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Weight to Volume relationships in soils's banner
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Weight to Volume relationships in soils

This calculator computes the volume and weight relationships in soils, which are useful relationships used in soil mechanics.

Calculation

Assumptions

  1. Unit weight of water,
    
    kN/m3
  2. Weight of air is zero, therefore
    
    
  3. The calculator assumes the known parameters are the soil sample mass
    
    , the over-dry soil sample mass
    
    , the volume of the soil sample
    
    (based on the test tube dimensions) and soil specific gravity
    
    (determined from lab tests). This is a typical situation.

Input

Soil sample values:

2446​
5777​
3523​
2446​
1077​

Output

Weight-volume relationships:

0.61​
0.38​
69.4%​
15.6%​
1.95​
19.1​
1.68​
16.52​
2.71​
26.59​
2.06​
20.23​
1.06​
10.42​

Explanation

Weight-Volume Relationships

A soil mass with total volume

and total weight

is shown below with its three phases of soil mass (soil solids, air and water).
Soil mass and it's three phases [Adapted from Source]

In most cases you will know the soil sample mass

, the over-dry soil sample mass

, the volume of the soil sample

(based on the test tube dimensions) and soil specific gravity

(determined from lab tests).
👉Note, you can either work in mass (with units

) or weight (with units

). If you work in mass, your densities will be in

while if you work in weight, your densities will be in

. Remember also if you use mass, take

and if you use weight, take

.
We can then determine the remaining mass and volume quantities:
  1. Volume of soil solids,
    
    which is derived using the definition of solid unit weight
    
    and the definition of soil specific gravity,
    
    . Therefore,
    
    
👉Note,

is typically within the range 2.65 (average from granular soils) and 2.80 (average for cohesive soils).
  1. Volume of voids,
    
    
  1. Volume of water,
    
    
  2. Volume of air,
    
    
We now know all our mass and volume quantities (

). We can then define the following weight-volume relationships commonly used in soil mechanics:
  1. Void ratio,
    
    
  2. Porosity,
    
  3. Degree of saturation,
    
    which can range between zero for a completely dry soil, to 1 for a fully saturated soil
  1. Moisture content,
    
    
  2. Unit weight,
    
    , also known as moist unit weight or total unit weight since it includes weight of water and soil solids
  3. Dry unit weight,
    
    
  4. Solid unit weight,
    
    
  5. Saturated unit weight,
    
    for
    
    (i.e.
    
    ) is when the soil is completely saturated
  6. Submerged (buoyant) unit weight,
    
    for
    
    is when the soil is below the ground water table

Weight-Volume Relationships for



Useful weight-volume relationships can be developed by considering a soil sample with

as shown below.
Therefore, the volume of voids

.
Weight-volume relationships for [Adapted from Source]

Weight-volume relationships can then be derived in terms of

. Here are some common forms:
  1. Moist unit weight,
    
    
  2. Dry unit weight,
    
    
  3. Degree of saturation,
    
    
  1. Saturated unit weight,
    
    
  2. Submerged unit weight,
    
    
The derivation of the above equations are found in Advanced Soil Mechanics by Braja M. Das.

Weight-Volume Relationships for



Useful weight-volume relationships can also be developed by considering a soil sample with

as shown below.
Therefore, the volume of voids

.
Weight-volume relationships for [Adapted from Source]

Weight-volume relationships can then be derived in terms of

. Here are some common forms:
  1. Moist unit weight,
    
    
  2. Dry unit weight,
    
    
  1. Saturated unit weight,
    
    
The derivation of the above equations are found in Advanced Soil Mechanics by Braja M. Das.

References

  1. Advanced Soil Mechanics by Braja M. Das
  2. Soil Phase Diagram and Relationship Formulas

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