Soil Index Definitions – Voids Ratio, Porosity, Bulk Unit Weight, and Dry Unit Weight Which of the following statements correctly define common index/weight relationships used in soil mechanics?

Introduction / Context:
Clear definitions of geometric and weight-based soil indices are crucial for classification, compaction control, and seepage/stability calculations. Four basic quantities—voids ratio, porosity, bulk unit weight, and dry unit weight—appear across nearly all geotechnical computations.

Given Data / Assumptions:

• Three-phase system: solids, water, and air.
• Volumes: V = V_s + V_v; masses/weights defined accordingly.
• Quasi-static conditions and standard temperature for unit weights.

Concept / Approach:

Definitions: e = V_v / V_s (voids ratio). n = V_v / V (porosity). Bulk unit weight γ = W / V (total weight per total volume). Dry unit weight γ_d = W_s / V (weight of solids per total volume). These are consistent and inter-related via n = e / (1 + e). Correct understanding prevents mistakes in compaction, saturation, and strength estimations.

Step-by-Step Solution:

Verification / Alternative check:

Handbooks and codes present identical relationships and show conversions (e ↔ n) using n = e/(1 + e).

Why Other Options Are Wrong:

Because (a)–(d) are all correct, any single choice would be incomplete. Hence “All of the above” is the only complete selection.

Common Pitfalls:

Mixing up e with n; using mass density instead of unit weight (weight density) without unit consistency; forgetting that γ_d < γ unless soil is oven-dry.

Final Answer:

All of the above