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Review of Vadose Zone Flow and Transport Models
Published in L.G. Wilson, Lorne G. Everett, Stephen J. Cullen, Handbook of Vadose Zone Characterization & Monitoring, 2018
John H. Kramer, Stephen J. Cullen
Analytical models use exact mathematical solutions of partial differential equations to represent flow and transport. Hydraulic properties are assumed to be homogeneous in the domain of interest. Approximate anisotropics can be treated through modification of axes scales. Moisture content at any point in space is correlated through pre-characterized soil moisture relations for the soils of interest. In the vadose zone, the nonlinear aspects of the variable hydraulic-conductivity relationships are estimated with continuous functions. Model outputs are exact solutions to the continuously variable pressure field through time and space. New developments in analytical solutions to saturated-flow problems employ the analytic element method (Strack, 1989), which facilitates application to irregular domains by linking analytic solutions across element boundaries. This approach will probably soon be applied to the vadose zone as well.
Analytic element modeling of steady two-dimensional flow
Published in Mark Bakker, Vincent Post, Analytical Groundwater Modeling, 2022
Pumping wells form an important part of the two-dimensional solutions that have been discussed so far. The principle of superposition allows for the solution of problems with an arbitrary number of wells, and the method of images allows for the simulation of straight specified-head and no-flow boundaries. The organization of solutions with multiple wells becomes cumbersome when the number of wells grows. The analytic element method is a modeling technique that facilitates the superposition of many solutions, including wells.
Analytical and numerical assessment of a preliminary support design – a case study
Published in Cogent Engineering, 2021
Sylvanus Sebbeh-Newton, Shaib Abdulazeez Shehu, Prosper Ayawah, Azupuri A. Kaba, Hareyani Zabidi
Numerical modeling techniques are valuable tools in underground excavation designs since opening geometry, strength parameters, and in-situ stresses are considered. In civil and mining engineering, numerical modeling is used to analyze the rock mass behavior and its impact on infrastructure and support mechanisms. To determine the displacement and plastic region around an opening and to verify the empirically recommended support designs, numerical methods such as Discrete Element Method (DEM), Finite Element Method (FEM), Boundary Element Method (BEM), and Analytic Element Method (AEM) have been implemented by several researchers (Ghadimi Chermahini & Tahghighi, 2019; Kanik & Gurocak, 2018; Morris & Johnson, 2009; Rehman et al., 2020; Xing et al., 2019). For this study, Phase2 V. 7.0, a FEM software, was used to model the deformations and plastic zones around the tunnel. Phase2 was selected because of its plastic modeling capabilities, ability to handle multiple materials, and automatic mesh generation function. This code only allows 2-D analysis of non-linear deformations.