The man was operating the excavator on Yerba Buena Road near Yellow Hill Road on Saturday when the hole opened up.
He was rescued, but the excavator remained inside the sinkhole for at least the next day.
In Malibu, Mulholland Highway was closed because of mudslides and large rocks blocking the road.
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In Burbank, residents were caught off guard by a heavy downpour. Pools of water built up on sidewalks and streets Sunday night.
But people who were out and about came prepared with umbrellas and raincoats.
"The second day. It's a rainy day and I hate it. I hate this rain," resident Sergey Krasnov said.
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The storm brought strong winds and rains to the region Saturday, raising the threat of mud and debris flows in recent burn areas. It ended up causing numerous problems.
The wet weather also made driving hazardous all weekend, and residents were urged to stay in if they could. But commuters could face more slick highways and slow-moving traffic Monday morning as more showers come into the region.
"If you pay attention and you know what you do when you're driving, you'll enjoy everything," one man said.
Caltrans said Topanga Canyon Boulevard was shut down between PCH and Grandview Drive because of a mudslide.
The series of storms is expected to taper off by Tuesday.