Following the accident at the Fukushima nuclear power plant, high concentrations of radiation seepage into the ocean through radionuclide transfer via groundwater has been observed. In order to prevent further radionuclide permeation into the groundwater, it was decided to delimit the area around the turbines and reactors with an ice wall several meters deep. This purpose of the wall is to restrict the influx of the groundwater into the radioactive zone, as well as the escape of groundwater from the same zone, inevitably contaminated with radionuclides. To this end, vertical cooling devices shall be situated around the perimeter of the nuclear power plant, as demonstrated in the figure below.
Plan of cooling device arrangement around the perimeter of the Fukushima power plant
Geological investigations of the area made it possible to determine the physicochemical properties of the ground and the speed of the groundwater displacement (see the section below).
Geological section of the ground near the Fukushima
Waterproof rock layer is marked green.
Landfill, where the movement of groundwater takes place, is marked yellow.
R/B and T/B are reactor and turbine buildings respectively.
Water flows are marked by blue arrows.
Computer simulation of the artificial ground freezing in the specified area with the Frost 3D specialized software can be employed to test the proposed design solutions and confirm or reject their viability on the basis of the derived data.
For computer simulation on the basis of the geometric dimensions of the considered domain and geological and lithological structure of the grounds, the following dimensions for the computational domain were introduced: length — 450 m, width — 210 m, height – 30 m.
The geological and lithological structure of the ground in the considered domain was reproduced on the basis of the information obtained from the test boreholes.
When creating the 3D geometric model, the foundations and footings of the reactors and turbines were taken into account.
The footings of the reactors and turbines are found at a depth of approximately 10 m and their temperature is assumed to correspond to the temperature inside the building for thermal analysis purposes.
The layout of reactor and turbine foundations and footings in the Frost 3D software
According to the preliminary estimates, about 30 km of vertical cooling devices, each being 30 m in length, is necessary for the ground freezing requirements of this project. With a distance of 1 m between each device, a total of 1,073 devices will need to be installed around the perimeter of the nuclear power plant. To power the cooling, 14 cooling units with a capacity of 400 kW each are required.
A 3D geometric model of the Fukushima nuclear power plant was hence created in the Frost 3D software package on the basis of the geological and lithological structure of grounds, the arrangement of foundations and basements of the reactors, turbines and other constructions, as well as the arrangement of vertical cooling devices (see the figures below).
3D model of the ground and cooling devices in Frost 3D
Frost 3D: 3D geometric model of the infrastructure elements of the Fukushima nuclear power plant
When conducting thermal analysis, following thermophysical properties of grounds were applied:
Table 1 – Thermophysical properties of the terrain around the Fukushima nuclear power plant
Thermal conductivity of ground in thawed state, [W/m*К] 
Thermal conductivity of ground in frozen state,
[W/m*К]

Heat capacity of ground in thawed state,
[MJ/m^{3}*К]

Heat capacity of ground in frozen state,
[MJ/m^{3}*К]


Landfill 
2.20 
3.40 
2.78 
2.03 
Rock 
2.00 
2.16 
2.40 
1.95 
Geological survey data demonstrates that filtration in the landfill layer is about 0.1 m/day, while filtration in the rock layer is somewhat lower.
The change of temperature over time was specified on the surface of the computational domain. Here we used the average maximum temperature to simulate the worst possible climatic scenario for ground freezing.
Specifying temperature on time dependence in Frost 3D
A zero heat flux was specified on the lower and side boundaries of the computational domain. The boundaries of the simulation area are situated far enough from the area of interest so as not to interfere with the computation of heat processes for the considered period of time.
In simulating the thermal fields, the 3D geometry of simulated area was discretized with a hexahedral mesh containing 17,828,087 nodes.
Hexahedral computational mesh created with Frost 3D
The simulation period consisted of 2 years, starting from Sept 1, 2014.
The time taken by the Frost 3D software package to perform the entire computation was 3 hours on a PC with an Intel Core i7 3770 CPU (running at 3.4 GHz and with 16 GB RAM), and less than 6 minutes with an Nvidia Tesla K20c.
Below are the results of the simulation of the temperature distribution in the considered area for various moments in time.
Dec 1, 2014 – Temperature distribution after 3 months of cooling device operation
Sept 01, 2016 – Temperature distribution after 2 years of cooling device operation
For a more detailed visualization of the simulation results, we considered the temperature distribution in a restricted section of the simulated area, marked by a red rectangle in the figure below.
Area of the computational domain (in red) for further analysis of thermal fields and unfrozen water distribution
Sept 2, 2014 – Temperature distribution after 1 day of cooling device operation
Dec 10, 2014 – Temperature distribution after 2 months of cooling device operation
The freezing front is more clearly visible when considering the distribution of the quantity of frozen water in the ground pores.
Frozen water distribution in the sections after half a year demonstrates complete ground freezing in the vicinity of the cooling devices.
Beyond this time, further operation of the cooling devices in maximum power mode is no longer necessary, and the cooling elements can be switched to temperature maintenance mode.
Moreover, the distributions shown below of the quantity of frozen water after half a year of operation demonstrate that further cooling will not significantly influence the growth of the freezing front:
Aug 31, 2016 – Temperature distribution after 2 years of cooling device operation
In conclusion, modern computer technologies render prediction of temperature distributions and the unfrozen moisture content around the Fukushima nuclear power plant feasible. This provides a crucial opportunity to verify the adequacy of the design solutions for the construction of an ice wall around the perimeter of the Fukushima nuclear power plant.