If the cutting length is x meters, there are two situations, one is that the remaining part of the wire with the original length of 12 meters is longer, and the other is that the remaining part of the wire with the original length of 13 meters is longer, so these two situations are solved respectively:

1)( 13-x)/( 12-x)= 8/ 13

13( 13-x)= 8( 12-x)

169- 13x=96-8x

73 = 5 times

x= 14.6

Obviously inconsistent with the reality, rule out this situation.

2)( 12-x)/( 13-x)= 8/ 13

13( 12-x)= 8( 13-x)

156- 13x = 104-8x

52 = 5 times

x= 10.4

Answer: The length of the excavation section is10.4m..