The void ratio of an unconsolidated soil heap of volume 1000 m³ is 1.0. If the soil heap is consolidated to a volume of 800 m³, the corresponding void ratio is _____ (round off up... The void ratio of an unconsolidated soil heap of volume 1000 m³ is 1.0. If the soil heap is consolidated to a volume of 800 m³, the corresponding void ratio is _____ (round off up to 2 decimals). Read more

Steps to Solve

1. Identify Initial Conditions
   The initial void ratio ($e_1$) is given as $1.0$ and the initial volume ($V_1$) is $1000 , m^3$.

2. Calculate Initial Volume of Void Spaces
   To find the initial volume of voids ($V_v1$), use the formula:
   $$ V_v1 = e_1 \times V_s $$
   where $V_s$ is the volume of solids.
   Since
   $$ V_s = V_1 - V_v1 $$
   we can express void volume in terms of total volume and void ratio:

Let $V_s = V_1 / (1 + e_1) = 1000 / (1 + 1.0) = 500 , m^3$. Thus,
$$ V_v1 = 1000 - 500 = 500 , m^3. $$

3. Determine New Conditions After Consolidation
   The new volume ($V_2$) after consolidation is $800 , m^3$. We assume that the volume of solids remains unchanged ($V_s = 500 , m^3$).

4. Calculate New Void Ratio
   The new volume of voids ($V_v2$) can be found as:
   $$ V_v2 = V_2 - V_s = 800 - 500 = 300 , m^3. $$
   Now, calculate the new void ratio ($e_2$):
   $$ e_2 = \frac{V_v2}{V_s} = \frac{300}{500} = 0.6. $$

5. Round to Two Decimal Places
   Finally, round the new void ratio to two decimal places, which gives:
   $$ e_2 = 0.60. $$