一个冻土的渗透系数模型及其验证

张升; 颜瀚; 滕继东; 张训; 盛岱超

doi:10.11779/CJGE202011021

一个冻土的渗透系数模型及其验证 English Version

张升^{1, 2,},
颜瀚¹,
滕继东^{1, 2, ,},
张训¹,
盛岱超^{1, 2}

1.
中南大学土木工程学院,湖南　长沙　410075
2.
中南大学高速铁路建造技术国家工程实验室,湖南　长沙　410075

基金项目:

国家自然科学基金优秀青年科学基金项目 51722812

国家自然科学基金项目 51878665

国家自然科学基金高铁联合基金重点项目 U1834206

中南大学研究生自主探索创新项目 2019zzts611

详细信息

作者简介:
张升(1979—),男,博士,教授,主要从事计算土力学的教学与研究工作。E-mail：zhang-sheng@csu.edu.cn

通讯作者:
滕继东, E-mail：jdteng@csu.edu.cn

中图分类号: TU43
计量
- 文章访问数: 355
- HTML全文浏览量: 87
- PDF下载量: 211
出版历程
- 收稿日期: 2019-12-29
- 网络出版日期: 2022-12-05
- 刊出日期: 2020-10-31

New model for hydraulic conductivity of frozen soils

ZHANG Sheng^{1, 2,},
YAN Han¹,
TENG Ji-dong^{1, 2, ,},
ZHANG Xun¹,
SHENG Dai-chao^{1, 2}

1.
Department of Geotechnical Engineering, Central South University, Changsha 410075, China
2.
National Engineering Laboratory for High Speed Railway Construction, Changsha 410075, China

摘要

摘要: 寒区冻胀、融沉等冻害的核心问题是水热耦合迁移过程,而冻土渗透系数的确定是研究这类问题的关键。不同于正温条件下土的渗透系数,冻土的渗透系数涉及液态水在土、冰两种固相物质内的流动机制。如何更精确、简洁地表达冻土的渗透系数,一直没有得到很好的解决。本文基于土中冰的赋存形态,结合正温渗透系数Kozeny-Carman方程推导过程,考虑冰颗粒的阻碍作用,提出一个新的冻土渗透系数模型。本文模型通过和文献中其他学者的模型以及试验数据的比较,可以较好地吻合试验数据,验证了本文模型的合理性。相较于既有的经验模型或复杂的数学模型,本模型只有一个拟合参数,形式简洁,有明确物理依据,具有一定的应用价值。
- 渗透系数 /
- 冻土 /
- KC方程 /
- 冻结特征曲线
Abstract: One of the core issues in studying the problems such as frost heave and thaw weakening in cold regions is the process of hydro-thermal coupling migration. Determination of the hydraulic conductivity of frozen soils is the critical point to understand this process. Different from that of soils at positive temperatures, the hydraulic conductivity of frozen soils involves the liquid water flow in soil grains and ice particles. How to better express the hydraulic conductivity of frozen soils is an outstanding issue in the literatures. In this study, a new hydraulic conductivity model for frozen soils is proposed on the basis of a derivation process of the Kozeny-Carman equation, which is consistent to the determination of hydraulic conductivity at positive temperatures. By comparing with the models in the literatures and experimental data, the model in this study can match the experimental data well, which verifies the rationality of the proposed model. Compared with the existing empirical models or the mathematical models in the literatures, this model has only one fitting parameter. Besides the proposed model has a clear physical basis and is simple in form, which is easy to apply.
- hydraulic conductivity /
- frozen soil /
- Kozeny-Carman equation /
- soil freezing characteristic curve

HTML全文

图 1 土中成冰示意图

Figure 1. Growth of ice in soils

下载: 全尺寸图片幻灯片

图 2 不同模型计算曲线的对比

Figure 2. Predicted results for different models

下载: 全尺寸图片幻灯片

图 3 S_u对渗透系数的影响

Figure 3. Influences ofS_u on hydraulic conductivity

下载: 全尺寸图片幻灯片

图 4 不同SFCC模型对渗透系数预测的影响

Figure 4. Influences of different SFCCs on prediction of hydraulic conductivity

下载: 全尺寸图片幻灯片

图 5 ε 对渗透系数的影响

Figure 5. Influences ofε on hydraulic conductivity

下载: 全尺寸图片幻灯片

图 6 illite clay拟合曲线

Figure 6. Model results for illite clay

下载: 全尺寸图片幻灯片

表 1 冻土渗透系数分类表

Table 1 Models for predicting hydraulic conductivity of frozen soils

类型	编号	公式	文献	相关参数
I类	1	$k = k_{- 1} {\| T \|}^{a}$	Nixon^[5]	k_-1：-1℃时冻土的渗透系数T：温度
I类	1	$k = k_{- 1} {\| T \|}^{a}$	Nixon^[5]	a:k与T在双对数曲线上的斜率
II类	2	$k = k_{s} {(\frac{θ_{u}}{θ_{s}})}^{γ}$	O'Neill等^[6]	k_s：饱和渗透系数θ_u：未冻水含量θ_s：饱和含水率 $γ$ ：经验系数,取9
II类	3	$K = K_{0} {(1 - s)}^{3}$	Mao等^[7]	s：冰占比K₀：无冰条件下的固有渗透率
III类	4	$\begin{array}{l} k_{r} = k_{r, c} + k_{r, a}, \\ k_{r, c} = {\begin{cases} 1 (h_{m} \geq h_{m, a}) \\ {\frac{1}{2} e r f c [\frac{\ln (h_{m} / h_{m, median})}{\sqrt{2} σ}]}^{l} \cdot \\ {\frac{1}{2} e r f c [\frac{\ln (h_{m} / h_{m, median})}{\sqrt{2} σ} + \frac{σ}{\sqrt{2}}]}^{2} (h_{m} < h_{m, a}) \end{cases} \\ k_{r, a} = \frac{k_{a}}{k_{s}} = \frac{1}{k_{s}} [\frac{ρ_{a} g}{π η_{a} D_{e}} (1 - n) δ^{3}] \end{array}$	Lebeau等^[8]	k_r：相对渗透系数k_a：由毛细水贡献的渗透系数k_r,c：由毛细水贡献的相对渗透系数k_r,a：由薄膜水贡献的相对渗透系数 h_m：基质水头h_m,a：饱和时对应的基质水头h_m,median：毛细管孔隙半径中值对应的基质水头l：毛细模型参数σ：对数表示下,毛细管孔隙半径的标准差ρ_a：薄膜水密度η_a：薄膜水的动力黏度D_e：当量直径δ：水膜厚度

下载: 导出CSV

表 2 试验用土的土性参数

Table 2 Properties of measured soils

土样名称	S_s	n	θ₀	k
Manchester silt fraction	2.32×10⁷	0.37	0.37	1.58×10^-8
Chena silt	1.68×10⁷	0.48	0.48	7.13×10^-9
Calgary silt	1.89×10⁷	0.35	0.35	1.04×10^-9
Illite clay	1.249×10⁸	0.66	0.66	1.11×10^-7

下载: 导出CSV

表 3 SFCC拟合参数取值

Table 3 Parameter of SFCC

土样名称	θ_w,o	h_m,median	σ
Manchester silt fraction	0.09	-9.85	0.51
Chena silt	0.14	-8.54	0.46
Calgary silt	0.26	-5.52	0.53
Illite clay	0.57	-1.47	0.65

下载: 导出CSV

参考文献(15)

[1]	SHENG D, ZHANG S, NIU F, et al. A potential new frost heave mechanism in high-speed railway embankments[J]. Géotechnique, 2014, 64(2): 144-154. doi: 10.1680/geot.13.P.042
[2]	ZHANG S, TENG J, HE Z, et al. Canopy effect caused by vapour transfer in covered freezing soils[J]. Géotechnique, 2016, 66(11): 927-940. doi: 10.1680/jgeot.16.P.016
[3]	TENG J, SHAN F, HE Z, ZHANG S, et al. Experimental study of ice accumulation in unsaturated clean sand[J]. Géotechnique, 2019, 69(3): 251-259. doi: 10.1680/jgeot.17.P.208
[4]	芮大虎, 郭成, 芦明, 等. 冻结作用下黏土中水、盐迁移试验研究[J]. 冰川冻土, 2019, 41(1): 109-116. https://www.cnki.com.cn/Article/CJFDTOTAL-BCDT201901012.htm RUI Da-hu, GUO Cheng, LU Ming, et al. Experimental study on water and salt migrations in clay under freezing effect[J]. Journal of Glaciology and Geocryology, 2019, 41(1): 109-116. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BCDT201901012.htm
[5]	NIXON J F. Discrete ice lens theory for frost heave in soils[J]. Canadian Geotechnical Journal, 1991, 28: 843-859. doi: 10.1139/t91-102
[6]	O'NEILL K, MILLER R D. Exploration of a rigid ice model of frost heave[J]. Water Resources Research, 1985, 21(3): 281-296. doi: 10.1029/WR021i003p00281
[7]	MAO L, WANG C Y, TABUCHI Y. A multiphase model for cold start of polymer electrolyte fuel cells[J]. Journal of The Electrochemical Society, 2007, 154(3): B341-B351. doi: 10.1149/1.2430651
[8]	LEBEAU M, KONRAD J M. An extension of the capillary and thin film flow model for predicting the hydraulic conductivity of air-free frozen porous media[J]. Water Resources Research, 2012, 48(7): 7523.
[9]	TENG J, KOU J, YAN X, et al. Parameterization of soil freezing characteristic curve for unsaturated soils[J]. Cold Regions Science and Technology, 2019. doi: 10.1016/j.coldregions.2019.102928.
[10]	TENG J, KOU J, ZHANG S, SHENG D. Evaluating the influence of specimen preparation on saturated hydraulic conductivity using nuclear magnetic resonance[J]. Vadose Zone Journal, 2019. doi: 10.2136/vzj2018.
[11]	YU B, LI J. A geometry model for tortuosity of flow path in porous media[J]. Chinese Physics Letters, 2004, 21(8): 1569-1571. doi: 10.1088/0256-307X/21/8/044
[12]	HORIGUDHI K, MILLER R D. Hydraulic conductivity functions of frozen materials[C]//Proceedings of the fourth International Conference on Permafrost. Washington D C: National Academy Press, 1983: 504-508.
[13]	POLING B E, PRAUSNITZ J M, O'CONNELL J P. The Properties of Gases and Liquids[M]. New York: McGraw-Hill, 2001.
[14]	LIU Z, YU X. Physically based equation for phase composition curve of frozen soils[J]. Transportation Research Record: Journal of the Transportation Research Board, 2013, 2349(1): 93-99. doi: 10.3141/2349-11
[15]	REN X, ZHAO Y, DENG Q, et al. A relation of hydraulic conductivity - void ratio for soils based on Kozeny-Carman equation[J]. Engineering Geology, 2016, 213: 89-97. doi: 10.1016/j.enggeo.2016.08.017