Seepage Boundary Research Articles

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

We derive and analyze a solver-friendly finite element discretization of a time discrete Richards equation based on Kirchhoff transformation. It can be interpreted as a classical finite element discretization in physical variables with nonstandard quadrature points. Our approach allows for nonlinear outflow or seepage boundary conditions of Signorini type. We show convergence of the saturation and, in the nondegenerate case, of the discrete physical pressure. The associated discrete algebraic problems can be formulated as discrete convex minimization problems and, therefore, can be solved efficiently by monotone multigrid methods. In numerical examples for two and three space dimensions we observe $L^2$-convergence rates of order $\mathcal{O}(h^2)$ and $H^1$-convergence rates of order $\mathcal{O}(h)$ as well as robust convergence behavior of the multigrid method with respect to extreme choices of soil parameters.

Phreatic Line Predicted Method-Based SVM for Stability Analysis of Tailing Dam

Phreatic surface is one of the most important factors to influence tailing dam security degree. Due to the extremely complicated seepage boundary conditions of tailing dam, the calculation results adopting two-dimensional simplified theory may be greatly different from the measured results. It is urgent need of an accurate calculation method to forecast phreatic surface. Based on analysis of affecting factors of phreatic surface in tailing dam, the phreatic surface SVM predicted method is bring forward to predict the phreatic surface. According to the daily observation of phreatic surface, the phreatic surface SVM predicted model obtained. Finally, a tailings dam projects is given to illustrate stability analysis method of tailings dam based on Phreatic predicted Method-based SVM.

Forecast Model of Phreatic Surface on Tailings Dam Based on GM-GRNN Theory

Due to the extremely complicated seepage boundary conditions of tailing dam, the calculation results adopting two-dimensional simplified theory may greatly different from the measured results. It is urgent need of an accurate calculation method to forecast phreatic surface. In-depth analysis of factors affecting tailings dam phreatic surface, phreatic surface prediction model based on GRNN and GM (1,1) was established. A tailing dam engineering is tested using this model. It shows that the model uses the advantages of "accumulative generation" of a Gray prediction method, which weakens the original sequence of random disturbance factors, and increases the regularity of data. It also makes full advantage of the GRNN approximation performance, which has a fast solving speed, describes the nonlinear relationship easily, and avoids the defects of Gray theory.

Effect of the Lower Boundary Condition and Flotation on Colloid Mobilization in Unsaturated Sandy Sediments

In unsaturated soil columns, the boundary condition imposed at the column outlet may cause experimental artifacts. Our objective was to study in situ colloid mobilization during transient, unsaturated flow as affected by the boundary condition at the column outflow. We conducted colloid mobilization experiments by infiltrating unsaturated sandy sediment columns under different bottom boundary conditions: a seepage and a suction control. The mechanisms of colloid mobilization were investigated using force calculations (adhesive and interfacial forces), complemented with flotation experiments, where colloids in the bulk fluid and at the liquid–gas interface were measured separately. More colloids were mobilized under seepage than under suction‐controlled boundary conditions. The shape of the colloid breakthrough curves also differed: for the seepage boundary, the maximum of the colloid concentration occurred at the beginning of the column outflow, but for the suction‐controlled boundary, colloid concentrations in the outflow increased gradually before reaching a maximum. Colloid mobilization increased with flow rate and decreased with ionic strength for both boundary conditions; however, colloids were mobilized even at ionic strength exceeding the critical coagulation concentration (CCC). Flotation experiments showed that colloids were located both in the bulk fluid and at the liquid–gas interface at electrolyte concentrations less than the CCC, but only at the liquid–gas interface when the CCC was exceeded. Theoretical considerations confirm that interfacial forces at the liquid–gas interface exceeded adhesive forces at all ionic strengths. Both experiments and theory show that the liquid–gas interface had a dominant effect on colloid mobilization.

A variational inequality formulation for unconfined seepage problems in porous media

In the existing variational inequality formulations for the unconfined seepage problem in porous media, the seepage point, namely the exit point of the free surface, is a singular point and how to locate the seepage point exactly has been an open issue. By generalizing Darcy’s law applied solely to the saturated zone in an earth dam to the entire dam including the no-flow zone, a new variational inequality formulation is presented. The new formulation imposes a boundary condition of Signorini’s type on the potential seepage boundary and the seepage point turns out to be such a point that makes both inequalities in Signorini’s complementary condition become equalities. Singularity of the seepage point is accordingly eliminated. A strategy is developed for overcoming the mesh-dependency in the finite element implementation.

Evaluation of probabilistic flow in two unsaturated soils

A variably saturated flow model is coupled to a first-order reliability algorithm to simulate unsaturated flow in two soils. The unsaturated soil properties are considered as uncertain variables with means, standard deviations, and marginal probability distributions. Thus, each simulation constitutes an unsaturated probability flow event. Sensitivities of the uncertain variables are estimated for each event. The unsaturated hydraulic properties of a fine-textured soil and a coarse-textured soil are used. The properties are based on the van Genuchten model. The flow domain has a recharge surface, a seepage boundary along the bottom, and a no-flow boundary along the sides. The uncertain variables are saturated water content, residual water content, van Genuchten model parameters alpha (α) and n, and saturated hydraulic conductivity. The objective is to evaluate the significance of each uncertain variable to the probabilistic flow. Under wet conditions, saturated water content and residual water content are the most significant uncertain variables in the sand. For dry conditions in the sand, however, the van Genuchten model parameters α and n are the most significant. Model parameter n and saturated hydraulic conductivity are the most significant for the wet clay loam. Saturated water content is most significant for the dry clay loam.

Groundwater withdrawal from a hill with uniformly sloped seepage faces

A new kind of free boundary is introduced, namely, the projection on the horizontal plane of the interzonal boundary between a seepage face and a phreatic surface. This “seepage boundary” is demonstrated to show certain mathematical similarities to a phreatic surface, viewed in a vertical plane. A variation on Zhukovsk's method is employed to derive a formula for the deformation of the seepage boundary on the side of a hill due to groundwater withdrawal. The modified Zhukovski function, being many valued, is handled by Strack's extension of the Schwartz‐Christoffel transformation. It is finally pointed out that more complicated problems could be solved by a modified hodograph method.

Fluid flow in partially saturated, welded-nonwelded tuff units

A discrete fracture, porous matrix model and a composite medium model were used to study hydrological responses to cycles of pulse infiltration at Yucca Mountain, a potential site for a nuclear waste repository. The pulses were applied to fractures at the top of a vertical column composed of alternating layers of welded and nonwelded volcanic tuff. For average infiltration rates of 0.1 mm/yr, pulses expressed as short durations separated by periods up to 5000 yr, most effects of the transient infiltration pulses were damped by the Paintbrush nonwelded unit. The effects of eastern tilting of the units at Yucca Mountain on the steady state fluid flow distribution were studied using a two-dimensional model. Ghost Dance Fault was modeled as a seepage face. Under the expected flux conditions, saturation increased just to the west of the fault, but the water did not enter the fault with the seepage boundary condition.