C402 Pilot reported the left main landing gear failed during taxi for take off. The aircraft was removed from the runway with the help of airport operations and the aircraft taken back to the ramp for maintenance.

Narrative

When ready to taxi from the ramp I contacted ground and was instructed to back taxi on Runway XX. I entered Runway XX from taxiway 1 and back taxied the entire length of the runway at normal taxi speed. Upon reaching the departure end of Runway XX I slowed the plane and turned right at a diagonal in order to provide room to do a 180 degree back to the left for takeoff. I initiated the turn to the left with rudder when I had sufficient space. The turn started but then the plane lurched left and stopped. After this I was unable to move the plane in any direction. At this time I thought I had a problem with the nose gear. I called the Tower and reported that I had a problem with my nose gear and that we could not move on the runway. I called the [company] and reported the problem. I told the passengers that we had a mechanical problem with the gear and that they would be returning when transport arrived. I called [the company] and reported the problem. The Passengers were calm throughout. The Tower closed the runway and sent Operations personnel with a tug; and also a bus for the Passengers. I shut down and secured the engines. I kept the Passengers on the plane as it was windy and cold outside and I didn't want them loose on the runway until transport arrived. When the bus arrived after about 10 minutes I opened the door and deplaned the Passengers. They boarded the bus. ZZZ operations personnel arrived with a tug and at this time we determined that the problem was with the left main gear and not the nose gear. The left main axle appeared to be broken and the tire was wedged against the strut. Operations brought a dolly to the plane for the left main gear. While waiting for the dolly we offloaded the bags and had them returned to the gate on the bus. We attached the dolly to the left main gear and towed the plane back to the non-secured ramp. I secured the airplane and wrote up the problem. No Passengers or Personnel were injured during this incident. The plane was secured on the ramp at about XA:30. I believe that the axle failed on the left main gear.