Issue 
La Houille Blanche
Number 7, Novembre 1971



Page(s)  601  616  
DOI  https://doi.org/10.1051/lhb/1971041  
Published online  23 March 2010 
Ondes phréatiques sinusoïdales
Ingénieur à la société SolExpert international
The Boussinesq equation is concerned with the elementary case of confined ground water extending indefinitely inland and directly connected either to the sea or to a sinusoïdal tidal river. It contains a reference length x0 (defined in Table 1) which is a function of diffusion coefficient (K.E./ y w for confined ground water) and tidal period, t0. The other formulae given in Tables I and II relate to the situations described by the diagrams in Table I. For ground water extending under the sea bed, there appears a coefficient a whose value, always less than unity, depends on the elastic moduli of water and the terrain. Given also is the formula for ground water extending a finite distance seaward and inland up to impermeable boundaries set at the same distance from the coastline. By changing the signs in heavy type, formulae are obtained for (a) ground water directly connected to a constantlevel inland lake and (b) ground water partially connected to the sea, in such a way that the limiting amplitude on the seaward side is equal to a times the amplitude of the tide. The above is concerned only with perfectly confined ground water. Should the ground water roof be semipermeable with a constant level or almost constantlevel reservoir above the roof (e.g. the sea, a lake or a marsh), a seepage situation arises which is characterized by the length B. In this case, use is made of a coefficient 0 (> 1) which is a function of x0/B. This coefficient 0 multiplies the reduced variables U and X when these appear in exponential or hyperbolic functions and divides them in the case of trigonometric functions. In this manner formulae are obtained for the above seepage situation, with the reserve that a must be able to be set equal to one wherever the ground water extends beneath the sea i.e. the permeable soil should be sufficiently compressible and should not contain air or gas pockets. Formulae for confined ground water directly connected to the sea may be applied to freesurface ground water provided level variations may be neglected in comparison with the mean water depth. Table III summarises formulae for ground water of infinite inland extent connected to a river whose level variation is nonsinusoidal. They may readily be adapted to ground water passing beneath the river. This arsenal of formulae is certainly not complete. However, in practice difficulties arise in the main on account of the following : (i) Sea waves and, above all, river waves are not perfectly sinusoidal. Equivalent waves may be calculated by applying the same rules for the sea or river as for the pressure levels. In particular, time lags at halftide should be used. (ii) Homogeneous soils do not exist and the evidence supplied by phreatic wave deformations is often ambiguous. For example, if there are three observation pipes set inland at increasing distances X1, X2, X3 from the coast and if the amplitude decreases more slowly between X3 and X2 than between X1 and X2, then there are two possible explanations : there could either be a permeable or partially permeable boundary close to X3. or the diffusion coefficient might be smaller (or the seepage greater) between X1 and X2 than between X2 and X3. Nevertheless, the study of ground water waves is generally of considerable interest because it is an easy way of obtaining an indication of largescale groundwater behaviour.
© Société Hydrotechnique de France, 1971