Which of the following factors contributes most significantly to the risk of overturning when operating on a slope?

The gradient of the slope is the most significant factor contributing to the risk of overturning when operating a hydraulic excavator on a slope. As the gradient increases, the center of gravity of the excavator becomes more unstable, leading to a greater likelihood of tipping over.

On steeper slopes, the weight distribution and balance of the excavator are adversely affected, which can cause it to lose stability. The mechanical design of the excavator and its operating characteristics are particularly sensitive to changes in slope gradient, making it crucial for operators to assess the terrain before beginning work.

While factors like depth of excavation, weather conditions, and type of excavator attachment can affect overall safety and performance, the gradient of the slope directly influences the balance and stability of the machine during operation. Thus, careful consideration of the slope's gradient is essential to mitigate the risk of overturning.