They are generally not a consistent intensity during the event. Yes, it can be moderate for a bit and then more intense shortly later. There are several different waves that move at different speeds from the earthquakes epicenter and which decay at different rates relative to distance from the epicenter. One categorization is P, S, and surface wave. The time of arrival of each wave and their intensities depend on many variables. I think it is possible for the later arrival to be much larger and more destructive than the first, but I'm a bit hazy on the details.
Anecdote, I was in a small earthquake in Tokyo, the initial thump woke me up and I rolled over under the dining table (sleeping on the floor as a guest) then the bigger vibrations arrived a few seconds later. The building was well designed for earthquakes, but in the moment I figured that, not knowing how big the rest of the earthquake will be, it was probably best to get cover anyway. I think cover is just about increasing the probability by some small amount that you could end up alive under the rubble if the building were to collapse.
https://science8sc.weebly.com/uploads/1/3/2/7/132773018/publ...
Anecdote, I was in a small earthquake in Tokyo, the initial thump woke me up and I rolled over under the dining table (sleeping on the floor as a guest) then the bigger vibrations arrived a few seconds later. The building was well designed for earthquakes, but in the moment I figured that, not knowing how big the rest of the earthquake will be, it was probably best to get cover anyway. I think cover is just about increasing the probability by some small amount that you could end up alive under the rubble if the building were to collapse.