# Hydraulic Performance of Geotextile Sand Containers for Coastal Defenses

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Wave Reflection of Emerged Structures

- -
- for a regular (monochromatic) wave, the definition is ${K}_{r}={H}_{r}/{H}_{i}$, where ${K}_{r}$ is the reflection coefficient, ${H}_{r}$ is the reflected wave height and ${H}_{i}$ is the incident wave height;
- -
- for random (irregular) waves, in wave flume tests, this definition could not be applied, and the reflection coefficient is calculated as ${K}_{r}=\surd \left({E}_{r}/{E}_{i}\right)$, where ${E}_{r}$ is the reflected wave energy, and ${E}_{i}$ is the incident wave energy.

_{0}is the wavelength evaluated in deep water.

#### 2.2. Wave Transmission and Induced Piling-Up for Submerged Barriers

#### 2.3. The GSC Structural Stability

_{c}and weight W required to avoid sliding and overturning. In order to design stable bags, the shape changeability of elements during wave attack must also be considered. In [34]’s formulae, deformation coefficients are introduced to consider the changes of the areas affected by the strengths. These coefficients depend on the magnitude of the deformation, the degree of filling of the bag, the inclination of the exposed face of the structure, the wave conditions, the stiffness of the geotextile and the properties of the filling material. In particular, it is assumed that the bag is 80% filled, the deformation angle is 45° and the effective length not affected by deformation is 0.8l

_{c}. The equilibrium relationships are obtained by considering the dimensional ratios of the geotextile bags as follows: the length of the container equal to l

_{c}, the height of the container equal to l

_{c}/5 and the width of the container equal to l

_{c}/2. The weight of the container is $W=0.1{\rho}_{s}g{l}_{c}^{3}$, where g is the gravitational acceleration and ρ

_{s}the density of the sand.

_{i}/6 from the free surface; μ is the coefficient of friction between the non-woven geotextile material bags (estimated as 0.48) and $\mathsf{\Delta}=\left({\rho}_{s}-\rho \right)/\rho $ is the density of the sand relative to the water, with ρ and ρ

_{s}the densities of water and sand, respectively; C

_{D}, C

_{L}and C

_{M}are the drag, lift and inertia coefficients respectively; KS

_{CD}, KS

_{CL}and KS

_{CM}are the relative deformation factors and KS

_{R}the resistance deformation factor (see [34]).

_{CD}, KO

_{CL}, KO

_{R}and KO

_{CM}are the deformation factors (see [34]).

_{c}is given by Equations (7) and (8).

_{D}, C

_{L}and C

_{M}. The drag and lift coefficients mainly depend on the Reynolds number. The laboratory conditions should agree with the range of applicability in which the force and deformations coefficients are obtained.

^{4}–10

^{6}. The present experimental study satisfied almost all such conditions.

## 3. GSC Features and Application

## 4. Experimental Setup

^{3}, identified by the nominal weight of 5 t (once filled with sand), and the weight (or mass per unit area) of the fabric is 1500 g/m

^{2}.

_{50}= 0.6 mm, with no fine materials below 0.3 mm, and a density of ρ

_{s}= 1800 kg/m

^{3}. All the physical model here presented used 4.1 kg of sand to fill approximately 80% of the volume of each container in order to ensure that the geometric dimensions of model containers (25 × 20 × 5.5 cm

^{3}) suitable to adequately reproduce the dimensions of the prototype bag and were able to resist to two possible modes of failure (sliding and overturning) during most of the wave attacks. As reported in [37], small-scale models present some limitations on the simulation of all the engineering properties of GSC material. The material of the geotextile container was reproduced at a reduced scale, considering the ability of the model to simulate the water permeability of the prototype by using the Reynolds similitude criterion. Particular care was taken in the choice of the bag fabric for the physical model on a reduced scale, respecting the filtering capacities. In Table 1, the main properties of GSC used in the model compared to the prototype reported. The main characteristic to be reproduced for the physical modeling of the geocontainer material is the capacity of the bag (of the model) to simulate the water permeability, i.e., the so-called filtering water flow (of the prototype), due to the wave impact. Therefore, among the different hydrodynamic similarity criteria that can be adopted, the Reynolds’ one was chosen, which is governed by the general relationship between velocity, time and geometric length of the prototype and of the model, respectively, and from which the filtration rate of the fabric for the physical model can be derived. With the adopted geometric scale ratio of 1:10, the reduction of the scale for the reproduction of the filtering flow, according to the above-mentioned Reynolds similitude criterion, becomes equal to 10:1. Therefore, since the filtering capacity of the prototype fabric, with a grammage of 1500 g/m

^{2}, is approximately 17 l/(m

^{2}·s), a geotextile material with a permeability of the order of 170 l/(m

^{2}·s) was sought for the reduced scale model. The correct fabric size for this exact feature was, however, too thin and not able to adequately retain the used filling sand. The filling material was not scaled in the model to avoid that the fine parts will be removed from the container during the wave action, due to the retaining problems for thinner geotextiles and, also, to maintain similar chemical characteristics of the filling material in the prototype (no flocculation conditions, etc.). Therefore, the geotextile fabric with a weight of 100 g/m

^{2}and a permeability of 120 l/(m

^{2}·s) were adopted, which was the most suitable compromise to satisfy both the required filtering capacity and the retaining of the filling material.

#### 4.1. Test Configurations for the Adherent Revetment Structure

#### 4.2. Test Configurations for Submerged Breakwaters

_{c}= −0.032 m and a top berm width of 1.25 m), while the second configuration consisted of six overlapping layers of containers (for a submergence R

_{c}= −0.087m and a top berm width of 1.0 m). Both breakwaters had the seaside slope of 1:2 and the landside slope of 1:2.5, and they were tested with a water depth h of 0.42 m, so representing typical beach defense structures placed at a depth of 4.2 m. The vertical z-axis points upward, and the origin is placed at the still water level; hence, the seabed is placed at z = −h. The regular arrangement of the geobags is difficult to obtain in real conditions; however, the general behavior of a GSC breakwater with the same geometrical characteristics can be analyzed.

_{s}= 0.18 m and 0.20 m and peak periods T

_{p}= 3.0 s and 2.7 s, respectively. Both the two configurations with different submergences and berm widths were attacked by all the aforementioned waves.

## 5. Experimental Results

#### 5.1. Wave Reflection

_{r}is expressed as the ratio between the height of the reflected wave H

_{r}and the height of the incident wave H

_{i}(K

_{r}= H

_{r}/H

_{i}). The reflection coefficient value has been evaluated by the Least Squares Method applied to measurements from three probes [43,44]. This is a technique of separation of wave heights (incident and reflected) operating in the frequency domain that considers the simultaneous measurements of the water surface displacement at three suitable positions in which three probes are located. The analysis was performed by also considering higher harmonics.

_{r}coefficient are the wave period T, the water depth h, the wave steepness H

_{i}/L, the permeability P of the structure and the slope α of the structure.

_{r}decreases as the wave steepness increases, finding a greater dependence on the wave period than on the wave height. A more detailed analysis of the results reveals that the use of the slope of 1:2 reduces significantly the value of K

_{r}compared to the slope of 1:1, even though, in the case of a GSC structure with a slope angle of 1:2, some problems of stability emerged. In this case, due to the smaller overlapped areas among neighboring containers, the container results were more exposed with respect to the structure with a slope of 1:1, in which the container structure was more compact, with a larger overlapping area between elements of different layers.

_{r}of the GSC structure are about 50% higher than those typically obtained for rubble-mound structures with the same slope. A comparative analysis between the performance of the GSC structure with a permeable structure made by homogeneous stones, which reproduce a natural rubble-mound breakwater, was performed. The comparison was made for the case of a structure with seaside slope of 1:1 and a water depth at the toe of the structure h = 0.4 m.

^{−1}m/s. Therefore, the GSC structure can be assumed as a permeable structure due to the flow through the gaps between the overlapped layers of the sand containers; however, it presents a permeability smaller than that of a traditional natural rubble-mound breakwater.

_{r}with the surf similarity parameter, as frequently done in the literature. In Figure 10, our experimental data are also compared with different wave reflection formula from the literature. The wave reflection observed in our experiments is quite smaller than those proposed by the literature’s formula for impermeable structures. In particular, it is found that, for smaller structure slope and wavelength (smaller ${\xi}_{0}$), the experimental data better agree with the formula of [4] used for permeable structures, while larger reflection coefficient values were found with the increase of ${\xi}_{0}$. Such a result can be warranted, because wave energy dissipation occurs not only by means of the flow through a permeable structure but also by the drag force generated over the steps between different GSC layers. The surface drag force increases with the square of local velocities, which increase with an increased wave steepness and reduced period (smaller ${\xi}_{0}$). Such conditions induce larger drag forces, larger energy dissipation and therefore a reduction of available energy that generates a reflected wave. On the contrary, for larger values of ${\xi}_{0},$ the behavior of the GSC structure becomes more similar to that of impermeable structures. Indeed, we believe that, for larger values of ${\xi}_{0}$ (smaller structure slope and wave steepness or larger wave period), the GSC structure is not still able to behave like a traditional permeable structure: the data moves away from permeable line of [4]’s formula due to the decreasing of the velocities and the flow through the gaps between the overlapped layers being more difficult. Even if the two dissipation mechanisms become less significant, the macro-roughness between the steps of the stacked containers is still able to induce dissipation, which, on the contrary, is absent in an impermeable smooth slope, as well as the flow through the gaps of the layers; therefore, these are the reasons, because most of the reflection coefficient data are smaller than those predicted by the [4]’s formula for impermeable slopes.

#### 5.2. Wave Transmission of Submerged Barriers

_{t}expressed as the ratio between the height of the transmitted wave behind the breakwater and that of the incident wave (K

_{t}= H

_{t}/H

_{i}). Different wave characteristics were tested in the present study to evaluate the performance of the GSC structure.

_{c}= −0.087 m and R

_{c}= −0.032 m) is shown in Figure 11 and Figure 12.

_{c}) induces a larger and faster energy dissipation due to wave breaking. The wave height and period influence the position of the breaking point, moving it from the berm of the structure to the front slope face of the barrier.

_{c}, where a = H/2). Therefore, for the same submergence of the structure, it increases with the wave height, as shown in the left panel of Figure 11.

_{s}= 0.20 m and a peak period T

_{p}= 2.7 s is reported. Additionally, for random waves, the effect of the GSC barrier on the reduction of the incident wave height is significant.

_{c}and the incident wave height H (or H

_{s}), as usually done in the literature. The experimental results show a very good agreement with the trend of [8] obtained for low-crested rubble-mound breakwaters.

_{c}/H

_{s}, the role of the wave period is not clear, the role of the wave height and, mainly, of the submergence being more important. Most of the data are within the trend line of [8] and the lower limit of its confidence band. The results for the random waves are around the lower limit of the confidence band. Globally, GSC structures show lower transmission coefficients than rubble-mound barriers with the same submergence. Such results can be explained by the occurrence of both dissipation mechanisms: the wave breaking on the top berm or at the slope face and the impact of drag forces on the steps of the sloped shape of GSC structures. Moreover, even if the permeability of the submerged container structure is lower than a traditional breakwater, it dissipates also for the internal flow through the gaps between the layers.

#### 5.3. Piling-Up for Submerged GSC Breakwater

#### 5.4. Structural Stability Analysis of Geotextile Container Structures

_{s}is the stability number expressed as:

_{c}sinα (l

_{c}is the length of the container).

_{c}= 0.25 m, α is the front slope, which changes with the configurations (1:1, 1:1.5 and 1:2), and $\mathsf{\Delta}$ = 0.76, the dotted line indicates the beginning of the movement of the single element ${N}_{s}=2.0/\surd \xi ,$ and the red line marks the beginning of the global instability of the whole structure ${N}_{s}=2.75/\surd \xi $ (according to the studies of [33]. The red circles symbols refer to the global instability of the GSC structure, and the data in orange triangles refer to containers that move or slide, while the green squares symbols correspond to the elements that are almost stable. During each test, the containers, being deformable elements, are subjected to uplift force when wave uprush occurs, in which it is responsible for the reduced contact areas between overlapped elements. By inspecting Figure 17 a better agreement between experimental data and [33]’s results is observed for the GSC structure with slope 1:1.5 and 1:2, for which the initial movement of the elements, and the global instability corresponds, respectively, to the lower and the upper limits.

## 6. Conclusions

_{r}, such as the wave period T, the twave steepness H

_{i}/L, the water depth h, the permeability and the slope angle α. The last one is the most obvious, and certainly, it has a very strong influence. The experimental tests of [45] showed that the flow through the GSC structure is solely governed by the gaps between neighboring containers and that the flow through the sand filling in the containers can be neglected; therefore, our tested sand container structure can be assumed as a permeable structure. For what concerns the other parameters, it was found that K

_{r}increases with the increasing period and decreasing steepness. When the period becomes very long, the wave will be almost totally reflected from the breakwater when it is impermeable and largely transmitted through the breakwater when it is porous, thus giving little reflection. The response of the wave reflection to the period and steepness is consistent with energy dissipation considerations along a classical breakwater surface.

_{r}becomes comparable to that predicted by using the [4] formula for permeable structures. Such a result can be warranted, because the wave energy dissipation occurs not only by means of the flow through a permeable structure, but also by the drag force generated over the steps between different GSC layers. The surface drag is a nonconservative force that increases with the square of local velocities. Wave particles’ velocities increase with increased wave steepness and a reducing period. These changes induce larger drag forces, larger energy dissipation and, therefore, a reduction of available energy that generates a reflected wave. Conversely, a reduction in wave steepness or increase in period causes a reduction in local velocities and energy dissipation, thereby increasing reflection. Indeed, for longer waves, the reflection increases, and the GSC structure behaves more similar to an impermeable structure. Even if the experimental results data reside closer to [4] formula for impermeable structures, a residual capacity of dissipation induced by both the mechanisms still remains, indeed most of the experimental data have a smaller value of K

_{r}with respect to a smooth impermeable slope. With the Iribarren number a good parameter for the study of the reflection, a best-fit formula for the evaluation of the reflection coefficient K

_{r}for the GSC structure is proposed in the present study.

_{c}and the required weight W. The length l

_{c}should be large enough to ensure a proper overlapping, such an aspect being the most critical for the stability of GSC structures. When a steeper slope is used, the overall stability is the critical aspect, while, when a gentler slope is used, the single element is the cause of the failure due to the shorter overlapped length. The development of technology allows to make bigger geocontainers with respect to the past, overcoming some of the stability problems of GSC structures. Moreover, the technology allows to make a geocontainer in non-woven fabric with very high mechanical characteristics of toughness, strength and durability and large resistance to punching, abrasion and weathering; hence, nowadays, they are less vulnerable to vandalism or accidental acts.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Application of “Stopwave” as coastal revetments: Grottammare, Italy (

**left panel**) and Senigallia, Italy (

**right panel**).

**Figure 2.**Application of “Stopwave” as temporary groin in Senigallia, Italy (

**left panel**) or as pipeline protection (

**right panel**).

**Figure 3.**Sketch of the physical models in the wave flume of Dipartimento di Ingegneria Civile, Edile e Architteura, Università Politecnica delle Marche, Ancona (Italy): adherent revetment (

**upper panel**) and submerged breakwater (

**lower panel**).

**Figure 4.**Coastal adherent revetments of the geotextile sand container. Longitudinal views of GSCs with seaside slopes of 1:1 (

**upper panel**), 1:1.5 (

**middle panel**) and 1:2 (

**lower panel**).

**Figure 7.**Sketch and physical model of the submerged barrier with 7 layers of GSCs and a submergence R

_{c}= −0.032 m.

**Figure 8.**Sketch and physical model of the submerged barrier with 6 layers of GSCs and a submergence R

_{c}= −0.087 m.

**Figure 9.**Comparison of the experimental reflection coefficient of the GSC structure (circle red data) and rubble mound structure (blues square data) with Equation (4), proposed by Seeling and Arhens (1981) for impermeable (

**left panel**) and permeable (

**right panel**) structures.

**Figure 11.**Wave height evolution before, over and behind a submerged breakwater with R

_{c}= −0.087 m (left panel) and R

_{c}= −0.032 m (right panel) for regular waves with different wave heights H = 0.05 m–0.20 m and a wave period T = 2.0 s.

**Figure 12.**Wave height evolution before, over and behind a submerged breakwater with R

_{c}= −0.087 m (

**left panel**) and R

_{c}= −0.032 m (

**right panel**) for random waves with a significant wave height Hs = 0.20 m the peak period T

_{p}= 2.7s.

**Figure 13.**Wave transmission coefficients vs. nondimensional submergence for both regular and random waves. Trend line [8]. Regular waves with periods: T = 2.0 s (upward triangle), T = 2.5 s (diamond) and T = 3.0 s (square). Random waves with peak periods T

_{p}= 2.7 s (downward triangle) and T

_{p}= 3.0 s (circle). Submergence R

_{c}= −0.087 m (hot colors) and R

_{c}= −0.032 m (cold colors).

**Figure 14.**Piling-up behind the submerged breakwater with R

_{c}= −0.087 m (

**left panel**) and R

_{c}= −0.032 m (

**right panel**) for regular waves with different wave heights H = 0.05 m–0.020 m and a wave period T = 2.0 s.

**Figure 15.**Piling-up behind the submerged breakwater with R

_{c}= −0.087 m (

**left panel**) and R

_{c}= −0.032 m (

**right panel**) for random waves, with a significant wave height H

_{s}= 0.20 m the peak period T

_{p}= 2.7s.

**Figure 17.**Stability number ns vs. Iribarren’s parameter. Experimental data and line trends of [33]. Stable elements in green squares, sliding elements in orange triangles and global instability of the structure in red circle.

**Figure 18.**Configuration with slope 1:1. Instability of the structure in the stability test with H = 0.20 m, T = 2.0 s and h = 0.61 m.

**Figure 19.**Configuration with slope 1:1.5. Uplift and movement of some elements in the stability test with H = 0.20 m, T = 1.5 s and h = 0.40 m.

**Figure 20.**Configuration with slope 1:2. Sliding of some elements in the stability test with H = 0.20 m, T = 2.0 s and h = 0.40 m (

**left panel**) and removal of elements in the stability test with H = 0.20 m, T = 3.0 s and h = 0.40 m (

**right panel**).

Property | Model | Prototype |
---|---|---|

Tensile strenght (kN/m) | 6.7 | 85/130 |

Elongation (%) | >45 | >60 |

Permeability (L/m^{2}·s) | 120 | 17 |

Thickness (mm) | 0.6 | 8.7 |

Mass per area (g/m^{2}) | 100 | 1500 |

Opening size (mm) | 0.11 | 0.05 |

H (m) | T (s) | Slope 1:1 | Slope 1:1.5 | Slope 1:2 | |||
---|---|---|---|---|---|---|---|

h (m) | h (m) | h (m) | |||||

0.05 | 1.5 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.10 | 1.5 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.15 | 1.5 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.20 | 1.5 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.05 | 2.0 | 0.40 | 0.61 | - | - | 0.40 | 0.61 |

0.10 | 2.0 | 0.40 | 0.61 | - | - | 0.40 | 0.61 |

0.15 | 2.0 | 0.40 | 0.61 | - | - | 0.40 | - |

0.20 | 2.0 | 0.40 | 0.61 | - | - | 0.40 | - |

0.05 | 2.5 | 0.40 | 0.61 | - | - | 0.40 | 0.61 |

0.10 | 2.5 | 0.40 | 0.61 | - | - | 0.40 | 0.61 |

0.15 | 2.5 | 0.40 | 0.61 | - | - | 0.40 | 0.61 |

0.20 | 2.5 | 0.40 | 0.61 | - | - | 0.40 | 0.61 |

0.05 | 3.0 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.10 | 3.0 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.15 | 3.0 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.20 | 3.0 | 0.40 | 0.61 | 0.40 | - | 0.40 | - |

0.05 | 3.5 | 0.40 | 0.61 | - | - | 0.40 | - |

0.10 | 3.5 | 0.40 | 0.61 | - | - | 0.40 | - |

0.15 | 3.5 | 0.40 | 0.61 | - | - | 0.40 | - |

0.20 | 3.5 | 0.40 | 0.61 | - | - | 0.40 | - |

Regular Waves | 6 GSC Layers | 7 GSC Layers | ||||
---|---|---|---|---|---|---|

H (m) | T (s) | h (m) | R_{c} (m) | B (m) | R_{c} (m) | B (m) |

0.05 | 2.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.10 | 2.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.15 | 2.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.20 | 2.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.05 | 2.5 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.10 | 2.5 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.15 | 2.5 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.20 | 2.5 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.05 | 3.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.10 | 3.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.15 | 3.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.20 | 3.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

Random Waves | 6 GSC Layers | 7 GSC Layers | ||||

H_{s} (m) | T_{p} (m) | h (m) | R_{c}(m) | B(m) | R_{c}(m) | B(m) |

0.20 | 2.7 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

0.18 | 3.0 | 0.42 | −0.087 | 1.00 | −0.032 | 1.25 |

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## Share and Cite

**MDPI and ACS Style**

Corvaro, S.; Lorenzoni, C.; Mancinelli, A.; Marini, F.; Rocchi, S.
Hydraulic Performance of Geotextile Sand Containers for Coastal Defenses. *J. Mar. Sci. Eng.* **2022**, *10*, 1321.
https://doi.org/10.3390/jmse10091321

**AMA Style**

Corvaro S, Lorenzoni C, Mancinelli A, Marini F, Rocchi S.
Hydraulic Performance of Geotextile Sand Containers for Coastal Defenses. *Journal of Marine Science and Engineering*. 2022; 10(9):1321.
https://doi.org/10.3390/jmse10091321

**Chicago/Turabian Style**

Corvaro, Sara, Carlo Lorenzoni, Alessandro Mancinelli, Francesco Marini, and Stefania Rocchi.
2022. "Hydraulic Performance of Geotextile Sand Containers for Coastal Defenses" *Journal of Marine Science and Engineering* 10, no. 9: 1321.
https://doi.org/10.3390/jmse10091321