EFFECTS OF CYCLIC LOADING ON MECHANICAL · PDF file92 Effect of Cyclic Loading on Mechanical...

Suranaree J. Sci. Technol. 16(2):91-102

Geomechanics Research Unit, Institute of Engineering, Suranaree University of Technology, MuangDistrict, Nakhon Ratchasima 30000 Thailand. Tel.: 66-44-224-443; Fax.: 66-44-224-448; E-mail:[email protected]

* Corresponding author

EFFECTS OF CYCLIC LOADING ON MECHANICALPROPERTIES OF MAHA SARAKHAM SALT

Kittitep Fuenkajorn* and Decho PhueakphumReceived: Jan 22, 2009; Revised: Apr 22, 2009; Accepted: Apr 29, 2009

Abstract

Series of laboratory testing have been performed to assess the effects of cyclic loading on compressivestrength, elasticity and time-dependency of the Maha Sarakham rock salt. Results from the cyclic loadingtests indicate that the salt compressive strength decreases with increasing number of loading cycles,which can be best represented by a power equation. The salt elastic modulus decreases slightly duringthe first few cycles, and tends to remain constant until failure. It seems to be independent of the maximumloads within the range used here. Axial strain-time curves compiled from loci of the maximum load ofeach cycle apparently show a time-dependent behavior similar to that of creep tests under static loading.In the steady-state creep phase, the visco-plastic coefficients calculated from the cyclic loading test areabout an order of magnitude lower than those under static loading. The salt visco-plasticity also decreaseswith increasing loading frequency. Surface subsidence and cavern closure simulated using parameterscalibrated from cyclic loading test results are about 40% greater than those from the static loadingresults. This suggests that application of the property parameters obtained from the conventional staticloading creep test to assess the long-term stability of storage caverns in salt with internal pressurefluctuation may not be conservative.

Keywords: Fatigue, creep, elasticity, strength, viscosity, salt

Introduction

Rock salt around storage caverns will be subjectto cycles of loading due to the fluctuation ofcavern pressures during product injection andretrieval periods. Depending on the types ofstored products (e.g. petroleum, liquefied gasor compressed-air) and on the designed operatingschemes, the injection-withdrawal durations canrange from daily to annual, and the minimumand maximum cavern pressures can be as low

as 20% and as high as 90% of the in-situ stressesat the casing shoe (cavern top). Due to thecomplexity of cavern ground geometry and theneed to predict the future stability conditions(normally up to a few decades), the stabilityand operating pressures of the salt cavernshave commonly been analyzed and designed vianumerical modeling capable of handling time-dependent constitutive equations. A difficulty

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92 Effect of Cyclic Loading on Mechanical Properties of Salt

may arise in determining the representativeproperties of the salt under such cyclic loadingstates. Since the salt properties are loadingpath dependent (non-linear), the laboratorydetermined properties under static loads (ascommonly practiced) may not truly representthe actual in-situ salt behavior under cyclicloading.

The effect of cyclic loading on theelasticity and strengths of geologic materialshas long been recognized (Haimson, 1974;Allemandou and Dusseault, 1996; Bagde andPetros, 2005). A common goal of their studiesis to determine the fatigue strength of thematerials. It has been found that loading cyclescan reduce the material strength and elasticity,depending on the loading amplitude and themaximum applied load in each cycle (Zhenyuand Haihong, 1990; Singh et al., 1994; Rayet al., 1999; Kodama et al., 2000). Rareinvestigation has, however, been made toidentify the cyclic loading effect on the time-dependent properties and behavior of soft andcreeping materials such as salt.

The objective of this research is todetermine experimentally the effects of cyclicloading on compressive strength, elasticity,visco-elasticity and visco-plasticity of rock saltfrom the Maha Sarakham formation. The effortsprimarily involve mechanical characterizationtesting, creep testing and compression testingunder static and cyclic loads. Finite elementanalyses are performed to demonstrate theimpact of cyclic loading on the deformation ofsalt around a compressed-air storage cavern.

Rock Salt Specimens

The specimens tested here were obtained fromthe Lower Salt members of the Maha Sarakhamformation in the Sakhon Nakhon basin,northeastern Thailand. This salt unit is beingconsidered as a host rock for compressed-airenergy storage by the Thai Department ofEnergy. The rock salt is relatively pure halitewith a slight amount (less than 1-2%) ofanhydrite, clay minerals and ferrous oxide. The

average crystal (grain) size is about 5 � 5 � 10

mm. Warren (1999) gives detailed descriptions

of the salt and geology of the basin. The corespecimens with a nominal diameter of 60 mmtested here were drilled from depths rangingbetween 250 and 400 m.

Sample preparation followed the ASTMD4543 standard practice, as much as practical.Twenty-four specimens (L/D = 2.5) wereprepared for uniaxial compression tests, 76specimens (L/D of 0.5) for Brazilian tensiontests, 14 specimens (L/D = 2.5) for cyclicloading tests, and 10 specimens (L/D = 2.5)for uniaxial creep tests. The samples were cutand ground using saturated brine as lubricant.After preparation, the specimens were labeledand wrapped with plastic film. The specimendesignation was identified. Prior to mechanicaltesting, visual examination was made todetermine the type and amount of inclusions.

Characterization Testing

Uniaxial and triaxial compression and Braziliantension tests were conducted to obtain data forthe Maha Sarakham salt, and to determine thetest parameters for the subsequent creep andcyclic loading tests. The test procedure followedrelevant ASTM standard practices (ASTMD3967 and D7012). The elastic modulus(measured from unloading curves) of the salt is25.2 ± 1.9 GPa and the Poisson’s ratio is 0.37 ±0.11. The uniaxial compressive and Braziliantensile strengths are 34.7 ± 2.2 MPa and 1.5 ±0.4 MPa. Figure 1 shows the stress-strain curvesmonitored during the tests. The triaxial compres-sive strength tests use confining pressuresbetween 5.5 and 19.3 MPa. Based on theCoulomb criterion the internal friction angle iscalculated as 39 degrees and the cohesion as15 MPa (Figure 2). The Maha Sarakham saltstrengths and elasticity obtained here agreereasonably well with those obtained elsewhere(e.g., Hansen et al., 1984).

Creep Testing

Short- and long-term uniaxial creep tests wereperformed to determine the time-dependentproperties of the salt under isothermalcondition. The test procedure followed the

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93Suranaree J. Sci. Technol. Vol. 16 No. 2; April - June 2009

ASTM D7070-08 standard practice. For theshort-term testing, the applied constant axialstresses are relatively high, varying from 10 to30 MPa with the maximum test duration of 7hours. For the long-term testing, the appliedstresses vary from 7.8 to 12.6 MPa with themaximum test duration up to 30 days. Theshort-term test results are used to calibrate thevisco-elastic parameters, and the long-termresults calibrate the visco-plastic coefficient ofthe salt. Figures 3 and 4 plot the axial strain as a

function of time for the short- and long-termtesting.

Cyclic Loading Testing

A series of uniaxial cyclic loading tests wereperformed on the 60 mm diameter salt corespecimens using a servo-controlled universaltesting machine (Figure 5). The maximum axialstresses vary among sp ecimens from 15.9 MPato 34.6 MPa (about 40% to 100% of the

Figure 2. Mohr’s circles and Coulomb criterionrepresenting triaxial compressivestrengths of Maha Sarakham Salt

Figure 1. Results of uniaxial compressivestrength testing. Numbers indicatestress at failure

Figure 3. Results of the short-term uniaxialcreep tests

Figure 4. Results of the long-term uniaxialcreep tests

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Figure 5. Salt specimen placed in the Universal Testing Machine (model FastTrack 8800,Instron Company) for uniaxial cyclic loading test

Figure 6. Examples of cyclic loading test results for loading frequency of 0.03 Hz. Axialstress (σσσσσ1) plotted as a function of axial strain (εεεεε1). We can not explain why themachine records the decrease of axial strain in the first cycle

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compressive strength) while the minimum stresswas maintained constant at 0.15 MPa for allspecimens. This small minimum stress isrequired to ensure that the ends of the specimenremain in contact with the loading platensduring the test. The loading frequencies rangefrom 0.001 Hz to 0.03 Hz. The accumulatedaxial strain, fatigue stress (S) and time weremonitored during loading. Some examples ofaxial stress-strain curves measured duringloading are given in Figure 6. Figure 7 showsthe decrease of the failure (fatigue) stress as thenumber of loading cycle (N) increases, whichcan be represented by a power equation: S =32.33 N(-0.07). The behavior is similar to thoseobtained elsewhere for other geologic materials(Costin and Holcomb, 1981; Thoms and Gehle,1982; Passaris, 1982; Bagde and Petros, 2004,2005).

Figure 8 shows the axial strain-timecurves compiled from loci of the loading cycles.

The curves apparently show the transient,steady-state and tertiary creep phases which aresimilar to those obtained from the static creeptesting. It is understood here that the transitionpoint at which the strain rate changes from thesteady-state phase (constant volume) to tertiary(volume increase) phase is corresponding to thedilation strength of the salt (DeVries et al.,2003). The loading cycles also exponentiallydecrease the dilation strength of the salt, asshown in Figure 7.

For each specimen, the elastic modulusvalues calculated from the series of unloadingcurves are plotted as a function of loading cyclesin Figure 9. For all stress levels, the salt elasticityexponentially decreases as the number ofloading cycles increases, and nearly remainsconstant after about 50 to 100 cycles. Thecalculated elastic modulus values range from20 GPa to 35 GPa. They, however, tend to beindependent of the applied maximum loads used

Figure 9. Elastic modulus, E (top) and normalized elastic modulus, E/E0 (bottom) plotted asa function of number of loading cycles (N) up to failure

Figure 8. Axial strain-time curves fromuniaxial cyclic loading tests

Figure 7. Fatigue strength (S) plotted as afunction of numbers of loadingcycles at failure (N) and at dilation(ND)

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here, as also evidenced by the normalizedelastics modulus (E/E0) as a function of N inFigure 9, where E0 is the modulus measuredduring the first loading cycle.

Salt Property Calibration

To assess the effect of cyclic loading on thetime-dependent properties of salt, a simplerheological creep model is used to describe theconstitutive behavior of the salt underisothermal condition. The modular componentsof the creep model are given in Figure 10. It iswell recognized that several other constitutivemodels have been developed for describing thesalt behavior (Jaeger and Cook, 1979). Someare very sophisticated and capable of handlingcomplex thermo-mechanical behavior. Themodel used here, however, is simpler, and yetcapable of disclosing the impacts of cyclicloading separately for the visco-elastic andthe visco-plastic modes. It is probably morepractical to analyze the problem underisothermal conditions. In Figure 10, G1 and K1

are shear and bulk modulus; G2 and K2 are shearand bulk modulus in visco-elastic mode; andη2 and η4 are visco-elastic and visco-plasticcoefficients. These elastic and time-dependentparameters can be calibrated from thelaboratory test results using a regressionanalysis (Fuenkajorn and Serata, 1992, 1994;Serata and Fuenkajorn, 1992).

The constitutive model separates thestress tensors into deviatoric (σ ij) andvolumetric (σmδij) parts. These are related tothe strain tensors, εij (deviatoric) and σmδij

(volumetric) through the rheological formsshown in Figure 10. The detailed constitutiverelations are given by Serata et al. (1989) andSerata and Fuenkajorn (1992). The relations inelastic and visco-elastic states are as follows:

(1)

(2)

where and are the time derivatives ofthe respective deviatoric stresses and strains(stress and strain rates).

When the octahedral shear stress (τo)exceeds the octahedral shear strength (Ko),the viscoplastic behaviour can be described by:

(3)

Here, and represent the second timederivatives of the tensors and . Theoctahedral shear strength (Ko) is defined as:

(4)

where α is a yield surface coefficient and KA

and KB are an unconfined octahedral shearstrength and ultimate octahedral shear strength,C is the strain-softening coefficient varyingfrom 0 to 1, γo is the induced octahedral shearstrain, γc is the critical octahedral shearstrain, and P is the plastic transition pressure.These parameters can be obtained from theregression of the laboratory test results. Table 1summarizes the results obtained from the

Figure 10. Modular representation ofconstitutive equations used hereto describe the time-dependentbehavior of salt (modified fromFuenkajorn and Serata, 1994)

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regression analysis.The visco-plastic coefficients calculated

for both creep and cyclic loading tests is plottedas a function of the applied stress (calculatedin terms of the octahedral shear stress, τoct) inFigure 11. The visco-plastic coefficientsobtained from the creep testing are about 1-2orders of magnitude higher than those fromthe cyclic loading. They decrease exponentiallyas the applied stresses increase, which can bebest represented by: η4 = A.exp [B.τoct], whereA and B are empirical constants.

A higher loading frequency results in alower visco-plasticity of the salt. The constantA depends on the loading frequency (f)which can be determined from: A = 25.2 f (-0.18).The exponent B tends to be constant at 0.7,independent of the loading frequency range

used here (Table 2). By substituting the loadingfrequency equivalent to daily cycle (f = 11.6 �10-6 Hz) into this equation, the constant A forthe daily cycle operation can be calculated as190 GPa.day, and the visco-plastic coefficient(η4) becomes 1.8 GPa.day.

The axial strain-time curves obtained fromthe cyclic loading (as shown in Figure 8) alsoyield the critical octahedral shear strain (γc)for the salt. These strains correspond tothe transition point from plastic creep (novolume change) in steady-state phase todilation (volume increase) in the tertiaryphase. The critical shear strain decreasesexponentially with increasing octahedralshear stress. Figure 12 plots the measured γc

as a function of τoct, and shows their empiricalrelation.

Table 1. Visco-elastic and visco-plastic coefficients obtained from creep and cyclic loadingtests

Test σσσσσ1 τττττoct σσσσσmean ηηηηη2 ηηηηη4

methods (MPa) (MPa) (MPa) (GPa.day) (GPa.day)

7.8 3.7 2.6 1.200 29.1009.9 4.7 3.3 0.300 8.800

10.2 4.8 3.4 1.000 8.70011.2 5.3 3.7 1.000 8.900

Uniaxial creep test 11.4 5.4 3.8 0.700 7.4004.1 1.9 1.4 - 83.307.1 3.3 2.4 - 53.409.1 4.3 3.0 - 16.60

11.1 5.2 3.7 - 12.1014.1 6.6 4.7 - 3.500

20.0 9.4 6.7 0.011 0.06421.4 10.1 7.1 0.010 0.041

Cyclic loading test 23.0 10.8 7.7 0.006 0.022(f = 0.03 Hz) 24.3 11.5 8.1 0.003 0.015

24.9 11.7 8.3 0.003 0.01228.1 13.2 9.4 0.001 0.00530.0 14.1 10.0 - 0.002

16.0 7.5 5.3 - 0.355Cyclic loading test 21.6 10.2 7.2 - 0.075

(f = 0.001 Hz) 23.0 10.8 7.7 - 0.05327.0 12.7 9.0 - 0.01029.0 13.7 9.7 - 0.005

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Numerical Simulation

A finite element analysis with the creep modelabove is performed to demonstrate the impactof cyclic loading on the salt behavior around acompressed-air storage cavern subjecting todaily cycles of pressure injection and retrieval.For this example, the cavern is an uprightcylinder with a diameter of 50 m. The top andbottom of the cavern are at 500 m and 700 mdepths. Figure 13 shows the finite element meshfor this example. The analysis is made in axialsymmetry. The storage cavern model is subjectto a maximum pressure of 80% (8.1 MPa) anda minimum pressure of 20% (2.0 MPa) of thein-situ stress at the cavern top. Two sets ofproperty parameters are used, one calibratedfrom static loading tests, the other from cyclic

loading tests. Table 3 summarizes the keyparameters used in the simulations. Thevisco-plastic coefficient for the loadingfrequency equivalent to the daily cycle is usedin the simulations. Since the long-term creepdeformation of the storage cavern is theprimary concern, the effect of loading frequencyon the short-term properties (elastic andvisco-elastic parameters) are not considered inthe simulations. As a result, G1, K1, G2, K2, andη2 are assumed to be independent of theloading frequency. The elastic and visco-elasticparameters as listed in Table 3 represent theaverage of the values calibrated from the testresults. Both simulations assume a constantcavern pressure of 5.1 MPa which is averagedfrom the maximum and minimum storagepressures. The surface subsidence and cavern

Viscosity coefficients Loading A Bfrequency,

f (Hz)

Uniaxial Creep Test (UCT):- Visco-plasticity (η4) 0.19 × 10-6 382 -0.72

Uniaxial Cyclic Loading Test (CLT):- Visco-plasticity (η4): 0.001 87 -0.71- Visco-plasticity (η4): 0.030 46 -0.70

Table 2. Constants A and B for empirical equation: ηηηηη4 = A.exp [B.τττττoct]

Figure 12. Octahedral shear strain (γγγγγc) as afunction of octahedral shearstress(τττττoct) determined from cyclicloading tests

Figure 11. Visco-plasticity (ηηηηη4) as a functionof octahedral shear stress (τττττoct)obtained from creep tests (UCT)and cyclic loading tests (CLT)

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Table 3. Summary of property parameters used in numerical simulation

Key properties Static loading Cyclic loading

Elastic Parameters

Elastic Modulus, E (MPa) 25.20 25.200

Poisson’s Ratio, ν 0.37 0.370

Shear Modulus, G1 (GPa) 10.20 10.200

Bulk Modulus, K1 (GPa) 39.20 39.200

Visco-elastic Parameters

Visco-elastic Shear Modulus, G2 (GPa) 1.00 0.800

Visco-elastic Bulk Modulus, K2 (GPa) 3.80 2.900

Visco-elastic Coefficient, η2 (GPa.day) 0.50 0.007

Visco-plastic Parameter

Visco-elastic Plastic Coefficient, η4 (GPa.day) 3.40 1.800

(calculated for

daily cycle)

Critical Octahedral Shear Strain, γc (× 10-3) 5.00 2.000

closure induced by daily air injection-retrievalcycles during 12 months are calculated forthe two cases.

Figure 14 shows the surface subsidence(above the center of the cavern) and cavernclosure computed as a function of time during12 months of the operation. The simulationusing property parameters calibrated from thecyclic loading results shows subsidence andcavern closure of nearly twice that using thestatic loading results. The closure rate predictedfrom using cyclic loading parameters is higherthan that from static loading parameters. Thissuggests that parameters derived from staticloading may not be conservative for use in thesimulation of salt storage caverns that aresubject to repeated change of the internalpressure.

Discussions and Conclusions

The uniaxial cyclic loading tests as conductedhere not only provide the fatigue stress andcomplete strain-time curves of the salt, but also

reveal the dilation strength and critical shearstrain of the rock. These parameters can not beeasily obtained from the conventional testmethods (i.e., the compressive strength test andcreep test). The fatigue stress can help definethe operational life of storage caverns in salt,which depends also on the loading cycles andthe loading amplitudes (difference between themaximum and minimum storage pressures). Thecreep (viscosity) parameters are necessary todetermine the time-dependent deformation ofthe surrounding salt. The critical strain anddilation strength define the maximumdeformation before dilation strain or acceleratedcreep rate occurs under a given shear stress. Thisis useful for the design of the safe minimuminternal pressure for a gas or compressed-airstorage cavern in salt.

Under the test parameters used here, thecyclic loading can decrease the salt strength byup to 30%, depending on the maximum appliedload and the number of loading cycles. Theeffect of loading frequency on the salt strengthappears to be small as compared to the impacts

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from the magnitudes of the maximum load andthe loading amplitude. By using a simpleisothermal creep model, the visco-elastic andvisco-plastic coefficients of the salt can bedetermined from the static and the cyclicloading test results. Both parameters decreaseexponentially with increasing applied octahedralshear stress. They also decrease with increasingloading frequency. The results from storagecavern simulations suggest that the propertyparameters obtained from the static (creep)tests can under-estimate the cavern deformationand surface subsidence as compared to thosefrom the cyclic loading tests. This could lead toa non-conservative cavern design and stabilityanalysis. The effect of loading frequency on theelastic modulus of the salt can not be detectedhere. This is probably because of the narrowrange of the tested frequencies or the intrinsicvariability among the salt specimens, or both.

Acknowledgment

This research is funded by Suranaree Universityof Technology. Permission to publish this paperis gratefully acknowledged.

References

Allemandou, X. and Dusseault, M.B. (1996).Procedures for cyclic creep testing ofsalt rock, results and discussions.Proceedings of the 3rd Conference on theMechanical Behavior of Salt; Sept 14-16,1993; Clausthal-Zellerfeld, Trans TechPublications, p. 207-218.

ASTM D3967-86. Standard test method forsplitting tensile strength of intact rock corespecimens. In: Annual Book of ASTMStandards, American Standard Society forTesting and Materials, Philadelphia, PA.04.08.

Figure 13. Finite element mesh constructedto simulate an example of storagecavern in salt

Figure 14. Surface subsidence (top) andcavern closure (bottom) usingparameters from static and cyclicloading

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ASTM D4543-08. Standard practice forpreparing rock core specimens anddetermining dimensional and shapetolerances. In: Annual Book of ASTMStandards, American Standard Societyfor Testing and Materials, WestConshohocken, PA, 04.08.

ASTM D7012-07. Compressive strength andelastic moduli of intact rock corespecimens under varying states of stressand temperatures. In: Annual Book ofASTM Standards, American StandardSociety for Testing and Materials, WestConshohocken, PA, 04.08.

ASTM D7070-08. Creep of rock core underconstant stress and temperature. In:Annual Book of ASTM Standards,American Standard Society for Testingand Materials, West Conshohocken, PA,04.08.

Bagde M.N. and Petros, V. (2004). Experimentalinvestigation into fatigue behaviour ofintact sandstone and conglomerate rocktypes in uniaxial dynamic cyclic loading.Geophysical Research Abstracts, 6:07240.

Bagde, M.N. and Petros, V. (2005). Fatigueproperties of intact sandstone samplessubjected to dynamic uniaxial cyclicalloading. International Journal of RockMechanics and Mining Sciences, 42(2):237-250.

Costin, L.S. and Holcomb, D.J. (1981). Time-dependent failure of rock under cyclicloading. Tectonophysics, 79(3-4):279-296.

DeVries, K.L., Mellegard, K.D., and Callahan,G.D. (2003). Laboratory testing in supportof a bedded salt failure criterion. SMRI:Fall 2003 meting, 5-8 October 2003,Chester, United Kingdom, England.

Fuenkajorn, K. and Serata, S. (1992).Geohydrological Integrity of CAES inRock Salt,” Compressed-Air EnergyStorage: Proceedings of the SecondInternational Conference, Electric PowerResearch Institute, San Francisco, CA,July 7-9, 1992, p. 4.1-4.21.

Fuenkajorn, K. and Serata, S. (1994). Dilation-induced permeability increase aroundcaverns in rock salt. Proceedings of the1st North American Rock MechanicsSymposium; Jun 1-3, 1994; University ofTexas at Austin, A.A Balkema, Rotterdam,p. 648-656.

Haimson, B.C. (1974). Mechanical behavior ofrock under cyclic loading. Proceedingsof the 3rd Congress of the InternationalSociety for Rock Mechanics, Part A.Advances in Rock Mechanics: Reportof Current Research; Sept 1-7, 1974;Denver, National Academy of Sciences,Washington, D.C., p. 373-387.

Hansen, F.D., Mellegard, K.D., and Senseny,P.E. (1984). Elasticity and strength often natural rock salts. Proceeding ofthe 1st Conference on the MechanicalBehavior of Salt; Nov 9-11, 1981; ThePennsylvania State University, TransTech Publications: Clausthal Germany, p.71-83.

Jaeger, J.C. and Cook, N.G.W. (1979). Funda-mentals of Rock Mechanics. 3rd ed.Chapman and Hall, London, 475p.

Kodama, J., Ishizuka, Y., Abe, T., Ishijima, Y.,and Goto, T. (2000). Estimate of thefatigue strength of granite subjected tolong-period cyclic loading. Shigen-to-Sozai, 116:111-118.

Passaris, E.K.S. (1982). Fatigue characteristicsof rock salt with reference to undergroundstorage caverns. Proceedings ISRMSymposium on Rock Mechanics: Cavernsand Pressure Shafts; May 26-28, 1982;Aachen, Germany, Taylor & FrancisGroup, p. 983-989.

Ray, S.K., Sarkar, M., and Singh, T.N. (1999).Effect of cyclic loading and strain rate onthe mechanical behaviour of sandstone.Int. J. Rock Mech. Min. Sci., 6(4):543-549.

Serata, S. and Fuenkajorn, K. (1992). Formulationof a constitutive equation for salt.Proceedings of the Seventh InternationalSymposium on Salt; April 6-9, 1992;Kyoto, Japan, Elsevier Science Publishers,

_09-1003(091-102)Part-2.pmd 15/8/2552, 13:17101


p. 483-488.Serata S., Mehta, B., and Hiremath, M. (1989).

Geomechanical stability analysis forCAES cavern operation. Proceedings ofthe International Conference on Storageof Gases in Rock Caverns; June 26-28,1989; Trondheim, Norway, Rotterdam,p.129-136.

Singh, T.N., Ray, S.K., and Singh, D.P. (1994).Effect of uniaxial cyclic compression onthe mechanical behaviour of rocks. IndianJ. Eng. Mater. Sci., 1(2):118-120.

Thoms, R.L. and Gehle, R. (1982). Experimental

study of rock salt for compressed airenergy storage. Proceedings ISRMSymposium on Rock Mechanics: Cavernsand Pressure Shafts; May 26-28, 1982;Aachen, Germany, Taylor & FrancisGroup, p. 991-1002.

Warren, J. (1999). Evaporites: Their Evolutionand Economics. Blackwell Science,Oxford, 438p.

Zhenyu, T. and Haihong, M. (1990). Anexperimental study and analysis of thebehaviour of rock under cyclic loading.Int. J. Rock Mech. Min. Sci., 27(1):51-56.

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