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He benefited from a clash of shoulders between Germany's André Greipel and Colombia's Fernando Gaviria in the closing metres, when the former appeared to be on course for a first stage win of this year's race.
Porte came into the Tour in winning form, taking the Tour de Suisse to stamp his claims for at least a podium finish in Paris.
With van Avermaet not a specialist climber, Thomas could potentially take yellow today when the Tour resumes with a huge 158.5km mountain stage from Annecy to Le Grand Bornand. That increased his lead over Froome's teammate Geraint Thomas in second to 7 seconds and his own BMC teammate Tejay Van Garderen to 9 seconds.
Frenchman Warren Barguil, a former team mate of Degenkolb's who was also in the 2016 accident in Spain, said: "Everybody was saying he was finished, I'm so happy for him".
The good news for an ailing Martin - as well as the rest of the field - is they have just one more stage to complete before the event's first rest day. I think it's great for us to have those options to be able to play when it comes down to it, especially looking at rivals that have two or three options within their teams.
ITV SPORT Andre Greipel and Fernando Gaviria were battling on the side of the sprint
Up next on Stage 11 is a 108.5-kilometer (67-mile) leg from Albertville to the top of the La Rosiere summit on Wednesday.
While the Dutchman followed up Friday's success in Chartres with a Bastille Day victory in Amiens on stage eight, Cavendish could enjoy a respite from questions over his form as there was little he could have done differently this time.
"He has cuts and burns, so tomorrow it is going to be a tough day for sure", UAE Team Emirates director Philippe Mauduit said.
Froome punctured a tire on a gravel path atop the second climb up the beyond-category Montee du Plateau des Glieres, the first use of a dirt road by the Tour since 1987.
Greipel would instead end a frustrated second, while Gaviria missed out on a third stage win of the race by ending third. The single-day race included most of the men's route.More news: British cave diver mulls legal action over Musk's attack
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