Experimental study on the mechanism of ice layer formation in fractured rock masses in cold regions

The causes of cracks in cement blocks

As discussed in section “Experimental study of ice segregation and liquid water migration of rock”, for welded tuff (Akagawa and Fukuda⁵) and siliceous chalk (Murton et al.⁸) in the freezing test, it took a long time for a significant segregated ice layer to appear (> 1000 h), and for the relatively dense cement blocks, it should take even longer to produce the segregated ice layer, while this test lasted only 260 h. On the other hand, the segregated ice layer is generally perpendicular to the temperature gradient, while Crack-2 (Fig. 6) was in the same direction as the temperature gradient. In summary, the cracks on the cement blocks are most likely caused by in-situ volumetric expansion.

Discussion of water migration patterns and pathways

Water migrated in vapor and liquid forms during the test. Water vapor condensed in the upper half of the sample to form frost at the top, as shown in Fig. 5. The main channels for water vapor migration were the vertical through fracture and the gap between the sample and the plexiglass baffle. Possible channels for liquid migration were the vertical through fracture and blocks A and B. In Fig. 6, the migration height of the liquid water in the vertical through fracture is very limited, at approximately 18 cm from the bottom of the sample, and has not yet reached the negative temperature zone. Considering that the space is completely filled with liquid water would only amount to 12 ml of water. Cement blocks A and B are saturated before the test starts, and from analysis in 4.1, it can be seen that the cracks on the cement blocks are most likely caused by in-situ volumetric expansion, thus, liquid water migration inside blocks A and B during the test period can be inferred to be very small.

In summary, a large quantity of water migrates in vapor form during the test. The main channels of migration are the prefabricated fracture and the gap between the sample and the plexiglass baffle.

Novel mechanism of ice layer formation in fractured rock masses

The results presented in 3.1 ~ 3.3 and analysis in 4.1 ~ 4.2 lead to the following conclusions about the development of frost-heaving cracking in a fractured rock simulation model with a vertical through prefabricated fracture: (1) volumetric expansion produced a weak cross section in the negative temperature zone (because of pore development or the deterioration of the section strength by the prefabricated temperature measurement holes), resulting in initial cracks; (2) as the sample cooled, the water in the lower portion of the sample continuously migrated upward in vapor form to the negative temperature zone and condensed in the initial cracks; the subsequent expansion of the continuously growing ice crystals further expanded the crack; and (3) vapor migration stopped when the equilibrium condition was reached, and the ice crystals in the crack stopped growing.

Results from field research and the experiments presented above are used to propose a novel mechanism of ice layer formation in fractured rock masses, where the initial crack-frost effect can be described as follows: in rock masses with through fractures whose bottom is connected to the groundwater level, a drop in the surface temperature causes groundwater to migrate in vapor form through the fractures to the negative temperature zone and condense into frost in initial cracks (pre-existing or produced by in situ freezing). These frosts continuously accumulate and grow into an ice layer that expands the crack, resulting in frost-heaving damage to the rock mass. The entire process is shown in Fig. 10.

Formation of ice layer by initial crack-condensation effect.

Thus, there are three conditions for ice layer formation in a fractured rock mass: the positive temperature zone is replenished by water, the penetrating fractures serve as water vapor migration channels, and the negative temperature zone contains cracks (that are preexisting or generated during frost heave). These conditions are relatively common in bedrock in cold regions, which supports the initial crack-frost effect as a mechanism for ice layer formation in a fractured rock mass.

Driving force for water vapor migration

Assume that the water vapor in the rectangular plexiglass enclosure is in steady flow. Calculate the vapor migration due to the temperature gradient according to Eq. (2) in section “Vapor migration”.

For vapor migration in a rectangular plexiglass enclosure, the relation D_v = D₀ holds approximately, where D₀ is the free air diffusion coefficient, with a value of 10^-7m²/s; considering that the temperature in the freeze–thaw cycle chamber is 2 °C, the saturated vapor density is 6.5 g/m³; \(L\) is the latent heat of vaporization of water and is approximately equal to 2.50 kJ/g at 2 °C; the molar mass of water vapor \({\omega }_{w}\) is 18.016 g/mol;\(\nabla T\) = (2− (− 5))/0.3 = 7 K/0.3 m; the gas constant R = 8.31 J/(mol·K); and T is 275 K; then the vapor flux caused by the temperature gradient is \(-33.45\times {10}^{-7} \text{g}\cdot {\text{m}}^{-2}\cdot {\text{s}}^{-1}\). After 260 h under the test conditions, the flow section size is (0.15 \(\times \) 0.15−0.12 \(\times \) 0.1) = 0.0105 m², such that the total vapor migration induced by the temperature gradient is \(\left(33.45\times {10}^{-7}\mathrm{g}\cdot {\mathrm{m}}^{-2}\cdot {\mathrm{s}}^{-1}\right)\times 0.0105\; { \mathrm{m}}^{2}\times \left(260\times 3600\right)\; \mathrm{s}=328723\times {10}^{-7}\; \mathrm{g}\), which can be converted to volume of 0.0329 ml. Thus, the vapor migration induced by the temperature gradient is negligible compared to the overall migration of 221 ml recorded for the Mariotte’s bottle.

Therefore, the RH gradient is the main driving force for vapor migration in the rectangular plexiglass enclosure. In the approximately closed environment, the condensation of supersaturated water vapor into frost at the top of the sample where it was cold caused the RH of the air at the top of the sample to drop; thus, water vapor continuously migrated from the bottom to the top under the vapor pressure gradient, until the RH of the air at the top of the sample reached 100% again. The frost layer on the cold wall became increasingly thick during this cycle. The water vapor remained in a dynamic equilibrium until the frost layer stopped growing and then ceased migrating.

Frosting mechanism at cold wall surface

The formation process of frost layer on the wall in the negative temperature region of the specimen is similar to the frosting process on the cold surface of thermodynamic studies, as shown in section “Frost mechanism on cold surface”. However, the growth of the frost layer in a crack is somewhat different from that on a general cold surface. The growth of the frost layer in the fracture occurs in a semiclosed environment. Supersaturated vapor condenses on the upper and lower rock walls at cold temperatures, and the growth of the frost layer on the upper walls affects that on the lower walls and vice versa; in addition, the frost layer grows on any ice present in the initial crack; finally, the growth and expansion of the frost layer in the fracture is always affected by the overlying load. Therefore, the growth of frost layers in fractures needs further study based on the above conclusions.