The mechanics of collisional grain flows are applied to the intense bed-load transport of sediment. The velocity distribution and grain transport are determined analytically without any freely adjustable parameters. The flow is modeled as two fluid regions with continuous stress, velocity, and granular concentration overlying a stationary bed: a collision-dominated granular-fluid region and a wall-bounded turbulent-fluid shear region with saltating grains. A simple kinematic model for the saltation of grains is developed to predict the grain transport in the saltation zone and to provide the upper boundary conditions for the granular-fluid region. The velocity in the granular-fluid region is found to be approximately proportional to the applied shear stress raised to the 3/2 power under the assumption of a linearly varying volume concentration. The grain flux and energy dissipation are proportional to the applied shear stress raised to the 5/2 power. When compared with observations and previous models, the present formulation predicts significantly greater transport at extremely high stresses. Calculations of the energy dissipation are consistent with previous transport models that are based on energetics arguments.