• Philip's Infiltration Equation:
• Horizontal cumulative infiltration (driven solely by matric suction absorption):

$$I_h(t) = S \cdot t^{1/2} = 90\text{ mm at } 100\text{ min}$$

• Vertical cumulative infiltration (combines matric sorptivity and gravity transmission):

$$I_v(t) = S \cdot t^{1/2} + K_s \cdot t$$

• Calculation:

$$I_v(100) = 90\text{ mm} + (0.1\text{ mm/min} \times 100\text{ min}) = 90\text{ mm} + 10\text{ mm} = 100\text{ mm}$$

• Conclusion: Cumulative vertical infiltration at 100 min is 100 mm. (Correct answer: Option 4)