Ultrasonic sound speed of hydrating calcium sulphate hemihydrate; part 1, the calculation of sound speed of slurries and hardened porous material

Transcription

1 A.C.J. de ore and H.J.H. Brouwers Ulrasoni sound speed of hydraing alium sulphae hemihydrae; par, he alulaion of sound speed of slurries and hardened porous maerial Absra This arile fouses on he ompuaion of he sound veloiy hrough slurries and hardened produs. The purpose is o use he sound veloiy o quanify he omposiion of he fresh slurry as well as he hardening and hardened - porous - maerial. Therefore he volumeri models for hydraion of alium sulphaes given by Brouwers // is inegraed wih sound veloiy equaions found in lieraure. Furhermore he derived model is ompared wih experimenal daa. This shows ha he model of Robeys e al. /2/ gives good resuls for he ompuaion of sound veloiy hrough slurries, while he model of Ye /3/ give good resuls for he ompuaion of sound veloiy hrough hardened porous maerial. Inroduion Currenly he hydraion of hemihydrae o gypsum and emen is sudied by IR, SEM and Via ehniques. Beause he speed of hydraion is more diffiul o measure he hydraion urve and he differen proesses whih ake plae. For he measuremen of he hydraion of emen and onree in he las deade ulrasoni sound veloiy measuremens have been applied suessfully /2, 4, 5/. This mehod has he advanage over he more radiional mehods, suh as he aforemenioned Via-needle, SEM and IR, ha ulrasoni measuremens are oninuous /6/, and ha i provides informaion abou he mirosruure developmen and he relaed properies like srengh developmen /2/. Espeially for hemihydrae hydraion, due o he shor hydraion ime, is diffiul o sop he hydraion for disoninuous measuremens. The ulrasoni sound veloiy mehod used here is developed and paened by he Universiy of Sugar /7/ This arile will fous on he appliaion of he ulrasoni sound veloiy measuremen for assessing he hydraion urve of hemihydrae o gypsum. Therefore i will be ombined wih informaion abou he volume fraions of binders and hardened maerial during hydraion and he lassi hydraion-ime relaions given by Shiller /8/. Sound veloiy of maerials There are wo mehods o obain he sound speed of he maerials. The firs mehod is he use of values from lieraure. Table shows he sound speed hrough some maerials. Besides his mehod, here is a seond mehod o aquire he value of sound speed. This mehod is based on he elasi modulus and densiy of he maerial and reads () 55

2 Speifi densiy (kg/m 3 ) Sound speed (m/s) Elasi modulus (GPa) Bulk modulus (GPa) Shear modulus (GPa) Poisson raio Waer Air Seel Dihydrae Hemihydrae Anhydri Table Relevan physial properies of differen maerials /9-3/. wih he sound speed, he bulk modulus and he speifi densiy. This mehod is suiable for fluids and gases, bu is i no valid for solid maerials. For example, for seel = 70 GPa and = 7700 kg/m 3, yielding a sound veloiy of 4699 m/s, while ommonly aeped value of is sound speed is 5930 m/s /4/. insler /4/ poins ou ha he ompuaional mehod will deliver he so-alled bar sound speed. This is aused by he fa ha solids an suppor wo ypes of elasi waves (e.g. longiudinal and shear). In an isoropi solid of whih he dimensions are muh larger han he wavelengh of he aousi wave, he appropriae speed for he longiudinal waves is he bulk speed /4/. The bulk speed is for all maerials larger han he bar speed of he same maerial. The equaion for he bulk speed reads G 4 3 long. (2) Where and G are he bulk and shear modulus of he solid, respeively, and is densiy. The shear modulus of seel is 79.3 GPa. This yields o sound speed of 5980 m/s, whih is lose o he ommonly aeped value of 5930 m/s. Besides he speed in longiudinal direion, here is also a speed in he shear direion. The equaion for his direion reads G shear (3) Table shows he elasi, bulk and shear modulus of several maerials, as well as ha of waer and air. When applying Eq. () and (2), he resuls for (non-porous) gypsum are m/s, and m/s, respeively. The resuls of boh equaions are lower han he experimenal value of 6800 m/s provided by Losso and Viveiros /9/. The shear veloiy aording o Eq. (3) is m/s. So he Eqs. ()-(3) are appliable for fluids, bu are no suiable for solids, sine hey end o underesimae he sound veloiy hrough solids. This is even more rue for porous solids, whih also onain voids. In he nex seion he omposiion of a hemihydraes-waer-gypsum is addressed, used here for he developmen of a new model relaing sound veloiy and omposiional properies. 56

3 Parile Size [µm] Figure Parile size disribuion of -hemihydrae Experimens Maerials Wihin his researh -hemihydrae is used as he binder. The hemihydrae used during he experimens was produed from flue gas desulpharizaion gypsum, whih is ommonly used for he produion of gypsum plaserboards. The parile size disribuion (PSD) is shown in Figure. The used -hemihydrae onsiss of 97% pure hemihydrae and 3 % oher ompounds /5/. The hemihydrae has a Blaine value of 3025 m 2 /g and a densiy of 269 kg/m 3. The Blaine value desribes he fineness of he binder parile (hemihydrae). Hunger and Brouwers /6/ poin ou ha he Blaine es mehods are no appliable for powders wih higher fineness (i.e. pariles < 0 µm). The hemihydraes used, has 35% of he pariles smaller han 0 µm, herefore he Blaine value is less suiable. Anoher mehod o deermine he fineness of powder is he use of speifi surfae area (SSA). Hunger /7/ showed a mehod o alulae he speifi surfae area based on he PSD. Hunger and Brouwers /6/ showed ha here is a onsan raio beween Blaine value and ompued SSA. The Blaine value has o be muliplied by abou.7 o obain he SSA. Applied here, he SSA based on he given Blaine value would amoun 530 m 2 /g. The ompuaion of he SSA using he PSD depends on he shape of he pariles. For spheres he shape faor equals uniy. Using his shape faor, he SSA of he used hemihydrae would be 377 m 2 /g. However, hese powder pariles are no spherial, and he amoun of speifi surfae area is higher. To mah ompued SSA and Blaine value of 530 m 2 /g, here a shape-faor of.36 follows for -hemihydrae. I is noeworhy ha Hunger and Brouwers /6/ found a shape-faor of.8 for -hemihydrae. Measuremens The measuremens were exeued a he Maerialprüfungsansal of he Universiy of Sugar (Germany). The sound veloiy of 4 waer/binder raios is measured during he experimens. The 4 waer/binder-raios (wbr) are 0.63, 0.80,.25 and.59. Besides hese four mixures also a mixure wih wbr of.59 wih 0.40 % (m/m) aeleraor is esed. Table 3 shows he mix-designs used during he experimens. Figure 2 shows he measured sound veloiy during hydraion of he 4 mixures. 57

4 The hemihydrae hydraion experimens wih ulrasoni mehod were performed using he FreshCon sysem whih was developed a he Universiy of Sugar. The measuremens are performed in a onainer. Whih onsiss of wo polymeharylae walls and u-shaped rubber foam elemen in he ener, whih are ied ogeher by four srews wih spaers. The volume of he mold is approximaely 45 m 3 for he es. The measuremens were performed wih use of wo Panameris V06, 2.25MHz enre frequeny sensors. For he proessing of he measuring daa during he experimens, inhouse developed sofware (FRESHCON2) is used. More deailed informaion abou he FreshCon sysem and he measuremen proedure an be found in Reinhard and Grosse /4/. Mix design A B C D E Waer/hemihydrae raio Aelaor (m/m on hemihydraes) 0.40% Before hydraion Compued void fraion Measured sound veloiy (m/s) Afer hydraion Compued void fraion Measured sound veloiy (m/s) Table 2 Mix designs, ompued void fraions based on Brouwers // and he resuls of he ulrasoon measuremens /8/ Figure 2 Measured sound veloiy by Grosse and Lehmann /8/ wbr = 0.65 wbr = 0.8 wbr =.25 wbr =.59 wbr =.59a Time [min] 58

5 y = 363x - 54 R² = Void fraion Figure 3 Void fraion versus veloiy before hydraion based on he experimens of Grosse and Lehmann /8/ y = -2,659x + 3,80 R² = Figure 4 Void fraion versus veloiy afer hydraion based on he experimens of Grosse and Lehmann /8/ Void fraion The alulaed void fraions of he mixures in his researh, based on he model of Brouwers //, are given in Table 3. Table 3 also shows he measured ulrasoni veloiy by Grosse and Lehmann /8/. Figures 3 and 4 are graphi represenaions of he sound veloiy daa versus ompued void fraion from Table 3. I an be noied from he figures ha here is a lear relaion beween void fraion and veloiy as well before as afer hydraion, so = 0 and =, respeively. Bu he rend is exaly opposie before and afer hydraion. Before hydraion he veloiy inreases wih inreasing void fraion (i.e. waer onen), while he veloiy is dereasing wih inreasing void fraion afer hydraion. In he nex seion relaions will be esablished beween he volumeri omposiion (a = 0 and = ) and sound veloiy. Sound veloiy of slurries and porous media Sound veloiy of a slurry This sub-seion desribes he sound veloiy of a slurry, i.e. a suspension, onaining enrapped air. Robeys e al. /2/ presened a model for ulrasoni veloiy hrough fresh emen mixures, based on he heoreial model of Harker and Temple /9/ for 59

6 ulrasoni propagaion in olloids. Aording o hese models, he effeive wave veloiy ( e ) in a suspension is given by; 2 f s f e (4) 2 f s s f S S S Wih he subsrip f referring o he fluid anf s o he solid, and o he fluid volume fraion. The parameer S generally depends on he size and shape of he pariles, he void fraion and he oninuous phase visosiy /20/, bu i an be approximaed for spherial pariles in a fluid /2/ as 2 2 S (5) When also enrapped air is presen in he fluid, he ompressibiliy of he oninuous phase an be orreed assuming he air o be uniformly disribued f air waer air air (6) Wih air as he air volume fraion in he voids of he fluid and air he bulk modulus of air. Sound veloiy of solid The sound veloiy of a porous maerial an also alulaed direly from he individual sound veloiies of he individual phases. Roh e al. /22/ used a simple equaion o predi he effeive sound speed in a porous medium. This equaion reads e s ( ) (7) Wih s he sound speed in he non-porous maerial and he void fraion. Dalui e al. /23/ have added an exponen (8) n e s ( ) Wih exponen n being an empirial onsan. For -hemihydrae, Dalui e al. /23/ proposed n = 0.84 and s = 457 m/s. 60

7 Wbr Void fraion Measured veloiy Compued veloiy Derived onen (m/s) (Eq. (4)) C air V air /V HH A % 2.85 % B % 3.00 % C % 2.09 % D % 0.98 % E.59 a % 2.78 % air Table 3 Mix design, ompued void fraions aording o // and he resuls of he ulrasone measuremens /8/ A drawbak of hese empirial equaions is ha in he limi of he void fraion approahing uniy, a sound veloiy of zero is obained, whih is obviously no orre. Therefore, here an addiional erm is added o Eq. (7) and (8) whih akes in aoun he sound veloiy of he fluid: ( ) (9) e s f and n n e s ( ) f (0) Wih f being he sound speed of he fluid. Eqs. (7)-(0) are based on a parallel arrangemen. Anoher possibiliy is o use a series arrangemen /3/, and he equaion for his arrangemen reads s f e () f s Wih e as he effeive veloiy, s he veloiy of he solid phase, f he veloiy of he fluid and he void fraion. Applying he volumeri models o sound veloiy measuremens Sound veloiy of a slurry Table 3 shows he resuls of Eq. (4) wih s = 52.4 GPa, f = 2.2 GPa (Table ). The alulaed sound veloiies wih Eq. (4) are muh higher han he measured sound veloiy during he experimens. The main reason for his is he overesimaion of he fluid bulk modulus as desribed by Robeys e al. /2/. Therefore he bulk modulus of he fluid is orreed wih Eq. (6), wih he bulk modulus of air 42 kpa and he bulk modulus of waer 2.2 GPa (Table ). Based on his equaion, he air onen (C air ) of he pore fluid an be derived, whih is inluded in Table 3. Furher ompuaions reveal ha he volume fraion air divided by he volume fraion of he binder in he slurry lies in a very small range (Table 3). This ould indiae ha air enered he slurry on he surfae of he hemihydrae pariles and a ypial value is hus 2.7% (V/V) or 0 ml air per kg hemihydrae. Given he Blaine value of 3025 m 2 /g, his would mean ml air per m 2 hemihydrae surfae (= ml/m 2 ), orresponding o an air layer hikness of 32.8 nm. 6

8 s (m/s) A B C D E Table 4 Waer/binder raio Aelaor 0.40% Void fraion Measured Dire mehod Eq. (7) Eq. (8) Eq. (9) Eq. (9) Eq. (0) Eq. (0) Eq. () Eq. () Eq. () Resuls of he dire mehod (Eqs (7)- ()) wih sound veloiy(m/s), speifi densiy (kg/m 3 ), bulk moduli (GPa), shear moduli (GPa) and poison raio (-) aording o Table. Sound veloiy of solid The resuls of Equaion (7)-(0) are shown in Table 4. I an be noied ha he predied values based on Eq. (7) differ from he measured values. Eq. (30) resuls in a oo high veloiy for all measuremens when using he sound speed of 6800 m/s for gypsum (Table ). When using 457 m/s as sound veloiy of gypsum as given by Dalui e al. /23/, he measuremens for he firs wo experimens show good agreemen. Bu he values for he mixures wih higher waer/binder raio (e.g. higher void fraion) are oo low. Boh Eq. (9) and (0) lead o an overesimaion ompared wih he experimenal value. The predied values based on Eq. () are lose o he experimenal values for all waer/binder raios. For he lowes waer/binder raios he prediions are oo low, while for he higher waer/binder raios he prediion ends o overesimae he veloiy. The bes resuls for Eq. (7) are found wih he solid sound veloiy of 6800 m/s. Conlusions The model given by Robeys e al. /2/ for prediing he sound veloiy of slurry shows a good fi in he experimens assuming a onsan air onen of 2.7% (V/V) based on he volume of hemihydrae. In ase of he hardened (porous) maerial, he loses fi beween experimenal and predied value is found by he use of he dire mehod. The bes resuls were obained wih he series arrangemen based on he empirial sound veloiy values; Eq. () wih s = 6800 m/s and f = 497. Also he equaion of Dalui e al. /23/ (Eq. (8)) shows a good agreemen for he wo lowes void fraions, using wih s = 457 m/s and n =

9 Referenes // H. J. H. Brouwers, A hydraion model for Porland emen using he work of Powers and Brownyard, In press. Skokie, Illinois, U.S.: Porland Cemen Assoiaion, /2/ N. Robeys, E. Gruyaer, C. U. Grosse, and N. D. De Belie, Monioring he seing of onree onaining blas-furnae slag by measuring he ulrasoni p- wave veloiy, Cemen and Conree Researh, vol. 38, no. 0, pp , /3/ G. Ye, Experimenal sudy and numerial simulaion of he developmen of he mirosruure and permeabiliy of emenious maerials, PhD-Thesis, Delf Universiy of Tehnology, The Neherlands, /4/ H. W. Reinhard and C. U. Grosse, Coninuous monioring of seing and hardening of morar and onree, Consruion and Building Maerials, vol. 8, no. 3, pp , /5/ N. D. De Belie, C. U. Grosse, J. urz, and H. W. Reinhard, Ulrasound monioring of he influene of differen aeleraing admixures and emen ypes for shoree on seing and hardening behaviour, Cemen and Conree Researh, vol. 35, no., pp , /6/ R. Ylmén, U. Jäglid, B. Seenari, and I. Panas, Early hydraion and seing of Porland emen moniored by IR, SEM and Via ehniques, Cemen and Conree Researh, vol. 39, no. 5, pp , /7/ H. W. Reinhard, C. U. Grosse, A. Herb, B. Weiler, and G. Shmid, Verfahren zur Unersuhung eines ersarrenden und/oder erhärenden Werksoffs miels Ulrashall, Paen pending under No a he German Paen Insiuion, Munih, Germany, 999. /8/. Shiller, The ourse of hydraion: Is praial imporane and heoreial inerpreaion, Journal of Applied Chemisry and Bioehnology, vol. 24, no. 7, pp , 974. /9/ M. Losso and E. Viveiros, Sound insulaion of gypsum board in praie, presened a he The 2005 Congress and Exposiion on Noise Conrol Engineering, Rio de Janeiro, Brazil, /0/ C. Haeker e al., Modeling he linear elasi properies of Porland emen pase, Cemen and Conree Researh, vol. 35, no. 0, pp , // P. F. Shofield, I. C. Sreon,. S. nigh, and S. Hull, Powder neuron diffraion sudies of he hermal expansion, ompressibiliy and dehydraion of deueraed gypsum, Physia B: Condensed Maer, vol. 234, pp , 997. /2/ S. Meille and E. J. Garbozi, Linear elasi properies of 2D and 3D models of porous maerials made from elongaed objes, Modelling and Simulaion in Maerials Siene and Engineering, vol. 9, no. 5, pp , 200. /3/ CRC handbook of hemisry and physis., 89h ed. Boa Raon Fla. ;London: CRC; Taylor & Franis, /4/ L. insler, Fundamenals of aousis, 4h ed. New York: Wiley, /5/ Q. L. Yu and H. J. H. Brouwers, Mirosruure and mehanial properies of - hemihydrae produed gypsum: an insigh from is hydraion proess, Consruion and Building Maerials, 20. /6/ M. Hunger and H. J. H. Brouwers, Flow analysis of waer-powder mixures: Appliaion o speifi surfae area and shape faor, Cemen and Conree 63

10 Composies, vol. 3, no., pp , /7/ M. Hunger, An inegral design onep for eologial Self-Compaing Conree, PhD Thesis, Eindhoven Universiy of Tehnology, Eindhoven, The Neherlands, 200. /8/ C. U. Grosse and F. Lehmann, Ulrasound measuremens of he hydraion rae of hemihydraes. Sugar, Germany: Maerialprufungsansal, Universia Sugar, /9/ A. H. Harker and J. A. G. Temple, Veloiy and aenuaion of ulrasound in suspensions of pariles in fluids, J. Phys. D: Appl. Phys., vol. 2, no., pp , 988. /20/ J. C. Ausin, A.. Holmes, J. S. Tebbu, and R. E. Challis, Ulrasoni wave propagaion in olloid suspensions and emulsions: reen experimenal resuls, Ulrasonis, vol. 34, no. 2, pp , 996. /2/ T. E. Gómez Álvarez-Arenas, L. Elvira Segura, and E. Riera Frano de Sarabia, Charaerizaion of suspensions of pariles in waer by an ulrasoni resonan ell, Ulrasonis, vol. 39, no. 0, pp , /22/ D. Roh, D. Sang, S. Swikard, and M. DeGuire, Review and Saisial analysis of he Ulrasoni veloiy mehod for esimaing he porosiy fraion in Polyrysalline maerials. Cleveland, Ohio: NASA, 990. /23/ S.. Dalui, M. Royhowdhury, and.. Phani, Ulrasoni evaluaion of gypsum plaser, Journal of Maerials Siene, vol. 3, no. 5, pp , 996. Auhors: Ir. A.C.J. de ore Deparmen of Civil Engineering Fauly of Engineering Tehnology Universiy of Twene P.O. Box 27, 7500 AE Enshede The Neherlands Prof. Dr.Ir. H.J.H. Brouwers Fauly of Arhieure, Building and Planning Eindhoven Universiy of Tehnology P.O. Box 53, 5600 MB Eindhoven, The Neherlands 64