Extensive flooding can be the result of levee system failures most frequently caused by the piping process due to seepage. The proper description of the seepage line is affected by the difficulty of estimating the hydraulic parameters, mainly the soil hydraulic conductivity. Therefore, the development of simple methods for a quick analysis of extended levee systems is fundamental to identify critical points. In this context, a practical procedure, recently proposed, based on a simple vulnerability index is here enhanced and used to derive diagrams easily applicable for seepage vulnerability estimate, taking the hydraulic parameters’ uncertainty into account. The procedure is applied for the Tiber River, in central Italy, and the Tanaro River, in northern Italy, by analyzing 67 and 6 levees, respectively. The results show that the method provides the highest seepage probabilities for levees affected by failures in the past. Therefore, the procedure seems to be able to identify the levees that require detailed investigations. Finally, the Italian levee database (DANTE) is presented as a dynamic geospatial tool for collecting all the available data/information on levee systems to usefully support authorities with the charge of hydraulic risk mitigation for identifying the most vulnerable levees.

INTRODUCTION

A properly designed and constructed levee system can often be an effective structural measure for repelling floodwaters and to provide barriers against inundation to protect urbanized and industrial areas. However, the delineation of flood-prone areas and the related hydraulic hazard mapping taking account of uncertainty are usually developed with scarce consideration of the possible occurrence of a levee breach along river channels. The study of critical flood wave routing is typically carried out by assuming that the levee system remains undamaged during the passage of flood because it is designed not to fail. However, flooding is often the result of levee failures and, hence, the vulnerability of levee systems needs to be properly investigated. Different countries worldwide already use levee risk assessment methods developed in the context of research activities addressed to understanding and predicting failure modes (e.g., in the USA, UK, and the Netherlands).

The levee failures can be caused by several factors (ASCE 2011; ICOLD 2013): (1) overtopping, (2) scouring of the foundation, (3) seepage/piping of levee body/foundation, and (4) sliding of the foundation. The piping caused by seepage is one of the most dominant failure mechanisms (Cheng 1993; Colleselli 1997; USACE 1999), influenced by the levee's geometrical configuration, hydraulic conditions, and material properties (e.g., permeability, cohesion, porosity).

The levee failure caused by internal soil erosion occurs when soil particles are carried away by the hydrodynamic forces of the flowing water. The potential failure modes depend on the location of the internal erosion pathway, e.g., through the levee body, the foundation, from the embankment into the foundation, etc. (ICOLD 2013; Zhang et al. 2016) and on the specific internal erosion mechanism, e.g., backward erosion piping, internal migration, scour or internal instability (ICODS 2015). Most of the studies treating the issue of piping (Bligh 1910; Lane 1935; Sellmeijer & Koenders 1991, to cite a few) have stated that the parameters which play a role in this mechanism are the hydraulic head, H, the seepage line, L, and the configuration and material composition of the potential erosion layer. The stability was identified through a coefficient considered for design purposes and which represents the critical piping gradient, Hc/L, with Hc the critical head. The information used about the material composition and the configuration of the sand layer characterizes the different methods. If classical empirical approaches are used (Bligh 1910; Lane 1935), a qualitative indication of the material composition is required, while using more advanced approaches (Sellmeijer & Koenders 1991; Nagy & Toth 2005; Van Beek et al. 2011; Rice & Polanco 2012; Mazzoleni et al. 2014a) information regarding variables, such as permeability, grain distribution, and thickness of soil layer are required. The piping process might also occur for levees that are not in direct interaction with rivers as, e.g., transportation embankments (Polemio & Lollino 2011). Recently, agencies responsible for the maintenance of levees acknowledged the role of animal and rodent burrows in adversely impacting the structural integrity of levees (Orlandini et al. 2015). In this context, the importance to understand the hydraulic behavior of levees during a flood is of paramount importance and often it is addressed through numerical simulation models (Zumr & Císlerová 2010), the applicability of which may be limited by scarce knowledge of the levee hydraulic properties of soil. Moreover, a combined research based on experiments and conceptual model has been carried out and relevant results are found in the scientific literature, providing more insight on the influence of the dominant material parameters of the piping process (Sellmeijer et al. 2011; Van Beek et al. 2011).

In this context, developing operational procedures enabling the most vulnerable levees to be identified, even when the hydraulic parameters characterizing the seepage within the body and foundation are not known or partially known, is fundamental (Take & Bolton 2003; Camici et al. 2015).

On this basis, it is of considerable interest to do the following:

  • Develop simple and practical procedures for assessing levee vulnerability to seepage, in order to investigate quickly the extended levee systems (Mazzoleni et al. 2014a). For this purpose, fragility curves (Vorogushyn et al. 2009, 2010) might be used in order to identify the most critical points in the levee system where detailed investigations should be performed and from which potential flood-prone areas can be assessed (Aureli & Mignosa 2004; Di Baldassarre et al. 2009).

  • Implement and make an operational, structured, and continuously updated levee database, to be used as an integrated tool of a decision support system, where a searchable inventory of information is available as a key resource supporting decisions and actions affecting levee safety. Under this umbrella, likewise Vorogushyn et al. (2009), but giving solely evidence to the seepage matter Camici et al. (2015), proposed a practical procedure for levee vulnerability to seepage based on a simple vulnerability index, which is assessed according to hydraulic and geometric characteristics of the levee and taking into account uncertainty in the hydraulic parameters.

In this context, the procedure developed by Camici et al. (2015) is here extended and used to derive fragility curves from which a refined seepage vulnerability index is identified considering the case of dimensionless levees. It is worth noting that the vulnerability is defined as the condition occurring when the seepage line in the embankment intercepts the landside of the levee during the passage of a flood. The proposed approach brings into play not only geometric characteristics, but also the uncertainty linked to the hydraulic soil parameters of embankment, as permeability and porosity, and other quantities, like flood duration and groundwater capacity, all embedded into a single parameter. Moreover, the method focuses on the seepage through the levee body and aims to identify the probability of occurrence of a critical condition, necessary but not sufficient, that would allow the soil particles’ erosion through the levee embankment and potentially lead to the extreme consequence, that is, the levee piping and the resulting longitudinal structure collapse.

The analysis is of interest for decision-makers to easily estimate the seepage probability of levees of which only the geometry is known. The procedure is embedded in the Italian earthen levee database (Database nazionale ArgiNature in TErra, DANTE) addressed at civil protection purposes. Indeed, DANTE aims to collect comprehensive information on national levees and historical breach failures to be exploited in the framework of operational management and monitoring of levees that form the basis to initialize the seepage vulnerability procedure. Two embanked rivers in Italy are used to show the potential of seepage vulnerability methodology also in the framework of the DANTE database.

LEEVE VULNERABILITY TO SEEPAGE

The internal erosion of embankments occurs when soil particles are carried away, typically in suspension, by the hydrodynamic forces of the flowing water in the levee body or foundation. Internal erosion potential failure modes can be grouped in different categories related to the physical location of the erosion pathway: through the levee body, through the foundation, from the embankment into the foundation, along the embankment–foundation contact, along or into embedded structures such as conduits or spillway walls (ICOLD 2013; Zhang et al. 2016). Moreover, various specific internal erosion mechanisms can occur: backward erosion piping, internal migration (stoping), scour, internal instability (suffusion and suffosion) (for more details see http://www.usbr.gov/ssle/damsafety/risk/BestPractices/Chapters/IV-4-20150617.pdf).

The description of the seepage flows within the levee body is significantly affected by the uncertainty in the soil parameters’ estimate, such as the particle size distribution and the soil porosity and hydraulic conductivity (Vorogushyn et al. 2009). To overcome this issue, fragility curves taking the soil hydraulic parameters’ uncertainty into account would allow the effective estimation of the probability that the seepage line in the levee body intercepts the landside, and as a consequence, to identify the vulnerability to seepage. Under this logical framework, an expeditious procedure, based on a simple vulnerability index, is proposed and described herein.

Vulnerability index and fragility curves

Let us consider a levee with known geometry by using the quantities L= foot levee, H= saturation depth of infiltration line along the horizontal distance, x, and Hs= levee depth (see Figure 1).
Figure 1

Vulnerability index to seepage for a levee with known geometry (for symbols see text).

Figure 1

Vulnerability index to seepage for a levee with known geometry (for symbols see text).

To assess the length of the seepage pathway, many solutions of the classical ‘heat equation’ may be used (Pavlovsky 1960; Marchi 1961; Supino 1965; Ahmad et al. 1993; Chahar 2004, to cite a few).

In this study, the solution proposed by Marchi (1961) is applied considering, however, the distinction between embankment and foundation soil: 
formula
1
where h0= hydraulic head in the river above the water table = (h0 + a), with h0= maximum water level in the main river channel above river bed, a= distance between the groundwater level and the river bed. Moreover, ξ is the soil porosity, Ks and K′s are the soil hydraulic conductivity of the levee body and foundation, respectively, H0 is the water table below the levee, D is the duration of flood and erf represents the error function, i.e., twice the integral of the Gaussian distribution with zero mean and variance equal to 0.5. Focusing on the seepage within the levee body solely, the first term of the right-hand side of Equation (1) is solved to identify the distance at which the seepage line intercepts the ground level (h= 0), i.e., the maximum length of the seepage line, xmax (Figure 1). If the saturation line is embedded in the embankment, the line does not intercept the levee landside, therefore the seepage is assumed avoided. In this context, Equation (1) is rewritten for a dimensionless levee and where the parameter a is assumed equal to zero (H=h, see Figure 1), yielding: 
formula
2
with x* = x/L and h* = H/Hs and the quantity δ is defined as: 
formula
3
Equation (2) involves parameters such as Ks and δ that cannot be easily determined by simple monitoring.

The dimensionless maximum length of the seepage line, = xmax/L, is then identified by imposing h* = 0 in Equation (2). The location of the seepage line is fundamental because it allows identification of the condition, necessary but not sufficient, for which the process may produce erosion up to the extreme consequence, that is the levee piping and the inevitable collapse. If the saturation line is embedded in the embankment, then the piping is surmised avoided, otherwise the seepage condition within the levee body would enable the piping (internal erosion).

In this context, the limit state function, Z, for the occurrence of piping is related to the length (1 +x′*) versus the maximum seepage length () along the foot levee itself. Specifically, for the dimensionless levee the simple function is (see Figure 1 for symbols): 
formula
4
where x′* = (1 − )cot(α), with α= slope of the levee riverside and (see Figure 1).
Based on Equation (4), the levee vulnerability to seepage is finally quantified through a practical vulnerability index, IVsee, defined as: 
formula
5
Specifically, when IVsee < 0, the seepage line is included within the levee body, while when IVsee ≥ 0 the seepage line intercepts the levee landside. Based on that, the higher the vulnerability index value the higher the vulnerability to seepage.

Based on Equation (5), the dimensionless and generally applicable fragility curves can be identified using a Monte Carlo sampling method to take the uncertainty on hydraulic levee parameters into account. For instance, Mazzoleni et al. (2014b) randomized with a Monte Carlo approach the geometry of the levee to assess fragility curves.

Among the parameters affecting the vulnerability index estimate, Ks and ξ are those typically unknown, whose estimate is characterized by high uncertainty if actual levees are considered. For that purpose, the sensitivity of the seepage line to the two parameters is first analyzed in this study to identify the most relevant parameter in the process description. Through a Monte Carlo approach and considering the probability distribution of Ks and ξ given in Vorogushyn et al. (2009), 1,000 Ks values are randomly sampled from a lognormal distribution with mean μKs = 10−5 ms−1 and standard deviation σKs = 25μKs (USACE 1999; Pohl 2000). Assuming ξ= 0.188, 1,000 seepage lines given by Equation (1), with a= 0, are computed and plotted in Figure 2(a). Likewise, 1,000 seepage lines (see Figure 2(b)) are generated for a fixed value of Ks = 10−5 ms−1 and a randomly sampled 1,000 different ξ values from a normal distribution with mean μξ = 0.188 and standard deviation σξ = 0.15μξ (Kanowshi 1977; Vorogushyn et al. 2009). As can be seen from Figure 2, the seepage line is more sensitive to the hydraulic conductivity, Ks, rather than the value of the soil porosity, ξ (USACE 1999; Pohl 2000; Vorogushyn et al. 2009).
Figure 2

Phreatic lines for: (a) different values of the hydraulic conductivity, Ks, with ξ= 0.188 and (b) different values of the soil porosity, ξ, with Ks=10−5 ms−1.

Figure 2

Phreatic lines for: (a) different values of the hydraulic conductivity, Ks, with ξ= 0.188 and (b) different values of the soil porosity, ξ, with Ks=10−5 ms−1.

Considering that the vulnerability is based on the seepage line, Equation (5), depending on Ks and δ, the latter characterizing the dependency of the seepage estimation from the flood duration, the foot levee and the water table, the fragility curves are developed considering the uncertainty in these two parameters through the following procedure:

  1. The uncertainty of the hydraulic conductivity value, identified as the most relevant parameter through the sensitivity analysis described above, is addressed by randomly generating 10,000 new Ks values from the lognormal distribution as defined above (Vorogushyn et al. 2009). In this case, there may be a wide variability for Ks (10−9 and 10−3m/s), evidence for which is also given by different works (e.g., USACE 1993; Fenton & Griffiths 1996; Pohl 2000). Moreover, such a wide variability allows taking into account the effect of seepage through both clays (Ks in the range 10−8 ÷ 10−12 m/s) and soils characterized by higher permeability (Ks up to 10−4 m/s).

  2. The range of variability of δ is identified on the basis of the maximum and minimum values for H0, D, L, and ξ. Assuming the range of variability of L (3–60 m), H0 (1–50 m), D (12–48 h), and ξ (0.095–0.288; Kanowski 1977), δ is varied from 80 to 10 × 106 s/m. Considering a uniform distribution, 10,000 values of δ are considered, and for each one, 10,000 value of Ks randomly sampled are associated. Therefore, 108 pairs of (Ks, δ) are then generated.

  3. For all possible pairs (Ks, δ), is computed through Equation (2) for different /Hs values, essentially depending on the return period of the flood.

  4. The vulnerability index is thus assessed by using Equation (5).

By way of example, the fragility curves are shown in Figure 3(a) and 3(b) for a fixed /Hs value and for a selected levee for which the geometry is known. Three δ values (referred to as delta1, delta2, and delta3) are shown between all the plausible values (defined during step 2). They refer to the same triplet (L, H0, ξ) at which three different durations of the flood wave equal to 12, 24, and 48 hours are associated, thus showing the time-dependency of the fragility curves. Figure 3(a) plots the seepage vulnerability index, IVsee, as a function of Ks, while Figure 3(b) provides for each δ value the cumulative probability of IVsee. From an operational point of view, by assigning the geometric characteristics of levee along with the porosity value, it is possible to assess the vulnerability of levee for different durations of flood. For instance, for delta2 (D= 24 h), the probability of no-seepage (IVsee0) is equal to about 0.4, while the complementary 0.6 value represents the probability of seepage occurrence. Moreover, it is worth noting that the cumulative frequency for IVsee = 0 is found equal to 0.3 for delta1, 0.4 for delta2, and higher than 0.5 for delta3. Therefore, as expected, a longer duration corresponds to a higher vulnerability to seepage.
Figure 3

Fragility curves for a fixed value of /Hs: (a) Ks, IVsee and (b) IVsee, cumulative probability. δ (delta) value increases from delta1 to delta3.

Figure 3

Fragility curves for a fixed value of /Hs: (a) Ks, IVsee and (b) IVsee, cumulative probability. δ (delta) value increases from delta1 to delta3.

Seepage vulnerability diagrams

Using the above procedure, for each IVsee the probability distribution of vulnerability can be expressed as a function of δ (Camici et al. 2015) from which a diagram for an operational vulnerability assessment can be identified for each riverside slope, α, and /Hs value.

A diagram is shown in Figure 4 for two characteristic riverside slope values: 1/2 (α ≅27°) and 2/3 (α ≅34°). In this way, an expeditious assessment of levee vulnerability to seepage, i.e., seepage probability, is made and can be used when the levee geometry, the flood duration, D, and the maximum water depth, i.e., the /Hs ratio, are known. Based on the computed seepage probability, different classes can be identified:
  • Seepage probability <0.3 → low vulnerability;

  • 0.3 ≤ Seepage probability <0.6 → mean vulnerability;

  • Seepage probability ≥ 0.6 → high vulnerability.

Figure 4

Seepage vulnerability diagram for riverside slope equal to: (a) 1/2 (α ≅27°) and (b) 2/3 (α ≅34°). For symbols see text.

Figure 4

Seepage vulnerability diagram for riverside slope equal to: (a) 1/2 (α ≅27°) and (b) 2/3 (α ≅34°). For symbols see text.

The limits of the vulnerability classes are identified as a first attempt for levee classification. However, the classes can be modified and adapted to the needs and requirements of the decision-makers by introducing, for instance, a much lower limit (i.e., 0.01) for identifying the levees with very low vulnerability.

Specifically, α value allows the reference diagram for the levee of interest to be selected. Then, δ and are assigned and by selecting the relevant curve it is possible to identify the seepage probability and, hence, the vulnerability class.

CASE STUDIES

The proposed procedure was applied for a large dataset of levees from different Italian basins. Among them, the case studies of the Tiber River basin, central Italy, and the Tanaro River in the Po River basin, northern Italy, are presented herein.

A reach 152 km long was selected in the Upper Tiber River basin, between the artificial lake of Montedoglio and Monte Molino gauged section subtending a drainage area of 5,279 km2 (see Figure 5(a)). Specifically, levees 33 and 34 are identified on the left and right river side, respectively.
Figure 5

Case studies: (a) Tiber River basin, central Italy; (b) Tanaro River basin, northern Italy.

Figure 5

Case studies: (a) Tiber River basin, central Italy; (b) Tanaro River basin, northern Italy.

The main channel of the Tanaro River, the major right tributary of the Po River, is 276 km long and the total drainage area is about 8,324 km2 (Figure 5(b)). The analysis was focused on the river reaches close to the main urban areas. A total number of six levees were selected, two on the left side near Cherasco city and the remaining levees identified are on both sides of the river, of which two are within Alessandria city, just upstream of the confluence with the Po River.

All available data were collected for the investigated levees and relevant technical-logistic record cards developed, as well as providing geometrical information for levee vulnerability assessment.

RESULTS

All the levees selected along the Tiber and the Tanaro River were analyzed through the proposed procedure to estimate their vulnerability to seepage.

The results provided by the fragility curves were finally verified through a comparison with levee failures occurring in the past during flood events. The analysis was implemented in the framework of the Italian Levee Database addressed to Civil Protection activities.

Seepage vulnerability

For the longitudinal structures along the Tiber River, H0 was assumed equal to 15 meters, ξ was set equal to 0.1 and three different relevant flood wave durations, i.e., 12, 24, and 48 hours, were considered. The analysis was carried out for three different return periods (50, 200, and 500 years), each one identifying a value of the /Hs ratio.

The results are summarized in Table 1 in terms of classes of vulnerability to seepage along with the computed seepage probabilities, for 50 years’ return period. As can be seen, the proposed expeditious methodology allows to quickly analyze a large dataset identifying the levees characterized by the larger seepage probabilities, to properly address detailed controls and investigations. In this case, seven levees, shown in italic font in Table 1, are found to be prone to seepage. Overall, for all the flood durations, most of the investigated levees were characterized by a low vulnerability class (specifically, about 45%, 34%, and 25% for D equal to 12, 24, and 48 hours, respectively).

Table 1

Tiber River: class of vulnerability to seepage (and seepage probability) for the investigated levees for the /Hs ratio computed for a return period of 50 years (D= flood wave duration)

Left side levee Vulnerability class (seepage probability)
 
Right side levee Vulnerability class (seepage probability)
 
D = 12 hr D = 24 hr D = 48 hr D = 12 hr D = 24 hr D = 48 hr 
Tv1sx overtopping overtopping overtopping Tv1dx high (0.60) high (0.69) high (0.74) 
Tv2sx overtopping overtopping overtopping Tv2dx overtopping overtopping overtopping 
Tv3sx low (0.04) low (0.06) low (0.09) Tv3dx overtopping overtopping overtopping 
Tv4sx mean (0.34) mean (0.41) mean(0.56) Tv4dx low (0.10) low (0.16) low (0.22) 
Tv5sx mean (0.34) mean (0.43) mean (0.58) Tv5dx overtopping overtopping overtopping 
Tv6sx overtopping overtopping overtopping Tv6dx overtopping overtopping overtopping 
Tv7sx overtopping overtopping overtopping Tv7dx low (0.24) mean (0.33) mean (0.38) 
Tv8sx low (0.03) low (0.05) low (0.07) Tv8dx low (0.01) low (0.03) low (0.05) 
Tv9sx low (0.01) low (0.03) low (0.04) Tv9dx overtopping overtopping overtopping 
Tv10sx low (0.01) low (0.03) low (0.05) Tv10dx mean (0.52) high (0.66) high (0.73) 
Tv11sx null null null Tv11dx overtopping overtopping overtopping 
Tv12sx mean (0.31) mean (0.36) mean (0.50) Tv12dx low (0.05) low (0.09) low (0.15) 
Tv13sx mean (0.42) mean (0.56) high (0.68) Tv13dx low (0.29) mean (0.35) mean (0.49) 
Tv14sx low (0.29) mean (0.35) mean (0.49) Tv14dx low (0.25) mean (0.34) mean (0.40) 
Tv15sx low (0.25) mean (0.34) mean (0.40) Tv15dx null null null 
Tv16sx low (0.22) low (0.29) mean (0.35) Tv16dx low (0.29) mean (0.35) mean (0.49) 
Tv17sx low (0.05) low (0.07) low (0.11) Tv17dx low (0.14) low (0.21) low (0.26) 
Tv18sx low (0.19) low (0.23) mean (0.30) Tv18dx low (0.11) low (0.20) low (0.24) 
Tv19sx low (0.22) low (0.29) mean (0.35) Tv19dx low (0.21) low (0.25) mean (0.34) 
Tv20sx low (0.14) low(0.21) low (0.26) Tv20dx low (0.22) low (0.29) mean (0.35) 
Tv21sx low (0.08) low (0.14) low (0.21) Tv21dx low (0.21) low (0.26) mean (0.34) 
Tv22sx null null null Tv22dx low (0.26) mean (0.34) mean (0.42) 
Tv23sx overtopping overtopping overtopping Tv23dx low (0.15) low (0.22) low (0.28) 
Tv24sx null null null Tv24dx low (0.12) low (0.20) low (0.24) 
Tv25sx null null null Tv25dx null null null 
Tv26sx null null null Tv26dx null null null 
Tv27sx null null null Tv27dx null null null 
Tv28sx null null null Tv28dx null null null 
Tv29sx mean (0.55) high (0.68) high (0.74) Tv29dx low (0.29) mean (0.35) mean (0.49) 
Tv30sx null null null Tv30dx mean (0.49) high (0.64) high (0.72) 
Tv31sx null null null Tv31dx low (0.08) low (0.12) low (0.20) 
Tv32sx null null null Tv32dx mean (0.36) mean (0.49) high (0.63) 
Tv33sx low (0.06) low (0.09) low (0.15) Tv33dx low (0.10) low (0.20) low (0.23) 
       Tv34dx mean (0.41) mean (0.56) high (0.67) 
Left side levee Vulnerability class (seepage probability)
 
Right side levee Vulnerability class (seepage probability)
 
D = 12 hr D = 24 hr D = 48 hr D = 12 hr D = 24 hr D = 48 hr 
Tv1sx overtopping overtopping overtopping Tv1dx high (0.60) high (0.69) high (0.74) 
Tv2sx overtopping overtopping overtopping Tv2dx overtopping overtopping overtopping 
Tv3sx low (0.04) low (0.06) low (0.09) Tv3dx overtopping overtopping overtopping 
Tv4sx mean (0.34) mean (0.41) mean(0.56) Tv4dx low (0.10) low (0.16) low (0.22) 
Tv5sx mean (0.34) mean (0.43) mean (0.58) Tv5dx overtopping overtopping overtopping 
Tv6sx overtopping overtopping overtopping Tv6dx overtopping overtopping overtopping 
Tv7sx overtopping overtopping overtopping Tv7dx low (0.24) mean (0.33) mean (0.38) 
Tv8sx low (0.03) low (0.05) low (0.07) Tv8dx low (0.01) low (0.03) low (0.05) 
Tv9sx low (0.01) low (0.03) low (0.04) Tv9dx overtopping overtopping overtopping 
Tv10sx low (0.01) low (0.03) low (0.05) Tv10dx mean (0.52) high (0.66) high (0.73) 
Tv11sx null null null Tv11dx overtopping overtopping overtopping 
Tv12sx mean (0.31) mean (0.36) mean (0.50) Tv12dx low (0.05) low (0.09) low (0.15) 
Tv13sx mean (0.42) mean (0.56) high (0.68) Tv13dx low (0.29) mean (0.35) mean (0.49) 
Tv14sx low (0.29) mean (0.35) mean (0.49) Tv14dx low (0.25) mean (0.34) mean (0.40) 
Tv15sx low (0.25) mean (0.34) mean (0.40) Tv15dx null null null 
Tv16sx low (0.22) low (0.29) mean (0.35) Tv16dx low (0.29) mean (0.35) mean (0.49) 
Tv17sx low (0.05) low (0.07) low (0.11) Tv17dx low (0.14) low (0.21) low (0.26) 
Tv18sx low (0.19) low (0.23) mean (0.30) Tv18dx low (0.11) low (0.20) low (0.24) 
Tv19sx low (0.22) low (0.29) mean (0.35) Tv19dx low (0.21) low (0.25) mean (0.34) 
Tv20sx low (0.14) low(0.21) low (0.26) Tv20dx low (0.22) low (0.29) mean (0.35) 
Tv21sx low (0.08) low (0.14) low (0.21) Tv21dx low (0.21) low (0.26) mean (0.34) 
Tv22sx null null null Tv22dx low (0.26) mean (0.34) mean (0.42) 
Tv23sx overtopping overtopping overtopping Tv23dx low (0.15) low (0.22) low (0.28) 
Tv24sx null null null Tv24dx low (0.12) low (0.20) low (0.24) 
Tv25sx null null null Tv25dx null null null 
Tv26sx null null null Tv26dx null null null 
Tv27sx null null null Tv27dx null null null 
Tv28sx null null null Tv28dx null null null 
Tv29sx mean (0.55) high (0.68) high (0.74) Tv29dx low (0.29) mean (0.35) mean (0.49) 
Tv30sx null null null Tv30dx mean (0.49) high (0.64) high (0.72) 
Tv31sx null null null Tv31dx low (0.08) low (0.12) low (0.20) 
Tv32sx null null null Tv32dx mean (0.36) mean (0.49) high (0.63) 
Tv33sx low (0.06) low (0.09) low (0.15) Tv33dx low (0.10) low (0.20) low (0.23) 
       Tv34dx mean (0.41) mean (0.56) high (0.67) 

The levees affected by failure during the severe flood of November 2005 are in bold font.

By way of example, the fragility curves developed for the Tv13sx levee are displayed in Figure 6. Tv13sx stands for the ‘13th’ levee located on Tiber, Tv, in left river side, sx. As can be seen, this levee is found to be characterized by high vulnerability (seepage probability = 0.68) when the 48 hr flood wave duration was considered.
Figure 6

Tiber River: fragility curves for the levee Tv13sx for return period = 50 years (/Hs = 0.95) (a) (Ks, IVsee) and (b) (IVsee, cumulative probability). Delta1, delta2, and delta3 correspond to flood duration equal to 12, 24, and 48 hours, respectively.

Figure 6

Tiber River: fragility curves for the levee Tv13sx for return period = 50 years (/Hs = 0.95) (a) (Ks, IVsee) and (b) (IVsee, cumulative probability). Delta1, delta2, and delta3 correspond to flood duration equal to 12, 24, and 48 hours, respectively.

In Table 1, the river sections where a breach occurred during the flooding event on November 2005 having a magnitude of 50 years and duration of about 30 hours are shown in bold. As can be seen, the procedure estimates mean/high vulnerability for those levees that collapsed during the event without overtopping. Only for the Tv17sx levee, affected by a breach during the flood, the procedure provides a low vulnerability to seepage. In this case, a detailed study should be carried out to investigate whether the failure event was due to the external factors as, for instance, the presence of animal/rodent burrows (Camici et al. 2015).

For the Tanaro (Ta) River, H0 and ξ are set equal to 30 meters and 0.1, respectively. The same flood durations, i.e., 12, 24, and 48 hours, are considered for the analysis that is carried out only for 200 years’ return period. The results, summarized in Table 2, show that two of the investigated levees are overtopped; one is characterized by low vulnerability, while three are found prone to seepage. Specifically, for Ta1sx and Ta2dx the highest probabilities are computed and are found higher than 0.55 when the longest flood duration is considered. Figure 7 shows the results for Ta1sx that is characterized by mean vulnerability for all the investigated flood durations.
Table 2

As for Table 1, but for the Tanaro River and for a return period of 200 years

Left side levee Vulnerability class (seepage probability)
 
Right side levee Vulnerability class (seepage probability)
 
D = 12 hr D = 24 hr D = 48 hr D = 12 hr D = 24 hr D = 48 hr 
Ta1sx mean (0.34) mean (0.42) mean (0.56) Ta1dx overtopping overtopping overtopping 
Ta2sx overtopping overtopping overtopping Ta2dx mean (0.34) mean (0.41) mean (0.57) 
    Ta3dx low (0.28) mean (0.35) mean (0.48) 
    Ta4dx low (0.06) low (0.09) low (0.17) 
Left side levee Vulnerability class (seepage probability)
 
Right side levee Vulnerability class (seepage probability)
 
D = 12 hr D = 24 hr D = 48 hr D = 12 hr D = 24 hr D = 48 hr 
Ta1sx mean (0.34) mean (0.42) mean (0.56) Ta1dx overtopping overtopping overtopping 
Ta2sx overtopping overtopping overtopping Ta2dx mean (0.34) mean (0.41) mean (0.57) 
    Ta3dx low (0.28) mean (0.35) mean (0.48) 
    Ta4dx low (0.06) low (0.09) low (0.17) 

The levees affected by failure during the severe flood of November 1994 are in bold.

Figure 7

As for Figure 6, but for the Tanaro River levee Ta1sx, return period = 200 years (/Hs = 0.79).

Figure 7

As for Figure 6, but for the Tanaro River levee Ta1sx, return period = 200 years (/Hs = 0.79).

It is worth noting that the information on historical levee breaches along the Tanaro River substantially supports the results of the analysis. Specifically, during the very severe flood that affected the Po River basin on November 1994 with a magnitude of nearly 200 years: the Ta2sx and Ta1dx levees collapsed because overtopping occurred; the three most vulnerable levees identified by the proposed methodology, i.e., Ta1sx, Ta2dx, and Ta3dx, were affected by failure processes; for Ta4dx levee, characterized by very low seepage probabilities, there is no evidence of structural failure.

National levee database

The vulnerability procedure is embedded in a dynamic geospatial database (Database nazionale delle ArgiNature in TErra, DANTE), recently developed by CNR-IRPI for the Italian Civil Protection Department of the Presidency of Council of Ministers. DANTE collects data on levee properties and historical levee failures that have been structured in such a way that the presented vulnerability procedure can be used directly by decision-makers. For that, DANTE is structured as a dynamic geospatial tool useful for sharing and managing levee information in one common place and in one common structure for national and general public use, supporting authorities with the charge of hydraulic risk mitigation in identifying operationally levee seepage vulnerability. Specifically, DANTE is directed at collecting comprehensive available data about Italian levees and historical breach failures and provide information about: (1) location and condition of levees; (2) geometrical properties; (3) photographic documentation; and (4) historical failures. DANTE can be updated in order to include all available and potentially useful information, such as data on the levee material when available.

The vulnerability assessment methodology was implemented for the database so that the assessment of vulnerability to overtopping (Camici et al. 2015) and seepage could be addressed. Moreover, information on management, control and maintenance and flood hazard maps developed by assuming the levee system undamaged/damaged during the flood event are provided as well. The database consulting starts from the home page where a set of items (Region, Province, River, etc.) allows the user to select only the levees of interest. As DANTE is mainly directed at public authorities in charge of hydraulic risk prevention and management, the levees’ selection can also be based on the vulnerability class to overtopping and/or seepage as well as on the availability of flooding hazard maps. For each levee, the relevant data can be displayed, including a technical-logistic record card, the vulnerability classes to overtopping and seepage and flooding hazard maps with and without levee collapse. Figure 8 shows the main structure of the database along with an example for levees with high seepage vulnerability and flooding map for the Tiber basin. As can be seen, DANTE represents a sound tool since decision-makers can address expeditious assessment of levee embankment vulnerability to seepage and infer the consequent flood-prone areas.
Figure 8

DANTE web-page.

Figure 8

DANTE web-page.

CONCLUSIONS

A practical and expeditious procedure to evaluate the vulnerability to seepage for earthen levees was enhanced herein and tested for two selected case studies in Italy. At the present, the proposed method is developed considering the seepage line analysis in the embankment only, while future investigations are planned to embed the foundation soil as well. A simple vulnerability index was identified and can be conveniently adopted for levees wherein the hydraulic parameters of soils are unknown or partly known. The procedure takes the uncertainty of the hydraulic parameter into account to estimate the fragility curves and provides the probability of vulnerability of a levee to seepage which quickly enable investigation of the extended levee systems to identify the most likely critical points where detailed investigations are required.

The fragility curves developed herein are a new perspective which enables the estimation of the seepage probability as a function of the water depth in the channel and the quantity δ depending on the flood duration, the foot levee, the soil porosity, and the water table. Based on these curves, the vulnerability can be easily identified without needing to know the hydraulic conductivity in the embankment, which is a critical parameter not easy to assess.

The results obtained for the Tiber River, in central Italy, and the Tanaro River, in northern Italy, by analyzing 67 and six levees, respectively, compared with the information on historical levee failures suggest that the method seems to be able to identify the most vulnerable levees, for which detailed investigations should be carried out.

The results of the vulnerability analysis are included, along with all the other available data in the Italian levee database (Database nazionale delle ArgiNature in TErra, DANTE) recently developed by IRPI-CNR for the Civil Protection Department. DANTE is presented as a dynamic geospatial tool addressed to collect all the available data/information on levee systems and to usefully support authorities with the responsibility of hydraulic risk mitigation.

ACKNOWLEDGEMENTS

This work was partly supported by the agreement between the Civil Protection Department and the National Research Council-IRPI. We thank the Editor, the anonymous reviewer, Roberto Ranzi and Stefano Barontini for their valuable comments and suggestions.

REFERENCES

REFERENCES
Ahmad
S.
Kashyap
D.
Mathur
B. S.
1993
Mathematical modelling of saturated-unsaturated flow to drains
.
Journal of Irrigation and Drainage Engineering
119
(
1
),
18
33
.
ASCE/EWRI Task Committee on Dam/Levee Breaching
2011
Earthen embankment breaching
.
Journal of Hydraulic Engineering
137
(
12
),
1549
1564
.
Aureli
F.
Mignosa
P.
2004
Flooding scenarios due to levee breaking in the Po river
.
Proceedings of the Institution of Civil Engineers – Water Management
157
(
1
),
3
12
.
Bligh
W. G.
1910
Dams, barrages and weirs on porous foundations
.
Engineering News Record
64
(
20
),
708
710
.
Camici
S.
Barbetta
S.
Moramarco
T.
2015
Levee body vulnerability to seepage: the case study of the levee failure along the Foenna stream on 1 January 2006 (central Italy)
.
Journal of Flood Risk Management
.
doi: 10.1111/jfr3.12137
.
Chahar
B. R.
2004
Determination of length of a horizontal drain in homogeneous earth dams
.
Journal of Irrigation and Drainage Engineering
130
(
6
),
530
536
.
Cheng
S. T.
1993
Statistics of dam failures
. In:
Reliability and Uncertainty Analyses in Hydraulic Design
(
Yen
B. C.
Tung
Y. K.
, eds).
ASCE
,
Reston, VA
, pp.
97
105
.
Colleselli
F.
1997
Problemi idraulici e strutturali delle arginature in terra (Hydraulic and Structural Issue for Earthen Levees)
,
La difesa idraulica del territorio, Ed. Bios
,
Italy
, pp.
107
128
.
Di Baldassarre
G.
Castellarin
A.
Montanari
A.
Brath
A.
2009
Probability weighted hazard maps for comparing different flood risk management strategies: a case study
.
Natural Hazards
50
,
479
496
.
doi: 10.1007/s11069-009-9355-6
.
Fenton
G. A.
Griffiths
D. V.
1996
Statistics of free surface flow through stochastic earth dam
.
Journal of Geotechnical Engineering
122
(
6
),
427
436
.
ICODS (Interagency Committee on Dam Safety)
2015
Evaluation and Monitoring of Seepage and Internal Erosion
,
Federal Emergency Management Agency
,
FEMA P-1032
.
ICOLD
2013
Internal Erosion of Existing Dams, Levees, and Dikes, and Their Foundations
.
Bulletin 164 Preprint
,
International Commission on Large Dams
,
Paris
,
France
.
Kanowski
H.
1977
Ein Beitrag zur zerstörungsfreien Untersuchung von Flussdeichen
.
PhD Thesis
,
Dresden University of Technology
,
Germany
.
Lane
E. W.
1935
Security from underseepage
.
Transactions of the American Society of Civil Engineers
100
,
1235
1351
.
Marchi
E.
1961
Sulla filtrazione attraverso gli argini fluviali (On the infiltration process within levees)
. In:
Proceedings of VII Convegno di Idraulica e Costruzioni Idrauliche
,
Palermo
,
Italy
.
Mazzoleni
M.
Bacchi
B.
Barontini
S.
Di Baldassarre
G.
Pilotti
M.
Ranzi
R.
2014a
Flooding hazard mapping in floodplain areas affected by piping breaches in the Po River, Italy
.
Journal of Hydrologic Engineering
19
(
4
),
717
731
.
Mazzoleni
M.
Barontini
S.
Ranzi
R.
Brandimarte
L.
2014b
Innovative probabilistic methodology for evaluating the reliability of discrete levee reaches owing to piping
.
Journal of Hydrologic Engineering
20
(
5
),
04014067
.
Nagy
L.
Toth
S.
2005
Detailed Technical Report on the Collation and Analysis of Dike Breach Data with Regards to Formation Process and Location Factors. Technical Report
,
H-EURAqua Ltd.
,
Hungary
.
Orlandini
S.
Moretti
G.
Albertson
J. D.
2015
Evidence of an emerging levee failure mechanism causing disastrous floods in Italy
.
Water Resources Research
51
(
10
),
7995
8011
.
doi: 10.1002/2015WR017426
.
Pavlovsky
N. N.
1960
Collected Works, Akad, Nauk USSR, Leningrad
.
Pohl
R.
2000
Aspekte der Sicherheit von Deichen mit inhomogenem Aufbau
.
Wasser Abfall
11
,
52
57
.
Polemio
M.
Lollino
P.
2011
Failure of infrastructure embankments induced by flooding and seepage: a neglected source of hazard
.
Natural Hazards and Earth Systems Sciences
11
,
3383
3396
.
Rice
J. D.
Polanco
L.
2012
Reliability-based under seepage analysis in levees using a response surface – Monte Carlo simulation method
.
Journal of Geotechical and Geoenvironmental Engineering
138
(
7
),
821
830
.
Sellmeijer
J. B.
Koenders
M. A.
1991
A mathematical model for piping
.
Applied Mathematical Modeling
115
(
6
),
646
651
.
Sellmeijer
J. B.
Lopez De La Cruz
J.
van Beek
V. M.
Knoeff
J. G.
2011
Fine tuning of the backward erosion piping model through small scale, medium scale and IJKdijk experiments
.
European Journal of Environmental and Civil Engineering
15
(
8
),
1139
1154
.
Supino
G.
1965
La filtrazione attraverso gli argini e nelle falde sotterranee (The Filtration Process through Levees and Groundwater)
.
Le reti idrauliche. Patron Ed.
Bologna
,
Italy
, pp.
439
485
.
USACE
1993
Seepage analysis and control for dams, Engineer Manual
.
USACE
1999
Risk-based analysis in geotechnical engineering for support of planning studies. Engineer Technical Letter, 1110-2-556, US Army Corps of Engineers
.
Van Beek
V. M.
Knoeff
J. G.
Sellmeijer
J. B.
2011
Observations on the process of piping by underseepage in cohesionless soils in small, medium and large-scale experiments
.
European Journal of Environmental and Civil Engineering
15
(
8
),
1115
1137
.
Vorogushyn
S.
Merz
B.
Apel
H.
2009
Development of dike fragility curves for piping and micro-instability breach mechanisms
.
Natural Hazards and Earth System Sciences
9
,
1382
1401
.
Vorogushyn
S.
Merz
B.
Lindenschmidt
K. E.
Apel
H.
2010
A new methodology for flood hazard assessment considering dike breaches
.
Water Resources Research
46
(
8
),
W08541
.
Zhang
L.
Peng
M.
Chang
D.
Xu
Y.
2016
Dam failure risk assessment. In:
Dam Failure Mechanisms and Risk Assessment
, Chapter 12.
John Wiley & Sons Singapore Pte. Ltd
, pp.
307
321
,
Zumr
D.
Císlerová
M.
2010
Soil moisture dynamics in levees during flood events – variably saturated approach
.
Journal of Hydrology and Hydromechanics
58
(
1
),
64
72
.