

采用的几何和力学参数基准值如下：H=20 m,H₁=10 m,H₂=5 m,H₃=5 m。m=0.1, $ρ$ =0.25。E_p=150 MPa,E_sp=20 GPa。E_s1=E_s2=3 MPa,E_s3=9 MPa。k_v1=k_v2=k_v3=10^-8 m/s。

（1）桩的贯入比的影响

图4给出长芯SDCM桩贯入比 $β$ =L_sp/H的变化对复合地基固结速率的影响,计算时地基土为均质土,E_s3=3 MPa,搅拌桩壳长度与芯桩长度的比值 $β_{1}$ =L_p/ L_sp=0.67保持不变。图4表明,复合地基的固结速率随着长芯SDCM桩贯入比的增加逐渐增大,当 $β$ >0.75以后,复合地基固结速率的增加率显著增大。

图 4 β对固结速率的影响

Figure 4. Influences of β on consolidation rate

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（2）搅拌桩壳的刚度和几何尺寸的影响

图5～7分别给出上部SDCM桩置换率m、搅拌桩壳长度与芯桩长度之比 $β_{1}$ =L_p/L_sp和搅拌桩壳压缩模量E_p的变化对复合地基固结速率的影响。在图5固结度曲线计算中,芯桩截面积保持不变,即m_iρ_i=mρ=0.025,m越大表示搅拌桩壳的厚度越大。图5～7计算结果表明,搅拌桩壳的厚度、长度和压缩模量的变化对悬浮长芯SDCM桩复合地基的固结速率没有影响。

图 5 　m对固结速率的影响

Figure 5. Influences of m on consolidation rate

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图 6 β₁对固结速率的影响

Figure 6. Influences of β₁ on consolidation rate

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图 7 E_p对固结速率的影响

Figure 7. Influences of E_p on consolidation rate

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（3）芯桩刚度和含心率的影响

图8,9分别给出芯桩的截面含芯率 $ρ$ 和压缩模量E_sp的变化对复合地基固结速率的影响。图8表明,芯桩含芯率 $ρ$ 的变化对悬浮长芯SDCM桩复合地基固结速率近乎没有影响。当含芯率 $ρ$ 增大时,仅在固结前期复合地基的固结速率会略微减小,但降幅非常小,可以忽略不计。从图9中可见,芯桩压缩模量E_sp的变化对悬浮长芯SDCM桩复合地基前期的固结速率有一定影响。随着E_sp数值的增加,前期复合地基固结速率随之减小,但降幅并不大。总的来看,芯桩刚度的变化对复合地基固结速率的影响不大。

图 8 ρ对固结速率的影响

Figure 8. Influence of ρ on the consolidation rate

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图 9 E_sp对固结速率的影响

Figure 9. Influences of E_sp on consolidation rate

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（4）下卧层土体刚度的影响

图10给出下卧层土压缩模量E_s3取不同数值情况下悬浮长芯SDCM桩复合地基的U_s-T_u曲线。图10表明,复合地基的固结速率随下卧层土刚度的增加而增大。这说明,将芯桩的桩端置于承载力较大的持力层上可加速复合地基的固结。

图 10 E_s3对固结速率的影响

Figure 10. Influences of E_s3 on consolidation rate

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6. 结论

（1）本文固结解析解是基于加固区等竖向应变假定获得的,因此,它更适用于刚性基础下悬浮长芯SDCM桩复合地基的固结分析。

（2）桩的贯入比和下卧层土的刚度是影响悬浮长芯SDCM桩复合地基固结快慢的主要因素。桩的贯入比和下卧层土的压缩模量越大,悬浮长芯SDCM桩复合地基的固结越快。

（3）芯桩截面含芯率的变化不会影响悬浮长芯SDCM桩复合地基的固结速率。芯桩刚度的增加会略微减小固结前期复合地基的固结速率,对后期复合地基的固结速率没有影响。

（4）搅拌桩壳的厚度、长度和刚度的变化对悬浮长芯SDCM桩复合地基的固结速率没有影响。

图 1 复合地基固结模型

Figure 1. Consolidation model for composite ground

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图 2 有限元模型

Figure 2. FEM model

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图 3 解析解和有限元解的比较

Figure 3. Comparison between analytical results and FEM results

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图 4 β对固结速率的影响

Figure 4. Influences of β on consolidation rate

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图 5 　m对固结速率的影响

Figure 5. Influences of m on consolidation rate

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图 6 β₁对固结速率的影响

Figure 6. Influences of β₁ on consolidation rate

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图 7 E_p对固结速率的影响

Figure 7. Influences of E_p on consolidation rate

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图 8 ρ对固结速率的影响

Figure 8. Influence of ρ on the consolidation rate

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图 9 E_sp对固结速率的影响

Figure 9. Influences of E_sp on consolidation rate

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图 10 E_s3对固结速率的影响

Figure 10. Influences of E_s3 on consolidation rate

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