Step 1: Understanding the Concept:
This question concerns the design of stable earthen irrigation channels. The side slopes of a channel must be stable against erosion and slumping. The maximum stable slope depends on the type of soil the channel is excavated in. The slope is expressed as a ratio of horizontal distance to vertical distance (H:V).
Step 2: Detailed Explanation:
1. The stability of an earthen slope depends on the angle of repose of the soil material when it is saturated with water. If the side slope is cut steeper than the angle of repose, the bank will fail.
2. Different soil types have different stable slopes. Cohesive soils like clay can stand on steeper slopes than non-cohesive soils like sand.
3. For permanent irrigation channels, which are expected to be stable over a long period, conservative design practices are used.
4. The slope is given as a ratio H:V. A steeper slope has a smaller number for H. For example, a 1:1 slope is steeper than a 2:1 slope.
5. Let's look at typical recommended side slopes for different soils in channel design:
Very hard clay or rock: 0.5:1 (steepest)
Stiff clay, loam: 1:1
Sandy loam, loose soils: 1.5:1
Sandy soils: 2:1 to 3:1 (flattest)
6. The question asks for a general rule for permanent channels, which are often constructed in common alluvial soils (loams and sandy loams). A slope of 1.5:1 (1 1/2 to 1) is a very common and widely accepted standard as a maximum steepness for unlined earthen channels in average soil conditions to ensure long-term stability. Slopes steeper than this (like 1:1 or 0.5:1) are generally not used unless the soil is very cohesive or the banks are protected.
7. The option "1 1/2 to 1" represents this standard safe slope.
Step 3: Final Answer:
To ensure stability, permanent irrigation channels in common soils should generally not have side slopes steeper than 1.5 Horizontal to 1 Vertical. Therefore, option (B) is the correct answer.