Sand dunes become sedimentary rock through cementation. This happens in several stages. First, after the sand dune forms, it is usually buried below the Earth’s surface as newer sand dunes cover it. Second, during and after the dune is buried, water within the ground begins to move through it. The water flows in the spaces or pores between individual sand grains. This water often contains dissolved silica (SiO₂) or calcium (Ca) and carbonate (CaCO₃). If the chemical conditions are right, the third stage, cementation, will occur. Quartz or calcite crystals will precipitate in the spaces between the sand grains. They will grow until the spaces are filled up, effectively cementing the sand together. 

Sand Mountain in Fallon, Nevada

Sand dunes in Oregon, USA