# The Role of Hydraulic Hysteresis on the Hydrological Response of Pyroclastic Silty Covers

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- investigation of the wetting/drying paths of an instrumented reconstituted ash layer exposed to weather forcing over four consecutive years;
- selection of a suitable model for analysis of the hydraulic hysteresis and calibration of the parameters required to simulate the soil behavior;
- analysis of the role of the hydraulic hysteresis of a virtual slope in response to a critical event, and comparison with the results obtained by the usual non-hysteretic approaches.

## 2. Materials and Methods

#### 2.1. Test Device and Investigated Soil

^{3}(height 75 cm, surface area 1.3 m

^{2}) [12]. It was located in Naples and studied with weather forcing comparable to that usually experienced by slopes composed of the same materials that are potentially affected by landslide events in Campania. Monteforte Irpino ash [16] was laid down in the lysimeter. Such a material was produced in the last 10,000 years by the volcanic centre of Somma-Vesuvius. The finest component of the soil (a silt with some clay, Figure 2) was non-plastic due to the absence of active minerals. The field porosity was as high as 70% with peaks attaining 80%. The layer was put in place by means of dry pluvial deposition at the same field porosity (70%) and exposed to the atmosphere for several hydrological years. Specifically, during the timespan of September 2010–August 2014, the soil surface was left bare to reduce the complexity of the involved dynamics and the generated data was used for analysis. A geotextile sheet was placed at the bottom of the soil layer. In that investigation, a weather station monitored the atmospheric variables. Rainfall infiltration and evaporative fluxes were obtained by regularly weighing the tank through three load cells. The evaporative flux was also indirectly obtained by measuring the different water energetic terms at the soil–atmosphere interface. The hydrological variables, suction (s) and volumetric water content (θ), were monitored at four different depths (at 15, 30, 50, and 70 cm) using jet-fill tensiometers and time domain reflectometry (TDR) probes.

#### 2.2. Modeling Approaches

_{w}the unit weight of water. The use of such an equation requires soil characterization through both the SWCC and the hydraulic conductivity function (HCF).

_{e}is the so-called “effective saturation degree”, θ

_{s}and θ

_{r}the saturated and the residual volumetric water content of the soil, and n and α (kPa

^{−1}) are two empirical parameters.

_{s}represent the current and the saturated hydraulic conductivity, respectively.

_{r}= θ

_{r}

^{w}= θ

_{r}

^{d}; n

^{w}= n

^{d}= n); the differences concern only the values of the saturated volumetric water content (θ

_{s}

^{d}being higher than θ

_{s}

^{w}) and of the coefficient α (α

^{d}being less than α

^{w}). Compared to other models based on a scaling procedure [27,28], the PL model allows prevention of the artificial pumping error, that is, the non-closure of the scanning loops in simulated cyclic paths, which is considered to be an aberration rather than a soil property [29]. This is avoided by collecting all the reversal points experienced by the soil. Preserving the “memory” of the various wetting–drying cycles to which they have been subjected allows paths to draw closed scanning loops.

_{Δ}

^{dw}, S

_{e}

_{Δ}

^{dw}) located on a main or a scanning curve and ending at a wetting-to-drying turn point is expressed by the following equation:

_{e}

^{w}is the effective saturation degree calculated with the van Genuchten equation (Equation (2)) for the main wetting curve; s

_{Δ}

^{dw}, S

_{e}

_{Δ}

^{dw}are the s and S

_{e}values corresponding to the starting drying-to-wetting turn point; and s

_{Δ}

^{wd}and S

_{e}

_{Δ}

^{wd}are the values corresponding to the wetting-to-drying turn point.

_{Δ}

^{wd}, S

_{e}

_{Δ}

^{wd}) and ending at a drying-to-wetting reversal point (s

_{Δ}

^{dw}, S

_{e}

_{Δ}

^{dw}) is expressed by the similar equation:

_{e}

^{d}is the effective saturation calculated by the van Genuchten equation (Equation (2)) with (θ

_{s}

^{d}, θ

_{r}, α

^{d}, n) parameters.

_{e}–s plan where, for sake of simplicity, the ideal condition of a closed main hysteresis loop at saturation (neglecting air entrapment) is assumed. The initial soil state is represented by point a (θ

_{s}

^{d}= θ

_{s}

^{w}) corresponding to a condition close to full saturation. A first desaturation process is supposed to follow the main drying curve up to point b. The subsequent wetting path would lead the soil state from b to c along the curve obtained by scaling the main wetting curve in such a way to pass through the reversal points a and b. A further hypothetical drying path c–d is obtained by scaling the main drying curve which, in this case, should pass through the reversal points b and c. The final wetting path d–a is defined by scaling the main wetting curve again, which moves through the points a, c, and d.

_{∆}is the water content at the reversal point Δ and θ

_{s}

_{∆}is the water content achieved for null suction starting from Δ. The minimum value of θ

_{s}

_{∆}is θ

_{s}

^{w}, which is obtained by assuming θ

_{∆}= θ

_{r}.

## 3. Results and Discussion

#### 3.1. Lysimeter Results

#### 3.2. Model Calibration and Validation

_{s}

^{d}, θ

_{s}

^{w}, θ

_{r}, α

^{d}, α

^{w}, n, k

_{s}) has been obtained as follows. Four of them, i.e., θ

_{s}

^{d}, θ

_{r}, α

^{d}, n, were deduced by the experimental main drying curve obtained by imposing forced evaporation on an initially saturated soil sample in a ku-pF apparatus up to suction values of about 70 kPa. Dried soil cores were then placed in Richards’ plate up to 1000 kPa [10,35]. The last three parameters (θ

_{s}

^{w}, α

^{w}, k

_{s}) were determined by calibration of the data provided by the lysimeter monitoring activity (§2.1) in the first year (Figure 4a). The parameters were validated through the data collected in the remaining three years (Figure 4b–d).

^{w}/α

^{d}ratio of 1.4, while literature indicates a value of 2 which appears to be suitable for many soils [35]. A hysteresis factor has also been analytically quantified through the effective hysteresis indicator proposed by Gebrenegus and Ghezzehei [38], which computes the maximum deviation in effective saturation between the two main curves. In Figure 7, the computed value is compared with the cloud of points provided by literature catalogues for a wide spectrum of materials, from fine-grained to coarse-grained soils [39,40,41]. Such a value falls around the middle of the cloud, indicating an intermediate behavior due to an intermediate grain size distribution (see Figure 2). Following the assessed value, the value of R computed according Equation (4) is about 16.5.

^{−6}m/s, which is well higher than the value (k

_{s}= 3 × 10

^{−7}m/s) obtained through laboratory tests [10], while it is equivalent to those carried out in the interpretation of monitoring results neglecting hysteresis [42].

#### 3.3. Numerical Experiments on the Effects of Hydraulic Hysteresis in Landslide Triggering

#### 3.3.1. Investigated Scenarios and Organization of Obtained Results

- (1)
- (2)
- the lowermost boundary condition is modeled as a seepage surface, which behaves as an impervious boundary when suction remains higher than zero, and as a draining surface when it vanishes; this is the condition that has been recognized, through special targeted experiments, at the contact between ash and pumice layers [44];
- (3)
- two alternative hypotheses are adopted for the initial conditions: (A) constant piezometric head and (B) constant volumetric water content; the latter obviously results in an initial non-equilibrated suction profile;
- (4)
- a persistent 100 mm/day constant rainfall, slightly higher (~1.2 × 10
^{−6}m/s) than the hydraulic conductivity of fully saturated soil, is imposed at the uppermost boundary condition; this is a realistic scenario in the considered geomorphological context, where such a daily rainfall intensity occurs every 2–3 years.

- -
- full hysteretic soil behavior (HB);
- -
- main drying curve (MDC);
- -
- main wetting curve (MWC);
- -
- the curve obtained by averaging the experimental results of Rianna et al. [12] at a depth of 50 cm (AC).

#### 3.3.2. Case A: Persistent Rainfall; Hydrostatic Initial Suction Profile

_{0}, was univocally identified for all (s, θ) relationships, but only for the HB assumption, as this was not described by a single curve. For this last, θ

_{0}has been conventionally established on the MDC (Figure 8a,b). The differences in soil behavior depending on the selected (s, θ) relationship are synthesized by the computed NST values.

_{av}, which is operative along the wetting path (as proxy, was considered the geometric mean), and the overall water content, Δθ, required to lead to zero suction. In the examined case (first column of Figure 8 and Figure 9), the values assumed by such parameters are as detailed in Table 2.

_{av}and Δθ clearly influences the soil response. In fact, the lower k

_{av}, the longer NST; conversely, the higher Δθ, the longer NST.

#### 3.3.3. Case B: Persistent Rainfall; Uniform Initial Volumetric Water Content

_{av}keep different values leading to different NSTs. In this case too, the initial conditions for HB were applied to MDC.

_{0}value of 0.55, which corresponded to a suction value of 8 kPa for MWC, 16 kPa for MDC (and HB), and 12 kPa for AC. The values of dominant factors and NSTs are reported in Table 3.

_{av}, but the smaller variation in Δθ for the cases characterized by a lower hydraulic conductivity (MWC and HB) lead to smaller NST differences.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Froude, M.J.; Petley, D.N. Global fatal landslide occurrence from 2004 to 2016. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 2161–2181. [Google Scholar] [CrossRef] - Pagano, L.; Picarelli, L.; Rianna, G.; Urciuoli, G. A simple numerical procedure for timely prediction of precipitation–induced landslides in unsaturated pyroclastic soils. Landslides
**2010**, 7, 273–289. [Google Scholar] [CrossRef] - Rianna, G.; Pagano, L.; Urciuoli, G. Rainfall patterns triggering shallow flowslides in pyroclastic soils. Eng. Geol.
**2014**, 174, 22–35. [Google Scholar] [CrossRef] - Iverson, R.M. Landslide triggering by rain infiltration. Water Resour. Res.
**2000**, 36, 1897–1910. [Google Scholar] [CrossRef] [Green Version] - Cascini, L.; Guida, D.; Romanzi, G.; Nocera, N.; Sorbino, G. A preliminary model for the landslides of May 1998 in Campania Region. In Proceedings of the International Symposium on The Geotechnics of Hard Soils—Soft Rocks, Naples, Italy, 12–14 October 1998; Evangelista, A., Picarelli, L., Eds.; 1998; Volume 3, pp. 1623–1652. [Google Scholar]
- Olivares, L.; Picarelli, L. Shallow flowslides triggered by intense rainfalls on natural slopes covered by loose unsaturated pyroclastic soils. Geotechnique
**2003**, 532, 283–287. [Google Scholar] [CrossRef] - Nocentini, M.; Tofani, V.; Gigli, G.; Fidolini, F.; Casagli, N. Modeling debris flows in volcanic terrains for hazard mapping: The case study of Ischia Island (Italy). Landslides
**2015**, 12, 831–846. [Google Scholar] [CrossRef] - Picarelli, L.; Evangelista, A.; Rolandi, G.; Paone, A.; Nicotera, M.V.; Olivares, L.; Scotto di Santolo, A.; Lampitiello, S.; Rolandi, M. Mechanical properties of pyroclastic soils in Campania Region. In Proceedings of the 2nd International Workshop on Characterisation and Engineering Properties of Natural Soils, Singapore, 29 November–1 December 2006; Tan, T.S., Phoon, K.K., Height, D.W., Leroueil, S., Eds.; Taylor & Francis Group: London, UK, 2006; Volume 4, pp. 2331–2384. [Google Scholar]
- Nicotera, M.V.; Papa, R.; Urciuoli, G. An experimental technique for determining the hydraulic properties of unsaturated pyroclastic soils. Geotech. Test. J.
**2010**, 33, 263–285. [Google Scholar] - Pirone, M.; Papa, R.; Nicotera, M.V.; Urciuoli, G. In situ monitoring of the groundwater field in an unsaturated pyroclastic slope for slope stability evaluation. Landslides
**2015**, 12, 259–276. [Google Scholar] [CrossRef] - Damiano, E.; Olivares, L.; Picarelli, L. Steep–slope monitoring in unsaturated pyroclastic soils. Eng. Geol.
**2012**, 137, 1–12. [Google Scholar] [CrossRef] - Rianna, G.; Pagano, L.; Urciuoli, G. Investigation of soil–atmosphere interaction in pyroclastic soils. J. Hydrol.
**2014**, 510, 480–492. [Google Scholar] [CrossRef] - Comegna, L.; Damiano, E.; Greco, R.; Guida, A.; Olivares, L.; Picarelli, L. Field hydrological monitoring of a sloping shallow pyroclastic deposit. Can. Geotech. J.
**2016**, 53, 1125–1137. [Google Scholar] [CrossRef] [Green Version] - Olivares, L.; Picarelli, L. Modelling of flowslides behaviour for risk mitigation. In Proceedings of the 6th International Conference on Physical Modelling in Geotechnics, Hong Kong, China, 4–6 August 2006; Taylor & Francis: London, UK, 2006; Volume 1, pp. 99–112. [Google Scholar]
- Cascini, L.; Cuomo, S.; Pastor, M.; Sorbino, G.; Piciullo, L. SPH run–out modelling of channelized landslides of the flow type. Geomorphology
**2014**, 214, 502–513. [Google Scholar] [CrossRef] - Pirone, M.; Papa, R.; Nicotera, M.V.; Urciuoli, G. Evaluation of the Hydraulic Hysteresis of Unsaturated Pyroclastic Soils by in Situ Measurements. Proced. Earth Planet. Sci.
**2014**, 9, 163–170. [Google Scholar] [CrossRef] [Green Version] - Comegna, L.; Damiano, E.; Greco, R.; Guida, A.; Olivares, L.; Picarelli, L. Investigation on the hydraulic hysteresis of a pyroclastic deposit. In Proceedings of the International Workshop on Volcanic Rocks and Soils, Ischia, Italy, 24–25 September 2015; pp. 161–162. [Google Scholar]
- Basile, A.; Ciollaro, G.; Coppola, A. Hysteresis in soil water characteristics as a key to interpreting comparisons of laboratory and field measured hydraulic properties. Water Resour. Res.
**2003**, 39, 1355. [Google Scholar] [CrossRef] - Comegna, L.; Rianna, G.; Lee, S.; Picarelli, L. Influence of the wetting path on the mechanical response of shallow unsaturated sloping covers. Comput. Geotech.
**2016**, 73, 164–169. [Google Scholar] [CrossRef] - Richards, L.A. Capillary conduction of liquids through porous mediums. Physics
**1931**, 1, 318–333. [Google Scholar] [CrossRef] - Van Genuchten, M.T. A closed form equation for predicting the hydraulic conductivity. Soil Sci. Soc. Am. J.
**1980**, 44, 892–898. [Google Scholar] [CrossRef] - Mualem, Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res.
**1976**, 12, 513–522. [Google Scholar] [CrossRef] - Viaene, P.; Vereecken, H.; Diels, J.; Feyen, J. A statistical analysis of six hysteresis models for the moisture retention characteristic. Soil Sci.
**1994**, 157, 345–355. [Google Scholar] [CrossRef] - Pham, H.Q.; Fredlund, D.G.; Barbour, S.L. A study of hysteresis models for soil-water characteristic curves. Can. Geotech. J.
**2005**, 42, 1548–1568. [Google Scholar] [CrossRef] - Bashir, R. Quantification of Surfactant Induced Unsaturated Flow in the Vadose Zone. Ph.D. Thesis, McMaster University, Hamilton, ON, Canada, 2007. [Google Scholar]
- Parker, J.C.; Lenhard, R.J. A model for hysteretic constitutive relations governing multiphase flow: 1. Saturation–pressure relations. Water Resour. Res.
**1987**, 23, 2187–2196. [Google Scholar] [CrossRef] - Scott, P.; Farquhar, G.; Kouwen, N. Hysteretic effects on net infiltration. In Advances in Infiltration; ASCE: Reston, VA, USA, 1983; pp. 163–170. [Google Scholar]
- Kool, J.B.; Parker, J.C. Development and evaluation of closed–form expressions for hysteretic soil hydraulic properties. Water Resour. Res.
**1987**, 23, 105–114. [Google Scholar] [CrossRef] - Werner, A.D.; Lockington, D.A. Artificial pumping errors in the Kool– Parker scaling model of soil moisture hysteresis. J. Hydrol.
**2006**, 325, 118–133. [Google Scholar] [CrossRef] - Land, C.S. Calculation of Imbibition Relative Permeability for Two– and Three–Phase Flow from Rock Properties. Soc. Pet. Eng. J.
**1968**, 8, 149–156. [Google Scholar] [CrossRef] - Lenhard, R.J.; Parker, J.C. A Model for Hysteretic Constitutive Relations Governing Multiphase Flow 2. Water Resour. Res.
**1987**, 23, 2197–2206. [Google Scholar] [CrossRef] - Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. Crop Evapotranspiration: Guidelines for Computing Crop Requirements. Irrigation and Drainage Paper No. 56; FAO: Rome, Italy, 1998. [Google Scholar]
- Rianna, G.; Reder, A.; Pagano, L. Estimating actual and potential bare soil evaporation from silty pyroclastic soils: Towards improved landslide prediction. J. Hydrol.
**2018**, 562, 193–209. [Google Scholar] [CrossRef] - Pagano, L.; Reder, A.; Rianna, G. Effects of vegetation on hydrological response of silty volcanic covers. Can. Geotech. J.
**2018**. [Google Scholar] [CrossRef] - Fredlund, D.G.; Rahardjo, H.; Fredlund, M.D. Unsaturated Soil Mechanics in Engineering Practice; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2012. [Google Scholar]
- Hopmans, J.W.; Šimůnek, J.W.; Romano, N.; Durner, W. Inverse Methods. In Methods of Soil Analysis—Part 4—Physical Methods; Dane, J.H., Topp, G.C., Eds.; SSSA Book Ser. 5; SSSA: Madison, WI, USA, 2014; pp. 963–1008. [Google Scholar]
- Šimunek, J.; Šejna, M.; Saito, H.; Sakai, M.; van Genuchten, M.T. The Hydrus–1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media. Version 4.17. Hydrus Software Series 3; Department of Environmental Sciences, University of California Riverside: Riverside, CA, USA, 2013. [Google Scholar]
- Likos, W.J.; Lu, N.; Godt, J.W. Hysteresis and Uncertainty in Soil Water–Retention Curve Parameters. J. Geotech. Geoenv. Eng.
**2014**, 140, 04013050. [Google Scholar] [CrossRef] - Gebrenegus, T.; Ghezzehei, T.A. An index for degree of hysteresis in water retention. Soil Sci. Soc. Am. J.
**2011**, 75, 2122–2127. [Google Scholar] [CrossRef] - Yang, C.; Sheng, D.; Carter, J.P. Effect of Hydraulic Hysteresis on Seepage Analysis for Unsaturated Soils. Comput. Geotech.
**2012**, 41, 36–56. [Google Scholar] [CrossRef] - Huang, H.C.; Tan, Y.C.; Liu, C.W.; Chen, C.H. A novel hysteresis model in unsaturated soil. Hydrol. Process.
**2005**, 19, 1653–1665. [Google Scholar] [CrossRef] - Reder, A.; Rianna, G.; Pagano, L. Physically based approaches incorporating evaporation for early warning predictions of rainfall–induced landslides. Nat. Hazards Earth Syst. Sci.
**2018**, 18, 613–631. [Google Scholar] [CrossRef] - Di Crescenzo, G.; Santo, A. Debris slides–rapid earth flows in the carbonate massifs of the Campania region (Southern Italy): Morphological and morphometric data for evaluating triggering susceptibility. Geomorphol.
**2005**, 66, 255–276. [Google Scholar] [CrossRef] - Reder, A.; Pagano, L.; Picarelli, L.; Rianna, G. The role of the lowermost boundary conditions in the hydrological response of shallow sloping covers. Landslides
**2017**, 14, 861–873. [Google Scholar] [CrossRef] - Feddes, R.A.; Bresler, E.; Neuman, S.P. Field test of a modified numerical model for water uptake by root systems. Water Resour. Res.
**1974**, 10, 1199–1206. [Google Scholar] [CrossRef]

**Figure 4.**First column (

**a**,

**c**,

**e**,

**g**): matric suction–volumetric water content paths observed at depth of 50 cm over four hydrological years: yellow = fall–SON (September-October-November), blue = winter–DJF (December-January-February), green = spring–MAM (March-April-May), black, red = summer–JJA (June-July-August); in the box, readings made in other years and zooms of key paths are also reported. Second column (

**b**,

**d**,

**f**,

**h**): daily precipitation and reference evaporation assessed through the FAO approach: yellow = fall–SON, blue = winter–DJF, green = spring–MAM, red = summer–JJA.

**Figure 6.**Observed (grey dots) and simulated (black line) matric suction–volumetric water content paths for the four hydrological years: 2010–2011 (

**a**), 2011–2012 (

**b**), 2012–2013 (

**c**), and 2013–2014 (

**d**). Main drying curve: red dashed line; main wetting curve: blue dot-line hatching.

**Figure 7.**Hysteresis factor as function of parameter n of the van Genuchten model. Hollow circles: data provided by literature datasets, filled circles: values calculated in the present investigation.

**Figure 8.**

**First and second row**: volumetric water content–suction (s–θ) plane;

**third row**: suction–hydraulic conductivity (s–k) plane. Black dashed line: main drying curve; dot-line hatching: main wetting curve; continuous grey line: average curve; black line: scanning paths; thick lines: paths followed in the numerical experiments.

**First column**: hydrostatic initial condition with 10 kPa at 1.5 m.

**Second column**: hydrostatic initial condition with 30 kPa at 1.5 m.

**Third column**: constant volumetric water content (0.55).

**Figure 9.**Results of analyses conducted up to suction vanishing at a depth of 1.5 m.

**First row**: cumulative infiltrated water (dotted black line: cumulated rainfall).

**Second row**: suction evolution.

**Third row**: volumetric water content evolution. Fourth row: hydraulic conductivity evolution.

**First column**: hydrostatic initial condition with 10 kPa at 1.5 m.

**Second column**: hydrostatic initial condition with 30 kPa at 1.5 m.

**Third column**: constant volumetric water content (0.55). Hydraulic behavior are identified as in Figure 8.

**Figure 10.**Calculated matric suction profiles through the soil hydrostatic initial conditions. Figures refer to different time steps (day). (

**a**) MDC; (

**b**) MWC; (

**c**) AC; (

**d**) HB.

**Table 1.**Parameters regulating the hydraulic behavior of investigated soil under the different adopted characterizations: MDC (main drying curve), MWC (main wetting curve), and AC (average curve).

Hydraulic Characterization | θ_{s} | θ_{r} | α (1/kPa) | N | k_{s} (m/s) |
---|---|---|---|---|---|

MDC | 0.679 | 0.260 | 0.07 | 1.9 | 1.00 × 10^{−6} |

MWC | 0.626 | 0.260 | 0.10 | 1.9 | 3.00 × 10^{−7} |

AC | 0.679 | 0.288 | 0.11 | 1.9 | 1.00 × 10^{−6} |

**Table 2.**Dominant factors (k

_{av}= average hydraulic conductivity; Δθ = overall water content) in case A: HB (hysteretic behavior), MDC (main drying curve), MWC (main wetting curve), and AC (average curve).

Hydraulic Characterization | Δθ | k_{av} (m/s) |
---|---|---|

HB | 0.04 | 3.90 × 10^{−7} |

MDC | 0.07 | 2.25 × 10^{−7} |

MWC | 0.11 | 1.00 × 10^{−7} |

AC | 0.12 | 2.39 × 10^{−7} |

**Table 3.**Dominant factors (k

_{av}= average hydraulic conductivity; Δθ = overall water content) and NST (null suction time) in case B: HB (hysteretic behavior), MDC (main drying curve), MWC (main wetting curve), and AC (average curve).

Hydraulic Characterization | Δθ | k_{av} (m/s) | NST (Days) |
---|---|---|---|

HB | 0.09 | 1.72 × 10^{−7} | 3.0 |

MDC | 0.13 | 2.34 × 10^{−7} | 2.8 |

MWC | 0.08 | 1.55 × 10^{−7} | 3.5 |

AC | 0.13 | 2.22 × 10^{−7} | 2.9 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rianna, G.; Comegna, L.; Pagano, L.; Picarelli, L.; Reder, A.
The Role of Hydraulic Hysteresis on the Hydrological Response of Pyroclastic Silty Covers. *Water* **2019**, *11*, 628.
https://doi.org/10.3390/w11030628

**AMA Style**

Rianna G, Comegna L, Pagano L, Picarelli L, Reder A.
The Role of Hydraulic Hysteresis on the Hydrological Response of Pyroclastic Silty Covers. *Water*. 2019; 11(3):628.
https://doi.org/10.3390/w11030628

**Chicago/Turabian Style**

Rianna, Guido, Luca Comegna, Luca Pagano, Luciano Picarelli, and Alfredo Reder.
2019. "The Role of Hydraulic Hysteresis on the Hydrological Response of Pyroclastic Silty Covers" *Water* 11, no. 3: 628.
https://doi.org/10.3390/w11030628