Jianfeng Liu ,Xiaosong Qiu ,Jianxiong Yang ,Chao Liang ,Jingjing Dai ,Yu Bian

a State Key Laboratory of Hydraulics and Mountain River Engineering,Sichuan University,Chengdu,610065,China

b CNPC Key Laboratory of Oil and Gas Underground Storage Engineering,Langfang,065007,China

c College of Water Resource and Hydropower,Sichuan University,Chengdu,610065,China

Keywords: Rock salt Cyclic mechanical loading Shear band Dilation band Underground gas storage (UGS)

ABSTRACT Great potential of underground gas/energy storage in salt caverns seems to be a promising solution to support renewable energy.In the underground storage method,the operating cycle unfortunately may reach up to daily or even hourly,which generates complicated pressures on the salt cavern.Furthermore,the mechanical behavior of rock salt may change and present distinct failure characteristics under different stress states,which affects the performance of salt cavern during the time period of full service.To reproduce a similar loading condition on the cavern surrounding rock mass,the cyclic triaxial loading/unloading tests are performed on the rock salt to explore the mechanical transition behavior and failure characteristics under different confinement.Experimental results show that the rock salt samples present a diffused shear failure band with significant bulges at certain locations in low confining pressure conditions (e.g.5 MPa,10 MPa and 15 MPa),which is closely related to crystal misorientation and grain boundary sliding.Under the elevated confinement (e.g.20 MPa,30 MPa and 40 MPa),the dilation band dominates the failure mechanism,where the large-size halite crystals are crushed to be smaller size and new pores are developing.The failure transition mechanism revealed in the paper provides additional insight into the mechanical performance of salt caverns influenced by complicated stress states.

1.Introduction

The use of underground caverns in low permeability formations,such as rock salt for gas storage,has been identified as an appropriate option to meet seasonal energy demand(Alkan et al.,2007;Martin-Clave et al.,2021).Compared to gas tanks on the ground surface,underground gas storage(UGS)has several advantages,e.g.low construction cost,small surface footprint and good isolation away from surface influences.The large volume and sustainable operating pressure make it possible for the salt cavern to hold more than 60 times the volume of the surface gas tank (Michalski et al.,2017).Considering the enormous potentials of the UGS,numerous salt caverns have been built worldwide.The first UGS system in China has been built in Jintan,Jiangsu Province,and two other blocks have also been designed in Henan and Yunnan provinces,China (Liu et al.,2020).

An important concern with respect to the UGS is the stability of rock salt during full-service period.Accompanied by the gas injection and recovery,the rock salt may undergo complex loading/unloading conditions (Yang et al.,2020;Yang and Fall,2021a).Generally,conventional natural gas storage is operated on an annual cycle(Liu et al.,2020).For example,gas is injected when the production exceeds demand in summer,and it is withdrawn in winter.With the development of new energy storage methods,i.e.compressed air energy storage (CEAS) (Lund and Salgi,2009) and hydrogen storage(Ozarslan,2012),the mechanical performance of rock salt under cyclic loading/unloading is receiving more and more attention.The loading cycle in the new storage methods can reach daily or hourly (Ozarslan,2012),which makes the pressure fluctuation more frequent in the cavern.In this circumstance,the mechanical transition behavior and failure mechanism of rock salt are of importance to the operation of gas storage cavern.

As a promising solution to support renewable energy,e.g.wind energy or solar energy,the pressure acting on the cavern rock mass is so complicated,which is not able to be totally reproduced in the laboratory (Peng et al.,2020).To investigate the mechanical behavior of rock salt under a similar condition,various kinds of experiments have been conducted to understand the brittle and ductile behaviors of rock salt under different stresses.For example,Liu et al.(2014)and Lin et al.(2022)conducted uniaxial and triaxial cyclic tests to study the damage evolution characteristics of rock salt,which provides basic guidance for the design of gas caverns.Alkan et al.(2007)conducted conventional triaxial tests to explore the compressive behavior following the dilatancy of rock salt and defined the dilatancy boundary using the acoustic emission (AE)data.To investigate the fatigue of rock salt due to cyclic loading,Fan et al.(2020) conducted discontinuous cyclic compression tests to study the time interval effect,which was proved to have a marked influence before and after rock presents dilatant behavior.In addition,the dynamic compression property of rock salt under different confining pressures was also investigated (e.g.Li et al.,2019).

Although the aforementioned researches have demonstrated the mechanical behavior of rock salt under static and dynamic cyclic loading tests,the mechanical transition behavior and failure mechanism of rock salt under different confinement are still immature.Confining pressure has been proved to significantly affect the rock salt deformation and the damage evolution (Baud et al.,2006;Xie et al.,2011;Lu et al.,2020;Yang and Fall,2021b;Dai et al.,2023).The aim of this study is to explore the failure of mechanical transition mechanism of rock salt under complex triaxial stress states,in order to provide a good understanding for the mechanical performance of UGS.

2.Experimental set-up

The rock salt samples were extracted from a borehole in a potential gas storage salt cavern.The sample color is slightly different because the rock salt has impurity content that affects its visual appearance.The samples were cut with dimension of ratio of 1:2(diameter to height),with an approximate diameter of 80 mm and an averaged density of 2.1 g/cm3.The detailed information of each sample and obtained mechanical data are summarized in Table 1.The test was conducted based on the procedures and guidelines of International Society of Rock Mechanics and Rock Engineering,where the MTS-815 rock mechanics test system was used (see Fig.1).The test system has an axial load capacity of 4600 kN,a measurement range of circular extensometer from-2.5 mm to 15 mm,and axial extensometer range of ± 5 mm.The test sensor accuracy is able to reach 0.5% of rated output (RO).The maximum confining pressure can be up to 140 MPa.

Table 1Rock salt samples tested in this study.

Fig.1.MTS-815 rock mechanics test system.

To investigate the mechanical behavior transition and failure mechanism of rock salt under different confinement,the tests were conducted under an axial displacement-controlled loading system with different confining pressures,i.e.5 MPa,10 MPa,15 MPa,20 MPa,30 MPa and 40 MPa.The applied loading path in the test is illustrated in Fig.2.Firstly,the confining pressure was applied to the rock specimen with an increasing rate of 3 MPa/min until the desired value was reached,e.g.5 MPa,10 MPa,15 MPa,20 MPa,30 MPa and 40 MPa,in the triaxial experiment.Secondly,the deviatoric stress was applied through displacement controlled loading mode at a rate of 0.5 mm/min,and then the deviatoric stress level was unloaded to zero.In each subsequent loading cycle,the deviatoric stress was increased and then the specimen was unloaded again to zero.Finally,the triaxial loading cycle is continued in this way until the specimen failed.

Fig.2.Triaxial cyclic loading path: (a) applied axial strain versus elapsed time with different confining pressures of 5 MPa,10 MPa,15 MPa,20 MPa,30 MPa and 40 MPa,(b)deviatoric stress versus elapsed time.

3.Results

In the following,the compressive stress and strain are shown as positive.

3.1.Axial,lateral and volumetric deformation

To investigate the deformation characteristics of rock salt under different confining pressures,the axial,lateral and volumetric strains with respect to time are presented in Fig.3.In the figure,the axial and lateral deformations are obtained directly from the measured deformation by displacement sensors,and the volume change is calculated by these values.It should be pointed out that due to the limited measurement range in circular direction,the lateral strain may not be obtained after the circular deformation exceeds the measurement range.Thus,the recorded lateral strain is stopped when the maximum range is reached,and this maximum lateral range is much smaller than the axial range.

Fig.3.Rock salt strain with respect to time for different confining pressures of: (a)σ3=5 MPa,(b)σ3=10 MPa,(c)σ3=15 MPa,(d)σ3=20 MPa,(e)σ3=30 MPa,and (f)σ3=40 MPa.Note: ε1,ε3 and εV are axial strain,lateral strain and volumetric strain,respectively.

The axial strain increases continuously with the applied loading,and undergoes a slight decrease when the loading is stopped.As the rock salt is a soft rock,the effect of unloading on the deformation bounce back is not significant.Since the rock sample is subjected to shear stress,the sample has an expansive deformation in the lateral direction,and the lateral strain goes up in a smaller rate than the deformation rate in axial direction.Based on the deformation in lateral and axial directions,the volume change of sample can be calculated.When the sample is loaded to a maximum compaction value (see Fig.4),the sample elastic deformation ends(also stage I in Fig.5).It is also seen from Fig.4 that the stage of elastic deformation lasts for a long time period with increasing confining pressure.

Fig.4.Volumetric strain change with axial strain under different confining pressures.εV and ε1 are the volumetric strain and axial strain,respectively.

Fig.5.Stress-strain curve of rock salt subjected to cyclic loading/unloading with: (a)σ3=5 MPa,(b)σ3=10 MPa,(c)σ3=15 MPa,(d)σ3=20 MPa,(e)σ3=30 MPa,and (f)σ3=40 MPa.ε1,ε3 and εV are the axial strain,lateral strain and volumetric strain,respectively.

Accompanied by the damage initiation due to stable microcrack growth,the compaction volume of rock salt sample undergoes a decreasing trend from the maximum(also the zero derivative point of volumetric strain with respect to time).When the volume change reaches zero,it indicates the onset of shear-induced dilation,and the plastic behavior starts dominating the sample deformation.The rock salt is subjected to irreversible plastic deformation.The dilation volume continues increasing with the triaxial loading cycle until the sample fails.

It is seen from Fig.3 that the axial strain value at sample failure moment has a rising trend from σ3=5 MPa-20 MPa(see Fig.3ac),then almost keeps unchanged from σ3=20 MPa to 40 MPa(see Fig.3d-f),indicating the decreased material strength.Following the strength theory (Baud et al.,2006;Tao et al.,2021),there are generally two modes representing the failure of rock salt:(1)Shear failure at low confining pressures with the failure envelope described by the Mohr-Coulomb (MC) criterion,and (2) dilation localization at elevated confining pressure with the failure envelope described by elliptical yield cap.This transitional failure behavior will be further explored through analysis of critical stress state theory.

Determinations of damage initiation and the onset of shearinduced dilation are fundamental to recognize the deformation behavior of rock salt,which is controlled by the volume change.To investigate the effect of confining pressure on damage and dilation onset,the volume change with respect to axial strain is illustrated in Fig.4.As the circular deformation at σ3=40 MPa exceeds the measurement range at an early time that the dilation onset does not occur yet,we use a linear fitting line to determine the dilation onset,which is obtained at axial strain of 19.3%.With increase of the confining pressure,the damage initiation and dilation onset occur at a larger value of axial strain.There are several reasons for this behavior: (1) At a lower effective pressure condition,the confinement of rock salt sample is difficult to withstand the applied deviatoric loading,thus the sample presents dilatant behavior easily starting from compaction volume.(2) The higher confining pressure on the sample leads to the complete closure of both intergranular and intragranular pore spaces(Wong et al.,1997;Lyu et al.,2021).As a result,the compressed material presents a harder stiffness,which may better resist the transition from compaction to dilatancy.To provide a good understanding of the rock salt mechanical behavior at different stages,the full-scale stress-strain relation will be explored in the following subsection.

3.2.Stress-strain characteristics

Basically,the rock stress-strain behavior is divided into four stages:elastic deformation,damage initiation,plastic deformation,and post-peak failure (Alkan et al.,2007).The triaxial cyclic loading/unloading tests conducted on rock salt show similar mechanical behaviors except that post-peak failure stage is not obvious for samples subjected to confining pressure of 20-40 MPa,as presented in Fig.5.

(1) Stage I:elastic deformation.Due to the soft property of rock salt and high confining pressure applied,the elastic deformation stage lasts for a short time.In most cases,the viscoelastic deformation representing the closure of primary pores and cracks due to compaction,linear-elastic deformation as well as the brittle-ductile transition are distinguished.For the soft property of rock salt in the study,the boundary between these different behaviors is not obvious,thus we incorporate the above behaviors into Stage I.The boundary of elastic deformation is characterized by the maximum compaction in the volumetric strain curve (ends at pointA),where the increase rate in axial strain is higher than that in lateral strain,indicating the volume change due to crack closure is dominated by shear stress.

(2) Stage II:damage initiation.Due to the stable crack growth in rock salt,the lateral strain increases rapidly with higher shear stress,leading to the occurrence of permanent damage.Correspondingly,the sample gradually undergoes a compression-to-dilatancy transition behavior.This stage ends at the pointBfor which the sample completely shows a dilatant behavior,corresponding to εV=0 in Fig.5.With the increase of confining pressure from 5 MPa to 40 MPa,the dilatancy onset occurs at a larger axial strain value,which are 1.4%,2.8%,3.4%,8.7%,9.4% and 19.3%,respectively.

(3) Stage III:plastic deformation.The volume dilation and crack growth continue at this stage.An obvious axial stress drop occurs at the 3rd loading step due to the change of loading mode,e.g.from axial stress-controlled mode to displacement-controlled mode.As the confining pressure increases from 5 MPa to 20 MPa,the compressed sample presents a stronger bearing capacity for plastic deformation(e.g.the peak stresses are 59.1 MPa,79.28 MPa and 87.25 MPa,respectively,in Fig.5a-c),which may be related to the crystalline microstructure property (Li et al.,2019).Then the bearing capacity decreases gradually with the confining pressure from 20 MPa to 40 MPa (e.g.the peak stresses of 114.87 MPa,112.91 MPa and 104.5 MPa,respectively,as shown in Fig.5d-f),which is associated with the intragranular cracking that dominates the shear-induced dilation (Wong et al.,1997;Baud et al.,2006).The peak stress evolution with respect to confining pressure also represents distinct failure characteristics.This stage ends at the pointCfor which the peak deviatoric stress is reached.It is also noted that the confining pressure improves the flow plasticity of rock salt,where the duration of Stage III is becoming longer from confining pressure of 5-15 MPa,and then presents a decreasing trend from σ3=20 MPa to σ3=40 MPa.For example,the allowed range of axial strain increases from 16.9% to 36.6% in σ3=5-15 MPa,then shows a decreasing trend from 32.1% to 20.7% in σ3=20-40 MPa.In addition,when the confining pressure is larger than 20 MPa(e.g.see Fig.5d-f),the peak stress occurs at a high strain value and subsequently the sample fails quickly.

(4) Stage IV:post-peak failure.After the applied loading exceeds the peak stress,the rock salt shows softening behavior,and it can still have a residual modulus.The cyclic loading/unloading process improves the rheology ability of rock salt,where the stiff solid particles are gradually separated with soft solid particles.As a result,the failure of rock salt typically presents a local bulge scenario,as validated in Section 3.5.The post-peak stage at lower confining pressure(e.g.5 MPa,10 MPa and 15 MPa)lasts for a relatively longer time period(see Fig.5a-c),while this stage is very short under elevated confining pressure (e.g.20 MPa,30 MPa and 40 MPa in Fig.5d-f).This is due to different failure morphology of rock salt,e.g.shear failure at confining pressure of 5-20 MPa and dilation localization at confining pressure of 20-40 MPa(see Section 3.5).

3.3.AE events

AE activity is closely associated with the different damage degrees of rock salt when subjected to loadings,including microcracking,shear fracturing and pore collapsing(Wong et al.,1997).In the triaxial loading/unloading tests of rock salt,the representative data of AE activity are recorded and given in Fig.6.The deviatoric stress (blue line),accumulative AE count (green line),and AE rate(gray line)are plotted with respect to the axial strain.The boundary of elastic deformation(pointA),the onset of shear-induced dilation(pointB),and the boundary of failure (pointC) are marked in the figure,which corresponds to different deformation stages in Fig.5.

At the elastic deformation stage (Stage I),the accumulative AE shows a small value,and the stage lasts for a short time.At the damage initiation stage(Stage II),intense AE activities are observed for samples under low confinement(see Fig.6a-c),while elevated confining pressure is easier to resist crack initiation and as a result the observed AE activities become sparse(see Fig.6d-f).Therefore,the accumulated AE under higher confinement is smaller.

The continuous loading/unloading enlarges the deformation of rock salt,and the sample presents a plastic deformation at Stage III.Accompanied by the development of intergranular cracking in the rock salt,the continuous increase of accumulative AE is related to the shear fracture of cemented grain contacts (Menendez et al.,1996).The multilevel loading/unloading cycles leads to the grain movement relative to one another,and improves the hardening property of rock salt.When the sample is subjected to a stress close to the peak deviatoric stress,and the grain is hard to move,the accumulative AE could remain constant (see Fig.6a-c).While for the samples subjected to higher confining pressure (e.g.20 MPa,30 MPa and 40 MPa),the material is undergoing a continuous hardening stage until reaching the peak strength.Thus,the accumulative AE continues going up at Stage III,accompanied by intense AE activities (see Fig.6d-f).

Finally,the continuous loading leads to the failure of rock salt at Stage IV,and an abrupt surge in accumulative AE is observed that is accompanied by decrease of the deviatoric stress in Fig.6a-c,due to the sound shear band(see Fig.8a-c).For the samples subjected to higher confining pressure in Fig.6d-f,the decrease in the deviatoric stress and abrupt increase of accumulative AE are not obvious as the shear-induced dilation is playing a dominant role,which may be related to the crack extending across the grains and resulting in pore collapse(Baud et al.,2006).Thus the rock fails due to dilation band,as seen from the failure morphology in Fig.8d-f.

3.4.Critical stress state

Based on the analysis,several critical stress states are identified to characterize the failure features and to provide a basis for rock salt deformation.Under different confining pressures,the cyclic loading/unloading leads to different degrees of hardening property in rock salt;as a result the rock salt samples present different failure characteristics,e.g.failure either in the form of shear band or in the mode of dilation.Based on the theory of critical stress state(Wong et al.,1997;Ougier-Simonin and Zhu 2015),the deviatoric stress with respect to mean stress is presented in Fig.7,where the critical stress state line including the MC envelope and elliptical cap envelope are incorporated.

In the brittle regime with shear band failure,the rock strength and stress value at dilation onset (B) have a positive correlation with the mean stressp=（σ1+2σ3）/3 when the confining pressure is greater than 20 MPa.Many previous studies have validated that this dependent behavior is affected by the porosity,cementation and clay content (Vernik et al.,1993).The strength data(black circular symbols) map out the shear failure envelope in the stress space,which can be fitted by the MC criterion.The used equation is given by

In the dilation localization regime,the strength shows a negative correlation with the mean stress at the critical stress state,perhaps due to the property of grain crushing.By observing the behavior of other rock types in the stress space,similar mechanical behavior is also recorded,e.g.sandstone deformation in Baud et al.(2006,2021),where the strength will decrease to a low value with a higher confining pressure.Following Baud et al.(2021),the failure envelope in the dilation localization regime can be represented by an elliptical yield cap as

wherea,bandcare the model parameters.Based on the experimental data in Table 1,the cap for rock salt has values ofa=40 MPa,b=115 MPa,andc=58 MPa.Due to the limited dataset for rock salt,the failure theory in different regimes needs to be further explored by experiments,which may be partly validated by analyzing the failure morphology under different confining pressures.

3.5.Failure morphology

The failure morphology of rock salt samples at the end of test is given in Fig.8.As the applied confining pressure increases gradually,the failure mode has an obvious transition from diffused shear band at σ3=5 MPa,10 MPa and 15 MPa to dilation band at σ3=20 MPa,30 MPa and 40 MPa.Another scenario is that the failure angles with respect to horizontal direction increase with the higher confining pressure,except that the shear failure does not occur when the confining pressure is larger than 20 MPa.

Fig.8.Failure morphology of rock salt samples under different confining pressures(modified from Lin et al.,2022).

When the applied confining pressure is at a relatively lower level,e.g.5 MPa and 10 MPa,the large-size halite crystals play a dominant role in resisting the deformation.The plastic strain hardening behavior is unable to withstand the shear deformation,thus the rock salt sample presents a diffused shear failure band with significant bulge at certain locations due to the relatively soft property.As the confining pressure continues increasing,the capacity of plastic strain hardening becomes stronger and therefore the shear failure angle is larger (see Fig.8a-c).

When the confining pressure reaches 20 MPa,the strain hardening capacity is so strong that shear-induced dilation band instead of shear band occurs (see Fig.8d-f).There are two reasons accounting for this specific scenario.

(1) Higher confining pressure restrains the arbitrary deformation of soft part and less local large bulge is observed.

(2) When the large-size halite crystals are crushed to be smaller parts,the stiff solid particles begin to deform towards the soft areas and the strain-hardening capacity becomes stronger due to higher confining pressure.As a result,the rock salt shows a significant expansive behavior with reconstructed solid particles,thus the localized band structure perpendicular to the minimum stress is formed (see Fig.8d-f).

4.Discussion

Under complicated triaxial stress states,the failure mode of deformation bands may be classified as per the work of Du Bernard et al.(2002): shear band with parallel shear offset,compaction band with band shortening,and dilation band with predominant band extension (see Fig.9).In this study,the dilation band in rock salt is localized in a thin tabular zone (sometimes interpreted by axial splitting (Issen and Challa,2008)),which is spatially associated with shear band that is originating at its tips and transforming towards the extensional quadrants.This localized zone of dilatant deformation is formed perpendicular to the minimum compressive principal stress σ3,which is consistent with the observed scenario in granular material (Du Bernard et al.,2002).

Fig.9.Diagram describing the coexistence of shear,compaction and dilation band under triaxial stress state.

In comparison to the formation of shear band characterized by grain sliding and pore collapse,the formation of dilation band at elevated confinement may result in an increase in porosity and permeability (Issen and Rudnicki,2000).Since the formation of dilation band is accompanied by the breaking of grain bond in axial direction,the splitting of two discrete surfaces continues with the applied loading and is restrained by the material cohesion,thus significant bulge area is observed,as shown in Fig.8e and f.Therefore,the rock salt sample deformation under high confinement is in a relatively homogeneous manner until the peak stress is reached.The shear band develops when the stress path exceeds the MC failure envelope,which can be explained by the critical stress state theory (see Fig.7).

According to the microstructural analysis in Martin-Clave et al.(2021),shear deformation observed in halite crystals after triaxial tests may be associated with crystal misorientation and grain boundary sliding.Following the crystal misorientation and grain rotation,shear band appears in the form of micro-fractures with an angle from the direction of applied σ1.The cyclic loading leads to the grain boundary migrating from a halite grain to the neighboring grain boundary (Martin-Clave et al.,2021),which is likely to proceed more easily under elevated confinement.

When the applied confining pressure is high enough that the dilation band dominates the failure mechanism,the large-size halite crystals are crushed to smaller size and new pores are developing(Martin-Clave et al.,2021).Intragranular cracking,grain migration as well as grain lattice recrystallization are proceeding in a sequential manner.The cyclic loading leads to the localization of these reconstructed grains that a dilation band is formed at a certain location.With the grain bond being broken in the dilation band,the above process continues in other areas where the axial cohesion is still active.By the repeated micro-scale processes,the macroscopic bulge transforms to a larger size bulge in the same area of rock salt sample (see Fig.8).

5.Conclusions

Complicated pressure loadings acting on the surrounding rocks have significant impacts on the performance of salt cavern during the full-service time period.To reproduce similar loading conditions,the cyclic triaxial loading/unloading tests have been performed on the rock salt to explore the mechanical behavior transition and failure mechanism under different confinement.

Experimental results have shown distinct mechanical behavior and failure characteristics under different stress states.In low confining pressure conditions (e.g.5 MPa,10 MPa and 15 MPa),shear band appears in the form of micro-fractures with an angle from the direction of applied σ1,which is closely associated with crystal misorientation and grain boundary sliding.While in the elevated confinement (e.g.20 MPa,30 MPa and 40 MPa),the dilation band is the dominating failure mode.

Overall,the failure transition mechanism revealed in the context would have implications for investigating mechanical performances of salt cavern under complicated stress states.However,more experiments under higher confinement are needed to better understand the failure characteristics of rock salt.

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.

Acknowledgements

This research was financially supported by the Science and Technology Department of Sichuan Province Project,China (Grant Nos.2022YFSY0007,2021YFH0010),the National Scientific Science Foundation of China (Grant No.U20A20266).