# Quantification of Groundwater Hazards Related to Fluvial Floods via Groundwater Flow Modelling: A Review

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Rationale

#### 2.2. Hazardous Situations

- Flood protection structures are subjected to forces acting on their subsurface parts. In addition to earth pressure, forces caused by the groundwater underflowing the foundations must be taken into account. The most critical horizontal (F
_{h}) and vertical (F_{v}) water pressure forces are shown in Figure 2a. - An increase in the piezometric head in the confined aquifer behind the FPM may result in uplift acting on impervious fluvial topsoil (Figure 2b). Similarly, pressure due to the increase of the groundwater level (piezometric head) may affect the subsurface parts of the buildings with deep foundations (Figure 2c). Such uplift can cause ruptures in the topsoil and buildings, resulting in localized concentrated leakage, significant deformation of foundation slabs, or even global structural instability. This may also initiate waterlogging of the objects (Figure 2d).
- In cases when permeable soils crop out to the terrain, seepage may occur behind the FPM. This causes loading of soils by a pressure gradient, which may result in the internal erosion of susceptible soils (Figure 2d) in the form of external suffusion or boiling. These processes in the progression phase may often endanger the stability of the FPM.
- In case of long-term floods, in combination with the permeable aquifer, waterlogging of the area behind the FPM may occur due to seepage onto the terrain (Figure 2d).

- Damming of the groundwater level (GWL) in an aquifer behind the FPM (Figure 3a) may cause a significant permanent rise of groundwater levels, resulting in waterlogging of subsurface parts of buildings in the area.
- If groundwater resources occur behind the FPM, impervious subsurface elements may block the natural bank infiltration from a river and thus deteriorate the water source, respective to a decrease the yield of wells (Figure 3b). This may also result in a significant decrease of GWL in the protected area and cause unacceptable overloading of wells.

#### 2.3. Hazard Quantification

- piezometric head h;
- water pressure p, horizontal (F
_{h}) and vertical (F_{v}) water pressure forces acting on the surface of subsurface structures, topsoil layer, and the FPM; - pressure, or hydraulic gradient (grad p, grad h), which acts on the soil as a volumetric force and may cause its internal instability;
- waterlogging of the area is quantified by the affected area A, where water seeps onto terrain;
- seepage amount Q when dealing with pumped water from wells.

#### 2.4. Data Acquisition

## 3. Groundwater Flow Modelling

#### 3.1. Modelling Procedure and Types of Models

- The description of a real system where the area of interest is identified, and management problems and potential hazards are formulated.
- The objectives of modelling have to be carefully defined together with expected outcomes (see Section 2). This involves the analysis of both flood and non-flood situations.
- The conceptual model consists of a set of assumptions related to the geometry, shape, and boundaries of the domain, as well as aquifer materials and their properties (homogeneity, isotropy, porosity, hydraulic conductivity, compressibility, etc.). According to the expected character of the flow, the dimension and time regime (steady, transient) of the model are defined (Table 2).
- The mathematical formulation (model) is represented by a set of governing equations, plus initial and boundary conditions.
- The computer code appropriate for the problem solution has to be selected [47,48,49]. Pre- and post- processing are necessary parts of the data analysis, preparation, and presentation. To this end, engineering approaches are combined with efficient post-processing methods which enable the display of spatial and temporal data using CAD systems and thematic maps within GIS tools.
- The numerical model should be subject to calibration and verification based on data from groundwater level observations and pumping amount measurements. The calibrated and verified model may be used for the simulation of scenarios that answer posed questions and achieve defined objectives.

- one-dimensional (1D) groundwater flow model for cases where parallel seepage in a flat aquifer with small hydraulic gradients is expected (Dupuit assumption)—this model may be used for both confined and unconfined aquifers;
- two-dimensional model in the horizontal plane (2Dh) applicable for large and complex aquifers with small hydraulic gradients (Dupuit assumption)—this model may be used for both confined and unconfined aquifers;
- two-dimensional model in the vertical plane (2Dv), which can be used for parallel flow with significant variation in flow direction in the vertical plane, both for confined flow and flow with a phreatic surface;
- three-dimensional model (3D) for flow both in confined and unconfined conditions.

- preliminary analysis is carried out using a 1D model;
- complex analysis of flood propagation to the aquifer using a transient 2Dh model;
- modelling of the conditions during a non-flood period using a steady state 2Dh model;
- detailed analysis of conditions at the FPM using a steady state 2Dv model;
- if necessary, the detailed steady state 3D modelling of singularities, where no dimensional approximations exist, may be considered.

#### 3.2. One-Dimensional Model

#### 3.3. 2Dh Model of Flow in a Horizontal Plane

_{i}is aquifer transmissivity (this generally may differ in two directions; however, in practice, isotropy in the horizontal plane is acceptable). Other variables are analogical to the ones described below Equation (1).

_{x}, n

_{y}are direction cosines related to the outer normal vector to the boundary with prescribed flux q

_{p}(per unit width of the boundary). At the “no flow” boundary, Equation (5) may be applied with q

_{p}= 0. This kind of BC is applied along expected no-flow lines (perpendicular to groundwater table contours), which are usually located rather far from the area of interest.

_{0}over the flow domain at t = 0:

- Subsurface elements of the FPM may unacceptably increase the water level in the aquifer behind the FPM (Figure 3a), increase the water pressure on the floors and walls of cellars, and cause dampness of walls and even waterlogging of the terrain. The situation may be crucial in case of the infiltration of rainwater in urban areas behind the FPM.
- If riverbank infiltration supports the water supply provided by wells close to the riverbank, subsurface elements of the FPM may reduce the yield of affected water sources (Figure 3b).

#### 3.4. 2Dv Model of Flow in a Vertical Plane

_{p}= 0 holds on the phreatic surface.

_{p}and z

_{s}are the phreatic surface level and seepage face, respectively [15]. To find the free water level and seepage face, special iterative techniques may be used [47].

#### 3.5. 3D Model

_{p}= 0.

_{a}, where p

_{a}is atmospheric pressure, or p ≥ 0 if the atmospheric pressure is used as the reference pressure.

#### 3.6. Discussion of Uncertainties

- The geological composition of the area, such as the thickness of individual layers (aquifer, topsoil, etc.), which is usually derived from a limited number of boreholes or pits;
- limited understanding about overall hydrogeological and hydrological conditions, i.e., time-dependent groundwater flow regime, the direction and amount of groundwater flow, inflows and infiltration to an aquifer—the uncertainties are governed by the extent of monitoring network and frequency of readings;
- the knowledge about geological and hydrogeological properties of topsoil and aquifer soils, namely granulometry, porosity, hydraulic conductivity, and storativity, which are derived from laboratory and field testing, but in many cases only use empirical formulae supplemented by single hydraulic tests (pumping tests);
- the rate of interaction between the river and aquifer, which may be influenced by local clogging;
- boundary conditions, both at the riverside and behind the FPM, are derived from flood hydrographs which are not routinely statistically assessed in terms of their shape and flood volume;
- infiltration rates during the simulated event.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Groundwater flow during a flood. (

**A**) no flood protection, (

**B**) flood protection. Blue arrows represent water flow direction, red arrows change of water table/piezometric head.

**Figure 2.**Hazards during a flood: (

**a**) load on the foundations of the FPM, (

**b**) uplift on the topsoil layer, (

**c**) loading of the subsurface parts of civil structures behind the FPM, (

**d**) seepage onto terrain, waterlogging, internal erosion of soils due to high hydraulic gradients behind the FPM.

**Figure 3.**Hazards during a non-flood period: (

**a**) damming of the groundwater on the protected area side, (

**b**) effect on the yield of groundwater sources of subsurface parts of the FPM.

**Figure 4.**Flood wave propagation into an aquifer–piezometric head at selected distances from the Vltava river bank.

**Figure 6.**(

**a**) Maximum levels of piezometric head in a confined aquifer during a flood, (

**b**) Difference between piezometric head and terrain level (zones at risk with “-”).

**Figure 7.**(

**a**) Non-flood FPM applied; (

**b**) Complete enclosure of the aquifer with a fully penetrating cut-off wall, with measures taken to allow groundwater to flow in and out; (

**c**) Extensive partly penetrating cut-off wall.

**Figure 10.**Hydraulic gradients in a cross section of FPM (same as Figure 9). Arrows represent groundwater flow direction.

**Figure 12.**Comparison of piezometric heads on the base of a surface layer: (

**a**)—only impervious topsoil, (

**b**)—anthropogenic layer on the surface. Blue ellipse indicates detail of a levee with the descending tunnel ramp shown in Figure 13.

**Figure 13.**Detail of a levee with the descending tunnel ramp; scenario B according to Figure 12.

Period | Hazard | Potential Consequences |
---|---|---|

Flood | Temporary increased water pressure on subsurface parts of FPM | Loss of stability of FPM, flooding of protected area |

Temporary increased water pressure on aquifer topsoil behind FPM | Collapse of topsoil layer, internal erosion of subbase soil, collapse of FPM | |

Temporary rise of water table/piezometric head in protected territory, seepage behind FPM on terrain, increased hydraulic gradients below FPM | Soil instability due to seepage, internal erosion, loss of stability of FPM | |

Temporary rise of water table in protected territory | Temporary waterlogging of terrain behind FPM | |

No flood | Permanent rise of groundwater table/piezometric head, damming due to subsurface elements of FPM | Permanent waterlogging of terrain and structures behind FPM, increased pressure on underground parts of structures |

Permanent reduction of bank infiltration due to impermeable subsurface parts of FPM | Reduction of water extracted from groundwater resources, groundwater level drawdown, overloading of wells |

Problem | Type of Model | Solution Method |
---|---|---|

preliminary assessment of the propagation of a flood wave into an aquifer | 1D—transient | analytical methods for simplified boundary and initial conditions, numerical methods |

complex spatial assessment of flood wave propagation into a larger aquifer, assessment of piezometric head and pressure in the aquifer, assessment of local stability of the topsoil and structures behind FPM, delimitation of waterlogged areas | 2Dh—transient | numerical methods |

assessment of the effect of subsurface elements of FPM during non-flood periods, changes in the yield of affected water sources, piezometric head and pressure in an aquifer, assessment of the stability of structures behind FPM, hazard of waterlogging | 2Dh—steady state | numerical methods |

detailed assessment of the local conditions in the vicinity of FPM, stability of FPM and other structures for the peak flood water level scenario, assessment of non-flood scenarios | 2Dv—steady state | numerical methods |

solutions at places with complex geometrical conditions and a general flow direction, such as FPM that cross subsurface conduits, tunnels, etc. | 3D—steady state | numerical methods |

Period | Hazard | Interpretation | Figure |
---|---|---|---|

Flood | Increased water pressure on subsurface parts of FPM and structures behind FPM, detailed analysis | Map of pressure head, safety factor, cross sections with piezometric contours, pressure diagrams | Figure 2a,c, Figure 5, Figure 8 and Figure 9 |

Increased water pressure on aquifer topsoil behind FPM | Flood wave propagation diagrams, maps of piezometric head, uplift pressures, safety factor | Figure 2b, Figure 4, Figure 5, Figure 6, Figure 7a, Figure 8, Figure 12 and Figure 13 | |

Rise of piezometric head in protected area, seepage on terrain | Flood wave propagation diagrams, cross section with piezometric contours and hydraulic gradients | Figure 4, Figure 5, Figure 9 and Figure 10 | |

Temporary rise of water table in protected territory | Flood wave propagation diagrams, map of maximum piezometric head differences, map of waterlogged area | Figure 4, Figure 5 and Figure 6a | |

No flood | Rise of groundwater table/piezometric head, damming due to subsurface parts of FPM | Map of piezometric head differences and terrain, differences before and after construction of FPM | Figure 6b and Figure 7 |

Permanent reduction of bank infiltration due to impermeable/semipermeable subsurface parts of FPM | Map of differences in phreatic/piezometric surface, cross section through wells, drop in yield | Figure 3, Figure 6b, and Figure 7b,c |

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**MDPI and ACS Style**

Říha, J.; Julínek, T.; Duchan, D.
Quantification of Groundwater Hazards Related to Fluvial Floods via Groundwater Flow Modelling: A Review. *Water* **2023**, *15*, 1145.
https://doi.org/10.3390/w15061145

**AMA Style**

Říha J, Julínek T, Duchan D.
Quantification of Groundwater Hazards Related to Fluvial Floods via Groundwater Flow Modelling: A Review. *Water*. 2023; 15(6):1145.
https://doi.org/10.3390/w15061145

**Chicago/Turabian Style**

Říha, Jaromír, Tomáš Julínek, and David Duchan.
2023. "Quantification of Groundwater Hazards Related to Fluvial Floods via Groundwater Flow Modelling: A Review" *Water* 15, no. 6: 1145.
https://doi.org/10.3390/w15061145