Solution:

Infiltration Index:

The infiltration index is defined as the ratio of the average infiltration rate to the maximum rainfall intensity.

Formula:

Infiltration Index = (Average Infiltration Rate) / (Maximum Rainfall Intensity)

Given:

Rainfall in 4 successive 12 hours period = 40, 80, 90 and 30 mm.

Calculation:

Step 1: Find the total amount of rainfall in 48 hours

Total amount of rainfall = 40 + 80 + 90 + 30 = 240 mm

Step 2: Find the maximum rainfall intensity

Maximum rainfall intensity = Highest amount of rainfall in a single period / Duration of the period

Maximum rainfall intensity = 90 mm / 12 hours = 7.5 mm/hour

Step 3: Find the average infiltration rate

Average infiltration rate = Total amount of rainfall / Duration of the storm / Catchment area

Duration of the storm = 48 hours

Catchment area = Area of the catchment that receives rainfall

Assuming the catchment area to be 1 hectare (10,000 square meters)

Average infiltration rate = 240 mm / (48 hours x 10,000 m²) = 0.5 mm/hour

Step 4: Find the infiltration index

Infiltration Index = (Average Infiltration Rate) / (Maximum Rainfall Intensity)

Infiltration Index = 0.5 mm/hour / 7.5 mm/hour = 0.067

Therefore, the infiltration index for the given storm is 0.067.

Explanation:

The infiltration index is used to estimate the infiltration capacity of the soil during a rainfall event. It is an important parameter in hydrological modeling and design of stormwater management systems. The infiltration index is calculated by dividing the average infiltration rate by the maximum rainfall intensity. The higher the infiltration index, the more water can infiltrate into the soil and the lower the runoff volume. In this case, the infiltration index is quite low, indicating that a significant amount of the rainfall will result in runoff, and may cause flooding or erosion in the catchment area.