First of all, we need to define what erosion is. Simply defined, erosion is the prevention of the displacement of soil particles from one position to another either by water or wind. Furthermore, we need to understand the primary function that the geomembrane performs. A geomembrane is a class of impermeable geosynthetics that primarily prevents water from passing through it.
How then can a geomembrane prevent erosion? In hydraulic structures such as a dam, erosion may be due to excessive upward pore pressure that could lead to the piping of the soil at the points where the insitue soil weight is less than the upward pore pressure. To prevent the situation, for example, downstream of a dam, the flow net may be elongated with the use of a geomembrane that may be placed upstream of the dam to cover a pre-determined area that will lower the residual pore pressure downstream to prevent erosion.
Geomembranes may be deployed for other uses which include the lining of:

Canals conveying wastewater to prevent contamination of the ground
Fish ponds to conserve the water for habitation
Landfills and waste ponds to prevent soil pollution
Foundations of buildings and civil engineering structures to control underground water for Waterproofing purposes
Pipelines to prevent corrosion and tunnels for waterproofing
Structures as a separation medium especially when contamination is to be prevented.

In Nigeria, you can get quality imported geomembrane from a group of experienced seasoned engineers, with free technical advice, from any of these companies: Geotextile & Gabions Ltd, N0.9, Challawa Crescent, Barnawa-Kaduna, Nigeria Phone 08185285346 or Gabions Geomembrane & Geotextile Ltd at No. 3, Printing Road, Kaduna-Nigeria. Phone 0703 784 5174