A study on frost heave and thaw settlement of soil subjected to cyclic freeze-thaw conditions based on hydro-thermal-mechanical coupling analysis
Introduction
China is the country covering the third largest area of frozen soil in the world. In China, the distribution zone of permafrost and seasonally frozen soil accounts for approximately 21% and 53% respectively of the country's land (Xu et al., 2001; Yershov, 2004). Many structures (e.g. houses, roads, bridges, channels, etc.) early built on the seasonally frozen soil had been damaged to different degrees, e.g. cracking, tilting, collapse. (Andersland and Ladanyi, 2003; Li et al., 2014; Özgan et al., 2015). The direct reason for the damages is due to the soil deformation caused by the freeze-thaw (FT) environments. The complex physical process occurs inside the soil subjected to FT conditions causing the movement of water and heat, phase change, stress redistribution, and soil FT deformation (frost heave and thaw settlement) (Cui et al., 2014; Lai et al., 2014; Lu et al., 2018; Zhou et al., 2018). In this process, the physical structure and soil characteristics change considerably.
Many studies as to the effect of FT cycles on soil physical mechanical properties have been carried out. Viklander (1998) obtained the changes in soil permeability and volume after cyclic FT conditions, and shown that the volume of loose soil decreases, but the previously dense soil became loose. The same conclusion has been obtained by Qi et al. (2008) under different test conditions. Xie et al. (2015) used the soil samples from the Qinghai-Tibet plateau for FT cycle experiments, founding that the uniaxial compressive strength and cohesion decreased with increasing soil volume and porosity. FT experiments on soft soil in Shanghai area shown that, soil hydraulic conductivity increased dramatically after FT due to the increased percentage of large pore and the many newly formed micro-cracks (Tang and Yan, 2015). The compressibility of soil involving pre-consolidation pressure and index of compression and swell, is impacted substantially by FT, and the effect on frozen and unfrozen zones is different. The volumetric strain in short term could be viewed as the result caused by the change of soil physical properties at the end of thaw (Fan et al., 2019). Li et al. (2014) studied the FT hazards on a canal in the northeast of China, discussing the mechanism of ice lens forming or melting in FT conditions, and modeling the FT damage process. In addition, the number of FT cycles is an important factor for studying the effect of FT cycling. The number is larger, the physical parameters (e.g., elastic modulus, effective cohesion, internal friction angle and so on) of expansive soils become smaller unless the number exceeds a certain threshold value (Tang et al., 2018). Lu et al. (2018) found the impact of FT cycles on the characteristic variables of deformation mainly existed in the first FT cycle, which may be that the first cycle impacted most notably on soil structure and pore distribution.
Frost heave and thaw settlement are common under FT conditions. The volume change caused by water freezing and ice melting is the visualized reason for soil deformation in the FT environment (Lu et al., 2018; Zhou et al., 2018)(Lu et al., 2019). The movement of moisture and heat in soil is the further explanation of the inner mechanism (Liu and Yu, 2011; Sarsembayeva and Collins, 2017; Wu et al., 2021). Scholars have done extensive efforts to explain the mechanism of frost heave legitimately. Capillary model (Penner, 1959), hydrodynamic model (Harlan, 1973), segregation potential model (Konrad and Morgenstern, 1980), rigid ice model (Gilpin, 1980; O'Neill and Miller, 1985), semiempirical approaches (Han and Goodings, 2006), and thermomechanical model (Cui et al., 2000) are the previous theoretical achievements for describing the process of frost heave. Most of these models did not consider or unilaterally consider the action of stress in frozen soil. In addition, considering the interaction of the forces between the soil skeleton and ice particles, water pressure, and the energy change caused by the ice-water phase transition, Li et al. (2000) put forward a mathematic model coupling heat-moisture-deformation. Lots of studies have been carried out on the problem of coupling multi-field (water, heat, stress), which has improved and developed the previous theory (Lai et al., 2014; Liu and Yu, 2011; Thomas et al., 2009; Yin et al., 2018; Zhang et al., 2018; Zhang et al., 2021a; Zhang and Michalowski, 2015; Zhou and Li, 2012; Zhou et al., 2021). The soil frost heave, the distribution and growth of discrete ice lens, the change of water-heat-stress fields can be modeled by the improved theoretical models(Zhang et al., 2021b). However, these efforts were rarely applied to the simulations for modeling frost heave and thaw settlement of soil subjected to FT cycles (Zhang and Michalowski, 2015).
It can be seen that predicting the FT deformation of soil in the seasonally frozen region is important, and the work of applying the previous theoretical achievements of frost heave is limited. Therefore, it is necessary to study the influence of FT environment on soil deformation and carry out corresponding experiments to compare the difference between simulation and test and verify the applicability and usefulness of the previous frost heave theory. In this research, a hydro-thermal-mechanical coupling mathematical model based on the basic water transport equation, heat continuity equation, and energy conservation equation is applied for simulating the frost heave and thaw settlement of soil under cyclic FT conditions. Moreover, the mercury injection porosimetry (MIP) test is adopted for explaining the micro-mechanism of soil deformation corresponding to the coupled process.
Section snippets
Mathematical model
To establish the mathematical model of the frozen soil, the following assumptions are made:
- (a)
The model is simplified to a one-dimensional problem without considering the lateral factors;
- (b)
Water transport in the soil conforms to Darcy's law;
- (c)
The deformation of the soil and ice particles is zero;
- (d)
The soil column is saturated, isotropic and elastic;
- (e)
There is a continuous function between the content of the unfrozen water and temperature.
The relationship between the density, mass and volume of the three
Experimental process
The soil samples used in this experiment came from Northeast China, where is a typical seasonally frozen region. The basic physical natures of this soil are given in Table 1. It can be seen that the fraction of clay grains (<0.005 mm) is 35.8%, whereas the fraction of silt grains (0.075–0.005 mm) is high (54.6%), thus the soil was determined as silty clay. Other principal basic physical properties were measured in the laboratory and are listed in Table 2. According to the Unified Soil
Results and discussions
The temperature curve in the soil column at different times is simulated, and the first cyclic FT process (0–72 h) is selected for analysis. Fig. 8 shows the change in the temperature field at different times inside the soil during the first cycle, and the dotted line refers to the freezing temperature of the soil. Fig. 8 (a) is the distribution of temperature at the soil freezing stage. Since the larger the temperature gradient, the faster the heat is transferred. Hence, the change of
Conclusions
Based on mass conservation, energy conservation, Darcy's law and the Clapeyron equation, one-dimensional coupled govern equations for the saturated frozen soil are derived. Through the analysis of numerical simulation results and the comparison with experimental values, conclusions from the above discussions can be obtained.
The model predicts the change situation in the physical fields of temperature, water, and soil deformation. From the above results it can be seen that this mathematic model
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors are grateful for the financial support for the study presented in this paper from the Shanghai Sailing Program (Grant No. 19YF1415500), the National Key R&D Program of China (Grant No. 2019YFC1520500), and the National Natural Science Foundation of China (Grant No. 41772303).
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