Verb + away + at vs verb + noun + away

[capcap23]

What is the reason that the preposition 'at' is used in these examples?
Does removing the preposition 'at' change anything in the meaning?

Within a few years inflation had eaten away all the economic gains.
Waves had eaten away at the sand dunes.

He gradually chipped away at her confidence.
He used a chisel to chip away the rock.

 

[Barque]

Waves had eaten away at the sand dunes.

With "at", it means the waves had eroded the sand dunes but the dunes hadn't disappeared.

Waves had eaten away the sand dunes. Without "at", it means the dunes had been completely eaten away.

He used a chisel to chip away the rock.

This suggests he removed all the rock by chipping at it.

He used a chisel to chip away at the rock.
With "at", it just means he took a chisel to the rock. He may or may not have removed it all.

If you said "He had used a chisel to chip at the rock", it'd mean he'd chipped at it but not removed it all.

 

[capcap23]

In these sentences "verb + away + at", does 'at' mean 'in the direction of'?

 

[jutfrank]

No. It places the location of the eating away.

 

[Tarheel]

"Within a few years inflation had eaten away all the economic gains "

Those economic gains were eroded (eaten away) to the point of nothing. No direction is indicated.

 

[Barque]

He chipped away at [something]. = He did some chipping on/to [something]. Without any further context we don't know if he removed it entirely or not. The subsequent sentences or the context will tell you that.

He chipped away [something]. = He removed something by chipping at it.

The first describes the action. The second describes the action and the result.