Procedure for determination of filtration coefficient of sheet piling fences from composite profiles

. When designing structures made of sheet piles, it is often necessary to evaluate their filtration characteristics. The base material of the tongue is waterproof, however, groundwater filtration is carried out through special lock joints. The publication considers the procedure for experimental determination of the filtration coefficient of locking joints of sheet-pile fences made of polymer composite profiles based on the results of laboratory tests. Considering the mathematical model of filtration processes, it is based on a modified empirical Forchheimer dependence generalizing nonlinear filtration laws. The diagram of the test unit is given in the work. Using a specially developed method, the values of filtration coefficients at different pressure gradient values were obtained. It was found that when the sealing material is integrated into the locking joint zone, it is possible to achieve the value of the sheet-pile guard filtration coefficient of less than 10 -10 m/s. The obtained results are of interest for solving the problems of the device of anti-filtration curtains with the use of composite sheet piles.


Introduction
When designing various structures from sheet metal profiles, it is often necessary to evaluate not only the bearing capacity of the proposed system, but also its filtration characteristics.The peculiarity of the tongue-and-tongue fencing in the soil consists in the presence of special locking joints in the tongue-and-tongue elements, characterized by the length and width of the path, leading to changes in the nature of water filtration and the appearance of additional hydraulic resistances.When excavating a pit in water-saturated soils, water is filtered through locks, carrying out thin fractions of soil particles.As a result, they gradually "get stuck" in the gap between the lock elements and "self-sealing" of the fence ("colmation" effect).In some cases, forced sealing of tongue locking joints is required, for example, when arranging hydraulic structures, anti-filtration barriers in pressure water-bearing layers of soil, pit enclosures in adjacency to existing buildings, when removal of soil particles that weakens the natural base of the existing foundation is not allowed, or it is necessary to completely prevent the possibility of water ingress through the tongue enclosure.It is especially important to use pre-sealing when installing antifiltration screens around landfills of various types of waste and tailings dumps.This type of structure is subject to increased requirements for the guaranteed value of the maximum value of the filtration coefficient, shown in Table 1.Under these conditions, a special waterproofing of its locking joints is performed before the tongue is submerged.Analysis of the results of similar studies in the field of tongue-and-tongue locks sealing made it possible to establish that to ensure the expected value of the sheet-and-tongue barrier filtration coefficient of less than 1 • 10 −10 m/s, additional sealing of the butt joint is required.
Numerous experiments on water filtration in sandy soils confirm the full validity of Darcy's law (line №1 in Fig. 1).At the same time, experiments with silty-clay soils show a systematic deviation from this law (dependence № 2 in Fig. 1).In clay soils, especially dense soils, at relatively small values of the filtration head gradient may not occur.Increasing the gradient leads to a gradual, very slow development of filtration.Finally, at some hydraulic gradient values, a constant filtration mode is established.
In many cases, the initial curvilinear section and the law of laminar filtration for siltyclay soils are excluded from consideration in the form of: K -is the filtration coefficient of silty-clay soil, determined in the interval of dependence between points a and b; v -filtration rate (water flow rate through the unit area of the soil cross-section, including the cross-section area of the pore space and the soil skeleton); J 0 -is the initial head gradient, the section on axis i shown in Figure 1, cut off by the continuation of line a-b to the intersection with this axis [1].
With the effective head gradient less than the initial value, filtration practically does not occur in water-saturated soil.It can be assumed from this that a similar situation can be observed with the use of sealing materials and a small pressure gradient.
Along with an analytical description of filtration processes, modeling is used in practice, which considers the filtration process as a prototype, and a similar process as an analogue model.The analogy between the studied filtration process and its model is achieved provided that the mathematical dependencies describing these processes turn out to be mutually identical when the characteristics included in them are multiplied by certain scale factors.
The similarity between the prototype and the analogue can be established for the same physical process studied in relation to different geometry of the prototype and its model (physical modeling), or in relation to processes of different physical essence, but corresponding to the general principle of conservation of mass and energy (mathematical modeling of the filtration process) [2].
The method of using the physical model and dependencies of Darcy's law has found application in studies of filtration processes in the locking joints of steel sheet metal fences [3,4,5], the results of which are also presented in commercial review publications [6,7].

Methods
The filtration coefficient K is the filtration rate at a pressure gradient of one.By Darcy's law: Q -liquid volumetric flow rate, F -flow cross-sectional area.
The filtration coefficient may otherwise be defined as the filtration flow rate related to the cross-sectional area of the flow at a gradient of one.In hydrogeological calculations, the filtration coefficient is measured in meters per day or in centimeters per second.
Permeability is the property of rocks to pass through liquids, gases and their mixtures in the presence of a pressure drop (head).The permeability factor is the flow rate of a liquid having a viscosity of 1 MPa*s, filtered through a cross section of 1 cm2 at a pressure drop of 0,1 MPa.It is measured in darsi (1 darsi=1,02•10-8 cm2).
The permeability factor can be expressed by the formula: Q -has dimension cm3/s, μ -coefficient of dynamic viscosity of liquid, MPa*s, ∆llength of filtration path where ∆P pressure changes, cm, ∆P -pressure drop, MPa, F -has dimension cm2.
The relationship of the filtration coefficient K with the permeability coefficient C expressed by the formula: γ -volumetric weight of the liquid, N/cm3.At very low and high filtration rates, deviations from Darcy's law can be observed due to the non-Newtonian properties of the fluid.Deviations from Darcy's law may be of a different nature depending on the rheological behavior of the pure fluid [8].
An empirical dependence generalizing nonlinear filtration laws, called the two-term Forchheimer formula, has become widespread [9]: [10] discusses filtration in heterogeneous fractured-porous media.Referring to the analysis of technical documentation from deposits with fractured reservoirs, the experiments of Fencher, Lewis, Burns and Lindquist's the authors describe the movement of liquid in cracks by the nonlinear two-term Forchheimer law.
Forchheimer's filtration law is proposed to be used for the number Re (Reynolds number) of the order of units, when when a liquid moves in the winding intrapore space of a material, the inertia of a liquid cannot be neglected [8].For considerable filtration rates according to [8,16], Darcy's law is corrected by Forchheimer's bicimensional law, in which, at low Reynolds numbers, the linear term calculated with respect to particle size dominates, and the quadratic term for large Reynolds numbers.For intermediate values of Reynolds number, another term is added to the equation of Forchheimer's law in [17].
At low filtration rates, the velocity square can be neglected, and the pressure gradient will depend only on the first term, the movement will be inertial, corresponding to Darcy's law.

∆𝑃 𝐿 ⁄ = 𝜇 • 𝑣 𝐶 ⁄
Based on formula 6, we express the permeability factor: In the formula (8), the volume flow rate of the liquid Q is represented as the volume of the filtrate V of the τ passing per unit time.Expressing the filtration coefficient from formula 5 and substituting formula (8) instead of С we get: In practical application to the problem of determining the filtration coefficient of the tongue-and-tongue lock L s the thickness of the material used for sealing in the direction orthogonal to the plane of the tongue, F is the area of the sealant filtering surface.
Formula ( 9) confirms the possibility of determining the filter coefficient of the tongueand-tongue lock by an indirect parameter.The value of the liquid pressure is taken as an indirect value.
For laboratory research, a specialized installation was developed.

Fig. 2. Test installation diagram
The plant is equipped with:  a system that creates and maintains a constant pressure of the fluid acting on the lock joint sample;  constant fluid pressure control devices;  measuring device providing measurement of liquid pressure in the test bench system throughout the test time;  instruments for measuring liquid level, test time;  a sealed storage device that must collect the filtrate passed through the sample; A sample lock joint of the composite tongue is installed in the test unit.It is allowed to install the sample both vertically and horizontally.The test unit is filled with working fluid.Chemical compounds or mixtures of compounds provided by the operating conditions of the sheet pile are used as working fluid.Filtrate collection device is installed in such a way as to accumulate filtrate passed only through lock connection, excluding possibility of other liquid ingress into it.
The level of constant overpressure is increased to the required value.This operation takes up to 5 minutes to complete.Constant pressure level intervals shall have a pitch of not more than 0.1 MPa.Constant pressure is maintained by the system providing error of not more than 0.01 MPa.The temperature of the liquid in the constant overpressure system shall be 20±2ºC throughout the test.At least once in 6 hours, the volume of filtrate and the time during which this volume has accumulated are recorded.
The minimum estimated period is 24 hours.The unit interval is 300-360 minutes.If during this time the filtration coefficient determined for each unit measurement interval differs from the average value of the filtration coefficient determined for the 3rd last unit measurements by no more than 5%, then the filtration mode is considered to be steady.Also, the filtration mode is considered stable if during the evaluation period the filtrate is absent or its volume does not exceed the accuracy limit of the measuring cylinders.
After removal from the test unit, the sample is cut orthogonally to the line of the lock joint into at least 5 equal parts.The technology of this operation should exclude the possibility of changing the actual state of the lock connection.The effects capable of causing misalignment of the connected products, change in the state and actual distribution of the sealing material in the space of the lock joint should be excluded.The deviation of the length of the locking joint of each of the obtained fragments from Lm/n should not exceed 10 mm, where n is the number of fragments of the sample.After that thickness of sealing layer of lock joint and minimum distance between elements of lock joint are measured in places of sealant presence on ends of fragments of sample with accuracy of not less than 0,1 mm.

Results and discussion
In accordance with the proposed procedure, a fragment of the locking joint of the sheet metal barrier with an integrated sealing material was tested.

Conclusions
The method of using the physical model as an analogue of the filtration process allows applying the dependencies of the Darcy law obtained on the basis of the physical model to determine the filtration coefficient of the sinus joint of the full-size sheet pile fence by an indirect parameter -the one-sided pressure of the liquid ΔР on the surface of the sheet pile fence and on its connection of the groove-ridge type with known initial parameters: Ffiltration surface area; L is the thickness of the joint at the point through which the filtration occurs (or the thickness of the sealant in the direction of the tongue plane); ϒ -volumetric weight of the liquid used; V -filtrate volume, using dependence (9).
When evaluating the characteristics of the filtration processes of the prototype physical model, based on the similarity principle, the use of a filtration coefficient obtained by an indirect method will not contradict the known mathematical dependencies (in particular, Darcy's law) that are used to analytically describe the filtration processes.Thus, the method of determining the filtration coefficient by an indirect method on a physical model can be used to estimate the filtration coefficient of a prototype physical model.This work was financially supported by the Ministry of Science and Higher Education of Russian Federation (grant # 075-15-2021-686).Tests were carried out using research equipment of The Head Regional Shared Research Facilities of the Moscow State University of Civil Engineering

Fig. 1 .
Fig. 1.Dependence of filtration rate in soil on hydraulic gradient.

Table 1 .
Requirements to the filtration coefficient of anti-filtration screens.

Table 3 .
Results of evaluation of lock joint parameters after testsGuided by formula 9, we can confidently say that the value of the filtration coefficient of the tongue-and-tongue guard lock joint established according to the test results of the sample is less than 6,95 • 10 -13 m/s.