The exit gradient is the ratio of

Question

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Option B: head loss to length of Flow field at exit

Explanation & Concepts:
The exit gradient ($i_e$) is defined as the hydraulic gradient at the downstream end of a seepage path where water emerges from the soil. It is calculated as the ratio of the head loss over the last flow element length to the length of that flow element.

Working Principle: As water seeps under a hydraulic structure (like a weir), it follows flow lines. At the exit, the seepage force acts upwards against the submerged weight of the soil. If the exit gradient is too high, the upward seepage force exceeds the submerged weight, leading to piping or boiling failure of the soil.

Key Formulas: $i_e = \frac{\Delta h}{\Delta l}$ — Definition of exit gradient; $i_c = \frac{G_s - 1}{1 + e} \approx 1.0$ — Critical hydraulic gradient for piping analysis

Key Points: Exit gradient must be kept below the critical hydraulic gradient ($i_c$) to ensure stability.; The factor of safety against piping is defined as $FS = \frac{i_c}{i_e}$.; Lane's weighted creep theory or Khosla's theory is often used to calculate hydraulic gradients for structures.; Piping failure occurs when the exit gradient causes the soil particles to lose intergranular pressure.

Advantages: Provides a quantitative measure to assess foundation safety against piping.; Essential for designing cut-off walls and upstream/downstream aprons.

Disadvantages: Requires complex flow net analysis for precise determination in heterogeneous soil.; Sensitive to local soil permeability variations.

Applications: Design of barrages and weirs on permeable foundations.; Evaluation of seepage stability in earthen dams.; Excavation support systems in high groundwater tables.

Additional Info: Kholsa's theory provides empirical formulas for exit gradients based on the geometry of the structure.. Option A is incorrect because slopes are geometric properties, not hydraulic gradients.. Option C is incorrect because the total head over total length represents the average hydraulic gradient, not the local gradient at the exit.

Answer: B is correct — The exit gradient is the hydraulic gradient at the downstream end, representing the ratio of head loss to the length of the flow field at the point of exit.

Exam Tip: Always ensure the exit gradient is less than the critical hydraulic gradient (typically 0.8 to 1.0) with a factor of safety between 4 and 5.

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Option A: Slope to flow line

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Option C: total head to total length

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Option D: Slope to equipotential line

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