METHOD OF INDEPENDENT VARIABLES

# 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.

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.

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

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

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