HIGH-TEMPERATURE TRIAXIAL TORSIONAL CREEP ... - CiteSeerX
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Engineering and Design Design 94 94 (1986) (1986) 137-151 137-151 Nuclear Engineering North-Holland, Amsterdam
HIGH-TEMPERATURE TRIAXIAL HIGH-TEMPERATURE T R I A X I A L TORSIONAL T O R S I O N A L CREEP C R E E P TESTS T E S T S OF O F CONCRETE C O N C R E T E AT AT V A R I O U S HYGRAL H Y G R A L CONDITIONS CONDITIONS VARIOUS Z d e n S k P. BAZANT B A Z A N T * and a n d Santosh S a n t o s h PRASANNAN P R A S A N N A N ** Zdenek Geomaterials, The Technological Institute, Northwestern University. University, Evanston, IL 60201. 60201, USA USA Center for Concrete and Geomaterials, Received 8 October 1985 1985 Received
Results of an initial series of six-day creep tests under a program aimed at establishing fundamental deformation properties of concrete at high temperatures under triaxial loading with shear and various hygral conditions, both constant and transient, are n1Ported. reported. The tests are conducted in a novel novel large triaxial torsional testing machine with hygrothermal control. Tested are cylinders of six inch diameter, sealed or unsealed, loaded by compressive axial force, chamber pressure and torque. Some specimens are sealed wet, some are sealed after drying in an oven, and some are let to dry during the test. Significant is the fact that hygro-thermal differences in creep at various hygro-thermal conditions are observed. Particularly interesting is strains. The results are of interest for the formulation of changes affect not only normal creep strains but also shear creep strains. analysis of nuclear reactor accidents, radioactive waste disposal, disposal, and fire fire resistance. resistance. constitutive relations needed for the analysis
Introduction 1. Introduction Assessment of safety of concrete structures structures for Assessment nuclear reactors, reactors, as well as certain certain problems radioacnuclear problems of radioacwaste disposal, disposal, fire resistance, and and chemical techtive waste need for a better knowledge of nology vessels, pose pose the need better knowledge constitutive relation for concrete than than available at the constitutive present. Much experimental experimental research research has has bbeen e e n carried carried present. Much out to meet these needs, and and considerable considerable information information out has been been gathered gathered over the last two two decades decades has [1,8-13,15-24]. Nevertheless, certain certain rather rather serious gaps [1,8-13,15-24]. remain, especially for temperatures temperatures above 100°C. 100°C. Most Most remain, up to now now have been been limited to uniaxial comprescomprestests up and dried concrete which which has lost its pore pore water water sion and due to heating. heating. Attempts Attempts to seal the specimens specimens have due been been made, made, however, the the seals bulged bulged under under internal internal steam steam pressure, pressure, and and water water still exited exited the the specimens specimens and and collected under under the the seal. The The only only way way to keep keep pore pore water water in in the the specimen specimen is to to apply apply lateral lateral pressure pressure that that is at at least least equal equal to to the the saturation saturation steam steam pressure pressure for the the given temperature. temperature. Hence, Hence, triaxial triaxial loading loading is required required for the the basic basic tests tests at at constant constant water water content. content. Uniaxial Uniaxial stress stress response response of of the the material material at at saturation saturation water water concontent tent is a meaningless, meaningless, nonexistent nonexistent property property at at tempertemperatures 100°C. To atures over 100°C. To carry carry out out a uniaxial uniaxial test test at at * Professor of Civil Engineering and Director. ** Graduate Graduate Research Assistant.
*.
constant constant water content, content, it would in fact be necessary to apply the lateral pressure pressure only on the vapor in the surface pores and and not on the solids, which is technically impossible. Yet, in massive concrete walls, or in nonmassive concrete walls subjected subjected to rapid rapid heating heating or sealed by a steel liner, pore water water does not have sufficient time to escape prior prior to the heating heating of concrete. Finite Finite element analysis analysis reveals that that these conditions conditions are typical of many many accident accident situations. situations. Some experimental experimental information information was obtained obtained [4] for the behavior behavior of hardened paste under hardened Portland Portland cement cement paste under triaxial loading loading (without (without shear) shear) at various hygral conditions, including specimens that that are sealed wet, sealed dry, and and unsealed, unsealed, drying during during the test. However, it is unclear to to which which extent extent the the results results of these these tests, carried carried unclear out on on small small cylinders cylinders of of 15 mm mm diameter, diameter, can can be be out applied to concrete. concrete. Some Some rather rather limited limited information information applied has also been been reported reported [9,14] for the the response response of of conhas crete at biaxial biaxial stress stress and and for shear shear failure, however, crete these tests were were limited limited to temperatures temperatures under under 100°C, these 100°C, which the the drying drying rates rates are are two orders orders of of magnitude magnitude for which slower [2,3,5] [2,3,5] and and the specimen specimen retains retains most most of of its slower moisture for a considerable considerable length length of of time time even if ununmoisture sealed. sealed. Most of of the the previous previous high high temperature temperature testing testing of of Most concrete was was restricted restricted to to uniaxial uniaxial loading loading and and speciconcrete mens freely loosing loosing their their moisture moisture (e.g., Naus, Naus, 1981). 1981). mens Some limited limited data data are are available available on on triaxial triaxial loading loading Some
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Bazant. S. Prasannan / Creep tests of Ba~.ant, of concrete
without torsion, but only for dried specimens (Thelandersson. dersson, 1983; Schneider, 1982) and on the shear failure load of non homogeneously stressed notched specimens nonhomogeneously (Naus, 1981). Limited data data is also available for torsional loading alone (Illston, 1973) of mortar No mortar specimens. No data data exist for deformation under shear stress, either alone or in combination with axial stresses and pressure, and for triaxial behavior of concrete in massive (or lined) walls. In response to these needs, a testing program program concerned with the multiaxial deformation of concrete at temperatures temperatures over 100°C and various hygral conditions has been initiated at Northwestern Northwestern University, and the results of the initial test series are now reported.
Northwestern University. The machine has a test chamNorthwestern ber with a cylindrical cavity 216 mm (8.5 in.) in diameter and 686 mm (27 in.) in length. The maximum axial load is 5 MN (1.13 million Ibs), lbs), the maximum torque is 5.6 kNm kNm (50000 in. Ib), lb), and the maximum chamber pressure is 138 MPa MPa (20000 psi). The axial and torque loadings have closed-loop servocontrol. Tests can be conducted at temperatures from room to 600°C 0 (1110 F). The chamber pressurizing fluid is either water (1110°F). or gas (e.g., air or nitrogen). For a detailed description of this novel testing machine, shown in figs. 1 and 2, see ref. [7].
3. Test specimens specimens 2. Testing Testing machine The tests are conducted in a unique, large testing machine which was recently rendered operational at
The test specimens were cylinders of diameter 152 mm (6 in.) and length 305 mm (12 in.). The specimens were solid rather rather than hollow, even though torsional loading was used. A thin-wall cylinder might have been easier for evaluation, however, a wall thickness of 50
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day (fig. 7). After one day, one of the conditions is changed. For the sealed specimens, it is necessary to apply before heating a certain small confining confining pressure at least equal to the saturation vapor pressure for the given temperature (found, e.g., in ASTM Steam Tables). The effect of an increase of the confining confining pressure, resulting in a purely volumetric deformation, is observed upon increasing increasing the confining confining pressure on the second day. The axial compressive stress is superimposed on the third day and the torque is superimposed on the fourth day. Sudden environmental environmental changes are made on the fifth day, and finally, finally, on the sixth day the specimen is unloaded and creep recovery is monitored. In the present program, all stress levels were intended to remain less than about half of the failure
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P. Bazalll, L. Z.P. Ba2ant, S. S. Prasannan Prasannan // Creep Creep tests tests of of concrete concrete
values. For For torsional torsional loadings, loadings, the the axial axial load load and and the the values. confining pressure pressure were were always always such such that that the the maximum maximum confining principal stress stress would would always always be be compressive compressive and and not not principal too close close to to zero, zero, in in order order to to avoid avoid possible possible failure failure of of too the specimen specimen during during the the tests tests due due to to tensile tensile fracture. fracture. the The initial initial temperatures temperatures for for half half of of the the tests tests are are over over The 120°C, and and for for comparison comparison the the remaining remaining tests tests are are 120°C, conducted at at an an elevated elevated temperature temperature of of 65°C, 65°C~ equal equal to to conducted the temperature temperature presently presently allowed allowed by by codes codes for for nuclear nuclear the reactor vessels. vessels. For For comparison, comparison, aa room room temperature temperature reactor test is is also also carried carried ou out. t. test temperature Note that the specimens which are at a temperature of 65°C can be assumed to maintain during the short 100%; they would test period a pore humidity of almost 100%; in fact need several several years to reach hygral equilibrium with the environment. However, the specimens heated over 100°C can be assumed to lose most of their evaporable pore water content within about one or two hours, i.e., reach pore relative humidity of essentially portland 0%. This is because the pore water diffusivity of portland cement concrete increases approximately 200-times temperature passes above 100°C, as diswhen the temperature covered in 1977 [2].
5. Test results ( a - p ) shows the response response curves of axial strain strain Fig. 8 (a-p) and maximum maximum shear shear strain strain as a function of time, in the and actual time scale. Fig. 9 (a-d) ( a - d ) shows comparison comparison of the actual strains due to applied applied loads, and and fig. 10 (a-d) ( a - d ) shows strains comparisons of the strains strains caused caused by temperature temperature incomparisons For the axial normal normal strains, strains, the strains strains are crease. For plotted plotted per per unit unit stress; stress; for torsion, torsion, they are are plotted plotted as the the measured measured maximum maximum shear shear strain strain divided by by the maximum maximum shear shear stress stress as calculated calculated from the torque torque assuming assuming a linear linear stress stress distribution distribution along along the the radius. radius. Thus, Thus, the the plotted plotted response response curves represent represent the the compliance. a - d ) shows ance. Fig. 11 ((a-d) shows aa comparison comparison of of the the creep creep recovery strains strains at at the the end end of of each each test. test. The The strains strains due due to to loading loading changes changes and and to to environenvironmental mental changes changes were were determined determined graphically, graphically, exploiting exploiting the the fact that that within within aa one-day one-day interval interval other other than than the the first one one the the response response curves curves are are nearly nearly straight straight in in the the logarithmic logarithmic time time scale scale (fig. 12). 12). Thus, Thus, aa graphical graphical exextrapolation trapolation in in the the semilog semilog plot plot is quite quite reliable, reliable, and and the the effect effect of of the the change change of of environment environment or or load load can can be be determined of the the measured measured response response determined as as the the difference diffeFence of from from aa smooth smooth extrapolation extrapolation of of the the previous previous response response plotted plotted in in the the log-time log-time scale scale (fig. 12). 12). In In this this manner, manner, one of tests tests the the need need for for one can can avoid avoid for for the the present present types types of testing testing companion companion load-free load-free specimens specimens subjected subjected to to the the
same same environmental environmental history, history, in in order order to to determine determine the the difference difference between between the the two two tests. tests. The The avoidance avoidance of of comparison comparison specimens specimens improves improves the the test test results results because because this this difference difference exhibits exhibits aa large large statistical statistical scatter scatter as as the the properties properties of of aa companion companion specimen specimen are are never never the the same. same, due due to to the the random random nature nature of of the the material. material. For For some some of of the the loading loading cases, cases, two two tests tests were were run. run. These These were were the the cases cases indicated indicated by by the the diamond-shaped diamond-shaped data data points points in in figs. figs. 9, 9, 10 10 and and II. 11. These These points, points, as as well well as as their their smoothing smoothing curves, curves, represent represent the the averages averages from from two two tests. tests. The The coefficient coefficient of of variation variation for for the the measured measured values for each pair of the curves for the same load never exceeded 15%. 15%. All other data points and curves represent the results of single tests for each loading case.
6. Observations from from tests and their interpretations As we can see from fig. fig. 9a, at 120°C the axial creep strain under triaxial loading with 0, oz -- p == 0.3 I: f j (where Ie' fc ' == standard s t a n d a r d cylinder c y l i n d e r strength, s t r e n g t h , p = chamber chamber pressure, pressure, 0, oZ == axial normal stress) is larger for a specimen sealed wet than than it is for a specimen sealed dry or for an unsealed unsealed specimen immersed in water. Also, the creep rate does not seem to decrease noticeably even after 24 h of loading, while the creep rate of a sealed specimen specimen at 25°C 25°C diminishes diminishes with time (fig. 9a) (and (and is generally much much smaller). In previous tests of very small specimens specimens of hardened hardened Portland paste [4] it was established Portland cement cement paste established that that the creep nite rate of a fully dried specimen is about about 10% of that that for a fully saturated saturated specimen, at room temperature. temperature. observed only on on specimens specimens that that have This behavior behavior is observed This been dried dried to to thermodynamic thermodynamic equilibrium equilibrium prior prior to to loadloadbeen Due to to the the extremely extremely small value of of moisture moisture ing. Due of concrete concrete at at temperatures temperatures below below 100°C, diffusivity of 100°C, the state of of thermodynamic thermodynamic equilibrium equilibrium can can be achieved state within aa reasonable reasonable time time period period only only if the the specimen specimen is within extremely thin thin ( === 1 mm). mm). An An often often used used alternative alternative is to to extremely dry the the specimen specimen by by heating heating to to 105°C 105°C but but this this slightly dry alters the the microstructure. microstructure. The The decrease decrease of of the the creep creep rate rate alters at aa lower lower moisture moisture content content was was discovered discovered only only relaat recently (in (in the the 1960's) 1960's) and and came came as aa surprise. surprise. tively recently Up to to that that time time itit was was believed believed that that the the creep creep rate rate Up increases rather rather than than decreases decreases due due tto drying. However, However, increases o drying. this increase, increase, often often termed termed the the Pickett Pickett effect, is now now this known to to be be due due to to the the effect effect of of the the rate rate of of humidity humidity known change, combined combined with with the the effect effect of of distributed distributed cracking cracking change, (strain-softening, see see ref. ref. [6]). [6]). The The same same effects effects were were (strain-softening, previously found found to to be be exhibited exhibited by by very very small small cement cement previously paste specimens specimens at at temperatures temperatures over over 100°C 100°C [4]. paste
Z.P. e e p tests z.P. Ba~ant, Bazant, S. S. Prasannan Prasannan //C rCreep tests of of concrete concrete
The transient transient effect effect of of the the rate rate of of water water content content is is The rather short-lived, short-lived, due due to to the the fact fact that that moisture moisture diffudiffurather sivity increases increases about about 200-times 200-times upon upon heating heating over over sivity (2). Thus, Thus, whenever whenever heating heating starts starts over over 100°C lOOoe lOOoe [2]. 100°C before loading, loading, the the tests tests essentially essentially occur occur at at aa dried dried before is the the reason reason that that aa much much lower lower state, and and the the drying drying is state, is observed observed than than for aa sealed sealed specimen. creep rate rate is creep The comparisons between between the the sealed sealed and and unsealed unsealed The make sense, of of course, course, only only for triaxial triaxial loadloadspecimen make ing. Without Without the the confining confining chamber chamber pressure pressure itit would would ing. be impossible impossible to to prevent rupture rupture of of the the seal seal due due to to be vapor pressure and and keep the the specimen saturated. saturated. internal vapor creep (i.e., at at constant water water content) Uniaxial basic creep does not not exist above 100°C. lOO°e. does effects of of the the pore pore water water As seen from fig. 9a, the effects are similar for concrete specimens at at high temcontent are peratures, however, the magnitude of the effect is much of a fully dried smaller; the ratio of the creep rates of specimen and a fully saturated specimen is about 0.6 rather than 0.1. This reduced effect is probably caused rather by the restraining action of the aggregate in concrete, but still it is interesting that this restraining action but reduces not only the total creep rate magnitudes but also their relative values. Explanation of this phenomenon in terms of the composite nature of concrete deserves further study. The specimens (in tests 1-3) 1-3) were exposed to a 0 temperature of 120 e for 24 h before loading. Since the 120°C specimens were simultaneously simultaneously under pressure, the condition was similar to autoclaving, autoclaving, a curing process used to accelerate hydration. The analogy with autoclaving autoclaving is, however, fully fully applicable only if additional water is forced into the specimen due to external pressure, as it happens in an autoclave. Ingress of water is of course prevented when the specimen is sealed, but for unsealed specimens tested in water one must assume that water penetrates into the specimen. In such specimens, specimens, the autoclaving autoclaving effect is probably much stronger, which might explain explain 0 why specimens e specimens immersed in pressurized water at 120 120°C show a distinctly distinctly smaller creep rate than do the specimens sealed in the initial initial wet state; see fig. fig. 9a. By contrast, at lower temperature (65°e) (65°C) the creep rates of the specimens specimens sealed wet and the unsealed unsealed specimens specimens immersed immersed in water are about the same (fig. 9b). The behavior at high temperatures is again again qualitatively qualitatively similar similar to that observed previously previously on very very small small cecement paste specimens specimens (4). [4]. Rather interesting interesting is is the fact (fig. 9a) that, at least within within the the first first 24 24 hh period, period, the the creep creep rate rate at at high high temperature temperature does does not not decrease decrease significantly significantly with with the the one-day one-day duration duration while while at at room room temperature temperature itit does. does.
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Apparently, of gradual gradual Apparently, at at high high temperature temperature the the idea idea of exhaustion exhaustion of of the the sites sites of of weakened weakened bonds bonds in in the the solid solid microstructure (6) does does not not quite quite apply. apply. It It must must be be that that microstructure [6] new new sites sites of of potential potential load load ruptures ruptures are are gradually gradually genergenerated ated by by the the creep creep deformation. deformation. Thus, Thus, at at high high temperatemperatures, tures, creep creep might might be be better better d~scribed d~scribed as as aa viscous viscous deformation. deformation. Progressive Progressive microcracking microcracking might might also also play play role. aa role. The of aa specimen sealed sealed wet wet and and tested tested The axial axial creep creep of at at 65°C 65°e is is seen to to be be lower lower (fig. (fig. 9b) 9b) than than itit is is at at 120°C, 120 0 e, but but the the creep creep of of an an unsealed unsealed specimen in in water water under under triaxial loading shows the opposite opposite behavior, i.e., it is greater greater at at 65°C 65°e than it is at at 120°C 120 0 e (figs. 9a,b). Furthermore, the creep creep of of an an unsealed specimen in water water at at 65°C 65°e under uniaxial loading is greater greater than that that of of a specimen under triaxial loading, aOzz -- pP being the same. The difference seems to be too large to be attributed to the creep due to confining pressure, which means that that linear superposition might not be applicable. Note of a sealed wet specimen Note also that the creeps of and an unsealed specimen in water are about the same at 65°C 65°e (fig. 9b). The present tests confirm for uniaxial as well as triaxial loading the fact, known before only for uniaxial loading [13], [13), that the creep rate (after a fixed loading duration) of unsealed specimens does not increase monotonically monotonically with temperature. As established by Marrchal [13), the uniaxial tests show first an Man!chal [13], increase of creep according to the activation energy 0 70 ° to 90 90°C, theory up to about 70° e, then an abrupt decline 100°C is passed, and with a further increase of as lOOoe temperature again a smooth increase of the creep rate according to the activation energy theory. In the light of the present test, as well as the previous [4], the tests of very small cement paste specimens (4), decline of the creep rate of unsealed specimen as the 100°C is passed is due to the loss of pore threshold of lOOoe water. In fact, comparison of the responses of these 100°C is physically physically unspecimens above and below lOOoe justified, since since one specimen specimen is wet and the other is dry. specimen sealed wet above lOOoe, 100°C, Of course, to keep the specimen inevitable to use triaxial triaxial loading loading with sufficient sufficient it is inevitable confining pressure, and then a monotonic monotonic smooth inconfining single activation activation crease of the creep rate according to a single energy appears to take place. It may also be noted that monotonic temperature dependence dependence of the when the monotonic unsealed (dried) specimens specimens above above lOOoe 100°C is creep rate of unsealed manner extrapolated to room temperature in a smooth manner (according to the same activation activation energy energy curve), curve), the (according creep rate appears to be about the same as for a predried specimen specimen (although (although at at room room temperature temperature this this predried can be be tested tested only only on on extremely extremely thin thin specimens, specimens, about about 11 can mm mm thick). thick).
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z. I'.P. Ba.~ant, Bacanl. S. Prasannan PraSafllWIl / Creep Creep tests o[ of concrete COllerel/' Z.
The torsional torsional creep creep of of aa specimen specimen sealed sealed wet wet at at The observed to to be, be, as as in in the the case case of of axial axial creep, creep, t120°C 2 0 ° C is observed higher than than that that of of aa specimen specimen sealed sealed dry dryas as that that higher as well as of an an unsealed unsealed specimen specimen (fig. 9c). 9c). However, However, the the creep creep of of of an unsealed unsealed specimen specimen is higher higher than than that that of of aa specimen specimen an and so so is the the creep creep rate. rate. Moreover, Moreover, the the sealed dry, dry, and sealed torsional creep creep in unsealed unsealed specimens specimens at at 120°C 120°C due due to aa torsional torque superimposed superimposed on on constant constant triaxial triaxial loading loading does does torque not appear appear to to be be proportional proportional to to the the maximum maximum shear shear not T, ,.), i.e., the the creep creep strain strain appears appears to to stress value (max (max r,,.), stress depend nonlinearly nonlinearly on on stress stress (fig. 9c). depend accordance with with these these observations, observations, it appears appears In accordance of deviatoric deviatoric to volumetric volumetric creep creep increases increases that the the ratio ratio of that with temperature. temperature. This This means means that that the the creep creep Poisson Poisson with of concrete concrete also also increases increases with with temperature. temperature. PreviPreviratio of ratio ously, in tests tests of of cement cement paste paste [4], [4). the the creep creep Poisson Poisson ously, ratio was observed observed to increase increase from 0.25 at room room temtemratio perature to to 0.46 0.46 at at 200°C. 200°e. The The behavior behavior of of concrete concrete perature now appears appears to be be qualitatively similar. The The explanation explanation now of this this phenomenon phenomenon might might be be that that the the contribution contribution to of creep from the changes changes of of thickness thickness of the interlayer interlayer creep space and and gel pores pores becomes becomes less at at higher higher temperatures temperatures space contribution due due to interparticle interparticle sliding sliding than is the contribution than resulting from bond bond ruptures. ruptures. resulting of the creep creep rate rate caused caused by sudden sudden The changes changes of The environmental variations variations are are rather rather interesting. interesting. Such Such environmental changes have apparently apparently not not yet been been observed observed for high changes temperatures temperatures and and triaxial loading. loading, When When the temperatemperature ture is rapidly rapidly raised from 120°C 120°C to 200°e, 200°C, the axial creep rate rate increases increases considerably. considerably. The The increase increase is larger for the specimen sealed wet than unsealed than for the unsealed specimen water (fig. lOa). specimen in water 10a). If the temperature temperature is held constant pressure is dropped constant at 120°e. 120°C, the pressure dropped to zero, water water is allowed to evaporate evaporate from the chamber. chamber, and and the unsealed unsealed specimen initially submerged submerged in water water is allowed to dry. dry, then then the creep rate seems to initially decrease decrease and and then increase. In all cases. cases, the creep rate increase increase in excess of the steady-state steady-state creep rate. rate, induced induced by a sudden sudden environmental environmental change change during the creep test. test, is not constant constant but rapidly decays to zero. An unsealed specimen in water, heated during during the creep test from 65°C to 120°C, shows a larger creep rate increase than than a specimen sealed wet. If the unsealed specimen is allowed to dry. dry, the creep rate increase is even larger (fig. lOb). 10b). The creep rate increase for an unsealed unsealed specimen in water is higher for heating from 0 0 65°e e than for heating from 120 e to 200°e. 65°C to 120 120°C 120°C 200°C. This behavior is, however, reversed. reversed, for the sealed specimens. mens, Again, the creep rate increase is not constant constant but decays with time. The initial torsional creep rate increase due to heating from 120°C to 200°C during the creep test is the
highest highest for the the sealed sealed specimen specimen (fig 10c). JOc). Generally, Generally. the the initial initial creep creep rate rate increases increases for torsion torsion and and axial axial loading loading at of the the at rapid rapid heating heating are are similar similar (figs. 10a,c). lOa.c). Drying Drying of specimen at at constant constant temperature temperature of of 120°C 120 0 e increases in
Engineering and Design Design 94 94 (1986) (1986) 137-151 137-151 Nuclear Engineering North-Holland, Amsterdam
HIGH-TEMPERATURE TRIAXIAL HIGH-TEMPERATURE T R I A X I A L TORSIONAL T O R S I O N A L CREEP C R E E P TESTS T E S T S OF O F CONCRETE C O N C R E T E AT AT V A R I O U S HYGRAL H Y G R A L CONDITIONS CONDITIONS VARIOUS Z d e n S k P. BAZANT B A Z A N T * and a n d Santosh S a n t o s h PRASANNAN P R A S A N N A N ** Zdenek Geomaterials, The Technological Institute, Northwestern University. University, Evanston, IL 60201. 60201, USA USA Center for Concrete and Geomaterials, Received 8 October 1985 1985 Received
Results of an initial series of six-day creep tests under a program aimed at establishing fundamental deformation properties of concrete at high temperatures under triaxial loading with shear and various hygral conditions, both constant and transient, are n1Ported. reported. The tests are conducted in a novel novel large triaxial torsional testing machine with hygrothermal control. Tested are cylinders of six inch diameter, sealed or unsealed, loaded by compressive axial force, chamber pressure and torque. Some specimens are sealed wet, some are sealed after drying in an oven, and some are let to dry during the test. Significant is the fact that hygro-thermal differences in creep at various hygro-thermal conditions are observed. Particularly interesting is strains. The results are of interest for the formulation of changes affect not only normal creep strains but also shear creep strains. analysis of nuclear reactor accidents, radioactive waste disposal, disposal, and fire fire resistance. resistance. constitutive relations needed for the analysis
Introduction 1. Introduction Assessment of safety of concrete structures structures for Assessment nuclear reactors, reactors, as well as certain certain problems radioacnuclear problems of radioacwaste disposal, disposal, fire resistance, and and chemical techtive waste need for a better knowledge of nology vessels, pose pose the need better knowledge constitutive relation for concrete than than available at the constitutive present. Much experimental experimental research research has has bbeen e e n carried carried present. Much out to meet these needs, and and considerable considerable information information out has been been gathered gathered over the last two two decades decades has [1,8-13,15-24]. Nevertheless, certain certain rather rather serious gaps [1,8-13,15-24]. remain, especially for temperatures temperatures above 100°C. 100°C. Most Most remain, up to now now have been been limited to uniaxial comprescomprestests up and dried concrete which which has lost its pore pore water water sion and due to heating. heating. Attempts Attempts to seal the specimens specimens have due been been made, made, however, the the seals bulged bulged under under internal internal steam steam pressure, pressure, and and water water still exited exited the the specimens specimens and and collected under under the the seal. The The only only way way to keep keep pore pore water water in in the the specimen specimen is to to apply apply lateral lateral pressure pressure that that is at at least least equal equal to to the the saturation saturation steam steam pressure pressure for the the given temperature. temperature. Hence, Hence, triaxial triaxial loading loading is required required for the the basic basic tests tests at at constant constant water water content. content. Uniaxial Uniaxial stress stress response response of of the the material material at at saturation saturation water water concontent tent is a meaningless, meaningless, nonexistent nonexistent property property at at tempertemperatures 100°C. To atures over 100°C. To carry carry out out a uniaxial uniaxial test test at at * Professor of Civil Engineering and Director. ** Graduate Graduate Research Assistant.
*.
constant constant water content, content, it would in fact be necessary to apply the lateral pressure pressure only on the vapor in the surface pores and and not on the solids, which is technically impossible. Yet, in massive concrete walls, or in nonmassive concrete walls subjected subjected to rapid rapid heating heating or sealed by a steel liner, pore water water does not have sufficient time to escape prior prior to the heating heating of concrete. Finite Finite element analysis analysis reveals that that these conditions conditions are typical of many many accident accident situations. situations. Some experimental experimental information information was obtained obtained [4] for the behavior behavior of hardened paste under hardened Portland Portland cement cement paste under triaxial loading loading (without (without shear) shear) at various hygral conditions, including specimens that that are sealed wet, sealed dry, and and unsealed, unsealed, drying during during the test. However, it is unclear to to which which extent extent the the results results of these these tests, carried carried unclear out on on small small cylinders cylinders of of 15 mm mm diameter, diameter, can can be be out applied to concrete. concrete. Some Some rather rather limited limited information information applied has also been been reported reported [9,14] for the the response response of of conhas crete at biaxial biaxial stress stress and and for shear shear failure, however, crete these tests were were limited limited to temperatures temperatures under under 100°C, these 100°C, which the the drying drying rates rates are are two orders orders of of magnitude magnitude for which slower [2,3,5] [2,3,5] and and the specimen specimen retains retains most most of of its slower moisture for a considerable considerable length length of of time time even if ununmoisture sealed. sealed. Most of of the the previous previous high high temperature temperature testing testing of of Most concrete was was restricted restricted to to uniaxial uniaxial loading loading and and speciconcrete mens freely loosing loosing their their moisture moisture (e.g., Naus, Naus, 1981). 1981). mens Some limited limited data data are are available available on on triaxial triaxial loading loading Some
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Bazant. S. Prasannan / Creep tests of Ba~.ant, of concrete
without torsion, but only for dried specimens (Thelandersson. dersson, 1983; Schneider, 1982) and on the shear failure load of non homogeneously stressed notched specimens nonhomogeneously (Naus, 1981). Limited data data is also available for torsional loading alone (Illston, 1973) of mortar No mortar specimens. No data data exist for deformation under shear stress, either alone or in combination with axial stresses and pressure, and for triaxial behavior of concrete in massive (or lined) walls. In response to these needs, a testing program program concerned with the multiaxial deformation of concrete at temperatures temperatures over 100°C and various hygral conditions has been initiated at Northwestern Northwestern University, and the results of the initial test series are now reported.
Northwestern University. The machine has a test chamNorthwestern ber with a cylindrical cavity 216 mm (8.5 in.) in diameter and 686 mm (27 in.) in length. The maximum axial load is 5 MN (1.13 million Ibs), lbs), the maximum torque is 5.6 kNm kNm (50000 in. Ib), lb), and the maximum chamber pressure is 138 MPa MPa (20000 psi). The axial and torque loadings have closed-loop servocontrol. Tests can be conducted at temperatures from room to 600°C 0 (1110 F). The chamber pressurizing fluid is either water (1110°F). or gas (e.g., air or nitrogen). For a detailed description of this novel testing machine, shown in figs. 1 and 2, see ref. [7].
3. Test specimens specimens 2. Testing Testing machine The tests are conducted in a unique, large testing machine which was recently rendered operational at
The test specimens were cylinders of diameter 152 mm (6 in.) and length 305 mm (12 in.). The specimens were solid rather rather than hollow, even though torsional loading was used. A thin-wall cylinder might have been easier for evaluation, however, a wall thickness of 50
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day (fig. 7). After one day, one of the conditions is changed. For the sealed specimens, it is necessary to apply before heating a certain small confining confining pressure at least equal to the saturation vapor pressure for the given temperature (found, e.g., in ASTM Steam Tables). The effect of an increase of the confining confining pressure, resulting in a purely volumetric deformation, is observed upon increasing increasing the confining confining pressure on the second day. The axial compressive stress is superimposed on the third day and the torque is superimposed on the fourth day. Sudden environmental environmental changes are made on the fifth day, and finally, finally, on the sixth day the specimen is unloaded and creep recovery is monitored. In the present program, all stress levels were intended to remain less than about half of the failure
148 148
P. Bazalll, L. Z.P. Ba2ant, S. S. Prasannan Prasannan // Creep Creep tests tests of of concrete concrete
values. For For torsional torsional loadings, loadings, the the axial axial load load and and the the values. confining pressure pressure were were always always such such that that the the maximum maximum confining principal stress stress would would always always be be compressive compressive and and not not principal too close close to to zero, zero, in in order order to to avoid avoid possible possible failure failure of of too the specimen specimen during during the the tests tests due due to to tensile tensile fracture. fracture. the The initial initial temperatures temperatures for for half half of of the the tests tests are are over over The 120°C, and and for for comparison comparison the the remaining remaining tests tests are are 120°C, conducted at at an an elevated elevated temperature temperature of of 65°C, 65°C~ equal equal to to conducted the temperature temperature presently presently allowed allowed by by codes codes for for nuclear nuclear the reactor vessels. vessels. For For comparison, comparison, aa room room temperature temperature reactor test is is also also carried carried ou out. t. test temperature Note that the specimens which are at a temperature of 65°C can be assumed to maintain during the short 100%; they would test period a pore humidity of almost 100%; in fact need several several years to reach hygral equilibrium with the environment. However, the specimens heated over 100°C can be assumed to lose most of their evaporable pore water content within about one or two hours, i.e., reach pore relative humidity of essentially portland 0%. This is because the pore water diffusivity of portland cement concrete increases approximately 200-times temperature passes above 100°C, as diswhen the temperature covered in 1977 [2].
5. Test results ( a - p ) shows the response response curves of axial strain strain Fig. 8 (a-p) and maximum maximum shear shear strain strain as a function of time, in the and actual time scale. Fig. 9 (a-d) ( a - d ) shows comparison comparison of the actual strains due to applied applied loads, and and fig. 10 (a-d) ( a - d ) shows strains comparisons of the strains strains caused caused by temperature temperature incomparisons For the axial normal normal strains, strains, the strains strains are crease. For plotted plotted per per unit unit stress; stress; for torsion, torsion, they are are plotted plotted as the the measured measured maximum maximum shear shear strain strain divided by by the maximum maximum shear shear stress stress as calculated calculated from the torque torque assuming assuming a linear linear stress stress distribution distribution along along the the radius. radius. Thus, Thus, the the plotted plotted response response curves represent represent the the compliance. a - d ) shows ance. Fig. 11 ((a-d) shows aa comparison comparison of of the the creep creep recovery strains strains at at the the end end of of each each test. test. The The strains strains due due to to loading loading changes changes and and to to environenvironmental mental changes changes were were determined determined graphically, graphically, exploiting exploiting the the fact that that within within aa one-day one-day interval interval other other than than the the first one one the the response response curves curves are are nearly nearly straight straight in in the the logarithmic logarithmic time time scale scale (fig. 12). 12). Thus, Thus, aa graphical graphical exextrapolation trapolation in in the the semilog semilog plot plot is quite quite reliable, reliable, and and the the effect effect of of the the change change of of environment environment or or load load can can be be determined of the the measured measured response response determined as as the the difference diffeFence of from from aa smooth smooth extrapolation extrapolation of of the the previous previous response response plotted plotted in in the the log-time log-time scale scale (fig. 12). 12). In In this this manner, manner, one of tests tests the the need need for for one can can avoid avoid for for the the present present types types of testing testing companion companion load-free load-free specimens specimens subjected subjected to to the the
same same environmental environmental history, history, in in order order to to determine determine the the difference difference between between the the two two tests. tests. The The avoidance avoidance of of comparison comparison specimens specimens improves improves the the test test results results because because this this difference difference exhibits exhibits aa large large statistical statistical scatter scatter as as the the properties properties of of aa companion companion specimen specimen are are never never the the same. same, due due to to the the random random nature nature of of the the material. material. For For some some of of the the loading loading cases, cases, two two tests tests were were run. run. These These were were the the cases cases indicated indicated by by the the diamond-shaped diamond-shaped data data points points in in figs. figs. 9, 9, 10 10 and and II. 11. These These points, points, as as well well as as their their smoothing smoothing curves, curves, represent represent the the averages averages from from two two tests. tests. The The coefficient coefficient of of variation variation for for the the measured measured values for each pair of the curves for the same load never exceeded 15%. 15%. All other data points and curves represent the results of single tests for each loading case.
6. Observations from from tests and their interpretations As we can see from fig. fig. 9a, at 120°C the axial creep strain under triaxial loading with 0, oz -- p == 0.3 I: f j (where Ie' fc ' == standard s t a n d a r d cylinder c y l i n d e r strength, s t r e n g t h , p = chamber chamber pressure, pressure, 0, oZ == axial normal stress) is larger for a specimen sealed wet than than it is for a specimen sealed dry or for an unsealed unsealed specimen immersed in water. Also, the creep rate does not seem to decrease noticeably even after 24 h of loading, while the creep rate of a sealed specimen specimen at 25°C 25°C diminishes diminishes with time (fig. 9a) (and (and is generally much much smaller). In previous tests of very small specimens specimens of hardened hardened Portland paste [4] it was established Portland cement cement paste established that that the creep nite rate of a fully dried specimen is about about 10% of that that for a fully saturated saturated specimen, at room temperature. temperature. observed only on on specimens specimens that that have This behavior behavior is observed This been dried dried to to thermodynamic thermodynamic equilibrium equilibrium prior prior to to loadloadbeen Due to to the the extremely extremely small value of of moisture moisture ing. Due of concrete concrete at at temperatures temperatures below below 100°C, diffusivity of 100°C, the state of of thermodynamic thermodynamic equilibrium equilibrium can can be achieved state within aa reasonable reasonable time time period period only only if the the specimen specimen is within extremely thin thin ( === 1 mm). mm). An An often often used used alternative alternative is to to extremely dry the the specimen specimen by by heating heating to to 105°C 105°C but but this this slightly dry alters the the microstructure. microstructure. The The decrease decrease of of the the creep creep rate rate alters at aa lower lower moisture moisture content content was was discovered discovered only only relaat recently (in (in the the 1960's) 1960's) and and came came as aa surprise. surprise. tively recently Up to to that that time time itit was was believed believed that that the the creep creep rate rate Up increases rather rather than than decreases decreases due due tto drying. However, However, increases o drying. this increase, increase, often often termed termed the the Pickett Pickett effect, is now now this known to to be be due due to to the the effect effect of of the the rate rate of of humidity humidity known change, combined combined with with the the effect effect of of distributed distributed cracking cracking change, (strain-softening, see see ref. ref. [6]). [6]). The The same same effects effects were were (strain-softening, previously found found to to be be exhibited exhibited by by very very small small cement cement previously paste specimens specimens at at temperatures temperatures over over 100°C 100°C [4]. paste
Z.P. e e p tests z.P. Ba~ant, Bazant, S. S. Prasannan Prasannan //C rCreep tests of of concrete concrete
The transient transient effect effect of of the the rate rate of of water water content content is is The rather short-lived, short-lived, due due to to the the fact fact that that moisture moisture diffudiffurather sivity increases increases about about 200-times 200-times upon upon heating heating over over sivity (2). Thus, Thus, whenever whenever heating heating starts starts over over 100°C lOOoe lOOoe [2]. 100°C before loading, loading, the the tests tests essentially essentially occur occur at at aa dried dried before is the the reason reason that that aa much much lower lower state, and and the the drying drying is state, is observed observed than than for aa sealed sealed specimen. creep rate rate is creep The comparisons between between the the sealed sealed and and unsealed unsealed The make sense, of of course, course, only only for triaxial triaxial loadloadspecimen make ing. Without Without the the confining confining chamber chamber pressure pressure itit would would ing. be impossible impossible to to prevent rupture rupture of of the the seal seal due due to to be vapor pressure and and keep the the specimen saturated. saturated. internal vapor creep (i.e., at at constant water water content) Uniaxial basic creep does not not exist above 100°C. lOO°e. does effects of of the the pore pore water water As seen from fig. 9a, the effects are similar for concrete specimens at at high temcontent are peratures, however, the magnitude of the effect is much of a fully dried smaller; the ratio of the creep rates of specimen and a fully saturated specimen is about 0.6 rather than 0.1. This reduced effect is probably caused rather by the restraining action of the aggregate in concrete, but still it is interesting that this restraining action but reduces not only the total creep rate magnitudes but also their relative values. Explanation of this phenomenon in terms of the composite nature of concrete deserves further study. The specimens (in tests 1-3) 1-3) were exposed to a 0 temperature of 120 e for 24 h before loading. Since the 120°C specimens were simultaneously simultaneously under pressure, the condition was similar to autoclaving, autoclaving, a curing process used to accelerate hydration. The analogy with autoclaving autoclaving is, however, fully fully applicable only if additional water is forced into the specimen due to external pressure, as it happens in an autoclave. Ingress of water is of course prevented when the specimen is sealed, but for unsealed specimens tested in water one must assume that water penetrates into the specimen. In such specimens, specimens, the autoclaving autoclaving effect is probably much stronger, which might explain explain 0 why specimens e specimens immersed in pressurized water at 120 120°C show a distinctly distinctly smaller creep rate than do the specimens sealed in the initial initial wet state; see fig. fig. 9a. By contrast, at lower temperature (65°e) (65°C) the creep rates of the specimens specimens sealed wet and the unsealed unsealed specimens specimens immersed immersed in water are about the same (fig. 9b). The behavior at high temperatures is again again qualitatively qualitatively similar similar to that observed previously previously on very very small small cecement paste specimens specimens (4). [4]. Rather interesting interesting is is the fact (fig. 9a) that, at least within within the the first first 24 24 hh period, period, the the creep creep rate rate at at high high temperature temperature does does not not decrease decrease significantly significantly with with the the one-day one-day duration duration while while at at room room temperature temperature itit does. does.
149 149
Apparently, of gradual gradual Apparently, at at high high temperature temperature the the idea idea of exhaustion exhaustion of of the the sites sites of of weakened weakened bonds bonds in in the the solid solid microstructure (6) does does not not quite quite apply. apply. It It must must be be that that microstructure [6] new new sites sites of of potential potential load load ruptures ruptures are are gradually gradually genergenerated ated by by the the creep creep deformation. deformation. Thus, Thus, at at high high temperatemperatures, tures, creep creep might might be be better better d~scribed d~scribed as as aa viscous viscous deformation. deformation. Progressive Progressive microcracking microcracking might might also also play play role. aa role. The of aa specimen sealed sealed wet wet and and tested tested The axial axial creep creep of at at 65°C 65°e is is seen to to be be lower lower (fig. (fig. 9b) 9b) than than itit is is at at 120°C, 120 0 e, but but the the creep creep of of an an unsealed unsealed specimen in in water water under under triaxial loading shows the opposite opposite behavior, i.e., it is greater greater at at 65°C 65°e than it is at at 120°C 120 0 e (figs. 9a,b). Furthermore, the creep creep of of an an unsealed specimen in water water at at 65°C 65°e under uniaxial loading is greater greater than that that of of a specimen under triaxial loading, aOzz -- pP being the same. The difference seems to be too large to be attributed to the creep due to confining pressure, which means that that linear superposition might not be applicable. Note of a sealed wet specimen Note also that the creeps of and an unsealed specimen in water are about the same at 65°C 65°e (fig. 9b). The present tests confirm for uniaxial as well as triaxial loading the fact, known before only for uniaxial loading [13], [13), that the creep rate (after a fixed loading duration) of unsealed specimens does not increase monotonically monotonically with temperature. As established by Marrchal [13), the uniaxial tests show first an Man!chal [13], increase of creep according to the activation energy 0 70 ° to 90 90°C, theory up to about 70° e, then an abrupt decline 100°C is passed, and with a further increase of as lOOoe temperature again a smooth increase of the creep rate according to the activation energy theory. In the light of the present test, as well as the previous [4], the tests of very small cement paste specimens (4), decline of the creep rate of unsealed specimen as the 100°C is passed is due to the loss of pore threshold of lOOoe water. In fact, comparison of the responses of these 100°C is physically physically unspecimens above and below lOOoe justified, since since one specimen specimen is wet and the other is dry. specimen sealed wet above lOOoe, 100°C, Of course, to keep the specimen inevitable to use triaxial triaxial loading loading with sufficient sufficient it is inevitable confining pressure, and then a monotonic monotonic smooth inconfining single activation activation crease of the creep rate according to a single energy appears to take place. It may also be noted that monotonic temperature dependence dependence of the when the monotonic unsealed (dried) specimens specimens above above lOOoe 100°C is creep rate of unsealed manner extrapolated to room temperature in a smooth manner (according to the same activation activation energy energy curve), curve), the (according creep rate appears to be about the same as for a predried specimen specimen (although (although at at room room temperature temperature this this predried can be be tested tested only only on on extremely extremely thin thin specimens, specimens, about about 11 can mm mm thick). thick).
150
z. I'.P. Ba.~ant, Bacanl. S. Prasannan PraSafllWIl / Creep Creep tests o[ of concrete COllerel/' Z.
The torsional torsional creep creep of of aa specimen specimen sealed sealed wet wet at at The observed to to be, be, as as in in the the case case of of axial axial creep, creep, t120°C 2 0 ° C is observed higher than than that that of of aa specimen specimen sealed sealed dry dryas as that that higher as well as of an an unsealed unsealed specimen specimen (fig. 9c). 9c). However, However, the the creep creep of of of an unsealed unsealed specimen specimen is higher higher than than that that of of aa specimen specimen an and so so is the the creep creep rate. rate. Moreover, Moreover, the the sealed dry, dry, and sealed torsional creep creep in unsealed unsealed specimens specimens at at 120°C 120°C due due to aa torsional torque superimposed superimposed on on constant constant triaxial triaxial loading loading does does torque not appear appear to to be be proportional proportional to to the the maximum maximum shear shear not T, ,.), i.e., the the creep creep strain strain appears appears to to stress value (max (max r,,.), stress depend nonlinearly nonlinearly on on stress stress (fig. 9c). depend accordance with with these these observations, observations, it appears appears In accordance of deviatoric deviatoric to volumetric volumetric creep creep increases increases that the the ratio ratio of that with temperature. temperature. This This means means that that the the creep creep Poisson Poisson with of concrete concrete also also increases increases with with temperature. temperature. PreviPreviratio of ratio ously, in tests tests of of cement cement paste paste [4], [4). the the creep creep Poisson Poisson ously, ratio was observed observed to increase increase from 0.25 at room room temtemratio perature to to 0.46 0.46 at at 200°C. 200°e. The The behavior behavior of of concrete concrete perature now appears appears to be be qualitatively similar. The The explanation explanation now of this this phenomenon phenomenon might might be be that that the the contribution contribution to of creep from the changes changes of of thickness thickness of the interlayer interlayer creep space and and gel pores pores becomes becomes less at at higher higher temperatures temperatures space contribution due due to interparticle interparticle sliding sliding than is the contribution than resulting from bond bond ruptures. ruptures. resulting of the creep creep rate rate caused caused by sudden sudden The changes changes of The environmental variations variations are are rather rather interesting. interesting. Such Such environmental changes have apparently apparently not not yet been been observed observed for high changes temperatures temperatures and and triaxial loading. loading, When When the temperatemperature ture is rapidly rapidly raised from 120°C 120°C to 200°e, 200°C, the axial creep rate rate increases increases considerably. considerably. The The increase increase is larger for the specimen sealed wet than unsealed than for the unsealed specimen water (fig. lOa). specimen in water 10a). If the temperature temperature is held constant pressure is dropped constant at 120°e. 120°C, the pressure dropped to zero, water water is allowed to evaporate evaporate from the chamber. chamber, and and the unsealed unsealed specimen initially submerged submerged in water water is allowed to dry. dry, then then the creep rate seems to initially decrease decrease and and then increase. In all cases. cases, the creep rate increase increase in excess of the steady-state steady-state creep rate. rate, induced induced by a sudden sudden environmental environmental change change during the creep test. test, is not constant constant but rapidly decays to zero. An unsealed specimen in water, heated during during the creep test from 65°C to 120°C, shows a larger creep rate increase than than a specimen sealed wet. If the unsealed specimen is allowed to dry. dry, the creep rate increase is even larger (fig. lOb). 10b). The creep rate increase for an unsealed unsealed specimen in water is higher for heating from 0 0 65°e e than for heating from 120 e to 200°e. 65°C to 120 120°C 120°C 200°C. This behavior is, however, reversed. reversed, for the sealed specimens. mens, Again, the creep rate increase is not constant constant but decays with time. The initial torsional creep rate increase due to heating from 120°C to 200°C during the creep test is the
highest highest for the the sealed sealed specimen specimen (fig 10c). JOc). Generally, Generally. the the initial initial creep creep rate rate increases increases for torsion torsion and and axial axial loading loading at of the the at rapid rapid heating heating are are similar similar (figs. 10a,c). lOa.c). Drying Drying of specimen at at constant constant temperature temperature of of 120°C 120 0 e increases in
