Can normal titans dig the ground? I know normal titans are not intelligent but in one of the episodes of season 1 we see that they can learn to climb the trees in order to reach the scouts. 
So why none of them tried digging a tunnel in the ground to pass the walls?
1. Can normal titans dig the ground?

Yes, they can. In Season 2 Episode 10 we see


   Ymir digging herself out of the ground as a pure titan.


2. So why none of them tried digging a tunnel in the ground to pass the walls?

In Season 1 Episode 25 at around 15 minutes the intermission cards state the following (synopsis):


   Once a miner tried to dig under wall Sheena. At some point, however,
 the ground was so hard that his shovel broke. He wondered if the
 people were surrounded by walls not only above the ground, but below
 the ground, too.
 
 The next day the miner disappeared and was no longer findable. Unsure
 what to do, his friend eventually went to the Garrison, and told them
 the whole Story. The Military Police and the Garrison
 organized a large-scale search party. But they never found a trace of
 the miner, nor even the pit he'd dug. And one day, his friend also
 vanished, never to be seen again.


From this we can conclude that titans cannot get past the walls through digging.