Introduction:
The distribution of circular load refers to the way in which a load is distributed around a circular area. This distribution is important in various civil engineering applications, such as the design of foundations, pavements, and retaining walls. Different methods have been developed to determine the distribution of circular load, and one of the prominent methods is the Boussinesq's method.

Boussinesq's method:
The Boussinesq's method is a widely used method for calculating the distribution of circular load. It was developed by the French mathematician Joseph Valentin Boussinesq in the 19th century. This method provides a simplified approach to estimate the stresses and displacements caused by a circular load on an elastic half-space.

Key principles:
The Boussinesq's method is based on the following key principles:

1. Assumption of linearity: The method assumes that the soil or material is linearly elastic, meaning that the stress-strain relationship follows Hooke's law.

2. Two-dimensional analysis: The method considers the problem in two dimensions, assuming axisymmetric conditions. This simplification allows for easier calculations and analysis.

3. Indirect approach: Instead of directly calculating the stresses and displacements at any point, the method calculates the influence coefficients or influence factors. These factors represent the effect of a unit load at a reference point on the stresses and displacements at any other point.

Calculation procedure:
The calculation procedure in Boussinesq's method involves the following steps:

1. Determine the influence coefficients: The influence coefficients are calculated using the Boussinesq's formula, which relates the stress or displacement at a given point to the applied load and the distance from the load to the point.

2. Apply superposition principle: The influence coefficients are then used to calculate the stresses and displacements at any desired point by applying the principle of superposition. This principle states that the total effect of multiple loads can be obtained by adding the effects of individual loads.

3. Consider boundary conditions: The method takes into account the boundary conditions, such as the presence of a rigid foundation or other loads nearby, to accurately determine the distribution of circular load.

Advantages and limitations:
The Boussinesq's method has several advantages, including its simplicity, suitability for circular loads, and its ability to provide approximate solutions for practical engineering problems. However, it also has limitations, such as the assumption of linear elasticity, neglecting the effect of soil layers, and the need for further refinement for complex loading conditions.

Conclusion:
In conclusion, the Boussinesq's method is a widely used method for determining the distribution of circular load in civil engineering applications. It provides a simplified approach based on the principles of linearity, two-dimensional analysis, and the use of influence coefficients. While this method has its limitations, it remains a valuable tool for estimating the stresses and displacements caused by circular loads on elastic half-spaces.