Review Reports - Experimental Study on the Frozen Creep Mechanics of Sandstone in the Tarangole Coal Mining Area

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

From my perspective, although the manuscript demonstrates a solid familiarity with the recent literature on rock behavior under freeze–thaw conditions, the theoretical integration remains predominantly descriptive rather than analytical. Most of the cited studies are used to corroborate similar experimental observations; however, a conceptual synthesis that clearly positions the present study relative to existing models of freeze-induced damage, freeze-induced strengthening, and temperature-dependent creep behavior is lacking.

In particular, the distinction between dynamic creep governed by viscoelastic mechanisms and dynamic creep controlled by ice-pressure-induced microcracking is not sufficiently discussed. The effect of frozen pore pressure is mentioned implicitly but is not addressed within a thermo-hydro-mechanical (THM) framework, which significantly limits the mechanistic interpretation of the results.

In my view, this deficiency reduces the manuscript’s potential contribution to theoretical development, positioning it primarily within the domain of local engineering applications rather than advancing fundamental understanding.

The experimental design is extensive and generally well organized; however, it exhibits a degree of methodological heterogeneity that should be discussed more explicitly.

Strengths

The main strengths of the study include:

integration of field investigations with laboratory testing;
use of multiple mechanical testing methods (UCS, triaxial compression, and creep tests);
rigorous temperature control during experimental procedures.

Methodological Issues

Sample size

For the triaxial and creep flow tests, the number of specimens is relatively limited. In the absence of statistical analysis, it is difficult to assess whether the observed variations are:

mechanically significant, or
primarily the result of the inherent heterogeneity of sandstone.

Lithological variability

Several types of sandstone (fine-, medium-, and coarse-grained) are investigated; however:

it is unclear whether the observed differences are predominantly controlled by grain size, cementation, or porosity;
quantitative correlations between physical properties (e.g., porosity, water absorption) and creep parameters are missing.

Scaling of results

The authors extrapolate laboratory-scale results to rock mass behavior; however:

the effect of natural discontinuities is not discussed;
the long-term influence of in situ stress conditions is not evaluated.

The results indicate a significant increase in compressive strength and a reduction in creep rate with decreasing temperature. While this observation is consistent with the existing literature, the interpretation is sometimes overly simplified.

Critical Observations

The increase in strength is attributed almost exclusively to the water–ice phase transition, without adequately considering:

internal stress redistribution;
volumetric constraint imposed by ice formation;
potential latent microcracking processes that may become active under higher stress levels.

Furthermore, the identification of −5 °C as an “optimal” temperature is debatable:

the optimization criterion is not rigorously defined;
it is unclear whether this value is universally applicable or strictly dependent on local conditions (water content, porosity, stress state).

As a result, this conclusion risks being interpreted as normative, even though it is only contextually supported by the presented data.

The use of a temperature-dependent power-law model is appropriate for the phenomenological description of creep behavior. However:

the model parameters are obtained exclusively through numerical fitting, without:
- sensitivity analysis;
- independent validation;
the proposed model is not compared with established formulations (e.g., Burgers, Nishihara, extended Kelvin–Voigt models).

Therefore, the proposed models should be regarded as data-fitting tools rather than generalizable constitutive laws.

The recommendation to prioritize mining operations during the cold season is logical and experimentally supported. However, the manuscript does not adequately address:

risks associated with repeated freeze–thaw cycles;
long-term cumulative degradation;
implications for the stability of support structures.

Without these clarifications, the practical applicability of the results remains partial.

Overall Critical Conclusion

The manuscript is experimentally robust, well documented, and relevant to mining engineering in cold regions. However, its scientific impact is limited by:

the absence of deep theoretical integration;
the lack of statistical and microstructural analyses;
the tendency to draw generalized conclusions from a locally focused study.

Author Response

Authors’ responses to the comments of Reviewer #1:

1, From my perspective, although the manuscript demonstrates a solid familiarity with the recent literature on rock behavior under freeze–thaw conditions, the theoretical integration remains predominantly descriptive rather than analytical. Most of the cited studies are used to corroborate similar experimental observations; however, a conceptual synthesis that clearly positions the present study relative to existing models of freeze-induced damage, freeze-induced strengthening, and temperature-dependent creep behavior is lacking.

>Response: Thank you for your valuable advice. We have supplemented this with a conceptual synthesis that explicitly links the present study to existing models of freeze–thaw-induced damage, freeze–thaw-induced enhancement, and temperature-dependent creep behavior. Here, the discussion specifically addresses the distinction between dynamic creep controlled by viscoelastic mechanisms and that induced by microcracking from ice pressure. Moreover, we have incorporated a discussion of freeze–thaw rocks within the thermo-hydro-mechanical (THM) framework. These refinements are intended to enhance the foundational theoretical depth of the manuscript. On the other hand, we have refined the specificity of the study in the methodology section.

>Implemented:

Supplementary conceptual synthesis of freeze–thaw damage within the THM framework is illustrated in Lines 279–348.

4.1. Development of a thermo-hydro-mechanical (THM) theoretical model

Based on the results of in-situ mechanical investigations, the mechanical properties of the rocks in the study area were obtained. In this subsection, we establish the concept of a model for freeze-thaw- induced damage, freeze-thaw-induced enhancement, and temperature-dependent creep behavior of sandstone within the THM framework. This concept reflects the correlation between dynamic creep controlled by viscoelastic mechanisms and that induced by microcracking from ice pressure, with the aim of providing a theoretical basis for subsequent in-situ testing.

In the coupled THM model for saturated sandstone, the equation of state is primarily used to describe how the physical properties of pore water and soil particles (such as density and viscosity) vary with changes in variables like temperature and pressure. Under the condition of varying temperatures, considering that density, porosity, and liquid viscosity are all affected by temperature, we adopt the small deformation assumption and express the fluid density ρ_l, porous medium density ρ_s, and porosity ϕ as functions of the variables to be solved (pore pressure p and temperature T).

The viscosity of water, μ_l, varies negligibly with pressure and can be considered negligible; nevertheless, it changes significantly with temperature. To account for this, a polynomial expression is used to represent the viscosity of water, as follows:

(1)

Where, a₀=1.794×10^-3; a₁=5.720×10^-2; a₂=1.137×10^-3; a₃=1.364×10^-5; a₄=8.828×10^-8; a₅=2.344× 10^-10.

Besides, the expressions for parameters ϕ, ρ_l, and ρ_s are given respectively as shown in Equations (2)~(4).

(2)

(3)

(4)

Differentiating Equation (4) with respect to time t yields:

(5)

Among them, c_ϕ represents the pore compressibility coefficient of the sandstone; β_ϕ denotes the pore thermal expansion coefficient of the sandstone; ρ_l0 represents the initial density of the fluid, kg/m³; ρ_s0 denotes the density of the porous medium, kg/m³; c_l is the compressibility coefficient of the fluid; β_l is the thermal expansion coefficient of the fluid; K_m is the bulk modulus of the sandstone, MPa; and β_Tm is the linear thermal expansion coefficient of the sandstone. Moreover, σ′ represents the effective stress, MPa; and tr(σ′) denotes the trace of the effective stress.

Then, by eliminating certain redundant variables, the seepage differential equation for p and T is derived:

(6)

By solving the temperature field equation, the temperature distribution within an object can be obtained, thereby providing a theoretical basis for optimizing design, process control, and understanding heat-related phenomena. In frozen soil, the modes of heat transfer include thermal radiation, heat conduction, and heat convection [28,29]. In the THM coupling model for saturated sandstone, the temperature field equation serves as the core equation describing heat transfer and energy conservation, fundamentally representing the mathematical formulation of the law of energy conservation. Herein, in a non-isothermal seepage system, the material system or spatial volume contains both solid and liquid components, and their thermodynamic characteristic parameters differ. Therefore, it is necessary to examine them separately [16].

(1) Heat transfer equation for the rock matrix in porous media

(7)

Where, C_s represents the specific heat capacity of the sandstone, m²/(s‧°C); and λ_s denotes the thermal conductivity coefficient of the solid, W‧(m‧K)^‒1.

(2) Heat transfer equation for the fluid in porous media

(8)

Where, v represents the fluid seepage velocity, m·s^‒1, which we express as a relative velocity and can be obtained from Darcy's law; C represents the specific heat capacity of water, m²/(s‧°C); (ρC)_eq represents the equivalent volumetric heat capacity; L represents the latent heat of the ice-water phase change, kJ‧kg^‒1, taken as 333 kJ‧kg^‒1; θ_l denotes the volumetric fraction of the liquid phase; and Q_G denotes the heat source term, W‧m^‒3. In other words, in Equation (8), the first and second terms on the left-hand side represent the heat conduction term and the convection term, respectively; the third term denotes the latent heat of the ice-water phase change; the fourth term accounts for the work done by fluid pressure; as well as the fifth term represents the rate of change of thermal strain energy within the system.

In this study, the stress equation is based on the assumptions of linear thermo- elasticity. The total strain consists of stress-induced strain, pressure-induced strain, and thermal strain, expressed as the algebraic sum of these three components. Therefore, the total strain of the sandstone skeleton can be written as:

(9)

In Equation (9), expressing stress in terms of strain yields:

(10)

Where, G denotes the shear modulus; I represents the stress invariant.

Taking the trace of Equation (10), and rearranging using the relation 2G + 3λ = 3K_b, yields:

(11)

Where, K_b represents the bulk modulus of the overall system, and β_Tb denotes the linear thermal expansion coefficient of the overall system. Differentiating both sides of the equation with respect to time t and applying mathematical transformations yields:

(12)

Thus, the stress σ′ encompasses both the macroscopic stress σ and the internal pore pressure pI; that is, their constitutive relationship can be expressed as σ′=σ+pI. Based on this, the THM coupling constitutive equation can be written as:

(13)

In addition, the refinement of the Methods section and the highlighting of its innovative aspects are illustrated in Lines 342–347.

Based on the conclusion drawn in Section 3 that medium- and fine-grained sand- stone have better rock integrity and rock strength, this section analyzes the mechanical characteristics of these two types of sandstone under different working conditions. The method innovation lies in its comprehensive analysis of the influence mechanisms of multiple factors—such as geological group, particle size, evaluation indicators, sampling depth, temperature, and creep rate—on the mechanical behavior of sandstone.

2, The experimental design is extensive and generally well organized; however, it exhibits a degree of methodological heterogeneity that should be discussed more explicitly.

>Response: Thank you for your valuable advice. We have supplemented the THM theoretical model in the on-site testing method section and applied it to discuss the influence of other factors on the mechanical properties of freeze-thawed rocks.

>Implemented: As shown in Lines 372-386. Based on the THM theoretical model, the test results show that, firstly, compared with the thermal properties at normal temperature, under freeze-thaw conditions, the thermal conductivity values of medium and fine sandstones are higher than their specific heat capacity values (Figure 9). Secondly, factors such as lithology, stratum, frozen temperature, and depth can have a significant impact on the thermal conductivity and specific heat capacity of the samples. Finally, the thermal conductivity of medium and fine sandstone at normal temperature ranges from 0.51 to 1.89 W/mK, and the specific heat capacity of the rock at normal temperature is between 0.26 and 1.4 MJ/m³K. Its value increases with the increase in the rock's moisture content. The thermal conductivity of the sample at -10°C is within the range of 1.23 to 1.71 W/mK, and the specific heat capacity is between 0.24 and 0.34 MJ/m³K. This fully demonstrates that the frozen temperature range of -8.86 to -13.65°C differs significantly from the empirical values of similar strata. Thus, compared with other temperature options and in consideration of actual engin- eering requirements, setting the freezing temperature at approximately -5°C is more reasonable.

3, Strengths

The main strengths of the study include: integration of field investigations with laboratory testing; use of multiple mechanical testing methods (UCS, triaxial compression, and creep tests); rigorous temperature control during experimental procedures.

>Response: Thank you for your valuable advice. Thank you for your positive evaluation of our research.

4, Methodological Issues—Sample size

For the triaxial and creep flow tests, the number of specimens is relatively limited. In the absence of statistical analysis, it is difficult to assess whether the observed variations are: mechanically significant, or primarily the result of the inherent heterogeneity of sandstone.

>Response: Thank you for your valuable advice. We have already explained the limitations associa- ted with the sample size. In the actual triaxial and creep mechanical tests, we used multiple sample sets for testing. However, due to sample complexity, we selected only a subset of more representative data for this study. For instance, in Table 5, during the actual experiment, we conducted three sets of tests under similar conditions (Groups A, B, C, and D). As a result, the data from these three test groups showed relatively small differences. Therefore, under the same test conditions, we selected only the most representative key data—for example, formation depth and sample thickness. It is precisely for this reason that all the authors unanimously agree that the results of this research are reliable; therefore, we have made appropriate revisions to the manuscript.

>Implemented: As shown in Lines 408-413. In this study, we conducted mechanical tests on three groups of samples under similar conditions (24 samples in total). The results showed that the test outcomes were consistent across the three groups. Therefore, we present only the most representative dataset. The specific sample grouping is shown in Table 5 below. The experimental results of freezing rocks are shown in Figure 10.

5, Lithological variability

Several types of sandstone (fine-, medium-, and coarse-grained) are investigated; however: it is unclear whether the observed differences are predominantly controlled by grain size, cementation, or porosity; quantitative correlations between physical properties (e.g., porosity, water absorption) and creep parameters are missing.

>Response: Thank you for your valuable advice. We have clearly presented the differences in the mechanical properties of sandstone with varying particle sizes. Here, the fundamental cause of this difference in the sandstone within the study area is the microstructure—specifically, porosity—which is determined by grain size, followed by the nature of internal cementation. In addition, we have established the quantitative relationship between its physical properties (such as porosity, ϕ, and water absorption rate, v) and the creep parameters.

>Implemented: The explanation for the differences in the mechanical properties of sandstones with varying particle sizes is located in Lines 229–236.

The higher values in the data correspond to medium- and fine-grained sandstone, which are located in the Zhiluo Formation and the Yan'an Formation, respectively. The medium- and coarse-grained sandstone samples collected from the borehole during this inspection have loose cementation and are highly prone to softening and disintegration upon contact with water (Figure 6). Herein, the fundamental cause of this difference in the sandstone within the study area lies in its microstructure— specifically, porosity—which is controlled by grain size and the nature of internal cementation.

The quantitative relationship between the physical properties of sandstone (such as porosity, ϕ, and water absorption rate, v) and the creep parameters is expressed in Equations (2) and (5).

(2)

(3)

6, Scaling of results

The authors extrapolate laboratory-scale results to rock mass behavior; however: the effect of natural discontinuities is not discussed; the long-term influence of in situ stress conditions is not evaluated. The results indicate a significant increase in compressive strength and a reduction in creep rate with decreasing temperature. While this observation is consistent with the existing literature, the interpretation is sometimes overly simplified.

>Response: Thank you for your valuable advice. The innovation of this research lies in combining indoor and field mechanical testing methods to investigate the influence mechanisms of multiple factors—including geological group, particle size distribution, evaluation indicators, sampling depth, temperature, and creep rate—on the mechanical behavior of sandstone in the study area. Therefore, the influence of natural discontinuity surfaces and in-situ stress conditions was not addressed. Due to space limitations, we plan to analyze the impact of these two factors in future work. In addition, we have optimized the explanation of the “observation results”.

>Implemented: As shown in Lines 476-493. As shown in Figure 12, based on the results of the uniaxial compression test in Section 4.3, we discuss the influence of different freezing temperatures and surrounding rock pressures on the fine-grained sandstone in the study area. From Figure 12(b), it can be seen that the triaxial compressive strength increases with increasing confining pressure, and the difference in compressive strength becomes more pronounced as the temperature decreases (from -5°C to -15°C). For instance, when the temperature is -15°C, the difference in strength between sample F-5-14 and F-5-7 is 12.2 MPa, which is much greater than the difference of 0.8 MPa at -5°C. In addition, the Poisson's ratio of fine-grained sandstone is less affected by changes in triaxial compressive strength, but gradually decreases with increasing temperature (Figure 12(c)). The internal friction angle of fine-grained sandstone does not change significantly with variations in temper- ature and confining pressure (Figure 12(d)). This is because the friction angle reflects the roughness of the sliding surface, and the freezing of internal water in the sandstone has a relatively small impact on the "roughness" of the rock [39,40]. We can conclude that the internal friction angle of the fine-grained sandstone in the study area is approximately 30°. Hence, in actual freeze-thaw engineering, the mechanical strength of fine-grained sandstone gradually weakens as the temper- ature drops, and the rock becomes more brittle.

7, Critical Observations

The increase in strength is attributed almost exclusively to the water–ice phase transition, without adequately considering: internal stress redistribution; volumetric constraint imposed by ice formation; potential latent microcracking processes that may become active under higher stress levels.

>Response: Thank you for your valuable advice. In the Discussion section of Part 4, we have already noted that redistribution of internal stress, volume constraints induced by ice formation, as well as potential microcracking may become active at higher stress levels.

>Implemented: As shown in Lines 546-551. On the other hand, during the water-ice phase transition, as confining stress increases, the fracture mode of sandstone gradually shifts from axial splitting to multi-surface tensile-shear fracturing, indicating stress redistribution within the rock mass. Addition- ally, volume constraints induced by ice formation and the potential reactivation of pre-existing fractures may become more pronounced at higher stress levels [41,42]. As shown in Lines 779-783. Zheng, Z.D.; Shi, Z.M.; Wang, M.X.; Lin, H.; Li, J.T.; Han, D.Y.; Li, K.H.; Jiang, C. Fatigue fracture and energy evolution characteristics of sandstone under water-ice phase transitions via the discrete element method. Comput. Geotech. 2025, 179, 107023. https://doi.org/10.1016/j.compgeo.2024.107023. Zhang, D.C.; Lu, G.J.; Wu, J.; Nie, W.; Ranjith, P.G. Effects of Ultralow Temperature and Water Saturation on the Mechanical Properties of Sandstone. Rock Mech. Rock Eng. 2023, 56, 3377-3397. https://doi.org/10.1007/s00603-023-03229-y.

8, Furthermore, the identification of −5 °C as an “optimal” temperature is debatable: the optimization criterion is not rigorously defined; it is unclear whether this value is universally applicable or strictly dependent on local conditions (water content, porosity, stress state). As a result, this conclusion risks being interpreted as normative, even though it is only contextually supported by the presented data.

>Response: Thank you for your valuable advice. We have refined the notion of optimal temperature. In this study, we primarily investigated the influence of subzero temperatures (-20 to 0°C) on various sandstone types. By comparing the UCS values of sandstone at -20°C, -15°C, -10°C, as well as -5°C, we find that the strength at -5°C is the highest among these low temperatures. This result offers preliminary guidance for practical engineering applications; however, the final determination of the optimal temperature requires further experimental validation.

>Implemented: As shown in Lines 384-386. Thus, compared with other temperature options and in consideration of actual engineering requirements, setting the freezing temperature at approximately -5°C is more reasonable. As shown in Lines 464-471. The results of the stress-strain curve show that at -5°C, the stress value under high confining pressure is greater than that under low confining pressure (Figure 11(a)). At -10°C, the stress value under high confining pressure was initially higher than that under low confining pressure, then became lower, and eventually stabilized, indicating that the sample was damaged (Figure 11(b)). Similarly, damage occurred in the sample at -15°C (Figure 11(c)). Therefore, it was found that when the sample temperature was maintained at -5°C, no damage occurred, which can provide theoretical support for the mining of mineral energy resources. As shown in Lines 639-642. A freezing temperature of -5°C is suggested to be more appropriate. While this provides preliminary guidance for construction, the final optimal temperature needs to be verif- ied through more additional experimental data.

9, The use of a temperature-dependent power-law model is appropriate for the phenomenological description of creep behavior. However: the model parameters are obtained exclusively through numerical fitting, without: sensitivity analysis; independent validation; the proposed model is not compared with established formulations (e.g., Burgers, Nishihara, extended Kelvin–Voigt models). Therefore, the proposed models should be regarded as data-fitting tools rather than generalizable constitutive laws.

>Response: Thank you for your valuable advice. In Sections 4.5-4.6, the proposed model is treated as a data-fitting tool. The emphasis is placed on highlighting the triaxial creep behavior of fine- grained sandstone at a test temperature of -5°C. In future work, we will further validate the experi- mental results by integrating them with numerical simulation outcomes. Moreover, in Section 4.1, we extended the constitutive model to incorporate temperature dependence.

>Implemented: As shown in Lines 657-662. This research represents a preliminary exploration of the mechanical principles underlying mining operations in the Tarangole mining area of China. However, from the perspective of safe engineering practices, certain limitations remain. In the future, numerical simulations and machine learning methods will be integrated to validate the findings from engineering investigations and mechanical tests, with the aim of better meeting the on-site guidance requirements of practical engineering projects.

As shown in Lines 311-348.

(1) Heat transfer equation for the rock matrix in porous media

(7)

Where, C_s represents the specific heat capacity of the sandstone, m²/(s‧°C); and λ_s denotes the thermal conductivity coefficient of the solid, W‧(m‧K)^‒1.

(2) Heat transfer equation for the fluid in porous media

(8)

(9)

In Equation (9), expressing stress in terms of strain yields:

(10)

Where, G denotes the shear modulus; I represents the stress invariant.

Taking the trace of Equation (10), and rearranging using the relation 2G + 3λ = 3K_b, yields:

(11)

(12)

(13)

10, The recommendation to prioritize mining operations during the cold season is logical and experimentally supported. However, the manuscript does not adequately address: risks associated with repeated freeze–thaw cycles; long-term cumulative degradation; implications for the stability of support structures. Without these clarifications, the practical applicability of the results remains partial.

>Response: Thank you for your valuable advice. We have already supplemented the document with an analysis of the risks associated with repeated freeze-thaw cycles, the long-term cumulative degrad -ation effects, and the impact on the stability of the supporting structure. Repeated freeze-thaw cycles directly cause deterioration of the mechanical properties of sandstone, notably a significant reduct- ion in rock strength and stiffness. The damage to rocks caused by freeze-thaw cycles originates from changes in their internal microstructure, which constitutes the fundamental cause of the deterioration of their macroscopic properties. Moreover, when microdamage caused by freeze-thaw cycles accumu- lates to a certain extent, it leads to intensified macroscopic deformation and a change in the damage mode. Finally, the hazards to engineering rock masses are mainly manifested in inducing rock slope instability, reducing foundation bearing capacity, and damaging surrounding rock masses.

>Implemented: As shown in Lines 551-559. Repeated freeze-thaw cycles directly cause deterioration of the mechanical properties of sandstone, notably a significant reduction in rock strength and stiffness. The damage to rocks caused by freeze-thaw cycles originates from changes in their internal microstructure, which constitutes the fundamental cause of the deterioration of their macroscopic properties. Besides, when microdamage caused by freeze-thaw cycles accumulates to a certain extent, it leads to intensified macroscopic deformation and a change in the damage mode. Finally, the hazards to engineering rock masses are mainly manifested in inducing rock slope instability, reduc- ing foundation bearing capacity, and damaging surrounding rock masses.

11, Overall Critical Conclusion

The manuscript is experimentally robust, well documented, and relevant to mining engineering in cold regions. However, its scientific impact is limited by: the absence of deep theoretical integration; the lack of statistical and microstructural analyses; the tendency to draw generalized conclusions from a locally focused study.

>Response: Thank you for your valuable advice. We have extended the sandstone freeze-thaw theory based on THM coupling and enhanced the comprehensive analysis of the experimental results.

>Implemented: As shown in the full text (Section 4.1~Section 4.5).

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for the opportunity to review the manuscript entitled "Experimental study on the frozen creep mechanics of sandstone in the Tarangole coal mining area," submitted for publication in the journal Applied Sciences. The research addresses a problem relevant to energy and operational security in northern China: the mechanical behavior of sandstones under artificial and natural freezing conditions in the Ordos Basin.

Despite the relevance of the topic, the manuscript in its current state presents deficiencies in three fundamental areas:

1) The energy statistics presented in the introduction contain errors of magnitude that compromise the initial credibility of the text.

2) There are gaps in the description of the experimental protocols (sample preparation, saturation, thermal control) that hinder reproducibility.

3) The analysis of the creep mechanisms and the recommendation of operating temperatures lack a discussion based on the micromechanics of the ice-rock interface and advanced constitutive models.

Below, I present the observations, required corrections, and expansion suggestions, integrating the most recent literature and verified official data.

Abstract
The abstract acts as the "showcase" of the research. Currently, it presents statements that are either too generic or potentially inaccurate from the perspective of advanced rock mechanics.

Lines 21-23: "sandstone in the area is prone to softening and disintegration, classified as soft to moderately soft rock, with a basic quality grade of IV-V." This classification is qualitative. The literature on the Zhiluo and Yan'an Formations in Ordos indicates that these sandstones have variable porosity and cementation, which drastically affect their UCS (Uniaxial Compressive Strength).

Please include in the abstract the specific range of UCS values (in MPa) obtained in the natural and saturated states. For example: "classified as soft to moderately soft rock (UCS range: 1.5–10.5 MPa in natural state), with a basic quality grade of IV-V." This provides the reader with an immediate technical reference.

Lines 24-25: "The recommended freezing temperature is -5°C based on empirical values." This statement is problematic. Although -5°C may be economical, frozen rock mechanics demonstrate that strength continues to increase significantly below this temperature due to the freezing of water in micropores and nanopores. Recent studies indicate that at -5°C, the rock is in an intensive transition phase where properties are unstable. Maximum strength and creep stability are typically achieved at lower temperatures (-15°C to -20°C).

Please qualify this recommendation. If you recommend -5°C, you must explicitly clarify that it is an "economic-operational compromise" and not a mechanical optimum. Otherwise, the statement contradicts your own subsequent findings on the strength increase at -20°C.

Line 28: "The water-ice phase transition induced by low temperatures significantly enhances the overall strength..."
The abstract mentions the phase transition but ignores the role of saturation. The reinforcing effect of ice is negligible if the rock is dry and maximal if it is saturated. Since the manuscript does not detail the saturation state in the abstract, this conclusion lacks context.

Please specify the humidity conditions: "The water-ice phase transition in saturated samples induced by..."

Introduction
Line 46: The authors state that crude oil production reached "763 million tonnes." This figure is incorrect. According to China's National Bureau of Statistics (NBS) and reports from January 2025, domestic production was 213 million tonnes, a modest increase over previous years driven by offshore and unconventional fields. The figure of "763 million" suspiciously coincides with the European Union's final energy consumption target for 2030 (763 Mtoe) mentioned in energy efficiency directives. It is likely that the authors mistakenly used data from a global or European source. Please verify this figure.
A production figure of "5.16 billion tonnes" is cited. The official NBS figure for 2024 is 4.76 billion tonnes, which already represents a record high. The figure of 5.16 could refer to total coal consumption (production + net imports), since China imported approximately 540 million tons in 2024, which would add up to an available supply of close to 5.3 billion tons. However, the text explicitly says "production." Please clarify whether the figure includes imports.
Gas production is cited as "303 million tonnes." Natural gas is typically measured in cubic meters or cubic feet. Production in 2024 was 246.4 billion cubic meters (bcm). The figure of 303 million tonnes is far from the actual production and could be confused with reduced emissions in other sectors or aggregated import data. Please verify the figure and use the standard metric "cubic meters" to avoid ambiguity.

Line 51: The manuscript mentions that renewable energy contributed 34% of electricity generation. Recent data from 2024 indicate that installed non-fossil capacity exceeded 50%, and clean generation (solar + wind + hydro) covered more than 80% of demand growth, although coal remains the foundation. It is important for the authors to update their narrative to reflect that, while coal production peaked, its relative share of new capacity is declining in the face of the explosive expansion of solar and wind power in regions such as Inner Mongolia.

Section 2 of the manuscript ("Engineering Background") is too superficial for a study that aims to link lithology with flow mechanics. Tarangole is not a generic mine; it possesses unique hydrogeological and metallogenic characteristics that must be discussed.

The manuscript mentions "mudstone, sandstone of various grain sizes, and coal seams" (Line 160). However, it omits a relevant detail documented in the Ordos geological literature: the coexistence of uranium and coal.

Please note that the Tarangole mining area is recognized for its sandstone-type uranium deposits hosted in the Zhiluo Formation (Middle Jurassic), which directly overlies the coal-rich Yan'an Formation (Lower Jurassic). The mechanical significance of the uranium mineralization and associated alteration (kaolinization, chlorite, pyrite) in the Zhiluo sandstones also affects their mechanical and permeability properties. Altered sandstones can behave differently under freezing due to changes in pore structure and matrix chemistry. Please discuss whether the "medium- and coarse-grained" sandstone samples are from the Zhiluo Formation (coal roof) and whether they show signs of hydrothermal alteration or mineralization, as this introduces heterogeneity into the creep tests.

Line 76: The text mentions "extremely complex hydrogeological conditions." Please specify that the main challenge is the Lower Cretaceous pore-fissure aquifer (Zhidan/Luohe Formation) and the Zhiluo Formation aquifer. The high permeability and groundwater flow in these layers are the main reason for using the well freezing method. The groundwater flow rate affects ice wall formation. Although the study is laboratory-based, the discussion should link the thermal conductivity results (Section 4.1) to the actual in-situ water flow. High thermal conductivity in the laboratory is favorable, but advective flow at the site can counteract it.

Section 4.1
The study evaluates the effect of freezing, the main mechanism of which is the transformation of pore water into ice. However, the degree of saturation of the tested samples is not specified. Were they dry, naturally saturated, or vacuum saturated (100%)?
Recent research demonstrates that the strength of frozen sandstone depends critically on its water content. In dry samples, the effect of temperature (-10°C vs. -20°C) is negligible because there is no ice to act as a cementing agent. If the samples were partially saturated, the reported strength increase (5 MPa) could vary considerably.

Please add a subsection detailing: Saturation Method (e.g., immersion for 48 hours or vacuum according to ASTM D4525). Initial porosity and average moisture content of samples from groups A, B, C, and D. Exact dimensions of the specimens (diameter x height), verifying that they meet the 1:2 ratio required for triaxial tests.

A temperature of -5°C is recommended, but testing is performed at -10°C and -20°C. However, the cooling rate is not described. Rapid cooling (thermal shock) can induce microcracks due to differential expansion between the mineral grains and pore water, weakening the sample before testing. Slow cooling better simulates field conditions. Additionally, it is relevant to report the stabilization time at the target temperature before applying the load (>12 hours is recommended to ensure internal thermal equilibrium). Please include the temperature vs. time curve of the freezing process and the type of environmental chamber used.

Section 4.4
The study uses staged loading, but it lacks details on the duration of each load step and the deformation stabilization criterion used to decide when to apply the next load increment. Without these criteria, it is impossible to determine whether the observed "stable creep" (Fig. 13) is truly stable or if the test simply did not wait long enough.

The discussion of the results (Sections 4.2–4.5) is descriptive but lacks mechanistic depth. It is suggested that the manuscript be enriched by integrating the following modern theoretical concepts.

The manuscript observes an increase in strength at low temperatures. The authors should discuss the "ice bonding" mechanism and the effect of "cryogenic suction pressure." As the temperature drops from -5°C to -20°C, the unfrozen water content decreases, even in micropores and nanopores (<5.9 nm). This increases the matrix stiffness. However, they should also consider the volumetric expansion damage of the ice (9%), which can propagate pre-existing cracks.

The recommendation of -5°C should be theoretically critiqued. At -5°C, a significant amount of water in the fine pores of the clayey sandstone (common in Zhiluo) remains liquid, facilitating viscous creep. At -20°C, the matrix is much more stable. The authors must justify whether the energy savings of operating at -5°C outweigh the increased risk of long-term creep.

The study presents creep fitting equations (Eq. 9 and 10) that appear to be empirical power laws. Cutting-edge research on frozen rock creep has shifted towards fractional-order creep models. These models better capture the nonlinear nature and historical "memory" of the viscoelastic-plastic material than traditional models (such as Nishihara or Burgers) or simple power laws. If the authors cannot reanalyze their data with fractional models, they should at least discuss in the conclusion that these models could offer a better fit for the accelerated creep stage and long-term damage, citing recent work. If data is available, it is suggested that creep stages be correlated with Acoustic Emission (AE) events, as this allows for the identification of the onset of microstructural damage before macroscopic failure, which is critical in the design of frozen wells. If AE was not measured, this should be suggested as future work.

Finally, I kindly request that you restructure the manuscript, making the following changes:

1. Create a “Materials and Methods” section and include there, in a complete and reproducible manner, the sample preparation, water status/saturation, freezing/thermal control protocol, equipment, and the testing procedure (including staged loading criteria).

2. Clearly separate “Results” and “Discussion”:

• In Results, present only the experimental findings (curves, tables, parameters, observations).

• In Discussion, focus on the interpretation, comparison with literature, proposed mechanisms, and the justification for operational recommendations.

Author Response

Authors’ responses to the comments of Reviewer #2:

1, The energy statistics presented in the introduction contain errors of magnitude that compromise the initial credibility of the text.

>Response: Thank you for your valuable advice. We have corrected the data in the Introduction.

2, There are gaps in the description of the experimental protocols (sample preparation, saturation, thermal control) that hinder reproducibility.

>Response: Thank you for your valuable advice. We have refined the experimental plan.

3, The analysis of the creep mechanisms and the recommendation of operating temperatures lack a discussion based on the micromechanics of the ice-rock interface and advanced constitutive models.

>Response: Thank you for your valuable advice. We have already included these contents in the main text.

4, Lines 21-23: "sandstone in the area is prone to softening and disintegration, classified as soft to moderately soft rock, with a basic quality grade of IV-V." This classification is qualitative. The literature on the Zhiluo and Yan'an Formations in Ordos indicates that these sandstones have variable porosity and cementation, which drastically affect their UCS (Uniaxial Compressive Strength).

>Response: Thank you for your valuable advice. We have added the specific UCS values obtained in the natural and saturated states to the Abstract section.

>Implemented: As shown in Lines 21-23. 1) the sandstone in the area is prone to softening and disintegration, classified as soft to moderately soft rock (UCS range: 5.14–10.26 MPa in natural state), with a basic quality grade of IV–V.

5, Lines 24-25: "The recommended freezing temperature is -5°C based on empirical values." This statement is problematic. Although -5°C may be economical, frozen rock mechanics demonstrate that strength continues to increase significantly below this temperature due to the freezing of water in micropores and nanopores. Recent studies indicate that at -5°C, the rock is in an intensive transition phase where properties are unstable. Maximum strength and creep stability are typically achieved at lower temperatures (-15°C to -20°C).

>Response: Thank you for your valuable advice. We have optimized this statement.

>Implemented: As shown in Lines 25-26. The recommended freezing temperature is -5°C, based on engineering experience and economic considerations.

6, Line 28: "The water-ice phase transition induced by low temperatures significantly enhances the overall strength..."

The abstract mentions the phase transition but ignores the role of saturation. The reinforcing effect of ice is negligible if the rock is dry and maximal if it is saturated. Since the manuscript does not detail the saturation state in the abstract, this conclusion lacks context.

Please specify the humidity conditions: "The water-ice phase transition in saturated samples induced by..."

>Response: Thank you for your valuable advice. We have already optimized this sentence.

>Implemented: As shown in Lines 29-31. 4) The water-ice phase transition induced by low temper- atures significantly enhances the overall strength, stiffness, and deformation resistance of saturated sandstone.

7, Line 46: The authors state that crude oil production reached "763 million tonnes." This figure is incorrect. According to China's National Bureau of Statistics (NBS) and reports from January 2025, domestic production was 213 million tonnes, a modest increase over previous years driven by offshore and unconventional fields. The figure of "763 million" suspiciously coincides with the European Union's final energy consumption target for 2030 (763 Mtoe) mentioned in energy efficiency directives. It is likely that the authors mistakenly used data from a global or European source. Please verify this figure.

>Response: Thank you for your valuable advice. We have reviewed this figure and made the necess- ary corrections.

>Implemented: As shown in Lines 45-48. The survey revealed that the total production of fossil fuels has gradually increased, reaching 246.4 billion m³, 213 million tonnes, and 4.76 billion tonnes in 2024 (Figure 1(c), (d), and (e)), respectively.

8, A production figure of "5.16 billion tonnes" is cited. The official NBS figure for 2024 is 4.76 billion tonnes, which already represents a record high. The figure of 5.16 could refer to total coal consumption (production + net imports), since China imported approximately 540 million tons in 2024, which would add up to an available supply of close to 5.3 billion tons. However, the text explicitly says "production." Please clarify whether the figure includes imports.

>Response: Thank you for your valuable advice. We have verified the data and corrected it to 4.76 billion tons.

9, Gas production is cited as "303 million tonnes." Natural gas is typically measured in cubic meters or cubic feet. Production in 2024 was 246.4 billion cubic meters (bcm). The figure of 303 million tonnes is far from the actual production and could be confused with reduced emissions in other sectors or aggregated import data. Please verify the figure and use the standard metric "cubic meters" to avoid ambiguity.

>Response: Thank you for your valuable advice. We have verified the data and corrected it to 246.4 billion m³.

>Implemented: As shown in Lines 45-48. The survey revealed that the total production of fossil fuels has gradually increased, reaching 246.4 billion m³, 213 million tonnes, and 4.76 billion tonnes in 2024 (Figure 1(c), (d), and (e)), respectively.

10, Line 51: The manuscript mentions that renewable energy contributed 34% of electricity generation. Recent data from 2024 indicate that installed non-fossil capacity exceeded 50%, and clean generation (solar + wind + hydro) covered more than 80% of demand growth, although coal remains the foundation. It is important for the authors to update their narrative to reflect that, while coal production peaked, its relative share of new capacity is declining in the face of the explosive expansion of solar and wind power in regions such as Inner Mongolia.

>Response: Thank you for your valuable advice. We have refined the wording of this section.

>Implemented: As shown in Lines 52-55. Driven by the dual carbon goals, China's energy mix conti- nues to optimize. Although coal production has peaked, its proportion in newly installed capacity is gradually decreasing, especially in regions like Inner Mongolia, where solar and wind energy are rapidly surging [6,7].

11, Section 2 of the manuscript ("Engineering Background") is too superficial for a study that aims to link lithology with flow mechanics. Tarangole is not a generic mine; it possesses unique hydrogeological and metallogenic characteristics that must be discussed.

>Response: Thank you for your valuable advice. We have already described the hydrogeological and mineralization characteristics of the mining area in the “Engineering Background” section.

>Implemented: As shown in Lines 150-156. As shown in Figure 3, the ore body is in the form of a plate or lens, and its orientation is basically parallel to the strata. The vertical distance from this interface to the lower Ziluo Formation is 60 m to 100 m. The mining area has complex hydrogeological conditions, and coal seam extraction faces the direct threat of roof water. In terms of metallogenic characteristics, in addition to coal resources, it is also a typical representative of the "Tale-type" sandstone-type uranium deposit, presenting a unique resource assemblage of coal- uranium coexistence.

12, The manuscript mentions "mudstone, sandstone of various grain sizes, and coal seams" (Line 160). However, it omits a relevant detail documented in the Ordos geological literature: the coexistence of uranium and coal.

>Response: Thank you for your valuable advice. We have expanded the concept to include the “coexistence of uranium and coal”.

>Implemented: As shown in Lines 154-156. In terms of metallogenic characteristics, in addition to coal resources, it is also a typical representative of the "Tale-type" sandstone-type uranium deposit, presenting a unique resource assemblage of coal-uranium coexistence.

13, Please note that the Tarangole mining area is recognized for its sandstone-type uranium deposits hosted in the Zhiluo Formation (Middle Jurassic), which directly overlies the coal-rich Yan'an Formation (Lower Jurassic). The mechanical significance of the uranium mineralization and associated alteration (kaolinization, chlorite, pyrite) in the Zhiluo sandstones also affects their mechanical and permeability properties. Altered sandstones can behave differently under freezing due to changes in pore structure and matrix chemistry. Please discuss whether the "medium- and coarse-grained" sandstone samples are from the Zhiluo Formation (coal roof) and whether they show signs of hydrothermal alteration or mineralization, as this introduces heterogeneity into the creep tests.

>Response: Thank you for your valuable advice. In the main text, we have supplemented the discussion on whether the medium coarse-grained sandstone samples are from the Zhiluo Formation (coal roof) and whether they show signs of hydrothermal alteration or mineralization. In the core drilling and indoor mechanical tests on sandstone, medium-grained sandstone was sourced from the Zhiluo Formation, whereas coarse-grained sandstone was not used. No mineralization occurred during these tests.

>Implemented: As shown in Lines 202-205. In the core drilling and indoor mechanical tests on sandstone, medium-grained sandstone was sourced from the Zhiluo Formation (coal roof), whereas coarse-grained sandstone was not used. No mineralization occurred during these tests.

14, Line 76: The text mentions "extremely complex hydrogeological conditions." Please specify that the main challenge is the Lower Cretaceous pore-fissure aquifer (Zhidan/Luohe Formation) and the Zhiluo Formation aquifer. The high permeability and groundwater flow in these layers are the main reason for using the well freezing method. The groundwater flow rate affects ice wall formation. Although the study is laboratory-based, the discussion should link the thermal conductivity results (Section 4.1) to the actual in-situ water flow. High thermal conductivity in the laboratory is favorable, but advective flow at the site can counteract it.

>Response: Thank you for your valuable advice. We have already provided a detailed answer to this question.

>Implemented: As shown in Lines 77-81. However, during the mine construction period, the hydrogeological conditions became extremely complex due to the high permeability of the Cretaceous porous-fissure aquifer and the Zhiluo Formation aquifer. This led to extremely difficult and costly construction treatment, and it was also the main reason for the eventual adoption of the freezing method [13]. As shown in Lines 372-386. Based on the THM theoretical model, the test results show that, firstly, compared with the thermal properties at normal temperature, under freeze-thaw conditions, the thermal conductivity values of medium and fine sandstones are higher than their specific heat capacity values (Figure 9). Secondly, factors such as lithology, stratum, frozen temperature, and depth can have a significant impact on the thermal conductivity and specific heat capacity of the samples. Finally, the thermal conductivity of medium and fine sandstone at normal temperature ranges from 0.51 to 1.89 W/mK, and the specific heat capacity of the rock at normal temperature is between 0.26 and 1.4 MJ/m³K. Its value increases with the increase in the rock's moisture content. The thermal conductivity of the sample at -10°C is within the range of 1.23 to 1.71 W/mK, and the specific heat capacity is between 0.24 and 0.34 MJ/m³K. This fully demonstrates that the frozen temperature range of -8.86 to -13.65°C differs significantly from the empirical values of similar strata. Thus, compared with other temperature options and in consideration of actual engi- neering requirements, setting the freezing temperature at approximately -5°C is more reasonable.

15, Section 4.1

The study evaluates the effect of freezing, the main mechanism of which is the transformation of pore water into ice. However, the degree of saturation of the tested samples is not specified. Were they dry, naturally saturated, or vacuum saturated (100%)?

>Response: Thank you for your valuable advice. The test sample was vacuum-saturated.

>Implemented: As shown in Line 358. Here, the test sample was vacuum-saturated.

16, Recent research demonstrates that the strength of frozen sandstone depends critically on its water content. In dry samples, the effect of temperature (-10°C vs. -20°C) is negligible because there is no ice to act as a cementing agent. If the samples were partially saturated, the reported strength increase (5 MPa) could vary considerably.

>Response: Thank you for your valuable advice. In this study, all test samples were in a vacuum- saturated state; therefore, the results obtained are reliable.

>Implemented: As shown in Line 358. Here, the test sample was vacuum-saturated.

17, Please add a subsection detailing: Saturation Method (e.g., immersion for 48 hours or vacuum according to ASTM D4525). Initial porosity and average moisture content of samples from groups A, B, C, and D. Exact dimensions of the specimens (diameter x height), verifying that they meet the 1:2 ratio required for triaxial tests.

>Response: Thank you for your valuable advice. We have already provided an explanation in a sub- section.

>Implemented: As shown in Lines 390-401. In this study, four groups of rock samples—namely, A, B, C, and D—were selected for triaxial compression tests. All specimens were processed into standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm, strictly satisfying the 2:1 height-to-diameter ratio requirement specified for triaxial testing. In terms of physical properties, the initial porosity of each sample group ranged from 13.8% to 16.5%, and the average water content ranged from 1.8% to 2.5%. To simulate the real underground environment, all samples were subjected to a rigorous vacuum saturation procedure. The specific process included drying at a constant temperature of 105°C, followed by vacuum pumping for 4 hours and subsequent immersion in deionized water for 48 hours, in accordance with ASTM D4525 [28]. This ensured complete saturation of the samples and established a reliable experimental foundation for subsequent mechanical property testing.

18, A temperature of -5°C is recommended, but testing is performed at -10°C and -20°C. However, the cooling rate is not described. Rapid cooling (thermal shock) can induce microcracks due to differential expansion between the mineral grains and pore water, weakening the sample before testing. Slow cooling better simulates field conditions. Additionally, it is relevant to report the stabilization time at the target temperature before applying the load (>12 hours is recommended to ensure internal thermal equilibrium). Please include the temperature vs. time curve of the freezing process and the type of environmental chamber used.

>Response: Thank you for your valuable advice. This research was based on triaxial creep tests. Under different low-temperature conditions, saturated sandstone at -5°C exhibited higher strength. Herein the tests were conducted using the GCTS electro-hydraulic servo-controlled low-temperature, high-pressure rock triaxial testing system, which enabled precise temperature control and synch- ronized data acquisition. A cooling period of 14 hours was applied to the sandstone specimens to ensure thermal equilibrium throughout the sample.

>Implemented: As shown in Lines 401-405. Moreover, the tests were conducted using the GCTS electro-hydraulic servo-controlled low-temperature, high-pressure rock triaxial testing system, which enabled precise temperature control and synchronized data acquisition. A cooling period of 14 hours was applied to the sandstone specimens to ensure thermal equilibrium throughout the sample.

19, Section 4.4

The study uses staged loading, but it lacks details on the duration of each load step and the deformation stabilization criterion used to decide when to apply the next load increment. Without these criteria, it is impossible to determine whether the observed "stable creep" (Fig. 13) is truly stable or if the test simply did not wait long enough.

>Response: Thank you for your valuable advice. We have supplemented detailed information on the duration of each loading step in the staged loading and unloading creep test, as well as on the deformation stability criterion used to determine when to apply the next loading increment.

>Implemented: As shown in Lines 501-505. In this staged loading and unloading creep test, each loading step lasted 25 hours, and the deforma- tion stability criterion for applying the next load level was defined as an axial creep strain rate of less than 1×10^‒4 mm/mm/h over the final 5 hours— ensuring consistent test conditions and reliable results.

20, The discussion of the results (Sections 4.2–4.5) is descriptive but lacks mechanistic depth. It is suggested that the manuscript be enriched by integrating the following modern theoretical concepts.

>Response: Thank you for your valuable advice. Herein we have deepened our understanding of the freezing-thawing mechanism in sandstone, as presented in the manuscript.

>Implemented: As shown in Lines 536-545. As the temperature drops from -5°C to -15°C, the pore water gradually freezes, including the water in micro- and nano-scale pores. This enhances the cementation effect of ice on particles (ice bonding) and the suction force generated by capillary action (low-temperature suction), thereby increasing the apparent stiffness of the rock mass. However, the phase change of water is accompanied by a volume expansion of approximately 9%, which can cause local stress concentrations in confined spaces, leading to the initiation and propagation of microcracks. Therefore, during the low-temperature freezing process, the mechanical behavior of sandstone results from a competition between the strengthening effect of ice bonding and suction and the weakening effect of frost heave-induced damage.

21, The recommendation of -5°C should be theoretically critiqued. At -5°C, a significant amount of water in the fine pores of the clayey sandstone (common in Zhiluo) remains liquid, facilitating viscous creep. At -20°C, the matrix is much more stable. The authors must justify whether the energy savings of operating at -5°C outweigh the increased risk of long-term creep.

>Response: Thank you for your valuable advice. We have revised the statement of the research findings. In this research, considering the compressive strength of sandstone at different freezing temperatures, the rock samples exhibited higher strength at -5°C than at -10°C and -15°C—a finding recommended for practical application, given its favorable balance of mechanical performance, economic feasibility, and field experience.

22, The study presents creep fitting equations (Eq. 9 and 10) that appear to be empirical power laws. Cutting-edge research on frozen rock creep has shifted towards fractional-order creep models. These models better capture the nonlinear nature and historical "memory" of the viscoelastic-plastic material than traditional models (such as Nishihara or Burgers) or simple power laws. If the authors cannot reanalyze their data with fractional models, they should at least discuss in the conclusion that these models could offer a better fit for the accelerated creep stage and long-term damage, citing recent work. If data is available, it is suggested that creep stages be correlated with Acoustic Emission (AE) events, as this allows for the identification of the onset of microstructural damage before macroscopic failure, which is critical in the design of frozen wells. If AE was not measured, this should be suggested as future work.

>Response: Thank you for your valuable advice. For the creep constitutive model, we acknowledge the advantages of fractional-order models in describing nonlinear creep behavior and have expanded the discussion on their applicability and future research directions in the Conclusion section. Regarding acoustic emission monitoring, data were not collected simultaneously due to limitations of the testing equipment. This limitation is addressed in the Discussion section, and acoustic emission technology will be incorporated in future work to investigate micro-damage evolution and precursor identification during the creep stage. The reviewers’ suggestions are highly valuable for enhancing the academic rigor of this paper and guiding subsequent research.

>Implemented: As shown in Lines 657-664. This research represents a preliminary exploration of the mechanical principles underlying mining operations in the Tarangole mining area of China. However, from the perspective of safe engineering practices, certain limitations remain. In the future, numerical simulations and machine learning methods will be integrated to validate the findings from engineering investigations and mechanical tests, with the aim of better meeting the on-site guidance requirements of practical engineering projects. In addition, acoustic emission technology will be introduced in future work to investigate the micro- damage evolution and precursor identification during the creep stage.

As shown in Lines 311-348.

(1) Heat transfer equation for the rock matrix in porous media

(7)

Where, C_s represents the specific heat capacity of the sandstone, m²/(s‧°C); and λ_s denotes the thermal conductivity coefficient of the solid, W‧(m‧K)^‒1.

(2) Heat transfer equation for the fluid in porous media

(8)

(9)

In Equation (9), expressing stress in terms of strain yields:

(10)

Where, G denotes the shear modulus; I represents the stress invariant.

Taking the trace of Equation (10), and rearranging using the relation 2G + 3λ = 3K_b, yields:

(11)

(12)

(13)

As shown in Lines 662-664. In addition, acoustic emission technology will be introduced in future work to investigate the micro-damage evolution and precursor identification during the creep stage.

23, Finally, I kindly request that you restructure the manuscript, making the following changes:

Create a “Materials and Methods” section and include there, in a complete and reproducible manner, the sample preparation, water status/saturation, freezing/thermal control protocol, equipment, and the testing procedure (including staged loading criteria).
Clearly separate “Results” and “Discussion”:

In Results, present only the experimental findings (curves, tables, parameters, observations).
In Discussion, focus on the interpretation, comparison with literature, proposed mechanisms, and the justification for operational recommendations.

>Response: Thank you for your valuable advice. As this research primarily focuses on indoor tests, field tests, and theoretical analysis, we have made minor adjustments to the logical structure of the manuscript.

>Implemented: As shown in the full text (Section 3 and Section 4).

Special thanks to you for your helpful comments.

We tried our best to improve the manuscript and made some changes to the manuscript. These changes do not influence the content or framework of the paper. We did not list here all of the changes, but we marked them in the revised manuscript. We appreciate the work of the editor and reviewers, and we hope that the corrections will be met with your approval. Once again, thank you very much for your comments and suggestions.

Best Regards

Dr. Sicheng Wang (Chongqing University)

202220021074t@stu.cqu.edu.cn

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors made all the requested corrections.