Influence of immersion depth of the sheet pile on the intensity of suffusion processes in pressure hydraulic structures

. The research examines the influence of constructive features of a pressure hydraulic structure on the intensity of suffusion processes in the tailwater. The equations of non-vortex filtration fluid motion under a hydraulic structure in the form of a sheet pile wall are calculated by the finite element method using the Neumann and Dirichlet boundary conditions. The influence of immersion depth of the sheet pile on the erosion processes in the tailwater is investigated. The possibility of protecting the pressure head structure by creating an apron in the tailwater which prevents soil suffusion is analyzed. Calculations show that the greatest pressure gradients are observed at the sheet pile tip and at the outlet to the tailwater. From the point of view of the suffusion process, the zone at the lower end of the sheet pile is not dangerous; therefore, predictions about the suffusion intensity for a particular structure should be made on the basis of the output gradients at the tailwater border. Calculations show that the constructive features of a pressure hydraulic structure have a significant impact on the processes of suffusion and pile heave. The graphs are based on the calculation results; they clearly demonstrate that the filtration rate in the structure tailwater sharply decreases with an increase in the depth of driving the sheet pile, regardless of the soil type of the structure base. Besides, an additional protective effect is provided by a structure in the apron tailwater.


Introduction
The abruptly changing pressure movement of groundwater under a hydraulic structure causes a number of negative phenomena that must be taken into account both in the design and in the operation of pressure hydraulic structures. Foremost, significant additional pressure on the structure base which must be considered in the static calculations of the structure arises during the liquid filtration movement under the dam.
Furthermore, filtration can cause significant water losses from the headwater for certain soils of the structure base.
Finally, if the velocities of the liquid filtration movement exceed the permissible values, then erosion in the structure tailwater (suffusion) is possible; as a result, there is a loss of structure stability followed by its displacement in the tailwater direction.
2 Assessment of possible soil erosion in the structure tailwater depending on the constructive features of the latter The factors influencing the intensity of the suffusion processes are investigated in the paper. In this case, the liquid pressure movement in a flat section of the structure is considered. It is known that the steady motion of groundwater is described by the following differential equations [1, 2,3,4,5]  Equation (2) was solved by the finite difference method owing to discretizing the filtration area in order to determine the pressure at the hydraulic structure base (Figures 1 -4).
The values of the pressure function H (x, y) were determined at each node of the computational grid superimposed on the filtration region. Laplace differential equation was approximated by the corresponding differences to perform calculations by the finite difference method. As a result, equation (2)  where Hm,n -value of the pressure function imposed on the grid filtration area at the considered node.
The grid dimensions are taken to be the same along the x and y axes to simplify calculations, then equation Equations (4) were compiled for each node of the calculated filtration area to compute the pressure in the filtration zone.
Two types of boundary conditions were considered in the calculations: • Dirichlet conditions, according to which the pressure value was set on the bottom line in the headwater and tailwater; • Neumann conditions, according to which the filtration area and the structure contours bounded by the design grid were considered impenetrable.

Calculation results
The analysis of the depth influence of driving the sheet pile on the suffusion processes intensity was carried out on the basis of the above calculation methodology.
Equation systems for calculating the filtration process for various structural schemes of a pressure hydraulic structure are given below. The discrete scheme and the outcomes of solving the equations corresponding system are displayed in the diagrams. Calculations are performed in the Mathcad program.

Fig. 5.
Dependence of the filtration rate in the structure tailwater on the soil plugging depth for gravel (k=3,5*10 -3 ). The asterisk shows the filtration rate value during the apron structure. Fig. 6. Dependence of the filtration rate in the structure tailwater on the soil plugging depth for medium-sized sand (k=5*10 -4) . The asterisk shows the filtration rate value during the apron structure.

Conclusion
The conducted graphs prove that the filtration rate in the structure tailwater decreases sharply with an increase in the sheet pile depth. The process nature does not depend on the soil type of the structure base.
Besides, the structure in the apron tailwater gives a supplementary essential effect. Note that a flexible asphalt concrete mat can be used as an apron, since this part of the structure does not bear significant loads. Its task is to exclude the possibility of suffusion at the sheet pile base.
The outcomes of the above calculations are best approximated by the following exponential relationships