膨胀土生态治理研究进展

白玉霞; 常顺; 肖衡林; 李丽华; 何俊; 邱季; 周文卓; 邓永锋

doi:10.11779/CJGE2024S20025

膨胀土生态治理研究进展 English Version

白玉霞^1,,
常顺¹,
肖衡林^1, ,,
李丽华¹,
何俊¹,
邱季¹,
周文卓¹,
邓永锋^{1, 2}

1.
湖北工业大学土木建筑与环境学院河湖健康智慧感知与生态修复教育部重点实验室; 湖北武汉 430068
2.
东南大学交通学院, 江苏南京 211189

基金项目:

国家自然科学基金项目 52208339

国家自然科学基金项目 U22A20232

国家自然科学基金项目 52278347

河湖健康智慧感知与生态修复教育部重点实验室开放研究基金项目 HGKFZP007

湖北省自然科学基金创新发展联合基金项目 2022CFD172

详细信息

作者简介:
白玉霞(1991—)，女，博士，主要从事特殊土改良、微生物岩土、岩土体边坡生态修复与稳定性评价等方面的研究工作。E-mail: byxhhu@163.com

通讯作者:
肖衡林, E-mail: xiao-henglin@163.com

中图分类号: TU443
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出版历程
- 收稿日期: 2024-06-20
- 刊出日期: 2024-09-30

Research progress in ecological treatment of expansive soil

1.
School of Civil Engineering, Architecture and Environment, Hubei University of Technology; Key Laboratory of Intelligent Health Perception and Ecological Restoration of Rivers and Lakes, Ministry of Education, Wuhan 430068, China
2.
School of Transportation, Southeast University, Nanjing 211189, China

摘要

摘要: 膨胀土是一种遇水急剧膨胀变形、失水迅速收缩开裂的问题土，需对其进行治理以满足工程要求。对近年来新发展的膨胀土生态治理材料进行了归纳、总结，并根据其组分、特点分为地聚合物类、离子固化剂、有机高分子材料类、微生物与酶类和生物胶类，并阐述了各类固化剂的材料特点、固化效果及作用机理，均符合新时代发展要求，可作为一种可持续的、环保的、多功能的技术大范围推广应用，最后从生态治理和推广应用角度探讨了目前需要克服的问题。
- 膨胀土 /
- 生态治理 /
- 固化效果 /
- 改性机制 /
- 研究进展
Abstract: The expansive soil is a kind of problematic soil that rapidly expands and deforms when encountering water and rapidly shrinks and cracks when losing water. It needs to be treated to meet the engineering requirements. The newly developed ecological treatment materials for the expansive soil in recent years are summarized and categorized, and the are classified according to their components and characteristics into-geopolymer, ion curing agent, organic polymer material, microorganism and enzyme, and biopolymer. The material characteristics, treatment effectiveness, and stabilization mechanisms of various treatment materials are elaborated, and they all meet the requirements of the new era and can be widely promoted and applied as a sustainable, environmentally friendly and versatile technology. Finally, the urgent issues that need to be addressed from the perspectives of ecological governance and promotion are discussed.
- expansive soil /
- ecological treatment /
- stabilization effect /
- stabilization mechanism /
- research progress

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0. 引言

沿海地区的水下地下工程建设不可避免地会受到的地下水渗流影响^[1]，将导致施工区域软土地基沉降，造成周围建筑物和地面的不均匀沉降。为保持原有地层稳定，人工冻结技术在岩土工程中广泛应用^[2]，包括海底隧道和城市地铁建设^[3]。流速较大条件下易出现冻结壁不闭合的现象^[4]，不能满足施工设计的要求。

在人工冻结过程中，确定地层的冻结范围是非常重要的。基于热势叠加理论，Hu等^[5]和Pimentel等^[6]推导了静水和渗流条件下不同冻结形式下的稳态温度场的理论公式，用来预测圆形冻结壁的厚度和平均温度^[7]。地下水渗流的存在使等温线向下游移动，下游冻结壁厚度大于上游^[8]。但现有的解析解不能揭示多孔介质冻结过程中渗流与各物理场的耦合机制。

当存在地下水渗流时，水流携带的热量导致冻结区的解冻^[9]，研究渗流条件下冻结过程中的多场耦合机制是必要的。考虑冻结过程中多场耦合变化，建立了渗流条件下人工冻结过程多场耦合数值模型^[10]。饱和土的冻结过程涉及多场、多相，针对沿海地区地下水含盐量高的问题^[11]，在多孔介质理论框架下建立多场宏观模型，模拟地下水渗流条件下的冻结过程。

本文建立了渗流条件下砂地层在人工冻结时的水-盐-热-力耦合模型。充分考虑非对流通量对传热传质的影响，固体颗粒对盐的解吸和吸附作用，以准确模拟人工冻结过程。采用Navier-Stokes方程来考虑渗流过程中流体的动量守恒，研究了单管冻结条件下，不同渗流速度下滨海砂地层中各组分的分布规律。

1. 控制方程

1.1 固体基质质量守恒方程

多孔介质中固体基质的质量守恒方程为^[12]：

$\frac{1}{{(1 - n)}}\frac{{\partial n}}{{\partial t}} + \frac{1}{{(1 - w_{\text{p}}^{\text{s}})}}\frac{{\partial w_{\text{p}}^{\text{s}}}}{{\partial t}} + {\beta _{{\text{sT}}}}\frac{{\partial T}}{{\partial t}} = {\beta _{{\text{sP}}}}\frac{{\partial {P_{\text{l}}}}}{{\partial t}} + \frac{{\partial {\varepsilon _{\text{v}}}}}{{\partial t}} 。$

(1)

式中： $w_{\text{p}}^{\text{s}}$ 为固体颗粒吸附盐的质量分数；T为温度； ${P_{\text{l}}}$ 为孔隙水力压力。

1.2 水分守恒方程

多孔介质中水分质量守恒方程的展开式为

$\begin{array}{l} n{S^{\text{l}}}(1 - w_{\text{p}}^{\text{l}}){\beta _{{\text{lp}}}}{\rho ^{\rm{l}}}\frac{{\partial {P_{\text{l}}}}}{{\partial t}} + {\text{div}}(\rho _{\text{w}}^{\text{l}}{{\boldsymbol{q}}^{\text{l}}}) - {\text{div}}({\boldsymbol{j}}_{\text{p}}^{\text{l}}) \hfill \\ = - \frac{{\partial {m_i}}}{{\partial t}} - \frac{{\partial m_{\text{p}}^{\text{l}}}}{{\partial t}} + n\rho _{\text{w}}^{\text{l}}\frac{{\partial {S^i}}}{{\partial t}} + n\rho _{\text{w}}^{\text{l}}\frac{{{S^{\text{p}}}}}{{\partial t}} - {S^{\text{l}}}\rho _{\text{w}}^{\text{l}}\frac{{\partial n}}{{\partial t}} + \hfill \\ n{S^{\text{l}}}{\rho ^{\text{l}}}\left[ {(1 - w_{\text{p}}^{\text{l}}){\beta _{{\text{lw}}}} + 1} \right]\frac{{\partial w_{\text{p}}^{\text{l}}}}{{\partial t}} - n{S^{\text{l}}}\rho _{\text{w}}^{\text{l}}\frac{{\partial {\varepsilon _{\text{v}}}}}{{\partial t}} + \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;(1 - w_{\text{p}}^{\text{l}})n{S^{\text{l}}}{\beta _{{\text{lT}}}}{\rho ^{\text{l}}}\frac{{\partial T}}{{\partial t}} 。 \end{array}$

(2)

式中： ${\beta _{{\rm{lp}}}}$ 为液相压缩率； ${\beta _{{\text{lT}}}}$ 为液体热膨胀系数； ${\beta _{{\text{lw}}}}$ 为浓度依赖系数； $\partial {m_i}/\partial t$ 为冰的结晶速率； $\partial m_{\text{p}}^{\text{l}}/\partial t$ 为结晶盐水合物的形成速率； ${\boldsymbol{j}}_{\text{p}}^{\text{l}}$ 为盐在液相中的非对流通量； $\rho _{\text{w}}^{\text{l}}$ 为液态的水密度； ${\rho ^{\text{l}}}$ 为液相的密度； $w_{\text{p}}^{\text{l}}$ 溶解盐的质量分数。

冰的质量守恒方程为^[13]

$\frac{1}{n}\frac{{\partial n}}{{\partial t}} + \frac{1}{{{S^{\text{i}}}}}\frac{{\partial {S^{\text{i}}}}}{{\partial t}} + \frac{{\partial {\varepsilon _{\text{v}}}}}{{\partial t}} = \frac{1}{{n{S^{\text{i}}}{\rho ^{\text{i}}}}}\frac{{\partial {m_{\text{i}}}}}{{\partial t}} \text{, }\;$

(3)

式中， ${\rho ^{\text{i}}}$ 为冰的密度。

1.3 盐分守恒方程

考虑冻结多孔介质液相中盐溶液的非对流通量，溶液的质量守恒为

$\frac{{\partial (n{S^{\text{l}}}\rho _{\text{p}}^{\text{l}})}}{{\partial t}} + {\text{div}}(n{S^{\text{l}}}\rho _{\text{p}}^{\text{l}}{{\boldsymbol{v}}^{\text{l}}}) + {\text{div}}({\boldsymbol{j}}_{\text{p}}^{\text{l}}) = - \frac{{\partial {m_{\text{p}}}}}{{\partial t}} - \frac{{\partial m_{\text{p}}^{\text{l}}}}{{\partial t}} 。$

(4)

式中： ${\boldsymbol{j}}_{\text{p}}^{\text{l}}$ 为冻土中盐的非对流通量； $\partial {m_{\text{p}}}/\partial t$ 为结晶盐的相变速率。

可得到展开的溶液质量守恒方程：

$\begin{array}{l} \frac{1}{n}\left( {1 - \frac{{{\rho ^{\text{s}}}w_{\rm{p}}^{\rm{s}}}}{{{\rho ^{\text{l}}}w_{\text{p}}^{\text{l}}}}} \right)\frac{{\partial n}}{{\partial t}} - \frac{1}{{{S^{\text{l}}}}}\frac{{\partial {S^{\text{i}}}}}{{\partial t}} - \frac{1}{{{S^{\text{l}}}}}\frac{{{S^{\text{p}}}}}{{\partial t}} + \frac{{\partial {\varepsilon _{\text{v}}}}}{{\partial t}} + \\ \left[ {{\beta _{{\text{lp}}}} + \frac{{(1 - n)w_{\text{p}}^{\text{s}}{\rho ^{\text{s}}}}}{{n{S^{\text{l}}}{\rho ^{\text{l}}}w_{\text{p}}^{\text{l}}}}{\beta _{{\text{sP}}}}} \right]\frac{{\partial {P^{\text{l}}}}}{{\partial t}} + \frac{{(1 - w_{\text{p}}^{\text{l}}{\beta _{{\text{lw}}}})}}{{w_{\rm{p}}^{\rm{l}}}}\frac{{\partial w_{\text{p}}^{\text{l}}}}{{\partial t}} + \\ \frac{1}{{w_{\text{p}}^{\text{l}}}}\frac{{(1 - n){\rho ^{\text{s}}}}}{{n{S^{\text{l}}}{\rho ^{\text{l}}}}}\frac{{\partial w_{\text{p}}^{\text{s}}}}{{\partial t}} - \left[ {\frac{{(1 - n)w_{\text{p}}^{\text{s}}{\rho ^{\text{s}}}}}{{n{S^{\text{l}}}{\rho ^{\text{l}}}w_{\text{p}}^{\text{l}}}}{\beta _{{\text{sT}}}} + {\beta _{{\text{lT}}}}} \right]\frac{{\partial T}}{{\partial t}} \\ \;\; = \frac{{{\text{div}}({\rho ^{\text{l}}}w_{\text{p}}^{\text{l}}{{\boldsymbol{q}}^{\text{l}}}) + {\text{div}}({\boldsymbol{j}}_{\text{p}}^{\text{l}}) - \frac{{\partial {m_{\text{p}}}}}{{\partial t}} - \frac{{{\upsilon _{\text{l}}}{M_{\text{l}}}}}{{{M_{\text{p}}}}}\frac{{\partial {m_{\text{p}}}}}{{\partial t}}}}{{n{S^{\text{l}}}{\rho ^{\text{l}}}w_{\text{p}}^{\text{l}}}} 。 \end{array}$

(5)

式中： $w_{\text{p}}^{\text{l}}$ 为液相中盐的质量分数； ${\boldsymbol{j}}_{\text{p}}^{\text{l}}$ 冻为土中盐的非对流通量； ${{\boldsymbol{q}}^{\text{l}}}$ 为液相相对流动体积； ${M_{\text{l}}}$ 为液体的摩尔质量； ${M_{\text{p}}}$ 为结晶盐的摩尔质量。

考虑多孔介质中盐的吸附-解吸效应，冻土中盐分的沉积动力学公式为

$\begin{array}{l} (1 - n){\rho ^{\text{s}}}\frac{{\partial w_{\text{p}}^{\text{s}}}}{{\partial t}}{\text{ + div}}\left[ {(1 - n){\rho ^{\text{s}}}{{\boldsymbol{v}}^{\text{s}}}} \right] \\ = {k_{ad}}n{S^l}{\rho ^l}w_p^l - {k_{de}}(1 - n){\rho ^s}w_p^s \text{, }\; \end{array}$

(6)

式中， ${k_{{\text{ad}}}}$ 和 ${k_{{\text{de}}}}$ 分别为吸附系数和解吸系数。

结晶盐的质量守恒方程为^[13]

$\frac{1}{n}\frac{{\partial n}}{{\partial t}} + \frac{1}{{{S^{\text{p}}}}}\frac{{\partial {S^{\text{p}}}}}{{\partial t}} + \frac{{\partial {\varepsilon _{\text{v}}}}}{{\partial t}} = \frac{1}{{n{\rho ^{\text{p}}}{S^{\text{p}}}}}\frac{{\partial {m_{\text{p}}}}}{{\partial t}} \text{, }\;$

(7)

式中： ${\rho ^{\text{p}}}$ 为结晶盐的密度。

1.4 能量守恒方程

多孔介质冻结过程中的能量守恒与热容和热传导度有关，能量守恒方程表示为

$\begin{array}{l} \left[ {(1 - n){\rho ^{\text{s}}}{c_{\text{s}}} + n{S^{\text{l}}}{\rho ^{\text{l}}}{c^{\text{l}}} + n{S^{\text{i}}}{\rho ^{\text{i}}}c_{\text{i}}^{\text{i}} + n{S^{\text{p}}}{\rho ^{\text{p}}}c_{\text{p}}^{\text{p}}} \right]\frac{{\partial T}}{{\partial t}} + \hfill \\ {\text{div}}\left[ {(c_{\text{p}}^{\text{l}}{\boldsymbol{j}}_{\text{p}}^{\text{l}} - {\rho ^{\text{l}}}{c^{\rm{l}}}{{\boldsymbol{q}}^{\text{l}}})(T - {T_0}) - {\lambda _{{\text{eff}}}}\nabla T} \right] \hfill \\ \;\;\;\;\;\;\;\;\;\;= {L_{{\text{wi}}}}\frac{{\partial {m_{\text{i}}}}}{{\partial t}} + {L_{{\text{sc}}}}\frac{{\partial {m_{\text{p}}}}}{{\partial t}} + {L_{{\text{lp}}}}\frac{{{\upsilon _{\text{l}}}{M_{\text{l}}}}}{{{M_{\text{p}}}}}\frac{{\partial {m_{\text{p}}}}}{{\partial t}} 。\end{array}$

(8)

式中：g为重力加速度矢量； ${\lambda _{{\text{eff}}}}$ 为冻土有效导热系数； ${c_{\text{s}}}$ ， ${c^{\text{l}}}$ ， $c_{\text{i}}^{\text{i}}$ 和 $c_{\text{p}}^{\text{p}}$ 分别代表固体颗粒、液相、冰和结晶盐的热容； ${L_{{\text{wi}}}}$ ， ${L_{{\text{lp}}}}$ ， ${L_{{\text{sc}}}}$ 分别为水、冰的相变潜热、自由水、结合水相变潜热和溶液-结晶盐的相变潜热。

1.5 动量守恒方程

人工冻结过程中的各向异性和渗流状态影响着砂土地层的冻结状态，在动量守恒中引入Navier-Stokes方程来描述渗流的动量守恒。土体冻结过程中π相的动量守恒方程为

${\rho ^\pi }{n^\pi }\frac{{d{{\boldsymbol{v}}^\pi }}}{{dt}} - div({n^\pi }{{\boldsymbol{\sigma }}^\pi }) - {\rho ^\pi }{n^\pi }{{\boldsymbol{g}}^\pi } = {\dot m^\pi } 。$

(9)

式中： ${{\boldsymbol{\sigma}} ^\pi }$ 为π相的应力张量； ${\dot m^\pi }$ 为π相与其他相的动量交换， ${{\boldsymbol{g}}^\pi }$ 为π相的体积密度。

可得到土体的动量守恒方程：

$\begin{array}{l} n{\rho ^{\rm{l}}}\left( {{F_{\rm{g}}} - \frac{{\nabla {P^{\rm{l}}}}}{{{\rho ^{\rm{l}}}}} + {\mu _{\rm{l}}}{\nabla ^2}{{\boldsymbol{v}}^{\rm{l}}}} \right) - {\rm{div}}({\boldsymbol{\sigma}} ' + {S^{\rm{l}}}{P^{\rm{l}}} + {S^{\rm{i}}}{P^{\rm{i}}} + {S^{\rm{p}}}{P^{\rm{p}}}) - \\ \left[ {(1 - n){\rho ^{\rm{s}}} + n{S^{\rm{l}}}{\rho ^{\rm{l}}} + n{S^{\rm{i}}}{\rho ^{\rm{i}}} + n{S^{\rm{p}}}{\rho ^{\rm{p}}}} \right]{\boldsymbol{g}} = {\dot m^\pi } 。 \end{array}$

(10)

式中：F_g为单位质量力；μ_l为液相的动力黏度； ${P^{\rm{i}}}$ 为冰压力； ${P^{\rm{p}}}$ 为孔隙中盐结晶压力； ${\boldsymbol{\sigma}} '$ 为有效应力。

1.6 边界条件

将耦合方程（1）~（3），（5）~（8），（10）代入COMSOL Multiphysics进行求解。边界与外部存在热对流和热交换和水、盐供应。要解耦合方程，必须满足下列边界条件：

$\left. \begin{array}{l} ({\rho }_{\text{w}}^{\text{l}}{{\boldsymbol{q}}}^{\text{l}}-{{\boldsymbol{j}}}_{\text{p}}^{\text{l}})\cdot {\boldsymbol{n}}={\overline{P}}^{\text{l}}\text{ }\text{, }\;\\ ({\rho }^{\text{l}}{w}_{\text{p}}^{\text{l}}{{\boldsymbol{q}}}^{\text{l}}+{{\boldsymbol{j}}}_{\text{p}}^{\text{l}})\cdot {\boldsymbol{n}}={\overline{w}}_{\text{p}}^{\text{l}}\text{ }\text{, }\;\\ \left[({\rho }_{\text{w}}^{\text{l}}{c}_{\text{w}}^{\text{l}}{{\boldsymbol{q}}}^{\text{l}}+{c}_{\text{p}}^{\text{l}}{{\boldsymbol{j}}}_{\text{p}}^{\text{l}})\cdot (T-{T}_{0})-{\lambda }_{\text{eff}}\nabla T\right]\cdot {\boldsymbol{n}}=\overline{T}\text{ }\text{, }\;\\ \sigma \cdot {\boldsymbol{n}}={\overline{\varepsilon }}_{\text{v}}\text{ }。 \end{array} \right\}$

(11)

2. 理论验证

结合Wang等^[14]的渗流条件下人工冻结过程温度场验证本文理论模型。模型试验如图 1所示，箱体中间设置一根外径为42 mm的冷冻管。整个模型的初始温度为10℃，冻结管的初始温度为-30℃。在箱体0.4 m处设置D轴。表 1给出了本研究使用的物理参数，模型试验所用砂土的干密度为1612 kg/m³，孔隙率为0.33，渗透系数为2.28×10⁻⁴ m/s。理论模型中D轴的温度分布结果与试验结果对比如图 2所示。可以看出理论分析结果与模型试验结果基本一致。

图 1 Wang等^[14]的模型试验示意图

Figure 1. Sketch of model tests conducted by Wang et al.^[14]

下载: 全尺寸图片幻灯片

表 1 数值模型中物理参数^[12]

Table 1. Physical parameters for numerical simulation^[12]

名称	符号	值	单位	名称	符号	值	单位
吸附系数	k_ad	2.5×10^-4	s^-1	水冰相变潜热	L_wi	6.01	kJ·mol^-1
解吸系数	k_de	1.5×10^-4	s^-1	液相压缩率	β_lp	1×10^-7	kPa^-1
固相热膨胀系数	β_sT	7.8×10^-6	K^-1	液体热膨胀系数	β_lT	2.1×10^-4	K^-1
浓度依赖系数	β_lw	0.6923	—	液态水密度	$\rho _{\text{w}}^{\text{l}}$	1000	kg·m^-3
冰的密度	$\rho _{}^{\text{l}}$	917	kg·m^-3	摩尔气体常数	R	8.2	J·mol^-1·K^-1
结晶盐密度	$\rho _{}^{\text{p}}$	1460	kg·m^-3	结晶盐的物质的量	M_p	0.142	kg·mol^-1
盐的动力学参数	K_p	1.8×10^-3	s^-1	液相的物质的量	M_l	0.018	kg·mol^-1
吸湿膨胀系数	β_s	1.5×10^-4	—	固体热容	c_s	850	J·kg^-1·K^-1
冰的动力学参数	K_i	5.82×10^-3	s^-1	冰的热容	$c_{\text{i}}^{\text{i}}$	2090	J·kg^-1·K^-1
自由水结合水相变潜热	L_lp	73.04	kJ·mol^-1	结晶盐的热容	$c_{\text{p}}^{\text{p}}$	1743	J·kg^-1·K^-1
盐、结晶盐相变潜热	L_sc	2.34	kJ·mol^-1	固相压缩率	β_sp	2×10^-4	kPa^-1

下载: 导出CSV

| 显示表格

图 2 不同渗流速度下D轴上Wang等^[14]的试验中温度分布与理论验证

Figure 2. Verification of proposed theory with model tests conducted by Wang et al^[14] and spatial temperature distribution at (a) 0 m/d and (b) 3 m/d seepage velocity on D axis

下载: 全尺寸图片幻灯片

3. 参数研究

通过参数化研究，分析了不同渗流速度和温度梯度下各组分在砂层中的空间分布。砂土层模型试验渗流如所示。模型边界目标参数如所示，砂层中 $w_{{\text{p0}}}^{\text{l}}$ 和T₀的初始值分别为0.005和10℃。冻结管壁温度设为-27℃，渗流只存在于砂层底部。冰饱和度Sⁱ、结晶盐饱和度S^p、吸收盐含量 $w_{{\text{p0}}}^{\text{s}}$ 的初始条件和边界条件均为0。选取图 2中位于砂层中4条轴线D_c，D_s，I_c，I_s，绘制温度、冰、盐、位移分布图。

图 3 砂地层模型

Figure 3. Sketch of sand stratum model

下载: 全尺寸图片幻灯片

表 2 参数分析中使用的目标参数

Table 2. Target parameters used in parametric studies

项目	P_l0/kPa	T_p/℃	T₀/℃	$w_{{\text{p0}}}^{\text{l}}$	$w_{\text{p}}^{\text{l}}$	渗流/(m·d^-1)
试验	$\gamma _{\text{w}}^{}\Delta H$	-30	10	—	—	0, 3
渗流	$\gamma _{\text{w}}^{}\Delta H$	-27	13	0.005	0.005	0, 5, 10

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不同渗流速度的下部砂层中温度沿D轴和I轴分布情况如图 4所示。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70 h后，在沿着D轴方向上的砂层上游的温度增加8.8℃，下游最高降低了13.2℃，如图 4（a）所示。当渗流速度从0 m/d增加到10 m/d，人工冻结70 h后，冻结管左右两侧的沿着I轴的温度升高了6.2℃，如图 4（b）所示。

图 4 在不同渗流速度下，冻结10，75 h后，砂层中温度分布

Figure 4. Distribution of temperature along (a) D axis and (b) I axis in sand stratum after 10 and 75 hours of freezing under different seepage velocities

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不同渗流速度对下部砂层中含冰量沿D轴和I轴分布情况如图 5所示。渗流导致水分开始冻结的位置沿着D轴向下游移动。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70 h后，在沿着D轴方向上的砂层上游水分冻结的位置向下游移动了63.5%，下游中水分冻结的位置向下游移动了173.2%，如图 5（a）所示。当渗流速度从0 m/d增加到10 m/d，即人工冻结70 h后，冻结管左右两侧的沿着I轴的水分冻结范围缩减了37.8%，如图 5（b）所示。

图 5 在不同渗流速度下，冻结10，75 h后，砂层中冰含量分布

Figure 5. Distribution of ice content along (a) D axis and (b) I axis in sand stratum after 10 and 75 hours of freezing under different seepage velocities

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不同渗流速度对下部砂层中结晶盐量沿D轴和I轴分布情况如图 6所示。图 6（a）给出了沿着渗流方向上结晶盐含量随着渗流和冻结时间变化的分布情况，盐分析出的位置沿着D轴向下游移动。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70 h后，在沿着D轴方向上的砂层上游盐分开始析出的位置向下游移动了65.1%，下游中盐分开始析出的位置向下游移动了182.7%。当渗流速度从0 m/d增加到10 m/d，即人工冻结70 h后，冻结管左右两侧的沿着Ⅰ轴的盐分的析出范围缩减了42.7%，如图 6（b）所示。

图 6 在不同渗流速度下，冻结10，75 h后，砂层中结晶盐含量分布

Figure 6. Distribution of crystalline salt content along (a) D axis and (b) I axis in sand stratum after 10 and 75 hours of freezing under different seepage velocities

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不同渗流速度对下部砂层吸附盐含量沿D轴和I轴分布的影响如图 7所示。渗流削弱了下游的盐分吸附能力。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70 h后，在沿着渗流的D轴方向上，砂层上游的吸附盐突变位置向下游移动了52%，下游的吸附盐突变位置向下游移动了32%，如图 7（a）所示。当渗流速度从0 m/d增加到10 m/d，即人工冻结70 h后，冻结管左右两侧的沿着I轴的吸附盐突变范围向冻结管方向缩小了16.2%，如图 7（b）所示。

图 7 在不同渗流速度下，冻结10，75 h后，砂层中吸附盐含量分布

Figure 7. Distribution of adsorbed salt content along (a) D axis and (b) Ⅰ axis in sand stratum after 10 and 75 hours of freezing under different seepage velocities

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不同渗流速度对下部砂层中土体位移沿D轴和I轴分布情况如图 8所示。随着冻结时间的增加，砂地层在冻胀和盐胀的作用下土体位移逐渐增加。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70 h后，在沿着D轴方向上的砂层上游的土体位移降低了33.4%，下游的土体位移降低了14.3%，如图 8（a）所示。当渗流速度从0 m/d增加到10 m/d，即人工冻结70 h后，冻结管左右两侧的沿着I轴的土体位移降低了23.1%，如图 8（b）所示。

图 8 在不同渗流速度下，冻结10，75 h后，砂层中位移分布

Figure 8. Distribution of soil displacement along (a) D axis and (b) I axis in sand stratum after 10 and 75 hours of freezing under different seepage velocities

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4. 结论

本文推导了渗流条件滨海砂土层人工冻结的水-盐-热-力学耦合模型。利用COMSOL Multiphysics软件对导出的微分方程进行求解。理论计算结果与文献中实验室模型试验结果吻合较好，验证了模型的准确性。通过参数分析，研究了不同渗流速度下的砂地层中各组分的空间分布情况。得出以下3点结论。

（1）在砂层冻结后，地层中的孔隙被堵塞，砂层底部上游的高温流体穿过地层的左右两侧下游流动。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70 h后，砂层上游的最高温度增加8.8℃。冻结管左右两侧的土体位移降低了23.1%，渗流削弱了冻结效果，减小了冻结导致的土体位移。

（2）在垂直于渗流方向上，冻结管左右两侧的冰、结晶盐对称分布。在人工冻结70 h后，随着渗流速度从0 m/d增加到10 m/d，砂层上游水分冻结位置向下游移动63.5%，下游中水分冻结位置向下游移动173.2%，冻结管左右两侧的水分冻结范围缩减37.8%。

（3）冻结区域中盐分的吸附能力是被抑制的。随着渗流速度从0 m/d增加到10 m/d，在人工冻结70h后，砂层上游的吸附盐突变位置向下游移动52%，下游的吸附盐突变位置向下游移动32%，冻结管左右两侧的吸附盐突变范围向冻结管方向缩小16.2%。

图 1 不同固化剂改善膨胀土UCS与自由膨胀率效果^{[5, 8, 10, 13, 15-21]}

Figure 1. Efficiencies of UCS and free expansion rate of stabilized expansion soil with different kinds of treatment materials ^{[5, 8, 10, 13, 15-21]}

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图 2 各类固化剂改良膨胀土SEM图

Figure 2. SEM images of different stabilizers-improved expansive soil

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图 3 聚合物改良膨胀土机理示意图

Figure 3. Schematic diagram of mechanism of polymer-modified expansive soil

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图 4 EICP改良膨胀土机理示意图

Figure 4. Schematic diagram of mechanism of EICP-improved expansive soil

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