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Technical Note Effect of strain rate on the mechanical properties of salt rock W G Liang a n Y S Zhaoa S G Xua M B Dusseaultb aMining Technology Institute Taiyuan University of Technology Taiyuan Shanxi 030024 China bEarth and Environmental Sciences Department University of Waterloo Waterloo Ontario Canada N2L 3G1 a r t i c l e i n f o Article history Received 19 December 2009 Received in revised form 24 April 2010 Accepted 15 June 2010 Available online 1 July 2010 1 Introduction Salt rock is a special material in rock engineering With its physical properties of tight fabric and low permeability as well as its mechanical properties of low strength and ductility it has become a favored medium for waste disposal and oil and gas storage since early in the last century when it began to be thoroughly studied More recently achievements documented in the six conferences on the mechanical behavior of salt since 1984 and other publications have greatly increased knowledge of salt rock behavior As the strength of salt rock is somewhat low generally the loading rate for compression tests is also slow However loading strain rate e affects the mechanical properties of the salt rock Studies have been carried out on many different rock types examining the effect of eon rock strength and deformation characteristics For example eeffects on dynamic tensile strength of Inada granite and Tage tuff were studied by Cho et al 1 loading evalues for the granite and the tuff were 4 24 13 18 and 0 46 6 82 s respectively It was found that the dynamic tensile strength of the two rock types increased rapidly with e After studying the porosity change of Mugla marble by heat treatment compressiontestsunder evaluesof2 10 5 5 10 7 s were conducted by Mahmutoglu 2 It was found that the compressive strength decreased sharply with strain rate decrease For dry specimens the percentage of the strength decrease is about 44 whereas the relative strength decrease for saturated specimens is much larger It was suggested by Qi et al 3 that the deformation and failure of rock under low strain rates were controlled mainly by thermally activated mechanisms With strain rate increases a phonon damping mechanism appears and gradually plays a dominant role in the deformation process Li and Wang 4 studied the fracture toughness of marble under high loading rates using the Hopkinson bar method and found that the toughness increased signifi cantly with the loading rate Yang et al 5 carried out tests on limestone under different loading rates and found that the peak strength increased with the loading rate at the same time the strain at peak strength increased linearly with strain rate He also found that the failure mode of the rock seldom changed with the loading rate There are also many other studies 6 13 of the strain rate effect on mechanical properties of rocks however reports of strain rate effects on mechanical properties of salt rock are less well documented To investigate this in the laboratory we conducted uniaxial compression tests on salt rock including halite and thenardite under loading evalues of 2 10 5 2 10 4 and 2 10 3 s These results were generated as part of a more general investigation of the performance of gas storage operations in salt caverns 2 Sampling and methodology 2 1 Samples In this paper rock salt refers to rock with a dominant mineral component of halite NaCl whereas salt rock is a more general designation for all rocks with a dominant mineral component of highly soluble salts generally of evaporitic origin including NaCl KCl carnallite bischofi te tachyhydrite thenar dite mirabilite glauberite anhydrite and so on Samples were cored from two evaporite deposits in Jiangsu Province China The evaporites are saline lake sediments of Tertiary age One type of lithology is rock salt halite with the major deposit located 900 1100 m deep the other salt rock lithology is dominated by the mineral thenardite Na2SO4 sodium sulfate and is buried about 2000 m deep Both are of evaporative crystallization origin and have the desired properties Contents lists available at ScienceDirect journal homepage International Journal of Rock Mechanics however the thenardite samples were pure and homogeneous Samples were transported to the Taiyuan University of Technology TYUT laboratory after careful packaging In the laboratory samples were processed according to ISRM suggested methods Nine cylindrical specimens with aspect ratios of 2 1 were eventually prepared eight of which were successfully tested six rock salt specimens and two thenardite specimens For the six rock salt specimens uniaxial compression tests with three different loading rates were conducted while the two thenardite specimens were tested with two lower loading rates Generally 3 5 specimens are suggested to be prepared for each test to guarantee reliability but we were hampered by a lack of acceptable quality core To compare loading rate differences with the limited specimen set only two specimens for each test could realistically be assigned The reason we nevertheless choose to present our test results here is that they were found to be reasonably consistent and hence are likely to be reliable 2 2 Test and equipment The main purpose of the test was to study the loading rate effect on mechanical properties of salt rock during uniaxial compression All the experiments were performed on servo controlled mechan ical test equipment TYT 600 Fig 1 manufactured by Jilin Jinli Test Technology Co Ltd Changchun China The maximum load capacity of the frame is 6 0 104kg the minimum displacement rate is 1 0 10 3mm s and loading rates can be varied with the servo control system 2 3 Methodology For the experiment three uniaxial compression displacement rates were chosen leading to evalues of 2 0 10 5 2 0 10 4 and 2 0 10 3 s a factor of 100 As mentioned before two each of the six rock salt specimens were assigned to be tested under one loading strain rate and the two thenardite specimens were tested under the two lower strain rates of 2 0 10 5and 2 0 10 4 s FollowingISRMsuggestedmethods 14 the uniaxial compression tests for each strain rate were carried out on the same mechanical test equipment 3 Experimental results The uniaxial compression test results with different strain rates are listed in Table 1 Figs 2 6 are the resulting stress strain s e curves from the specimens during the tests It was found that the s e curves are comb shaped and that stress fl uctuations in the rock salt were observed at the lowest eof 2 0 10 5 s The two s ecurves for the specimens tested at this lowest evalue are shown in Figs 2 and 3 3 1 Relationship between strength and strain rate From Table 1 and thes ecurves it is found that the peak strength of rock salt is little affected by the strain rate within the chosen range for e Average UCS values are 13 6 13 9 and 12 4 MPa respectively for evalues of 2 0 10 5to 2 0 10 4 and 2 0 10 3 s Also the UCS of the tested rock salt is consistently lower than that of ten natural rock salts in the U S A 15 We believe the reason for the lower strength is that the Jiangsu salt deposits were formed in a different style and at a different geologic time Most salt deposits in North America were formed in the Jurassic Permian or Devonian periods some bedded salts have been recrystallized and salt from salt domes has undergone extensive recrystallization deformation and porosity reduction domal salts are less porous than bedded salts and older salts are less porous than younger salts in general The salt deposits in Jiangsu China were salt lake deposits formed in the Tertiary Eocene and have not undergone repeated recrystallization orlargescalecreepdeformationassociatedwithtectonic mobilization or diapirism All things being equal salt from a younger deposit should be somewhat weaker and less rigid than salt from an older deposit However the strain rate effect on the salt strength is similar to that reported by Farmer and Gilbert 16 at evalues of 5 0 10 3and 2 0 10 4 s where they also report that thes e curves for their rock salt under confi ning stresses of 3 5 7 14 35 42 MPa were quite similar This is an aspect of rock salt behavior that is substantially different Oil supplying system Data collection and controlling center Uplifting and descending platform Tested specimen Test equipment frame Fig 1 Schematic diagram of the test equipment W G Liang et al International Journal of Rock Mechanics if the loading rate was increased by an order of magnitude the apparent cohesion increased by 6 1 and this ratio was about the same for the UCS uniaxial tensile strength indirecttensilestrength andfracturetoughness Similarly Jeong et al 12 note that the UCS of Kumamoto andesiteincreasedlinearlywithdecreasingwatervapor pressure for the same eand with increasing ein the range 0 95 10 6 1 91 10 4 s Li et al 13 conducted dynamic triaxial compression tests for the Bukit Timah granite with four strain rates 10 4 s 10 3 s 10 1 s 100 s and six confi ning pressures It was concluded that the compressive strength generally increases with increasing strain rate and confi ning stress Also the rate of increase of compressive strength with strain rate is lower at higher confi ning pressure The e effect can be explained by energy theory Damage of material is the result of development of through going micro fractures and during a short but rapid loading process with a large e the development of micro fractures in the material lags the increment of loading This means that the response and deformation speed of grains in the material is slower than the faster loading rate just as we note with deformation hysteresis when we compare rock response with the rate of load decrease during the unloading process of a compressed material Because Table 1 Experimental results for the tested specimens SpecimenLoading rate s Ultimate strength MPa Elastic modulus GPa Poisson s ratioDeformation modulus GPa Stress of volume expanding MPa Lithology 12 0 10 513 273 540 150 9712 75Rock salt 22 0 10 513 831 70 220 8912 59Rock salt 32 0 10 415 363 420 281 9010 02Rock salt 42 0 10 412 492 590 241 099 19Rock salt 52 0 10 312 404 540 142 3811 6Rock salt 62 0 10 312 292 280 181 4512 24Rock salt 72 0 10 515 2615 20 30 12 82Thenardite 82 0 10 414 694 610 19 14 45Thenardite 0 2 4 6 8 10 12 14 00 511 522 5 Axial strain Stress MPa Peak strength 13 27MPa Plastic deformation Fig 2 Stress strain curve of halite with loading eof 2 0 10 5 s specimen 1 0 2 4 6 8 10 12 14 16 00 511 522 53 Stress MPa Peak strength 13 83MPa Plastic deformation Axial strain Fig 3 Stress strain curve of halite with loading eof 2 0 10 5 s specimen 2 0 2 4 6 8 10 12 14 16 18 00 511 522 5 Axial strain Stress MPa 3 4 Peak strength 15 36MPa Peak strength 12 49MPa Plastic deformation Fig 4 Stress strain curve of halite with loading eof 2 0 10 4 s 0 2 4 6 8 10 12 14 00 511 522 5 Axial strain Stress MPa 5 6 Peak strength 12 40MPa Peak strength 12 29MPa Plastic deformation Fig 5 Stress strain curve of halite with loading eof 2 0 10 3 s W G Liang et al International Journal of Rock Mechanics these are important factors affecting the UCS Finally the thenardite was buried 1000 m deeper than the rock salt and was thus more compressed i e lower porosity and hence stronger 3 2 Relationship between deformation failure and strain rate The strain rate also has an evident relationship to the strain to failure of the rock salt with an increasing evalue the strain at peak strength is less For example the strain to failure is 1 3 1 7 specimens 1 2 when e 2 0 10 5 s however it decreases to 0 3 0 7 specimens 5 6 when eis increased to 2 0 10 3 s If we defi ne a normalized secant deformation modulus E0as the value of axial strain at the point of peak strength divided by the peak strength then on average E0 0 93 1 50 and 1 92 GPa for the three progressively more rapid evalues Obviously the deformation modulus is increasing with ein a manner similar to the elastic modulus However the deformation modulus increment with strain rate increase is larger than that of the elastic modulus The deformation modulus increases by 52 and 28 with eincreasing from 2 0 10 5to 2 0 10 3 s whereas elastic modulus increases by 15 and 14 respectively The difference is because of plastic deformation of the specimen the more rapid the strain rate the less the plastic deformation compared to elastic deformation Empirically using a logarithmic expression to link the strain rate and deformation modulus E0 0 2ln e 3 2 This equation is sketched in Fig 8 giving a reasonable fi t over the erange used Poisson s ratio relationships are less clear nis found to decrease with strain rate with the exceptions of specimens 1 and 2 which were tested at e 2 0 10 5 s On average nin the rock salt specimens decreases from 0 26 to 0 16 as eincreases from 2 0 10 4to 2 0 10 3 s and a similar trend is found for thenardite ndecreases from 0 30 to 0 15 as eincreases from 2 0 10 5to 2 0 10 3 s As these are low values compared to 0 2 4 6 8 10 12 14 16 18 00 511 5 Axial strain Stress MPa 7 8 Peak strength 15 26MPa Peak strength 14 69MPa Plastic deformation Fig 6 Stress strain curve of thenardite under uniaxial compression loading strain rate of 7 is 2 0 10 5 s and 8 is 2 0 10 4 s Shear plane of thenardite Grains of thenardite Grains of halite Fig 7 Damaged specimens of halite and thenardite with sloughing crystal grains the left thenardite specimen damaged in the style of shearing along a relatively planar surface the right halite specimen damaged in style of brittle tensile fracture along grains W G Liang et al International Journal of Rock Mechanics for thenardite shear develops along a relatively planar surface Fig 7 The failure style difference is because of different rock fabrics the grain size of the rock salt crystallite is larger than that of the thenardite and the presence of intercrystalline silt in the rock salt weakens the bonding between adjacent halite crystals and tensile parting can happen more easily in orientations close to 901 tos3 Compared with the homogeneous thenardite with small pure grains impure rock salt breaks much more easily with a tensile brittle failure demon strated as the development of approximately columnar surfaces in the unconfi ned condition 3 3 Volume dilation stress during compression Generally the compressives ecurve of these rocks can be divided into fi ve stages Fig 9 Stage I is closing of pre existing microcracks or pore space oriented at suitable angles to the applied stress This stage is less obvious for salt rock because of its low porosity but there is usually intercrystalline extensional damage from the sampling and de stressing process Stage II is elastic and largely recoverable deformation Stage III is characterized by the onset of dilation and by a near linear increase in volume which is offset by the continuing compression It is supposed that microcrack propagation occurs in a stable manner during this stage Its upper boundary is the point of maximum compaction and zero volume change and the stress at the point of zero volume change has been called the critical stress for volume dilation it is about 80 of peak stress for most rock specimens If the stress increases continuously after the critical stress is passed stage IV characterized by positive dilation takes place with an acceleration of microcracking and the internal structure is rendered more porous and debonded until stage V the cessation of dilation occurs What we will examine here is the critical stress for volume dilation of the specimen under different strain rates It can be shown from diagrams of volumetric strain versus stress Figs 10 and 11 that the critical stress of volume dilation is different for the two groups of specimens which were compressed under e 10 4and 10 3 s respectively Forthespecimens compressed under e 10 4 s the critical stress for volume dilation is 9 6 and 8 6 MPa for specimens 3 and 4 about 63 and 69 of their peak stress However this increases to 94 and 96 for specimens 5 and 6 when eincreases to 10 3 s obviously the stress triggering fast microcrack development is less under a low strain rate than at a high strain rate This may be y 0 203Ln x 3 1909 0 0 5 1 1 5 2 2 5 00 00050 0010 00150 0020 0025 Deformation modulus GPa Strain rate s Fig 8 Deformation modulus vs loading eof specimens I II III IV V O A B C D Fig 9 Common stress strain curve of compression for rock materials 4 0 2 4 6 8 10 12 14 5 4 3 2 1012 volume strain stress MPa Critical stress Axial strain Fig 10 Volume strain and axial strain versus stress during uniaxial compression test with loading eof 2 10 4 s 6 0 2 4 6 8 10 12 14 16 5 4 3 2 1012 Volume strain Stress MPa Axial strain Critical stress Fig 11 Volume strain and axial strain versus stress during uniaxial compression test with loading eof 2 10 3 s W G Liang et al International Journal of Rock Mechanics this stress fl uctuation phenomenon persisted till the specimen underwent strain weakening This phenomenon was also noted in Ref 29 during mechan ical tests on specimens of salt rock comprised of laminated halite and non salt interlayers At e 1 10 4 s a stress drop phenomenon was observed before the axial stress reached peak value The stress drop was about 4 MPa and it was concluded that the hard brittle interlayer was suffering fracture while the halite remained intact The stress drop thus resulted from the mechan ical differences between halite and the interlayer material To explore the deformation properties at e 2 0 10 5 s we conducted supplementary tests with another three rock salt specimens unfortunately we did not have identical samples from the same salt deposit as the former specimens 1 and 2 The supplementary tests were carried out with three new specimens from the Hongze salt deposit also in Jiangsu Province but the burial depth is similar to that of the thenardite about 2000 m In the latter uniaxial compression experiment the stress fl uctua tion