# METHOD OF INDEPENDENT VARIABLES

- Break up of a complex profile of a weir to simple three elementary.
- This break up shows the theoretical profiles.
- Actually, the usual weir section consists of a combination of all the three elementary profiles.
- In addition to this, the floor also has some thickness.
- Khosla solve the actual profile of the weir by an empirical method know the method of independent variables.
- According to this method, the actual complex profile is broken into a number of simple profiles know elementary profiles.
- Each elementary profile is then treat independently of the others.
- Each elementary profile is independently amenable to mathematical treatment.
- The pressures at key points are read from Khosla’s curves.
- The key points are the junction points of the floor and pile and bottom points of different piles.
- The pressures read from Khosla’s curves are true for individual elementary profiles.
- But when all the profiles are combin into one complex form, which is actually the condition, corrections for pressures will have to be applie.
- When different elementary profiles are combin, they influence the pressures due to mutual interference of the piles.
- The thickness and slope of the floor also affect the pressures at key points.
- In order to find out the pressures at various key points for the weir as a whole, following corrections for the pressures will have to be applied.

1. Correction for the thickness of the floor.

2. Correction for the mutual interference of piles.

3. Correction for the sloping floor.

**1. Correction for the thickness of the floor.**

- Figure 15.8 shows the details of key points for profiles one each at the upstream end, downstream end, and intermediate point.
- Assume the thickness of the floor negligibly small.
- E and C are the key points at the top of the floor.
- E point is on the U/S side and C on the D/S side of the pile.
- Let E1 and C1 be the corresponding key points at the bottom of the floor.
- Pressures at points E1 and C1 for each profile are computed as follows:

(i) Pile at the U/S end.

- For point E no correction is require the pressure at this point is not going to interfere with the pressure system of any other pile.

\[Correction -for -point.C_{1}= \frac{(\phi _{D}-\phi _{C})t_{1}}{d_{1}}(Additive)\]

\[Pressure- at,C_{1}= \phi _{C_{1}}= \phi _{C}+\frac{(\phi _{d}-\phi _{C})t_{1}}{d_{1}}\]