单向冻结条件下非饱和铅污染黄土热-质迁移研究

doi:10.11988/ckyyb.20230983

raybet体育在线院报 ›› 2025, Vol. 42 ›› Issue (5): 174-183.DOI: 10.11988/ckyyb.20230983

单向冻结条件下非饱和铅污染黄土热-质迁移研究

罗玚¹^,²(), 周凤玺¹(), 罗崇亮³

¹ 兰州理工大学土木工程学院,兰州 730050
² 兰州工业学院土木工程学院,兰州 730050
³ 兰州交通大学土木工程学院,兰州 730050

收稿日期:2023-09-09 修回日期:2023-12-21 出版日期:2025-05-01 发布日期:2025-05-01
通信作者:
周凤玺(1979-),男,甘肃会宁人,教授,博士,主要从事岩土工程方面的教学和科研工作。E-mail: geolut@163.com
作者简介:
罗玚(1983-),男,甘肃定西人,讲师,博士,主要从事环境岩土工程方面的教学和科研。E-mail: eduly1111@163.com
基金资助:
国家自然科学基金项目(11962016); 国家自然科学基金项目(51978320); 甘肃省基础研究创新群体项目(20JR5RA478); 甘肃省教育厅高校教师创新基金项目(2023A-164); 甘肃省青年博士基金项目(2023QB-050)

Heat-Mass Migration of Unsaturated Lead-contaminated Loess under Unidirectional Freezing Conditions

LUO Yang¹^,²(), ZHOU Feng-xi¹(), LUO Chong-liang³

¹ College of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China
² College of Civil Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China
³ College of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730050, China

Received:2023-09-09 Revised:2023-12-21 Published:2025-05-01 Online:2025-05-01

摘要/Abstract

摘要：

为研究单向冻结条件下非饱和铅污染黄土中热-质迁移及土体变形规律,首先,建立单向冻结条件下铅污染黄土中水-热-污染物-力耦合数学模型;其次,利用有限元法数值模拟了负温条件下土体温度、体积含水率及污染物浓度的变化规律,结合室内试验验证了模型的有效性;最后,分析了温度梯度、土体初始饱和度及污染物初始浓度等因素对污染物迁移、结晶及土体变形的影响。研究表明:负温作用引起土体内污染物由暖端向冷端迁移,随温度降低,冻结区污染物浓度达到峰值后渐趋稳定;负温梯度增大,负温端污染物浓度增大,污染物溶解度下降,结晶量增长;冻结区污染物的浓度随初始饱和度的增大而增加;污染物初始浓度升高,结晶体积含量随之升高,但相对于冰晶体膨胀量,污染物结晶膨胀对土体位移影响不明显。

关键词: 单向冻结, 非饱和黄土, 铅污染, 热-质迁移

Abstract:

[Objective] The western regions of China are home to vast seasonal frozen soil areas. The unregulated discharge of industrial wastewater in these regions has resulted in soil contamination with heavy metal ions. Under negative temperature conditions, unsaturated soils exhibit complex water migration and phase transition processes. This study aims to study the heat-mass migration and soil deformation in unsaturated lead-contaminated liess under undirectional freezing conditions. [Methods] We utilized theoretical modelling together with laboratory test to investigate the heat, moisture, and pollutant migration patterns and the associated soil deformation characteristics in unsaturated lead-contaminated loess under unidirectional freezing conditions. First, based on the principles of mass conservation, energy conservation, and stress equilibrium, the study developed the water mass conservation equation, pollutant mass conservation equation, energy conservation equation, and soil stress equilibrium equation for lead-contaminated loess under unidirectional freezing conditions. Special attention was given to the impact of the pollutant crystallization process on moisture and heat, as well as the hindrance effect of liquid water phase changes on the soil’s hydraulic conductivity. In addition, the elastic modulus of the soil under freezing conditions was reasonably corrected, and the dynamic transformation of lead acetate crystals during the cooling process was incorporated. Key linking variables, such as the solubility of pollutants and solid-liquid ratio, were introduced. This led to the construction of a multi-field coupling mathematical model that fully reflected the heat-mass migration laws and soil deformation characteristics in contaminated soils. Next, a three-dimensional soil column calculation model was established using COMSOL Multiphysics simulation software to simulate the redistribution processes of moisture, heat, and pollutants in contaminated loess under unidirectional freezing conditions. The study particularly examined the changes in temperature, volumetric water content, and lead ion volumetric molar concentration. Simultaneously, the initial and boundary conditions used in the numerical calculation were applied to actual soil columns, with the model’s reliability verified by laboratory soil column test results. Finally, parameterized analysis systematically explored the impact of factors such as temperature gradient, soil initial saturation, and initial pollutant concentration on pollutant migration, crystallization, and soil deformation. [Conclusion] The study found that: (1) the water-heat-pollutant-force coupling model established in this paper effectively simulated the dynamic migration processes of the temperature field, moisture field, and lead ions in unsaturated loess under negative temperature conditions. Negative temperature induced complex physical and chemical processes within the soil, causing water and pollutant redistribution.(2) Under negative temperature conditions, ice-water phase transitions occurred at the freezing front, with the air pressure slightly lower than the atmospheric pressure. This generated a vacuum suction effect, causing moisture to migrate from the unfrozen zone into the freezing region, further promoting the freezing phase transition. During this migration, pollutants also accumulated in the freezing zone. As the temperature continued to drop, pollutants concentrated, reaching a peak before gradually stabilizing.(3) With an increase in the negative temperature gradient, the intensity of the ice-water phase transition at the freezing front increased, making the vacuum suction effect more pronounced. This led to an increase in the migration of pollutants toward the negative temperature end, causing the pollutants to gradually accumulate in the freezing zone and significantly increasing the amount of pollutant crystallization.(4) Under the same saturation conditions, as the initial concentration of pollutants within the soil increased, the volume of pollutant crystallization under negative temperature conditions also rose. The expansion of pollutant crystals also increased, but compared to the expansion of ice crystals, the effect of pollutant crystallization expansion on soil displacement was not significant.

Key words: unidirectional freezing, unsaturated loess, lead contamination, heat-mass migration

中图分类号:

TU431土和地基的应力

罗玚, 周凤玺, 罗崇亮. 单向冻结条件下非饱和铅污染黄土热-质迁移研究[J]. raybet体育在线院报, 2025, 42(5): 174-183.

LUO Yang, ZHOU Feng-xi, LUO Chong-liang. Heat-Mass Migration of Unsaturated Lead-contaminated Loess under Unidirectional Freezing Conditions[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(5): 174-183.

图/表 10

图1 试验仪器及装置

Fig.1 Schematic diagram of experimental instruments and setup

表1 耦合模型边界条件

Table 1 Boundary conditions of coupled model

边界条件	浓度C/(mol·L^-1)	饱和度S_w	温度T/K
初始	0.664	0.4	274.65(1.5℃)
上边界	—	—	269.15(-4.0℃)
下边界	—	0.4	—

表2 耦合模型计算参数

Table 2 Calculation parameters of coupled model

参数名称	取值	参数名称	取值
醋酸铅晶体密度 ρ_c/(kg·m^-3)	1 330	冰密度ρ_i/ (kg·m^-3)	917
土体骨架密度 ρ_s/(kg·m^-3)	1 850	水的摩尔浓度C_w/ (mol·L^-1)	55.6
饱和土体渗透系数 K_s/(m·s^-1)	6×10^-9	土体纵向弥散度 α_L/m	0.2
气体摩尔常数R/ (J·(mol·K)^-1)	8.21	污染物扩散系数D₀/ (m²·s^-1)	5×10^-9
固液比相关参数B	0.65	液态水质量热容C_w (J·(kg·K)^-1)	4 200
土体质量热容C_s/ (J·(kg·K)^-1)	890	冰质量热容C_i/ (J·(kg·K)^-1)	2 100
冰水相变潜热L_i/ (J·kg^-1)	3.5×10³	污染物结晶潜热L_c/ (J·kg^-1)	7.3×10⁴
液态水导热系数λ_l/ (W·(m·K)^-1)	0.56	土体骨架导热系数λ_s/ (W·(m·K)^-1)	1.38
冰导热系数λ_i/ (W·(m·K)^-1)	2.22	水摩尔质量m_w/ (g·mol^-1)	18
晶体污染物分子质量 M_C/(g·mol^-1)	385	水活度降低系数k_f/ (kg·K·mol^-1)	1.86
冻结膨胀系数α_i	0.09	结晶膨胀系数α_c	0.1
结晶水摩尔质量M_w/ (g·mol^-1)	54	污染物分子质量M_c/ (g·mol^-1)	331
VG模型参数l	0.5	VG模型参数m	0.5
最大含水率θ_s	0.52	残余含水率θ_r	0.06
比水容量计算参数a₀	2.65

图2 浓度及温度变化云图

Fig.2 Cloud maps of concentration and temperature variation

图3 温度及导热系数变化曲线

Fig.3 Temperature and thermal conductivity variation curves

图4 液态水体积含量、冰体积含量、液态水扩散率变化曲线

Fig.4 Variation curves of volumetric water content, volumetric ice content, and liquid water diffusion rate

图5 浓度及顶点位移变化曲线

Fig.5 Concentration and displacement variation curves

图6 温度变化对污染物浓度、污染物结晶体积含量及土柱顶点位移影响

Fig.6 Curves showing the impact of temperature variation on pollutant concentration, pollutant crystallization, and displacement at the top of the soil column

图7 初始饱和度变化对污染物浓度、污染物结晶体积含量及土柱顶点位移的影响

Fig.7 Curves showing the impact of initial saturation variation on pollutant concentration,pollutant crystalli-zation, and displacement at the top of the soil column

图8 初始浓度变化对污染物结晶体积含量及土柱顶点位移的影响曲线

Fig.8 Curves showing the impact of initial concentra-tion on pollutant crystallization and displacement at the top of the soil column

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单向冻结条件下非饱和铅污染黄土热-质迁移研究

Heat-Mass Migration of Unsaturated Lead-contaminated Loess under Unidirectional Freezing Conditions

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