Influence factor 'I' in the context of this question refers to the factor by which the applied vertical load is multiplied to determine the vertical stress at a specific point in soil. The correct answer, option 'C', states that the influence factor 'I' depends on the location of a point with respect to load.

Explanation:
Location of a point with respect to load:
The location of a point with respect to the applied load plays a significant role in determining the influence factor 'I'. The vertical stress at a point in soil depends on its proximity to the applied load. The closer the point is to the load, the higher the vertical stress it experiences. As the distance from the load increases, the influence factor 'I' decreases.

Other factors mentioned in the options:
a) Applied vertical load:
Although the applied vertical load affects the vertical stress distribution in soil, it does not directly determine the influence factor 'I'. The influence factor 'I' is a measure of the effect of the load on a specific point in soil, rather than the overall load itself.

b) Type of soil:
The type of soil does influence the behavior of the soil under load, but it does not directly determine the influence factor 'I'. Different soils have different properties, such as cohesion and friction angle, which affect their response to applied loads. However, the influence factor 'I' is specifically related to the location of a point with respect to the load.

d) Soil modulus:
The soil modulus, which represents the stiffness of the soil, also affects the response of soil to applied loads. However, it does not directly determine the influence factor 'I'. The influence factor 'I' is primarily determined by the location of a point with respect to the load, as discussed earlier.

Conclusion:
In summary, the influence factor 'I' depends on the location of a point with respect to the applied load. This factor is used to determine the vertical stress at a specific point in soil, and it decreases as the distance from the load increases. The other factors mentioned in the options, such as applied vertical load, type of soil, and soil modulus, do have an impact on the behavior of soil under load, but they do not directly determine the influence factor 'I'.