Introduction

The construction depth of western mines has reached kilometers. During the well construction process, it is necessary to cross deep and water rich Cretaceous soft rock formations. The artificial freezing method is widely used due to its unique advantages. A large number of scholars have conducted in-depth research on the Cretaceous strata, but there are still some serious safety issues in engineering construction1,2,3. Especially after the excavation of the vertical shaft is completed, the frozen wall will be in a long-term thawing state. Rock engineering may cause deformation and instability, leading to ultimate failure4,5,6. Therefore, in-depth research is needed on the mechanical properties of rocks in a thawed state.

Scholars at home and abroad have done a lot of work on the mechanical properties of low-temperature rocks and achieved certain research results7,8,9,10. At present, in-depth research is mainly conducted through a combination of theoretical analysis, indoor experiments, and numerical simulations11,12,13. Liu et al.14 discuss the characteristics of frozen rock mass and the failure mechanism of frozen rock slope, and gives the types and failure modes of frozen rock slope, based on field investigation and literature review. Kun et al.15 study the destruction process of frozen rock under different confining pressures by triaxial rheometer, ultrasonic velocity analyzer and Lf-NMR. Based on the hydration signal, the energy and strength equations for rock aperture under different confining pressures are derived. Fractal dimension was used to characterize the pore structure. The study founded that the strength and deformation ability of frozen rocks are enhanced. Li et al.16 introduce the damage factor into the basic rheological element, and establish the non-linear creep damage constitutive model and freeze-thaw rock equation to describe non-linear creep characteristics under a constant load. Han et al.17 investigate the deformation damage mechanisms and evolution patterns of saturated red sandstone with initial non-penetrating cracks of varying depths (20 mm, 30 mm, 40 mm) under freeze-thaw cycling conditions without external water replenishment and with naturally varying saturation levels relevant freeze-thaw cycle experiments and strain monitoring were conducted. After low-temperature treatment, rocks are mainly affected by frost heave force18,19,20,21,22. Therefor, He et al.23 establish the frost heave failure mechanical model of the trapezoidal channel lining in the open system based on the elastic foundation beam theory, considering the relationship between the normal frost-heave force and the interface adfreeze force, and the analytical solution was obtained to calculate deformation and internal force of lining. Qiu et al.24 carry out the low-temperature frost heaving deformation test and uniaxial compression test of different types of rock specimens to study the effects of porosity and elastic modulus on the freezing deformation of rocks. Zhou et al.25 establish a one-dimensional hydrothermal stress model of bi-directional freezing to investigate the frost heave force on the lining of permafrost tunnels and verify the layered segregation ice in the surrounding rock of these tunnels, so as to study the evolution law of segregated ice from the surrounding rock in permafrost tunnels based on the theory of hydro-thermal coupling and segregated ice. Lv et al.26 conduct frost heave experiments on saturated sandstone and tuff with an open crack, under uniform and unidirectional freezing conditions. Through experiments, it was found that frost heave of crack in sandstone with high permeability is more significant under uniform freezing condition than that under unidirectional freezing condition. And frost heave of crack in tuff with low permeability is more significant under unidirectional freezing condition.

After low-temperature treatment of the rock, it was found that some water still did not freeze27,28. The change in unfrozen water content directly affects the strength of frozen rocks. The initial content of unfrozen water in frozen soil cannot be directly measured through experiments, and is mainly obtained through theoretical deduction29,30. Nowadays, nuclear magnetic resonance technology has been introduced into the field of geotechnical engineering, which can accurately detect changes in unfrozen water content in rock and soil at different temperatures28,31,32. Huang et al.33 propose a theoretical model that accommodates the relationship between freezing strain and unfrozen water content considering the phase transition according to saturated poroelasticity theory. Using this model, the unfrozen water content can be accurately calculated by measuring the freezing strain of saturated rock. Li et al.34 establish a mathematical physical model based on similarity theory to obtain curves relating the temperature and unfrozen water content during thawing. The model was validated using experimental data and data from previous studies. Wan et al.35 develop an analytical model based on equivalent contact angle to predict the unfrozen water content. The unfrozen water content is related to the freezing temperature, which is an important indicator reflecting the freezing state of rock and soil mass. Therefore, the variation law of unfrozen water content in rocks at different temperatures needs to be further studied.

This article takes the return air shaft of Xinzhuang Coal Mine in Gansu Province as the engineering background, and selects the saturated sandstone of the Cretaceous system as the research object. Conduct triaxial compression tests under different temperature and confining pressure conditions to obtain corresponding strength parameters. Combining nuclear magnetic resonance technology to obtain the changes in unfrozen water content, this paper analyzes the relationship between the strength changes of frozen rocks during thawing and unfrozen water, and establishes corresponding functional relationships. The research results provide theoretical and technical support for future studies on the long-term stability of frozen walls.

Testing process

Sample preparation

The experimental sandstone is a soft rock of the rich water Cretaceous system, with well-developed and clear joint planes, taken from the Xinzhuang coal mine in Gansu Province, China, as shown in Fig. 1.

Fig. 1
figure 1

Sandstone sample.

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Process the rock into specimens with dimensions of Φ 50 mm × 100 mm. Test the processed rock samples using an ultrasonic testing analyzer (model UTA-2000 A). Select rock samples near the average value of longitudinal waves to reduce the error caused by the discreteness of rock samples on the experimental results. The basic physical parameters are shown in Table 1.

Table 1 Basic physical parameters.
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Test preparation

Test the prepared sandstone to obtain relevant parameters of saturated sandstone, as follows:

  1. (1)

    Place the prepared standard rock sample in an oven. Dry the sample at 105 °C for 24 h. After completion, place the vacuum saturator. Vacuum for 2 h, saturate for 24 h, and then seal and store.

  2. (2)

    Freeze the saturated sandstone sample in the refrigerator to − 30 °C for 24 h.

  3. (3)

    Thaw the samples separately to − 20 °C, − 10 °C, − 6 °C, − 4 °C, − 2 °C, 0 °C, and 20 °C. Observe the changes in T2 spectra of saturated sandstone at different temperatures using a large aperture nuclear magnetic resonance imaging (NMR) analyzer. Analyze the relationship between saturated sandstone temperature and unfrozen water content.

Strength test

Conduct conventional strength tests on saturated sandstone at different temperatures using the GCTS testing system (type RTX-1500) to obtain the full stress-strain curves under different conditions and corresponding strength parameters as shown in Fig. 2. The specific process is as follows:

  1. (1)

    Clamp the sample frozen to − 30 ℃ with a rubber sleeve. Place test strips on both ends of the specimen.

  2. (2)

    Place the sample in the loading system of GCTS. After adjusting the axial and radial displacement sensors, gently lower the three-axis pressure cylinder.

  3. (3)

    Use the temperature control system of GCTS equipment to raise the temperature at a rate of 10 °C/h and adjust it to − 20 °C. After maintaining a constant temperature for 8 h, conduct a uniaxial compression test under this condition.

  4. (4)

    Repeat the above work. Perform uniaxial compression tests on saturated sandstone thawed to − 10 °C, − 6 °C, − 4 °C, − 2 °C, 0 °C, and 20 °C, respectively.

  5. (5)

    Repeat steps (1) to (4). Conduct triaxial compression tests on the thawing process of saturated sandstone under confining pressures of 2 MPa, 4 MPa, and 6 MPa.

  6. (6)

    Record in detail the maximum axial load and full stress-strain curve at the time of failure.

Fig. 2
figure 2

GCTS test system.

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Experimental results

Nuclear magnetic test

Using a nuclear magnetic resonance imaging analyzer to observe the microstructure of sandstone, the T2 spectrum distribution curve during the thawing process of saturated sandstone was obtained, as shown in Fig. 3. According to previous research, different relaxation times (T2) in nuclear magnetic resonance experiments correspond to different states of water occurrence. When the relaxation time is less than 3 ms, it corresponds to adsorbed water. When the relaxation time is between 3 ms and 33 ms, it corresponds to capillary water. When the relaxation time is greater than 33 ms, it corresponds to free water36,37.

Fig. 3
figure 3

T2 spectrum distribution curve of saturated sandstone at different temperatures.

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From Fig. 3, it can be seen that the T2 spectral characteristic curve of the sample still has a relatively obvious signal intensity, indicating that there is still a certain amount of pore water in the rock that has not frozen. And under low temperature conditions, the pore water in the sample mainly exists in the form of adsorbed water, with less free water and capillary water content, almost negligible. During the thawing process of saturated sandstone, as the temperature rises to room temperature, the content of free water and capillary water increases significantly, while the relative adsorbed water content decreases significantly. In summary, the main components that freeze in saturated sandstone at low temperatures are free water and a certain amount of capillary water. Adsorbed water forms an unfrozen water film on the surface of minerals due to the effect of adsorption force.

The thawing process of saturated sandstone can be described as follows: as the temperature gradually increases from − 20 °C, the free water in saturated sandstone first thaws, ice crystals begin to decrease, and the unfrozen water film on the surface of mineral particles gradually dissipates. After free hydrolysis and freezing to a certain extent, capillary water begins to melt. The temperature continues to rise, and the pore ice gradually decreases, while the relative pore water gradually increases. After reaching a temperature of 0 °C, the unfrozen water film completely disappears, completing the thawing process as shown in Fig. 4.

Fig. 4
figure 4

Saturated sandstone thawing process.

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Triaxial compression test

The stress-strain curves of saturated sandstone in the Cretaceous system have common characteristics under different temperature conditions, mainly manifested in four stages: compaction stage, elastic stage, plastic yield stage, and failure stage, as shown in Fig. 5.

The compaction phenomenon becomes less and less obvious as the temperature decreases. The load gradually increases and the compaction stage slowly ends. The original crack propagation is accompanied by the generation of new cracks, and the crack propagation is stable, with a curve that approximates a straight line. The stress at which cracks begin to propagate is the initiation stress (σc). After the load continues to increase and reaches the yield stress (σf), the curve shows an upward convex shape. Pores and cracks further develop. At this point, the radial growth should accelerate compared to before. There is a turning point in volumetric strain. When the load reaches the peak stress (σs), the curve drops sharply, and cracks begin to appear on the surface of the specimen until failure.

Fig. 5
figure 5

Axial stress-strain curve of saturated sandstone under different temperature and different confining pressure.

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Discussion

Changes in unfrozen water content at different temperatures

Under low magnetic fields, it is almost impossible to detect the NMR signal of ice in frozen rocks (free induction decay)38. Therefore, the Free Induced Decay (FID) signal can be used to measure the unfrozen water content in frozen rocks39,40. The unfrozen water content of saturated sandstone under different temperature conditions can be obtained by Eq. (1).

$$\omega ^{\prime } = \frac{{{\text{FID}}_{{\text{F}}} }}{{{\text{FID}}_{{\text{R}}} }} \cdot \omega$$
(1)

Where ω′ represents the unfrozen water content under different temperature conditions, FIDF is the FID signal value under different temperature conditions, FIDR is the FID signal value under normal temperature conditions, ω is the water content of saturated sandstone at room temperature.

According to Eq. (1), the unfrozen water content of saturated sandstone under different temperature conditions can be obtained, as shown in Fig. 6. The unfrozen water content of saturated sandstone is 0.57% at a temperature of − 20 °C. As the temperature rises to − 6 °C, the increase in unfrozen water content ranges from 6.03 to 10.98%. During the temperature range of − 6 °C to − 2 °C, the unfrozen water content increased by 28.11–23.63%. At a temperature of − 2 °C, there is still 1.24% unfrozen water. When the temperature rises to 0 °C, there is 2.37% unfrozen water in saturated sandstone. The water content of saturated sandstone at room temperature is 14.23%. Overall, like frozen soil, rocks also exhibit significant supercooling phenomena. Therefore, based on the changes in unfrozen water content at different temperatures, the temperature range of − 20 °C to 20 °C can be divided into three stages: freezing cessation (− 20 °C to − 6 °C), stable freezing (− 6 °C to − 2 °C), and rapid freezing (− 2 °C to 20 °C).

Fig. 6
figure 6

Unfrozen water content of saturated sandstone under different temperature conditions.

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Characteristic stress analysis of sandstone at different temperatures

The damage and destruction of rocks are mainly caused by the initiation, propagation, and penetration of existing cracks under load, as well as the emergence of new cracks, resulting in significant deformation of the rock and causing damage. Therefore, in the triaxial compression test of saturated sandstone, in addition to considering the peak strength (σs) of the rock, it is also necessary to consider the crack closure stress (σcc), initiation stress (σci), and expansion stress (σf) of the rock. And these three stresses can be obtained through the change curve of rock crack volume during compression testing, as shown in Fig. 7.

Fig. 7
figure 7

Characteristic stress-strain curve of sandstone.

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The volumetric strain of rocks is composed of elastic volumetric strain and crack volumetric strain generated by internal crack development, as shown in Eq. (2).

$$\varepsilon _{{\text{v}}} = \varepsilon _{{\text{v}}}^{{\text{e}}} + \varepsilon _{{\text{v}}}^{{\text{c}}}$$
(2)

Where εv represents the total volumetric strain of the rock, \(\varepsilon _{{\text{v}}}^{{\text{e}}}\) is the elastic volumetric strain of the rock, \(\varepsilon _{{\text{v}}}^{{\text{c}}}\) is the volume strain of rock cracks.

According to Hook’s Law:

$$\left\{ {\begin{array}{*{20}l} {\varepsilon _{{\text{v}}}^{{\text{e}}} = \varepsilon _{{\text{1}}}^{{\text{e}}} + \varepsilon _{{\text{2}}}^{{\text{e}}} + \varepsilon _{{\text{3}}}^{{\text{e}}} } \hfill \\ {\varepsilon _{{\text{v}}} = \varepsilon _{1} + 2\varepsilon _{2} } \hfill \\ \end{array} } \right.$$
(3)

According to Eqs. (2) and (3), the crack volume strain of saturated sandstone in triaxial compression test is:

$$\varepsilon _{{\text{v}}}^{{\text{c}}} = (\varepsilon _{1} + 2\varepsilon _{2} ) - \frac{{1 - 2\upsilon }}{E}\left( {\sigma _{1} + 2\sigma _{3} } \right)$$
(4)

According to the characteristic stress-strain curve combined with Eq. (4), the characteristic stresses of saturated sandstone under different temperatures and confining pressures can be obtained, as shown in Table 2.

Table 2 Conventional strength parameters of saturated sandstone at different temperatures.
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According to Table 2, as the temperature decreases, the closure level of saturated sandstone gradually decreases, while the initiation and expansion levels gradually increase. The macroscopic manifestation is that as the temperature decreases, the compaction stage becomes less obvious, the elastic stage increases relatively, and the plastic stage decreases relatively, as shown in Fig. 5.

As shown in Fig. 8, during the thawing process of saturated sandstone, the peak intensity changes by about 20% when the temperature rises from − 20 ℃ to -4 ℃. When the temperature rises from − 4 ℃ to -2 ℃, the peak intensity changes by about 60%. When the temperature rises from − 2 ℃ to 20 ℃, the peak intensity changes by about 20%, and other characteristic stresses have similar trends of change. From this, it can be inferred that the frozen wall will remain in a thawing state for a certain period of time after the excavation of the vertical shaft is completed. According to Fig. 4; Table 2, as the temperature increases, the intensity gradually decreases, especially when the temperature rises from − 4 ℃ to -2 ℃, the intensity decreases significantly. And different confining pressure conditions exhibit the same pattern of change. Therefore, in the later stage of frozen wall monitoring, special attention should be paid to the deformation of the surrounding rock at around − 4 ℃.

Fig. 8
figure 8

The relationship between characteristic stress and temperature of saturated sandstone under different confining pressures.

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Analysis of the relationship between unfrozen water and characteristic stress

As shown in Fig. 8, the characteristic stress of saturated sandstone is closely related to temperature changes. The unfrozen water content is an important indicator reflecting the frozen state of rock and soil mass. Therefore, there is a certain relationship between the compression failure of saturated sandstone at different temperatures and the content of unfrozen water. The peak intensity are exponentially related to the unfrozen water content, and the correlation is significant, as shown in Fig. 9. The intensity parameters are exponentially related to the unfrozen water content, and the correlation is significant, as shown in Fig. 10.

When the temperature drops from 0 ℃ to − 2 ℃ (rapid freezing stage), the unfrozen water content is 1.24%. 47.68% of the pore water in sandstone freezes. At this point, the peak intensity increased by 16.28–18.72%, the internal friction angle decreased by 2.22%, and the cohesion increased by 5.57%. When the temperature drops from − 2 ℃ to −  6 ℃ (stable freezing stage), the unfrozen water content is 0.68%. Compared to − 2 ℃, 45.09% of unfrozen water in sandstone freezes. At this point, the peak intensity increased by 78.35–84.21%, the internal friction angle decreased by 10.78%, and the cohesion increased by 17.77%. When the temperature drops from − 6 ℃ to − 20 ℃ (freezing stop stage), the unfrozen water content is 0.57%. Compared to − 6 ℃, 16.35% of unfrozen water in sandstone freezes. At this point, the peak intensity increased by 36.31–40.66%, the internal friction angle decreased by 14.93%, and the cohesion increased by 62.69%.

Fig. 9
figure 9

The relationship between the peak strength of saturated sandstone and unfrozen water content under different confining pressures.

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Fig. 10
figure 10

The relationship between the strength parameters of saturated sandstone and unfrozen water under different confining pressures.

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At low temperatures, the cohesive effect of rocks is mainly influenced by capillary action and ice bonding. And the ice bonding effect plays a major role. The internal friction effect is mainly affected by the surface friction of particles and the biting force between bonded particles. In the rapid freezing stage, the main components that freeze are free water, capillary water, and partially adsorbed water. The content of pore ice is relatively low. The volume expansion effect is relatively insignificant. The degree of damage to the particle skeleton structure is relatively low. Therefore, the decrease in internal friction angle of sandstone is relatively small. Due to the significant reduction of free water, capillary action plays a major role in promoting cohesion. The increase in cohesion is not significant. In the stable freezing stage, the unfrozen water content decreases and the pore ice significantly increases. Form an unfrozen water film on the surface of the particles. At this point, the proportion of ice bonding effect increases. Under the dual effects of capillary adhesion and ice bonding, the increase in cohesion is greater compared to the previous stage. At this point, the volume of pore ice expands significantly, severely damaging the particle skeleton structure. And pressure melting began to occur, causing the particle surface to become smooth and the internal friction angle to decrease significantly. During the freezing stop phase, the unfrozen water content is extremely low, and the unfrozen water film becomes thinner. At this point, the ice bonding effect plays a major role in the cohesive force. Therefore, the cohesion of sandstone significantly increases. At this point, the pressure melting effect is significant. Under the action of load, the surface of particles becomes smoother, resulting in a significant reduction in the internal friction angle of sandstone.

Damage mechanism of frozen sandstone

The process of rock failure at room temperature mainly involves stress field, chemical potential field, and seepage field. The compression failure of soft rock is mainly caused by particle dissolution diffusion sliding and water force interaction. After low-temperature treatment, the pore water inside saturated sandstone condenses into ice. In theory, the stress field should play a dominant role in the failure process of frozen sandstone. Under the action of shear stress, displacement occurs along weak structural planes, leading to the development of existing microcracks or the emergence of new cracks, while the other two fields have little effect on rock failure. As analyzed above, saturated sandstone still has a certain amount of pore water that has not frozen under low temperature conditions. During the loading process, under the influence of the chemical potential field, some minerals at the weak structural planes of sandstone dissolve in unfrozen water. Under the action of the seepage field, unfrozen water containing minerals diffuses throughout the entire weak structural plane, changing its shape and making it smooth, weakening the friction between rock particles. Weak structural planes expand and develop under sustained stress. As the melting point of ice gradually decreases with increasing pressure. Therefore, the pore ice in frozen rocks will melt under load, resulting in an increase in unfrozen water content, that is, frozen rocks exhibit pressure melting phenomenon. As the weak structural planes become wider and thicker, the contact area increases, the stress decreases, the chemical potential gradient decreases, and mineral diffusion slows down. Stress redistribution occurs at weak structural planes, resulting in increased stress. The increase in unfrozen water content continues to melt rock minerals, leading to further expansion of weak structural planes. Continue cycling until the rock is destroyed.

Conclusion

  1. (1)

    Saturated sandstone still has a certain amount of pore water that has not frozen under low temperature conditions. And like frozen soil, frozen sandstone also exhibits obvious supercooling phenomenon. At room temperature, pore water mainly exists in the form of free water, while at low temperatures, pore water mainly exists in the form of adsorbed water.

  2. (2)

    During the thawing process, the characteristic stress of saturated sandstone shows the same trend of change. As the temperature increases, the intensity gradually decreases. And the level of closure gradually increases, while the level of cracking and expansion gradually decreases. Macroscopically, as the temperature increases, the compaction stage becomes more pronounced, the elastic stage relatively decreases, and the plastic stage relatively increases., The same pattern is observed under different confining pressures.

  3. (3)

    According to the changes in unfrozen water content at different temperatures, the process of temperature − 20 °C~20 °C can be divided into three stages: freezing stop (− 20 °C~-6 °C), stable freezing (− 6 °C~-2 °C), and rapid freezing (− 2 °C~20 °C). And the compression failure of saturated sandstone is closely related to the unfrozen water content, showing an exponential function relationship. And the correlation is good. The same pattern is observed under different confining pressures.

  4. (4)

    During the thawing process of saturated sandstone, when the temperature rises to − 4 °C, there will be a sudden change in strength, with a significant decrease. Therefore, in the subsequent monitoring process of the frozen wall, when the temperature is around − 4 °C, it is necessary to strengthen the monitoring efforts to ensure the long-term stability of the frozen wall.