Finite Element Modeling of Partial Penetration Well Uplift Factors

Partially-penetrating wells have been used since the late 1700s for agricultural and construction dewatering and since the 1930s for flood protection structure seepage control. Systems design requires consideration of boundary conditions, foundation characteristics, and well losses to determine the needed number, size, spacing, and penetration of wells to achieve project objectives. Design often involves the estimation of flow to and head reduction from an infinite line of partially-penetrating artesian wells with a line source of seepage. Electrical analogy and physical models with theoretical studies led to the development of a design chart (nomogram) for this purpose by the 1950s. This nomogram has been widely employed and yields uplift factors which can be used to estimate flows and foundation head reductions for a given system geometry. While not as broadly employed for systems design, analytical solutions developed in the 1970s–1980s, and recent three-dimensional computer modeling can also be used to compute uplift factors. This paper offers a review of partial penetration artesian well systems design and provides finite element modeling-derived uplift factors. While isolated errors were identified in a few historical publications, this study further validates prior approaches, and shows that the various methods provide practically similar uplift factor solutions for well systems design.