Several mechanisms cause a granular material to strengthen over time at low applied stress. The strength is determined from the maximum frictional force F max experienced by a shearing plate in contact with wet or dry granular material after the layer has been at rest for a waiting time τ. The layer strength increases roughly logarithmically with τ only if a shear stress is applied during the waiting time. The mechanisms of strengthening are investigated by sensitive displacement measurements, and by imaging of particle motion in the shear zone. Granular matter can strengthen due to a slow shift in the particle arrangement under shear stress. Humidity also leads to strengthening, but is found not to be its sole cause. In addition to these time dependent effects, the static friction coefficient can also be increased by compaction of the granular material under some circumstances, and by a cycling of the applied shear stress.