# Effect of Animal Burrows on the Vulnerability of Levees to Concentrated Erosion

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simplified 2D Mechanism for the Stability of the Landside Slope near a Cavity

^{−8}, 10

^{−9}m/s, or even lower.

_{h}from the outer surface (Figure 3). This cavity is in communication with the river, thus, the internal pressure increases with the hydraulic level ($p={\gamma}_{w}H$, where H ≈ water level above the cavity, ${\gamma}_{w}$ = water unit weight), but no additional assumptions on the size and path of the tunnel are added. The hydraulic level H depends on the altimetric position of the cavity with respect to the increasing level of the river during a flood event. Soil shear strength is idealized by the Mohr–Coulomb failure criterion, and the parameters are friction angle ϕ and cohesion c.

_{h}, the expressions used for W and U are not valid, while for large values of L

_{h}, a circular failure of the slope is more likely to develop, as discussed in [5].

_{lim}which is considered the reference solution. The slope inclination influences the failure mechanism, indeed for small values of $\beta $, the minimum value of hydraulic head is obtained for $\theta <0$, and the opposite is observed for steeper slopes.

_{lim}is provided in the Supplementary Materials.

_{h}for different parameters. H

_{lim}always increases with L

_{h}, which means that this mechanism is unlikely for deep cavities. Cohesion c is the strength parameter that modifies H

_{lim}the most; indeed, small values of c significantly increase H

_{lim}for the same value of L

_{h}(Figure 5a). In contrast, the friction angle has a limited impact (Figure 5b). The evaluation of soil shear strength parameters, especially cohesion, is not trivial because the superficial soil layer can be damaged by anthropic and natural factors during the service life of the levee. When increasing β, higher H

_{lim}is obtained for the same L

_{h}(Figure 5c). This is due to geometrical effects, in fact, for a constant L

_{h}, the average depth of the sliding surface, as well as the length L′, increases, thus increasing the resistant forces. Cavities of a larger size drastically reduce the limit hydraulic head (Figure 5d): an increase of D by less than 10 cm can reduce H

_{lim}by more than 50 cm.

## 3. Bi-Dimensional Finite Element Analyses of the Stability of Landside Slope

_{lim}).

^{3}. These strength parameters are typical of sand–silt mixtures [16]. These materials often characterize the levee of the Po Plane in Italy; in particular, they are representative values of the case study of the Panaro river levee breach analyzed in Section 5 [17]. The cavity was assumed to be circular with a diameter D = 0.25 m and it was located at a variable distance L

_{h}(0.75 m–1.00 m–1.25 m–1.50 m) from the outer surface, which was inclined at an angle β = 30°. Model geometry, discretization, and boundary conditions are shown in Figure 6.

_{lim}was obtained.

_{h}. FEM provided slightly larger H

_{lim}compared to that of the simplified method.

_{LEM}) and with a continuous black line for FEM analyses (L

_{FEM}). The shape of the moving soil mass and the inclination of the sliding planes of the two different approaches were similar for small values of L

_{h}(Figure 7a). As the horizontal distance increased, the inclination of the sliding plane assumed an opposite rotation with respect to the horizontal, but the angle θ remained very small.

## 4. Three-Dimensional Finite Element Analyses of the Stability of Landside Slope

_{h}(0.75 m–1.00 m–1.25 m–1.50 m) from the outer surface, which was inclined at an angle β = 30°. Model geometry, discretization, and boundary conditions are shown in Figure 8. Loads and calculation phases were similar to the 2D case described in the previous section.

_{lim}was also greater for the spherical cavity than for the cylindrical one.

_{h}= 0.75 m model. The failure kinematics of the 3D FEM analyses were similar to those of the 2D simplified mechanism reported in Figure 7, thus validating the assumptions.

## 5. Documented Cases Possibly Attributable to This Mechanism

^{3}, a cavity diameter D = 0.3 m, and a possible position of the cavity at L

_{h}= 0.5 m, β = 33.7°, Equation (1) provides H

_{lim}= 0.46 m, which is in very good agreement with field observations.

^{3}, c = 3 kPa, ϕ = 31°, β = 35°, Equation (1) provides H

_{lim}= 1.6 m for L

_{h}= 0.7 m. This supports the hypothesis that a cavity, invisible from the surface, could have been the cause of failure.

## 6. Discussion

_{lim}. Three-dimensional FEM analyses confirmed the essential features of the phenomenon but provided higher resistances. This means that the results obtained with Equation (1) were conservative, which is comforting considering that reconstructing the accurate volumetric shape of a buried cavity is extremely difficult or even impossible.

## 7. Conclusions

_{lim}was mostly influenced by material cohesion, the diameter of the cavity, and distance from the surface. Soil friction angle and slope inclination had a minor effect. The shape of the unstable soil wedge assumed in the simplified LEM approach was confirmed by the results of 2D and 3D FEM analyses.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**D**is the stiffness matrix.

**B**is the strain-displacement matrix (contains the derivatives of the shape functions), and $\delta \tilde{\mathit{u}}$ is the nodal virtual displacement.

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**Figure 1.**Effect of animal burrows: (

**a**) structural weakening, (

**b**) altering pressure distribution, (

**c**) favoring piping, (

**d**) starting concentrated erosion.

**Figure 2.**(

**a**) Typical burrows produced by crayfish Procambarus clarkii on irrigation ditches (adapted from [4]); (

**b**) concentrated erosion though a mammal burrow in Panaro levee near Modena (Italy) (adapted from [5]. WILEY 2005); (

**c**) mammal burrow found on the land side of the Panaro levee near Modena (Italy).

**Figure 4.**Limit hydraulic head as function of inclination of failure surface; stars indicate the minimum point (D = 0.25 m, γ = 18 kN/m

^{3}, c = 3 kPa, ϕ = 31°, L

_{h}= 1 m).

**Figure 5.**Limit hydraulic level as function of L

_{h}(if not otherwise specified D = 0.25 m, γ = 18 kN/m

^{3}, c = 3 kPa, ϕ = 31°, β = 30°): (

**a**) effect of cohesion, (

**b**) effect of friction angle, (

**c**) effect of slope inclination, and (

**d**) effect of the cavity diameter.

**Figure 6.**(

**a**) Discretization and boundary conditions of the numerical global model; (

**b**) enlargement of the area around the cavity and definition of the problem characteristics.

**Figure 7.**Comparison between FEM and LEM failure kinematics for different values of L

_{h}: (

**a**) L

_{h}= 0.75 m, (

**b**) L

_{h}= 1.00 m, (

**c**) L

_{h}= 1.25 m, (

**d**) L

_{h}= 1.50 m (D = 0.25 m, γ = 18 kN/m

^{3}, c = 3 kPa, ϕ = 31°, β = 30°).

**Figure 8.**(

**a**) Discretization and boundary conditions of the numerical 3D global model; (

**b**) representation of the cylindric tunnel portion into the embankment; (

**c**) representation of the spherical den into the embankment.

**Figure 9.**Three-dimensional FEM failure kinematics: (

**a**) 3D representation of the soil mass expelled by the static load applied inside the spherical cavity; (

**b**) cross section of the failure mechanism associated with the spherical cavity geometry; (

**c**) 3D representation of the soil mass expelled by the static load applied inside the cylindrical cavity; (

**d**) cross section of the failure mechanism associated with the cylindrical cavity geometry.

L_{h} [m] | H_{lim-LEM} [m] | θ_{LEM} [°] | H_{lim-FEM} [m] | θ_{FEM} [°] |
---|---|---|---|---|

0.75 | 1.60 | −6.8 | 1.75 | −6 |

1 | 2.45 | −5.2 | 2.75 | +4 |

1.25 | 3.50 | −3.6 | 3.75 | +5 |

1.5 | 4.69 | −2.3 | 4.74 | +6 |

**Table 2.**Comparison between 3D FEM limit hydraulic level for different values of L

_{h}and the den’s geometry.

L_{h} [m] | H_{lim-FEM 3D Sphere} [m] | H_{lim-FEM 3D Cylinder} [m] |
---|---|---|

0.75 | 12.01 | 3.55 |

1 | 16.29 | 5.57 |

1.25 | 22.75 | 7.26 |

1.5 | 23.50 | 9.77 |

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**MDPI and ACS Style**

Ceccato, F.; Malvestio, S.; Simonini, P.
Effect of Animal Burrows on the Vulnerability of Levees to Concentrated Erosion. *Water* **2022**, *14*, 2777.
https://doi.org/10.3390/w14182777

**AMA Style**

Ceccato F, Malvestio S, Simonini P.
Effect of Animal Burrows on the Vulnerability of Levees to Concentrated Erosion. *Water*. 2022; 14(18):2777.
https://doi.org/10.3390/w14182777

**Chicago/Turabian Style**

Ceccato, Francesca, Stefano Malvestio, and Paolo Simonini.
2022. "Effect of Animal Burrows on the Vulnerability of Levees to Concentrated Erosion" *Water* 14, no. 18: 2777.
https://doi.org/10.3390/w14182777