Compressive strength prediction of Portland cement concrete with age using a new model

Peer review under responsibility of Housing and Building National Research Center.

Figures & data

Fig. 1 Relationship between compressive strength and age for clinker minerals and cement [14]. (a) Normal scale and (b) log scale.

Fig. 2 Relationship between compressive strength and age for concrete mixes [15]. (a) Normal scale and (b) log scale.

Table 1 Raw data from references [14–^[15][16]17,18,19].

Source	Mix	Age (days)
		1	3 (4)	7	14	28	56	112 (90)	224	365	730	1825
Ref. [14]	M1	–	18.2	26.9	–	37.5	42.2	–	–	46.2	48.7	–
	M2	–	17.3	23.9	–	36.3	41.6	–	–	49	50.4	–
	M3	–	19.4	26.6	–	36.1	39.9	–	–	44.9	46.5	–
	M4	–	19.8	28.9	–	41	45.7	–	–	56.9	–	65.4
	M5	–	16.2	23.4	–	37	43.8	–	–	54.3	–	65.1
	M6	–	17.6	27.2	–	44.7	50.2	–	–	56.1	–	63.9
	M7	–	27.3	34.9	–	47.5	50.7	–	–	–	–	65.2
	M8	–	23.1	33.5	–	47.4	52.9	–	–	56.5	–	–
	M9	–	17.8	27.9	–	39.6	45.1	–	–	48.9	–	53.7
	M10	–	17.7	25.4	–	37.7	43.1	–	–	–	–	–
	M11	–	19.7	29.6	–	42.1	48.7	–	–	54	–	63.7
	M12	–	19.4	27.8	–	41.2	46	–	–	56.1	–	61.5
	M13	–	23.9	34.4	38	42.4	46.1	47.9	48.8	50.8	55	59.7
	M14	–	21.4	31	39.2	41	51.2	51.6	55	56.6	61.2	62.2
	M15	–	25.4	33.8	43	44.4	53.9	54	58.2	57.3	61.3	69.2
	M16	–	20.8	29.8	36.8	41.4	44.3	47.9	49	50.1	52.3	53.6
	M17	–	24.3	33.7	39.6	45.5	48.6	51.3	54.4	55.6	61.3	63
	M18	–	21.6	30.2	37.9	42.9	46.9	50.7	52.7	53.5	60.2	58.3
	M19	–	18.9	27.2	35.2	40.3	45.5	48.3	50.9	52.4	56.2	54.8
	M20	–	21.6	30.7	36	40.2	44.5	49.8	53.2	54	58	59.4
	M21	–		23.2	30.6	39.6	45.4	53.2	55.9	60.2	–	62.3
	M22	–	27.1	34	41	44.7	49.4	53	54	55.7	58.8	58.3
	M23	–	21.7	32.7	41.6	47.6	53.4	55.4	60.5	59.5	61.7	63.8
	M24	–	19.5	28.2	35.3	42	48.5	51.1	54.8	57.2	58	66.3
	M25	–	20.7	30	35.7	42.6	44.7	52	50.7	57.6	59.1	68.5
	M26	–	24	33.5	39.5	44.9	50.2	51.3	53.2	52	54.8	56.6
	M27	–	23.1	31.4	37.4	40.6	43.5	48.2	50.9	51.7	56.2	54.7
	M28	–	21.3	32.1	40.7	46.2	51.4	54.5	59.6	58.3	61.5	62
	M29	–	20.8	34	41.1	50	–	57.2	60.5	57.2	59.4	61.1
	M30	–	19.5	27.5	35.4	39.6	46.7	51.5	53.5	52.8	53.9	58.3
	M31	–	19.3	33.4	40.6	45.4	49.1	52.3	54.6	58	61.5	–
	M32	–	19	24.6	33.2	41.2	47.2	54	57.8	60.7	60.2	–
	M33	–	23.6	32.2	38.5	43.2	48.8	50.6	54.8	56.7	51.9	–
	M34	–	21.8	30.3	37.9	42.4	46.1	47.2	54.2	57.8	58.6	–
	M35	–	25.7	35.7	42.1	47.6	52.5	54.2	–	59		58.7
	M36	–	22.9	33.1	39.9	45.6	48.8	54.3	56.3	58.8	58.1	61.3
	M37	–	24.5	33.1	38.2	44	47.1	52.3	53.3	51.8	55.5	58.8
	M38	–	25.7	34.4	38.8	45.1	49	55.7	58	55.4	58.6	57.2
	M39	–	30.5	41	47	56.5	57.3	51.3	59	52.5	63.2	63.3
	M40	–	17.6	27.2	–	44.7	50.2	–	–	–	–	–
	M41	–	27.3	34.9	–	47.5	50.7	–	–	–	–	–
	M42	–	28.8	40.2	43.9	49	55.2	53.3	58.4	62.3	63.4	65.1
	M43	–	29.1	35.2	42.8	46.3	49.7	48.5	50.8	53.1	58.6	58.6
	M44	–	28.8	43.6	50.6	50.6	56.3	58.8	59.2	63.8	64.7	64
	M45	–	23.5	32.9	42.4	48	52.8	53.2	56.4	59	57.8	62.6
	M46	–	24.3	33.7	41.9	47.3	50.4	54.8	57.9	58.6	58.3	64.3
	M47	–	25	–	–	47.4	52.7	51.4	52.9	–	54.6	–
	M48	–	25.7	38.2	44.9	52.3	53	54	54.3	59.1	62.1	66.1
Ref. [15]	M49	22	–	43	–	53	–	–	–	65	–	–
	M50	13	–	30	–	42	–	–	–	55	–	–
	M51	8	–	22	–	32	–	–	–	45	–	–
	M52	5	–	16	–	26	–	–	–	37	–	–
	M53	3	–	10	–	18	–	–	–	28	–	–
	M54	2	–	8	–	14	–	–	–	23	–	–
Ref. [16] nanosilica cured in water	0.0%	–	–	27.3	–	36.8	–	(42.3)	–	–	–	–
	0.5%	–	–	31.6	–	42.7	–	(46.5)	–	–	–	–
	1.0%	–	–	33.1	–	43.6	–	(48.1)	–	–	–	–
	1.5%	–	–	32.2	–	42.9	–	(47.7)	–	–	–	–
	2.0%	–	–	28.5	–	39.7	–	(44.3)	–	–	–	–
Ref. [16] nanosilica cured in lime	0.0%	–	–	27	–	35.4	–	(39.8)	–	–	–	–
	0.5%	–	–	32.1	–	48.1	–	(48.5)	–	–	–	–
	1.0%	–	–	35.5	–	50.4	–	(51.0)	–	–	–	–
	1.5%	–	–	38.9	–	53.8	–	(54.2)	–	–	–	–
	2.0%	–	–	42	–	56.2	–	(56.3)	–	–	–	–
Ref. [17]Silica fume 20 °C	0%	–	(60.2)	66.3	72.9	76.7	–	(87.7	–	–	–	–
	12%	–	(58.4)	66.3	80.6	86.7	–	(88.2	–	–	–	–
	16%	–	(57.5)	69.1	80.1	91.5	–	(94.1)	–	–	–	–
	20%	–	(49.6)	62.1	78.1	84.4	–	(95.5)	–	–	–	–
	24%	–	(54.5)	65.5	79.2	84.2	–	(102.7)	–	–	–	–
	28%	–	(65.0)	76.8	92.1	99.7	–	(119.8)	–	–	–	–
Ref. [17] silica fume 50 °C	0%	–	(61.7)	68.8	70.0	74.0	–	(82.4)	–	–	–	–
	12%	–	(72.6)	77.0	77.9	80.4	–	(79.2)	–	–	–	–
	16%	–	(83.9)	83.8	83.7	82.4	–	(89.0)	–	–	–	–
	20%	–	(87.2)	88.8	93.8	90.7	–	(95.5)	–	–	–	–
	24%	–	(94.8)	95.8	100.4	98.6	–	(101.7)	–	–	–	–
	28%	–	(99.6)	103.1	108.7	110.5	–	(110.3)	–	–	–	–
Ref. [18]	10 °C	3.67	17.33	24.67	–	33.33	–	–	–	Cem V, w/c = 0.4
	23 °C	12.0	23.67	29.33	–	39.67	–	–	–
	50 °C	21.33	31.0	36.0	–	45.0	–	–	–
Ref. [18]	10 °C	2.0	11.0	17.67	–	24.67	–	–	–	Cem V, w/c = 0.5
	23 °C	7.0	17.0	22.0	–	30.0	–	–	–
	50 °C	10.33	17.33	22.67	–	27.0	–	–	–
Ref. [19] metakaolin%	0%	19.07		50.23	57.1	62.6		(72.43)
	5%	21.5		53.8	58.97	63.5		(71.63)
	10%	22.43		62.3	69.23	71.0		(80.07)
	15%	20.23		64.8	74.67	76.0		(83.7)
	20%	19.33		66.47	75.73	82.47		(85.13)
	25%	15.73		62.5	69.77	73.93		(82.23)
	30%	14.53		60.53	72.33	76.73		(81.8)

Fig. 3 Relationship between compressive strength and grade constant (B).

Fig. 4 Relationship between grade constant (B) and rate constant (A).

Fig. 5 Relationship between calculated B values versus predicted corresponding ones using Eq. (10(10) $B=0.005{(f_c)}^{2.20}\text{with}{r}^2=0.91$(10) ).

Fig. 6 Relationship between calculated (A) values versus predicted corresponding ones using Eq. (11(11) $A=1.4035\text{ln}(B)+2.9956\text{with}{r}^2=0.98$(11) ).

Fig. 7 Actual compressive strength values predicted ones at different ages for different concrete mixes.

Fig. 8 Effect of using silica fume on strength development at 20 °C as per the proposed model [17].

Fig. 9 Effect of using metakaolin on the development of compressive strength as per the proposed model [19].

Fig. 10 Effect of using nano silica in concrete mixes on the development of strength as per the proposed model [16].

Fig. 11 Effect of temperature degree on the strength development as per the proposed model [18].

Fig. 12 Effect of temperature degree on the strength development at 50 °C as per the proposed model [19].

Fig. 13 Actual compressive strength values versus predicted ones at different ages for sample calculation example.

Table 2 Sample calculations.

w/c	Notes	1 day	7 days	28 days	1 year	A	B
0.9	^⁎	2	8	14	23	3.67	1.616
	^⁎⁎	1.62	8.75	13.84	23.21
0.8	^⁎	3	10	18	28	4.44	2.81
	^⁎⁎	2.81	11.47	17.63	28.99
0.7	^⁎	5	16	26	37	5.58	6.33
	^⁎⁎	6.3	17.2	25.0	39.2
0.6	^⁎	8	22	32	45	6.23	10.0
	^⁎⁎	10.0	22.1	30.7	46.6
0.5	^⁎	13	30	42	55	7.07	18.21
	^⁎⁎	18.2	31.97	41.77	59.92
0.4	^⁎	22	43	53	65	7.789	30.428
	^⁎⁎	30.42	45.58	56.38	76.38

* Experimental values [15].

⁎⁎ Predicted values using the proposed model Eqs. (9(8) $f=a_0+a_1{c}_1+a_2{c}_2+a_3{c}_3+a_4{c}_4$(8) –11(9) $f_t=A\text{ln}(t)+B$(9) ).