Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Active and passive earth pressures
Question Statement:
A homogenous anisotropic earthen dam of height 52 m with a free board of 2 m is constructed on an impermeable foundation. The horizontal and vertical hydraulic conductivities of soil used for the construction of the dam are 4.5×10⁻⁸ m s⁻¹ and 2.0×10⁻⁸ m s⁻¹, respectively. There are 6 flow channels and 25 equipotential drops in a square flownet drawn in the transformed dam section. If the downstream dam side is dry, the quantity of seepage per unit length through the dam in m³ day⁻¹ m⁻¹ is ____________ (rounded off to 3 decimal places).
Official Answer Key:
0.030 to 0.032
Step-by-Step Solution & Explanation
For an anisotropic soil, the flownet is drawn on a transformed section, and seepage discharge uses the equivalent (transformed) hydraulic conductivity k_eq = √(k_h×k_v):
k_eq = √(4.5×10⁻⁸ × 2.0×10⁻⁸) = √(9.0×10⁻¹⁶) = 3.0×10⁻⁸ m/s.
Head causing seepage, H = dam height − free board = 52−2 = 50 m (the head above the impermeable foundation driving through-seepage, taking the reservoir water surface at the crest minus freeboard).
Seepage per unit length, q = k_eq×H×(N_f/N_d) = 3.0×10⁻⁸ × 50 × (6/25) = 3.0×10⁻⁸×50×0.24 = 3.6×10⁻⁷ m³/s per m.
Converting to per day: 3.6×10⁻⁷ × 86400 = 0.0311 m³/day/m. Within official range 0.030–0.032.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.