Numerical modelling of the impact of flood wave cyclicality on the stability of levees

Sensitivity analysis applied to the flooding process is discussed in the paper. The analysis was done as part of the ISMOP project devoted to elaborating and designing a complex system for embankment monitoring and threat forecasting. The analysis was performed using selected geotechnical parameters that describe embankment state. It was shown that the sensitivity analysis method is very practical for detecting places where the largest vertical displacement and pore pressure distribution are observed. The sensitivity analysis was carried out for a single flood wave numerical experiment as well as for a double successive flood wave experiment. Comparison of the results allowed us to detect the places where the biggest differences in total relative sensitivity values are observed. Plots of these differences can help to indicate the particular places within the embankment that are the most influenced by successive flood waves and should be especially examined during field experiments as part of the ISMOP project.


Introduction
Reliable flood defence is an important issue for the maintenance of the security of any country.This is a key issue for not only lowland areas and environmental protection, but is also essential for densely populated areas with a high degree of industrialisation.A commonly used method of flood protection is river embankments.Without embankments, most countries would be regularly inundated during seasonal high water levels or other sudden weather phenomena resulting in intensive precipitation.Therefore, much attention is paid nowadays to issues related to the design, construction, and maintenance of river embankments.In addition to visual inspection and modern sensor technology, a lot of work is also carried out to update levee state assessments during high water conditions [1][2][3][4].The ISMOP project [5] is an example of such an experiment conducted currently in Poland.The main aim of the ISMOP project is to research complex systems for embankment monitoring and threat forecasting [6][7].For the purpose of this project, an experimental embankment was constructed in order to measure the impact of given flood wave scenarios on the river embankment.Considering the fact that experiments conducted during the tests cannot cover all possible scenarios for the development of flood waves, several numerical models were constructed to discover the parameters that have the most impact on flood waves.A sensitivity analysis method previously used for uncertainty analysis in a real geotechnical problem [8] was used to indicate the most significant parameters of flood waves in terms of embankment state.For each considered parameter, four sensitivity ratios are computed and can be separated into two categories: local and global.For the local category, input parameter value ‫ܮݔ‬ is varied within a small interval of a random set.In the global sensitivity ratio, the input value of a given parameter ‫ݔ‬ is varied across the whole range of a random set (fig. 1).Modified after [12].

Sensitivity analysis
Sensitivity score K SS is a more robust method of evaluating the uncertainty of a given model.It is obtained by normalising and weighting the sensitivity ratio value in an input parameter.It can be written with the following expression:

K K
The normalisation procedure makes the sensitivity score independent of the input value units of a given parameter.Sensitivity score K SS,i i= 1,2..N is calculated for all N number of basic parameters being considered.
The total relative sensitivity ߙሺ‫݅ݔ‬ሻ for each input variable is computed as a summation of all sensitivity scores (local and range) for each input parameter K SS,I on the respective results such as displacement, forces, pore pressure, or factor of safety.It can be written as (3):

Description of the geological model
Numerical calculations were performed using a numerical model of the experimental embankment built for the ISMOP project.The geometry of the assumed numerical model that is consistent with the cross-section through the experimental embankment is depicted in (fig.2).Material parameters for the assumed model are presented in the table below (Tab.1).

Figure 1 .
Figure 1.Local and range intervals and schematic representation of sensitivity calculated from sensitivity ratio.Modified after[12].

Figure 2 .
Figure 2. Geometry of the geological model assumed for the numerical calculation.

7 0703022 3 . 2 Figure 3 .
Figure 3. Parameters of flood wave: ascent (a), high plateau (b), descent (c), low plateau (d) and height of water (e).During the sensitivity analysis, two types of flood process were examined: a single flood wave, and IORRG ZDYHV FRPSULVLQJ WZR VXFFHVVLYH IORRG ZDYHV Two intervals of parameters were determined independently.The first set was determined by analysis of historical floods in Poland in the basin of the Vistula River where the experimental embankment was built [18].The second was assumed according to the ISMOP project documentation that applied certain limited values to the rate of water level changes and the height of water level (experimental knowledge).3DUDPHWHUV RI IORRG ZDYH ZDWHU regarded as basic variables DUH VXPPDULVHG LQ WDEOH 7KH UHIHUHQFH YDOXH RI HDFK IORRG ZDYH SDUDPHWHU ZDV DVVXPHG DV D PHDQ RI WKH YDOXHV RI WZR DVVXPHG LQWHUYDOV ([SHULPHQWDO LQYHVWLJDWLRQ ([SHUW NQRZOHGJH PLQ PD[ PLQ PD[ DVFHQW >K@ high plateau>K@ GHVFHQW >K@ low plateau >K@ ZDWHU KHLJKW >P@

4 . 1 Figure 4 .Figure 5 .
Figure 4. Sensitivity score values of flood wave parameters for the pore pressure distribution.

Figure 8 .
Figure 8. Sensitivity score values of double flood wave parameters for vertical displacement distribution.