PREDICTION OF CONCRETE COMPRESSIVE STRENGTH

PREDICTION OF CONCRETE COMPRESSIVE STRENGTH Dunja Mikuli (1), Ivan Gabrijel (1) and Bojan Milovanovi (1) (1) Faulty o Civil Engineering, University o Zagreb, Croatia Abstrat A ompressive strength o onrete is onsidered as its basi material property. The onventional pratie is that other mehanial and physial properties are brought into orrelation with the ompressive strength. Thereore, the predition o ompressive strength has always been o the greatest importane. A number o models or the predition o ompressive strength have been developed. Generally, these models ould be divided into three groups: 1. Models whih predit the ompressive strength o onrete ater 28 days or an ultimate ompressive strength or onrete o a ertain omposition. Conrete is assumed as a omposite ombined o ement, water, aggregate and air. 2. Models whih predit the development o ompressive strength with time rom a moment o asting. In these models onrete is onsidered homogenous. They are based on the experimentally obtained orrelation or onrete o a ertain omposition (e.g. maturity method). 3. Models where onrete is onsidered as a omposite and, on the basis o its omposition (w/ ratio, type o ement, type and paking density o aggregate), the ompressive strength o its onstituents and degree o the hydration time development o the ompressive strength are predited. This paper presents an overview o the models or onrete ompressive strength predition. 1. INTRODUCTION During the last 100 years, onrete has beome the most ommonly used onstrution material. The aessibility o materials or manuaturing, illing apabilities o resh onrete and its load-bearing apaity in hardened state have all ontributed to this. Sine the beginning o 20th entury, aspiration and tendeny exist to reate, that is, to manuature onrete, whih would have harateristis neessary or speii use. This problem has been solved in many dierent ways but it annot be said that it is entirely solved. Conrete is a omposite material whose properties depend on many parameters suh as properties o onstituents, a method and onditions o mixing, quality o plaing and ompation and a method and onditions o uring. 503

Conrete has great ompressive strength, thus its usage in strutures is oused on the exploitation o this property, that is, arrying o a ompressive load. Thereore, engineers and researhers wish to manuature onrete with a speii ompressive strength, but this is not an easy task. Models used to evaluate the ompressive strength o onrete have been developed sine the beginning o onrete usage. In this paper, overview o dierent models or predition o the onrete ompressive strength is presented. 2. MODELS FOR PREDICTION OF CONCRETE COMPRESSIVE STRENGTH The omplexity o ompressive strength development in onrete an be demonstrated by an ininite number o papers published on this subjet. The number o parameters involved in reating the harateristi o onrete alled ompressive strength is exeptionally large and the ways they aet the ompressive strength are still being investigated. We know that the ompressive strength is the harateristi o onrete whih an be pereived on a maro level, i.e. engineering level and that it is a result o mirostruture properties o onrete. Beause o the impossibility to researh mirostruture properties o onrete and also beause o the at that the methods o measuring on the nano and miro level still need to be developed, we are restrited on the phenomenologial observation and assoiation o inluene o dierent parameters on the ompressive strength o onrete. However, this does not mean that developing o mathematial models is a useless task. It means that it will be neessary to make a ertain number o experiments during the modelling, whih will help in the model alibration. In suh a manner, we an determine the onstants whih help to onsider the inluene o dierent parameters in an indiret manner. During years, a number o models or the predition o ompressive strength have been developed. Generally, these models an be divided into three groups: 1. Models whih predit the ompressive strength o onrete ater 28 days or an ultimate ompressive strength or onrete o a ertain omposition. Conrete is assumed as a omposite ombined o ement, water, aggregate and air. 2. Models whih predit the development o ompressive strength with time rom a moment o asting. In these models onrete is onsidered homogenous. They are based on the experimentally obtained orrelation or onrete o a ertain omposition (e.g. maturity method). 3. Models where onrete is onsidered as a omposite and on the basis o its omposition (w/ ratio, type o ement, type and paking density o aggregate), the ompressive strength o its onstituents and the degree o hydration time development o the ompressive strength is predited. 2.1 Predition o ompressive strength o onrete based on its omposition At the beginning o 20 th entury, Abrams suggested the empirial expression where the ompressive strength o onrete is dropping with inreasing o w/ ratio: A w/ (1) B 504

where A and B are onstants that have been experimentally determined and w/ is a water to ement ratio. Popovi has extended the Abrams es expression by taking into aount the amount o ement in onrete, as well as the amount o air: A 0 000637 0 0279 (2) w/ +, +, a B where, is mass o ement in 1m 3 o onrete and a is the amount o air in %. The expression (2) shows that the inrease o the amount o ement in onrete mixture results in the lower ompressive strength o onrete. The same inluene has the inrease o w/ ratio and the amount o air. Inreasing the ompressive strength on the aount o dereasing w/ ratio is dropping with the inreasing the amount o ement in the onrete mixture [1]. Many authors have suggested new expressions or prediting the ompressive strength o onrete, like or example Walz, Bolomey, and others. They have predited the ompressive strength o onrete by using inormation on the ompressive strength o ement [1]. Feret has predited the ompressive strength o onrete beore Abrams, by using the volume amount o ement in a ement paste: 2 v k v + vw + va where, v, v w i v a are volumes o ement, water and air in a onrete mixture, and k is the experimentally determined onstant. Models mentioned above are based on the dependene between the ement paste (w/ ratio, ompressive strength) and ompressive strength o onrete, that is, data about the ement paste properties and all other inluenes are taken into aount by oeiients. Restrains o this approah are notied with the development o high perormane onrete in whih aggregate has a signiiant inluene. De Larrard [2] and his assoiates have taken into aount the inluene o aggregate with a parameter alled Maximum Paste Thikness (MPT). The parameter MPT takes into aount the inluene o aggregate volume and the maximum size o aggregate. In their model, De Larrard and his assoiates expanded the Feret s model aording to the expression (4). The ompressive strength o onrete is reversely proportional to MPT. 2 v 1 Kg R28 013. v + vw + va MPT where, K g is a onstant that must be alibrated on some available experimental results, R 28 is a ompressive strength o ement ater 28 days, determined aording to EN 196-1. De Larrard also sets a model or the ompressive strength o onrete where onrete is a material made in two phases, one phase makes rigid and inert aggregate that is spattered in ement matrix (seond phase). The ompressive strength o matrix,m is deined as a ompressive strength o a ement paste multiplied by a term desribing the MPT eet: 013, (5),m,p MPT where,p is the paste strength. Paste strength an be alulated aording to the modiied Feret ormulae: (3) (4) 505

2,85 v,p 13,4 R28 v + vw + va Given ormulae an be used or prediting the ement paste s ompressive strength ater 28 days, ured in sealed onditions. The ompressive strength o onrete an be alulated by : a,m (7) b + 1,m where a and b are empirial onstants whih depend on an aggregate type. 2.2 Models whih predit the development o ompressive strength In aore mentioned models, the ompressive strength o hardened onrete is predited, that is the ompressive strength o onrete ater 28 or more days. In engineering pratie, it is oten useul to have inormation about the ompressive strength o onrete ater 3 or 7 days. Multiple mathematial models whih desribe the development o the onretre s ompressive strength in time have been suggested. The ollowing hyperboli equation or a strength gain is oten used: k(t t 0 ) (t),u (8) 1+ k(t t 0 ) where (t) average ompressive strength at age t,,u limiting strength, k rate onstant, t onrete age, t 0 age at start o strength development. Another model is so alled Sandinavian model (equation 9): α τ (t),u exp (9) t where is a time onstant and is a shape parameter [3]. Models shown in equations (8) and (9) are very good in desribing development o the ompressive strength o onrete with time but under a onstant uring temperature. The uring temperature is a parameter that probably has the greatest inluene on the rate o a hydration proess, thus on the rate o the ompressive strength development. Maturity method A maturity method enables taking into aount a mutual inluene o time and temperature on the onrete ompressive strength development. The maturity method is based on measuring the temperature in onrete with an aim to predit the development o ompressive strength during uring under the assumption that there is water available or the ement hydration. So ar, a ew dierent methods or omputing the maturity o onrete have been (6) 506

developed, but probably the most used method is the so alled equivalent age method. This method is based on the Arrhenius equation whih desribes the inluene o temperature on a hemial reation veloity. Aording to the Arrhenius equation, an equivalent age o onrete an be omputed using equation (10): e r t E 1 1 R T T r t(t) e t 0 where : t e (T r ) the equivalent age at the reerene temperature [h] E - apparent ativation energy [J/mol] R - universal gas onstant [J/mol K] T average absolute temperature o the onrete during interval t [K] T r absolute reerene temperature [K]. By using equation (12), the time intervals or temperature o onrete uring are being onverted to their equivalent time intervals or the onrete uring at a reerene temperature. This temperature dependene is desribed by the value o ativation energy (E). To take into aount the temperature inluene on the ompressive strength o onrete, the parameter t in equations (8) and (9) an be replaed with the parameter t e (T r ). Degree o hydration Beause o the at that onrete is hardening on the aount o ement hydration, the onrete strength development an be monitored by monitoring the proess o hydration. Thus, methods o prediting the ompressive strength are orreted with a parameter whih takes into aount a degree o hydration. The degree o hydration () is a parameter whih tells us to what extent the reation between a ement based material and water has developed. The degree o hydration is deined as a ratio o amount o hydrated ement and the initial amount o ement entering the reation (equation 11). The omplete hydration is deined as a stage in whih all ement has reated. amount o ement that has reated until age t α (t) (11) initial amount o ement at age t 0 In the equation 12, the ibmb model whih relates the ompressive strength with the degree o hydration is shown [4]. n α(t) α 0 1 1 α0 (t) (12) where: (t) degree o hydration at age t 1 ompressive strength at ompleted hydration proess n experimentally determined oeiient The inluene o temperature an be taken into aount with ativation energy, that is by using an equivalent age onept. In models shown in expressions (8), (9) and (12), onrete is onsidered as a homogeneous material. Correlation between the ompressive strength and the degree o hydration or (10) 507

maturity o onrete is experimentally determined and it is dierent or eah onrete mixture. 2.3 Models or predition o strength based on omposition and age o onrete In his paper [5], Popovis desribes the ollowing model alled Exponential ement model. In this model, a proess o the onrete strength development is divided in three onseutive stages: zeroth, irst and seond stage. The zeroth stage is a period immediately ater mixing and extends through the dormant period o hydration and part o the setting when the strength o the onrete is negligible. Strength starts to develop during the beginning o the irst stage and an be omputed by: a 1(t t S) ( S/ 300) a 2(t t S) ( S/ 300) 100 C3 e (100 C 3) e t 0 28 (13) a 1(28 t S) ( S/ 300) a 2(28 t S) ( S/ 300) 100 C3 e (100 C 3) e where: t strength o onrete developing during the irst stage 28 strength o onrete o the same omposition at 28 days but made with Type I portland ement and ured or 28 days on the temperature o 22.8 C ; 0 hypothetial strength that onrete would ahieve aording to the expression above, in perentage o the 28 day strength ; C 3 omputed C 3 S ontent o portland ement, perentage. It represents one o the two hardening omponents in the ement model. The seond omponent is everything else in the linker, that is, (100 C 3 ) ; a 1, a 2 rate parameters o the irst and seond hardening omponents, [1/day] ; S Blaine speii surae o the ement, [m 2 /kg] ; t age o onrete, [day] ; t S age when the irst stage o strength development is assumed to end, [day] ; The seond stage o the strength development starts when the rate o diusion takes the ontrol o hydration. The strength developed during the seond stage is assumed to be: ωlog(t / t ) (14) dt d where: dt strength the model predits during the seond stage experimental parameter t d age when the seond stage starts, [day] The onrete strength during the seond stage is omputed as a sum o the ompressive strengths aording to the irst stage model at the age t d and strength alulated aording to the seond stage model. Aording to the author o the model, it an be used or all the types o portland ement, dierent uring temperatures and strengths o onrete at the age o 1 day till 1 year, and a ewer number o experimental results is neessary than in other models or prediting the strength. On the other hand, the model should be upgraded or the appliation on mixed ements. De Larrad has expanded the model or the ompressive strength predition (equation 15) in suh manner that he introdued the so alled kineti parameter d(t) in the ompressive strength matrix. Then the ompressive strength an be omputed by: 508

2,85 (t) 13,4R d(t) + MPT + w + a,m 28 The kineti parameter d(t) is presented like a ement harateristi, and its value is onstant or onrete older than 7 days. Given expression must be enhaned i mineral admixtures (ly ash, silia ume) and illers are present in the onrete mixture. The equation is then: 2,85 d(7) SFI, ji j w a 0,13,m(t) 13,4R + 28 d(t) - 0,0023 + 1 +ρ MPT (16) t eq where: d(7) kineti parameter at the age o onrete o 7 days t time S FI Blaine speii surae o ement i iller mass in 1m 3 o onrete ement mass ement density eq equivalent mass o ement with mineral admixtures The model is made or the ompressive strength predition or the age o onrete o 1 day to 1 year. Conrete an onsist o aggregate with a normal mass and dierent rations, portland ement, water, air and mineral admixtures and illers. This model an predit, with orret alibration o parameters, the ompressive strength o onrete with an auray o 2-3 MPa [2]. 3 CONCLUSION In the paper, dierent models o prediting the ompressive strength o onrete have been shown. Every model has its limitations, that is onditions under whih it gives the best results. In every model there is a possibility or the improvement and expansion. What all models have in ommon is that they need to have a ertain number o experimental researhes to determine the unknown oeiients in equations or to ind suitable orrelations. Models presented in this paper were established by looking at the ompressive strength o onrete as a phenomenologial property, that is by experiments on a maro level. Very atual subjet o researhes at the moment is how to ompute the ompressive strength o onrete starting rom mirostruture, that is by making multi-sale models or prediting the onrete strength. Bentz and assoiates rom NIST institute have developed the Virtual Cement and Conrete Testing Laboratory whih they desribe in their paper [6]. A sotware they developed annot diretly predit the ompressive strength but an predit a modulus o elastiity, and then the ompressive strength an be estimated based on the orrelation o the ompressive strength and modulus o elastiity. 0,13 (15) 509

Figure 1 Mirostruture based predition o the ompressive strength o onrete To build a model o ompressive strength based on a mirostruture (Figure 1), the mirostruture properties and the hemial and physial bonds representing the origin o ompressive strength have to be known. However, that part o researh is still limited by the measuring tehniques apabilities. AKNOWLEDGEMENTS A review o the ompressive strength models presented in this paper is made as a part o the sientii projet inaned by the Croatian Ministry o Siene, Eduation and Sport named From Nano to Marostruture o Conrete (082-0822161-2990). REFERENCES [1] Mikuli, D. 'Theoretial model o onrete quality assurane', (in Croatian) University o Zagreb, Dissertation, 1993. [2] De Larrard, F., 'Conrete Mixture Proportioning, a Sientii Approah', E & FN Spon, (an imprint o Routledge),London, 1999). [3] Carino, N.J. and Lew, H.S. 'The Maturity Method: From Theory to Appliation', in Proeedings o the 2001 Strutures Congress & Exposition, Washington, D.C., May, 2001 (Amerian Soiety o Civil Engineers, Reston, Virginia, 2001.) 19 p. [4] Rostásy, F., Gutsh, A. and Krauß, M. 'Computation o stresses and raking riteria or early age onrete - Methods o ibmb'. IPACS projet report no: BE96-3843/2001:35-4, Task 3, 2001. [5] Popovis, S. 'History o Mathematial Model or Strength Development o Portland Cement Conrete', in ACI Materials Journal V.95, No. 5, September-Otober 1998. pp. 593-600. [6] Garbozi, E.J., Bullard, J.W. and Bentz, D.P. 'Virtual Testing o Cement and Conrete USA 2004' in Conrete International, Deember 2004. pp. 33-37. 510