非均质包气带土壤含水率分布定量刻画及其模拟

王铭森; 邓斌; 张晚祺; 孙志坚; 刘延锋; 张林

doi:10.19509/j.cnki.dzkq.tb20240256

非均质包气带土壤含水率分布定量刻画及其模拟

doi: 10.19509/j.cnki.dzkq.tb20240256

王铭森^{1, 2,},
邓斌¹,
张晚祺³,
孙志坚¹,
刘延锋¹,
张林^{4, 5, ,}

1.
中国地质大学（武汉）环境学院，武汉 430078
2.
中国地质调查局天津地质调查中心（华北地质科技创新中心），天津 300170
3.
湖北省水利水电规划勘测设计院有限公司，武汉 430064
4.
西安理工大学省部共建西北旱区生态水利国家重点实验室，西安 710048
5.
中国海洋大学环境科学与工程学院，山东青岛 266100

基金项目: 西安理工大学师资博士后科研启动经费（256082406）；天津市地质安全体检与风险评估示范（DD20243452）

详细信息

作者简介:
王铭森：E-mail：20171002222@cug.edu.cn

通讯作者:
E-mail：linzhang001@126.com

计量
- 文章访问数: 162
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-14
- 录用日期: 2024-07-17
- 修回日期: 2024-07-14
- 网络出版日期: 2024-11-26

Quantitative characterization and simulation of soil moisture distribution in heterogeneous vadose zone

WANG Mingsen^{1, 2
,},
DENG Bin¹,
ZHANG Wanqi³,
SUN Zhijian¹,
LIU Yanfeng¹,
ZHANG Lin^{4, 5
, ,}

1.
School of Environmental Studies, China University of Geosciences (Wuhan), Wuhan 430078, China
2.
Tianjin Geological Survey Center, China Geological Survey(North China Geological Science and Technology Innovation Center), Tianjin 300170, China
3.
Hubei Institute of Water Resources Survey and Design Co., Ltd., Wuhan 430064, China
4.
State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, Xi’an University of Technology, Xi’an 710048, China
5.
College of Environmental Science and Engineering, Ocean University of China, Qingdao Shandong 266100, China

More Information

Author Bio:
E-mail：20171002222@cug.edu.cn

Corresponding author: E-mail：linzhang001@126.com

摘要

摘要:
包气带作为连接植被与地下水的重要纽带，其岩性结构是影响地下水生态功能的主要因子之一，而包气带结构中的弱透水夹层对来自地面的入渗水流具有延迟滞后、局部蓄水作用（上层滞水），尽管该部分水量很小，但对于极端干旱区植被生态的维持具有一定供水意义。为了探究包气带岩性结构如何影响土壤含水率分布，设计了均质土柱（O），单薄夹层土柱（A），单厚夹层土柱（B）以及双夹层土柱（C）4个土柱，开展了室内层状非均质土柱释水实验和入渗实验；依据物理实验开展了变饱和水流数值模拟。实验过程中，细粒土夹层结构导致水分在夹层内部和夹层上下界面处滞留，形成了水分聚集区；相较于O柱，A柱、B柱和C柱释水过程持续时长分别增加了290，500和780 h，持水量分别增加了6.20，7.90和7.83 cm；数值模拟结果表明采用修正后的van Genuchten模型能更好地模拟层状土含水率剖面。细粒土夹层对入渗水下移特征会产生明显阻滞效应，水分主要滞留在夹层内部和夹层上下界面处，夹层厚度、层数增多会导致夹层内和夹层界面处均滞留更多水分，通过引入虚拟变量和毛细高度修正van Genuchten模型，并将其对应的相对渗透率方程分为三段式，可有效提升层状土壤含水率剖面模拟精度。
- 层状非均质 /
- 土壤水分分布 /
- 数值模拟
Abstract: Objective
The vadose zone serves as a critical link between vegetation and groundwater, with its lithological structure being one of the main factors influencing groundwater ecological functions. However, the weak permeable interlayer in the structure of the venous zone has a delayed and delayed effect on the infiltration flow from the ground and local storage (water retention in the upper layer). Although the water volume of this part is very small, it has certain water supply significance for the maintenance of vegetation ecology in extreme arid areas. In order to explore how lithologic structure affects soil water content distribution,
Methods
Four soil columns were designed: homogeneous soil column (O), thin interbedded soil column (A), single thick interbedded soil column (B) and double interbedded soil column (C). The indoor drainage and infiltration experiments are conducted on these layered heterogeneous soil columns. The numerical simulation of variable saturation flow is carried out based on physical experiments.
Results
During the experiment, the fine-grained soil interlayer structure causes water retention in the interlayer and at the upper and lower interfaces of the interlayer, forming a water accumulation area. Compared with column O, the water release duration of column A, column B and column C increased by 290 h, 500 h and 780 h, respectively, and the water holding capacity increased by 6.20 cm, 7.90 cm and 7.83 cm, respectively. The numerical simulation results show that the modified van Genuchten model can better simulate the layered soil moisture profile.
Conclusion
Fine-grained soil interlayer has a significant retarding effect on the underwater migration characteristics of infiltration, and water is mainly retained inside the interlayer and at the upper and lower interfaces of the interlayer. The increase in the thickness and number of interlayers will lead to more water retention inside the interlayer and at the interlayer interface. The corresponding relative permeability equation is divided into three stages, which can effectively improve the simulation accuracy of layered soil water content profile.
- layered heterogeneity /
- soil moisture distribution /
- numerical simulation

HTML全文

图 1 实验装置图(a)与土柱设计示意图(b)

5TE. ECH2O 5TE电容式土壤水分/温度/电导率传感器；60 cm，30 cm等数据. 5TE的安装位置；O柱. 均质土柱；A柱. 单薄层状土柱；B柱. 单厚夹层土柱；C柱. 双夹层土柱；下同

Figure 1. Experimental device diagram (a) and Schematic diagram of soil column design (b)

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图 2 土柱观测点体积含水率随时间动态变化图（图例数据为5TE的安装位置）

Figure 2. Dynamic change of volumetric moisture content of soil column observation point over time

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图 3 4个土柱含水率剖面分布图

Figure 3. Water content profile distribution of four soil columns

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图 4 不同模型模拟实验阶段4个土柱含水率误差图

Figure 4. Water content error diagrams of four soil columns in different simulated experiment stages

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图 5 不同模型模拟4个土柱最终时刻含水率剖面图

Figure 5. Water content distribution of four soil columns simulated by different models

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图 6 mVG模型渗透系数曲线图(a)和VG与mVG模型渗透系数曲线对比图(b)

Figure 6. Hydraulic conductivity curve of mVG model (a) and comparison diagram of hydraulic conductivity curve between VG and mVG model (b)

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表 1 数值模拟实验模型设置表

Table 1. Setting table of numerical simulation experiment model

土柱		O	A	B	C
柱高/cm		80
夹层分布高度/cm		无	50～60	45～60	20～30、50～60
初始条件		初始时刻土柱均饱和
持续时长/h	释水阶段	63	627	713	1268
持续时长/h	入渗阶段	187	73	87	132
上边界	释水阶段	零通量边界
上边界	入渗阶段	在实验初期0.1 h内，顶部为已知流量边界，入渗流量为10590 mL/h，在0.1 h后，顶部边界转换为零通量边界
下边界	释水阶段	底部为已知水头边界条件，水头变化依照实测值设置
下边界	入渗阶段	已知水头边界条件，水头为0 m

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表 2 不同SWCC模型及其对应的相对渗透系数模型表达式

Table 2. Different SWCC models and their corresponding relative permeability model expressions

模型名称	模型表达式	渗透系数表达式
van Genuchten（VG）模型	$\theta =\left\{ {\begin{array}{*{20}{l}} {{\theta _{\mathrm{r}}} + \dfrac{{({\theta _{\mathrm{s}}} - {\theta _{\mathrm{r}}})}}{{{{\left[1 + {{\left\| {\alpha{H_{\mathrm{p}}}} \right\|}^n}\right]}^m}}}}&{{H_{\mathrm{p}}} < 0} \\ {{\theta _{\mathrm{s}}}}&{{H_{\mathrm{p}}} \geqslant 0} \end{array}} \right.$	$K = \left\{ {\begin{array}{*{20}{l}} {{K_{\mathrm{s}}}{S_{\mathrm{e}}}^l{{[1 - {{(1 - {S_{\mathrm{e}}}^{\frac{1}{m}})}^m}]}^2}}&{{H_{\mathrm{p}}} < 0} \\ {{K_{\mathrm{s}}}}&{{H_{\mathrm{p}}} \geqslant 0} \end{array}} \right.$
Brooks-Corey（BC）模型	$\theta = \left\{ {\begin{array}{*{20}{c}} {{\theta _{\mathrm{r}}} + \dfrac{{({\theta _{\mathrm{s}}} - {\theta _{\mathrm{r}}})}}{{{{\left\| {\alpha {H_{\mathrm{p}}}} \right\|}^n}}}}&{{H_{\mathrm{p}}} < - \dfrac{1}{\alpha }} \\ {{\theta _{\mathrm{s}}}}&{{H_{\mathrm{p}}} \geqslant - \dfrac{1}{\alpha }} \end{array}} \right.$	$K = \left\{ {\begin{array}{*{20}{l}} {{K_{\mathrm{s}}}{S_{\mathrm{e}}}^{\frac{2}{n} + l + 2}}&{{H_{\mathrm{p}}} < - \dfrac{1}{\alpha }} \\ {{K_{\mathrm{s}}}}&{{H_{\mathrm{p}}} \geqslant - \dfrac{1}{\alpha }} \end{array}} \right.$
Log-Normal Distribution（LN）模型	$\begin{aligned}&\theta = {\theta _{\text{r}}} + Q\left[\dfrac{{\ln ({H_{\mathrm{p}}}/{h_{\mathrm{m}}})}}{\sigma }\right]({\theta _{\text{s}}} - {\theta _{\text{r}}}) \\&Q(x) = \int_x^\infty {\dfrac{1}{{{{(2{\text π})}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}}}{\text{exp}}( - \dfrac{{{x^2}}}{2})} {\mathrm{d}}x \end{aligned}$	$K = {K_{\mathrm{s}}}{S_{\mathrm{e}}}^{1/2}{(Q[{\mathrm{ln}}({H_{\mathrm{p}}}/{h_{\mathrm{m}}})/\sigma + \sigma ])^2}$
注：θ为体积含水率，cm³/cm³；θ_r为残余含水率，cm³/cm³；θ_s为饱和含水率，cm³/cm³；H_p表示压力水头，cm；α为拟合参数，cm⁻¹；n、m为曲线形状参数，无量纲；S_e表示土壤水饱和度；K为非饱和渗透系数，cm/h；K_s为饱和渗透系数，cm/h；l为拟合参数，通常取0.5；Q(x)为互补累计正态分布函数；x为自变量的统称；h_m为孔隙毛细管压力分布的峰值，cm；σ为孔隙毛细管压力分布的标准差；h_m和σ均为参数拟合值；下同

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表 3 不同SWCC模型参数表

Table 3. Different SWCC model parameters table

土壤类型	饱和渗透系数 K_s/(cm·h⁻¹)	模型	模型参数
土壤类型	饱和渗透系数 K_s/(cm·h⁻¹)	模型	α/(cm⁻¹)	n	m	l	h_m/cm	σ	θ_s/(cm³·cm⁻³)	θ_r/(cm³·cm⁻³)
中砂	86.88	BC	0.619	0.755	−	0.500	−	−	0.400	0
		VG	0.028	6.956	0.856	0.500	−	−	0.369	0.045
		LN	−	−	−	−	36.360	0.2439	0.364	0.037
粉土	2.16	BC	0.001	1.200	−	0.500	−	−	0.452	0.100
		VG	0.002	1.230	0.187	0.500	−	−	0.450	0.160
		LN	−	−	−	−	501.000	2.751	0.460	0.034

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表 4 A、B、C柱中夹层及夹层上下方5 cm持水量汇总

Table 4. Summary table of water holding capacity of 5 cm above and below the interlayers in columns A, B and C

土柱	A			B			C
土柱	上	夹层	下	上	夹层	下	上^a	夹层^a	下^a	上^b	夹层^b	下^b
持水量/cm	0.19	4.22	0.36	0.18	6.26	0.77	0.30	4.24	0.51	1.30	4.25	1.85
占比/%	1.10	24.50	2.09	0.95	33.09	4.06	1.62	22.86	2.75	7.01	22.91	9.97
总持水量/cm	17.22			18.92			18.55
注：^a为C柱中50～60 cm处的夹层，^b为C柱中20～30 cm处的夹层

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表 5 土柱实验中中砂和粉土的修正VG模型参数

Table 5. Modified VG model parameters of medium sand and silt in soil column experiment

土壤类型	θ_s	θ_r	α/(cm⁻¹)	n	K_s/(cm·h⁻¹)	l	θ_m/(cm³·cm⁻³)	θ_k/(cm³·cm⁻³)
中砂	0.3585	0.0580	0.0319	3.1803	86.88	0.5	0.2863	0.35
粉土	0.4500	0.0465	0.0031	1.0166	2.16	0.5	0.4400	0.45

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表 6 不同模型对3种土柱实验模拟含水率的RMSE和NSE

Table 6. RMSE and NSE of three soil columns simulated by different models

土柱	S-VG模型		S-BC模型		S-LN模型		S-mVG模型
土柱	NSE	RMSE	NSE	RMSE	NSE	RMSE	NSE	RMSE
A	0.8071	0.0869	0.6849	0.1013	0.9128	0.0483	0.9424	0.0461
B	0.8439	0.0629	0.8696	0.0706	0.9077	0.0581	0.9402	0.0572
C	0.7699	0.0874	0.7377	0.0950	0.8345	0.0675	0.8361	0.0638

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表 7 夹层上下方5 cm范围内的持水量实测值与模拟值

Table 7. Comparison of measured and simulated water holding values in the range of 5cm above and below the interlayer

土柱类型			S-VG模型		S-BC模型		S-LN模型		S-mVG模型
土柱类型	高度/cm	实测值/cm	模拟值/cm	误差/%	模拟值/cm	误差/%	模拟值/cm	误差/%	模拟值/cm	误差/%
A	60~65	0.1891	0.0771	−59.22	0.1274	−32.63	0.0993	−47.49	0.2127	+12.48
A	45~50	0.3566	0.2270	−36.34	0.2627	−26.33	0.2205	−38.17	0.3048	−14.53
B	60~65	0.1758	0.1012	−42.43	0.0567	−67.75	0.1412	−19.68	0.2127	+20.99
B	40~45	0.7713	0.3747	−51.42	0.5022	−34.89	0.6776	−12.15	0.6853	−11.15
C	60~65	0.3020	0.2532	−16.16	0.2518	−16.62	0.2885	−4.47	0.2914	−3.51
	45~50	0.5147	0.2245	−56.38	0.3510	−31.80	0.4717	−8.35	0.5286	+2.70
	30~35	1.3036	0.7548	−42.10	0.6268	−51.92	1.2136	−6.90	1.3080	+0.34
	15~20	1.7946	1.8479	+2.97	1.9064	+6.23	1.8390	+2.47	1.6870	−5.60

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