Providing a framework for optimizing a mixing design of reactive powder concrete (RPC)

Moghaddam, Farid Ghaffari; Akbarpour, Abbas; Firouzi, Afshin

doi:10.2478/otmcj-2020-0024

Figures & Tables

Optimal mixing design with respect to the weight of the compressive strength effect.

Optimal mixing design with respect to the weight of the low cost effect.

Optimal mixing design with respect to the weight of the water penetration effect.

Optimal mixing design with respect to the weight of the surface resistivity effect.

Optimal mixing design with respect to the weight of the modulus of elasticity effect.

An example of the dynamic sensitivity of the options.

The gradient sensitivity of the options.

Optimal mixing design with equal weighting between the criteria.

Mixture proportions of concrete_

No.	Mixtures	Cement content/type (Kg)	W/CM	PCE (kg/m³)	Silica fume (kg/m³)	Colloidal nanosilica (kg/m³)	Powdered nanosilica (kg/m³)	Quartz (0–75 μm), (kg/m³)	Sand (0–75 μm), kg/m³	Sand (0–5 mm), kg/m³	Gravel (5–9.5 mm), kg/m³	Gravel (9.5–19 mm), kg/m³	Quartz (0–1 mm), kg/m³	Quartz (75 μm to 6 mm), kg/m³
1	S62	900/II	0.28	48.7	225	9	90	1,000^*	–	–	–	–	–	–
2	S63	900/II	0.31	48.7	225	9	90	1,000^*	–	–	–	–	–	–
3	S64	900/V	0.28	44	180	18	18	–	1,000	–	–	–	–	–
4	S65		0.247	44	180	18	18	–	1,001	–	–	–	–	–
5	S68	900/V	0.27.4	46.5	180	18	18	–	–	1,000	–	–	–	–
6	S70	900/V	0.27.4	50	180	18	18	–	–	1,000^**	–	–	–	–
7	S72	900/II	0.25.1	52	180	18	–	–	1,100^**	–	–	–	–	–
8	S73	900/II	0.27.2	52	180	18	–	–	1,100^**	–	–	–	–	–
9	S76	900/II	0.30.4	56	165	18	–	1,000	–	–	–	–	–	–
10	S77	900/II	0.27.7	56	165	18	–	–	–	–	–	–	1,000	–
11	RP,S1	900/II	0.31	46	165	18	–	139	–	–	–	–	–	861
12	RP,S2	900/II	0.31	46	165	18	–	50	–	–	–	–	–	950
13	RP,S3	900/II	0.31	46	165	18	–	100	–	–	–	–	–	900
14	RP,S4	900/II	0.31	46	165	18	–	0	–	–	–	–	–	1,000
15	RP,O1	900/II	0.31	46	165	18	165	268	567^*	–	–	–	–	–
16	RP,O2	900/II	0.31	46	165	18	165	567	268^*	–	–	–	–	–
17	RP,O3	900/II	0.31	46	165	18	85	315	600^*	–	–	–	–	–
18	RP,O4	900/II	0.31	46	165	18	85	600	315^*	–	–	–	–	–
19	RP,M1	900/II	0.25	40	165	18	–	–	–	600	–	–	400	–
20	RP,M2	900/II	0.25	40	165	18	–	–	–	500	–	–	500	–
21	RP,M3	900/II	0.25	40	165	18	–	–	–	400	–	–	600	–
22	RP,M4	900/II	0.25	40	165	18	–	–	–	700	–	–	300	–
23	SCC1	400/II	0.48	12	60	..	120	–	–	820	750	–	–	–
24	SCC2	400/II	0.5	9	60	..	120	–	–	820	750	–	–	–
25	SCC3	400/II	0.45	9	70	..	74	–	–	900	525	225	–	–
26	SCC4	400/II	0.45	9	70	..	74	–	–	800	450	400	–	–
27	SCC5	400/II	0.45	9	70	..	74	–	–	900	225	525	–	–
28	C1	400/II	0.45	1.75	..	..	–	–	–	920	440	460	–	–
29	C2	400/II	0.45	1.75	..	..	–	–	–	900	220	700	–	–
30	C3	400/II	0.45	1.75	..	..	–	–	–	850	470	400	–	–

Chemical compositions (%) of quartz sand and silica fume_

	SiO₂	Al₂O₃	Fe₂O₃	CaO	Na₂O	K₂O
Quartz sand	96–98.8	0.151–1.65	0.2–0.7	0.2–0.5	0.03–0.08	0.03–0.1
Silica fume	90	1.3	1.1	1.7	0.5	0.3

Optimal framework for mixing design of the concrete_

No.	Optimum mixture	Aggregate	Cement (kg)/type	Silica fume (kg)	Powdered nanaosilica (kg)	Colloidal nanosilica (kg)	Concrete
1	S76	Quartz (0–75 μm)	900/II	165	–	18	RPC
2	S77	Quartz (0–1 mm)	900/II	165	–	18	MRPC
3	RPM	Quartz + sand (0–1 mm)	900/II	165	–	18
4	RPS	Quartz (75 μm–6 mm)	900/II	165	–	18
5	RPO	Quartz + Ottawa (0–75 μm)	900/II	165	85–165	18	RPC
6	S64–65	Sand (0–75 μm)	900/V	180	18	18
7	S72–73	Crystal sand (0–75 μm)	900/II	180	–	18
8	S62–63	Ottawa sand	900/II	225	90	9
9	S70	Crystal sand (0–5 mm)	900/V	180	18	18	MRPC
10	S68	Sand (0–5 mm)	900/V	180	18	18	MRPC
11	C	Gravel + sand	900/II	–	–	–	C
12	SCC	Gravel + sand	900/II	60–70	74–120	–	SCC

Prices reserved for consumable materials_

Materials	Quartz (ton)	PCE (kg)	Cement (ton)	Silica fume (ton)	Colloidal nanosilica (kg)	Ottawa sand (kg)	Gravel + sand (ton)	Crystal sand (ton)
Price, $	4	1.6	16	44	4.8	3.2	1.2	1.6

Properties of colloidal nanosilica, powdered nanosilica and silica fume_

	SiO₂, %	Size, nm	Specific surface area, m²/g	Salt content (%)	Type	Density, kg/m³ (lb/yd³)
Colloidal nanosilica	99.9	35	400	24	Combiner	1.05 (1.77)
Powdered nanosilica	99	20–30	160–200	100	Powder	0.150–0.220 (0.253–0.37)
Silica fume	90	229	20.7	100	Powder	2.1 (3.54)

Test results for the compressive strength, surface resistivity, water penetration and modulus of elasticity (Ed)_

No.	Mixtures	Compressive strength (28 days), MPa		Surface resistivity, kΩ·cm	Water penetration, mm	E_d, GPa

		23°C	80°C
1	S 62	138.8	–	95	9.5	56.68
2	S63	118.7	–	73	12.1	52.66
3	S64	146.3	–	63.9	12.4	59.32
4	S65	174.5	–	68	12.1	67.82
5	S68	100.6	–	79.1	10.5	49.17
6	S70	118.1	–	89.6	11	53.63
7	S72	120.2	–	107.9	7.5	55.98
8	S73	113.4	–	76.6	10	48.24
9	S76	137	193.5	125	6.1	78.53
10	S77	125.3	187	123	6.6	74.27
11	RP,S 1	98.1	125.3	154	5.2	48.82
12	RP,S2	96.5	127.2	104	5.4	49.29
13	RPS,3	97.6	118.3	112	6.1	50.87
14	RP,S4	95.2	115.4	195	4.2	48.68
15	RP,O1	89.8	112.4	174	4.4	42.05
16	RP,O2	93.5	127.2	121	5.5	43.87
17	RP,O3	95.4	118.6	158	4.1	49.85
18	RP,O4	91.4	115.9	83	7.4	42.61
19	RP,M1	121.2	174.3	124	6.4	65.63
20	RP,M2	119.4	161.2	92	9.5	61.97
21	RP,M3	105.4	145.4	113	7.5	63.97
22	RP,M4	104.3	138.3	180	4.5	59.37
23	SCC1	52.3	–	42.35	15	34.43
24	SCC2	48.9	–	37.5	18	33.76
25	SCC3	57.6	–	77.85	12	38.22
26	SCC4	55.1	–	33	14.3	34.98
27	SCC5	44.2	–	37	16	31.51
28	C1	38.2	–	5.2	21.5	41.57
29	C2	36.5	–	4.8	33.3	37.53
30	C3	35.4	–	7.3	35.5	34.64

Selection options in the software_

Mixtures, kg/m³	S62–63	S64–65	S72–73	S76	RPO	RPM	RPS	S68	S70	S77	SCC	C

Aggregate	Ottawa sand	Sand (0–75 μm)	Crystal sand (0–75 μm)	Quartz (0–75 μm)	Quartz (0–75 μm), Ottawa	Sand + quartz	Quartz (0–1 mm)	Sand (75 μm–6 mm)	Crystal sand (0–5 mm)	Quartz (0–1 mm)	Gravel + sand	Gravel +sand
Cement type	II	V	II	II	II	II	II	V	V	II	II	II
Silica fume	225	180	180	165	165	165	167	180	180	165	6–70	–
Powder nanosilica	90	18	–	–	85–165	–	–	18	18	–	74–120	–
Colloidal nanosilica	9	18	18	18	18	18	18	18	18	18	–	–
Concrete	RPC					MRPC					SCC	C

Providing a framework for optimizing a mixing design of reactive powder concrete (RPC)

Figures & Tables

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Mixture proportions of concrete_

Chemical compositions (%) of quartz sand and silica fume_

Optimal framework for mixing design of the concrete_

Prices reserved for consumable materials_

Properties of colloidal nanosilica, powdered nanosilica and silica fume_

Test results for the compressive strength, surface resistivity, water penetration and modulus of elasticity (Ed)_

Selection options in the software_

Paradigm

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