Deformation of Dupuit's parabola in a dam with sheet piling

If the flow in an earth dam is plane and steady, the shape of the phreatic surface can be approximated by Dupuit's parabola. Thin sheet piling in the dam, deforms the phreatic surface in the vicinity of the sheet piling and at its tip the hydraulic gradient is singular. If the length of the sheet pile is much smaller than the thickness of the dam, the flux through the dam per sheet pile length is equal to the undisturbed flux, whereas if the length of the sheet pile is much larger than the thickness of the dam the corresponding flux is negligible.     

Deformation of Dupuit''s parabola in a dam with sheet piling

If the flow in an earth dam is plane and steady, the shape of the phreatic surface can be approximated by Dupuit's parabola. Thin sheet piling in the dam, deforms the phreatic surface in the vicinity of the sheet piling and at its tip the hydraulic gradient is singular. If the length of the sheet pile is much smaller than the thickness of the dam, the flux through the dam per sheet pile length is equal to the undisturbed flux, whereas if the length of the sheet pile is much larger than the thickness of the dam the corresponding flux is negligible.Nomenclature a length of sheet pile - A auxiliary parameter - b thickness of dam - G Greens function - h height of phreatic surface - K hydraulic conductivity - Q flux per sheet pile length - Q ₀ reference flux - r, auxiliary variables - r ₀ auxiliary parameter - R half-strip in thex-y-plane with a cut - R ₁ strip in thex-y-plane - R₁ half-strip in thex-y-plane - R ₂ half space in the--plane - R radius of curvature of the tip of the sheet pile - z=x+iy complex variable inR,R ₁ andR₁ - w=+i complex in variable inR ₂ - h ² potential - ÷ unknown at a part of the boundary ofR ₂     

Steady Groundwater Flow to Drains on a Sloping Bed: Comparison of Solutions Based on Boussinesq Equation and Richards Equation

Analytical expressions for the scaling factor (A) in the Wooding and Chapman (J Geophys Res 71:2895–2902, 1966) solution for steady-state flow to drains on a sloping bed are presented. Otherwise A needs to be obtained by matching numerical and solutions. Corrections to various errors in other analytical solutions are given. The HYDRUS2D numerical model was used to generate results for steady-state flow to drains on a sloping bed which were compared to published Hele-Shaw cell results. The numerical results were used to compute both the pressure head on the bottom and the height of the phreatic surface. The numerical results for maximum water-table height are almost exactly the same as the published Hele-Shaw cell results and are greater than the numerical values for the maximum pressure heads on the sloping base. These HYDRUS2D model results were then compared with various analytical solutions, and it was found that Towner’s (Water Resour Res 11:144–147, 1975) solution gave the best results for both estimation of the maximum height of the phreatic surface and the position on the slope where this occurs.     

Propagation of a flush wave in a prismatic channel

By a water flush there is generally understood an unsteady-state flow of water, arising in millraces, with the breaching (rupture) of a dam. The special characteristics of a flush wave are also possessed by a flow in a lower millrace at some distance from the dam, with the overflow of water arising in the reservoir over the crest of the dam. Usually, the necessary information on the parameters of a flush wave with its motion in natural channels is obtained by numerical solution, in a digital computer, of the equations of not fully established one-dimensional flow [1–3]. These calculations are very labor-consuming and require rather detailed information on the channel. Therefore, it is of practical importance to clarify the overall laws governing the propagation of flush waves in schematized, in particular, in prismatic channels. In some cases, on the basis of such laws, it is possible to make a preliminary diagnosis of the expected scales of the phenomenon.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–44, January–February, 1975.     

Solution and its application of transient stream/groundwater model subjected to time-dependent vertical seepage

Based on the first linearized Boussinesq equation,the analytical solution of the transient groundwater model,which is used for describing phreatic flow in a semi- infinite aquifer bounded by a linear stream and subjected to time-dependent vertical seepage,is derived out by Laplace transform and the convolution integral.According to the mathematical characteristics of the solution,different methods for estimating aquifer parameters are constructed to satisfy different hydrological conditions.Then,the equation for estimating water exchange between stream and aquifer is proposed,and a recursion equation or estimating the intensity of phreatic evaporation is also proposed.A phreatic aquifer stream system located in Hualbei Plain,Anhui Province,China,is taken as an example to demonstrate the estimation process of the methods stated herein.     

Water discharge over a dam

A solution is given for a problem of plane steady motion of a heavy ideal incompressible liquid which is partially bounded from below by two planes positioned at an angle of ±30° to the horizontal. The problem may be interpreted as water discharge over a dam in the form of a wedge with apex angle 120°. The so-called fixed-weir rockfill dams have a profile similar to the one considered here [1]. The flow discharge coefficient, which is very close to the experimental value, is calculated for the dam in question.     

Sloping Saturated–Unsaturated Flow with Outflow at Seepage Face

Analytic series solutions are constructed for the phreatic free surface problem of two-dimensional steady downslope saturated–unsaturated flow, with water exiting at a seepage face. The region in free parameter space is delineated for which the water table intersects the upper surface, and the steady state with uniform constant irrigation rate, ceases to exist. The flow solution is extended to a case of the domain being more general than a parallelogram, with the upper and lower boundaries being piecewise linear. This geometry resembles that of large-scale rainfall simulators that are designed to test slope stability of wetted soil beds.     

An Analytical Solution for Unsteady Flow in a Phreatic Aquifer in the Case of Continuous Rise

In this study, we examine the classical problem of unsteady flow in a phreatic aquifer, induced by continuous rise of the water flux and head on its boundary. A closed-form analytical solution for the governing Boussinesq equation is derived for a semi-infinite aquifer.     

A preliminary approach of dynamic identification of slender buildings by neuronal networks

The study of the dynamic behavior of slender masonry structures is usually related to the preservation of the historic heritage. This study, for bell towers and industrial masonry chimneys, is particularly relevant in areas with an important seismic hazard. The analysis of the dynamic behavior of masonry structures is particularly complex due to the multiple effects that can affect the variation of its main frequencies along the seasons of the year: temperature and humidity. Moreover, these dynamic properties also vary considerably in structures built in areas where land subsidence due to the variation of the phreatic level along the year is particularly evident: the stiffness of the soil–structure interaction also varies. This paper presents a study to evaluate the possibility of detecting the variation of groundwater level based on the readings obtained using accelerometers in different positions on the structure. To do this a general case study was considered: a 3D numerical model of a bellower. The variation of the phreatic level was evaluated between 0 and −20 m, and 81 cases studies were developed modifying the rigidity of the soil–structure interaction associated to a position of the phreatic level. To simulate the dispositions of accelerometers on a real construction, 16 points of the numerical model were selected along the structure to obtain modal displacements in two orthogonal directions. Through an adjustment by using neural networks, a good correlation has been observed between the predicted position of the water table and acceleration readings obtained from the numerical model. It is possible to conclude that with a discrete register of accelerations on the tower it is possible to predict the water table depth.     

Steady Flow from an Array of Subsurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited

Kornev’s (Subsurface irrigation, Selhozgiz, Moscow-Leningrad, 1935) subsurface irrigation with a periodic array of emitting porous pipes is analytically modeled as a steady potential Darcian flow from a line source generating a phreatic surface. The hodograph method is used. The complex potential strip is mapped onto the triangle of the inverted hodograph. An analogy with the Deemter (Theoretische en numerieke behandeling van ontwaterings-en infiltratie stromings problemen (in Dutch). Theoretical and numerical treatment of flow problems connected to drainage and irrigation. Ph.D. dissertation, Delft University of Technology, 1950) drainage problem and Kidder (J Appl Phys 27(8):867–869, 1956) free-surface flow toward an array of oil wells underlain by a “wavy” oil–water interface is drawn. For a half-period of Kornev’s flow, the “wavy” phreatic surface has an inflection point. The “waviness” of the phreatic surface is controlled by the spacing between emitters, the strength of line sources, and the pipe pressure and radius. Numerical modeling with HYDRUS involved two factors which constrained the saturated–unsaturated flow: the positive pressure head at the outlet of the modeled domain and lateral no-flow boundaries, with a qualitative corroboration of analytical solutions for potential (fully saturated) and purely unsaturated flows. HYDRUS is also applied to a generalized Philip’s regime of an unsaturated flow past a subterranean hole, which is impermeable at its top and leaks at the bottom.     

Impact of a strip of compressible liquid on a barrier

The exact solution of the plane problem of the impact of a finite liquid strip on a rigid barrier is obtained in the linearized formulation. The velocity components, the pressure and other elements of the flow are determined by means of a velocity potential that satisfies a two-dimensional wave equation. The final expressions for them are given in terms of elementary functions that clearly reflect the wave nature of the motion. The exact solution has been thoroughly analyzed in numerous particular cases. It is shown directly that in the limit the solution of the wave problem tends to the solution of the analogous problem of the impact of an incompressible strip obtained in [1]. A logarithmic singularity of the velocity parallel to the barrier in the corner of the strip is identified. A one-dimensional model of the motion, which describes the behavior of the compressible liquid in a thin layer on impact and makes it possible to obtain a simple solution averaging the exact wave solution, is proposed. Inefficient series solutions are refined and certain numerical data on the impact characteristics for a semi-infinite compressible liquid strip, previously considered in [2–4] in connection with the study of the earthquake resistance of a dam retaining water in a semi-infinite basin, are improved. The solution obtained can be used to estimate the forces involved in the collision of solids and liquids. It would appear to be useful for developing correct and reliable numerical methods of solving the nonlinear problems of fluid impact on solids often examined in the literature [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 138–145, November–December, 1990.The results were obtained by the author under the scientific supervision of B. M. Malyshev (deceased).     

Unsteady flow over a rough bottom

The unsteady motion of an ideal incompressible fluid with a free surface, developing from a state of rest, is considered. The flow is assumed to be irrotational, continuous and two-dimensional; it may be the result either of an initial disturbance of the free boundary or of a given boundary pressure distribution. The rigid boundaries of the flow region are fixed, and the free surface does not cross them at any time during the motion. The fluid is located in a uniform gravity force field and there is no surface tension. A method which in the case of localized roughness of the bottom makes it possible to find the shape of the free surface at any moment of time with predetermined accuracy is proposed. The method involves reducing the initial linear problem to a Volterra integral equation of the second kind, the kernel of this equation being a nonlocal operator. This operator has a smoothing effect, which makes it possible to reduce the solution of the initial problem to the solution of an infinite, perfect lyregular system of Volterra integral equations for a denumerable set of auxiliary functions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–119, November–December, 1989.The author is grateful to I. V. Sturova and B. E. Protopopov for useful discussions and criticism.     

Simulated annealing based algorithm for node generation in seepage analysis with meshless method

Node generation plays an important role in meshless methods for seepage analysis with a free surface. A probabilistic algorithm based on a combination of simulated annealing and the generalized probabilistic Lloyd's method, which is related to centroidal Voronoi tessellations (CVTs), is used in seepage analyses with the element-free Galerkin method (EFG). The applications in this paper involve analyzing steady seepage in a rectangular dam, a dam with an inclined slope surface, and a dam with a horizontal drain. The results show that the algorithm can easily fit and update the changeable free surface, and obtains higher-quality node sets, particularly when simulating physical domains with complex geometrical boundaries.     

Water wave radiation by a submerged rough disc

A thin circular body is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the boundary of the body. Using a perturbation method, the problem is then reformulated by a sequence of simpler hypersingular equations over a flat disc making it well suited for an efficient previously used solution method. The first order approximation is computed and the hydrodynamic force due to heaving radiation motion are presented in terms of the added mass and damping coefficients for a polynomial cap and for a rough disc, modelled by a superposition of sinusoidal surfaces defined by randomly generated parameters. The solution exhibits larger maxima associated with smaller volume of submergence of the body. A slight shift of the damping coefficient maxima to lower frequencies is noticed for the caps. Rough discs with similar statistical properties exhibit different behaviours. Thus, it is the exact specific form of the rough disc that dictates the hydrodynamic force.     

On the movement of an LNAPL lens on the water table

The penetration of light nonaqueous phase liquids (LNAPLs) in quantities that lead to an accumulation in the form of a lens above the water table is considered. First, the three-phase vertical gravity-capillary equilibrium of water, NAPL, and air above the water table is specified. The hypothesis of ‘vertical equilibrium phase distribution’ is used to derive averaged asymptotic equations describing NAPL flow as a thin lens floating above the water table. Some problems of unsteady NAPL lens movement and the development of a NAPL mound, spreading along an inclined or horizontal phreatic surface are discussed and the analytical solutions are obtained.     

地震作用下水库坝体与水体相互作用数值模拟

地震作用下水库坝体受迫振动,推动坝后水体波动,造成水体动压作用于坝体,形成坝-水耦合作用,影响坝体安全.为了评估坝体振动引起的水面波动及坝体所受动水荷载作用,建立坝体动边界条件下的不可压水体运动数学模型,模拟了地震波作用下的坝后水体波动和动力荷载.结果 表明,在忽略坝体自身弹性变形的条件下,地震作用下坝体激发的水体表面...     

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.     

Computation of two-dimensional dam-break flood flows

Sudden total collapse of a dam holding back a reservoir of water, whenever it occurs, becomes formidably impressive in the extent of destruction with which it is associated. The movement on a dry bed of a two-dimensional flood wave resulting from the break of a dam has been one of the most important and challenging subjects in rapidly varied unsteady flows from the computational point of view. An implicit time-marching finite volume numerical scheme was developed and subsequently applied for the solution of the two-dimensional unsteady open channel flow equations written in conservation form. In order to avoid the problems associated with a conventional grid system, a body-fitted non-orthogonal local co-ordinate system was utilized. The proposed numerical technique was applied to determine the stage hydrographs, water surface profiles and velocities of flood flows resulting from suddenly breached storage dams. Predictions were compared with an analytical solution, with available numerical solutions using MacCormack's two-step explicit scheme and with experimental measurements. Agreement between predictions and measurements regarding the wave front advancement and stage hydrographs is considered to be satisfactory.     

三维非稳定渗流自由面边界积分项的精确数值计算

利用固定网格法分析三维非稳定渗流问题时,将要面对两项积分难题:以自由面及单元表面为边界的空间积分及以自由面为边界的曲面积分。针对常用的任意8结点6平面三维普通单元,提出采用坐标变换及等参变换技术求取空间积分项的精确数值解;至于曲面积分项,建议改用单元非饱和区部分表面作为积分边界,经过坐标变换及等参变换处理积分边界后,利用高斯数值积分可求出曲面积分项的精确数值解。通过一个普通单元及一项均质半无限边界堤坝的实例分析,表明此方法的精确性和稳定性良好。     

Asymptotic model of the axisymmetric breakdown of a vortex filament in an incompressible fluid

The axisymmetric flow of an incompressible fluid is considered. An exact solution of the Euler equations corresponding to the breakdown of a straight vortex filament of intensity ₀ into a vortex filament of lesser intensity and a conical vortex surface is obtained. It is shown that beyond the breakdown point in the region bounded by the conical vortex surface reverse flows occur. An investigation of the problem with allowance for viscous effects at large Reynolds numbers makes it possible to establish a relation between the free parameters entering into the solution of the Euler equations. The results obtained are useful for investigating the problem of the breakdown of a swirled jet, whose solution has recently been receiving much attention [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–52, November–December, 1989.