The Rise and Demise of Egypt’s Largest Pyramids


A Progression of Knowledge
How Were the Pyramids Actually Built?




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Property of RPC | Description | Recommended Values | Types of failure eliminated |
Reduction in aggregate size | Coarse aggregates are replaced by fine sand, with a reduction in the size of the coarsest aggregate by a factor of about 50. | Maximum size of fine sand is 600 µm | Mechanical, Chemical & Thermo-mechanical |
Enhanced mechanical properties | Improved mechanical properties of the paste by the addition of silica fume | Young’s modulus values in 50 GPa – 75 Gpa range | Disturbance of the mechanical stress field. |
Reduction in aggregate to matrix ratio | Limitation of sand content | Volume of the paste is at least 20% greater than the voids index of non-compacted sand. | By any external source (e.g., formwork). |
Components | Selection Parameters | Function | Particle Size | Types |
Sand | Good hardness Readily available and low cost. | Give strength, Aggregate | 150 µm to 600 µm | Natural, Crushed |
Cement | C3 S : 60%; C2S : 22%; C3A : 3.8%; C4AF: 7.4%. (optimum) | Binding material, Production of primary hydrates | 1 µm to 100 µm | OPC, Medium fineness |
Quartz Powder | fineness | Max. reactivity during heat-treating | 5 µm to 25 µm | Crystalline |
Silica fume | Very less quantity of impurities | Filling the voids, Enhance rheology, Production of secondary hydrates | 0.1 µm to 1 µm | Procured from Ferrosilicon industry (highly refined) |
Steel fibres | Good aspect ratio | Improve ductility | L : 13 – 25 mm Ø : 0.15 – 0.2 mm | Straight |
Superplasticizer | Less retarding characteristic | Reduce w/c | _ | Polyacrylate based |
P. Richard and M. Cheyrezy1 | S. A. Bouygues3 | V. Matte9 | S. Staquet10 | ||||
[1995] | [1997] | [1999] | [2000] | ||||
Non fibred | 12 mm fibres | 25 mm fibres | Fibred | Fibred | |||
Portland Cement | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Silica fume | 0.25 | 0.23 | 0.25 | 0.23 | 0.324 | 0.325 | 0.324 |
Sand | 1.1 | 1.1 | 1.1 | 1.1 | 1.423 | 1.43 | 1.43 |
Quartz Powder | -- | 0.39 | -- | 0.39 | 0.296 | 0.3 | 0.3 |
Superplasticizer | 0.016 | 0.019 | 0.016 | 0.019 | 0.027 | 0.018 | 0.021 |
Steel fibre | -- | -- | 0.175 | 0.175 | 0.268 | 0.275 | 0.218 |
Water | 0.15 | 0.17 | 0.17 | 0.19 | 0.282 | 0.2 | 0.23 |
Compacting pressure | -- | -- | -- | -- | -- | -- | -- |
Heat treatment temperature | 20ºC | 90ºC | 20ºC | 90ºC | 90ºC | 90ºC | 90ºC |
RPC 200 | RPC 800 | |
Pre-setting pressurization | None | 50 MPa |
Heat-treating | 20 to 90°C | 250 to 400°C |
Compressive strength (using quartz sand) | 170 to 230 MPa | 490 to 680 MPa |
Compressive strength (using steel aggregate) | -- | 650 to 810 MPa |
Flexural strength | 30 to 60 MPa | 45 to 141 MPa |
Property | HPC (80 MPa) | RPC 200 |
Compressive strength | 80 MPa | 200 MPa |
Flexural strength | 7 MPa | 40 MPa |
Modulus of Elasticity | 40 GPa | 60 GPa |
Fracture Toughness | <10³ J/m² | 30*10³ J/m² |
Abrasive Wear | 2.5 times lower |
Water Absorption | 7 times lower |
Rate of Corrosion | 8 times lower |
Chloride ions diffusion | 25 times lower |
Sl. No. | Sample | Specific Gravity | Particle size range |
1 | Cement, OPC, 53-grade [IS. 12269 – 1987] | 3.15 | 31 µm – 7.5 µm |
2 | Micro Silica [ASTM C1240 – 97b] | 2.2 | 5.3 µm – 1.8 µm |
3 | Quartz Powder | 2.7 | 5.3 µm – 1.3 µm |
4 | Standard sand, grade-1 [IS. 650 – 1991] | 2.65 | 2.36 mm – 0.6 mm |
5 | Standard sand, grade-2 [IS. 650 – 1991] | 2.65 | 0.6 mm – 0.3 mm |
6 | Standard sand, grade-3 [IS. 650 – 1991] | 2.65 | 0.5 mm – 0.15 mm |
7 | Steel fibres (30 mm) [ASTM A 820 – 96] | 7.1 | length: 30 mm & dia: 0.4 mm |
8 | Steel fibres (36 mm) [ASTM A 820 – 96] | 7.1 | length: 36 mm & dia: 0.5 mm |
9 | 20 mm Aggregate [IS. 383 – 1970] | 2.78 | 25 mm – 10 mm |
10 | 10 mm Aggregate [IS. 383 – 1970] | 2.78 | 12.5 mm – 4.75 mm |
11 | River Sand [IS. 383 – 1970] | 2.61 | 2.36 mm – 0.15 mm |
Materials | Mixture Proportions | |||
RPC | RPC-F* | HPC | HPC-F** | |
Cement | 1.00 | 1.00 | 1.00 | 1.00 |
Silica fume | 0.25 | 0.25 | 0.12 | 0.12 |
Quartz powder | 0.31 | 0.31 | - | - |
Standard sand grade 2 | 1.09 | 1.09 | - | - |
Standard sand grade 3 | 0.58 | 0.58 | - | - |
River Sand | - | - | 2.40 | 2.40 |
20 mm aggregate | - | - | 1.40 | 1.40 |
10 mm aggregate | - | - | 1.50 | 1.50 |
30 mm steel fibres | - | 0.20 | - | - |
36 mm steel fibres | - | - | - | 0.20 |
Admixture (Polyacrylate based) | 0.03 | 0.03 | 0.023 | 0.023 |
Water | 0.25 | 0.25 | 0.4 | 0.4 |
RPC | RPC-F | HPC | HPC-F | ||
NC* | HWC** | NC* | HWC** | NC* | NC* |
11 | 12 | 18 | 22 | 8 | 10 |
RPC | RPC with fibres | HPC | ||||
NC* | HWC** | NC* | HWC** | NC* | HWC* | |
Cumulative Charge passed in Coulombs | 4 (less than 10) | 94 | 140 | 400 | 250 | 850 |
ASTM C1202 classification | Negligible | Negligible | Very low | Very low | Very low | Very low |