Spatially distributed damage in sandstone under stress-freeze-thaw coupling conditions

Lifeng Fan,Yiding Fan,Yan Xi,Jingwei Gao

College of Architecture and Civil Engineering,Beijing University of Technology,Beijing,100124,China

Keywords:Rock damage Freeze-thaw (FT) cycles Uniaxial stress Coupling effects

ABSTRACT In the present study,we tried to understand the spatially distributed damage in sandstone samples under the coupled stress-freeze-thaw (SFT) conditions.Firstly,uniaxial compressive stresses (i.e.0 MPa,10 MPa,20 MPa,and 25 MPa)were applied to the samples,and then freeze-thaw(FT)cycles(0,8,16,and 24) were performed on the uniaxially stressed samples to realize the SFT coupling.Next,real-time CT scanning was conducted to observe the induced damage.The total porosity was introduced to quantitatively evaluate the damage degree.The local porosity variation,with the distance from the center of the sandstone sample,was analyzed to understand the spatial distribution of damage.Finally,the coupling effects of SFT on the damage gradient were discussed.The results indicate that the porosity rises with FT cycles,and the applied stresses can accelerate the increase in porosity.The damage increases exponentially with the distance from the center of the sample.The damage presents a spatial gradient distribution,not the commonly used uniform distribution in various studies.The damage gradient increases with FT cycles,and the increasing rate in damage gradient decreases at uniaxial stress of 0 MPa and 10 MPa first,but the increasing rate in damage gradient increases with FT cycles then at stress increasing to 20 MPa.

1.Introduction

The engineered rock is generally exposed to the coupled stressfreeze-thaw (SFT) conditions in cold regions (Huang et al.,2018;Deprez et al.,2020; Liu and Dai,2021; Qiao et al.,2021).Repeated freeze-thaw (FT) cycles can induce deterioration of rock microstructures,reducing macroscopic mechanical strength of rock and the service life of rock engineering (Jia et al.,2015; Zhang et al.,2020a).The stresses imposed during the FT cycles may further accelerate the strength deterioration of rocks and threaten engineering safety (Yahaghi et al.,2021; You et al.,2022).Therefore,understanding the damage characteristics of rocks under the coupled SFT conditions is essential for safety assessment and disasters prevention in cold region engineering.

The damage of rocks induced by FT cycles has been studied extensively (Ke et al.,2018; Feng et al.,2022).A wide range of physical and mechanical tests was performed on rocks in terms of FTcycles.The ultrasonic wave velocity(Wang et al.,2017),mass loss(Wang et al.,2016),static and dynamic compression strengths(Fan et al.,2020a),tensile and shear strengths (Ghobadi and Torabi-Kaveh.,2014; Mu et al.,2017; Liu et al.,2021),fracture property(Yin et al.,2019; Niu et al.,2021) and elastic modulus (Gao et al.,2021a) obtained from these tests were obtained to evaluate the damage characteristics of rock caused by FTcycles.The results show that the mechanical strength of rocks generally decreases and the ductility enhances with the FT cycles (Gao et al.,2020; Luo et al.,2020).The degradation of macroscopic mechanical behavior is closely related to the damage of mesostructures in rocks (Yang et al.,2021; Fan et al.,2021).Based on optical microscopy (Freire-Lista et al.,2015),scanning electron microscopy (SEM) (Martinez-Martinez et al.,2013; Fan et al.,2017) and X-ray computed tomography (CT) (De Kock et al.,2015; Sun et al.,2020; Fan et al.,2018),the mesostructure degradation characteristics of rocks under the FT cycles were further studied.The microscopic observations suggest that the FTcycles can induce the separation of mineral particles,enlargement of original pores,and generation of new pores(Park et al.,2015;Maji and Murton,2020;Zhou et al.,2020).As the FT cycles increase,the microscopic damage increases,leading to the deterioration of the macroscopic mechanical strength of rocks (Song et al.,2021a).During the FT cycles,the mesostructure deterioration may be related to the frost heaving force induced by the volume expansion of water-ice phase transition in rocks (Zhai et al.,2016) and the stress induced by the nonaffine deformation of mineral particles (Freire-Lista et al.,2016).Unfortunately,the above studies are mainly concerned with the deterioration of rocks merely subjected to the FT cycles.In practical engineering,most rocks are subjected to FTcycles and compressive stress(Zhang et al.,2015).When the compressive stress is low,the internal defects of rock,such as pores and cracks,may be compressed and closed(Gao et al.,2021b).However,the internal defects may be extended at higher compressive stress (Duan et al.,2019),making the mesoscopic damage of rock exposed to the FT cycles be more complicated.Therefore,understanding the damage characteristics of rocks induced by the coupled SFT is of practical significance.

The damage characteristics of rocks induced by the coupled SFT have attracted increasing attention.The result (Song et al.,2021b)shows that the damage induced by the coupled freeze-thaw-fatigue loading is greater than that induced by the FT cycles only.The shedding of minerals on the sample surface is more serious (Sun et al.,2019; Tao et al.,2021).Moreover,the increasing rate of sample porosity under the coupled loading-unloading-freeze-thaw is higher than that under FT cycles (Liu et al.,2019; Zhang et al.,2020b).The damage model proposed by Wang (1990,1992) was used for the heat affected zone under low cycle fatigue loading successfully.Based on the observations with the naked eye,the damage near the surface of the sample is more significant,indicating that the damage distribution is non-uniform in the sample(Zhu et al.,2021).For this,it seems that the damage caused by the coupled SFT may present a spatial gradient distribution.Previous studies mainly focus on the variation of total damage in the sample under the coupled SFT,which can be evaluated by macroscopic mechanical strength,P-wave velocity,and total porosity.However,quantitative evaluation of the spatial gradient distributions of the damage in rocks (e.g.sandstone) under the coupled SFT is still limited.Moreover,the coupled SFT effects on the spatially distributed damage in sandstone also remain unclear.

In this context,the gradient characteristics of spatially distributed damage in sandstone under the coupled SFT were analyzed used the real-time CT scanning system with a FT and loading device.Firstly,the damage characteristics of the surface,internal space and local section of the sandstone sample were observed intuitively under the coupled SFT based on the CT visualization technology.Secondly,the porosity variation with the distance of the center of the sample was quantitatively analyzed to understand the gradient characteristics of spatially distributed damage.Finally,the coupled SFT effect on the spatial gradient of the damage was discussed.

2.Methods

2.1.Sample preparation

The red sandstone is a common porous rock in engineering(Liu et al.,2020a).Compared with the dense rocks(granite and marble),the red sandstone is more susceptible to water and FT cycles,which may pose greater threats to engineering safety(Wang et al.,2016).Therefore,the red sandstone was studied in the present study.The red sandstone blocks were sampled from Yunnan Province,China.X-ray diffraction (XRD) tests were performed on red sandstone powder to analyze its mineral composition.As shown in Fig.1a,the mineral compositions were mainly of quartz(72.2%),clay minerals(10.8%),plagioclase (6.9%),calcite (6.6%),hematite (2.4%),and potassium feldspar (1.1%).

Fig.1.Red sandstone samples: (a) Composition of red sandstone; (b) Geometric dimensions and cross-section; and (c) Microstructure images of sandstone.

Cylindrical rock cores (a diameter of D=6 mm and a height of h=12 mm) were drilled in red sandstone blocks,as shown in Fig.1b.The microstructure images of sandstone were illustrated in Fig.1c.It shows that the average mineral particle size was about 0.2 mm,which was much smaller than the sample diameter(Zhang et al.,2020b).Both ends of the sample were carefully polished,with an accuracy of 0.05 mm.In previous studies about the spatial distribution characteristics of mesoscopic damage of rock,the observation resolution of CT image was 11-25 μm (Wang et al.,2018; Duan et al.,2019).In the present study,the CT image resolution was 16.58 μm for the sample with a diameter of D=6 mm and a height of h=12 mm,which was in the range from 11 to 25 μm.

2.2.Coupling of SFT cycling and real-time CT scanning

To understand the spatial gradient distributions of the damage in sandstone under the SFT coupling conditions,a suitable experimental technology should be used to achieve real-time internal space observation of the sample.The real-time CT system equipped with FT and loading device was selected in the present study.The conventional CT technology mainly was used to observe the pores and microcracks inside the sample after unloading at room temperature (25 C).However,compared with the conventional CT technology,the CT real-time scanning system with FT and loading device can be used to observe the pores and microcracks inside the sample under SFT coupling conditions.Using the real-time CT technology avoided the stress unloading effects on damage distribution inside samples.The tests under the SFT coupling were conducted on the red sandstone samples by the testing system,as shown in Fig.2a.The system contains the X-ray source,FT and loading device,rotating table and detector.The lowest temperature can reach-20 C in this device.The maximum load of the device was 5000 N,with a loading rate of 0.1-1.5 mm/min.The experimental procedures were described as follows:

(1) According to the previous studies (e.g.Liu et al.,2020a;Huang et al.,2021),the sample with a height of 12 mm and a diameter of 6 mm were vacuumed for 6 h at-0.1 MPa,and then soaked for 24 h in the vacuum device filled with water.Under this condition,the samples were saturated.

(2) Uniaxial compressive stress was implemented on the saturated sandstone samples.The saturated samples were put into the loading device.The samples were uniaxially loaded to the prescribed stress level using a displacement rate of 0.1 mm/min.Based on the program settings,the loading device can automatically adjust the loading platform position throughout the FT cycles to ensure that the force applied on the sample was always constant,and the error of the applied force was within 10 N.As the uniaxial compressive stress increased,the rock sample generally experienced the compaction,elastic deformation,stable crack propagation and unstable crack propagation.In the present study,the designed uniaxial compressive stress implemented on the sample must not cause unstable crack propagation.According to the previous studies(Yang,2016;Liu et al.,2020b),the stress threshold (σcd) from stable to unstable crack propagation was approximately 70%of the peak stress of the rock.In the present study,the peak stress of the saturated red sandstone was 40.9 MPa.The stress threshold (σcd) was approximately 28 MPa.Therefore,the designed maximum uniaxial compressive stress implemented on the sample was set as 25 MPa in this study.The designed stresses were further divided into the levels of 0 MPa,10 MPa,20 MPa and 25 MPa,respectively.

(3) The FT cycling treatments were conducted on the samples subjected to compression stress to realize the coupled SFT.According to previous studies of FT cycling effects on rock(Bai et al.,2020; Zhou et al.,2020; Chen et al.,2022),the-20 C and 20 C were selected as the freezing and thawing temperatures.Fig.2b shows the FT cycle which consists of one freezing stage and one thawing stage.In the freezing stage,the temperature decreased to-20 C and was kept constant for 2 h.This can ensure that the sample was frozen completely throughout the sample (Tao et al.,2021).In the thawing stage,the temperature increased to 20 C and remained for 2 h to ensure that the sample was thawed completely.A total of 24 times FT cycles were performed on each sample.

(4) The real-time CT scanning was conducted on the samples under the coupled SFT.The real-time CT scanning was tested at 0,8,16 and 24 FT cycles,respectively.During scanning,the cone beam X-ray from the X-ray source passed through the sample and then was captured by the detector (see Fig.2c).The X-ray information captured by the detector was processed to obtain the digital radiographs of the sample.The image treatments were further conducted on the digital radiographs to obtain a stack of two-dimensional (2D) CT images of the sample.

Fig.3.CT image processing: (a) Selection of analyzed region; (b) Specific location of the analyzed region; and (c) Image analysis process.

2.3.Mesoscopic damage analysis method

The CT images obtained from the CT scanning contained abundant information on sandstone porosity and matrix.Therefore,the CT images should be analyzed based on professional image processing technology.A region of interest should be selected before analyzing the characteristics of pores and the matrix of sandstone due to the end effects.Fig.3a shows the location of analyzed region.The volume data of the whole sample with a diameter of 6 mm and a height of 12 mm approximately included 362 lays of 2D CT images in the x-and y-direction and 724 layers of 2D CT images in zdirection,respectively.A region was selected in the sample along the z-direction in the present study,which ranged from the 97th to 627th layer.The corresponding size of the selected analyzed region was 6 mm in diameter and 8.804 mm in height.The specific location and size of the analyzed region were shown in Fig.3b.

Fig.4.Surface changes of the sample under the coupled SFT: (a) 0 MPa; (b) 10 MPa; (c) 20 MPa and (d) 25 MPa.

After selecting the analyzed region,the matrix and pores properties were analyzed,as shown in Fig.3c.First,the matrix of sandstone was segmented and the three-dimensional (3D) reconstruction was conducted to understand the coupled SFT effects on the sample surface.Then,the internal pores of sandstone were selected and the 3D reconstruction was conducted to study the coupling effect of SFT on spatial pores and microcracks inside the whole sample.Finally,the cross-section image of the samples was extracted and binarized to study the coupling effect of SFT on the damage of the local region of the sample.The detailed procedures of distinguishing the matrix of sandstone and pores and cracks can refer to the study of Gao et al.(2021b).

Fig.5.Spatial pore variation of sandstone under the coupled SFT: (a) 0 MPa; (b) 10 MPa; (c) 20 MPa and (d) 25 MPa.

3.Results

3.1.Surface damage variation of sandstone under the coupled SFT

Fig.4 shows the change of sample surface under the coupled SFT conditions.In Fig.4,the red region represents the matrix of the red sandstone sample and the black part represents pores and microcracks on the surface of the red sandstone sample.It is seen from Fig.4 that the micropores are generated on the surface of sandstone as FT cycles increase at 0 MPa,which may be induced by mineral particles shedding.At a uniaxial stress level of 10 MPa,the number of micropores increases with increasing FT cycles and are connected to form microcracks after 16 FT cycles.At 20 MPa,the microcracks are formed after 8 FT cycles,and the formation of microcracks is earlier compared with that at 10 MPa.At 25 MPa,the sandstone samples failed after 4 FT cycles,and the penetrating cracks appeared.During the FT cycles,the uniaxial stress generally intensified the damage of sandstone samples.

3.2.Spatial damage variation of sandstone under the coupled SFT

Fig.5 shows the 3D spatial damage variation of the sandstone sample under the coupled SFT.The green region represents the 3D pores and microcracks inside the sample,and the gray region represents the matrix of the samples.It is seen from Fig.5 that the internal damage of sandstone samples increases as the FT cycles increase.At 0 MPa,the pores in the samples increase slightly as the FT cycles increase.At 10 MPa,the internal pore number increases with increase of the FT cycles,and the pores are connected to form microcracks after 16 FT cycles.At 20 MPa,the microcracks are formed after 8 FT cycles.At 25 MPa,the penetrating cracks are formed in the whole sample after 4 FT cycles,and the sandstone samples lose the bearing capacity.

The parameter of volumetric porosity was introduced to quantitatively study the coupling effect of SFT on the spatial damage of sandstone at the stress levels of 0 MPa,10 MPa and 20 MPa.The stress level of 25 MPa was not considered due to the complete failure of the samples after 4 FT cycles.The volumetric porosity is defined as the ratio of the volume of the 3D spatial damage to the total volume of the analyzed region.The increase in the volumetric porosity indicates the increase in the spatial damage.

Fig.6 shows the coupling effects of SFT on the volumetric porosity.It is seen from this figure that the volumetric porosity increases with increase of the number of FTcycles at different stress levels.However,the increasing magnitudes of volumetric porosity with FT cycles are different at various stress levels.At 0 MPa,the volumetric porosity increases from 2.126%to 2.839%as the FTcycles increase from 0 to 24,with an increment of 33.537%.At 10 MPa,the volumetric porosity increases from 2.196% to 3.642% with the FT cycles increasing from 0 to 24,with an increase percentage of 65.847%.At 20 MPa,the increasing ratio of the volumetric porosity is 158.291%.The increasing ratio of volumetric porosity with FT cycles increases as the uniaxial compressive stress increases.

3.3.Cross-section damage variation of sandstone under the coupled SFT

Fig.6.Coupling effects of SFT on the volumetric porosity.

Fig.7 shows the 2D cross-sectional images of sandstone under the coupled SFT.Fig.7a-d shows the CT scanning images of crosssections under the coupled SFT.In the CT images,the black areas represent the pores and microcracks of rock.The binarization treatments were further performed on the CT scanning images to analyze the local pore distribution in sandstone.The pore and microcracks can be segmented by appointing specific grayscale values through the image processing software.The segmented pores and microcracks were presented using white color.Fig.7e-h shows the binarization images of cross-sections under the coupled SFT.The white areas represent the pore and the microcracks formed by the interconnection of multiple pores.It is seen from Fig.7 that the number of pores changes slightly with increase of the number of cycles at 0 MPa.At 10 MPa,the number of pores increases with the increasing cycles.At 20 MPa,the increase in the number of pores is larger than that at 10 MPa.At 25 MPa,failure occurs in sandstone samples after 4 FT cycles,and the penetrating cracks appear on the cross-section.In addition,the binarization images reveal that there are more pores near the surface of the sample than that in the middle part.

The areal porosity parameter is introduced herein to quantitatively describe the 2D damage variation of cross-sections under the coupled SFT.Areal porosity is defined as the ratio of the area of pore and microcracks on the cross-section to the total cross-sectional area.The area of the pores and microcracks can be calculated by counting the pixel number of white areas in Fig.7e-h.

Fig.8 shows the STF coupling effects on areal porosity.It is seen from Fig.8 that areal porosity increases with increase of the FT cycles,but the increasing magnitude is different at varied stress loads.The variation in areal porosity with the number of FT cycles is similar to that of volumetric porosity.At 0 MPa,the areal porosity increases from 2.152%to 2.753%as the FT cycles increase from 0 to 24,with an increment of 27.926%.At 10 MPa,the areal porosity increases from 2.212%to 4.805%with the FT cycles increasing from 0 to 24,which increases by 117.224%.At 20 MPa,the areal porosity increases by 187.142%.

4.Discussion

4.1.Gradient characteristics of spatially distributed damage under the coupled SFT

Fig.7.Cross-sectional CT images of sandstone under the coupled SFT at:(a)0 MPa;(b)10 MPa;(c)20 MPa;(d)25 MPa;and their binarization images at:(e)0 MPa;(f)10 MPa;(g)20 MPa and (h) 25 MPa.

To understand the spatial distribution characteristics of damage,the analyzed region was divided into several the-same-volume regions from the internal to the surface of the sample.Fig.9 shows the schematic diagram of the local region division,with the cylinder analyzed region measuring 248.9 mm3.It was first divided equally into three local regions,which were named as the local regions 1,3 and 5,respectively.Each local region had a volume of 83 mm3.To refine the local region division,the local regions 2 and 4 were further added.The local regions 2 overlapped with local regions 1 and 3.Similarly,local region 4 overlapped with local regions 3 and 5.The specific division methods used the one in Fan et al.(2020b).Fig.9a shows the location of local regions,Fig.9b the specific size of cross-sections of local regions,and Fig.9c-g the 3D reconstructed image of local regions after division.Table 1 shows the detailed dimensions of local regions.

Fig.7.(continued).

Fig.8.Coupling effects of SFT on areal porosity.

The porosity of the local region was calculated to quantitatively describe the damage degree of local regions under the coupled SFT.Fig.10 shows the relationship between porosity and distance from the center of the sample under the coupled SFT.It is seen from Fig.10a that the porosity almost remains constant as the distance from the center of the sample increases before applying FT cycles at 0 MPa.It indicates that the initial pore distribution is relatively uniform.After 8 cycles,16 cycles and 24 cycles,the porosities all increase exponentially as the distance from the center of the sample increases,suggesting that the damage of the external region is greater than that of the internal region.In addition,the damage difference between the external and internal regions increases with increase of the number of FT cycles.At 10 MPa and 20 MPa,the variation trends of porosity with distance from the center of the sample were similar to that at 0 MPa.However,the damage difference between the external and internal regions of the sample increases generally as the load increases under the same FT cycles.

Fig.9.Division of local regions:(a)Analyzed region;(b)Geometric parameters of cross-section of five local regions;(c)Local region 1;(d)Local region 2;(e)Local region 3;(f)Local region 4; and (g) Local region 5.

The experimental data in Fig.10 are further fitted exponentially to describe the variation in porosity with distance from the center of the sample:

where P is the porosity of local region,d is the distance from the center of the sample,P1is the porosity of the local region 1,d1is the distance from local region 1 to the center of the sample,and A and t are the fitting parameters.

Fig.10.Relationship between porosity and distance from the center of the sample under the coupled SFT: (a) 0 MPa; (b) 10 MPa and (c) 20 MPa.

The fitting parameters and correlation coefficients at 0 MPa,10 MPa and 20 MPa are shown in Tables 2-4.It can be seen that the exponential function can better describe the spatial damage distribution characteristics of sandstone under the coupled SFT with all correlation coefficients R2＞0.9.

Table 1 Division of local regions.

Table 2 The parameters of the fitting equation under the stress level of 0 MPa.

Table 3 The parameters of the fitting equation under the stress level of 10 MPa.

Table 4 The parameters of the fitting equation under the stress level of 20 MPa.

4.2.Coupling effects of SFT on the spatial gradient of damage

The spatial gradient coefficient was introduced to quantitatively describe the differences between the internal and external damage.The increase in gradient coefficient indicates the increase in differences between internal and external damage of the sample(Fan et al.,2020b).The calculation of the gradient coefficient is expressed as follows:

where ki(i=1,2,3 and 4) represents the slope of the line connecting two adjacent points in Fig.10,Pirepresents the porosity of the region i,Pi+1represents the porosity of the region i＋1 adjacent to region i,and direpresents the distance between the region i and adjacent region i＋1.

The spatial damage gradient coefficient () was defined as the mean value of the parameters k1,k2,k3,and k4.

Fig.11 shows the effect of coupled SFT on the spatial gradient of damage in sandstone.It illustrates that the gradient coefficient increases as the cycling number increases during the 24 FT cycles at 0 MPa,and the increasing rate in the gradient coefficient decreases as the cycling number increases.The variation trend of gradient coefficient with FT cycles at 10 MPa is similar to that at 0 MPa.However,the gradient coefficient at 10 MPa is greater than that at 0 MPa under the same FT cycles.This indicates that the damage difference between the internal and external regions at 10 MPa is greater than that at 0 MPa.At 20 MPa,the gradient coefficient also increases as the FT cycles increase,but the increasing rate in the gradient coefficient increases as the FTcycles increase during the 24 FT cycles.

For the saturated sandstone sample,the increase in pores and microcracks induced by the FT cycles and the softening effects of water may cause a decrease in the cohesion between mineral particles (Zhou et al.,2020).Mineral particles near the surface of the sample are more prone to shedding than those near the center of the sample (Zhu et al.,2021),which may further increase the pores and microcracks near the surface region of the sample.Therefore,the damage near the surface of the sample was larger than that near the center of the sample.The increase in stresses can increase the pore and microcracks induced by the FT cycles under the uniaxial SFT coupling conditions (Tao et al.,2021),which may further increase the shedding of mineral particles near the surface of the sample and increase the pores and microcracks near the surface of the sample.This may cause an increase in the damage gradient.

This study mainly focused on the uniaxial compressive SFT coupling effects on the spatial gradient distribution characteristics of the damage in the red sandstone sample.Further research should be conducted on the effect of the coupled confining pressurefreezing-thaw and the water saturation on the spatial distribution characteristics of the damage in the red sandstone sample.

Fig.11.Coupling effects of SFT on the spatial gradient of damage in sandstone.

5.Conclusion

In the present study,the spatial gradient distribution characteristics of damage in red sandstone under the coupled uniaxial compressive SFT were quantitatively studied by real-time CT.The main conclusions are drawn:

(1) The damage caused by the coupled SFT increases as the cycle number increases,and the increasing rate in damage increases as the applied stress increases.

(2) The damage in sandstone shows a spatial gradient distribution under the coupled SFT.The porosity increases as the distance from the center of the sample increases,and the damage near the surface of the sample is greater than that of the internal.The exponential function can be used to describe the porosity variation with the distance from the center of the sample.

(3) The damage gradient increases as the cycling number increases during the 24 FT cycles.The increasing rate of gradient decreases as the FT cycles increase at the stress levels of 0 MPa and 10 MPa.However,the increasing rate increases at the stress levels of 20 MPa.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We acknowledge the funding support from the National Natural Science Foundation of China (Grant No.12172019) and Beijing Natural Science Foundation (Grant No.JQ20039).