Sedimentation in reservoirs and dead storage life: A reservoir has total capacity of 10 million m³. If the average silt deposition is 0.1 million m³ per year, and assuming (as is common in preliminary design) that dead storage is 25% of total capacity, in how many years will the dead storage be filled?

Introduction / Context:
Reservoir capacity is commonly partitioned into dead storage (intended to trap sediment and unusable by outlet works), live or useful storage, and sometimes surcharge. Estimating the time for dead storage to silt up is essential for planning operational life and for scheduling desilting or dredging interventions. This problem tests basic sediment budgeting using simple proportional reasoning.

Given Data / Assumptions:

• Total capacity, C_total = 10 million m³.
• Annual sediment deposition, S = 0.1 million m³ per year.
• Assumption for preliminary design: dead storage is 25% of total capacity (a common textbook simplification stated explicitly here).
• All incoming sediment is trapped in dead storage (conservative assumption for life estimation).

Concept / Approach:
Dead storage volume V_dead is allocated to accommodate long-term siltation without affecting live storage. The time to fill dead storage is simply the ratio V_dead / S when trapping efficiency is high and routing effects are ignored. This is a first-approximation method suitable for exam problems and initial feasibility checks.

Step-by-Step Solution:
Compute dead storage volume: V_dead = 0.25 * C_total = 0.25 * 10 = 2.5 million m³.Annual silt deposition S = 0.1 million m³/year.Time to fill dead storage: t = V_dead / S = 2.5 / 0.1 = 25 years.

Verification / Alternative check:
If dead storage were not specified, filling the entire reservoir would take 10 / 0.1 = 100 years. With the explicit 25% allocation, the dead storage life becomes one quarter of that value, i.e., 25 years, confirming the result.

Why Other Options Are Wrong:

• 10, 15, 20 years: underestimate the dead storage volume or overestimate siltation rate.
• 50 years: double the correct time; would correspond to dead storage of 5 million m³ (50%).

Common Pitfalls:

• Using total capacity instead of dead storage capacity.
• Ignoring the stated assumption and choosing 100 years (for total fill), which does not answer the dead-storage question.

Final Answer:
25 years