Yoshiyuki KUROKAWA*, Yasuo TANIGAWA*, Hiroshi MORI* and Rie KOMURA** ABSTRACT

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1 TRANSACTINS F THE JAPAN CNCRETE INSTITUTE VL A STUDY N THE SLUMP TEST AND SLUMP - FLW TEST F FRESH CNCRETE Yoshiyuki KURKAWA*, Yasuo TANIGAWA*, Hiroshi MRI* and Rie KMURA** ABSTRACT The slurnp test is a popular consistency test and is applied in the quality control testing of fresh concrete at construction sites. It is a well-known that the property of fresh concrete can be expressed approximately by Bingham's rnodel with yield value and plastic viscosity. The purpose of this study is to improve the rnethod of estimating rheological constants of fresh concrete using the slurnp test, which has been proposed by the authors earlier, and to discuss the factors affecting the slumping behavior by using the viscoplastic finite elernent rnethod. 1. INTRDUCTIN The slurnp test has been established as a method for the quality control of concrete. Sorne theoretical investigations into this testing method, based on rheology, have been reported (1-3). It has been made clear by these investigations that the slurnp value of fresh concrete increases with the yield value, and that the yield value can be estirnated approximately from the slump value. n the other hand, the plastic viscosity of fresh concrete, another constant of Bingham's rnodel, is a parameter relating to the flowing velocity, so it is difficult to estimate from the slurnp value. In the case of high-fluidity concrete and high-strength concrete, however, the evaluation of viscosity is critica1 to predict consistency. Therefore, both the method to estimate plastic viscosity frorn the relationship between the height of the top surface of fresh concrete (slumping) and the time during slurnp-flowing (4). and the rnethod to evaluate the flowing time to reach a certain flow value as the index of viscosity, have been proposed (5-7). In this study, the estimating method of rheological constants of fresh concrete based on slumping behavior is proposed by extending the theory reported by the authors (4). Various factors affeciing the behavior of fresh concrete in the slump test are discussed in comparkon with the results of analysis by using the viscoplastic finite element method proposed by the authors (). ure, School of Engineering, Nagoya University earch Laboratory, Nihon Cement Co., Ltd.

2 26 2. ITEMS MEASURED IN THE SLUMP TEST The items measured in the slump test and expanded slump test are as follows: 10 - o 1) Slump value SI. (crn) 2) Slump-flow value Sf: (mm) : Final 2 20 horizontal spread of material, measured in 30 two directions at right angles ) Slumping curve sl-t : Relationship SJ (mm) value sl., and the flowing time. 4) Slump-flowing curve sj-t : Relationship between the slump-flowing value and the flowing time. Though it is difficult to measure this curve exactly, the outline can be approximated from the time taken to reach a certain sl. An example of the relationship between the slump value S1. and the slump-flow value S is shown in Fig. 1. The slurnp value SI. is alrnost inversely proportional to the square of the slumpflow value S because of the constant voluine of the material. The theoretical curve obtained on the assumption that the final shape of the material in the slump test is a simple cuí cone of which the top radius is half of the bottom radius is also shown in Fig. 1. The experimental results are in good agreement with the analytical curve when 5 > 300mm. 3. ESTIMATIN F RHELGICAL CNSTANTS 3.1 YIELD VALUE ry (Pa) The yield value zy can be expressed by the function of the slump value SI. or slump-flow value Sf: based on the static equilibrium of externa1 forces and resistance stress (1-3). The equations to estimate the yield value of material with a density p=2300kglm3 are shown as follows: Fig.2 Comparison between estimated Fig.3 Relationship between yield value zy zy(s1.) and zyw 1 and slump-flow value S

3 SI. 27 where, G: Acceleration of gravity (=9.067m/sZ), H: Initial height of material (=30cm), Vol. : Volume of slump cone (m3) The companson of the yield value zy (SI.) estimated by Eq. (1) with ry (5 ) by Eq.(2) is shown in Fig. 2. In case of high-slump material whose zy(s1.) is lower than 200Pa, the final shape becomes almost flat, so the measured slump-flow value becomes lower than the theoretical result obtained on the assumption of cut cone shape, and zy (Sf.) becomes higher than zy (SI.). In case of the material whose v(s1.) is higher than 200Pa, contrady, its lower portion spreads, so the measured slump-flow value becomes higher than the theoretical result, and zy (Sf.) becomes lower than 9 (SI.). The relationship between the yield value zy estirnated from Eqs.(l) and (2) and the slump-flow value S is shown in Fig. 3. The yield value decreases linearly with increasing slumpflow value. 3.2 PLASTIC VISCSITY q (Pa. s) The plastic viscosity q can be estimated by cornpanson of the curvature of measured slumping curve with theoretical one (4). The theoretical slumping curve of material with density p =2300kg/m3 is expressed by the hyperbola function of time t(s) as follows: si. = SI PG q = SI. - 21,9 1 T +X 1 (3) The following functions are used to estimate the plastic viscosity q from the reaching time of slump-flowing to a certain value t~f(7). In those functions, t5m is the reaching time of slumpflowing s to 500mm. Assurning that the ratio of top to bottom radii is constant, the plastic viscosity q can be estimated from the slump value SI. or the slump-flow value S$ and the time t503 = q= 7 p G SI. { f.^ ( SI. - H ) + D2 H } 7200 ( f.^ H - D2 H ) 7 p G D2 H ( Sf.2 - D2 ) ( Sf.2 - f.^ ) 7200 Sf.4 ( f.^ - D2 ) tsf,, 77 ( Si., tsm) = ( 0.70 sf. q(sf.,t,,)= x SI. ) tsm where, D: Bottom radius of slump cone (=200mm) The theoretical equation to estimate the plastic viscosity q with the ratio of top to bottom radii corrected by the slump value SI. and the slump-flow value S are shown as follows:

4 2 Fig.4 Comparison between estimated q values sf ímm) Fig.5 Relationship between plastic viscosity q and slump-flow value S' 7pGD2HS1.( Sf.2-sf.2) q= 7200 Sf.* { f.^ H - Sf.2 ( H - SI. )}'f. ' If the value of slump-flowing ' s at a measured time is nearly Sf., the estimation accuracy of the plastic viscosity decreases, because the theoretical slump-flowing value s& becomes the slumpflow value SJ at infinite time. Figure 4 shows a companson of the plastic viscosities of high-fluidity concrete estimated from Eqs. (4), (5) and (6). As obvious in this figure, q(s5, bm ) is alrnost equal to q(si., S',m ). Therefore, it can be considered that the estimation of the plastic viscosity from Eq. (5) is convenient and practica1 in case of high-fluidity concrete. Figure 5 shows a companson of the plastic viscosities q(sl.) estimated by companng the measured slumping curve with Eq. (3), q(sl., t5m) and q(s'. tsm). The value of q(s1.) is lower and less variable than the values of q(sl., f5m) or q(sf., fsm), because the slump values SI. measured by the slumping curve used in the companson are almost constant, but the slump-flow values Sf of these materials vary. 1 ~ 500Pa - Tensile stress i1 =600Pa.b - Compressive stress 4. FACTRS AFFECTING SLUMPING BEHAVIR Slumping behavior can be measured under conditions of less confinement at the material boundary, and be easily analyzed theoretically or numerically. In actual concrete flow, however, vanous factors complicate the slumping behavior. In this section, the adequacy of the assumption used in this theory is discussed by companng the theoretical results with the analytical ones obtained by using the dynamic viscoplastic finite element method (VFEM), where the effect of bulk elasticity is considered (). 4.1 STRESS DISTRIBUTIN The stress distnbution in flowing material at the beginning of Without slipping resistance W;th slipping resistance Fig.6 Stress distribution in material

5 ~~ 29 \- t= 10s A0 o 4 zc without slipping with slipping resistance resistance 711 Fig.7 Deformation of material obtained by VFEM Fig. Relationship between slumping value sl. and slump-flowing value s$ slumping (0.02sec) obtained by VFEM is shown in Fig. 6, where the principal stresses at the integration points of each element are shown. As obvious in this figure, almost equivalent compressive and tensile stresses exist in vertical and horizontal directions at the beginning of slumping, and the influence of slipping resistance stress is hardly recognized SHAPE F SLUMPING MATERIALS t (s) Fig.9 Measured slumping curve and It is assumed in this theory that the shape of slump-flowing curve the slumping material is always a cut cone. However, the practica1 shapes of material after slump testing vary with the fluidity of the matrix mortar, the volume fraction of coarse aggregate and so on. An example of the deformation of slumping material is shown in Fig. 7. According to this figure, ignonng the slipping resistance on the bottom surface, the top portion caves in significantly and the slump-flow becomes higher. n the other hand, in cases with slipping resistance, the slump flow is lower and the shape of the material is almost a cut cone. The companson of the slumping value sl. and the slump-flowing value s$ obtained by this theory with those using VFEM are shown in Fig.. The curves in this figure hardly vary with the plastic viscosity. The curves obtained by VFEM without slipping resistance and those obtained by this theory are almost unchangeable against the change of yield value. According to this figure, the curve by VFEM with siipping resistance almost corresponds to the theoretical one, because the shape of the material maintains a cut cone shape. The slumping curve and the slump flowing curve measured by VTR by using fresh concrete with W/C=30% are shown in Fig. 9. At first, the concrete tends to shrink in vertical direction, and then spreads slightly in horizontal direction. The slump-flowing curve is smoother than the slumping curve, because of the influence of the contact with cone, and this tendency is more remarkable in case of high-fluidity concrete. 4.3 SLIPPING RESJSTANCE N BITM SURFACE o h- v 2 m E - E 6 The comparisons of the slumping and slump-flowing curves obtained using this theory with those obtained by VFEM are shown in Fig. 10. The slipping resistance stress, which increases

6 30 -\o E 59 q =ópa.s ] I I -\o E - $9 N t (s) - 10 E - i u - i (a) Effect of yield value (b) Effect of plastic viscosity Fig. 10 Comparison of theoretical and numerical slumping and slump-flowing curves t (s) Fig. 1 1 Comparison of theoretical, numerical and experimental slumping curves (with slipping resistance) f (s) Fig. 12 Initial slumping curve with increasing slipping velocity, is considered on the bottom surface in VFEM (,9). According to these slumping curves, the numerical results without slipping resistance are in good agreement with the theoretical ones. However, the final slump value S1. and the curvature by VFEM are slightly lower and higher, respectively, than the theoretical results. This tendency becomes more remarkable in case of the numerical results with slipping resistance. Therefore, the yield value and the plastic viscosity estimated by this theory become higher and lower, respectively. n the other hand, the same tendency in slumping curves is observed in slump-flowing curves. The difference between the slump-flow value. 5 calculated by VFEM and theory becomes considerably larger than in the case of slumping curves. ne of the causes of this difference is considered to be incorrect parameters related to the slipping resistance used in this calculation. Therefore, investigation of the behavior of slipping resistance in detail is needed (9). The measured slumping curve, the theoretical one and the nurnerical one by VFEM with slipping resistance are compared in Fig. 11. The yield valuery and the plastic viscosity r/ of this concrete were estimated from the numerical curve by VFEM as ~y =100(Pa) and r/ =00(Pa. s),

7 31-9 E' v < mr4 m Gravel content (X 60kg/m3) QI gz E v E - g" m,? gg ch s o I Gravel content ( X 60kg/m3) Fig. 13 Relationship between slump value, slump-flow value, rheological constants and gravel content and from the theoretical curve as TY =350(Pa) and 7 =500(Pa. s). Bc 4.4 INERTIA FRCE The theory of slumping is constructed based on static equilibrium of forces, so the inertia force is not considered in this study. As a result, the estimation accuracy decreases slightly in case of the slumping with high velocity. The initial shape of the slumping curve is shown in Fig. 12. The VFEM used is a dynamic method, so the effect of inertia force can be considered. In case of high-fluidity concrete, however, the effect of inertia force is minimal because of slow flow due to its high viscosity. 4.5 RESTRAiNT BY SLUMP CNE The deformation of material is restrained in a horizontal direction while the material touches the slump cone, so the beginning of slumping is affected by the lifting of the cone. The authors have reported the relationship between the lifting velocity of the slump cone and the slumping curve, by using a numerical method (3). Furthermore, it can be recognized from the measured slumping curves shown in Fig. 11 that the deformation of material is restrained in the initial few seconds. Therefore this period must be excepted when this theory is applied to estimation. 4.6 CNE SIZE AND SHAPE Recently, various kinds of concretes has been developed and used, so the shape and size of the ordinary slump cone are not always the best for such concretes. Though this theory can be applied to various cne sizes and shapes, the range where good accuracy of estimation can be obtained must be investigated. 4.7 CARSE AGGREGATE The relationships between the slump value, the slump-flow value, the rheological constants and the gravel contents are shown in Fig. 13. It can be said that the slump-flow value is more sensitive to the content of coarse aggregate than is the slump value.

8 32 5. CNCLUSIN In this paper, a new method to estimate the rheological constants by improving the theory of slumping was proposed. The assumptions used in this theory were confirmed by comparkon with the numerical resuit obtained by the viscoplastic finite element method or the experimental one, and the factors affecting the slumping behavior were discussed. ACKNWLEDGEMENT The authors would like to acknowledge Mr. Kazuki Nishinosono (Nagoya University) and Mr. Tsunehiro Kunieda (Daido Institute of Technology) for their cooperation. Financia1 support by Grand-in-Aid for Scientific Research by the Ministry of Education, and from the Foundation of Cement Association of Japan are gratefully acknowledged. REFERENCES (1) Murata, J., " Flow and Deformation of Fresh Concrete," Materiaux et Construction, Vo1.17, No. 9, 194, pp (2) Mizuguchi, H., " Correlation between Yield Value, Plastic Viscosity and Consistency of Plain Fresh Mortar and Concrete," Proceedings of the Japan Concrete Institute, Vol. 7, July 195, pp (in Japanese). (3) Tanigawa, Y. and Mori, H., " Evaiuation of Consistency of Fresh Concrete - What Properties are Estimated by Slump Value? -," Concrete Joumal, Vol. 25, No. 5, May 197, pp (in Japanese). (4) Tanigawa, Y., Mori, H., Kurokawa, Y. and Komura, R., " Rheologicai Study on Slumping Behavior of Fresh Concrete," Transactions of the Japan Concrete Institute, Vol. 14, December 1992, pp. 1-. (5) Kasai, Y., Hiraishi, S., Tobinai, K. and sada, K., " Experimental Study on Mix Proportion, Consistency, Strength and Shrinkage of Flowing Concrete with rdinary Strength" Proceedings of the Japan Concrete Institute, Vol. 14, No. 1, June 1992, pp (in Japanese). (6) Yamaguchi, S., Kishitani, K., Sugimoto, M. and Yamamoto, T., " Study on High Fiuid Concrete using Superplasticizer of Polycarboxyiic Acid Type," Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, A, August 1992, pp (in Japanese). (7) Kurokawa, Y., Tanigawa, Y., Mori, H. and Komura, R., " Study on Slumping Test of Fresh Concrete," Transactions of the Japan Concrete Institute, Vol. 15, December 1993, pp () Tanigawa, Y., Mori, H., Kurokawa, Y. and daka, S., " Flow Simulation of Fresh Concrete by Dynamic Viscopiastic Analysis," Transactions of the Japan Concrete Institute, Vol. 14, December 1992, pp (9) Mon, H. and Tanigawa, Y., " Simuiation Method of Flow of Fresh Concrete Subjected to Vibration," Journal of Structural and Construction Engineenng, Transactions of Architectural Institute of Japan, No. 3, June 19, pp (in Japanese).