基于规范考虑水分迁移下饱和正冻土的各向异性冻胀系数研究

葛辉; 郭春香; 张蕾

doi:10.16030/j.cnki.issn.1000-3665.202312037

基于规范考虑水分迁移下饱和正冻土的各向异性冻胀系数研究

1.
兰州交通大学土木工程学院，甘肃兰州　730070

2.
陕西省水利电力勘测设计研究院, 陕西西安　710001

基金项目: 国家自然科学基金项目（41902272）；甘肃省自然科学基金项目（20JR10RA235）

详细信息

作者简介: 葛辉（1996—），男，硕士研究生，主要从事冻土工程研究。E-mail：645459556@qq.com

通讯作者: 郭春香（1978—），女，博士，副教授，主要从事冻土工程研究、寒区工程数值计算研究。E-mail：guocx@mail.lzjtu.cn

中图分类号: TU445

收稿日期: 2023-12-22

修回日期: 2024-06-19

刊出日期: 2025-07-15

Anisotropic frost heaving coefficient of saturated permafrost considering moisture migration process based on standards

1.
School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou, Gansu　730070, China

2.
Shaanxi Province Institute of Water Resources and Electric Power Investigation and Design, Xi’an, Shaanxi　710001, China

More Information

Corresponding author: GUO Chunxiang, guocx@mail.lzjtu.cn

Received Date: 22 December 2023

Revised Date: 19 June 2024

Publish Date: 15 July 2025

摘要

摘要:
正冻土冻胀是寒区工程产生冻害的关键因素，其冻胀过程是水热力相互耦合的动态作用结果，在开放系统中，温度、温度梯度、含水率、水分补给强度等都是影响正冻土冻胀变形的重要因素。冻土冻胀是水分迁移产生的竖直方向分凝冻胀和原位冻胀的共同作用，其冻胀力学特性属于各向异性。参考规范内土体含冰量随冻结的变化过程，考虑泊松比、地下水位深度、降温速率等因素，得到正冻土的在冻结过程中水平与竖直方向的冻胀系数的计算方法，通过对比粉土和粉质黏土的冻胀系数，计算结果与试验结果吻合较好。案例中粉土在−0.2～−3.0 °C、0.2～1.0 m范围内竖向冻胀系数为−1.37×10⁻³～−7.67×10⁻³，水平向冻胀系数为−0.81×10⁻³～−4.85×10⁻³，差值百分比为10.4%～77.7%，说明考虑分凝冻胀产生的各向异性是必要的。研究提出的水平与竖直方向的冻胀系数计算方法，可以为科研和设计工作提供参考依据。
- 正冻土 /
- 水分迁移 /
- 温度 /
- 地下水位深度 /
- 冻胀系数
Abstract:
Frost heave in positive permafrost is a critical factor leading to frost damage of engineering in the cold region. The frost heave process results from the dynamic interaction of hydro-thermal forces. In an open system, factors such as temperature, temperature gradient, water content, and water supply intensity significantly influence the deformation of positive permafrost frost heave. Frost heave in permafrost is the combined effect of vertical segregated frost heave due to moisture migration and in-situ frost heave, and its mechanical characteristics of frost heave are anisotropic. This study, referencing the standard process of ice content variation in soils during freezing, takes into account factors such as Poisson’s ratio, groundwater table depth, and cooling rate. the calculation methods for the frost heave coefficients in the horizontal and vertical directions during the freezing process of positive permafrost were derived. By comparing the frost heave coefficients of silt and silty clay, the results show good agreement with experimental data. In the case study, the vertical frost heave coefficient of silt ranges from −1.37×10⁻³ to −7.67×10⁻³, and the horizontal frost heave coefficient ranges from −0.81×10⁻³ to −4.85×10⁻³ within the temperature range of −0.2 °C to −3.0 °C and a depth range of 0.2 m to 1.0 m. The percentage difference ranges from 10.4% to 77.7%, indicating the necessity of considering the anisotropy resulting from segregated frost heave. The calculation methods for horizontal and vertical frost heave coefficients in this study can provide valuable information for frost damage of engineering in the cold region.
- permafrost /
- moisture migration /
- temperature /
- depth of water table /
- frost heaving coefficient

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图 1 土体冻胀弹性微元体示意图

Figure 1.

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图 2 冻胀系数h_w=0.2 m计算值与h_w=0 m试验值对比图

Figure 2.

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图 3 相同地下水位高度冻胀系数计算值与试验值对比图

Figure 3.

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图 4 不同温度不同地下水深度冻胀系数差值百分比

Figure 4.

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图 5 不同地下水深度z方向冻胀系数随温度变化图

Figure 5.

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图 6 z方向冻胀系数随地下水位深度变化图

Figure 6.

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表 1 不同土质不同温度下的温度修正系数

Table 1. Temperature correction coefficient under different soil types and temperatures

土质	塑性指标	温度修订系数
土质	塑性指标	−0.2 °C	−0.5 °C	−1.0 °C	−2.0 °C	−3.0 °C	−5.0 °C	−10.00 °C
砂土	—	0.35	0.22	0.15	0.08	0.07	0.05	0.02
粉土	I_p≤10	0.70	0.50	0.30	0.20	0.15	0.15	0.10
粉质黏土	10<I_p≤13	0.90	0.65	0.50	0.40	0.35	0.30	0.25
粉质黏土	13<I_p≤17	1.00	0.80	0.70	0.60	0.50	0.45	0.40
黏土	17<I_p	1.10	0.90	0.80	0.70	0.60	0.55	0.50
注：I_p为塑性指数；—表示不适用。

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表 2 季节冻土冻胀性分类

Table 2. Frost heaving classification of seasonal frozen soil

土质	$ {w_{\text{0}}}/\% $	h_w/m	$ \eta /\% $	冻胀等级	冻胀类别
黏性土	w₀≤w_p+2	＞2.0	$ \eta $≤1.0	Ⅰ	不冻胀
	w₀≤w_p+2	≤2.0	1.0<$ \eta $≤3.5	Ⅱ	弱冻胀
	w_p+2<w₀≤w_p+5	＞2.0	1.0<$ \eta $≤3.5	Ⅱ	弱冻胀
	w_p+2<w₀≤w_p+5	≤2.0	3.5<$ \eta $≤6.0	Ⅲ	冻胀
	w_p+5<w₀≤w_p+9	＞2.0	3.5<$ \eta $≤6.0	Ⅲ	冻胀
	w_p+5<w₀≤w_p+9	≤2.0	6.0<$ \eta $≤12.0	Ⅳ	强冻胀
	w_p+9< w₀≤w_p+15	＞2.0	6.0<$ \eta $≤12.0	Ⅳ	强冻胀
	w_p+9< w₀≤w_p+15	≤2.0	$ \eta $＞12.0	Ⅴ	特强冻胀
粉土	w₀≤19	＞1.5	$ \eta $≤1.0	Ⅰ	不冻胀
	w₀≤19	≤1.5	1.0<$ \eta $≤3.5	Ⅱ	弱冻胀
	19< w₀≤22	＞1.5	1.0<$ \eta $≤3.5	Ⅱ	弱冻胀
	19< w₀≤22	≤1.5	3.5<$ \eta $≤6.0	Ⅲ	冻胀
	22< w₀≤26	＞1.5	3.5<$ \eta $≤6.0	Ⅲ	冻胀
	22< w₀≤26	≤1.5	6.0<$ \eta $≤12.0	Ⅳ	强冻胀
	26< w₀≤30	＞1.5	6.0<$ \eta $≤12.0	Ⅳ	强冻胀
	26< w₀≤30	≤1.5	$ \eta $＞12.0	Ⅴ	特强冻胀
注：w₀为冻前天然含水率。

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表 3 土体参数及边界条件

Table 3. Soil parameters and boundary conditions

参数	试验1	试验2
土质	粉土	粉质黏土
降温速率/（°C∙h⁻¹）	−2.00	−0.07
初始含水率/%	22.00	23.45
泊松比	0.25	0.33
孔隙率	0.30	0.20
塑限含水率/%	21.70	18.50

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表 4 不同h_w、不同温度下的$ {{\boldsymbol{\alpha}} _{\boldsymbol{z}}} $

Table 4. $ {{\boldsymbol{\alpha}} _{\boldsymbol{z}}} $ at different water table depths and temperatures

温度 /°C	$ {\alpha _{\textit{z}}}/{10^{ - 3}} $
温度 /°C	h_w=0.2 m	h_w=0.4 m	h_w=0.5 m	h_w=0.6 m	h_w=0.8 m	h_w=1 m
0	0	0	0	0	0	0
−0.2	−7.67	−6.26	−5.98	−5.79	−5.55	−5.41
−0.5	−6.05	−4.64	−4.36	−4.17	−3.93	−3.79
−1.0	−6.05	−4.64	−4.36	−4.17	−3.93	−3.79
−2.0	−4.44	−3.03	−2.75	−2.56	−2.32	−2.18
−3.0	−3.63	−2.22	−1.94	−1.75	−1.51	−1.37
−5.0	—	—	—	—	—	—
−10.0	−3.63	−2.22	−1.94	−1.75	−1.51	−1.37

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表 5 不同温度下的${\boldsymbol{ \eta}} $及${{\boldsymbol{\alpha}} _{\boldsymbol{z}}} $试验值

Table 5. Experimental values of ${\boldsymbol{ \eta}} $, ${{\boldsymbol{\alpha}} _{\boldsymbol{z}}} $ at different temperatures

温度/°C	η/%	α_z/10⁻³
0	0	0
−0.5	0.2	−4.00
−1.8	1.6	−8.89
−3.5	2.2	−6.29
−5.0	2.9	−5.80
−7.5	3.4	−4.53
−9.4	3.6	−3.83
−11.5	3.8	−3.30

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表 6 不同温度不同地下水位深度各向异性冻胀系数比较

Table 6. Comparison of anisotropic frost heave coefficients at different temperatures and different groundwater depths

h_w/m	冻胀系数	计算值
h_w/m	冻胀系数	−0.2 ℃	−0.5 ℃	−2.0 ℃	−3.0 ℃
0.2	α_z/10⁻³	−7.67	−6.05	−4.44	−3.63
	α_x,y/10⁻³	−4.85	−3.23	−1.62	−0.81
	差值百分比	36.8%	46.6%	63.5%	77.7%
0.4	α_z/10⁻³	−6.26	−4.64	−3.03	−2.22
	α_x,y/10⁻³	−4.85	−3.23	−1.62	−0.81
	差值百分比	22.5%	30.4%	46.5%	63.5%
0.5	α_z/10⁻³	−5.98	−4.36	−2.75	−1.94
	α_x,y/10⁻³	−4.85	−3.23	−1.62	−0.81
	差值百分比	18.9%	25.9%	41.1%	58.2%
0.6	α_z/10⁻³	−5.79	−4.17	−2.56	−1.75
	α_x,y/10⁻³	−4.85	−3.23	−1.62	−0.81
	差值百分比	16.2%	22.5%	36.7%	53.7%
0.8	α_z/10⁻³	−5.55	−3.93	−2.32	−1.51
	α_x,y/10⁻³	−4.85	−3.23	−1.62	−0.81
	差值百分比	12.6%	17.8%	30.2%	46.4%
1.0	α_z/10⁻³	−5.41	−3.79	−2.18	−1.37
	α_x,y/10⁻³	−4.85	−3.23	−1.62	−0.81
	差值百分比	10.4%	14.8%	25.7%	40.9%

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表 7 不同温度下地下水位深度对冻胀系数影响

Table 7. Influence of groundwater depth on frost heave coefficient at different temperatures

温度/°C	$ {\alpha _{\textit{z}}}（{h_{{\mathrm{w}}}} = 0\;{{\mathrm{m}}}）/{10^{ - 3}} $	$ {\alpha _{\textit{z}}}（{h_{{\mathrm{w}}}} = 1\;{{\mathrm{m}}}）/{10^{ - 3}} $	冻胀系数减小百分率/%
0	0	0	0
−1	−5.88	−3.79	35.5
−2	−8.58	−2.18	74.6
−3	−7.05	−1.37	80.6
−5	−5.80	—	—
−10	−3.68	−1.37	62.8

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