Elsevier

Cold Regions Science and Technology
冷区科学与技术

Volume 223, July 2024, 104207
第 223 卷,2024 年 7 月,104207
Cold Regions Science and Technology

Numerical simulation of frost heaving damage of earth-rock dam berms in cold regions with thermo-hydro-mechanical coupling
冻土地区温湿机械耦合对土石坝坝体冻胀破坏的数值模拟

https://doi.org/10.1016/j.coldregions.2024.104207 Get rights and content 获取权利和内容

Highlights 亮点

  • Berm frost heaving damage is caused by soil-rock mixture freezing and ice thrust.
    冻土膨胀损坏是由土壤-岩石混合物冻结和冰推力引起的。

  • Water migration from inside to slope is a key factor of berm frost heaving damage.
    水从内部向斜坡的迁移是堤坝冻胀破坏的关键因素。

  • Study berm frost heaving damage by considering thermo-hydro-mechanical coupling.
    研究冻胀破坏通过考虑热-水-力学耦合。

  • Analyze the temperature, moisture, and displacement fields of earth-rock dams.
    分析土石坝的温度、湿度和位移场。

  • Validate calculation results by comparing them with measured data.
    验证计算结果,通过将其与测量数据进行比较。

Abstract 摘要

In order to investigate the freezing damage problem of berms of earth-rock dams in cold regions, an earth-rock dam in a cold region was selected as the research object in this study. A finite element model, considering the effect of thermo-hydro-mechanical coupling, has been developed to solve the problem by combining the characteristics of the earth-rock dam. The whole process of freezing damage of berms under the influence of the reservoir level and the water migration of the dam filling was investigated, and the laws in temperature, humidity and displacement of earth-rock dams were analyzed. The calculated displacement field was then compared with the measured frozen deformation data to validate the results of the finite element simulation. The results showed that the freezing influence range of the dam slope was about 2 m, the range of temperature influence on the dam slope mainly depended on the depth of freezing, and the temperature change in the shallow range (0–2 m) of the dam slope was influenced by the outside air temperature. Also, the internal temperature of the dam body was small relative to the shallow dam slope, and there was a certain hysteresis. In addition, the effect of negative temperature was such that the shallow pore water phase of the dam slope turned into ice, manifesting macroscopically as a reduction in unfrozen water content. Water phase change, water migration from the dam filling to the dam slope, and the movement of the ice peak towards the dam body were found to be the main causes of berm freezing and expansion damage. The calculated amount expansion (due to freezing) of the dam slope was found to be in the range of 20–30 cm with a maximum value of 36 cm, which was consistent with the measured results. It was also found that the freezing and expansion damage of the berm is mainly caused by the joint action of freezing and expansion of the soil and rock mixture such as gravel bedding and dam filling, as well as the ice thrust force. It is expected that the results of this research can provide a basis for the design of berms of earth-rock dams in cold regions.
为了研究寒冷地区土石坝的冻害问题,本研究选取了寒冷地区的一座土石坝作为研究对象。通过结合土石坝的特性,开发了一个考虑热-水-力学耦合效应的有限元模型,以解决该问题。研究了水库水位和坝体填筑水迁移对土石坝坝肩冻害过程的整个影响过程,并分析了土石坝的温度、湿度和位移规律。然后将计算得到的位移场与测量的冻胀变形数据进行比较,验证有限元模拟的结果。结果显示,坝坡的冻害影响范围约为 2 米,冻害对坝坡的影响范围主要取决于冻结深度,坝坡浅层(0-2 米)的温度变化受外界空气温度影响。此外,坝体内部的温度相对浅层坝坡较小,存在一定的滞后现象。 此外,低温效应使得大坝斜坡的浅层孔隙水相变成了冰,宏观上表现为未冻结水含量的减少。水相变化、大坝填料向大坝斜坡的水迁移以及冰峰向大坝主体的移动,被发现是坝体冻结和膨胀损害的主要原因。计算得出的由于冻结引起的坝体膨胀量在 20-30 厘米的范围内,最大值为 36 厘米,与测量结果一致。还发现,坝体的冻结和膨胀损害主要是由砂石垫层和大坝填料等土石混合物的冻结和膨胀,以及冰推力共同作用引起的。本研究的成果有望为寒冷地区土石坝坝体的设计提供基础。

Keywords 关键词

Earth-rock dams
Berms
Frost damage
Thermo-hydro-mechanical coupling
Numerical simulation

地球岩石坝 堤坝 冰冻损害 热水力学耦合 数值模拟

1. Introduction 1. 引言

Currently, earth-rock dams have become one of the most common types of dams in cold regions. By the end of 2020, there were 22,579 reservoir dams in cold regions of China, of which earth-rock dams accounted for approximately 82% (National Reservoir Register, 2017). The damage forms of earth-rock dam berms in cold regions mainly include freeze-thaw frost expansion, ice pushing, ice pulling, and wave damage (Sun et al., 2002). Among them, the freeze-thaw damage in earth-rock dam berms is the most common issue in cold regions (Woo et al., 2009; Prat et al., 2012; Huang et al., 2017; Ekaterina et al., 2018; Qin et al., 2019). The dam of Liuhe Reservoir in Qing'an County, Heilongjiang Province, for example, adopts a 30 cm thick dry masonry berm. According to the dam safety monitoring data, different degrees of freeze-thaw frost expansion damage have occurred on the berm of this dam, with a maximum amount of 20–30 cm. The dam of Liugou Reservoir in Kuitun City, Xinjiang Uygur Autonomous Region, can be cited as another example that adopts concrete panel berms. According to the field investigation in 2016, the average misalignment of 41 concrete panels of the upstream slope of the Liugou Reservoir dam was about 8 cm, while the maximum misalignment was about 13 cm. As another example, the Zhangjiazuitou Reservoir dam in Xiji County, Ningxia, can be mentioned, where the maximum frost expansion of the upstream slope was about 23 cm. It has been reported that the slope of the Zhangjiazuitou Reservoir dam was damaged by freeze-thaw frost expansion after 3 to 5 freeze-thaw cycles. Therefore, it is necessary to conduct research on the mechanisms of freeze-thaw damage to earth-rock dam berms.
目前,土石坝已成为寒冷地区最常见的坝型之一。截至 2020 年底,中国寒冷地区的水库坝共有 22,579 座,其中土石坝占约 82%(国家水库登记册,2017 年)。寒冷地区土石坝坝体的破坏形式主要包括冻融膨胀、冰推、冰拉和波浪破坏(孙等,2002 年)。其中,土石坝的冻融破坏在寒冷地区是最常见的问题(Woo 等,2009 年;Prat 等,2012 年;黄等,2017 年;Ekaterina 等,2018 年;秦等,2019 年)。例如,黑龙江省青安县刘河水库采用 30 厘米厚的干砌石坝体。根据大坝安全监测数据,该坝体上发生了不同程度的冻融膨胀破坏,最大破坏量为 20-30 厘米。新疆维吾尔自治区库尔勒市刘沟水库的另一个例子采用了混凝土面板坝体。 根据 2016 年的现场调查,李沟水库大坝上游斜坡的 41 块混凝土面板的平均偏差约为 8 厘米,而最大偏差约为 13 厘米。以宁夏西吉县张家咀水库大坝为例,其上游斜坡的最大冻胀约为 23 厘米。据报道,张家咀水库大坝在经历了 3 到 5 个冻融周期后,斜坡受到冻融膨胀破坏。因此,有必要对土石坝坝体的冻融破坏机制进行研究。

Soil freezing effect is the main cause of frost damage in engineering structures such as earth-rock dam berms in cold regions. Currently, some scholars (Wang et al., 2015; Xie et al., 2015; Tang et al., 2018; Lu et al., 2019; Qu et al., 2019; Tang et al., 2020; Tang et al., 2022; Qiu et al., 2023) have studied the mechanical properties of soils after freeze-thaw cycles. For instance, Tang et al. (2020) investigated the effects of water and rock contents on the shear strength of soil-rock mixture at the freezing-thawing interface. Tang et al. (2022) studied the strength degradation behaviors and pore structure changes of soil-rock mixtures containing various amounts of rock after freeze-thaw cycles. Qiu et al. (2023) investigated the shear and creep properties of soil-rock mixture specimens under different freeze-thaw cycles and rock contents to reveal the creep failure mechanisms of soil-rock mixture using large-scale direct shear and direct shear creep tests. Furthermore, as the freezing damage process involves the interaction of moisture, temperature, and stress fields within the soil (Zhu et al., 2007), many scholars have applied the thermo-hydro-mechanical multi-field coupling theory to study the soil freezing effect (Harlan, 1973; Taylor and Luthin, 1978; Konrad, 1987; Mu and Ladanyi, 1987; Li et al., 2001; Nishimura et al., 2009; Lu et al., 2011; Peppin and Style, 2013; Lai et al., 2014; Sun et al., 2023). Harlan (1973) established a coupled water-heat model based on the theory of water migration in unsaturated permafrost and pioneered the modern theory of coupled analysis. Konrad (1987) predicted the physical and mechanical parameters of permafrost using numerical simulation based on the relationship between free water content and temperature in permafrost. Li et al. (2001) considered the frozen soil body as a space elastic body and established a coupled mathematical model of thermo-hydro-mechanical interaction for the soil body in the freezing process, and presented the corresponding discrete equations and their solutions. Peppin and Style (2013), based on a generalization of the Clapeyron equation, concluded that the resistance of the pre-fused membrane has an effect on water migration. Sun et al. (2023) presented the development of a coupled modeling approach to simulate the cryogenic thermo-hydro-mechanical (THM) processes associated with freezing soil, which was then implemented in the combined finite-discrete element method (FDEM) code for multi-physics simulation.
土壤冻结效应是寒冷地区土石坝等工程结构遭受冻害的主要原因。目前,一些学者(王等,2015 年;谢等,2015 年;唐等,2018 年;陆等,2019 年;曲等,2019 年;唐等,2020 年;唐等,2022 年;邱等,2023 年)研究了冻融循环后土壤的力学性质。例如,唐等(2020 年)研究了水分和岩石含量对冻融界面土壤-岩石混合物剪切强度的影响。唐等(2022 年)研究了不同冻融循环和岩石含量下土壤-岩石混合物的强度退化行为和孔隙结构变化。邱等(2023 年)在不同冻融循环和岩石含量下,研究了土壤-岩石混合物标本的剪切和蠕变性质,通过大规模直接剪切和直接剪切蠕变试验揭示了土壤-岩石混合物的蠕变失效机制。此外,冻结损害过程涉及土壤中的水分、温度和应力场的相互作用(朱等,)。2007 年),许多学者应用热-水-力学多场耦合理论研究土壤冻结效应(Harlan, 1973; Taylor 和 Luthin, 1978; Konrad, 1987; Mu 和 Ladanyi, 1987; Li 等, 2001; Nishimura 等, 2009; Lu 等, 2011; Peppin 和 Style, 2013; Lai 等, 2014; Sun 等, 2023)。Harlan (1973) 基于不饱和永冻土中水分迁移理论建立了水热耦合模型,开创了现代耦合分析理论。Konrad (1987) 根据永冻土中自由水含量与温度的关系,使用数值模拟预测了永冻土的物理和力学参数。Li 等 (2001) 将冻结土体视为空间弹性体,并在冻结过程中建立了土体热-水-力学相互作用的耦合数学模型,提出了相应的离散方程及其解。Peppin 和 Style (2013),基于克莱普隆方程的一般化,得出预熔膜的阻力对水分迁移有影响的结论。Sun 等。 (2023) 提出了结合建模方法来模拟冻结土壤相关的低温热-水-力学(THM)过程的发展,并将其在结合有限元-离散元方法(FDEM)代码中实现,用于多物理模拟。

From the above review, it is evident that considering the thermo-hydro-mechanical multi-field coupling in the numerical model is crucial for the study of soil freezing expansion. Considering such a coupling effect not only allows the investigation of soil frost heave, but also provides a means for further investigation of frost heave damage in engineering structures located in cold regions (Michalowski and Zhu, 2006; Yang et al., 2006; Zhang et al., 2014; Cai et al., 2019; Qin et al., 2019; Deng et al., 2021; Zhelnin et al., 2022; Chen et al., 2023; Gao et al., 2023). Zhang et al. (2014) developed a three-field thermo-hydro-mechanical coupling model considering the action of freeze-thaw cycles to study the distribution law of temperature field and deformation field of the Hada Railway, and evaluated the stability of high-speed railroad foundations in the seasonal freezing zone based on the results of the study. Qin et al. (2019) established a mechanical model suitable for the frost-heaving damage of concrete face slabs of earth-filled dams based on the mechanical analyses and engineering practice. They then used the mechanical model to conduct the numerical analysis for an engineering example, and showed that their proposed model is reliable and accurate. Gao et al. (2023) presented a novel assembled channel lining for reducing frost heave destruction and demonstrated its anti-frost heave effect. Chen et al. (2023) utilized the Northern Xinjiang Water Conveyance Canal as a case study to systematically analyze the causes of the deterioration of expansive soil canals in cold regions and investigate its failure mechanism.
从上述综述可以看出,在数值模型中考虑热-水-力学多场耦合对于研究土壤冻结膨胀至关重要。考虑到这种耦合作用不仅允许研究土壤冻胀,还为在寒冷地区工程结构中进一步研究冻胀损害提供了途径(Michalowski 和 Zhu, 2006; Yang 等, 2006; Zhang 等, 2014; Cai 等, 2019; Qin 等, 2019; Deng 等, 2021; Zhelnin 等, 2022; Chen 等, 2023; Gao 等, 2023)。Zhang 等(2014)开发了一个考虑冻融循环作用的三场热-水-力学耦合模型,用于研究哈达铁路的温度场和变形场分布规律,并根据研究结果评估了季节性冻结区高速铁路基础的稳定性。Qin 等(2019)基于力学分析和工程实践,建立了适用于土坝混凝土面板冻胀损害的机械模型。 他们然后使用机械模型对一个工程示例进行了数值分析,并表明他们提出的模型是可靠和准确的。高等人(2023 年)提出了一种新型组装式渠道衬砌,以减少冻胀破坏,并展示了其抗冻胀效果。陈等人(2023 年)以新疆北部引水渠为例,系统分析了寒冷地区膨胀土渠道退化的原因,并探讨了其失效机制。

From the literature review, we found that there is currently a lot of research on the freezing damage of water transmission channels in highway engineering, railway engineering, and water conservation engineering, but little research is available on the freezing damage of earth-rock dam berms. The freezing damage of earth dam is completely different from the damage of highways, railways and water transmission channels mainly due to the difference in structure and form of seepage control. Also, the dam berm is subjected to water pressure, ice pressure, wave pressure, etc., which complicates the freezing damage process, especially in water level fluctuation areas (see Fig. 1). According to the Chinese standard of milled earth and stone dam design specification (SL274–2020, 2020) on the requirements for the selection of berm thickness, the thickness of the concrete slab berm in practical engineering should be in the range of 0.15 to 0.20 m, and the total thickness of the berm and bedding is less than the depth of the frozen layer. The infiltration of reservoir water into the surface layer of the dam berm results in the saturation of the soil-rock mixture in the dam body shallow fill and gravel material bedding. When the temperature drops below zero, the continuous migration of moisture from the internal structure of the dam towards the surface of the dam slope exacerbates frost heave damage. The ice pushing and ice pulling generated after the freezing of the reservoir surface, along with the freezing of the gravel bedding beneath the berm and the filling of the dam body, together contribute to the frost heave damage of the dam berm.
从文献综述中,我们发现目前在公路工程、铁路工程和水利工程中对水传输管道的冻害研究较多,但对于土石坝坝体的冻害研究相对较少。土坝的冻害与公路、铁路和水传输管道的冻害完全不同,主要是由于渗流控制结构和形式的差异。此外,坝体受到水压、冰压、波压等作用,使得冻害过程更为复杂,尤其是在水位波动区域(见图 1)。根据《碾压式土石坝设计规范》(SL274-2020,2020)中关于坝体厚度选择的要求,实际工程中混凝土面板坝体的厚度应在 0.15 至 0.20 米之间,坝体和垫层的总厚度应小于冻结层的深度。 水库水渗透到坝肩的表层,导致坝体浅填土石混合物和坝肩砾石垫层中的土壤饱和。当温度降至零度以下时,水分从大坝内部结构持续向大坝斜坡表面迁移,加剧了冻胀破坏。水库表面冻结后产生的冰推和冰拉,与坝肩和坝体填充物下的砾石垫层冻结共同作用,共同导致坝肩的冻胀破坏。

Fig. 1
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Fig. 1. Illustration of frost damage of earth and rock dam berms in cold regions: (a) Frost damage to berms in areas of water level change; (b) Ice-thrust damage to berms.
图 1. 寒冷地区土石坝冻害的示意图:(a) 水位变化区域的坝体冻害;(b) 冰推坝体。

In this study, an earth-rock dam in a cold region was selected as the research object. A finite element model, taking into account the effect of thermo-hydro-mechanical coupling, has been developed to solve the problem by combining the characteristics of earth-rock dams. The whole process of freezing damage of berms in the action of the reservoir level and the water migration of the dam filling was investigated, and the laws of changes in temperature, humidity and displacement of earth-rock dams were analyzed. In order to verify the accuracy of the finite element model, the results of the finite element calculations for the displacement field were compared with the measured data. The findings of this paper can provide a scientific basis for the study of freezing damage of berms of earth-rock dams in cold regions.
在本研究中,选择了一个寒冷地区的土石坝作为研究对象。通过结合土石坝的特性,开发了一个考虑热-水-力学耦合效应的有限元模型来解决问题。研究了水库水位作用下坝体冻害的全过程以及坝体填筑的水迁移,分析了土石坝温度、湿度和位移的变化规律。为了验证有限元模型的准确性,将位移场的计算结果与测量数据进行了比较。本文的研究成果可以为寒冷地区土石坝坝体冻害的研究提供科学依据。

2. Coupled thermo-hydro-mechanical equations for freezing expansion of earth-rock dams
2. 冻结膨胀的土石坝耦合热-水-力学方程

The frost heaving damage of berms of earth-rock dams in cold regions is very serious in winter. When the internal temperature and moisture conditions of the dam body reach the initial frost heave conditions, the dam fill and gravel cushion will undergo frost heave, and then the berm will be damaged by frost heave, causing the berm to lose its protective capabilities. The relationship between temperature, moisture and stress inside an earth-rock dam is very complex, and the three interact and check and balance each other. Temperature changes inside the dam body will cause water migration in the dam body, and will also cause frost heave deformation of the berm. Therefore, it is very necessary to consider the thermo-hydro-mechanical coupling in the analysis of the dam body.
寒冷地区土石坝的冻胀破坏在冬季非常严重。当坝体内部的温度和湿度条件达到初始冻胀条件时,坝体填料和砾石垫层会发生冻胀,然后坝体由于冻胀作用受损,导致坝体失去防护能力。土石坝内部的温度、湿度和应力之间的关系非常复杂,三者相互作用,相互制约。坝体内部的温度变化会导致坝体内部的水分迁移,也会引起坝顶的冻胀变形。因此,在分析坝体时考虑热-水-力学耦合是非常必要的。

2.1. Basic assumptions 2.1. 基本假设

When freezing occurs in an earth-rock dam, the microstructure and dynamics of the interaction region involving the dam fill, gravel, water, and ice become more complex. In order to facilitate calculations, the present numerical model performs calculations according to the following assumptions:
当土石坝发生冻结时,涉及坝体填充物、砾石、水和冰的相互作用区域的微观结构和动力学变得更加复杂。为了便于计算,当前的数值模型根据以下假设进行计算:

(1) The soil inside the earth-rock dam model is homogeneous, continuous, and isotropic.
(1)地球岩坝模型内的土壤是均质、连续和各向同性的。

(2) The hydraulic and thermal conductivity coefficients in frozen soil and thawing soil are constant.
(2)结冻土和融土的水力和热导系数是恒定的。

(3) The migration of internal vapor water is not considered, but the water migration of liquid water is considered.
(3)内部水蒸气的迁移不予考虑,但液态水的迁移予以考虑。

(4) Soil particles, gravel bedding, and solid ice are incompressible, and only the volume change caused by frost heaving of water in the soil is considered.
(4) 土粒、碎石垫层和固体冰是不可压缩的,只考虑土壤中水分冻胀引起的体积变化。

(5) The coefficient of permeability is the same for all places in the soil and gravel bedding.
(5)土壤和碎石垫层中的渗透系数在所有地方都相同。

(6) Heat transfer is only considered as heat conduction, and ignores the effect of air convection.
(6) 热传递仅考虑热传导,忽略了空气对流的影响。

(7) The effect of pore water pressure and the external load of the slope protection structure are ignored.
(7) 忽略了孔隙水压力和斜坡防护结构的外部载荷的影响。

2.2. Differential equation for unfrozen water migration
2.2. 不结冰水分迁移的微分方程

According to Richard's equation and taking into account the blocking effect of pore ice on unfrozen water migration, the differential equation for unfrozen water migration is (Lu and Likos, 2012):(1)θut+ρIρwθ1t=Dθθu+kgθuwhere θu is the volumetric water content of unfrozen water in frozen soil, and kg is the coefficient of permeability of the soil in the direction of gravitational acceleration.
根据理查德的方程,并考虑到孔隙冰对未冻结水迁移的阻挡效应,未冻结水迁移的微分方程为(Lu 和 Likos, 2012): (1)θut+ρIρwθ1t=Dθθu+kgθu 其中, θu 表示冻结土壤中未冻结水的体积含水量,k g 是土壤在重力加速度方向的渗透系数。

The diffusivity of water in permafrost is calculated as follows (Taylor and Luthin, 1978):(2)Dθu=kθucθu·Iwhere kθu is the permeability of the soil (m/s), and cθu is the specific water capacity (1/m). In addition, I is the impedance factor that represents the blocking effect of pore ice on the migration of unfrozen water, and is calculated by the following formula:(3)I=10θI
冻土中水的扩散系数计算如下(Taylor 和 Luthin, 1978): (2)Dθu=kθucθu·I 其中, kθu 是土壤的渗透性(m/s), cθu 是特定水容量(1/m)。此外,I 是孔隙冰对未冻结水迁移的阻塞效应的阻抗因子,通过以下公式计算: (3)I=10θI

2.3. Heat transfer control equation
2.3. 热传递控制方程

For the two-dimensional coupled thermo-hydro-mechanical problem, considering the latent heat of phase change as the heat source, the heat transfer control equation can be expressed by Fourier's law as (Tao, 2006):(4)ρCθTt=λθ2T+L·ρIθItwhere is the differential operator which is /x/yfor a two-dimensional problem; T is the transient temperature of the soil (°C); t is the time (s); θ is the volumetric water content; θI is the pore ice volume content; x and y are horizontal and depth coordinates (m), respectively; ρ and ρI are the density of soil and ice (kg/m3), respectively; L is the latent heat of the phase transition, which takes the value of 334.5 kJ/kg; λθ is the coefficient of thermal conductivity (W/m • °C); and Cθ is the volumetric heat capacity (J/kg • °C).
对于二维耦合热-水-力学问题,将相变的潜热作为热源,热传递控制方程可以由傅里叶定律表示为(Tao, 2006): (4)ρCθTt=λθ2T+L·ρIθIt 其中, 是微分算子,对于二维问题为 /x/y ;T 是土壤的瞬时温度(℃);t 是时间(s); θ 是体积含水量; θI 是孔隙冰体积含量;x 和 y 分别是水平和深度坐标(m); ρρI 分别是土壤和冰的密度(kg/m 3 );L 是相变的潜热,其值为 334.5 kJ/kg; λθ 是热导率的系数(W/m • °C);和 Cθ 是体积热容量(J/kg • °C)。

2.4. Calculation equation of soil deformation
2.4. 土壤变形的计算公式

During the freezing process of the soil, assuming that the soil particles and gravel bedding are incompressible and isotropic, the expansion deformation of the soil is calculated as follows (Xu et al., 2001):(5)ε=0.09θ0θu+1.09Δθwhere ε is the soil expansion deformation, θ0 is the initial water content, θu is the unfrozen water content, and Δθ is the migration water content.
在土壤冻结过程中,假设土壤颗粒和卵石垫层不可压缩且各向同性,土壤的膨胀变形计算如下(徐等,2001): (5)ε=0.09θ0θu+1.09Δθ 其中, ε 表示土壤膨胀变形, θ0 表示初始含水量, θu 表示未冻结含水量, Δθ 表示迁移含水量。

2.5. Phase change dynamic equilibrium relationship
2.5. 相变动态平衡关系

Xu et al. (2001) obtained an empirical relationship for the volume content of unfrozen water in frozen soil through an extensive set of experiments. It can be expressed as follows:(6)ω0ωu=TTfB,T<Tfwhere Tf is the temperature of the soil in freezing (°C), ω0 is the initial water content of the soil (%), ωu is the water content of unfrozen water at negative temperature (%), and B is a constant depending on the soil type and salt content.
徐等人(2001 年)通过一系列广泛实验,得到了冻结土壤中未冻结水分体积含量的实证关系。其表达式如下: (6)ω0ωu=TTfB,T<Tf 其中, Tf 是土壤冻结时的温度(°C), ω0 是土壤的初始含水量(%), ωu 是负温度下未冻结水分的含水量(%),B 是依赖于土壤类型和盐分含量的常数。

In this study, the linkage equation is established based on the concept of “solid-liquid ratio” proposed in the literature (Bai et al., 2015), which can be expressed as:(7)BI=θIθu=1.1TTfB1.1T<Tf0TTfwhere BI is the solid-liquid ratio. Also, the factor 1.1 is the density ratio of water and ice.
在本研究中,基于文献( Bai 等,2015)提出的“固液比”概念,建立了联系方程,可以表示为: (7)BI=θIθu=1.1TTfB1.1T<Tf0TTf 其中, BI 表示固液比。此外,因子 1.1 是水和冰的密度比。

Thus, a coupled equation for pore ice, unfrozen water, and temperature can be obtained as:(8)θI=BIT·θu
因此,可以得到孔隙冰、未冻结水和温度的耦合方程为: (8)θI=BIT·θu

3. Finite Element Model 3. 有限元模型

3.1. Model 3.1. 模型

According to the typical profile of an earth-rock dam in the cold region, Comsol Multiphysics finite element software is used to establish the model. The model and arrangement of measurement points are shown in Fig. 2. In general, the Comsol Multiphysics has the property of convergence, and the convergence can be achieved by dividing the domain into smaller elements, regardless of the shape of the element. Therefore, the shape of the elements only affects the convergence rate, and if the number of elements is chosen appropriately, it does not have a significant effect on the accuracy of the calculation results. Here, the discretization of the domain into elements or grids is based on the coupling characteristics of the problem, where a total of 2697 elements are generated, with 44 fixed-point elements and 631 boundary elements. A schematic of the numerical model is shown in Fig. 3.
根据寒冷地区土石坝的典型剖面,使用 Comsol Multiphysics 有限元软件建立模型。模型及测量点的布置如图 2 所示。通常,Comsol Multiphysics 具有收敛性,无论元素的形状如何,通过将域分割成更小的元素,可以实现收敛。因此,元素的形状仅影响收敛率,如果适当选择元素的数量,它对计算结果的准确性影响不大。在这里,基于问题的耦合特性对域进行离散化,生成了总共 2697 个元素,其中 44 个固定点元素和 631 个边界元素。数值模型的示意图如图 3 所示。

Fig. 2
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Fig. 2. Computation model.
图 2. 计算模型。

Fig. 3
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Fig. 3. Mesh division of numerical model.
图 3. 数值模型的网格划分。

3.2. Boundary conditions 3.2. 边界条件

The upstream dam slope ab is the reservoir level boundary, cd is the downstream water level boundary, and efgh is the impervious boundary.
上游坝坡 ab 是水库水位边界,cd 是下游水位边界,而 efgh 是不透水边界。

3.2.1. Temperature field boundary conditions
3.2.1. 温度场边界条件

The bc boundary is in contact with the external badlands, because the temperature change curve with time is approximated as a sinusoidal curve with a period of about 365 days. Therefore, the bc temperature boundary is set as a sinusoidal curve with time, and the temperature change from November 15, 2021 to February 15, 2022 is simulated based on the measured temperature in the toe area of the earth-rock dam. The boundary bh below the reservoir level and the boundary gf on the lower bottom surface take constant values.
bc 边界与外部荒漠接触,因为随时间变化的温度曲线近似为周期约为 365 天的正弦曲线。因此,bc 温度边界设置为随时间变化的正弦曲线,基于 2021 年 11 月 15 日至 2022 年 2 月 15 日期间地球岩坝趾部区域测量的温度进行模拟。水库水平以下的 bh 边界和下底面的 gf 边界取常数值。

The bc temperature boundary is as follows:(9)Ts=3.973+10.3sin2π8760th+3π4where th is the time increment.
bc 温度边界如下: (9)Ts=3.973+10.3sin2π8760th+3π4 其中 th 是时间增量。

The temperatures at the boundary bh below the reservoir water level and the bottom boundary gf have constant values. This study takes the temperature value of the boundary bh below the reservoir level as 5 °C, the temperature value of the boundary gf at the lower bottom surface as 3 °C, and the temperature boundaries ag and df on both sides as adiabatic boundaries.
边界 bh 在水库水位以下和底部边界 gf 的温度具有恒定值。本研究将边界 bh 在水库水平以下的温度值设定为 5°C,将底部表面下方的边界 gf 的温度值设定为 3°C,并将两侧的温度边界 ag 和 df 设定为等温边界。

3.2.2. Hydraulic boundary conditions
3.2.2. 液压边界条件

The simulation process does not consider the influence of groundwater and surface water recharge. The reservoir water level elevation is 1832.85 m, the water content of soil in saturated zone is 28%, and the water content of soil in unsaturated zone decreases step by step from the infiltration line to the top of the dam. The water content of soil on the top of the dam is 3%.
模拟过程不考虑地下水和地表水补给的影响。水库水位高度为 1832.85 米,饱和区土壤含水量为 28%,非饱和区土壤含水量从渗入线到大坝顶部逐级减少。大坝顶部土壤含水量为 3%。

3.2.3. Displacement field boundary conditions
3.2.3. 移动场边界条件

In order to facilitate the convergence of numerical results, the horizontal displacements at the ag and df boundaries on both sides of the model are fixed, while only the vertical displacements are allowed. The horizontal and vertical displacements at the bottom boundary gf of the model are both constant. In other words, on both sides of the model, we assumed ux=0 (similar to a roller support), while at the bottom of the model, we considered ux=0 and uy=0 (similar to a fixed support).
为了促进数值结果的收敛,模型两侧的 ag 和 df 边界处的水平位移被固定,仅允许垂直位移。模型底边界 gf 处的水平和垂直位移都是恒定的。换句话说,模型两侧我们假设了 ux=0 (类似于滚珠支座),而在模型底部,我们考虑了 ux=0uy=0 (类似于固定支座)。

3.3. Parameter selection 3.3. 参数选择

The physical and mechanical parameters of the materials for each partition of the dam body in the numerical model are shown in Table 1.
数值模型中,大坝主体每个分区的材料物理和机械参数如表 1 所示。

Table 1. Physical and mechanical parameters of the materials for each partition of the dam body.
表 1. 水坝主体各分区材料的物理和机械参数。

Dam body zoning 坝体分区Heat capacity 热容量
C (kJ/kg·°C)
Thermal conductivity 热导率
λ (J/m·°C) λ(A/m·°C)
Permeability coefficient 渗透系数
k (cm/s) k (厘米/秒)
Density 密度
ρ (kg/m3) ρ (kg/m³)
Elastic modulus 弹性模量
E (MPa)
Poisson ratio 泊松比
ν
Dam filling 填坝8901.382.13 × 10−617431.00 × 1040.300
Concrete slab 混凝土板8401.861.00 × 10−724002.40 × 1040.167
Gravel cushion 碎石垫层9201.415.00 × 10−521352.50 × 1040.320
Mucky 污浊5521.251.00 × 10−614003.000.300
Cover weight 封面重量8901.382.13 × 10−617431.00 × 1040.300
Bedrock 基石9201.861.00 × 10−721352.50 × 1040.320

4. Analysis of results 4. 结果分析

4.1. Temperature field analysis
4.1. 温度场分析

Fig. 4 shows the cloud map of the temperature field distribution of the earth-rock dam in the period from November 15, 2021 to February 15, 2022. As can be seen from the figure, during the temperature decrease stage (i.e., from November 15 to January 10), the temperature decreases from 3 °C to −16 °C, the temperature of the surface layer of the dam slope (0–2 m) decreases from 3 °C to −10 °C, and the temperature of the surface layer of the dam slope reaches a minimum value of −10 °C in January 9. But, during the temperature rise stage (i.e., from January 10 to February 15), the temperature increases from −17 °C to 3 °C, and the temperature of the surface layer of the dam slope (0–2 m) gradually increases and reaches a maximum value of −1 °C on February 15.
图 4 显示了从 2021 年 11 月 15 日至 2022 年 2 月 15 日期间地球-岩石坝温度场分布的云图。从图中可以看出,在温度下降阶段(即从 11 月 15 日至 1 月 10 日),温度从 3°C 下降至-16°C,坝坡表层(0-2m)的温度从 3°C 下降至-10°C,坝坡表层的温度在 1 月 9 日达到最低值-10°C。但在温度上升阶段(即从 1 月 10 日至 2 月 15 日),温度从-17°C 上升至 3°C,坝坡表层(0-2m)的温度逐渐上升,在 2 月 15 日达到最高值-1°C。

Fig. 4
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Fig. 4. Cloud maps of temperature field distribution on (a) November 15th, (b) January 10th and (c) February 15th.
图 4. 温度场分布的云图,分别为(a)11 月 15 日,(b)1 月 10 日和(c)2 月 15 日。

The maximum frost depth of the earth-rock dam was about 2 m, indicating that the temperature variation in the surface layer of the dam slope (0–2 m) was large, and the temperature variation inside the dam body decreased with increasing distance from the dam slope.
土石坝的最大冻土深度约为 2 米,这表明大坝斜坡表层(0-2 米)的温度变化较大,而大坝主体内部的温度变化随距斜坡距离的增加而减小。

In order to study the temperature change of the surface layer of the dam slope with the air temperature, one temperature measurement point was arranged on the upper level of the dam and three temperature measurement points were arranged on the upstream slope of the dam. The temperature change curve of different measurement points with time is shown in Fig. 5. From the figure, it can be seen that the temperature of measuring points 1, 2, and 3 shows a downward trend and then an upward trend with the change of air temperature. On November 15, the temperatures at measurement points 1, 2 and 3 were all 3 °C, and on January 10, they were − 16, −10 and − 8 °C, showing a decrease of 19, 13 and 11 °C, respectively. In summary, the degree of influence of air temperature on the temperature measurement points from large to small is as follows: measurement point 1 > measurement point 2 > measurement point 3 > measurement point 4.
为了研究大坝边坡表层温度随大气温度的变化,我们在大坝的上部设置了 1 个温度测量点,在大坝的上游斜坡设置了 3 个温度测量点。不同测量点随时间的变化温度曲线如图 5 所示。从图中可以看出,测量点 1、2、3 的温度随大气温度的变化呈现出先下降后上升的趋势。11 月 15 日,测量点 1、2、3 的温度均为 3°C,而 1 月 10 日,它们的温度分别为-16°C、-10°C 和-8°C,分别下降了 19、13 和 11°C。综上所述,大气温度对温度测量点的影响程度从大到小依次为:测量点 1 > 测量点 2 > 测量点 3 > 测量点 4。

Fig. 5
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Fig. 5. Temperature time series graph for different measuring points.
图 5. 不同测量点的温度时间序列图。

Since the measuring point 1 was relatively close to the crest surface of the dam, it was more affected by the air temperature and therefore its temperature changes were greater. Measurement points 2 and 3 were located beneath the gravel bed and concrete slab at a considerable distance from the dam slope. With slow temperature transfer and minor impact on the soil temperature, the temperature amplitude at measuring points 2 and 3 was consequently small. Measuring point 4 was located below the water level of the upstream dam slope, and its temperature was basically unchanged due to the small change in water temperature.
由于测量点 1 相对较接近大坝的顶部表面,因此它更受气温影响,因此其温度变化更大。测量点 2 和 3 位于砾石床和混凝土板下,与大坝斜坡相距甚远。由于温度传递缓慢且对土壤温度影响较小,因此测量点 2 和 3 的温度振幅相应较小。测量点 4 位于上游大坝斜坡的水位以下,由于水温变化较小,其温度基本未变。

In summary, the effect of freezing on the influence range of the dam slope was about 2 m, the temperature influence range of the dam slope was mainly related to the freezing depth, and the temperature change of the shallow 0–2 m range of the dam slope was affected by the outside air temperature. Also, the internal temperature of the dam body exhibited a relatively small amplitude compared to the shallow layers of the dam slope and displayed a certain degree of hysteresis. The frost damage to an earth-rock dam berm is different from frost damage to the slopes of highways, railways, water conveyance channels, etc. This distinction primarily arises from the unique characteristics of earth-rock dam structures, where the upper part of the dam consists of concrete slabs, gravel bed, and geomembrane. Additionally, another distinguishing factor is that the berms of the dam are exposed to high water pressure.
摘要,冷冻对大坝边坡影响范围的影响约为 2 米,大坝边坡的温度影响范围主要与冷冻深度有关,大坝边坡浅层 0-2 米范围的温度变化受到外界空气温度的影响。此外,大坝主体的内部温度波动幅度相对较小,与大坝浅层相比,显示出一定程度的滞后性。土石坝的坝肩冻害与公路、铁路、输水渠道等的冻害不同,这种差异主要源于土石坝结构的独特性,其中大坝的上部由混凝土板、碎石层和防渗膜组成。另外,另一个区别是大坝的坝肩承受着较高的水压。

4.2. Moisture field analysis
4.2. 湿度场分析

Fig. 6 shows the cloud map of moisture field distribution of the earth-rock dam in the period from November 15, 2021 to February 15, 2022. As can be seen from the figure, during the temperature decrease stage (i.e., from November 15 to January 10), the moisture in the surface layer of the dam slope (0–2 m) continues to freeze, while the unfrozen water content gradually decreases. Due to the high initial water content in the reservoir level change area, the unfrozen water content decreases significantly. During the temperature rise stage (i.e., from January 10 to February 15), the temperature of the surface layer of the dam slope is still below 0 °C, the ice layer is not yet thawed, and the change in unfrozen water content is relatively small.
图 6 显示了从 2021 年 11 月 15 日至 2022 年 2 月 15 日地球岩坝水分场分布的云图。从图中可以看出,在温度下降阶段(即从 11 月 15 日至 1 月 10 日),坝坡表层(0-2 米)的水分持续冻结,而未冻结的水分含量逐渐减少。由于水库水位变化区域的初始含水量较高,未冻结的水分含量显著减少。在温度上升阶段(即从 1 月 10 日至 2 月 15 日),坝坡表层的温度仍低于 0°C,冰层尚未融化,未冻结水分含量的变化相对较小。

Fig. 6
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Fig. 6. Cloud maps of moisture field distribution on (a) November 15th, (b) January 10th and (c) February 15th.
图 6. 湿度分布的云图,分别在(a)11 月 15 日,(b)1 月 10 日和(c)2 月 15 日。

From November 15 to February 15, the unfrozen water content in the surface layer of the dam slope (0–2 m) changed more and the unfrozen water content inside the dam body did not change much, indicating that temperature is an important factor affecting the change of water content.
从 11 月 15 日至 2 月 15 日,大坝斜坡表层(0-2 米)的未冻结水分含量发生了更多变化,而大坝主体内部的未冻结水分含量变化不大,这表明温度是影响水分含量变化的重要因素。

The unfrozen water content of the four typical measurement points over time is shown in Fig. 7. It can be seen that the unfrozen water content of measuring points 1, 2 and 3 shows a trend of decreasing and then increasing. On December 1, the unfrozen water content of the above measurement points was 1.1, 9.1 and 13.1%. Also, the unfrozen water content at this time reached the lowest value at point 1 and decreased by 2.9%. Furthermore, the unfrozen water content of measurement points 2 and 3 dropped by 8.0% and 4.9%. On January 16, the unfrozen water content of measurement points 2 and 3 reached the lowest values of 11.0% and 7.5%. With the increase in air temperature, they increased to 16% and 10% on February 15, while the unfrozen water content of measuring point 1 increased to 3.8%. Measuring point 4 was located below the reservoir water level, and experienced slight changes in water temperature and did not freeze. Throughout the simulation process, the unfrozen water content of measuring point 4 remained constant at 28%.
图 7 显示了四个典型测量点随时间的未冻结水分含量。可以看出,测量点 1、2 和 3 的未冻结水分含量呈现出先减后增的趋势。12 月 1 日,上述测量点的未冻结水分含量分别为 1.1%、9.1% 和 13.1%。此时,测量点 1 的未冻结水分含量达到最低值,减少了 2.9%。此外,测量点 2 和 3 的未冻结水分含量分别下降了 8.0% 和 4.9%。1 月 16 日,测量点 2 和 3 的未冻结水分含量降至最低,分别为 11.0% 和 7.5%。随着气温的升高,到 2 月 15 日,测量点 2 和 3 的未冻结水分含量分别增加至 16% 和 10%,而测量点 1 的未冻结水分含量增加至 3.8%。测量点 4 位于水库水位以下,经历了轻微的水温变化,未冻结。在整个模拟过程中,测量点 4 的未冻结水分含量保持不变,始终为 28%。

Fig. 7
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Fig. 7. Cloud map of unfrozen water content distribution.
图 7. 未冻结水分分布的云图。

In summary, the degree of influence of air temperature on the unfrozen water content from large to small is in the order: measurement point 2 > measurement point 3 > measurement point 1 > measurement point 4. Due to the proximity of measuring points 2 and 3 to the infiltration zone of the reservoir water level in the dam berm surface layer, the initial water content of measuring points 2 and 3 was relatively high. When the negative temperature was transferred from the surface layer of the dam slope to the measurement points 2 and 3, the pore water in measurement points 2 and 3 underwent phase transition to ice. As a result, the unfrozen water content of measuring points 2 and 3 rapidly decreased, and this decrease was more significant compared to the measurement point 1. Measuring point 1 was near the top of the dam, with initially had a lower water content. Temperature had a relatively small effect on the unfrozen water content at measuring point 1.
总结而言,空气温度对未冻结水分含量的影响程度从大到小的顺序为:测量点 2 > 测量点 3 > 测量点 1 > 测量点 4。由于测量点 2 和 3 靠近大坝坝肩表面层蓄水位的渗透区域,测量点 2 和 3 的初始水分含量相对较高。当负温从大坝斜坡的表层传递到测量点 2 和 3 时,测量点 2 和 3 中的孔隙水经历了相变成为冰。因此,测量点 2 和 3 的未冻结水分含量迅速减少,这种减少比测量点 1 更为显著。测量点 1 靠近大坝顶部,初始水分含量较低。温度对测量点 1 的未冻结水分含量的影响相对较小。

The infiltration of reservoir water in the surface layer of the dam berm makes the shallow fill layer of the dam slope reach saturation, and the negative temperature makes the shallow pore water phase of the dam slope turn into ice, which is macroscopically manifested in the decrease of unfrozen water content. Also, the cooling intensity during the freezing process is small, and the freezing front moves downward at a slow pace. The phase change of pore water in the shallow soil-rock mixture at the dam slope, the migration of moisture from the dam fill to the dam slope, and the movement of the freezing front to the interior of the dam body are the main factors of the freezing damage of the berm.
大坝坝肩表层的水库水渗透使得大坝斜坡的浅填层达到饱和状态,负温使得大坝斜坡的浅层孔隙水相转化为冰,宏观表现为未冻结水含量的减少。此外,冻结过程中的冷却强度较小,冻结前沿移动速度缓慢。大坝斜坡浅层土石混合物中的孔隙水相变、大坝填料向大坝斜坡的水分迁移以及冻结前沿向大坝主体内部移动是大坝坝肩冻结损害的主要因素。

4.3. Displacement field analysis
4.3. 移动场分析

Fig. 8, Fig. 9 show the cloud map of vertical and horizontal displacement field distribution of the earth-rock dam in the period from November 15, 2021 to February 15, 2022. As can be seen from the figures, during the temperature decrease stage (i.e., from November 15 to January 10), obvious frost deformation occurs in the reservoir level change area of the upstream dam slope of the earth-rock dam, with a maximum amount of 30 cm. During the temperature rise stage (i.e., from January 10 to February 15), the frost deformation area of the upstream dam slope of the earth-rock dam in the reservoir water level fluctuation zone remains almost unchanged, and the amount of frost deformation continues to increase, with a maximum amount of 36 cm.
图 8、图 9 显示了从 2021 年 11 月 15 日至 2022 年 2 月 15 日期间,土石坝在该时间段内的垂直和水平位移场分布的云图。从图中可以看出,在温度下降阶段(即从 11 月 15 日至 1 月 10 日),土石坝上游坝坡的水位变化区域出现了明显的冻胀变形,最大变形量为 30 厘米。在温度上升阶段(即从 1 月 10 日至 2 月 15 日),土石坝上游坝坡在水库水位波动区域的冻胀变形区域几乎保持不变,冻胀变形量继续增加,最大变形量为 36 厘米。

Fig. 8
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Fig. 8. Vertical displacement cloud maps on (a) November 15th, (b) January 10th and (c) February 15th.
图 8. (a)11 月 15 日,(b)1 月 10 日和(c)2 月 15 日的垂直位移云图。

Fig. 9
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Fig. 9. Horizontal displacement cloud maps on (a) November 15th, (b) January 10th and (c) February 15th.
图 9. (a)11 月 15 日,(b)1 月 10 日和(c)2 月 15 日的水平位移云图。

Fig. 10 shows the variation of vertical displacements against time. It can be seen that with the change of temperature, the vertical displacements of measuring points 1, 2 and 3 increase and stabilize in February. The temperature at the measuring point 4 is 5 °C and no freezing of water occurs at this location. Consequently, no freezing expansion deformation takes place at this point (measuring point 4). It can also be seen that the degree of influence of air temperature on the freezing and expansion deformation from large to small is in the order: measurement point 3 > measurement point 2 > measurement point 1 > measurement point 4.
图 10 显示了垂直位移随时间的变化。可以看出,随着温度的变化,测量点 1、2 和 3 的垂直位移增加并在二月份稳定。测量点 4 的温度为 5°C,此处没有发生水的冻结,因此在这一点(测量点 4)没有发生冻结膨胀变形。也可以看出,从大到小影响空气温度对冻结和膨胀变形的程度顺序为:测量点 3 > 测量点 2 > 测量点 1 > 测量点 4。

Fig. 10
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Fig. 10. Vertical displacement time series graph for different measuring points.
图 10. 不同测量点的垂直位移时间序列图。

When the temperature decreases, the vertical displacement of measuring point 1 increases slowly, and the displacement increases from 0 cm to 6 cm on February 15. The vertical displacements of measuring points 2 and 3 show two stages of increase and stabilization, and the incremental displacements are 33 cm and 36 cm respectively on February 15. At measurement point 1, the low initially water content results in a relatively small volume increase produced by water freezing into ice. Therefore, the freezing expansion amount at measuring point 1 is relatively low. Measuring point 2 has a relatively high initial water content and is significantly influenced by temperature. Additionally, under the influence of water migration, water continuously accumulates from the interior of the dam towards the shallow layer of the dam slope. Hence, the freezing expansion deformation at measurement point 2 is significant.
当温度下降时,测量点 1 的垂直位移缓慢增加,从 2 月 15 日的 0cm 增加到 6cm。测量点 2 和 3 的垂直位移显示了增加和稳定两个阶段,2 月 15 日的增量位移分别为 33cm 和 36cm。在测量点 1 处,初始含水量较低,导致由水结冰产生的体积增加相对较小。因此,测量点 1 的结冰膨胀量相对较低。测量点 2 的初始含水量相对较高,受温度影响较大。此外,在水迁移的影响下,水从大坝内部持续向大坝斜坡的浅层积累。因此,测量点 2 的结冰膨胀变形显著。

At the surface of the concrete slabs in the reservoir level change area of the upstream dam slope of the earth-rock dam, the measurement points were marked. The elevations of measurement points 1, 2, 3, and 4 were 1839.9 m, 1833.8 m, 1834.4 m, and 1830.3 m, respectively. Subsequently, the displacement measurements were conducted using a total station according to the monitoring technical specifications of earth-rock dams. The key monitoring period was from November 15, 2021 to February 15, 2022, and measurements of the elevation at measurement points were conducted every 7 days. The monitoring results of vertical displacements at the measurement points are shown in Table 2. The comparative graph of numerical simulation results and measured data is shown in Fig. 11. It can be seen from Table 2 and Fig. 11 that the numerical simulation results of the displacement field for the earth-rock dam are generally consistent with the measured data. The main freezing zone is located within an elevation range of approximately 2 m from the dam ice surface, with a frost heave amount ranging from 20 to 30 cm.
在上游土石坝的水库水位变化区域的混凝土板表面,标记了测量点。测量点 1、2、3 和 4 的高程分别为 1839.9 米、1833.8 米、1834.4 米和 1830.3 米。随后,根据土石坝监测技术规范,使用全站仪进行了位移测量。关键监测期为 2021 年 11 月 15 日至 2022 年 2 月 15 日,每 7 天对测量点的高程进行一次测量。测量点的垂直位移监测结果见表 2。数值模拟结果与测量数据的比较图见图 11。从表 2 和图 11 可以看出,土石坝位移场的数值模拟结果与测量数据总体上是一致的。主要冻结区位于大坝冰面约 2 米的高度范围内,冻胀量在 20 到 30 厘米之间。

Table 2. Calculated and measured vertical displacement for dam slope measuring points at different times.
表 2. 不同时点大坝边坡监测点的计算和测量垂直位移。

Data 数据Calculate value at measuring point 2 (cm)
计算测量点 2(厘米)的值
Measured value at measuring point 2 (cm)
测量点 2 的测量值(cm)
Calculate value at measuring point 3 (cm)
计算测量点 3(厘米)的值
Measured value at measuring point 3 (cm)
测量点 3 的测量值(cm)
November 22nd 11 月 22 日3.62.83.82.6
November 29th 11 月 29 日6.55.37.46.3
December 6th 12 月 6 日9.28.411.310.2
December 13th 12 月 13 日12.311.214.914.1
December 20th 12 月 20 日16.414.820.619.1
December 27th 12 月 27 日21.120.326.125.3
January 3rd 一月三日24.123.229.527.9
January 10th 1 月 10 日28.227.333.331.2
January 17th 1 月 17 日30.929.135.233.7
January 24th 1 月 24 日32.531.236.134.9
February 1st 二月一日33.231.936.535.5
February 8th 2 月 8 日33.732.436.735.6
February 15th33.832.536.835.7
Fig. 11
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Fig. 11. Comparative graph of numerical simulation results and measured data.

The main cause of the above phenomenon is that in the main freezing zone, the infiltration of reservoir water into the surface layer of the dam berm results in a higher initial water content and a greater freezing depth in the fill of the shallow layer of the dam slope, and the occurrence of frost heave of the gravel bedding and the shallow layer of the dam body is more. During the temperature decrease stage, the negative temperature is continuously transferred from the concrete slab to the gravel bedding and dam body fill. When the temperature drops below zero, the in-situ water in the shallow layer of the dam slope freezes. Simultaneously, the internal water in the dam body overcomes the resistance and continuously migrates towards the freezing front, intensifying frost heave. This results in frost heaving in the soil-rock mixture of the dam body shallow fill and gravel bedding, causing a gradual increase in the displacement of the dam berm. After the freezing of the reservoir surface, the ice pushing and ice pulling contribute to further increase the displacement of the dam berm, with a maximum value of 36 cm.
以上现象的主要原因是,在主冷冻区,水库水渗透到坝肩表层导致该层的初始含水量增加,填筑物的浅层冻土深度加大,坝体浅层的冻胀现象更为明显。在温度下降阶段,负温持续从混凝土板传递到砾石垫层和坝体填筑物。当温度降至零度以下时,坝肩浅层的原位水开始冻结。同时,坝体内部水分克服阻力,持续向冻结前沿迁移,加剧了冻胀现象。这导致坝体浅层填筑物和砾石垫层的土石混合物发生冻胀,引起坝肩逐渐位移增加。水库表面冻结后,冰推和冰拉作用进一步增加了坝肩的位移,最大值达到 36 厘米。

The main cause of frost heaving damage of the dam berm is the combined effect of frost heaving of the soil-rock mixture of the gravel bedding and dam slope fill, along with the force exerted by the ice pushing. Frost heaving results in the uplift and dislocation of the dam berm, as well as an increase in the porosity of the shallow layer fill of the dam slope and gravel bedding. This results in the loss of protective capacity for the berm. Under the continuous scouring of factors such as wind and waves, it eventually leads to the collapse and sliding of the berm.
大坝坝肩冻胀破坏的主要原因是砂垫层和坝坡填料中土石混合物的冻胀效应,以及冰推力的作用。冻胀导致坝肩的抬升和位移,以及坝坡浅层填料和砂垫层的孔隙度增加,从而降低了坝肩的防护能力。在风浪等持续冲刷因素的作用下,最终导致坝肩的坍塌和滑移。

5. Conclusions 结论:

This paper deals with the problem of frost damage of earth-rock dams in cold regions. The Comsol Multiphysics finite element software was used to establish a computational model for the earth-rock dam considering the thermo-hydro-mechanical coupling. The freezing damage process of earth-rock dam berm under the influence of reservoir water level and water migration was then investigated, and the temperature, moisture, and displacement fields of an earth-rock dam were analyzed in a period from November 15, 2021 to February 15, 2022. The following conclusions can be drawn:
本文探讨了寒冷地区土石坝冻害问题。使用 Comsol Multiphysics 有限元软件建立了考虑热-水-力学耦合的土石坝计算模型。在水库水位和水迁移的影响下,研究了土石坝坝体的冻害过程,并分析了从 2021 年 11 月 15 日至 2022 年 2 月 15 日期间土石坝的温度、湿度和位移场。可以得出以下结论:

  • (1)

    The freezing damage of an earth-rock dam berm has its own characteristics. The structure of an earth-rock dam berm and the corresponding seepage control is complex. Furthermore, this structure is often subjected to multiple and substantial loads, including water pressure, ice pressure, wave pressure, etc. The freezing damage of the berm is mainly caused by the freezing expansion of the gravel bedding and dam body fill in the water level fluctuation zone, together with the effects of ice pushing and ice pulling.
    土石坝坝体的冻害具有其自身的特点。土石坝坝体的结构及其相应的渗流控制复杂。此外,这种结构经常承受多种和大量载荷,包括水压、冰压、波压等。坝体的冻害主要由水位波动区中的砾石垫层和坝体填料的冻胀以及冰推和冰拉效应引起。

  • (2)

    The main cause of frost heaving damage of the dam berm is the combined effect of frost heaving of the soil-rock mixture of the gravel bed and the filling of the dam slope, along with the ice pushing and ice pulling generated after the freezing of the reservoir surface. Frost heaving results in the uplift and dislocation of the dam berm, and under the continuous scouring from factors such as wind and waves, it may eventually lead to the collapse and sliding of the berm.
    大坝坝体冻胀破坏的主要原因是砾石床土石混合物的冻胀效应与大坝边坡填筑的共同作用,以及水库表面结冰后产生的冰推和冰拉效应。冻胀导致大坝坝体的上抬和位移,随着风浪等因素的持续冲刷,最终可能导致坝体的坍塌和滑移。

  • (3)

    The infiltration of reservoir water in the surface layer of the dam berm makes the shallow fill layer of the dam slope reach saturation, and the negative temperature makes the shallow pore water phase of the dam slope turn into ice, which is macroscopically manifested in the decrease of unfrozen water content. Also, the cooling intensity during the freezing process is small, and the freezing front moves downward at a slow pace. The main factors of the freezing damage of the berm are the phase change of pore water in the shallow soil-rock mixture at the dam slope, the water migration from the dam fill to the dam slope, and the movement of the freezing front to the interior of the dam body.
    坝肩表面层的水库水渗透使得坝坡的浅填层达到饱和状态,负温使得坝坡的浅层孔隙水相转化为冰,宏观上表现为未冻结水含量的减少。此外,冻结过程中的冷却强度较小,冻结前沿以缓慢的速度向下移动。坝肩冻结损害的主要因素包括坝坡浅层土石混合物中的孔隙水相变,坝填料向坝坡的水迁移,以及冻结前沿向坝体内部的移动。

  • (4)

    The calculation results of the vertical displacement at the measured points of the earth-rock dam agree with the measured data, which confirms the accuracy of the present finite element model.
    测量点处的土石坝垂直位移计算结果与测量数据相符,这证实了当前有限元模型的准确性。

  • (5)

    This study only considered the impact of liquid water migration on soil frost heaving damage, and did not consider the impact of gaseous water migration. In addition, during the simulation process, it was assumed that the soil particles and gravel bed were incompressible, and only the volume change due to frost heaving of water in the soil was considered. Further research should be conducted to address these limitations.
    本研究仅考虑了液态水迁移对土壤冻胀破坏的影响,并未考虑气态水迁移的影响。此外,在模拟过程中,假设土壤颗粒和砾石床不可压缩,仅考虑了土壤中水冻胀引起的体积变化。应进一步研究以解决这些限制。

CRediT authorship contribution statement
作者贡献声明:CRediT

Zhuo Li: Validation, Supervision, Project administration, Investigation, Funding acquisition. Xinyi Liu: Writing – original draft, Software, Investigation, Data curation. Yi Sun: Writing – review & editing, Methodology, Investigation, Formal analysis. Xin Jiang: Writing – original draft, Data curation.
卓丽:验证,监督,项目管理,调查,资金获取。新仪刘:原始草稿撰写,软件,调查,数据管理。易孙:审稿与编辑,方法学,调查,正式分析。新疆:原始草稿撰写,数据管理。

Declaration of competing interest
利益冲突声明

The authors declare no known competing personal relationships or financial interests that could have appeared to influence the work reported in this paper.
作者声明,没有已知的个人关系或财务利益冲突,这些可能会影响本论文中报告的工作。

Acknowledgements 致谢

This research was supported by the National Natural Science Foundation of China (No. 51979173, No. 52109123).
这项研究得到了中国国家自然科学基金(项目编号:51979173,52109123)的支持。

Data availability 数据可用性

Data will be made available on request.
数据在请求时将提供。

References

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