Resistance load due to skin friction for a pile varies with the length of the pile (L), the diameter of the pile (D), and the cohesion of the soil (C). The correct answer is option 'D' because the resistance load due to skin friction is influenced by the product of these three factors, which is LDC.

Explanation:
1. Resistance load due to skin friction:
- When a pile is driven into the ground, it experiences resistance from the surrounding soil. This resistance can be divided into two components: end bearing resistance at the pile tip and skin friction along the pile shaft.
- Skin friction is the resistance developed between the surface of the pile and the adjacent soil. It is caused by the frictional forces acting between the pile and the soil particles.

2. Factors influencing skin friction:
a) Length of the pile (L):
- The length of the pile is an important factor affecting the skin friction resistance. As the length of the pile increases, the surface area in contact with the soil also increases, resulting in higher skin friction.
- Therefore, skin friction load is directly proportional to the length of the pile (L).

b) Diameter of the pile (D):
- The diameter of the pile also influences the skin friction resistance. A larger diameter pile has a larger surface area in contact with the soil, which increases the frictional forces.
- Thus, skin friction load is directly proportional to the square of the diameter of the pile (D^2).

c) Cohesion of the soil (C):
- The cohesion of the soil is a measure of its internal strength. It represents the attraction between soil particles and their ability to resist shear forces.
- Cohesion plays a significant role in skin friction resistance. Higher cohesion results in increased resistance to sliding along the pile shaft.
- Therefore, skin friction load is directly proportional to the cohesion of the soil (C).

3. Product of the factors:
- The resistance load due to skin friction is influenced by the product of the length of the pile, diameter of the pile, and cohesion of the soil. Mathematically, it can be represented as:
Resistance load due to skin friction ∝ L * D^2 * C
=> Resistance load due to skin friction = LDC

Conclusion:
The correct answer is option 'D' because the resistance load due to skin friction for a pile varies with the product of the length of the pile (L), the square of the diameter of the pile (D^2), and the cohesion of the soil (C).