• To derive the Mass of Water Added (MOWA)

Mass of Water Added (MOWA)

Definition: MOWA is the amount of water that must be added to a soil sample to bring it from its initial condition to a target condition (e.g., saturation), assuming the total volume remains constant.

\(\text{MOWA} = V_T(\gamma_{target} - \gamma)\)

If the target condition is saturation:

\(\text{MOWA} = V_T(\gamma_{sat} - \gamma)\)

Nomenclature & Variables

• \(V_T\) = Total volume of the soil sample
• \(\gamma_{sat}\) = Saturated unit weight
• \(\gamma\) = Soil initial unit weight
• \(w, s, T\) = water, solids, Total
• \(W, V\) = Weight, Volume

Derivation Logic

Core Principle: No matter how much water you add to the soil, the weight of soil solids remains constant.

1. Initial Condition:

• \(W_T = W_w + W_s\)
• \(V_T = V_v + V_s\)
• \(\gamma = \dfrac{W_T}{V_T}\)
• \(W_w = \gamma V_T - W_s\)

2. Saturated Condition:

• \(V_{T_2} = V_T\) (Water fills existing voids)
• \(W_{w2} = \gamma_{sat} V_T - W_s\)

3. Final Calculation:

The weight of water added is the difference between the final and initial water weights:

\(\text{MOWA} = W_{w2} - W_w\)

\(\text{MOWA} = \gamma_{sat} V_T - \gamma V_T\)