Seepage through earth dams

Abstract

The free surface in two-dimensional gravity flow systems is determined by a simple equation in one iterative cycle. The base pressures at the impervious boundaries, as well as the pore-water pressures or total hydraulic heads within the flow medium, can easily be determined after the free surface is located. Two problems are analyzed: vertical dam cores and earth dams or embankments with sloping sides. In both problems Dupuit-Forchheimer assumptions are eliminated. In the second case, the effects of both the upstream and downstream slopes are taken into consideration. Although the two cases are under steady-state conditions, it is believed that the method is promising for solving problems under transient conditions whether the flow system is two-dimensional or radial. Introduction. The upper boundary of theflow region in a gravity flow system must be determined before the solution of flow problems can be found. Two-dimensional problems of this type are shown in Figures' I and 2: a vertical dam core and an earth dam or embankment with sloping sides. The general equation for steady-state conditions is the two-dimensional Laplace equation: where As a matter of fact, equation 2 would be Bernoulli's equation for steady flow if the velocity head term were neglected; this is normally the case in ground flow systems. The derivation of equation I is based on the usual assumptions that the soil is homogeneous and isotropic and that Darcy's law is valid. Evaporation, capillary flow, infiltration, and leakage effects are also neglected. Rigorous mathematical solutions are available for gravity flow systems [Polubarinova-Kochina, 1962]. These solutions are more or less limited in their practical applications, however. This has led to the use of other methods, such as numerical solutions [Shaw and Southwell, 1941; Kashef et al., 1952], and to the introduction of some simplified assumptions, such as Dupuit-Forchheimer assumptions.The proposed method is essentially based on the relationship between the seepage force, the * A, proposed method; B, relaxation method.

A new model for soil–water drainage problems

“…According to [7], the discharge q is exactly given by Dupuit's equation [3], resulting in an excellent agreement. Note that the boundary condition h (x = 0) = 0 means no-flow at x = 0, whereas the actual flow is q.…”

“…1 from the x-and y-directions to a model in the x-direction only. Both Kashef [7] and Knight [3] obtained approximate models for seepage problems based on parabolic assumptions on φ.…”

Risk‐based planning analysis for a single levee

“…Levee fragility depends on levee geometry such as levee height, crown width, side slopes, and properties such as soil conductivity and compaction [ Kashef , ; USACE , ]. Here in addition to levee height , levee crown width is a second decision variable because of its influence on intermediate failure performance curves and the wide range of acceptable values [ USACE , ].…”

EXPANSION OF SALT‐WATER ZONE DUE TO WELL DISCHARGE1

“…Within the distance L, the total head hbx along the upper boundary of the artesian aquifer with respect to datum A-A (Figure 1) at any section x from the origin located at the ocean front is equal to (Kashef and Safar, 1975): The x values are taken positive to the left of the origin. Equation 2 has resulted from the hydraulic forces method (Kashef, 1965(Kashef, , 1967(Kashef, , 1968. The results of this equation were in very close agreement with the finite element method results (Kashef and Safar, 1975).…”