Probabilistic analysis of geomembrane puncture from granular material under liquid pressure

A simplified probabilistic analysis of geomembrane punctures from granular material was presented when subjected to liquid pressure. The probability distribution of contact force between geomembrane and granular material was obtained based on the principle of equal probability and assumptions that grains are spheres with constant size. A particle flow code PFC^3D was employed to simulate the contact process which indicates a good agreement with the theoretical probabilistic analysis. The odds of geomembrane puncture from grains of constant size were obtained by evaluating the puncture force which should not exceed the puncture resistance of geomembrane. The effects of grain radius, grain rigidity and liquid pressure were studied in more detail and displayed in graphs. Both high-level of liquid pressure and large grain can result in high risk of geomembrane puncture. The influence of grain rigidity on the geomembrane puncture odds is significant. For granular material with a grain size distribution, the geomembrane puncture odds can be estimated by the grain size distribution, served as weight function and it is a cautious design if the largest grain is chosen as the design grain size.