Underground Cable

You are given a 1km x 1km square area and you are told there is a straight line of cable hidden 1 meter below the ground that passes somewhere through this area.

An example of the hidden cable (red line) and digging lines (blue diagonal lines)

You need to dig in the ground in order to find it – a task which takes a lot of effort.
How will you dig the minimum length such that you still make sure you will find it.

For example: if you dig ~2.83km you will surely find the red line (the blue diagonals in the picture).