The Lugeon Test: Methodology, Interpretation, and Applications in Geotechnical Engineering

Rate Analysis for Cement Concrete Using Cement, Sand, and Crushed Metal Aggregate

Performing rate analysis for cement concrete involves calculating the costs of materials, labor, and equipment required for a specific volume of concrete. Here’s a step-by-step guide based on my experience in the field.

Step 1: Determine the Quantity of Concrete

First, we need to determine the quantity of concrete required. For this example, let's assume we need 1 cubic meter (m³) of concrete.

Step 2: Calculate the Dry Volume of Concrete

The dry volume of concrete is typically 1.54 times the wet volume to account for the voids in the mix. Therefore, for 1 m³ of wet concrete, the dry volume is:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Dry Volume</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.54</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.54</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">m³</span></span>}$$

Step 3: Determine the Mix Ratio

Assume we are using an M20 mix (1:1.5:3) for reinforced cement concrete (R.C.C) work. This means:

• 1 part cement
• 1.5 parts sand
• 3 parts aggregate

Step 4: Calculate the Quantities of Materials

Cement:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Cement</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\frac{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1</span></span>}}{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.5</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">3</span></span>}}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.54</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\frac{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1</span></span>}}{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">5.5</span></span>}}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.54</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.28</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">m³</span></span>}$$

Since the density of cement is 1440 kg/m³:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Weight of Cement</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.28</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1440</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">403.2</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">kg</span></span>}$$

Number of bags (assuming 1 bag = 50 kg):

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Number of Bags</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\frac{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">403.2</span></span>}}{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">50</span></span>}}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8.06</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\approx </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">bags</span></span>}$$

Sand:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Sand</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\frac{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.5</span></span>}}{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">5.5</span></span>}}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.54</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.42</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">m³</span></span>}$$

Aggregate:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Aggregate</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\frac{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">3</span></span>}}{\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">5.5</span></span>}}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1.54</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.84</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">m³</span></span>}$$

Step 5: Calculate the Cost of Materials

Cement:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Cost of Cement</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">\hspace{0.17em}</span></span>}\text{<span style="background-color: white;"><span style="font-size: medium;">bags</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">Rate per bag</span></span>}$$

Assuming the rate is ₹350 per bag:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Cost of Cement</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">350</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">2800</span></span>}$$

Sand: Assuming the rate is ₹1500 per m³:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Cost of Sand</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.42</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1500</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">630</span></span>}$$

Aggregate: Assuming the rate is ₹2000 per m³:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Cost of Aggregate</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.84</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">2000</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1680</span></span>}$$

Step 6: Calculate the Cost of Labor

Labor costs include the wages for masons, laborers, and equipment operators. Assume:

• Mason: ₹600 per day
• Laborer: ₹400 per day
• Equipment operator: ₹700 per day

For 1 m³ of concrete, we need:

• 1 mason for 1 day
• 2 laborers for 1 day
• 1 equipment operator for 1 day

Total labor cost:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Labor Cost</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">600</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span><span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">(</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">2</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">400</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">)</span></span><span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">700</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">2100</span></span>}$$

Step 7: Calculate the Cost of Equipment

Mechanical Vibrator: Assume the rental cost is ₹500 per day.

Formwork, Centering, and Scaffolding: Assume the cost is ₹1000 per m³.

Total equipment cost:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Equipment Cost</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">500</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1000</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1500</span></span>}$$

Step 8: Calculate Overheads and Profit

Assume overheads and profit are 15% of the total cost of materials, labor, and equipment.

Total cost before overheads and profit:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Total Cost</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">2800</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">630</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1680</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">2100</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1500</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8710</span></span>}$$

Overheads and profit:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Overheads and Profit</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">0.15</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">\times </span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8710</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1306.5</span></span>}$$

Step 9: Calculate the Total Cost

Total cost including overheads and profit:

$$\text{<span style="background-color: white;"><span style="font-size: medium;">Total Cost</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">8710</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">+</span></span>\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">1306.5</span></span>}<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">=</span></span>\text{<span style="background-color: white;"><span style="font-size: medium;">₹</span></span>}\mathrm{<span\; style="background-color:\; white;"><span\; style="font-size:\; medium;">10016.5</span></span>}$$

Conclusion

The rate analysis for 1 cubic meter of cement concrete using cement, sand, and crushed metal aggregate by machine mix for R.C.C work, including necessary formworks, centering, scaffolding, compaction by mechanical vibrator, and curing, with all lead and lift, excluding the cost of reinforcement, is approximately ₹10016.5.

This step-by-step process ensures that all components are accounted for, providing a comprehensive cost estimate for the concrete work. Regular updates and clear communication among stakeholders are essential to ensure accuracy and transparency in the rate analysis process. Remember the assumptions of rates varies location to location, So I hope this process gives you clear idea of steps of rate analysis.