My dogs eat grass like grazing cows..lol It is funny to watch them..of course they are as big as small pony/baby cow.. (Great Danes)
It is very normal for them to eat grass even my cats eat grass (throwing/gaging it back up is normal too).. like everyone has said it is a way for them to sooth their upset tummy.. So don't fret it.
Just remember don't spray any chemicals in your grass where the doggy plays and eats it can cause serious problems.