Coefficient of compressibility from e–σ′ change A soil sample’s void ratio decreases from 1.50 to 1.25 when the effective pressure increases from 25 t/m² to 50 t/m². Compute the coefficient of compressibility a_v (units: per t/m²).

Introduction / Context:
The coefficient of compressibility a_v is a one-dimensional parameter relating void ratio change to effective stress change within a pressure interval. It is used in settlement calculations and is distinct from the coefficient of volume compressibility m_v, which also includes division by (1 + e) for volumetric strain per unit stress.

Given Data / Assumptions:

• Initial void ratio e1 = 1.50; final void ratio e2 = 1.25.
• Initial σ′1 = 25 t/m²; final σ′2 = 50 t/m².
• Use incremental definition over the given range.

Concept / Approach:

By definition (incremental form): a_v = Δe / Δσ′ with Δe taken as a positive number for a reduction in e under an increase in stress when reporting magnitude over an interval (sign conventions vary; many texts report the magnitude).

Step-by-Step Solution:

Verification / Alternative check:

If m_v were requested, m_v = a_v / (1 + e_avg); here only a_v is needed, matching the provided options.

Why Other Options Are Wrong:

0.02 or 0.05 overstate compressibility for the given changes; 0.001 and 0.10 are off by an order of magnitude.

Common Pitfalls:

Using the wrong stress difference; confusing a_v with m_v; sign confusion when e decreases with increasing σ′.

Final Answer:

0.01 per t/m²