Why Khosla's theory; limits of correction

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).