Numerical 3D simulations of seepage and the seepage stability of the right-bank dam of the Dry Flood Control Reservoir in Racibórz

To reinforce the substrate, parts of the dam on the Racibórz Dolny reservoir were founded on gravel columns, and other parts on concrete columns (Design of JPP Consult 2015). Over the course of the reservoir’s exploitation, the presence of gravel columns will increase seepage, mainly in the vertical direction, which may have an effect on the seepage stability and the head of the groundwater table beyond the reservoir, as well as on the creation of flooding zones. This work analyses the effect of gravel columns and various lengths of the diaphragm wall on the seepage process over the course of the reservoir’s exploitation. Computations were conducted using 3D FEA for higher accuracy – differences between results of 2D and 3D modelling of seepage were discussed by Ahmed and Bazaraa 2009) or Jafari et al. (2016).

The work concerns the right-bank and frontal dam of the reservoir. This is a low dam (< 15 m), and it predominantly has a height of approximately 6–8 m, sporadically reaching up to 9 m. Two types of cross-sections are present in the analysed area according to the design (Hydroprojekt DHV Group, 2011, 2012): a dam made of loose materials with a diaphragm wall made of cohesive material, and a dam made up of local cohesive materials, utilising flood banks. The exterior dimensions of both types are identical and are as follows:

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crown elevation 197.50 m above sea level

Over a 532-metre-long segment (from km 0+000 to km 0+532), the dam has the form of a buttress of the existing railway embankment.

In the construction design, sealing of the dam’s substrate was planned in the form of a diaphragm wall made by deep soil mixing technology. This is to be found on the segments: km 2+150 to 4+500, km 4+940 to 5+210, km 6+380 to 7+490, km 7+580 to 8+300. Breaks in the diaphragm wall were designed to enable the free flow of water in periods without floods. The problem of these breaks was analysed in the simulation process.

The Racibórz Dolny reservoir is being built on the Oder River in the Śląskie voivodeship within the territory of four communes: Racibórz, Lubomia, Kornowac and Krzyżanowice, between the road bridge in Krzyżanowice, where it adjoins the Buków polder, and the frontal dam at kilometre 46+300, above the town Racibórz (about 56 thousand inhabitants). According to the design, water will only be impounded in the reservoir during a flood. Environmental costs of the reservoir were investigated for four exploitation variants by Panasiuk (2014).

The Racibórz Dolny reservoir consists of the frontal dam, along with gate-controlled spillway, the left-bank and right-bank dam along with accompanying devices, as well as operational facilities. Gravel mining areas are found within the reservoir’s basin (fig. 4). Localization of the reservoir is presented in Fig. 1, a view of the reservoir model is presented in Fig. 2.

Figure 1

Figure 2

Figure 3

Figure 4

Selected parameters of the reservoir are as follows (Hydroprojekt DHV Group, 2011, 2012):

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Top water level 195.20 m above sea level

After gravel deposits have been completely exploited, the reservoir’s volume is planned to rise to 300 million m3. Analysis of the influence of the volume of the Racibórz reservoir on flood damage for the Odra Basin was presented by Faganello & Attewill (2005).

According to the geological documentation (Mineral and Energy Economy Research Institute 2001, GEOSKOP 2014), the soils in the substrate of the right-bank dam are Quaternary (Pleistocene and Holocene) formations, below which Tertiary formations are found. In the area of the reservoir, the main water-bearing horizon is present in Quaternary sands and gravels, and it has a hydraulic connection with the Oder River. The chemical composition of groundwater was described in detail by Miotliński, Postma & Kowalczyk (2012). These soils are present throughout nearly the entire area of the right-bank dam at a depth of 0.3 ÷ 8.0 m below the ground level, and at km 1+480 and 2+280 of the dam, they are present directly under the soil layer. The overlay and underlay of the aquifer are made up of cohesive Holocene formations. Shallow suspended waters may also occur periodically in the overlay of cohesive soils. The groundwater table stabilised from 185.55 m above sea level to 191.72 m above sea level during the period from November 2013 to February 2015, and fluctuations of the GWT amount to approximately 2 m depending on the intensity and duration of precipitation and the water level in the Oder.

The following values of hydraulic conductivity were accepted for the distinguished geological layers, partially based on our own laboratory tests and on other geological engineering data as well:

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for Quaternary sands and gravels making up the main water-bearing horizon and for the body of the earth dam (Fig. 3) k = 2.2^*10-4 m/s

A 3D hydraulic model of seepage with a free or constrained water table was applied for simulations. A uniform water density distribution was accepted in the fluid continuity equation, and under this assumption, it has the form given by Strzelecki et al. (2008, 2015):

div(v→)=−ηspr∂H∂t,$$\begin{array}{} \displaystyle \ div \ (\vec v)=- {\eta}_{_{spr}}\frac{\partial H}{ \partial t}, \end{array}$$

where v⃗ is the flow rate vector, H is hydraulic head, and η_spr is the elastic storage coefficient of the aquifer. This is a small quantity, and its value fluctuates within the range of 10−<!-- - -->6÷<!-- ? -->10−<!-- - -->5[m−<!-- - -->1],$\begin{array}{} \displaystyle \ 10 ^{-6}\div 10 ^{-5}[m^{-1}], \end{array}$ and can be determined using the formula:

η<!-- ? -->spr=ρ<!-- ? -->g(β<!-- ? -->s+fβ<!-- ? -->w),$$\begin{array}{} \displaystyle \eta _{spr}=\rho g (\beta_{s}+f\beta_{w}), \end{array}$$

β_siβ_w are volumetric compressibility of the soil skeleton and water, respectively, ρ is the density of water flowing through the medium, f is the porosity of the soil medium and g is the earth’s gravitational acceleration.

After accounting for the equations of motion for the case of an isotropic medium in the form of:

vi=−<!-- - -->kH,i,$$\begin{array}{} \displaystyle \ v_{i}=-kH,_{i}, \end{array}$$

and defining the piezoconductivity coefficient as:

a=kη<!-- ? -->spr=kρ<!-- ? -->g(β<!-- ? -->s+fβ<!-- ? -->w),$$\begin{array}{} \displaystyle \ a = \frac{\ k}{ \eta }_{spr}= \frac{\ k}{\rho g(\beta_{s}+f\beta_{w})}, \end{array}$$

the continuity equation can be presented in the following form:

∇<!-- ? -->2H=−<!-- - -->1a∂<!-- ? -->H∂<!-- ? -->t.$$\begin{array}{} \displaystyle \nabla ^{2} H =-\frac{1}{a}\frac{\partial H}{\partial t}. \end{array}$$

This is the differential equation of transient seepage in a homogeneous and isotropic medium in an elastic flow regime, which has been discussed in many works, including those of Polubarinova-Kochina P. J. (1962) and Wieczysty A. (1982). This model is widely used in the example by Strzelecki (2014) for modelling of airport drainage system, also as its simplified 2D version, by Moharrami et al. (2015) for finding optimal geometry of cut off walls or Khalili Shayan & Amiri-Tokaldany (2015) for investigating the effectiveness of methods of reducing seepage and uplift pressure.

Due to the fact that the finite element mesh would number many millions of elements in a model of the entire reservoir area and that there would be large disproportions of the dam’s dimensions relative to the entire area, which could significantly affect the accuracy of numerical simulations, 3 separate numerical models of a smaller area were created to investigate the impact of the geometry of diaphragm wall on the seepage stability. It was recognised that the following models would be necessary to draw conclusions as to the role of gravel columns and the length of the diaphragm wall in the dam’s structure:

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a model containing part of the frontal dam and right-bank dam, for which no diaphragm wall, gravel columns and drainage ditch were provided for

The following assumptions were made when building the 3D seepage model:

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The geometry of the substrate for each of the three considered cases was introduced on the basis of a grid with a 3 m × 3 m mesh, which makes it possible to unambiguously define the shape of the dam.

The following boundary and initial conditions are present in the model:

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Dirichlet condition in the form of: H = H_b, defining a known hydraulic head at points on the bank with coordinates (x, y, z)

In the case of water flow through a clayey soil layer in which a condensed grid of gravel columns was placed, according to homogenization theory (Strzelecki et al. 1996, Auriault 1991), an anisotropic soil medium in terms of seepage properties was introduced, constituting the macroscopic equivalent of the actual soil medium. The representative VER element accepted by us is a cuboid prism with base dimensions of 12 m ^* 12 m and a height of 4 m. The VER accepted for simulations contains 25 gravel columns with a length of 4 m, and it has been presented in Fig. 5 along with generated finite elements. For clayey soil, a hydraulic conductivity equal to k = 10^-8m / s was accepted in simulations, and for gravel columns, k = 10^–3m / s.

Figure 5

Flow in the direction of the x axis under the action of a hydraulic head difference H equal to 12 m was accepted for calculations of the hydraulic conductivity in horizontal directions, and flow in the direction of the z axis under the action of a hydraulic head difference H equal to 4 m was accepted in the vertical direction, which gives a hydraulic gradient equal to 1 in both cases. The average value of the hydraulic conductivity was obtained after determining the flow through the water discharge surface from REV by the integration method and dividing this flow by the surface area equal to discharge (24 × 4 m for the horizontal direction and 24 × 24 m for the vertical direction). The average value of the hydraulic conductivity in the horizontal direction kxsr=2∗<!-- * -->10−<!-- - -->8ms$\begin{array}{} \displaystyle \ k _{xsr} = 2 ^{\ast} 10 ^{-8}\frac{m}{s} \end{array}$ and in the vertical direction k_xsr = üüü −<!-- - -->4ms$\begin{array}{} \displaystyle {}^{-4}\frac{m}{s} \end{array}$ was obtained. In the further part of this work, the areas in which gravel columns are present will be considered to be anisotropic.

The research conducted and discussed was intended to illustrate the following in a 3D numerical model:

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the effect of the designed diaphragm wall on the seepage process

Three separate numerical models concerning three locations of the right-bank dam were made. In the case of the part of the dam with a diaphragm wall, two cases with different diaphragm wall depths were analysed: depths of 10 m and 12.5, in order to analyse the impact of diaphragm wall length on results of numerical simulations obtained from the model.

Conducted simulations made it possible to draw the following conclusions:

Gravel columns in the clay layer have a decidedly unfavourable effect on the values of the obtained flows of water discharged on the air side, which affected the size of the flooded zones. However, considering that water pumps will be installed on the air side near the dam to pump excess water into the reservoir, such zones may not occur at all – greater pump output will be required for a shorter diaphragm wall.