1 Introduction

In China, cold regions include permafrost, glacial, and the majority of stable seasonal snow cover areas, accounting for 43.5% of the country's land area (Chen et al., 2006 ). With the accelerating construction of common rail, high–speed railway, water conveyance canals, tunnels, fast–passenger line, highway and other constructions in permafrost and seasonal frozen soil regions, and prevention of frost heave and freeze–thaw damages has aroused wide concern (Lai et al., 1998 , 2002; Ma et al., 2011 ; Li et al., 2013a ,b; Li et al., 2014 ; Sheng et al., 2014 ). Currently, large areas of expansive clayey soils have been discovered in seasonal frozen soil regions. For instance, the South–to–North Water Transfer Project (SNWTP) in China with three diversion routes, respectively named as the eastern, central and west lines, is under construction. The central diversion route is 1,200 km long, of which about 180 km is open channel, located in seasonally frozen zones, has to pass through the expansive soil land (Ng et al., 2003 ; Liu et al., 2015 ). However, there are few investigations on the behavior of expansive soils in cold regions.

Compacted expansive soils are often used as impervious liners in canals and cover materials in waste disposal landfills (Kaya and Durukan, 2004; Roberts and Shimaoka, 2008). As expansive soils contain active clay minerals like montmorillonite and illite, they have quite high swell–shrink potentials and are more prominent in cracking. The crack initiation, propagation, coalescence and interaction in liners or covers will provide preferential flow paths for water infiltration and dramatically increases hydraulic conductivity, resulting in the failure of anti-seepage systems. In cold regions, the most important factor determining the engineering behavior of fine–grained expansive soils is freeze–thaw cycles, which can change soils in volume, strength and compressibility, densification, unfrozen water content, bearing capacity and microstructure (Hohmann-Porebska, 2002). During soil freezing, ice crystals of various sizes and shapes tend to segregate in soils, resulting in the formation of characteristic micro- and macro-scale structures. As a result, soil behavior is fundamentally changed: crack propagation and stability failures occur following cycles of freeze–thaw (Altun et al., 2009 ). The cracking phenomenon in expansive soils resulting from freeze–thaw cycles in cold regions has also aroused attention by some researchers (e.g., Andersland and Al-Moussawi, 1987).

Laboratory experiments, field tests and numerical simulations have been carried out to investigate the cracking behavior of clayey soils subjected to desiccation and wet–dry cycles (Morris et al., 1992 ; Péron et al., 2009 ; Li and Zhang, 2011; Tang et al., 2011a ,b; Costa et al., 2013 ; DeCarlo and Shokri, 2014). Recently, some researchers have paid attention to expansive soils located in seasonally frozen zones. Bin-Shafique et al. (2011) described the laboratory evaluation of the effect of freezing–thawing cycles on strength and swell potential of fly ash and randomly oriented fiber stabilized expansive soil subbases. Olgun (2013) investigated how the strength, ductility and swelling properties of expansive soil under the F–T effect were changed by using the three additives in combination: lime, RHA and fiber. Fouli et al. (2013) found that expansive silicate clays are a common feature of prairie soils, and weather conditions such as frequent freezing and thawing, as well as a dry climate, increases the potential for shrinking, cracking and increasing soil permeability. Xu et al. (2016) proposed a comprehensive protection technology for expansive soil slopes in seasonally frozen zones with both waterproofing and drainage.

Up until now, few attempts have been made to investigate the cracking behavior of expansive soils under low temperature and freeze–thaw cycles. Thus, our present paper aims to investigate the evolution of surface cracks in expansive soils under freeze–thaw cycles and explain its cracking mechanism.

2 Materials and methods 2.1 Expansive soil and specimen preparation

The expansive soil specimens tested in this study were prepared with a natural expansive soil, which was taken from the construction field at the central route of South–to–North Water Transfer Project (SNWTP) in China. The index properties of the prepared expansive soil were presented in Table 1. Based on the plasticity properties, the soil was classified as CH according to Unified Soil Classification System (USCS).

The original expansive soil was firstly air–dried for about one week. It was then crushed with a hammer and sieved through a 2.0 mm sieve. The sieved soil was further added with sufficient water and mixed thoroughly until water content of the mixtures reached closely to liquid limit (62.0%), and then cured for about 24 hours to make the soil moisture distributed as homogeneous as possible. Thirdly, the mixed soil was poured into three open–faced rectangle containers. The plane dimensions of the containers were the same (360 mm long and 270 mm wide), but the depths were designed as 5, 10 and 20 mm to investigate the influence of soil layer thicknesses on crack patterns. Thin layers of petrolatum were pasted on the inner walls to reduce friction on the container's boundary. Also, the containers were slightly vibrated for about 3 min to eliminate air bubbles inside the expansive soil specimens. Finally, the surfaces of soil specimens were smoothed lightly with a grafter in order to better capture the soil cracking behavior.

2.2 Laboratory test apparatus and procedures

In this study, the cyclic freezing–thawing test on expansive soil specimens was performed in a closed system where no additional water was permitted to enter into the specimen. The freezing-thawing test-up was developed by Li et al. (2013a) , as shown in Figure 1. In a closed system, the freezing front cannot achieve continuous water supply during freezing because the rate of the downward frost penetration is generally faster than that of the upward moisture transportation (Dirksen and Miller, 1966; Wong and Haug, 1991). During one freezing-thawing process, the soil specimen was firstly frozen for 12 h at a temperature of –20 °C and then thawed for another 12 h at the room temperature (about 25 °C). It is noted that water evaporation from the specimen was permissible as the containers were open–faced and the specimen surface was open to air during the test. At the end of each freeze–thaw cycle, the tested specimen was weighed by using an electronic scale with a precision of 0.5 g and the corresponding water content was thus calculated. The freezing–thawing test for each specimen was stopped when the change of its water content was very small (less than 0.1%).

2.3 Image processing and fractal analysis

During the tests, cracks in the specimen surfaces were observed by using the image acquisition technique. At the end of each freeze–thaw cycle, the surface of each specimen was photographed with a digital camera to capture the crack patterns. The camera lens was fixed parallel to the specimen surface with a suitable distance to allow full coverage of the surface. It should be noted that the interval between specimen weighing and photographing ought to be as short as possible (less than 30 s) to minimize the influence of the environment temperature.

As presented in Figure 2, images taken by the digital camera were originally true color in a RGB format. To quantitatively analyze the geometric characteristics of cracks, the digital images need to be processed. The typical procedure of digital image processing includes two steps: (1) the color image of the crack patterns was converted into grayscale; (2) the gray image was further changed into a binary one with the threshold division method. After this process, the cracks and aggregates were simply distinguished in a black–white image, in which the black lines and white areas represent the crack networks and the aggregates, respectively.

It was found that crack patterns developed on the soil surface exhibit a hierarchical network structure that is fractal at a statistical level. Thus, in order to quantify the possible fractal property, the fractal dimension concept was applied to analyze the crack patterns of the soil specimens under freeze–thaw cycles. The crack patterns, obtained from the digital images, were firstly processed by use of MATLAB software, and then a program was developed to determine the corresponding fractal dimensions. The fractal dimensions of the crack patterns in different freeze–thaw cycles for each expansive soil specimen were estimated by using the box–counting method. The details of fractal analysis method have been described in a companion paper by Lu et al. (2016) .

3 Results and discussions 3.1 Water loss and crack patterns

As previously stated, the specimen was weighed at the end of each freeze–thaw cycle, thus the corresponding water content was determined. With the increase of the freeze–thaw cycles, the water contents of the specimens firstly decreased (i.e., water loss) at a nearly constant rate and then tended to a constant residual value (14.0%), approximately close to the shrinkage limit (13.8%) of the tested expansive clayey soil (Table 1). At the same time, a series of typical crack patterns were captured from the digital camera. Figure 3 shows the water loss process and typical crack patterns of the 10-mm-thick specimen after different freeze–thaw cycles. It was found that the evaluation of crack patterns was significantly related to the water loss process, which can be roughly divided into three stages: (1) before the 5th cycle of freeze–thaw, no obvious cracks could be visually observed on the specimen surface. However, the micro–fissures might initiate inside the soil specimen as a result of the repeated formation of the ice lenses. After six freeze–thaw cycles, some short, fine and irregular early–initiated cracks were visually captured on the specimen surface; (2) with the increase of freeze–thaw cycles, early–initiated cracks gradually developed and finally covered the whole specimen surface. Such a propagation process continued approximately to the 17th freeze–thaw cycle; (3) after 21 freeze–thaw cycles, cracking will no longer develop when the water content reaches to the shrinkage limit, and a relatively stable crack pattern was obtained. The final crack pattern basically presented an interconnected polygonal network. Similar experimental phenomena were also observed in specimens with the thickness of 5 mm and 20 mm.

The crack patterns of the soil specimens due to cyclic freezing–thawing are slightly different from those induced by desiccation shrinkage or cyclic wetting-drying. Figure 4a shows the desiccation–induced cracks in a soil specimen (after Vallejo, 2009). During the desiccation process, the soil specimen firstly developed a series of long and isolated cracks (referred as the first-generation cracks) and then the second-generation cracks formed, which orthogonally connect the first-generation cracks. As the desiccation time increased, shorter and more diversely oriented cracks developed, forming an approximately rectilinear crack pattern and greatly increasing the network connectivity. Figure 4b shows the typical surface shrinkage crack pattern of soil after different wet–dry cycles observed by Tang et al. (2008) . The soil surface became more fragmentized and the segments bounded by shorter and smaller cracks increased with the increase of wet–dry cycles. During the wetting–drying process, the crack pattern evolves approximately from a rectilinear pattern towards a hexagonal one, as also observed by Goehring et al. (2010) . However, as presented in Figure 3, the cracks after freeze–thaw cycles were shorter, more irregularly oriented, and the surface crack pattern slowly evolves from an irregularly rectilinear pattern towards a polygonal or quasi–hexagonal one.

3.2 Fractal dimension and cracking mechanism

Figure 5 shows the variations of fractal dimension D_F as well as water content w with the number of freeze–thaw cycles.

It can be seen that the computed fractal dimensions of the three soil specimens during cyclic freezing–thawing are within the theoretically allowable range of 1.0 and 2.0. The fractal dimension of each specimen increased with increasing freeze–thaw cycles until the corresponding water content decreased to its residual value (14.0%). When the residual water content was approached, the maximum fractal dimensions of the soil specimens with thicknesses of 5, 10 and 20 mm were approximately 1.6200, 1.5929 and 1.5897, respectively. The thinner soil specimen also has a relatively higher value of D_F and the cracks can be observed in fewer numbers of freeze–thaw cycles. The fractal dimension can be used to evaluate the spatial distribution of cracks, the density of cracks, and the tendency of the crack traces to fill the area in which they are embedded. The results presented in Figure 5 suggest that the successive freezing–thawing increases the complexity, density, roughness and interconnectivity of soil surface cracks. This phenomenon is more prominent in a thinner soil layer (i.e., the 5 mm thick soil specimen in this study), resulting in a faster increase of the corresponding fractal dimension with a higher maximum value.

When an expansive clayey soil is under open drying conditions, capillary suction is developed in the upper layer due to the formation of a water–air meniscus between clay particles. As water evaporation proceeds, the rising capillary suction exceeds the tensile strength of soil layer, leading to the occurrence of surface cracks (Tang et al., 2011a ). It is indicated that, upon drying, the soil suction due to capillary effect develops between clay particles is a key force to cause cracks in the soil mass. When an expansive soil suffers from repeated freezing–thawing, cracks develop not only attributed to capillary effect, but also owing to expansion effect and absorption effect. Upon thawing, water evaporation also occurred, similar to drying, leading to the increase of capillary suction (i.e., capillary effect); however, upon freezing, an expansionary tendency is created by the volume increase which results when the soil water freezes (i.e., expansion effect). In addition, as freezing of the soil water reduces the thickness of adsorbed water films around individual soil particles and packets of soil particles (i.e., absorption effect), soil suction increases in a manner similar to drying (Hamilton, 1966). The aforementioned three forces (i.e., the expansionary of water when frozen, the capillary effect induced suction and the absorption effect induced suction) tend to induce cracks in the soil mass. Therefore, the crack patterns under freeze–thaw cycles were more irregularly oriented than those induced by desiccation shrinkage or cyclic wetting–drying.

4 Concluding remarks

An expansive soil suffering from repeated freezing–thawing can also be cracking and the surface crack patterns exhibit a hierarchical network structure that is fractal at a statistical level. The cracks induced by freeze–thaw cycles are shorter, more irregularly oriented, and the surface crack pattern slowly evolves from an irregularly rectilinear pattern towards a polygonal or quasi-hexagonal one.

During the periodic freezing–thawing process, cracking of expansive soil is accompanied with water loss and will no longer develop until water content of the soil specimen decreases to the shrinkage limit. Water loss is closely related to the specimen thickness. The thinner soil specimen has a faster water loss, a faster increase of the corresponding fractal dimension with a higher maximum value, and cracks more easily than the thicker ones.

Moreover, the cracking under freeze-thaw cycles develops not only attributed to the capillary effect analogous to desiccation, but also owing to expansion and absorption effects.

Acknowledgments:

This paper was supported by "the Fundamental Research Funds for the Central Universities" (Grant No. 2015B25014) and "the Practical Innovation Program for Postgraduate Students of Jiangsu Province, China" (Grant No. SJZZ15_0058). The study was also a part of work in the project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) (Grant No. 3014–SYS1401). It is also gratefully appreciated to the organizing committee of "XI International Symposium on Permafrost Engineering (Magadan, Russia, Sept. 5-8, 2017)" for giving the opportunity to exchange this study.