**Correct Answer:**

The correct statement is option C: *Strength of a rock increases with an increase in strain rate.*

**Explanation:**

The strength of a rock refers to its ability to withstand stress and deformation. It is an important parameter in engineering and geology, as it determines the stability and behavior of rock masses. The strength of a rock can be influenced by various factors, including confining pressure, temperature, strain rate, and pore water pressure.

Let's examine each option and understand why option C is the correct statement.

a) Strength of a rock decreases with an increase in confining pressure:

When a rock is subjected to confining pressure, it experiences an increase in the applied stress from all sides. This confining pressure can help to enhance the strength and stability of the rock mass. Therefore, the statement that the strength of a rock decreases with an increase in confining pressure is incorrect.

b) Strength of a rock increases with an increase in temperature:

An increase in temperature can cause thermal expansion in rocks, leading to an increase in pore pressure and the potential for thermal fracturing. This can result in a decrease in the strength of the rock. Therefore, the statement that the strength of a rock increases with an increase in temperature is incorrect.

c) Strength of a rock increases with an increase in strain rate:

Strain rate refers to the rate at which a rock undergoes deformation. The strength of a rock is typically strain-rate dependent. Under high-strain-rate loading conditions, such as during seismic events or dynamic impacts, the strength of a rock increases. This is because the rate of deformation exceeds the rate at which the rock can deform internally, resulting in strain hardening and an increase in strength. Therefore, the statement that the strength of a rock increases with an increase in strain rate is correct.

d) Strength of a rock increases with an increase in pore water pressure:

Pore water pressure refers to the pressure exerted by water present within the pores of a rock. An increase in pore water pressure can reduce the effective stress acting on the rock, resulting in a decrease in strength. Therefore, the statement that the strength of a rock increases with an increase in pore water pressure is incorrect.

In conclusion, option C is the correct statement. The strength of a rock increases with an increase in strain rate.