Prediction Model for Autogenous Shrinkage of Concrete with Different Type of Cement

1. Prediction Model for Autogenous Shrinkage of Concrete with Different Type of Cement Shingo MiyazawaDepartment of Civil Engineering, Ashikaga Institute of Technology Ashikaga, Japan Ei-ichi TazawaResearch and Development Initiative, Chuo University Tokyo, Japan

2. Autogenous shrinkage should be considered in order to calculate • thermal stress in massive concrete • long term deflection in RC members • time dependent loss of prestressing force (JSCE,1998) Prediction of autogenous shrinkage

3. ？ ？ Prediction Model for autogenous shrinkage of concrete εc(t)＝γ·εc0(w/c)·β(t) (×10-6) (JSCE, 2002) Ultimate autogenous shrinkage εc0(w/c)＝ 3070exp{－7.2(w/c)} (0.2≦w/c＜0.5) 80 (0.5≦w/c) Effect of type of cement : γ=1.0 (OPC) γ？ (other type of cement) Development of autogenous shrinkage β(t)＝1－exp{－a(t－t0)b｝

4. Experimental Procedures

5. Materials • river sand • crushed stone (maximum size: 20mm) • polycarboxylic acid type superplasticizer (w/c 0.18～0.4) • air-entraining and water-reducing agent (w/c 0.5～0.65)

6. Measurement of autogenous shrinkage before demolding (JCI, 1996) start of measurements : initial set

7. 300mm Contact gauge Measurement of autogenous shrinkage after demolding (JCI, 1996) Measurements: 1 day, 3 days, 7 days, 28 days, ……2 years Curing: 20℃

8. Test results (1) - Effect of type of cement on autogenous shrinkage -

9. w/c=0.22 w/c=0.4 w/c=0.25 w/c=0.5

10. Autogenous shrinkage of cement paste with various types of cement (Tazawa & Miyazawa, 1992)

11. ○ △ ☆ ○ △ ☆ ○ W/C=0.30 ▲ ◇ △ △ ○ ☆ ▲ ◇ □ ◇ ▲ ☆ ◇ □ ▲ □ □ ★ ★ ★ Age: 7, 14, 28, 70 days Original length : 24 hours from casting 1000 ★ εc(t)＝γ·εc0·β(t) (JSCE, 2002) Observed autogenous shrinkage (×10-6) 500 0 1000 500 Calculated autogenous shrinkage (×10-6) Autogenous shrinkage of cement paste at age t (×10-6) εp(t) ＝ A･αC3S(t)･(C3S%)＋B･αC2S(t)･(C2S%)＋C･αC3A(t)･(C3A%) ＋D･αC4AF(t)･(C4AF%)＋E･(Blaine)＋F (Tazawa & Miyazawa, 1992) αi(t) : degree of hydration of mineral compound (%) (Blaine) : Blaine fineness of cement (cm/g2) A, B, C, D, E and F : constants γ ＝－0.0042･(C3S%)－0.0049･(C2S%)＋0.125･(C3A%) 　　 ＋0.093･(C4AF%)＋0.00015･(Blaine)－0.90

13. Test results (2) - Development of autogenous shrinkage with time -

14. 65 40 30 22 25 17 20 Age (days) w/c（％） Strain Effect of w/c on autogenous shrinkage of concrete (OPC)

15. β(t)＝1－exp｛－a（t－to）b｝ εc (t) /εc (91) w/c=0.40 Age (days)

16. b = 0.251exp{2.49×(w/c)} a = 3.27exp{－6.83×(w/c)} a b ●obs. Cement: OPC ●obs. Cement: OPC w/c w/c

18. εc(t)＝γ·εc0·β(t) (×10-6) (JSCE, 2002) Ultimate autogenous shrinkage εc0＝ 3070exp{－7.2(w/c)} (0.2≦w/c＜0.5) 80 (0.5≦w/c) Effect of type of cement : γ=1.0 (OPC) Development of autogenous shrinkage β(t)＝[1－exp{－a(t－t0)b｝] a = 3.27exp{－6.83×(w/c)} b = 0.251exp{2.49×(w/c)}

19. Observed autogenous shrinkage (×10-6) Observed autogenous shrinkage (×10-6) Cement : OPC Age : 28 days NPCMPC LPC LPC Predicted autogenous shrinkage (×10-6) Predicted autogenous shrinkage (×10-6) Relation between predicted and observed autogenous shrinkage (Measured by 15 organizations)

20. Conclusions • Autogenous shrinkage of concrete is strongly dependent on type of cement. The coefficient γ in JSCE model, which describes the influence of cement type, has been determined on the basis of mineral composition of cement. • Development of autogenous shrinkage with time is dependent on w/c. The coefficients a and b in JSCE model, which describe the development of autogenous shrinkage, have been proposed as functions of w/c. • Autogenous shrinkage calculated form the proposed model was compared with the observed values, and it is proved that the model has adequate accuracy for practical purposes.

21. 予備

22. Observed autogenous shrinkage (×10-6) Cement : OPC Age : 28 days Predicted autogenous shrinkage (×10-6) (Measured by 15 organizations)

23. Observed autogenous shrinkage (×10-6) NPCMPC LPC LPC Predicted autogenous shrinkage (×10-6) (Measured by 15 organizations)

24. Figure 1 – Influence of cement type on autogenous shrinkage of cement paste.

25. ○ △ ☆ ○ △ ☆ ○ W/C=0.30 ▲ ◇ △ △ ○ ☆ ▲ ◇ □ ◇ ▲ ☆ ◇ □ ▲ □ □ ★ ★ ★ ★ Mineral compound (%) Cement C2S CaSO4 C3S C3A C4AF ○ 49.4 23.9 8.8 9.4 3.4 N 48.4 31.2 12.2 △ H 2.0 2.98 64.6 9.7 □ M 8.8 8.5 4.93 ◇ 1.9 13.7 3.91 S 58.0 18.5 ☆ 67.2 4.25 11.2 11.6 0.6 W 14.0 56.2 ▲ 1.8 3.74 O 20.7 2.4 ★ L 27.8 56.3 7.6 3.74 Age: 7, 14, 28, 70 days Original length : 24 hours from casting 1000 Observed autogenous shrinkage (×10-6) 500 0 1000 500 Calculated autogenous shrinkage (×10-6)

26. a b w/c 0.20 1.2 0.4 0.23 1.5 0.4 0.30 0.6 0.5 0.40 0.1 0.7 0.5-0.6 0.03 0.8 βas(t)＝1ｰexp｛ｰa（ｔｰｔo）b｝