Enter the following soil properties to calculate its saturated unit weight. This is crucial for geotechnical engineering applications.
Typically in kN/m³ or lb/ft³.
Ratio of soil solids density to water density (unitless).
Expressed as a percentage (%).
Results
—
Specific Gravity of Soil Solids ($G_s$):—
Water Content at Saturation ($w_s$):—
Unit Weight of Water ($\gamma_w$):—
Formula Used
The saturated unit weight ($\gamma_{sat}$) is calculated using the formula derived from the soil's properties:
$\gamma_{sat} = \frac{(G_s + e) \gamma_w}{1 + e}$, where $e = \frac{G_s w_s}{100}$ and $w_s$ is water content in decimal form.
We first determine the void ratio (e) using the specific gravity ($G_s$) and the water content at saturation ($w_s$), then substitute it into the saturated unit weight formula. The unit weight of water ($\gamma_w$) is assumed to be 9.81 kN/m³ or 62.4 lb/ft³ based on the input unit weight's likely units.
Saturated Unit Weight vs. Water Content
Saturated Unit Weight ($\gamma_{sat}$)Void Ratio ($e$)
Relationship between Saturated Unit Weight and Void Ratio across different soil conditions.
Soil Property Data
Property
Symbol
Value
Unit
Dry Unit Weight
$\gamma_d$
—
kN/m³ (assumed)
Specific Gravity of Solids
$G_s$
—
Unitless
Water Content at Saturation
$w_s$
—
%
Unit Weight of Water
$\gamma_w$
—
kN/m³ (assumed)
Void Ratio
$e$
—
Unitless
Saturated Unit Weight
$\gamma_{sat}$
—
kN/m³ (assumed)
Summary of input and calculated soil properties. Units are assumed based on common geotechnical practice for dry unit weight.
What is Saturated Unit Weight of Soil?
The saturated unit weight of soil is a fundamental geotechnical property representing the weight of soil per unit volume when all its void spaces are completely filled with water. In simpler terms, it's the weight of a soil sample when it's fully submerged and holding as much water as possible within its structure. This property is distinct from the dry unit weight (the weight of solids per total volume) and the moist unit weight (the weight of solids and pore water per total volume under partially saturated conditions). Understanding how to calculate saturated unit weight of soil is crucial for civil engineers, geologists, and construction professionals.
Who Should Use It?
Professionals involved in:
Foundation design: Determining bearing capacity and settlement.
Slope stability analysis: Assessing the risk of landslides.
Dam and levee construction: Ensuring structural integrity.
Site investigation and characterization: Classifying soil types and their behavior.
Anyone working with soil mechanics, especially where water content significantly influences soil behavior, will benefit from accurately calculating the saturated unit weight of soil.
Common Misconceptions
Confusing it with dry unit weight: Dry unit weight ($\gamma_d$) is the weight of soil solids only per unit volume, while saturated unit weight accounts for the weight of both solids and water filling the pores.
Assuming it's always higher than dry unit weight: This is generally true, as water adds weight. However, comparing it to moist unit weight requires careful consideration of the degree of saturation.
Overlooking the role of void ratio: The void ratio is a critical intermediate step. A higher void ratio generally leads to a higher saturated unit weight, assuming other factors remain constant.
Ignoring the unit weight of water: The density of water ($\gamma_w$) is a key component. Its value can vary slightly with temperature, but a standard value is typically used.
Saturated Unit Weight of Soil Formula and Mathematical Explanation
The calculation of the saturated unit weight of soil ($\gamma_{sat}$) is derived from fundamental principles of soil mechanics, relating the weights and volumes of soil solids and pore water. The process involves understanding the soil's solid components, its void spaces, and how water fills these voids.
The Core Formula
The primary formula for saturated unit weight is:
$\gamma_{sat} = \frac{G_s + e}{1 + e} \gamma_w$
Where:
$\gamma_{sat}$: Saturated Unit Weight of soil
$G_s$: Specific Gravity of Soil Solids (unitless)
$e$: Void Ratio (unitless)
$\gamma_w$: Unit Weight of Water (e.g., 9.81 kN/m³ or 62.4 lb/ft³)
Deriving the Void Ratio (e)
Often, the void ratio is not directly measured but calculated from other known properties. When a soil is saturated, the water content ($w_s$) is directly related to the void ratio and the specific gravity of solids. The relationship is:
$w_s = \frac{V_w \gamma_w}{V_s \gamma_s}$
Since $V_w = e V_s$ (volume of water equals void ratio times volume of solids) and $\gamma_s = G_s \gamma_w$ (specific gravity definition), we can substitute:
2.6 – 2.8 (typical for common minerals like quartz, feldspar)
$e$
Void Ratio
Unitless
0.1 – 1.5 (can be higher for organic or loose soils)
$w_s$
Water Content at Saturation
% or decimal
10% – 60% (highly variable, depends on void ratio and $G_s$)
$\gamma_w$
Unit Weight of Water
kN/m³ or lb/ft³
9.81 kN/m³ (fresh water at standard temp) or 62.4 lb/ft³ (fresh water at standard temp)
Practical Examples (Real-World Use Cases)
Example 1: Foundation Design for a Building
A civil engineer is designing a foundation for a new commercial building. The soil investigation reveals a medium-dense sand with the following properties:
Dry Unit Weight ($\gamma_d$): 17.0 kN/m³
Specific Gravity of Soil Solids ($G_s$): 2.67
Water Content at Saturation ($w_s$): 28%
Calculation Steps:
Convert water content to decimal: $w_{s(decimal)} = 28 / 100 = 0.28$
Interpretation: The saturated unit weight of this sand is approximately 19.18 kN/m³. This value is crucial for calculating the total stresses at various depths below the foundation, especially if the water table is high. Higher saturated unit weight contributes to higher total stress, which needs to be accounted for in bearing capacity and settlement calculations. This contrasts with the lower dry unit weight of 17.0 kN/m³, highlighting the significant increase in weight when the soil becomes saturated.
Example 2: Slope Stability Analysis for an Embankment
A geotechnical engineer is assessing the stability of an earth embankment. The fill material is a clayey silt with the following properties determined from lab tests:
Dry Unit Weight ($\gamma_d$): 15.5 kN/m³
Specific Gravity of Soil Solids ($G_s$): 2.70
Water Content at Saturation ($w_s$): 35%
Calculation Steps:
Convert water content to decimal: $w_{s(decimal)} = 35 / 100 = 0.35$
Interpretation: The saturated unit weight is approximately 18.38 kN/m³. For slope stability analysis, the effective stress is paramount. When the soil saturates, the pore water pressure increases, which reduces the effective stress and thus the shear strength of the soil. Knowing the saturated unit weight allows for the accurate calculation of total stresses and subsequently effective stresses under saturated conditions. This is critical for determining the factor of safety against slope failure. The calculation of how to calculate saturated unit weight of soil confirms that saturation significantly increases the soil's density compared to its dry state (15.5 kN/m³).
How to Use This Saturated Unit Weight Calculator
Our interactive calculator simplifies the process of determining the saturated unit weight of soil. Follow these simple steps:
Input Dry Unit Weight ($\gamma_d$): Enter the measured dry unit weight of the soil sample. This is usually provided in units like kN/m³ or lb/ft³. The calculator assumes consistent units for water.
Input Specific Gravity ($G_s$): Provide the specific gravity of the soil solids. This value is unitless and typically ranges between 2.6 and 2.8 for common minerals.
Input Water Content at Saturation ($w_s$): Enter the water content percentage (%) at which the soil is fully saturated.
Calculate: Click the "Calculate" button. The calculator will instantly display the primary result: the Saturated Unit Weight ($\gamma_{sat}$).
How to Read Results
Main Result ($\gamma_{sat}$): This is the highlighted, primary output, showing the calculated saturated unit weight of the soil in the assumed units (e.g., kN/m³).
Intermediate Values: Key values like the specific gravity ($G_s$), water content ($w_s$), and the unit weight of water ($\gamma_w$) used in the calculation are displayed for clarity. The calculated Void Ratio ($e$) is also shown.
Data Table: A table summarizes all input values and calculated outputs, reinforcing the data used and the results obtained.
Chart: Visualizes the relationship between the void ratio and the saturated unit weight, providing a graphical understanding of how these properties interact.
Decision-Making Guidance
Use the calculated saturated unit weight in conjunction with other soil parameters for:
Bearing Capacity Calculations: Higher saturated densities increase total stress.
Settlement Predictions: Understanding total weight is vital for predicting consolidation settlement.
Liquefaction Potential Analysis: Saturated conditions are a prerequisite for liquefaction.
Retaining Wall Design: Saturated soils exert different pressures on structures.
Always consult with a qualified geotechnical engineer for critical design decisions.
Key Factors That Affect Saturated Unit Weight Results
Several factors influence the calculated saturated unit weight of soil, and understanding them is key to accurate geotechnical analysis. The calculation of how to calculate saturated unit weight of soil is sensitive to these inputs:
Void Ratio ($e$)
This is arguably the most significant factor. The void ratio represents the volume of empty space between soil particles relative to the volume of the solids. Higher void ratios mean more space for water, thus increasing the total weight when saturated. For example, a loose, poorly graded sand will have a higher void ratio than a dense, well-graded gravel, leading to a higher saturated unit weight.
Specific Gravity of Soil Solids ($G_s$)
The specific gravity relates the density of the soil particles themselves to the density of water. Most common soil minerals (like quartz) have $G_s$ values around 2.65. However, soils containing heavier minerals or organic matter will have different $G_s$ values. A higher $G_s$ directly increases the saturated unit weight, as the solid particles themselves are denser.
Unit Weight of Water ($\gamma_w$)
While often treated as a constant (9.81 kN/m³ or 62.4 lb/ft³), the unit weight of water can vary slightly with temperature and salinity. In highly specialized or extreme temperature environments, this variation might become relevant. However, for most standard engineering applications, the assumed value is sufficient.
Soil Particle Characteristics (Shape and Gradation)
While not directly input variables in this simplified calculator, particle shape (e.g., rounded vs. angular) and gradation (particle size distribution) indirectly affect the void ratio. Angular particles tend to interlock less efficiently, potentially creating higher void ratios compared to rounded particles, all else being equal.
Compaction Effort
For engineered fills, the degree of compaction significantly impacts the void ratio and thus the saturated unit weight. A well-compacted soil will have a lower void ratio and higher dry unit weight compared to the same soil placed loosely. This will influence its saturated density as well.
Presence of Fines (Silt and Clay)
The proportion of fine particles (silt and clay) can influence the packing of coarser particles and the ability of the soil to hold water. Clays, in particular, can exhibit higher water contents due to their surface area and electrochemical forces, potentially affecting the overall void ratio and water retention characteristics.
Frequently Asked Questions (FAQ)
What is the difference between saturated unit weight and moist unit weight?
Moist unit weight is the weight of soil (solids + water) per unit volume under partially saturated conditions. Saturated unit weight is specifically when the voids are 100% filled with water, resulting in a higher density than typical moist conditions unless the soil is already saturated.
Can the saturated unit weight be less than the dry unit weight?
No. The dry unit weight considers only the weight of solids. Saturated unit weight includes the weight of solids plus the weight of water filling the voids. Water adds mass, so $\gamma_{sat}$ is always greater than $\gamma_d$ for any soil with a positive void ratio.
What happens if my soil is only partially saturated?
If the soil is partially saturated, you would use the moist unit weight calculation, which requires the degree of saturation (S) and the water content (w). The formula is more complex and depends on whether you know the void ratio or dry unit weight.
How does temperature affect the saturated unit weight?
Temperature primarily affects the unit weight of water ($\gamma_w$). Water is densest at about 4°C. At higher temperatures, water expands slightly, reducing its unit weight. While typically a minor effect in civil engineering, it can be considered in environments with significant temperature fluctuations.
Is the specific gravity of soil solids the same as the specific gravity of the soil mass?
No. Specific gravity of soil solids ($G_s$) refers only to the density of the solid particles. Specific gravity of the soil mass would need to account for the voids and water, making it dependent on the soil's density and saturation.
What is the typical range for the void ratio ($e$)?
The void ratio can vary widely. For dense granular soils, it might be as low as 0.2-0.4. For loose sands or normally consolidated clays, it can range from 0.5 to 1.0 or even higher for highly compressible clays or organic soils.
How accurate are the typical values for $G_s$ and $\gamma_w$?
The typical value for $G_s$ (around 2.65-2.8) is very accurate for most common mineral soils. $\gamma_w$ (9.81 kN/m³ or 62.4 lb/ft³) is standard for fresh water at typical ambient temperatures. Significant deviations would only occur with very unusual soil mineralogy or extreme environmental conditions.
Can I use this calculator if my input unit is in Imperial (lb/ft³)?
Yes. If you input your dry unit weight in lb/ft³, the calculator will use the corresponding standard value for the unit weight of water in Imperial units (62.4 lb/ft³) and provide the saturated unit weight in lb/ft³. Ensure all your inputs are in a consistent system (either metric or imperial).