The Big Dam Bridge is a pedestrian bridge over the Arkansas River that connects the Arkansas River Trail in Little Rock on the south side of the river to the Arkansas River Trail in North Little Rock on the north side of the river. The bridge was custom built for pedestrian use, and was added to the dam. Chunks of the dam that they removed to embed the pedestrian bridge now serve as markers on either side of the bridge.
The bridge has good parking areas that you can use to access the Arkansas River Trail or the singletrack Pfeifer Loop dirt trail, which then connects to other trails in Burns Park in North Little Rock.
The Big Dam Bridge 100 bicycle ride is a classic charity ride held in September, with distances of 16, 30, 50, 68, or 100 miles to benefit the Big Dam Bridge Foundation - http://www.bigdambridge.org/BDB100/
Another event is the Big Dam Bridge Twilight 5k Run held in July in the evening - http://www.bigdambridge.org/BDB_Events/event_calendar.htm
See more about the Big Dam Bridge Foundation here - http://www.bigdambridge.org/
The official web page from Pulaski County is here - http://www.bigdambridge.com/