The correct answer is A. Is directly proportional to the angle of internal friction of the soil.
The angle of internal friction is a measure of the resistance of a soil to shear stress. It is defined as the angle between the failure plane and the horizontal plane in a soil sample under shear stress. The shear strength of a soil is the maximum shear stress that a soil can withstand before failure. It is directly proportional to the angle of internal friction. This means that the higher the angle of internal friction, the higher the shear strength of the soil.
Option B is incorrect because the shear strength of a soil is not inversely proportional to the angle of internal friction. In fact, the two are directly proportional.
Option C is incorrect because the shear strength of a soil increases with increase in normal stress. This is because the normal stress provides a confining pressure that helps to hold the soil particles together.
Option D is incorrect because the shear strength of a soil decreases with decrease in normal stress. This is because the decrease in normal stress reduces the confining pressure, which allows the soil particles to move more easily and results in a decrease in shear strength.