Numerical modelling of levee stability based on coupled mechanical , thermal and hydrogeological processes

The numerical modelling of coupled mechanical, thermal and hydrogeological processes for a soil levee is presented in the paper. The modelling was performed for a real levee that was built in Poland as a part of the ISMOP project. Only four parameters were changed to build different flood waves: the water level, period of water increase, period of water decrease, and period of low water level after the experiment. Results of numerical modelling shows that it is possible and advisable to calculate simultaneously changes of thermal and hydro-mechanical fields. The presented results show that it is also possible to use thermal sensors in place of more expensive pore pressure sensors, with some limitations. The results of stability analysis show that the levee is less stable when the water level decreases, after which factor of safety decreases significantly. For all flooding wave parameters described in the paper, the levee is very stable and factor of safety variations for any particular stage were not very large.


Introduction
Levees are a popular method for protecting areas against floods.There are over 8,000 km of levees along the main rivers in Poland [1].The prevalence of this type of geotechnical structure makes levee monitoring a priority.Weak levees are dangerous for civil properties because they give a false impression of safety.
Nowadays, many people are looking for a universal and effective method for monitoring levee stability or predicting the time and place of their failure ([2-3]).Many projects (i.e.[4-5]) tried using thermal measurements (i.e. by using the properties of optical fibres to measure levee temperature) or other types of measurements to estimate fluid flow in levees.The aim of the ISMOP project (taken from the Polish title: Computer System for Monitoring River Embankments) is to create a complex threat forecasting system based on temperature and pore pressure sensors.To achieve this goal, an artificial full-size levee was constructed from materials commonly used for their construction.
Real measurements were preceded by numerical modelling for the mechanical, hydromechanical and thermal processes that occur during water level changes inside a water reservoir.In this paper, results of numerical modelling of the interactions between mechanical, hydromechanical and thermal processes are presented.These coupled numerical modellings were carried out in order to examine the influence of the flood wave process on the value of basic parameters that describe the state of the embankment.

Mathematical background
The numerical code FLAC can be used to solve thermal-groundwater-mechanical problems [7].All equations used in the FLAC code are described in the manual [7].Some are listed below.Thermal-groundwater coupling.

Groundwater-mechanical coupling
Heat transport in FLAC is described by Fourier ¶V law (4) where is the effective thermal conductivity defined in terms of the fluid and solid conductivities by the equation .
(5) Heat is transferred in porous media by two processes in the FLAC implementation.There is forced convection when the heat is carried by fluid motion and free convection when fluid motion is caused by density differences due to temperature variations.
The energy balance equation used in FLAC for convective-diffusive heat transport is shown below.(6) where T is temperature, is thermal flux, is fluid specific discharge, is volumetric heat source intensity, is a reference density of the fluid, is a specific heat of the fluid and is the effective specific heat which is defined as .(7) In the equation above and are solid matrix bulk density and bulk specific heat, respectively, n is porosity and S is saturation.The duration of the first stage (increasing water level) had almost no effect on the FoS value after the end of the experiment (varies from 3.181 to 3.193).The biggest difference for the final FoS value was observed for high water level (varies from 3.14 to 3.25) and low water level (from 3.09 to 3.26).The long low water level duration causes levee stability to be closer to the state before the experiment.

7 0703021 Figure 1 .Figure 2 .
Figure 1.Model of geology medium with levee Fluid transport is described by Darcy ¶V law(1) where k is fluid mobility coefficient (or ³SHUPHDELOLW\´ LQ FLAC terminology), is the fluid density and g is gravity.Fluid density in this equation is related to temperature changes as follows(2) where is the reference temperature and is the volumetric thermal expansion of the fluid.The relation of permeability k to hydraulic conductivity is .(3)Threeforces act on the solid matrix when fluid flows through a porous medium: solid weight, buoyancy, and drag or seepage force.All these forces are taken into account in the FLAC formulation.

Figure 6 .Figure 7 .Figure 8 .
Figure 6.Pore pressure [kPa] modelled for points A-D for a model with average wave parameters and water level [m]

Table 3 .
Factor of Safety for different wave shapes.Time of wave stages are presented in table 2. The value of FoS is presented in order from the shortest to the longest wave stage time of each stage.FLOODrisk 2016 -3 rd European Conference on Flood Risk Management