---
title: "Why Khosla's theory; limits of correction"
subject: "Irrigation and Drainage Engineering"
chapter: 5
key: "semester_6/irrigation_and_drainage_engineering:khosla-theory-appropriate-limitations"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-theory-appropriate-limitations
site: BCT Engineering
---

# Why Khosla's theory; limits of correction

Irrigation and Drainage Engineering · Chapter 5: Diversion Headworks

- Asked in: 2075 Bhadra, 3+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-theory-appropriate-limitations
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-5

## Question

Why is Khosla's theory more appropriate than other methods? Write down the limitation of mutual interference correction while applying Khosla's seepage theory.

## Short answer

Khosla's theory solves Laplace's equation for real seepage flow, providing pressure at key points, exit gradient, and sheet pile effects, unlike empirical Bligh's or Lane's theories. Mutual interference correction is empirical, inapplicable when intermediate pile ≤ outer pile and distance < 2× outer pile length, pairwise only for multiple piles, assumes vertical thin piles on horizontal floor in homogeneous infinite soil, and requires correct sign convention.

## Answer

#### Why Khosla's theory is more appropriate

- **Bligh's theory** assumes that the head loss is proportional to the creep length (a straight-line hydraulic gradient), gives equal weight to horizontal and vertical creep, and does not give the exit gradient or the pressure at key points. **Lane's theory** weights vertical creep three times the horizontal, but it is also empirical.
- **Khosla's theory** solves Laplace's equation for the flow of seepage water below the structure with the real boundary conditions (potential flow). It gives:
  - the pressure at any key point (not a straight line), so uplift and floor thickness can be designed properly;
  - the **exit gradient** $G_E$, which is the criterion for safety against piping;
  - the effect of the depth and position of the sheet piles (the pile at the downstream end is most effective in reducing the exit gradient, and the pile at the upstream end in reducing uplift);
  - allowance for complex profiles, through simple profiles and corrections for mutual interference, floor thickness and slope.
- Hence it represents the real seepage flow and is more rational and economical.

#### Limitations of the mutual interference correction

$$
C = 19\sqrt{\frac{D}{b'}}\left(\frac{d+D}{b}\right)\%
$$

1. It is empirical (based on electrical analogy tests) and approximate.
2. It does not apply to the effect of an outer pile on an intermediate pile if the intermediate pile is equal to or shorter than the outer pile and lies at a distance less than twice the length of the outer pile.
3. It accounts for the effect of two piles at a time only; for three or more piles, it is applied pairwise and added, so the result is approximate.
4. The piles are assumed vertical and thin, with a horizontal floor of negligible thickness; the foundation is assumed homogeneous, isotropic and of infinite depth.
5. The result depends on how the terms are measured: $b'$ is the distance between the two pile lines, $D$ is measured below the level at which the interference is wanted, and the sign must be applied correctly (positive for points upstream of the interfering pile, negative for points downstream of it).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is Khosla's theory more appropriate than Bligh's?
   A. It solves Laplace's equation for real boundary conditions and gives pressures and exit gradient
   B. It assumes a straight-line gradient
   C. It ignores sheet piles
   D. It is simpler
   Answer: A. Khosla gives true pressures and exit gradient; Bligh assumes straight-line loss. (Key point: Khosla vs Bligh)

2. Which pile helps exit gradient most?
   A. Upstream pile
   B. Intermediate pile
   C. The pile at the downstream end
   D. None
   Answer: C. The d/s pile is most effective for exit gradient; the u/s pile for uplift. (Key point: Pile effectiveness)

3. On which pile does the correction C = 19 sqrt(D/b')((d+D)/b) apply?
   A. The deeper pile D
   B. The smaller pile d, due to the influence of deeper pile D
   C. Both equally
   D. The floor
   Answer: B. The correction applies to the shallower pile d. (Key point: Interference correction)

4. Which is a limitation of the correction?
   A. It is exact
   B. It needs no spacing
   C. It is empirical and approximate, valid when piles are not too close
   D. It works for any floor
   Answer: C. It is empirical (electrical analogy) and approximate. (Key point: Limitation)

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