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A general method is presented to calculate the seepage discharge from a channel of a complex shape. The method is based on use of Hadamard's formula for the variation of the Green's function when the shape of the region for which the Green's function is known has changed. The method is applied to calculate the seepage from channels of a complex shape that may be considered almost trapezoidal (or triangular). A simple geometrical construction yields the trapezoidal (or triangular) equivalent channel from which the same quantity of water is lost. Graphs of seepage discharge in dimensionless form are given for trapezoidal and triangular channels.

In this investigation the uplift pressures under hydraulic works on porous foundations, such as are built at the falls in canals and rivers, have been determined. Two series of experiments have been carried out and the pressure distributions have been obtained for ordinary combinations of sheet pile and floor. A method of obtaining the pressure distribution approximately by the application of theory has also been indicated. Our thanks are due to Dr. E. McKenzie Taylor, the Director, for his keen interest in the problem.

The radial flow permeameter is used to define the coefficient of permeability of soil, bymeans of two dimensional seepage flow occuring horizontally throughout the soil sample, caused by making a suitable water pressure act on the porous pipe that is set in the middle of the cylindrical sample (See Fig. 1 and Phots 1 and 2).From the testing results of this newly-built apparatus, the writers are convinced to have been able to correct some of the common faults and errors of the conventional testers that have hitherto been in use.

This paper deals with the two-dimensional problem of steady seepage flow under gravity from a canal into a semi-pervious clay layer of finite thickness underlain by a freely permeable layer of sand and gravel in which the piezometric head is very near the canal water level. Two steps of conformal mapping are used and an approximation to the canal profile is adopted. In this approximation the specified canal width and depth are untouched.

A series of two-dimensional dispersion experiments were performed in a one and two layered porous medium. The experimental results were compared with a theoretical and a numerical solution both of which describe the two-dimensional dispersion of a miscible, second fluid through a unidirectional, seepage flow. The combined effect of longitudinal and lateral dispersion was considered in all cases. The experiments clearly, verified the theoretical and the numerical results.

Summary A number of problems of steady two-dimensional seepage flow around sheeted excavations in porous media have been investigated at the Building Research Station in recent years. This paper presents a general survey of the work carried out and summarizes the more important results which have been achieved. The assumptions of the theory of seepage flow are reviewed briefly and the difficulty of interpreting the practical value of theoretical results is discussed. Some relaxation solutions for one type of problem are given and graphs have been prepared in order to facilitate the application of equilibrium criteria. The application of the theory in the safe design of sheeted excavations is considered and some practical suggestions are offered.

Incipient motion tests were conducted for flow into and out of a porous bed. Seepage out of a bed does not affect incipient motion measurably because the seepage force is lost once a sediment particle rocks. Seepage into a bed may either enhance or hinder incipient motion, depending upon the relative effect of the boundary shear stress and the seepage force, both of which depend on the seepage flow. For a given hydraulic gradient the size of the sand grains is critical regarding incipient motion. For turbid water flow over a bed, fine particles of the mixture may become deposited in the bed, resulting in a concrete-like, more resistant bed. Typical values of the hydraulic gradient are given for flow out of a canal and in an ocean bed under oscillatory waves.

Unsteady problems concerning the displacement of gas and oil deposits in a seepage flow of stratal water are of specific interest to oil and gas hydrogeology, and in the planning and analysis of the processes of reservoir exploitation. Firstly, a change of the hydrogeological environment in a region of already formed deposits involves their displacement. Secondly, when one of two adjacent deposits is developed, a displacement of the other occurs in the artificial flow of stratal water which is produced. Papers [1–3] investigate the steady configuration of gas—water or water—oil contacts in the presence of a seepage flow of stratal water under the deposit. The unsteady problem considered below is a generalization of the problem in paper [3]. Its characteristic property is the presence of mobile boundaries separating the regions with flow of different fluids in the horizontal plane.

Geophysical methods appreciably increase the amount and quality of information provided by observations aimed at investigating the seepage regime of earth dams. The use of these methods for studying seepage processes is predetermined by a significant differentiation of electric, seismic and thermal properties of dry and water-saturated grounds. The seepage flow level is a contrast electric and seismic limit. A complex of electrometric, seismic and thermometric observations made so far allows to control the position and configuration of the depression surface in a dam supporting mass. Geophysical observations of the regime by resistivity and natural electric field methods allow to establish the presence of active zones of ground redeposition and mechanical suffosion and to assess the development of suffusion processes with time. Practice has shown that local suffosion zones can be isolated by geophysical methods long before their detection by field hydrotechnical observations. In order to increase the reliability of the results of regime geophysical investigations, the authors have devised special probability-statistical techniques for processing potential geophysical fields with recalculation to the area adjacent to the anomaly inducing objects. The positive results obtained in Central Asia and Transcaucasia permit to recommend extensive application of geophysical methods when conducting field observations of hydrotechnical structures.

Seepage under a flat apron in a two-layer ground consisting of homogeneous isotropic layers of equal thickness was investigated by means of the analytic theory of linear differential equations by Polubarinova-Kochina [1]. An approximate solution of the same problem for layers of different thickness by the methods of the variational calculus was given in [2]. The solution to such a problem for homogeneous anisotropic layers of different thickness by means of a special complex variable representation and linear conjugation was given in [3] by Prusov and the author of the present paper. The method of [3] is now used to investigate two-dimensional steady seepage flow under two aprons in a multilayer ground consisting of n homogeneous anisotropic layers of different thickness, the principal directions of anistropy of each layer having an arbitrary position relative to the horizontal.

The existing theory of immiscible fluid flow is extended to the seepage with nonzero initial shear stress of viscoplastic media. An analog of the Buckley-Leverett frontal-displacement theory is constructed.

A remark is made about a simplified derivation of boundary integral equations for Biot's linear consolidation theory in two dimensions. The method is traditional as has been done in thermoelasticity, but the generality and the simplicity are stressed for the treatment of linear elastic porous materials by the boundary element method.

In unlined underground rock caverns, liquid petroleum and petroleum gas can be stored by making use of natural or artificial ground water pressure. In case of applying the unlined underground storage caverns to the cracky rock mass, it seems to be most important that the behaviour of the ground water through the rock mass surrounding the caverns is studied in advance. This study, therefore, discusses the following subjects concerning unlined underground oil storage caverns. 1) The numerical study on the effects of natural ground water pressure on the storage caverns. 2) The numerical study on the effects of artificial ground water pressure on the storage caverns. 3) Model experiment about gas leakage into the crack of rock mass.

The streamfunction ψ can be used to describe two dimensional groundwater flow. Because the given properties of the flow can not be applied immediately to the streamfunction formulation this method was used only rarely or indirectly up to now.

The system is modelled by a non-homogeneous elliptic linear partial differential equation subject to non-homogeneous Dirichlet boundary conditions. After summarising some theoretical results and sketching the typical structure of an identification algorithm, which is based on the cost functional minimisation approach, we deal with some computational results.-from Author

An efficient iterative procedure for the analysis of unconfined three dimensional seepage flow is presented. The method is based on an invariant net of finite elements. The system equations are assembled and decomposed only once for the entire domain. Variations in the location of the free surface and the extent of the seepage surface are taken into account by slight modifications of the decomposed equations. The implementation of the method is described in the paper.

A series of centrifuge model tests was carried out in an attempt to study river bank failures due to seepage flow. The necessity of centrifuge modeling and the similarity law were discussed. The results of the model tests showed that capillary tension above phreatic surface plays an important role in stability, and that there seems to exist a critical value of velocity of fluid flow to trigger an initial failure. An analytical model to simulate the development of failure was also proposed.

Background It is well know that many shallow landslides are triggered by rainfalls. In previous studies of shallow landslide models, the effect of overland water flow on slope stability was ignored. Results In this paper, a physical model considered the effect of overland water flow on rainfall-induced shallow landslides is derived and applied to predict the landslides. The slope stability model is developed by considering the depth of overland water flow in infinite slope stability theory. Hillslope hydrology is modelled by coupling the overland uniform water flow equation with Rosso’s seepage flow equation. And then, the model is used to assess the slope stability in Dujiangyan of China, and the results is compare with Rosso’s model. Conclusions This model is simple, but has the capability of taking into account the effect of overland water flow in the triggering mechanism of shallow landslide. The results of case study show that the overland water flow can make an obvious effect on shallow landslides, so it is quite important to consider the overland water flow in shallow landslide hazard assessment.

The stepped spillway design has been used for more than 3,300 years. A simple structure is the gabion stepped weir. A laboratory study was performed herein in a large size facility. Three gabion stepped weirs were tested with and without capping, as well as a flat impervious stepped configuration. For each configuration, detailed air–water flow measurements were conducted systematically for a range of discharges. The observations highlighted the seepage flow through the gabions and the interactions between seepage and overflow. The air–water flow properties showed that the air concentration, bubble count rate and specific interface data presented lower quantitative values in the gabion stepped weir, compared to those on the impervious stepped chute, while higher velocities were measured at the downstream end of the gabion stepped chute. The re-oxygenation rate was deduced from the integration of the mass transfer equation using air–water interfacial area and velocity measurements. The aeration performances of the gabion stepped weir were lesser than on the flat impervious stepped chute, but for the lowest discharge. For the two configurations with step capping, the resulting flow properties were close to those on the impervious stepped configuration.

Laboratory tests were conducted to study the seepage flow conditions through a simulated grounded jam. Results indicated that nonlaminar seepage predominates and that the resulting relationship between the local flow and the upstream and downstream water depths may be applied to both steady and unsteady flow conditions.

Laboratory experiments have been conducted to investigate the acceleration mechanism of the void development in the backfill of a seawall. It is found that the rate of sand leakage is proportional to the air amount in the soil medium. Therefore, the larger void appears to accelerate the further enlargement of the void. Leakage of sand has been found to be closely related to the seepage flow due to the pressure gradient between the soil medium and the water. Therefore, propagation of the wave-induced pressure response influences the leakage of sand. Compressibility and permeability of soil medium have been found to be two significant parameters for the rate of leakage.

Fine-grain beaches are relatively common where the beach forms part of a larger coastal barrier system. In such a coastal system, different water levels could be present in the seaward side and back-barrier lagoon. The water level changes in the steady-state lagoon may potentially induce groundwater dynamics near the beach which would subsequently affect seepage flow into (or out of) the beach. The exchange of water could generate varying hydrodynamical and morphodynamical behaviour at the seaward boundary. Hence, it is important to gain insight into groundwater flow dynamics which results in exchange of water between sea, barrier and lagoon; especially for coastal engineers responsible for planning and managing such a coastal environment. In present work, a numerical model is developed to simulate flows through a coastal barrier and it is validated against prototype-scale experimental results, which can then be extended to model small time-scale groundwater flows that may be too expensive or impractical to set up in a lab.

This paper describes the use of a new item of laboratory equipment, a two-way permeameter for determination of the degree of permeability anisotropy of compacted or undisturbed samples of soil. The test is performed on a single sample of soil. The relevant theoretical solutions for seepage flow through the permeameter have been provided, based on exact solutions and manual sketching of flow nets.

The authors have presented an interesting description of the occurrence and development of seepage steps in the semi-arid Great Plains. Subsurface flow at the contact between the more permeable surficial mantle material and the underlying more impermeable weathered bedrock is shown to be responsible for the formation of these features. It appears that an additional requisite for the development of seepage steps is a mantle material which is sufficiently cohesionless, or which becomes essentially cohesionless upon saturation by rainfall, and in which the grains are sufficiently small (fine sand or silt size) to be eroded at an exposed face by the seepage flow emerging at the contact of the permeable and more impermeable zones. The grain-size analyses show that the mantle material of the area studied meets these requirements, with approximately 75 pct of the soil constituents being of silt and fine sand size and from 20 to 2pct only of clay size (equivalent diameter less than 0.002 mm).