考虑自由应变透水管桩桩周土径向非线性固结

宗梦繁; 张驿; 周晓龙; 吴文兵; 梅国雄

doi:10.12404/j.issn.1671-1815.2507372

科学技术与工程 ›› 2026, Vol. 26 ›› Issue (27) :11839-11845 DOI: 10.12404/j.issn.1671-1815.2507372

建筑科学

考虑自由应变透水管桩桩周土径向非线性固结

宗梦繁 ¹^,²^,³ ,
张驿 ³^,^* ,
周晓龙 ² ,
吴文兵 ⁴ ,
梅国雄 ⁵

作者信息 +

Radial Nonlinear Consolidation of Soil Around Permeable Pipe Pile Considering Free Strain

ZONG Meng-fan ¹^,²^,³ ,
ZHANG Yi ³^,^* ,
ZHOU Xiao-long ² ,
WU Wen-bing ⁴ ,
MEI Guo-xiong ⁵

Author information +

文章历史 +

摘要

透水管桩是一种具有优越排水性能和良好承载能力的新桩型,目前透水管桩在径向非线性固结方面鲜有考虑。为研究透水管桩径向非线性固结规律,在考虑自由应变和土体非线性特性(非线性压缩及非线性渗透)的基础上,建立透水管桩桩周土径向固结模型,利用有限差分法得出了透水管桩径向非线性固结有解答。进而分析非线性参数、边界排水能力和外荷载对桩周土径向非线性固结的影响,结果表明:压缩指数与渗透指数的比值对桩周土固结后期的影响更为显著,该比值增大将导致土体渗透性降低从而减缓桩周土固结;反之,该比值减小则显著加快固结速率。透水管桩排水能力的增强对桩周土固结具有明显促进作用,该作用集中于固结前期和中期,但对达到最终固结所需时间的影响较有限。

Abstract

The permeable pipe pile is a new type of pile with superior drainage performance and excellent bearing capacity. Currently, little consideration has been given to its radial nonlinear consolidation behavior. To investigate the radial nonlinear consolidation characteristics of permeable pipe piles, a radial consolidation model for the soil surrounding the pile was established, taking into account the free strain and the nonlinear consolidation properties of the soil (nonlinear compression and nonlinear permeability). Using the finite difference method, a solution for the radial nonlinear consolidation of permeable pipe piles was derived. Furthermore, the effects of nonlinear parameters, boundary drainage capacity, and external loads on the radial nonlinear consolidation of the soil surrounding the pile were analyzed. The results show that the ratio of the compression index to the permeability index has a more significant impact on the later stages of soil consolidation around the pile. A increase in this ratio leads to reduced soil permeability, thereby slowing down the consolidation of the surrounding soil. Conversely, a decrease in this ratio significantly accelerates the consolidation rate. Enhancing the drainage capacity of permeable pipe piles markedly promotes the consolidation of the surrounding soil, with this effect being concentrated in the early and middle stages of consolidation. However, its influence on the time required to achieve final consolidation is relatively limited.

Graphical abstract

关键词

非线性固结 / 透水管桩 / 软土 / 自由应变 / 有限差分法

Key words

nonlinear consolidation / permeable pipe pile / soft soil / free strain / finite difference method

引用本文

引用格式 ▾

宗梦繁, 张驿, 周晓龙, 吴文兵, 梅国雄. 考虑自由应变透水管桩桩周土径向非线性固结[J]. 科学技术与工程, 2026, 26(27): 11839-11845 DOI:10.12404/j.issn.1671-1815.2507372

ZONG Meng-fan, ZHANG Yi, ZHOU Xiao-long, WU Wen-bing, MEI Guo-xiong. Radial Nonlinear Consolidation of Soil Around Permeable Pipe Pile Considering Free Strain[J]. Science Technology and Engineering, 2026, 26(27): 11839-11845 DOI:10.12404/j.issn.1671-1815.2507372

登录浏览全文

4963

注册一个新账户忘记密码

透水管桩将竖向增强体和排水体的功能合二为一,通过快速排水固结来主动控制沉降、同步提高承载力^[1-2]。目前,常规管桩的桩周土固结研究已经较为成熟,而透水管桩作为一种新型技术,其在桩-土共同作用下的固结问题近年来逐渐受到国内外学者的关注。

在试验研究方面,文献[3 -5]采用模型试验和离心机试验验证了透水管桩具有良好的抗压性能和固结排水特性。在理论研究方面,Chen等^[6]建立了透水管桩周围土体的固结模型,通过假定透水管桩排水边界为半透水边界,推导出桩周土固结解析解答。杨伟涛等^[7]同样将透水管桩假定为半透水边界,推导出透水管桩复合地基固结的半解析解答。Duan等^[8]针对处于时变荷载环境的局部透水管桩,证实了该模型在分级加载中的适用性。随后Xiao等^[9]针对局部透水管桩求出了基于非均匀渗透系数的半解析解。Ma等^[10]将透水管桩排水边界视为阻碍型的连续排水边界,利用数值模拟方法研究了透水管桩贯入引起的桩周土体固结问题。此外,董砺威等^[11]把桩土界面渗透性在空间上的非均匀分布进行分析,分析了透水管桩排水效率随土层深度变化的规律。传统的小应变固结理论假定土体变形量相较于初始厚度较小,Hua等^[12]着重研究了黏土流变特性对透水管桩固结的影响。以上关于透水管桩周土固结的研究,主要采用等应变假定,并且聚焦于考虑变荷载作用以及土体流变特性的情况,然而针对自由应变以及桩周土非线性特性的研究尚显不足。

土体渗透性和压缩性对软土固结有着显著影响^[13]。在固结过程中,土体压缩系数和渗透系数并非始终不变,而是具有明显的非均质^[14-15]或非线性特征^[16-17]。Mesri等^[16]提出了孔隙比与有效应力及渗透系数相关的经典非线性模型。文献[18 -22]基于土体非线性模型,进一步考虑变荷载、阻碍型排水边界对软土一维非线性固结及竖井地基非线性固结进行了研究。此外,Li等^[23]提出孔隙比与压缩系数相关的非线性模型,吴思思等^[24]和胡闽等^[25]基于该非线性模型,利用有限差分法推导出一维固结解答。以上针对软土非线性固结的研究主要考虑一维固结以及竖井地基固结,对于透水管桩桩周土非线性固结问题仍需进一步研究。

采用Li等^[23]提出的软土非线性模型,考虑自由应变建立透水管桩桩周土径向非线性固结方程,采用有限差分法获得固结方程的解答。基于所得解答,详细分析透水管桩桩周土非线性固结特性。

1 透水管桩径向固结方程

透水管桩固结模型如图1所示,由于水平向渗流均对称流向透水管桩,因此可将三维图简化为二维图。

自由应变条件下考虑径竖向轴对称固结方程的表达式为

(1)$\frac{1}{\mathit{r}}\frac{\partial }{\partial \mathit{r}}\left(\frac{{\mathit{k}}_{\mathit{h}}}{{\mathit{\gamma }}_{\mathit{w}}}\mathit{r}\frac{\partial \mathit{u}}{\partial \mathit{r}}\right)$+$\frac{{\mathit{k}}_{\mathit{v}}}{{\mathit{\gamma }}_{\mathit{w}}}\frac{{\partial }^{2}\mathit{u}}{\partial {\mathit{z}}^{2}}$=$\frac{\partial {\mathit{\epsilon }}_{\mathit{v}}}{\partial \mathit{t}}$

式(1)中:u为超静孔隙水压力;ε_v为应变;r和z分别为径向和竖向坐标;t为时间;γ_w为水的重度。

考虑土体非线性压缩和非线性渗透模型^[23]为

(2)e=e₀+c_clg$\frac{{\mathit{a}}_{\mathit{v}}}{{\mathit{a}}_{\mathit{v}0}}$

(3)e=e₀+c_klg$\frac{{\mathit{k}}_{\mathit{h}}}{{\mathit{k}}_{\mathit{h}0}}$

式中:e和e₀分别为孔隙比和初始孔隙比;c_c和c_k分别为压缩指数和渗透指数;a_v和a_v0分别为压缩系数和初始压缩系数;k_h和k_h0分别为水平渗透系数和初始水平渗透系数。

由有效应力原理可知

(4)q₀=σ+u

式(4)中:σ为有效应力。

式(2)结合压缩系数的定义可得

(5)e=e₀-c_clg$\left[1+\frac{{\mathit{a}}_{\mathit{v}0}(\mathit{\sigma }-\mathit{\sigma }\mathit{\text{'}}{\mathit{ }}_{0})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]$

式(5)中:σ'₀为初始有效应力。

联合式(3)和式(5)可得

(6)k_h=k_h0

${\left[1+\frac{{\mathit{a}}_{\mathit{v}0}({\mathit{q}}_{0}-\mathit{u})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]}^{-\frac{{\mathit{c}}_{\mathit{c}}}{{\mathit{c}}_{\mathit{k}}}}$

根据式(4)和式(5)可以得到∂ε_v/∂t表达式为

(7)$\frac{\partial {\mathit{\epsilon }}_{\mathit{v}}}{\partial \mathit{t}}$=$\frac{1}{1+\mathit{e}}\frac{\partial \mathit{e}}{\partial \mathit{t}}$=$\frac{1}{1+\mathit{e}}\frac{\partial \mathit{e}}{\partial \mathit{\sigma }}\frac{\partial \mathit{\sigma }}{\partial \mathit{t}}$ =-$\frac{{\mathit{a}}_{\mathit{v}0}}{1+\mathit{e}}{\left[1+\frac{{\mathit{a}}_{\mathit{v}0}({\mathit{q}}_{\mathit{u}}-\mathit{u})\mathit{l}\mathit{n}10}{{\mathit{C}}_{\mathit{c}}}\right]}^{-1}\frac{\partial \mathit{\sigma }}{\partial \mathit{t}}$ =$\frac{{\mathit{a}}_{\mathit{v}0}}{1+\mathit{e}}{\left[1+\frac{{\mathit{a}}_{\mathit{v}0}({\mathit{q}}_{\mathit{u}}-\mathit{u})\mathit{l}\mathit{n}10}{{\mathit{C}}_{\mathit{c}}}\right]}^{-1}\frac{\partial \mathit{u}}{\partial \mathit{t}}$

将式(7)代入式(1),并且只考虑径向渗流的情况,可得固结方程为

(8)$\frac{\partial \mathit{u}}{\partial \mathit{t}}$=$\frac{{\mathit{c}}_{\mathit{h}0}(1+\mathit{e})}{\mathit{r}(1+{\mathit{e}}_{0})}{\left[1+\frac{{\mathit{a}}_{\mathit{v}0}({\mathit{q}}_{0}-\mathit{u})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]}^{1-\frac{{\mathit{c}}_{\mathit{c}}}{{\mathit{c}}_{\mathit{k}}}}\frac{\partial \mathit{u}}{\partial \mathit{r}}$+$\frac{1+\mathit{e}}{{\mathit{a}}_{\mathit{v}0}{\mathit{\gamma }}_{\mathit{w}}}\left[1+\frac{{\mathit{a}}_{\mathit{v}0}({\mathit{q}}_{0}-\mathit{u})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]\frac{\partial }{\partial \mathit{r}}\left({\mathit{k}}_{\mathit{h}}\frac{\partial \mathit{u}}{\partial \mathit{r}}\right)$

式(8)中:c_h为水平固结系数,其表达式为

(9)c_h=c_h0

$\frac{1+\mathit{e}}{1+{\mathit{e}}_{0}}{\left[1+\frac{{\mathit{a}}_{\mathit{v}0}({\mathit{q}}_{0}-\mathit{u})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]}^{1-\frac{{\mathit{c}}_{\mathit{c}}}{{\mathit{c}}_{\mathit{k}}}}$

式(9)中:c_h0为初始水平固结系数,可以表示为c_h0=k_h0(1+e₀)/(γ_wa_v0)。

考虑到透水管桩局部开孔特性,孔隙水的排出受到透水管桩的阻碍作用,同时边界孔压的变化与时间相关,因此将透水管桩的边界条件视为连续排水边界^[26],即

(10)u(r_w,t)=q₀e^-^bt

(11)${\left.\frac{\partial \mathit{u}}{\partial \mathit{r}}\right|}_{\mathit{r}={\mathit{r}}_{\mathit{e}}}$=0

(12)u(0,t)=q₀

式中:b值为反映透水管桩边界排水性能的界面参数,该值越大则透水管桩径向排水性能越强。

2 固结方程的求解

为便于求解,令U=u/q₀,R=r/r_e,R_w=r_w/r_e, T_h=c_h0t/

${\mathit{r}}_{\mathit{e}}^{2}$

。将无量纲化参数代入固结方程式(8),固结方程无量纲化为

(13)$\frac{\partial \mathit{U}}{\partial {\mathit{T}}_{\mathit{h}}}$=X_r$\frac{\partial \mathit{U}}{\partial \mathit{R}}$+W_r

$\frac{\partial }{\partial \mathit{R}}\left\{{\left[1+\frac{{\mathit{a}}_{\mathit{v}0}{\mathit{q}}_{0}(1-\mathit{U})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]}^{-\frac{{\mathit{c}}_{\mathit{c}}}{{\mathit{c}}_{\mathit{k}}}}\frac{\partial \mathit{U}}{\partial \mathit{R}}\right\}$

(14)X_r=$\frac{1+\mathit{e}}{\mathit{R}(1+{\mathit{e}}_{0})}{\left[1+\frac{{\mathit{a}}_{\mathit{v}0}{\mathit{q}}_{\mathit{u}}(1-\mathit{U})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]}^{1-\frac{{\mathit{c}}_{\mathit{c}}}{{\mathit{c}}_{\mathit{k}}}}$

(15)W_r=$\frac{1+\mathit{e}}{1+{\mathit{e}}_{0}}\left[1+\frac{{\mathit{a}}_{\mathit{v}0}{\mathit{q}}_{\mathit{u}}(1-\mathit{U})\mathit{l}\mathit{n}10}{{\mathit{c}}_{\mathit{c}}}\right]$

无量纲后的边界条件为

(16)U(R_w,T_h)=${\mathit{e}}^{-\mathit{\alpha }{\mathit{T}}_{\mathit{h}}}$

(17)${\left.\frac{\partial \mathit{U}}{\partial \mathit{R}}\right|}_{\mathit{R}=1}$=0

式中:α为无量纲化的界面参数,可以表示为α=(bH²)/c_h。

无量纲化后的初始条件为

(18)U(0,T_h)=1

采用拟线性扩散方程的隐式格式求解,差分求解空间步长ΔR,时间步长ΔT_h,计算公式为

(19)R_i=R_w+iΔR, i=1,2,…,n

(20) T_j=jΔT_h, j=1,2,…,N

式中:i为空间节点,j为时间节点。计算得ΔR=0.01,ΔT_h=10^-6。

则固结方程离散为

(21) $\begin{aligned} \frac{U_{i}^{j}-U_{i}^{j-1}}{\Delta T_{\mathrm{h}}}= & X_{i}^{j-1} \frac{U_{i+1}^{j}-U_{i-1}^{j}}{2 \Delta R}+\frac{W_{i}^{j-1}}{\Delta R} \times \\ & {\left[\alpha_{i+1 / 2}^{j-1} \frac{U_{i+1}^{j}-U_{i}^{j}}{\Delta R}-\alpha_{i-1 / 2}^{j-1} \frac{U_{i}^{j}-U_{i-1}^{j}}{\Delta R}\right] } \end{aligned}$

(22) $\begin{aligned} X_{i}^{j-1}= & \frac{1+e_{i}^{j-1}}{\left(R_{\mathrm{w}}+i \Delta R\right)\left(1+e_{0}\right)} \times \\ & {\left[1+\frac{a_{\mathrm{v} 0} q_{0}\left(1-U_{i}^{j-1}\right) \ln 10}{c_{\mathrm{c}}}\right]^{1-\frac{c_{\mathrm{c}}}{c_{\mathrm{k}}}} } \end{aligned}$

(23) $W_{i}^{j-1}=\frac{\left(1+e_{i}^{j-1}\right)}{\left(1+e_{0}\right)}\left[1+\frac{a_{v 0} q_{0}\left(1-U_{i}^{j-1}\right) \ln 10}{C_{\mathrm{c}}}\right]$

(24) $\alpha_{i+1 / 2}^{j-1}=\left[1+\frac{a_{\mathrm{v} 0} q_{0}\left(1-\frac{U_{i+1}^{j-1}+U_{i}^{j-1}}{2}\right) \ln 10}{C_{\mathrm{c}}}\right]^{-\frac{c_{\mathrm{c}}}{c_{\mathrm{k}}}}$

(25) $\alpha_{i-1 / 2}^{j-1}=\left[1+\frac{a_{\mathrm{v} 0} q_{0}\left(1-\frac{U_{i}^{j-1}+U_{i-1}^{j-1}}{2}\right) \ln 10}{C_{\mathrm{c}}}\right]^{-\frac{C_{\mathrm{c}}}{C_{\mathrm{k}}}}$

式(21)可以整理为

(26)

$\begin{array}{l} {\left[\frac{X_{i}^{j-1} \Delta T_{\mathrm{h}}}{2 \Delta R}-\frac{W_{i}^{j-1} \Delta T_{\mathrm{h}}}{(\Delta R)^{2}} \alpha_{i-1 / 2}^{j-1}\right] U_{i-1}^{j}+} \\ \quad\left[1+\frac{W_{i}^{j-1} \Delta T_{\mathrm{h}}}{(\Delta R)^{2}} \alpha_{i+1 / 2}^{j-1}+\frac{W_{i}^{j-1} \Delta T_{\mathrm{h}}}{(\Delta R)^{2}} \alpha_{i-1 / 2}^{j-1}\right] U_{i}^{j}- \\ \quad\left[\frac{X_{i}^{j-1} \Delta T_{\mathrm{h}}}{2 \Delta R}+\frac{W_{i}^{j-1} \Delta T_{\mathrm{h}}}{(\Delta R)^{2}} \alpha_{i-1 / 2}^{j-1}\right] U_{i+1}^{j}=U_{i}^{j-1} \end{array}$

式(26)的差分格式可简写为

(27)A^j^-1U^j=B^j^-1

式(27)中:A为三对角矩阵,相应的元素为

(28)A_ii=1+$\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}+1/2}^{\mathit{j}-1}$+$\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}-1/2}^{\mathit{j}-1}$

(29)A_i₍_i_-1)=$\frac{{\mathit{X}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{2\mathit{\Delta }\mathit{R}}$-$\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}-1/2}^{\mathit{j}-1}$

(30)A_i₍_i₊₁₎=-$\frac{{\mathit{X}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{2\mathit{\Delta }\mathit{R}}$-$\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}+1/2}^{\mathit{j}-1}$

(31)A_n₍_n_-1)=-$\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}-1/2}^{\mathit{j}-1}$-$\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}+1/2}^{\mathit{j}-1}$

(32)B₁=${\mathit{U}}_{\mathit{i}}^{\mathit{j}-1}$-$\left[\frac{{\mathit{X}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{2\mathit{\Delta }\mathit{R}}-\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{j}-1}\mathit{\Delta }{\mathit{T}}_{\mathit{h}}}{{\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{\mathit{\alpha }}_{\mathit{i}-1/2}^{\mathit{j}-1}\right]{\mathit{U}}_{0}^{\mathit{j}}$

(33)B_i=${\mathit{U}}_{\mathit{i}}^{\mathit{j}-1}$

径向平均固结度U_r为

(34)U_r=1-$\frac{{\int }_{{\mathit{r}}_{\mathit{w}}}^{{\mathit{r}}_{\mathit{e}}}2\mathit{\pi }\mathit{r}\mathit{u}\mathit{d}\mathit{r}}{{\int }_{{\mathit{r}}_{\mathit{w}}}^{{\mathit{r}}_{\mathit{e}}}2\mathit{\pi }\mathit{r}{\mathit{q}}_{0}\mathit{d}\mathit{r}}$=1-$\frac{2\sum _{\mathit{i}=0}^{\mathit{n}-1}{\int }_{{\mathit{R}}_{\mathit{i}}}^{{\mathit{R}}_{\mathit{i}+1}}\mathit{R}\mathit{U}\mathit{d}\mathit{R}}{1-{\mathit{R}}_{\mathit{w}}^{2}}$

假定在j时间点,径向区间[R_i, R_i₊₁]内的孔压线性分布,则有

(35)U^j=$\frac{({\mathit{U}}_{\mathit{i}+1}^{\mathit{j}}-{\mathit{U}}_{\mathit{i}}^{\mathit{j}})(\mathit{R}-{\mathit{R}}_{\mathit{i}})}{\mathit{\Delta }\mathit{R}}$+${\mathit{U}}_{\mathit{i}}^{\mathit{j}}$

则径向平均固结度可进一步表示为

(36)U_r=1-$\frac{2\sum _{\mathit{i}=0}^{\mathit{n}-1}{\mathit{S}}_{\mathit{i}}^{\mathit{j}}}{1-{\mathit{R}}_{\mathit{w}}^{2}}$

(37)${\mathit{S}}_{\mathit{i}}^{\mathit{j}}$=$\frac{({\mathit{U}}_{\mathit{i}}^{\mathit{j}}{\mathit{R}}_{\mathit{i}+1}+{\mathit{U}}_{\mathit{i}+1}^{\mathit{j}}{\mathit{R}}_{\mathit{i}})\mathit{\Delta }\mathit{R}}{2}$+$\frac{({\mathit{U}}_{\mathit{i}+1}^{\mathit{j}}-{\mathit{U}}_{\mathit{i}}^{\mathit{j}}){\left(\mathit{\Delta }\right.\mathit{R})}^{2}}{3}$

3 解答的验证与固结特性分析

3.1 解答的验证

透水管桩试验采用的参数如表1所示,涉及的其他参数取值分别为:c_c/c_k=0.4、α=16、k_h0=7.5×10^-8 m/s,与肖涛^[27]开展的透水管桩试验结果对比曲线如图2所示,可以看出本文解答与试验结果趋势基本一致,验证了该计算模型的正确性。

3.2 超静孔隙水压力分析

土体压缩指数c_c与渗透指数c_k的比值(即c_c/c_k)对透水管桩桩周土超静孔隙水压力的影响曲线如图3所示。从图3可以观察到,不同c_c/c_k对应的超静孔隙水压力演化曲线存在显著差异,且在固结中后期表现更为明显,表明土体非线性对径向固结影响更大。当时间因数T_h>2时,较低c_c/c_k对应的曲线已基本完成固结,而较高c_c/c_k对应的曲线仍存在显著超静孔隙水压力,表明土体压缩指数与渗透指数的比值越低,固结过程速率越快。这由式(6)可知,c_c/c_k越小,则固结过程中水平渗透系数越大,导致径向排水速率增大。

如图4所示为透水管桩半径r_w与透水管桩影响最大区域r_e的比值R_w对透水管桩桩周土超静孔隙水压力的影响。在其他参数固定的条件下,通过改变R_w的取值分析超静孔隙水压力的变化。从图4中可以观察出,随着R_w增大,曲线整体向左下方移动。这表明达到相同的超静孔隙水压力消散程度(如 u=40 kPa),所需的T_h时间会大大缩短。R_w=0.11的曲线最早进入平缓段,说明其超静孔隙水压力消散完成最快。这是因为R_w 值增大,意味着透水管桩自身的排水体积相对于其需要影响的土体范围更大,或者说排水路径更短、更通畅。这相当于增强了桩体的“排水能力”,使土体中的孔隙水能更快、更有效地通过桩体排出。

在固定其他参数的条件下,边界参数α对透水管桩桩周土超静孔隙水压力的影响曲线如图5所示。由图5可以看出,超静孔隙水压力随着α值的增大而减小,说明较大的α可有效促进桩周土的固结。与非线性参数相比,α对应的超静孔隙水压力曲线更小。当α>50,不同α得到的超静孔隙水压力曲线几乎重合,说明α取值超过50后,透水管桩的边界排水能力已达到饱和状态。此外,不同α值对应的孔压曲线的差异主要在固结前期,而在固结后期孔压曲线差距很小,说明透水管桩的排水边界条件对桩周土体固结前期的超静孔隙水压力消散速率具有更显著的影响,而在固结后期,其影响作用逐渐减弱。

如图6所示为不同时刻的超静孔隙水压力随径向分布情况。由图6可以看出,在时间取值较小的情况下,透水管桩附近超静孔隙水压力部分消散,而远离透水管桩的土体中超静孔隙水压力尚未开始消散,这是由于土体中的孔隙水通过透水管桩排出,超静孔隙水压力的消散由透水管桩附近扩散至远离透水管桩的土体中。当时间取值较大时,透水管桩附近超静孔隙水压力几乎完全消失,远离透水管桩的土体超静孔隙水压力也呈现消散的状态。此外,可以看出在透水管桩边界处超静孔隙水压力呈现出随时间增大而不断消散的状态,表明了透水管桩边界排水的时间效应。

3.3 平均固结度分析

在其他参数固定的条件下,外荷载q₀对径向平均固结度U_r的影响如图7所示。由图7可以看出,荷载大小主要对固结初期的固结速率的影响更大,而对固结后期的固结速率影响较小。当时间取值较小时,平均固结度随q₀取值的增大而减小,表示固结速率随外荷载值的增大而减小;反之,当时间取值较大时,平均固结度随q₀取值的增大而增大,但改变幅度较小。

透水管桩桩周土非线性对平均固结度的影响如图8所示。由图8可以看出平均固结度随非线性参数c_c/c_k取值的增大而减小。当c_c/c_k取值较小时,表明固结过程中土体的渗透系数随有效应力增加而下降的速率,远小于其压缩性增加的速率,因此土体虽然被压缩,但还能保持相对较好的透水性。当c_c/c_k取值增大时,渗透系数的下降速率变快,固结过程中土颗粒结构被压密,导致排水通道迅速变窄、堵塞。由图8可以看出土体非线性对桩周土的固结具有显著影响,工程中有必要考虑土体非线性才能更加精准预测固结速率。

4 结论

建立了透水管桩的径向非线性固结方程,得到了该方程的有限差分法解答,并详细分析了土体非线性特性、透水管桩参数对桩周土非线性固结过程的影响,最终得到以下结论。

(1)压缩指数与渗透指数的比值c_c/c_k增大时,会降低土体渗透性,进而延长固结时长。因此,当c_c/c_k增大时,固结速率会明显减缓,该现象在固结后期尤为显著;反之,降低c_c/c_k可显著提升桩周土的固结速率。

(2)透水管桩半径与最大影响区域半径的比值R_w对透水管桩周土的固结速率存在显著影响,固结速率随R_w取值的增大而升高。

(3)桩周土固结速率随透水管桩排水能力的增大而升高,且透水管桩的边界排水能力主要影响桩周土固结的前期与中期,对固结完成时间影响较小。

参考文献

原文顺序 | 出版日期 | 本文引用

[1]	周小鹏, 梅国雄. 考虑固结的透水管桩沉桩全过程有限元模拟[J]. 岩土力学, 2014, 35(S2): 676-682.

[2]	Zhou Xiaopeng, Mei Guoxiong. Finite element simulation of permeable pipe pile driving considering consolidation process[J]. Rock and Soil Mechanics, 2014, 35(S2): 676-682.

[3]	曾超峰, 薛秀丽, 梅国雄. 透水管桩技术研究进展[J]. 岩土工程学报, 2017, 39(S2): 228-231.

[4]	Zeng Chaofeng, Xue Xiuli, Mei Guoxiong. A review of recent advances in permeable pipe pile[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(S2): 228-231.

[5]	Ni P, Mangalathu S, Mei G, et al. Laboratory investigation of pore pressure dissipation in clay around permeable piles[J]. Canadian Geotechnical Journal, 2018, 55(9): 1257-1267.

[6]	Tang X, Lin W, Zou Y, et al. Experimental study of the bearing capacity of a drainage pipe pile under vacuum consolidation[J]. Journal of Zhejiang University-Science A, 2022, 23(8): 639-651.

[7]	Xu M, Ni P, Mei G. Centrifuge modelling of permeable pipe pile in consideration of pile driving process, soil consolidation, and axial loading[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2024.

[8]	Chen Z, Xiao T, Feng J, et al. Mathematical characterization of pile-soil interface boundary for consolidation analysis of soil around permeable pipe pile[J]. Canadian Geotechnical Journal, 2021, 58(9): 1277-1288.

[9]	杨伟涛, 陈征, 段亚茹, 等. 修正等应变假定下均匀开孔透水管桩复合地基固结解析解[J]. 工程科学与技术, 2024, 56(5): 230-239.

[10]	Yang Weitao, Chen Zheng, Duan Yaru, et al. Analytical solution for composite foundation with permeable pipe piles under uniform opening based on modified equal strain assumption[J]. Advanced Engineering Sciences, 2024, 56(5): 230-239.

[11]	Duan Y, Wu W, Wang T, et al. A semi-analytical solution for consolidation of soft ground improved by locally permeable pipe piles under time-dependent loads[J]. Computers and Geotechnics, 2023, 163: 105750.

[12]	Xiao T, Ni P, Chen Z, et al. A semi-analytical solution for consolidation of ground with local permeable pipe pile[J]. Computers and Geotechnics, 2022, 143: 104590.

[13]	Ma K, Gao Z, Zhang Y, et al. Analysis of accelerated consolidation effect of permeable pipe pile using coupled MPM-FEM method and continuous drainage boundary condition[J]. Computers and Geotechnics, 2024, 176: 106720.

[14]	董砺威, 吴文兵, 田乙, 等. 透水管桩沉桩后桩周土体黏弹性固结分析[J]. 岩石力学与工程学报, 2024, 43(S2): 4022-4031.

[15]	Dong Liwei, Wu Wenbing, Tian Yi, et al. Analysis on viscoelastic consolidation of soil around permeable pipe pile after pile driving[J]. Chinese Journal of Rock Mechanics and Engineering, 2024, 43(S2): 4022-4031.

[16]	Hua L, Tian Y, Gui Y, et al. Semi-analytical study of pile-soil interaction on a permeable pipe pile subjected to rheological consolidation of clayey soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2025, 49(3): 1058-1074.

[17]	张云鹏, 王宗琴, 宗梦繁, 等. 连续排水边界下成层陆域吹填地基一维固结解析解[J]. 地质科技通报, 2023, 42(3): 38-45.

[18]	Zhang Yunpeng, Wang Zongqin, Zong Mengfan, et al. Analytical solution for one-dimensional consolidation in layered filled soil based on continuous boundary conditions[J]. Bulletin of Geological Science and Technology, 2023, 42(3): 38-45.

[19]	苏若宾, 陈庚, 林民国, 等. 塑料排水板外土体淤堵的试验与固结计算方法研究[J]. 科学技术与工程, 2023, 23(12): 5210-5216.

[20]	Su Ruobin, Chen Geng, Lin Minguo, et al. Test and consolidation calculation method of soil clogging outside prefabricated vertical drain[J]. Science Technology and Engineering, 2023, 23(12): 5210-5216.

[21]	魏辉, 谢宇翔, 陈岩, 等. 考虑淤堵效应沿深度衰减的疏浚淤泥真空预压固结解析解[J]. 科学技术与工程, 2025, 25(29): 12639-12646.

[22]	Wei Hui, Xie Yuxiang, Chen Yan, et al. Analytical solution for vacuum preloading consolidation of dredged slurry considering clogging effect attenuating with depth[J]. Science Technology and Engineering, 2025, 25(29): 12639-12646.

[23]	Mesri G, Rokhsar A. Theory of consolidation for clays[J]. Journal of the Geotechnical Engineering Division, 1974, 100(8): 889-904.

[24]	宗梦繁, 吴文兵, 梅国雄, 等. 连续排水边界条件下土体一维非线性固结解析解[J]. 岩石力学与工程学报, 2018, 37(12): 2829-2838.

[25]	Zong Mengfan, Wu Wenbing, Mei Guoxiong, et al. An analytical solution for one-dimensional nonlinear consolidation of soils with continuous drainage boundary[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(12): 2829-2838.

[26]	江留慧, 李传勋, 杨怡青, 等. 变荷载下双层地基一维非线性固结近似解析解[J]. 岩土力学, 2020, 41(5): 1583-1590, 1598.

[27]	Jiang Liuhui, Li Chuanxun, Yang Yiqing, et al. Approximate analytical solutions for one-dimensional nonlinear consolidation of double-layered soil under time-dependent loading[J]. Rock and Soil Mechanics, 2020, 41(5): 1583-1590, 1598.

[28]	张驿, 马轲, 宗梦繁, 等. 多级线性加载下软土一维非线性固结分析[J]. 科学技术与工程, 2024, 24(18): 7804-7811.

[29]	Zhang Yi, Ma Ke, Zong Mengfan, et al. One-dimensional nonlinear consolidation analysis of soft soil under multi-stage linear loading[J]. Science Technology and Engineering, 2024, 24(18): 7804-7811.

[30]	薛晴, 李传勋, 郭霄. 考虑变荷载和变边界的软土大应变非线性固结分析[J]. 哈尔滨工业大学学报, 2024, 56(9): 131-139.

[31]	Xue Qing, Li Chuanxun, Guo Xiao. Analysis for large-strain nonlinear consolidation of soft soils considering time-dependent loading and drainage boundary[J]. Journal of Harbin Institute of Technology, 2024, 56(9): 131-139.

[32]	宗梦繁, 吴文兵, 梅国雄, 等. 连续排水边界下考虑指数渗流的软土一维非线性固结分析[J]. 工程力学, 2024, 41(7): 60-67.

[33]	Zong Mengfan, Wu Wenbing, Mei Guoxiong, et al. Analysis of one-dimensional nonlinear consolidation for soft soil considering exponential flow based on continuous drainage boundary[J]. Engineering Mechanics, 2024, 41(7): 60-67.

[34]	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): 1013-1025.

[35]	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): 1013-1025.

[36]	Li B, Fang Y G, Ou Z F. Asymptotic solution for the one-dimensional nonlinear consolidation equation including the pore evolution effect[J]. International Journal of Geomechanics, 2018, 18(10): 04018125.

[37]	吴思思, 罗文强, 李寅灿, 等. 连续排水边界下考虑变荷载的软土一维非线性固结分析[J]. 岩土力学, 2022, 43(6): 1503-1512.

[38]	Wu Sisi, Luo Wenqiang, Li Yincan, et al. Analysis of one-dimensional nonlinear consolidation of soft soil considering time-dependent loading with continuous drainage boundary[J]. Rock and Soil Mechanics, 2022, 43(6): 1503-1512.

[39]	胡闽, 曹文贵, 崔鹏陆, 等. 考虑变荷载与非达西渗流的软土一维非线性固结分析[J]. 长江科学院院报, 2024, 41(2): 151-158.

[40]	Hu Min, Cao Wengui, Cui Penglu, et al. One-dimensional nonlinear consolidation analysis of soft soil considering variable load and non-Darcy seepage[J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(2): 151-158.

[41]	梅国雄, 夏君, 梅岭. 基于不对称连续排水边界的太沙基一维固结方程及其解答[J]. 岩土工程学报, 2011, 33(1): 28-31.

[42]	Mei Guoxiong, Xia Jun, Mei Ling. Terzaghi’s one-dimensional consolidation equation and its solution based on asymmetric continuous drainage boundary[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(1): 28-31.