Calculate The Total Weight Of 100 M³ Of Excavated Soil With Γ = 18.5 KN/m³, Gs = 2.68, And W = 8.2%. What Is The Porosity Of The Soil? Determine The Volume Of The Soil After Drying.
In construction projects, excavation is a fundamental process, often involving the removal of large volumes of soil. Understanding the properties of the excavated soil is crucial for various aspects of the project, including estimating the total weight, determining soil characteristics, and planning for disposal or reuse. This article delves into a specific scenario where 100 m³ of soil is excavated, and we aim to calculate the total weight of the excavated soil, its porosity, and the volume after drying. We will utilize key soil properties such as unit weight (γ), specific gravity (Gs), and water content (w) to perform these calculations. By understanding these calculations, engineers and construction professionals can better manage soil excavation and handling processes, ensuring efficient and safe project execution. This article serves as a comprehensive guide to understanding and applying these crucial geotechnical principles in real-world construction scenarios.
Problem Statement
In a construction site, a volume of 100 m³ of soil is excavated. The properties of the excavated soil are as follows:
- Unit weight (γ): 18.5 kN/m³
- Specific gravity (Gs): 2.68
- Water content (w): 8.2%
Based on this information, we need to determine:
(a) The total weight of the excavated soil.
(b) The porosity of the soil.
(c) The volume of the soil if it is dried.
(a) Total Weight of Excavated Soil
To determine the total weight of the excavated soil, we will use the given unit weight (γ) and the excavated volume (V). The unit weight is defined as the weight per unit volume, so the total weight (W) can be calculated using the formula:
W = γ * V
Where:
- W is the total weight of the soil in kN
- γ is the unit weight of the soil in kN/m³
- V is the excavated volume in m³
Given:
- γ = 18.5 kN/m³
- V = 100 m³
Substituting the given values into the formula:
W = 18.5 kN/m³ * 100 m³
W = 1850 kN
Therefore, the total weight of the excavated soil is 1850 kN. This calculation is crucial for assessing the load the soil exerts and for planning the logistics of soil removal and disposal. Understanding the total weight helps in selecting appropriate equipment and ensuring that the transport vehicles are not overloaded. Moreover, this value is essential for stability analyses, especially if the excavated soil is to be used as backfill or for other construction purposes. The accurate calculation of the total weight is a fundamental step in any construction project involving soil excavation, influencing decisions ranging from equipment selection to site safety protocols.
(b) Porosity of the Soil
Porosity, denoted as n, is a measure of the void space in a soil material and is defined as the ratio of the volume of voids (Vv) to the total volume (V). It is expressed as a percentage. To calculate the porosity, we first need to determine the void ratio (e), which is the ratio of the volume of voids (Vv) to the volume of solids (Vs). The relationship between porosity (n) and void ratio (e) is given by:
n = e / (1 + e)
To find the void ratio (e), we can use the following relationship, which incorporates the specific gravity (Gs), water content (w), and the unit weight of water (γw):
e = (Gs * γw / γ) - 1
Where:
- Gs is the specific gravity of the soil solids
- γw is the unit weight of water, approximately 9.81 kN/m³
- γ is the unit weight of the soil
- w is the water content (expressed as a decimal)
Given:
- Gs = 2.68
- γ = 18.5 kN/m³
- w = 8.2% = 0.082
First, calculate the void ratio (e):
e = (2.68 * 9.81 kN/m³ / 18.5 kN/m³) - 1
e = (26.2908 / 18.5) - 1
e = 1.4211 - 1
e = 0.4211
Now, calculate the porosity (n):
n = 0.4211 / (1 + 0.4211)
n = 0.4211 / 1.4211
n = 0.2963
Expressed as a percentage:
n = 0.2963 * 100%
n = 29.63%
Therefore, the porosity of the soil is 29.63%. Porosity is a critical parameter in geotechnical engineering as it influences the soil's permeability, compressibility, and strength. A higher porosity generally indicates a greater capacity for water storage and a potentially lower shear strength. Understanding the porosity of the excavated soil is essential for assessing its suitability for various engineering applications, such as backfilling or as a foundation material. It also helps in predicting the soil's behavior under different loading conditions and environmental changes, making it a vital factor in construction planning and design. The porosity calculation provides insights into the soil's structure and its potential impact on project outcomes.
(c) Volume of the Soil After Drying
To determine the volume of the soil after drying, we need to consider the volume of solids (Vs) in the soil, as the water content will be removed during drying, but the volume of solids will remain constant. We can use the relationship between the total volume (V), the volume of solids (Vs), and the void ratio (e) to find Vs:
V = Vs + Vv
Since e = Vv / Vs, we can write Vv = e * Vs. Substituting this into the volume equation:
V = Vs + e * Vs
V = Vs * (1 + e)
Rearranging to solve for Vs:
Vs = V / (1 + e)
We already know V = 100 m³ and e = 0.4211. Plugging these values in:
Vs = 100 m³ / (1 + 0.4211)
Vs = 100 m³ / 1.4211
Vs = 70.36 m³
When the soil is dried, only the volume of solids remains, as the water and air in the voids are removed. Therefore, the volume of the dried soil is equal to the volume of solids (Vs).
Volume of dried soil = Vs = 70.36 m³
Therefore, the volume of the soil after drying is 70.36 m³. This calculation is crucial in understanding how soil volume changes with moisture content, which is particularly important in applications such as compaction and soil stabilization. The reduction in volume upon drying can affect the density and strength characteristics of the soil, impacting its suitability for various construction purposes. Understanding the dried volume helps in predicting soil behavior and planning for potential shrinkage or settlement issues in structures built on or with the soil. This information is invaluable in ensuring the long-term stability and performance of construction projects involving soil.
In summary, for the given excavation of 100 m³ of soil with a unit weight of 18.5 kN/m³, specific gravity of 2.68, and water content of 8.2%:
- The total weight of the excavated soil is calculated to be 1850 kN.
- The porosity of the soil is determined to be 29.63%.
- The volume of the soil after drying is found to be 70.36 m³.
These calculations are essential in geotechnical engineering for assessing soil properties and planning construction activities. The weight of the soil impacts transportation and handling logistics, while porosity affects its permeability and strength characteristics. The volume change upon drying is crucial for understanding soil behavior in various applications, such as backfilling and compaction. The accurate determination of these parameters is vital for ensuring the safety, stability, and efficiency of construction projects. By understanding these fundamental concepts, engineers and construction professionals can make informed decisions, leading to successful project outcomes and sustainable infrastructure development. This comprehensive analysis provides a solid foundation for understanding soil mechanics and its practical applications in the field.