Physical Danger
Let's get the worst-case scenario out of the way. As a civil engineer, you'll probably spend a good percentage of your time in your office. You'll obsess over survey data and environmental impact statements. You'll spend countless hours with your scientific calculator, double- and triple-checking your building load calculations and project estimates. You'll organize weekly electronic football pools for your officemates. Wait...disregard that.
Anyway, all that computer and smartphone work will most likely leave you with a haggard, cross-eyed look and a nasty case of calculator thumb. Hopefully that's all covered by workman's comp.
However, we would be remiss if we didn't touch on a few hazards that might lurk on your job sites. For example, let's say you're assessing the strength of a building under construction. While you're roaming around the building's foundation, you could get beaned by a screw (accidentally) dropped from a 200-foot-high scaffold. You could be checking the slope of a bank next to a newly constructed building...and be knocked on your keester by a pile of cascading rocks and dirt.
All of this stuff is theoretically possible...but our money is on the calculator thumb.