Total Strain Behavior of Mortar under Freeze-Thaw Cycles in Consideration of the in Coefficient of Thermal Expansion of Frost Damaged Mortar

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1 Total Stran Behavor of Mortar under Freeze-Thaw Cycles n Consderaton of the n Coeffcent of Thermal Expanson of Frost Damaged Mortar Evdon Scat 1, Fuyuan Gong 1*, Ueda Tamon 2 and Zhang Dawe 3 1 Graduate School of Engneerng, Hokkado Unversty, Japan 2 Faculty of Engneerng, Hokkado Unversty, Japan 3 College of Cvl Engneerng and Archtecture, Zhejang Unversty, Chna * Laboratory of Engneerng for Mantenance System, Graduate School of Engneerng, Hokkado Unversty, Kta 8, Nsh 13, Kta-ku, Sapporo, , Japan, evdonscat@gmal.com, gongfy7@gmal.com, ueda@eng.hokuda.ac.jp, davd@eng.hokuda.ac.jp ABSTRACT In ths paper, the total stran behavor durng freeze-thaw cycles (FTC) s presented as composed of expanson strans caused by ce formaton, shrnkage stran caused by movement of unfrozen water from small capllary pores to larger or partally flled pores, and thermal strans as a response of the materal to the change n temperature. The model whch s n mesoscale s based on expermental fndngs showng that the degree of saturaton dctates the behavor of mortar under FTC. Interestngly, for the enhancement of the model, supplementary expermental fndngs mply that the coeffcent of thermal expanson (CTE) of FTC subjected mortar changes n accordance to the damage t accumulated. Based on these fndngs, t s proposed that the change n CTE due to FTC damage should be ncorporated n the determnaton of the total stran durng FTC. Keywords: Frost damage, freeze-thaw cycles (FTC), coeffcent of thermal expanson (CTE), mosture, temperature BACKGROUDND Frost damage has long been a deteroraton problem n cold regons. Because of ts porous structure, concrete has the ablty to absorb mosture when t s n contact wth t. Ths makes concrete susceptble to frost damage once the mosture nsde freezes and causes dsruptve pressures. There has been plenty of research regardng the mechansm of freezng and thawng acton n concrete however no unfed mechansm has been wdely accepted (Chatterj, 1999). It s a known expermental fact the damage to freeze-thaw cycles (FTC) deterorates the mechancal propertes of concrete due to mcro crackng (Hassan, 23) and these results n the change n mcrostructure of concrete. The change n mcrostructure due to FTC may have an adverse effect on the coeffcent of thermal expanson (CTE) of concrete. Smlar wth the modulus of elastcty, the CTE of a

2 homogenous materal s unaffected by the change n mcrostructure. However, ths may not be the case for concrete a heterogeneous and multphase materal. CTE s an mportant property of concrete, t must be known to manage the expanson of concrete due rangng temperatures and predct the behavor of concrete structures durng ther servce lfe (Mallela et al., 25 and Uygunoglu et al., 29). Studes about the CTE of concrete commonly deal wth ts change due to elevated temperatures whle when used n desgn s usually derved from undamaged concrete (Scat et al., 212). As of the moment, t may not be realzed that the deteroraton due to FTC could unfavorably alter the CTE of concrete. Ths change n CTE should be consdered n modelng of the frost damage mechansm of concrete and could be of mportance n lfe cycle predcton of concrete structures. Ths study s presented as a part of a seres of studes whch ams to develop a mesoscale deformaton model of mortar under FTC, n whch, t s also a part of a bgger project amng to predct the structural performance of member wth frost damage (Ueda and Ara, 21). A prevous expermental study (Scat and Ueda 211) to clarfy the effect of temperature and mosture varaton have been performed. Based on the expermental fndngs the mesoscale deformaton model of mortar under FTC has been developed (Scat and Ueda 211). The proposed mesoscale deformaton model however does not consder the ncrease n pore structure durng FTC and further mprovement s needed. In order to enhance ths model, the collecton of data of deformatonal behavor of mortar under varaton n temperature and mosture s needed. Thus, the objectve of ths study s to further enhance the mesoscale deformaton model of mortar under FTC consderng the change n CTE observed from the collected data from a supplementary experment undertaken. THE MESOSCALE DEFORMATION MODELOF MORTAR UNDER FTC The mesoscale deformaton was frst proposed by Owa et al. (28). The model s developed to calculate the mosture content of free water, ce content and temperature at any locaton of mortar by solvng the coupled transfer equatons of mosture and heat n mortar consderng three phases of water (gas, lqud and sold) (Scat and Ueda, 211 and Owa et al., 28). The developed analytcal method n mesoscale, combnes mechancal analyss wth heat-mosture transfer analyss, to smulate the deformatonal behavor of mortar under FTC (Ueda and Ara, 21). The equatons shown below are heat and mosture equatons for three phases. These were derved from balance of heat and mosture (Matsumoto et al., 1993). μ μ t μ T μ T t (1) T C t R T R μ Tg μg H l l t (2) T μ H log (3) l e T where, s chemcal potental of mosture, s densty for each phase, T s absolute temperature, C s specfc heat, t s tme, s mosture content, s thermal conductvty, ' μ s mosture transfer rato n gas and lqud phase caused by chemcal potental gradent, ' μg s mosture transfer rato n gas phase caused by chemcal potental gradent, ' T s

3 Stran (µ) mosture transfer rato n gas and lqud phase caused by temperature gradent, s mosture transfer rato n gas phase caused by temperature gradent, R s evaporaton heat, T s freezng temperature of free water ( ºC), s ce content, s meltng heat. In the heat and mosture transfer analyss for three phases Owa et al (28) calculated the ce content and appled t n the followng equaton representng the expanson deformaton under freezng, whch s proporton to ce content, s assumed as: (4) where, ε s expanson stran under freezng and α s the constant. The method does not consder the effects of ncrease n pore structure, abrupt freezng of supercooled water nor shrnkage due to flow of unfrozen water. The relablty of the constant n Eq. (4) was not confrmed by experment due to the fact that the test method to measure t has not been developed when the model was proposed. Development of the Mesoscale Deformaton Model. The expermental methods used n ths study were dscussed n detal by Scat and Ueda (211). In the study (Scat and Ueda, 211), mortar specmens of 4mm x 4mm x 2mm was used. Ths sze s assumed to represent the deformaton of mortar n mesoscale under any temperature and mosture condton. Specmens were prepared nto three dfferent mosture condtons and then sealed to avod water uptake and loss, then undergone 5 FTC startng from 1ºC untl -28 C. Mosture condton ncludes, dry specmens to measure the thermal strans and 1% saturated and 68% saturated specmens to observe the behavour of mosture durng FTC. Obtaned specmens stran nclude strans due to temperature change and mosture content, to observe the effect of mosture durng FTC; thermal strans as shown n Fgure 1 obtaned from absolutely dry specmens and were excluded from the obtaned strans of saturated specmens. Fgure 2 and 3 are saturated specmen s stran wthout the thermal strans. Unform stran behavor s evdently observed durng the entre FTC for dry specmens n Fgure 1. Ths s because of the absence of mosture and the stran behavor s only nfluenced by the thermal expanson of the materal respondng to temperature change. For fully saturated specmens n Fgure 2 ncreasng stran behavour s observed, ths s ponted to be product of the volume expanson of water when t turns nto ce. Even specmens are sealed; there s an ncrease n stran as the FTC progresses whch s explaned that the pore structure s damaged by the expanson durng freezng, resultng n ncrease of pore sze n H l ' Tg FTC 1st 2nd 3rd 4th 5th Fgure 1 One freeze-thaw cycle (temperature hstory)

4 FTC 13 1st 2nd 3rd 4th 5th Fgure 2 Fully saturated specmen s strans FTC 1st 2nd 3rd 4th 5th Fgure 3 Partally saturated (68.4%) specmen s strans whch more volume of water can be frozen. Whle for partally saturated specmens, durng the entre FTC unform contracton s observed at the lowest temperature. These phenomena happened because there were ar vods large enough and not flled wth water; ths accommodates the ncrease n the volume of frozen water n the specmen (Ueda and Ara, 21), moreover these partally water flled pores permts unfrozen water from smaller pores to flow to freezng stes resultng n contracton. Detaled explanaton of the mechansm durng FTC n mortar s explaned further by the prevous study (Scat and Ueda, 211). Based on the presented expermental results (Scat and Ueda, 211) the expanson and shrnkng behavor under freezng process changes accordng to the mosture condton. Dependng on the mosture content ether contracton or expanson s domnant. Therefore, t was proposed that the total stran ε durng FTC s assumed as a combnaton of three stran components as seen n Eq. (5): s t (5) Where, ε s the expanson stran under freezng, ε s s the shrnkage stran under freezng, and ε t s thermal stran. The freezng expanson durng FTC as summarzed n the expermental fndngs s suggested as a product of ce formaton. Thus, t s proposed that the freezng expanson stran ε be a functon of ce content Ψ and s assumed as Eq.(6) consderng the fact that there would be no expanson for the water contents less than a certan value. c - (6)

5 Where, α s the materal constant dependng on mortar stffness and Ψ c s the ce content when the deformaton starts to depend on the ce content. Snce the contracton under freezng s caused by unfrozen water movement (Scat and Ueda, 21) whch s caused by chemcal potental dfference due to ce formaton Ψ, t s assumed that the deformaton depends on the unfrozen water content whch s a dfference between the water (mosture) content Ψ and ce content Ψ. The contracton durng freezng s expressed n Eq. (7). s s w (7) Where, unfrozen water content s Ψ w and α s s a value representng the contrbuton of unfrozen water content to the shrnkage, whch depends on the mortar stffness. The thermal stran s obtaned from Eq. (8) usng the lnear expanson coeffcent α t. T t t (8) Where s the temperature varaton. The calculaton of α s was obtaned from the expermental data for partally saturated specmen s stran of 68.4% n Fg. 5, by the fact that the behavor of the specmens durng the entre FTC s purely contracton. Based on calculated values of unfrozen water wth relaton to expermental strans, t was found out that α s s a functon of the unfrozen water content Ψ w as expressed n Eq. (9). Mosture content Ψ and ce content Ψ values were calculated usng equatons (1), (2), and (3) from heat and mosture balance for three phases ln 1272 f (9) w w The calculaton of the materal constant α was obtaned from the expermental data for fully saturated specmen s stran. Mosture content Ψ and ce content Ψ were calculated values usng equatons (1), (2), and (3) from heat and mosture balance for three phases. The value for Ψ c s assumed as equal to.3 based on observaton that durng ths water content the stran behavor dsplays sgnfcant ncrease. The calculated value for the materal constant α s equal to 2116 x 1-6. By combnng heat and mosture transfer equatons for three phases (sold, lqud, and vapor) whch calculates the mosture, temperature, and ce content n a specfed locaton of a specmen and the presented mesoscale model, the method s able to predct the stran behavor of a specmen under ambent temperature and mosture hstory. Furthermore, the relablty of the materal s constant and values (α and αs) were confrmed by an experment and the flow of unfrozen water was consdered. These were not prevously consdered n Owa s model. However, further enhancements of the model are stll needed. The next secton of the paper s the frst attempt to further mprove the model. DATA COLLECTION FOR THE ENHANCEMENT OF THE PROPOSED MESOSCALE DEFORMATION MODEL OF MORTAR For the refnement of the model, a secondary experment was done (Scat et al., 212). Fve dfferent mxture proportons were prepared n ths experment as shown n Table 1. Specmens were also condtoned to be fully saturated. Preparaton of the specmens before undergong FTC was explaned n detal by Scat et al. (212). To further observe the stran behavor durng FTC, saturated specmens undergone 3 FTC, the maxmum and lowest

6 temperature s smlar wth the prevous study (Scat and Ueda, 211). Dry specmens and saturated specmens stran durng FTC were observed. Specmen sze of 4 x 4 x 2mm was also used n ths experment and smlar (Scat and Ueda, 211) procedure and equpment were used to obtan the stran durng FTC. Expermental Results: The mosture behavor durng FTC were prmarly observed; as a requrement, thermal strans were removed from saturated specmens stran whch were obtaned from dry specmens from each mxture n Table 1. Fgure 4 shows strans (gray lnes) for all dry (undamaged to FTC) specmens for 1 FTC. It can be observed that durng the whole FTC, the stran behavor of the spepecmens remans constant as the number of cycle ncreases smlar wth the expermental results n the prevous secton. Ths s obvously because of the absence of mosture, and strans are due to temperature change. Table 1 Mx Proportons of Mortar Mxture Water-Cement Rato (%) Water (kg/m 3 ) Cement (kg/m 3 Fne aggregate ) (kg/m 3 ) A B C D E The results obtaned from fully saturated specmens are shown n Fgure 5 excludng the thermal strans. Large expansons can be observed at the ntal stages of the FTC. Ths s observed from Fgs. 5a, 5b, 5c and 5d. As explaned prevously (Scat et al., 211), these expansons are product of the volume expanson of water when t turns nto ce resultng n a temporary hydraulc pressure. If the stresses can t be releved by the matrx mcro cracks develop whch ncrease the pore volume of the specmens. As the FTC progresses, the postve stran comes to a pont where t decreases, and eventually reverses to contracton as can be observed agan from Fgs. 5a, 5b, 5c and 5d. Ths happens when enough pore space s created due to mcro crackng caused by large expanson strans n the ntal FTC, snce specmens are sealed and wthout water supply fllng the pores then mosture can be redstrbuted from gel pores or unfrozen water from smaller pores to the newly developed spaces creatng negatve hydraulc pressure whch results n the contracton of the system. However, for Fgure 5e the specmen dsplays an ncreasng contracton durng the entre FTC. To understand how ths behavor happened, we have to consder the pore structure of the specmen. To have contracton behavor, there should be avalable pore space where mosture can be redstrbuted (partal saturaton). It s a known matter that low water to cement (W/C) rato for concrete results n hgher pore volume whle low W/C rato as n the case for the specmen mentoned results n low pore volume, ndcatng that t could also have large volume of smaller pores than large pores. Due to low W/C, t may be possble that the specmen contan greater amount of small capllary and gel pores contanng unfrozen water responsble for contracton rather than large pores. Durng saturaton process t may also be dffcult for mosture to fll empty smaller pores resultng n partal saturaton of the specmen. These may be the cause of the unusual domnant contracton behavor of the sad specmen. Ths also suggests that the pore structure and mosture content of specmens dctates ther stran behavor durng FTC.

7 a) b) c) d) e) FTC 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 1th FTC 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 1th FTC 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 1th FTC 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 1th FTC 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 1th % Sat. Dry 1% Sat. Dry 1% Sat. Dry 1% Sat. Dry 1% Sat. Dry Fgure 4 Thermal strans (FTC damaged 1% Sat. and dry/undamaged) for Mxture a) A, b) B, c) C, d) D, and e) E

8 a) b) c) d) FTC 5th 1th 15th 2th 25th 3th Expansons Reverse to contracton FTC 5th 1th 15th 2th 25th 3th Expanson Reverse to contracton FTC 5th 1th 15th 2th 25th 3th Expanson Reverse to contracton FTC 5th 1th 15th 2th 25th 3th Expanson Reverse to contracton e) FTC 5th 1th 15th 2th 25th 3th Increasng contracton Fgure 5 Fully saturated specmens stran for mxture a) A, b) B, c) C, d) D, and e) E

9 Change n CTE due to Deteroraton by FTC. The stran behavor of specmens have been brefly dscussed. Detal dscusson has been provded by Scat et al. (212). From saturated specmens strans the reverse contracton seem to be too large to be caused by the movement of unfrozen water alone. Thus to verfy f ths behavor s caused by mosture movement or change of CTE of the specmen, a second test was performed. Ths was done by dryng the sad specmens (saturated specmens whch undergone FTC) to remove any remanng mosture. Then were resealed and subjected under FTC for 1 cycles. Thermal strans were then obtaned and compared wth the dry (undamaged) strans. Gong back to Fgure 4, t shows the results of thermal strans of specmens both for FTC damaged (red lne) and dry (undamaged) specmens (gray lnes). Observatons from the fgure suggest that thermal stran for FTC damaged specmens have ncrease sgnfcantly than dry specmens. The stran reached at the lowest temperature s almost twce as dry strans. Snce the CTE can be calculated n terms of the resultng strans, ths means that the CTE of the sad specmens have changed drastcally. Based on the results presented, durng FTC besdes the plastc expanson, plastc contracton are also observed whch contrbutes to the permanent deformaton ntated by changes n mcrostructure of the materal caused by mcro crackng durng freezng. Wth ths observed fndngs, hence t can be sad that the deformaton and deteroraton of mortar caused by mcro crackng of the system durng FTC s the man reason for the change of CTE of mortar specmens. In addton, t s a proven expermental fact that the damage due to FTC causng mcrocrackng degrades the modulus of elastcty of concrete, n whch, smlarly because of ths same damage the CTE of concrete changes drastcally. The change n both CTE and modulus of elastcty s dependent on the damage t accumulated or how the mcrostructure has changed (ncrease n pore structure), wth ths regard t s also approprate to say that wthout frost damage there wll be no change n CTE. Consderng ths fndng, for the enhancement of the deformaton model, the change n CTE of the specmens should therefore be consdered to smulate the stran behavor of specmens. For the calculaton of the total stran n Eq. 5, the component for the thermal stran ε t should be smplstcally revsed to the equaton below when deteroraton due to FTC takes place. d T d (1) Where ε d s the thermal stran for FTC damaged specmen and α d s the changed CTE value of FTC damaged mortar. When there s no FTC damage, Eq. 8 wll be used to calculate the strans due to temperature varaton. The change n CTE could be related to both modulus of elastcty and/or ncrease n pore structure durng FTC whch are both product of the mcrocrackng caused by frost damage. Ths s currently an ongong undertakng of the authors. CONCLUSIONS The sequental development of the mesoscale deformaton model has been presented. The model s based on the observed deformaton of mortar whch s nfluenced by the formaton of ce, movement of unfrozen water and thermal varaton. The model s combned wth heat and mosture transfer equatons for three phases (sold, lqud, and vapor) whch calculates the mosture, temperature, and ce content n a specfed locaton of a specmen. The method can predct the stran behavor of a specmen under ambent temperature and mosture hstory. However, as of the moment the model has many short comngs.

10 The frst attempt, to enhance the model s through the collecton of more dependable data. From the supplementary expermental fndngs, t was found that there s a reverse contracton durng FTC. Ths s explaned that when enough pore space has been created from ce expanson, the pressure s releved and allows the unfrozen water to flow to these partally flled pores whch results n the contracton. More nterestngly, expermental results show that the CTE of FTC damaged specmens change drastcally and ths change s dependent on the damage t accumulated durng FTC as a result of the mcrostructural change due to mcro crackng. Consderng the fndng on the change n CTE, for the calculaton of the total stran ε durng FTC when deteroraton takes place; the component for the thermal stran s calculated usng α d representng the change n CTE for FTC damaged specmens. The change n CTE could be related to both modulus of elastcty and/or ncrease n pore structure durng FTC whch are both product of the mcrocrackng caused by frost damage. Ths s currently an ongong undertakng of the authors. REFERENCES Chatterj, S. (1999). Aspect of the freezng process n a porous materal-water system Part 1. Freezng and the propertes of water and ce, Cement and Concrete Research, pp Hasan, M., Okuyama, H., and Ueda, T. (23) The damage mechansm and stran nduced n frost cycles of concrete. Proceedngs of the Japan Concrete Insttute, 25(1), pp Mallela, J., Abbas, A., Harman, T., Rao, C., Lu, R., and Darter, M.I. (25) Measurement and Sgnfcance of the Coeffcent of Thermal Expanson of Concrete n Rgd Pavement Desgn, Transportaton Research Record: Journal of the Transportaton Research Board, No. 1919, Washngton, D.C., pp Matsumoto, M., Gao, Y., and Hoko, S., (1993) Smultaneous Heat and Mosture Transfer durng Freezng-Meltng n Buldng Materals, CIB/W4 Meetng n Budapest, September. Owa, Y., Sato, Y., Ueda, T., and Matsumoto, K. (28) Analyss of deformatonal behavor of mortar under freezng and thawng acton, Advances n Concrete Structural Durablty, Proceedng of the Internatonal Conference on Durablty of Concrete Structures (ICDCS 28), Hangzou, Chna, November, pp Scat, E., and Ueda, T. (211) Development of a Meso-scale Deformaton Model of Mortar Under Freeze-Thaw Cycles Proceedngs of the Japan Concrete Insttute, Vol. 33, Osaka, Japan, July. Scat, E., Gong, F., Dawe, Z., and Ueda, T., (212) Degradaton of the Coeffcent of Thermal Expanson of Freeze-thaw Cycle (FTC) Damaged Mortar, The 5th Internatonal Conference of Asan Concrete Federaton, Pattaya, Chonbur, Thaland, October Ueda, T. and Ara, S. (21) Frost damage Model to Predct Structural Performance, Advances n Concrete Structural Durablty, Proceedng of the 2nd Internatonal Conference on Durablty of Concrete Structures (ICDCS 21), Sapporo, Japan, November, pp Uygunoglu, T., Topcu, I.B. (29) Thermal expanson of self-consoldatng normal and lghtweght aggregate concrete at elevated temperature, Constructon and Buldng Materals Vol. 23,