In the last decades, in Campania (southern
Italy), steep slopes mantled by loose air-fall pyroclastic soils
have been the seat of shallow, fast, rainfall-induced landslides. The
occurrence of such events has been the result of the combination of critical
rainstorms and of unfavourable initial conditions determined by antecedent
infiltration, evaporation, and drainage processes.
In order to understand the nature of the phenomena at hand and to clarify
the role of all influencing factors, an automatic monitoring station has
been installed in an area already subject to a recent killer flowslide
(December, 1999). The paper reports data collected in 2011 about volumetric
water content and suction (used to investigate the soil water retention
features) and rainfall depth and temperature (providing the boundary
conditions). In particular, the installation at the same depths of
tensiometers and time domain reflectometry (TDR) sensors allowed us to
recognise the hysteretic nature of the wetting and drying soil response to
weather forcing and its influence on the slope stability conditions.
The data reported in the paper are freely available at
10.5281/zenodo.4281166 (Comegna et al., 2020).
Introduction
The hydraulic response of unsaturated soils subjected to infiltration and/or
evaporation phenomena is usually modelled through the well-known Soil Water Retention Curve, SWRC,
correlating matric suction, s, with volumetric water content, θ.
Experimental evidence and theoretical considerations (e.g., Mualem, 1976;
Pham, 2002; Wheeler et al., 2003; Tami et al., 2004; Li, 2005; Tarantino,
2009; Yang et al., 2012; Pirone et al., 2014; Comegna et al., 2016c; Chen et
al., 2017, 2019; Rianna et al., 2019) indicate that the SWRC is
not univocal but may depend on soil initial conditions and on the induced
wetting or drying paths. This soil response, known as hydraulic hysteresis, may be related to
microscopic phenomena affecting the energy state of water at pore scale
(i.e. variations in contact angle during solid particle wetting and drying
or bottlenecks differently affecting filling and emptying of pores), as well
as macroscopic phenomena depending on the boundary conditions and on the
rate of the specific transient wetting and drying process (e.g. air entrapment).
Figure 1 shows the typical response of an initially saturated soil sample
subjected to drying and wetting cycles. During the first drying stage,
θ decreases from the initial value, θs,d, following a
path, known as the main drying curve, until attaining the minimum, corresponding to a high
s value, known as the residual volumetric water content, θr. In the subsequent wetting process, θ increases along a different
path, known as the main wetting curve (Fig. 1), until reaching a final maximum value,
θs,w, at s=0: θs,w is usually different from
θs,d because of some air entrapment that does not allow full
soil saturation. However, in some cases, if the wetting process is very
slow, it may occur that θs,w≅θs,d.
Typical hydraulic response of a soil sample subjected to drying
and wetting cycles. Along the main drying curve, the volumetric water content, θ,
continuously decreases with the matric suction, s, from the initial saturated
value, θs,d, until the minimum residual value, θr, is reached. Along the main wetting curve, θ continuously increases from the initial
residual value, θr , until the final maximum value, θs,w, is reached at s=0. If the continuous main drying (wetting)
stage is interrupted by a reverse wetting (drying) process, a different
scanning curve, located under (over) the main path, is travelled.
If a reverse process takes place along one of these paths, the main path is
abandoned, and a different scanning curve located between the two main paths is then
followed (Fig. 1). Scanning curves, which in turn may be characterised by
internal hysteretic loops, present a lower slope than the main curves: this
physically means that, starting from the same s value, the θ variation
corresponding to a given s change is smaller running a scanning curve rather than a main
curve. As shown in Fig. 1, the final part of a scanning path may coincide
with the nearest primary curve. This result has been experimentally
recognised by Tami et al. (2004) through some tests carried out on a
30∘ model slope consisting of a 40 cm thick layer of fine sands
overlying a 20 cm thick layer of gravelly sands and subjected to artificial
precipitation of different intensities. Figure 2a shows the scanning curves
obtained by fitting the coupled data measured by a tensiometer and a time
domain reflectometry (TDR) probe located at a depth of 30 cm (Fig. 2b)
during two consecutive drying stages (1–2, 2–3) and two consecutive wetting
stages (4–5, 5–6). The main drying and wetting curves had been independently
obtained through a Tempe cell and capillary rise tests. Therefore, the same
θ may be associated with different water potential energies, thus
with different s values within an interval defined by the highest and lowest
limits respectively imposed by the main drying curve and the main wetting
curve.
Even though often observed in laboratory experiments, the hydraulic
hysteretic response of unsaturated soils is still often neglected at slope
scale, being usually modelled by a single SWRC fitting all the available
experimental data. This choice is frequently due to the unavailability of
detailed field information. Most of the knowledge is in fact based on the
results of laboratory investigations and/or of physical modelling. These
tests, although very useful, are unavoidably not able to take into account
further aspects that could make the actual hysteretic response of natural
slopes quite different from what is observed in the lab, like the influence of
different boundary conditions, the role of root water uptake, the
atmospheric evaporative demand, etc.
Considering that the hydrological response could affect the stability
conditions of natural slopes, an automatic monitoring station was installed
in a shallow layer of loose pyroclastic soils covering a steep mountainous
area in a site of Campania Region (southern Italy), which in 1999 was the
seat of a rainfall-induced flowslide (Damiano et al., 2012). The
availability of continuous data, consisting of rainfall depth, temperature,
volumetric water content, and suction readings, allowed us to collect useful
information from January 2011 to January 2012 that has been also used
to estimate the slope stability conditions at the investigated depths.
Scanning curves (a) obtained from flume tests carried out by Tami
et al. (2004) during two consecutive drying stages (1–2, 2–3) and wetting
stages (4–5, 5–6). The 30∘ inclined model slope (b) consists of a
40 cm thick layer of fine sands that overlies a 20 cm thick layer of
gravelly sands. The volumetric water content, θ, and the matric
suction, s, are respectively measured by a time domain reflectometry (TDR)
probe and a tensiometer, both installed at a depth of 30 cm. The main drying
curve and the main wetting curve have been obtained through a Tempe cell and
capillary rise tests.
Data and methodsGeomorphological and climate framework
The investigated site is located at an elevation of 560 m a.s.l., on the
northeast facing slope of mount Cornito (Fig. 3a), 2 km from the town of
Cervinara (Campania Region, southern Italy), about 50 km northeast of
Naples. On 16 December 1999, the slope was involved in a disastrous
flowslide induced by a rainstorm of 320 mm in 50 h. The landslide body
entered the narrow Cornito stream reaching the town downslope (Fig. 3b),
where it caused heavy damage and five human deaths.
Geological surveys and geotechnical investigations reveal that the basal
Mesozoic–Cenozoic fractured limestones are overlain by air-fall sandy soils
resulting from the explosive volcanic activity of Somma–Vesuvius and
Phlegraean Fields (e.g., Fiorillo et al., 2001; Damiano et al., 2012). In
particular, the pyroclastic deposits consist of alternating layers of ashes
and pumices, more or less parallel to the bedrock surface, with a thickness
strongly dependent on the slope angle, ranging from some decimetres in the
steepest upslope zones (about 50∘ inclined) to more than 10 m at
the foot of the hill (Guadagno et al., 2011). In some verticals, some layers
were not found, possibly as a result of past landslides or of erosive
processes.
Cultivated chestnut trees are widespread on the slope except some areas
where the vegetation consists of shrubs and grass. When the tree foliage is
present, usually from May to late September, a dense underbrush grows,
mainly formed by ferns and other seasonal shrubs. In contrast, in October
leaves fall from the trees, and the underbrush disappears until the
following late spring. During late autumn and winter the ground is mostly
covered by a layer of litter, mainly originating from fallen chestnut
leaves. The seasonal variations in vegetation affect the soil hydrologic
response to meteorological forcing by (i) interception of the precipitation
and (ii) root water uptake (Comegna et al., 2013). Interception is caused by
canopy, understory, and litter. The total evapotranspiration flux,
distributed over the root depth according to the local value of soil water
potential, is highly variable throughout the year owing to the dormant
leafless vegetation in winter. Visual inspections in trenches dug during the
investigations that have been carried out on site showed that roots usually
extend across the entire soil depth up the basal limestones, with a maximum
density within the uppermost 0.50 m of soil cover becoming sparse below the
depth of 1.50 m.
Concerning climate, Fig. 4 shows mean monthly values of rainfall depth.
These have been calculated with the 2001–2017 data from the rain gauge
installed in Cervinara, at the elevation of 320 m a.s.l., by the
meteorological alert network managed by the “Functional Centre for
forecast, prevention and monitoring of risks and alerting for civil
protection” of Campania Civil Protection Agency. The mean annual rainfall
depth is around 1600 mm: as is typical of the Mediterranean climate, most
precipitation occurs between October and April, while summer is essentially
dry. Figure 4 also reports mean monthly values of temperature. Those have
been calculated with the data monitored from 1979 to 1998 by the
meteorological station of Montesarchio, managed by the National Hydrological
Service. This station is located 4 km from the test site and approximately
at the same elevation. These data have been used for the estimation with the
Thornthwaite expression (1948) of the monthly potential evapotranspiration,
PET. In particular, the estimated PET annual value is around 750 mm (Marino
et al., 2020).
Mean monthly values of rainfall depth, R, temperature, T, and
potential evapotranspiration, PET. R is calculated with the 2001–2017 data
from the rain gauge installed in Cervinara by the meteorological alert
network managed by the “Functional Centre for forecast, prevention and
monitoring of risks and alerting for civil protection” of Campania Civil
Protection Agency. T is calculated with the data monitored from 1979 to 1998
by the meteorological station of Montesarchio, managed by the National
Hydrological Service. PET is estimated with the Thornthwaite expression (1948).
Soil properties
Thanks to a number of field investigations and geotechnical laboratory tests
(carried out both on undisturbed and reconstituted soil samples), Damiano et
al. (2012) provide information about the physical and mechanical soil
properties (Table 1). In the monitored verticals, the soil deposit is 1.9 m
deep with a sloping angle of about 40∘ (Fig. 5). The local
stratigraphy consists of the following unsaturated soil layers: (1) topsoil,
10 cm thick; (2) coarse pumices, 40 cm thick; (3) ashes, 1.30 m thick; and (4) altered ashes, 10 cm thick, located just above the bedrock. The volcanic ash
is a sandy silt, the pumices are sandy gravels. The lowermost altered ashes
overlying the bedrock are representative of a deteriorated thin ash layer
with a grain size which is turning from sandy silt to clayey and silty sand,
featuring a plasticity index ranging in the interval of 10 %–30 %. The soil
porosity ranges between 50 % and 75 %. The shear strength parameters are
typical of essentially cohesionless coarse grains soils.
Main physical and mechanical properties of the pyroclastic
cover: specific unit weight, γs; unit weight, γ; porosity; cohesion, c′; friction angle, φ′.
Local stratigraphy of the monitored deposit and position of the
“Jet-fill” tensiometers (L2-1 and L2-2) and of the TDR sensors (S2-1,
S2-2). The ceramic tips of the tensiometers, L2-1 (z= 0.60 m) and L2-2 (z= 1.00), are respectively installed at the same depth, z, of the centres of
the TDR probes, S2-1 and S2-2.
Regarding the water retention properties, Fig. 6 shows the results of nine
laboratory wetting tests performed by Damiano and Olivares (2010). These
tests were carried out in the laboratory on a 40 cm thick model slope formed
with volcanic ashes taken from Cervinara and the nearby Monteforte Irpino
sloping site. The model slope, reconstituted at the maximum field porosity
of 75 % (Table 1), was subjected to artificial precipitation. The s and
θ measurements were respectively provided by a miniaturised
tensiometer and a TDR probe installed close to each other at depths from 1.5
to 8.5 cm. The initial s and θ values were respectively in the range of 15–60 kPa and 0.21–0.34 m3 m-3 (Fig. 6). Once infiltration started,
the experimental points of each test first ran a rather flat path and then
for s smaller than 4 kPa a more inclined path until full saturation. All the
points located along the steeper paths were fitted with the van Genuchten
equation (1980)
ϑ=ϑr+ϑs-ϑr1+αsnm,
where ϑs is the saturated volumetric water content, ϑr is the residual volumetric water content, and α, n, and m are fitting parameters. Assuming θs=0.75 m3 m-3 (that corresponds to the soil porosity), θr=0 (a value which is
consistent with the coarse-grained nature of the soil), and m=n-1n (according to Mualem, 1976), Table 2 shows the
best fitting α and n values. In order to help the interpretation of
the in situ hydrological response, the obtained curve will be assumed as a
possible reference main wetting curve.
Coupled values of matric suction and volumetric water content
measured during infiltration tests (Damiano and Olivares, 2010). The test
acronyms shown in the legend are those reported in the repository dataset
(Comegna et al., 2020). The main wetting curve is obtained by fitting all the
experimental points featuring matric suction values lower than 4 kPa with
the van Genuchten Eq. (1). The fitted van Genuchten parameters are shown in
Table 2.
Van Genuchten parameters (Eq. 1) fitted to the main wetting curve
shown in Fig. 6: saturated volumetric water content, θs;
residual volumetric water content, θr; and parameters α,
n, and m.
θs (m3 m-3)θr (m3 m-3)α (kPa-1)n (–)m (–)0.750.001.001.720.42Monitoring station
At the end of 2009, an automatic monitoring station was installed at the
elevation of 560 m a.s.l. next to the right side of the landslide triggered
in 1999 (Fig. 3b) to have continuous information about rainfall depth,
matric suction, and volumetric water content (Comegna et al. 2016a). Figure 7a shows a schematic representation of the installed devices, whose main
features are reported in Table 3. Rainfall was automatically recorded at a
hourly time step by a rain gauge (Fig. 7b) having a sensitivity of 0.2 mm.
Suction was measured by two “Jet-fill” tensiometers equipped with tension
transducers (Fig. 7c). The 7 cm long ceramic tips of the tensiometers, named
L2-1 and L2-2 (Fig. 5), were pushed into the soil at the depths z= 0.60 m and z= 1.00 m through small holes previously dug by a drill. The
uppermost part of the hole was then filled with a bentonite–cement mixture
to avoid any water infiltration. A careful maintenance was granted by
regularly checking the complete saturation of the instruments (especially
after long-lasting dry periods) and filling the tube with de-aired water in
order to remove air bubbles. Moreover, the instruments were carefully
checked during the coldest periods featuring temperatures lower than
0 ∘C when the de-aired water contained in the upper part of the
hydraulic circuit of the tensiometers could freeze, thus affecting the
correctness of the pressure transducer reading. If it occurred, we made note
of that in order to give a correct interpretation of the corresponding
registered data. During the cold periods we also controlled the
expanded volume of ice so that it did not break either the pressure transducer or the
plexiglass tensiometer tubes. Volumetric water content was measured by two
probes for time domain reflectometry (TDR), named S2-1 and S2-2 (Fig. 5),
that were installed in a row with the tensiometers at a distance of 30 cm
from them. Each sensor consists of three 40 cm long metallic rods (Fig. 7d)
having a diameter of 3 mm and spacing of 15 mm. The centres of S2-1 and S2-2
were respectively installed at the same depth of the ceramic tips of L2-1
and L2-2 (Fig. 5). Once vertically buried in the soil, the TDR probes were
connected through coaxial cables and a multiplexer to a Campbell Scientific
Inc. TDR-100 reflectometer (Fig. 7e). TDR readings provide the soil bulk
dielectric permittivity, εr, which can be converted to
θ through a calibration relationship (Topp et al., 1980). A specific
relationship was purposely found by Guida et al. (2012) through targeted
laboratory tests on undisturbed samples taken near the monitoring station;
the average error in the estimation of θ is ±0.02 m3 m-3. All the sensors were connected to the Campbell data logger
located about 5 m away (Fig. 7e). The monitoring station was powered by a
solar panel with a 12 V backup battery. The automatic acquisition and storage
of data were set with a time resolution of 6 h.
Hourly air temperature data are also available and are provided by the
Pietrastornina weather station (located at 495 m a.s.l. and 15 km from
Cervinara) that is managed by the “Functional Centre for forecast,
prevention and monitoring of risks and alerting for civil protection” of
Campania Civil Protection Agency.
Installed instruments: (a) schematic representation; (b) rain gauge;
(c) Jet-fill tensiometer; (d) TDR probe; and (e) data logger case. The main
features of the electronic instruments are reported by Table 3.
Main characteristics of the installed electronic
instruments.
Electronic sensorsCompanyModelMeasurement rangeTemperature rangeAccuracyData logger and dataacquisition systemCampbell ScientificInc. (Logan, UT, USA)CR-1000–-25 to +50 ∘C± (0.06 % of reading + offset) at0 to 40 ∘C for analogue voltageTime domain reflectometerCampbell ScientificInc. (Logan, UT, USA)TDR-100-2 to 2100 m (distance) and 0 to 7 µs (time)-40 to +55 ∘C±0.02 m3 m-3Multiplexer for TDRsystemCampbell ScientificInc. (Logan, UT, USA)SDM8 × 508-Channel-40 to +55 ∘CNot definedTension transducerSoil Moisture Equipment Corp. (Goleta, CA, USA)53010–85 cbar0 to +60 ∘C0.25 %Rain gaugeCampbell ScientificInc. (Logan, UT, USA)ARG1000–500 mm h-1–98 % at 20 mm h-1, 96 % at 50 mm h-1, 95 % at 120 mm h-1
The monitored s and θ data have been then used to carry out some
analyses aimed at estimating the slope stability conditions. In particular,
the factor of safety, FS (z;t), at depth z and time t has been calculated by the
following formula provided by the simplified infinite slope model that is
suitable for Cervinara slope (Greco et al., 2013; Comegna et al., 2016b):
FS(z;t)=tanφ′tanα+capp(z;t)γ⋅z⋅senα⋅cosα,
where φ′ is the friction angle, α is the slope angle, and
γ is the unit weight of the deposit (assumed homogeneous), while
capp, known as apparent cohesion, is a strength component changing with time according to
the s and θ variations. Vanapalli et al. (1996) provide the following expression for capp:
capp(z;t)=s(z;t)⋅ϑ(z;t)-ϑrϑs-ϑr⋅tanφ′.
Therefore, capp, and consequently FS, decreases with s due to
infiltration. Moreover, being an assigned FS obtained by different couples
of s and θ, it is possible to plot on a water retention plane
different iso–FS curves that could help to determine the current slope
stability conditions.
The following section (Sect. 3) describes the field data collected from 1 January 2011 to 31 January 2012: this period has been chosen
because of the abundance of data useful for a correct interpretation of the
annual hydrological response.
Section 4 reports some considerations concerning the influence of the
monitored hydraulic hysteresis on the slope stability conditions.
Results of field monitoring
Figure 8 shows the monthly cumulative precipitation in 2011 provided by the
rain gauge installed on the slope. The total cumulative rainfall was 1360 mm, a value lower than the mean yearly rainfall in the same area (Fig. 4).
A daily precipitation higher than 1 mm was recorded 99 times; the daily
rainfall exceeded the value of 50 mm only in five cases (16 February,
30 April, 19 September, 6 November,
5 December). March was the rainiest month, with a total
precipitation of 296 mm, i.e. 22 % of the yearly rainfall. The dry season
started in June, continuing until the end of October. In this season some
significant isolated rainy events characterised by daily precipitation
ranging between 17.4 and 19.2 mm occurred on 29 July, 7 September,
8 October, and 22 October; another more severe event
totalling 53 mm took place on 19 September. In the time interval
November–December, the cumulative rainfall was about 30 % of the annual
precipitation: the most intense daily rainfall occurred on 6 November (58 mm). Figure 8 also shows the average monthly values of minimum,
daily mean, and maximum temperature monitored at a hourly scale by the
Pietrastornina weather station. The daily mean air temperature was close to
average with a slightly warmer summer. The potential evapotranspiration can
hence be assumed to be close to the average estimated values shown in Fig. 4. In particular, the mean daily temperature was higher than 15 ∘C
from 19 May to 7 October, attaining values higher than
20 ∘C from 30 July to 18 September. The lowest
and highest average values were respectively measured in February (4 ∘C), and in August (31 ∘C). Although there are some
discrepancies due to the distance of the Pietrastornina weather station from
the investigated slope, the temperature date elaborated above can be
considered reliable.
Monthly cumulative rainfall and average monthly minimum
(Tmin), daily mean (Tmean), and maximum (Tmax) values of air
temperature monitored in 2011. Tmin, Tmean, and Tmax are
calculated with the data monitored by the Pietrastornina weather station
managed by the “Functional Centre for forecast, prevention and monitoring
of risks and alerting for civil protection” of Campania Civil Protection
Agency.
The information obtained by coupling θ and s data monitored at both
the investigated depths of 0.60 and 1.00 m is discussed in the following
subsections by distinguishing eight time windows characterised by different
weather conditions. For the sake of clarity, it has to be pointed out that the
tensiometers and the TDR probes sample different soil volumes; this might
lead to an imperfect matching of data. Due to some technical problems
related to the emptying of the tensiometers (occurring especially during the
warmest periods) or to some loss in battery power, the records present some
missing data. In particular, unfortunately no retention data are available
from 19 July to 4 November 2011 and from 6 December 2011 to 6 January 2012. Despite the gap, it allowed us to
recognise important aspects of the hysteretic hydrologic response of the
investigated deposit.
Time window A–B: 1 January–8 May 2011
The total precipitation in this time interval was 695 mm, which corresponds
to 51 % of the annual cumulative value. Until 12 March, the mean
daily air temperature ranges between 0.5 and 12.8 ∘C
(Fig. 9a), and then it steadily increases from 5.8 to
16.7 ∘C (with an increasing trend of 1.8 ∘C per month).
On 1 January, the θ and s values measured by S2-1 and L2-1 at
a depth of 0.60 m are respectively 0.39 m3 m-3 and 11 kPa (Fig. 9b).
These values are the result of the antecedent weather conditions; in
particular, the total precipitation in the previous 30 d had been 170 mm
and the mean daily air temperature 7 ∘C (Fig. 9a). As shown in
Fig. 9b, the θ measured in the examined window is 0.34–0.41 m3 m-3, while s ranges in the interval 3–16 kPa. During the dry
days, θ decreases with a rate of -1 % per month, while s tends to increase at an average rate of about 1.4 kPa per month. This drying path is
periodically reversed by some rainfall-induced wetting processes. In
particular, three sudden s drops are recorded on 23 January,
17 February, and 1 May due to very similar rainfall events
featuring a total precipitation of 48–58 mm cumulated over the antecedent
48 h.
At a depth of 1.00 m, θ, measured by S2-2, and s, measured by L2-2,
range respectively in the intervals 0.29–0.37 m3 m-3 and 4–16 kPa
(Fig. 9c). θ tends to decrease by -0.8 % per month, while s is
increasing at an average rate of about 1.0 kPa per month. These trends are
hence slower than at the shallower depth. This reflects a minor role of
evapotranspiration during winter and early spring (when the vegetation is
leafless). In this period, the soil profile is mainly drained downward by
gravity except during rainfall when the capillary gradient favours rapid
infiltration. The small variations in θ and s at both depths, despite
the large amount of precipitation, suggest that the soil cover is being
crossed by an intense downward flux without being retained (or being
retained only in a little part). Rainfall events can cause just temporary
small increments of θ followed by slower reductions. Indeed, at both
depths θ is steadily higher than the field capacity (i.e. about 0.25 m3 m-3).
All data have been reported in the water retention plane s–θ, shown
in Fig. 10a and b, together with the corresponding manual fitting
curves, named AB. At both investigated depths, the curve AB is quite flat
with an overall slope of about -0.4 % kPa-1.
Time window B–C: 8 May–22 June 2011
This window features a cumulative rainfall of 85 mm and a daily air
temperature ranging in the interval 10–24 ∘C, with an increasing
trend of 4.3 ∘C per month (Fig. 9a). During this season, vegetation
starts flourishing, thus accommodating the increasing evapotranspiration
demand and influencing the hydrological soil response through root water
uptake. The actual evapotranspiration may approach the limiting PET value
but very likely never reaches it because the atmospheric demand is not
fulfilled by soil water.
At depth z= 0.60 m, s ranges between 10 and 24 kPa, growing at a
rate of about 9 kPa per month. This matches a θ reduction that reaches the value of 0.25 m3 m-3 with a decreasing trend of -9 % per month
(Fig. 9b), which is more pronounced than during the previous time window due
to an intense root water uptake from the uppermost soil layer. Collected
data were fitted by the curve BC in Fig. 10a provided by Eq. (1),
identifying the best fitting α and n parameters shown in Table 4
(assuming again θs= 0.75 m3 m-3, θr=0, and m=n-1n). The path BC is clearly steeper than
the curve AB.
Van Genuchten parameters (Eq. 1) fitted to the curve BCD shown in
Fig. 10a: saturated volumetric water content, θs; residual
volumetric water content, θr; and parameters, α, n, and m.
At depth z= 1.00 m (Fig. 9c), until 6 June, θ and s
display little variations, moving respectively from 0.33 to
0.31 m3 m-3 and from 15 to 17 kPa. Measured values are again
well fitted by the curve AB (Fig. 10b). After this period, which is probably
still characterised by some gravitational downward drainage, the soil starts
drying quickly at this depth too, being forced by root water uptake. The
water content decreases at a rate of about -4 % per month, attaining a value
of 0.27 m3 m-3 at the end of this time window, while the
increasing s rate is similar to the one observed at 0.60 m. These data are
well fitted by the path CD (Fig. 10b), which is steeper than the path AB
but gentler than the curve BCD detected at 0.60 m because of a lower
evapotranspiration effect. The fitting parameters are reported in Table 5.
Besides evapotranspiration effects, the different responses observed at
the two depths might be justified also by small differences in grain size
and/or void ratio of the soil (Comegna et al., 2016a).
Van Genuchten parameters (Eq. 1) fitted to the curve CD shown in
Fig. 10b: saturated volumetric water content, θs; residual
volumetric water content, θr; and parameters, α, n, and m.
In this dry time interval the average daily temperature is 23.7 ∘C
with an increasing trend of 3.3 ∘C per month, and the cumulative
rainfall is 14 mm (Fig. 9a). The flourishing vegetation and the high
temperature suggest that evapotranspiration largely exceeds infiltration by
rainwater, causing drainage of the soil cover.
At z= 0.60 m, θ reaches a value of 0.17 m3 m-3, while s grows by about 22 kPa per month until a value of 35 kPa (Fig. 9b). It is worth noting that in the retention plane the path BC can properly fit recorded field data (Fig. 10a). At z= 1.0 m, θ reaches the value of 0.24 m3 m-3, while s increases with a rate of about 13 kPa per month, attaining a value of 34 kPa (Fig. 9c). In the retention plane, the field
data are well interpolated by the curve CD (Fig. 10b).
Hourly weather data (a), matric suction and volumetric water
content monitored from January to July 2011 at depth z= 0.60 m (b) and z= 1.00 (c), and factor of safety, FS (d), calculated by Eq. (2), provided by
the simplified infinite slope model, and assuming a homogeneous deposit with
slope angle α=40∘, unit weight γ=14 kN m-3, cohesion c′=0, friction angle φ′=38∘, θs=0.75 m3 m-3, and θr=0.
Volumetric water content and matric suction recorded from January
to July 2011 at depths z= 0.60 m (a) and z= 1.00 m (b) and iso–safety-factor curves. The main drying curve at z= 0.60 m is obtained by fitting
with Eq. (1) all the experimental points monitored from 8 May to
18 July 2011 (the fitted parameters are shown in Table 4). The main drying
curve at z= 1.00 m is obtained by fitting with Eq. (1) all the
experimental points monitored from 7 June to 18 July 2011 (the fitted
parameters are shown in Table 5). The main wetting curves at both depths
coincide with that derived by the infiltration tests (Damiano and Olivares,
2010) shown in Fig. 6. The safety factor, FS, is calculated by Eq. (2),
provided by the simplified infinite slope model assuming a homogeneous
deposit with slope angle α=40∘, unit weight γ=14 kN m-3, cohesion c′=0, friction angle φ′=38∘, θs=0.75 m3 m-3, and θr=0.
Time window E–F: 5–6 November 2011
In the time interval from 19 July to 4 November, during
which, as already stated, monitoring of θ and s stops, the air
temperature goes from the mean value of 24.6 ∘C, reached in
August, to 14.4 ∘C, in October. Regarding precipitation, from
September to October the rain gauge records a cumulative precipitation of
168 mm falling on only 9 isolated rainy days (Fig. 11a). Such
concentrated precipitation seems to have been recorded by the shallowest
sensors only. In fact, if the data acquired on 5 November are
compared to those monitored on 18 July, we can notice a θ
increase (from 0.17 to 0.24 m3 m-3) and an s decrease (from 35 to 22 kPa) at 0.60 m (Fig. 11b), while the sensors at z= 1.00 m (Fig. 11c)
record a small water content decrease (from 0.24 to 0.23 m3 m-3)
and an s increase (from 34 to 47 kPa).
The most intense daily rainfall in 2011 takes place on 6 November.
The total precipitation is 58 mm (Fig. 11a) and causes a θ increase
from 0.24 to 0.43 m3 m-3 (Fig. 11b) at 0.6 m and from 0.23 to
0.27 m3 m-3 at 1.0 m (Fig. 11c). At both depths the highest drop
in s is recorded; in fact, the decrease measured by L2-1 is from 22 kPa to
1.9 kPa (Fig. 11b), and the one recorded by L2-2 is from 47 to 13 kPa
(Fig. 11c). These data are represented in the water retention plane by the
paths EF (Fig. 12a and b) and are very different from those run in May and June.
It is worth noting that at the shallowest depth, the final point F reaches
the main wetting curve obtained by interpolating the flume tests described
in Sect. 2 (Fig. 5).
Time window F–G: 6 November–3 December 2011
This time interval is characterised by dry weather. In fact, one single
rainfall event only of 12 mm occurs on 22 November. The mean
temperature is about 10 ∘C. During this period, when the leaves of
deciduous trees fall, the vegetation enters a dormant phase, during which
very little water is needed. Hence, the atmospheric evapotranspiration
demand that is small, as is typical of winter months, is likely larger than the
amount of water actually extracted from the soil by the vegetation. An
essentially downward flow, initially driven by a high potential gradient due
to a wetter uppermost soil profile, is consequently favoured and then
progressively approaches a slow gravity-driven drainage. In fact, at z= 0.60 m, θ decreases from 0.43 to 0.28 m3 m-3, while s
increases from 1.9 to 20 kPa (Fig. 11b). In the water retention plane,
the corresponding drying path FG is located above the previous wetting path EF and is
about parallel to it (Fig. 12a). It is worth noting that at point G it
reaches the BCD curve running from May to July, confirming that drying
develops according to smoother paths and gently approaches the field
capacity (about 0.25 m3 m-3) when soil drainage is not forced by
root water uptake.
At z= 1.00 m, θ decreases from 0.27 to 0.25 m3 m-3, and s increases from 13 to 19 kPa (Fig. 11c). The corresponding drying path FG pursues backwards the previous path EF (Fig. 12b).
Time window G–H: 3–5 December 2011
On 5 December, after a precipitation of 98 mm in 48 h, θ
increases at both depths. In particular, at z= 0.60 m θ grows
from 0.28 to 0.40 m3 m-3, and s drops to 2.5 kPa (Fig. 11b). The
wetting curve GH overlaps the previous FG drying path (Fig. 12a). Again, the
final point H reaches the assumed main wetting curve.
At z= 1.00 m θ increases from 0.25 to 0.36 m3 m-3, less than above, while s decreases to 4.5 kPa. The final point H does not reach the assumed main wetting curve (Fig. 12b).
Time window H–I: 5–11 December 2011
No precipitation occur during this short time window. Available data concern
only depth z= 1.00 m. θ decreases from 0.36 to 0.31 m3 m-3, and s increases to 10 kPa (Fig. 11c). The drying path HI is located above and parallel to the wetting path GH (Fig. 12b).
Time window L–M: 7 January–31 January 2012
This period is characterised by negligible evapotranspiration owing to cold
temperatures and leafless vegetation. Hence, the observed θ and s
trends may be ascribed to gravitational downward drainage, which in the long
run would lead the soil cover to approach field capacity. Until 21 January 2012 s increases from 6 to 13 kPa at z= 0.60 m and from 10
to 14 kPa at z= 1.00 m. On that date, a 12 h cumulative 16 mm
rainfall causes a drop in s of 6 and 3 kPa respectively at the shallowest
and deepest tensiometers. Then s increases again until the final values of 12 kPa (z= 0.60 m) and 13 kPa (z= 1.00 m) associated with θ of 0.32 and 0.31 m3 m-3. All field data are quite well interpolated by the paths GH at z= 0.60 m (Fig. 12a) and HI at z= 1.00 m (Fig. 12b).
Monitored hourly weather data (a), matric suction and volumetric
water content from November 2011 to January 2012 at the depth z= 0.60 m
(b) and z= 1.00 (c), and factor of safety, FS (d), calculated by Eq. (2),
provided by the simplified infinite slope model, and assuming a homogeneous
deposit with slope angle α=40∘, unit weight γ=14 kN m-3, cohesion c′=0, friction angle φ′=38∘, θs=0.75 m3 m-3, and θr=0.
Volumetric water content and matric suction monitored from
November 2011 to January 2012 at depths z= 0.60 m (a) and z= 1.00 m
(b) and iso–safety factor curves. The main drying curve at z= 0.60 m is
obtained by fitting with Eq. (1) all the experimental points monitored from
8 May to 18 July 2011 (the fitted parameters are shown in Table 4). The
main drying curve at z= 1.00 m is obtained by fitting with Eq. (1) all
the experimental points monitored from 7 June to 18 July 2011 (the fitted
parameters are shown in Table 5). The main wetting curves at both depths
coincide with that derived by the infiltration tests (Damiano and Olivares,
2010) shown in Fig. 6. The safety factor, FS, has been calculated by Eq. (2), provided by the simplified infinite slope model and assuming a homogeneous
deposit with slope angle α=40∘, unit weight γ=14 kN m-3, cohesion c′=0, friction angle φ′=38∘, θs=0.75 m3 m-3, and θr=0.
Discussion
The paths plotted in Figs. 10 and 12 show that, at different times,
different values of s have been observed at both instrumented depths for the
same θ. The relationship between these two variables is then not
univocal. In particular, the difference depends on the initial conditions
(i.e. on the starting point). This reveals the hysteretic nature of the
hydrological soil response.
Therefore, all obtained paths should be considered as scanning curves
located between the main drying and the main wetting curve. In more detail,
the steepest drying paths obtained during the warmest days as a result of
intense evapotranspiration owing to flourishing vegetation (curve BCD at z= 0.60 m; curve CD at z= 1.00 m) tend to the assumed main drying curve.
It is also interesting to notice that, at 1.0 m depth, this final steeper
path is reached on 6 June, i.e. with a delay of about 1 month with
respect to the shallowest depth (where it was attained on 8 May). Such a result could be related to the delayed and mitigated
effect of evapotranspiration due to the water uptake by roots, which are
denser at depths less than 0.50 m but are present down to a depth of 1.50 m
more or less. During the periods of leafless vegetation and low
temperatures when the amount of evapotranspiration is modest, the drying
paths are less steep and well below the assumed upper boundary.
According to our field data, the internal hysteresis is not particularly
relevant. However, some little differences between the drying and the
wetting scanning paths have been recognised at both depths when the highest
θ is attained next to the main wetting curve. In particular, Fig. 10a shows that the scanning path observed at depth z= 0.60 m after the
rainfall event finished on 6 November (curve FG) is above that
previously monitored (curve EF); Fig. 10b shows that the scanning path
observed at depth z= 1.00 m after the rainfall event completed on
5 December (curve HM) is above the one monitored before that (curve
EH).
For the sake of clarity, it has to be pointed out that the tensiometers and the
TDR probes sample different soil volumes; this might lead to an imperfect
matching of data, i.e. any variation in s and in θ is not
simultaneously detected by the sensors. For instance, if the wetting front
advances downward, the 40 cm long TDR probe can detect it somewhat earlier
compared to the ceramic tip of the tensiometers (the centres of the two
sensors are aligned so the upper edge of the TDR probe is above the upper
edge of the tip). The temporal mismatch will be larger for steeper wetting
fronts. A similar issue would affect the edges of the sensors during vertical
(gravity-driven) drainage processes, while soil drying caused by root uptake
is expected to be more evenly distributed throughout the entire root zone.
These issues would certainly affect the coupling, especially in the initial
stage of infiltration and the drainage process, which are characterised by
steeper gradients. However, the measurements are acquired every 6 h,
and looking at Figs. 9 and 11, it appears that s and θ variations
at the two investigated depths 40 cm apart from each other are detected
nearly simultaneously. Hence, it is expected that the temporal mismatch may
affect only one or two measurement points during each of the wetting and drying
paths discussed in Figs. 10 and 11, which consist of many measurement
points as they refer to long lasting processes.
In order to estimate to what extent the slope stability conditions are
affected by the hysteretic response, some simple analyses have been carried
out by the infinite slope model. In particular, the factor of safety FS at
depth z has been calculated by Eq. (2). Assuming a homogeneous deposit with
slope angle α=40∘, unit weight γ=14 kN m-3, cohesion c′=0, friction angle φ′=38∘, θs=0.75 m3 m-3, and θr=0, the
variation of FS with time is only due to fluctuations of the apparent
cohesion, capp. In particular, φ′ being lower than α,
FS remains higher than 1 only if capp is higher than a threshold value
that could be calculated by Eq. (2). Regarding the examined case, at depths
z= 0.60 m and z= 1.00 m, slope stability is guaranteed respectively by
capp>0.3 kPa and capp>0.5 kPa.
Figures 9d and 11d show the fluctuations of FS during the period of
monitoring. At z= 0.60 m, FS ranges between a minimum value of 1.13,
attained on 6 November (Fig. 11d), and a maximum of 2.22 on 5 July,
(Fig. 9d), which respectively correspond to capp values of 0.8
and 6.6 kPa. At z= 1.00 m, FS ranges between 1.18 and 2.60 on 5 December and on 5 November (Fig. 11d), corresponding to a
capp interval of 1.5–11.6 kPa. The higher fluctuation of FS at the
shallowest depth, z= 0.60 m is obviously due to a higher s variation.
In Figs. 10 and 12 the iso–safety-factor curves, i.e. featuring constant
FS values, have been plotted. For a given s, FS increases with θ: this
means that the lower scanning curves correspond to worse safety conditions.
For instance, looking at Fig. 12, the FS values calculated along the
wetting path EF, which originates after the dry season, are lower than those
corresponding to the drying curve LM that starts after the rainfall events
occurring in November and in December; also, the changing rate of FS is
always remarkable along the scanning paths where little θ changes
can induce high s changes.
It is interesting to notice that the lowest FS value is attained at z= 0.60 m on 6 November, i.e. after the most intense rainfall event
recorded in 2011, when the wetting path reaches the assumed lower boundary
at point F (Fig. 12a), featuring s= 1.9 kPa and θ=0.43 m3 m-3. Starting from this condition, a further only hypothetical,
persistent, and intense rainfall event could have forced the point to follow
the final steeper branch of the main wetting curve. In particular, the
failure condition (FS = 1) would have been reached for θ=0.69 m3 m-3 (s= 0.40 kPa), i.e. for an increase Δθ=0.26 m3 m-3 (or a decrease Δs=-1.5 kPa). Such a
large increase in the water content indicates that landsliding in the area
at hand is not so obvious, being the consequence of exceptional weather
conditions as chronicles and statistical analyses suggest (Comegna et al.,
2017).
Data availability
The datasets, freely downloadable from https://doi.org/10.5281/zenodo.4281166 (Comegna et al., 2020), are
provided through the following five separate Excel files:
1_Field data_rainfall, containing the hourly
rainfall measured in the considered time period (1 January 2011–31 January 2012) by the rain gauge;
2_Field data_temperature, containing the
hourly temperature measured in the considered time period (1 January 2011–31 January 2012) by the weather station located
in the town of Pietrastornina and managed by the regional Civil Protection
Agency;
3_Field data_suction & moisture
content_z=0.6m, containing s and θ measured in the
considered time period (1 January 2011–31 January 2012)
at the depth z= 0.60 m respectively by tensiometer L2-1 and TDR probe
S2-1 at a time resolution of 6 h;
4_Field data_suction & moisture
content_z=1.0m, containing s and θ measured in the
considered time period (1 January 2011–31 January 2012)
at the depth z= 0.60 m respectively by tensiometer L2-2 and TDR probe
S2-2 at a time resolution of 6 h;
5_Flume infiltration tests, containing the s and θ
measured during nine flume tests induced by an artificial rainwater
infiltration, carried out by Damiano and Olivares (2010).
Conclusions
The set-up of an automatic field station allowed us to monitor the annual cyclic
hydrological response of a sloping deposit in pyroclastic air-fall soils.
Even though the relationship between measured volumetric water content and
suction values has to be carefully considered and has to account for all the factors
which can adversely affect its validity (small differences in grain size or
porosity, which is dependent also on the installation procedures of the
sensors in the soil; different soil volumes affecting the response of
sensors; different reliability in data interpretation), monitoring provided
useful information about the hydrological soil response.
In particular, collected data highlight the influence of the initial
conditions, which depend on the antecedent wetting and drying history and on the
weather-induced hydraulic paths. In fact, different volumetric water
contents can be associated with the same matric suction due to the
hysteretic soil response. Moreover, soil drying may be affected by
evapotranspiration due to water extraction by roots, which varies throughout
the seasons.
As indicated by simple stability analyses, in the examined period the slope
has been far from failure conditions. In particular, the hydraulic path
leading to slope failure should feature quite high volumetric water
content changes. This is very detectable by TDR sensors but is
characterised by suction changes that are so low (less than 2 kPa) and that are hardly
measurable by ordinary tensiometers. These results unavoidably raise some
questions on the best way to set up reliable early warning systems in areas
threatened by rapid landslides in shallow unsaturated granular soil covers.
These systems should be indeed based on (i) a monitoring system able to
provide real time updates about the weather-induced hydraulic paths and (ii) a forecasting model accounting for the soil water retention properties. Both
should be supported by the knowledge of the main drying and wetting curves
that bound the water retention domain.
Author contributions
LC, ED, RG, and LO installed the automatic monitoring station and took care
of the maintenance of the instruments. LC analysed the monitored field
data. ED and LO analysed the results of the laboratory infiltration tests to
assume a reliable main wetting curve. LC and LP jointly conceived and set up
the paper, discussing the issues with the other three authors. RG provided
considerations about the role of vegetation. The contributions of the
authors are equal.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The “Functional Centre for forecast, prevention and monitoring of risks and
alerting for civil protection” of Campania Civil Protection Agency is
gratefully acknowledged for providing temperature data.
The authors thank the four anonymous reviewers for their insightful comments
and suggestions that improved the quality of the manuscript.
Financial support
This research has been supported by the program VALERE 2019, financed by the Università degli Studi della Campania “Luigi Vanvitelli” (project title SEND).
Review statement
This paper was edited by Giulio G.R. Iovine and reviewed by four anonymous referees.
ReferencesChen, P., Mirus, B., Ning, L., and Godt, J. W.: Effect of Hydraulic
Hysteresis on Stability of Infinite Slopes under Steady Infiltration,
J. Geotech. Geoenviron. Eng., 143, 04017041,
10.1061/(ASCE)GT.1943-5606.0001724, 2017.Chen, P., Ning, L, and Wei, C.: General Scanning Hysteresis Model for
Soil–Water Retention Curves, Journal of Geotechnical and Geoenvironmental
Engineering, 145(12), 10.1061/(ASCE)GT.1943-5606.0002184, 2019.Comegna, L., Damiano, E., Greco, R., Guida A., Olivares, L., and Picarelli,
L.: Effects of the vegetation on the hydrological behavior of a loose
pyroclastic deposit, Procedia Environ. Sci., 19, 922–931,
10.1016/j.proenv.2013.06.102, 2013.Comegna, L., Damiano, E., Greco, R., Guida A., Olivares, L., and Picarelli,
L.: Field hydrological monitoring of a sloping shallow pyroclastic deposit,
Can. Geotech. J., 53, 1125–1137, 10.1139/cgj-2015-0344,
2016a.Comegna, L., Damiano, E., Greco, R., Guida A., Olivares, L., and Picarelli,
L.: Considerations on the Cervinara slope failure, Landslides and Engineered
Slopes – Experience, Theory and Practice, 2, 663–670,
10.1201/9781315375007, 2016b.Comegna, L., Rianna, G., Lee, S., and Picarelli, L.: Influence of the
wetting path on the mechanical response of shallow unsaturated sloping
covers, Comput. Geotech., 73, 164–169,
10.1016/j.compgeo.2015.11.026, 2016c.Comegna, L., De Falco, M., Jalayer, F., Picarelli, L., and Santo A.: The
role of the precipitation history on landslide triggering in unsaturated
pyroclastic soils, Advancing Culture of Living with Landslides, 4,
307–313, 10.1007/978-3-319-53485-5_35, 2017.Comegna, L., Damiano, E., Greco, R., Olivares, L., and Picarelli, L.:
Coupled monitoring of soil moisture and suction in pyroclastic air-fall
silty soils, Zenodo, 10.5281/zenodo.4281166, 2020.
Damiano, E.: Meccanismi di innesco di colate di fango in terreni
piroclastici, PhD Thesis, Università di Roma La Sapienza, 2004.
Damiano, E. and Olivares, L.: The role of infiltration processes in steep
slope stability of pyroclastic granular soils: laboratory and numerical
investigation, Nat. Hazards, 52, 329–350, 2010.
Damiano, E., Olivares, L., and Picarelli L.: Steep-slope monitoring in
unsaturated pyroclastic soils, Eng. Geol., 137–138, 1–12, 2012.Fiorillo, F., Guadagno, F. M., Aquino, S., and De Blasio, A.: The December
1999 Cervinara landslides: further debris flows in the pyroclastic deposits
of Campania (southern Italy), B. Eng. Geol.
Environ., 60, 171–184, 10.1007/s100640000093, 2001.Greco, R., Comegna, L., Damiano, E., Guida, A., Olivares, L., and Picarelli, L.: Hydrological modelling of a slope covered with shallow pyroclastic deposits from field monitoring data, Hydrol. Earth Syst. Sci., 17, 4001–4013, 10.5194/hess-17-4001-2013, 2013.Guadagno, F. M., Revellino, P., and Grelle, G.: The 1998 Sarno landslides:
conflicting interpretations of a natural event, Proceedings of the 5th
International Conference on Debris-Flow Hazards Mitigation: Mechanics,
Prediction and Assessment, Italian Journal of Engineering Geology and
Environment, Casa Editrice Universita La Sapienza, 10.4408/IJEGE.2011-03.B-009, 2011.
Guida, A., Comegna, L., Damiano, E., Greco, R., Olivares, L., and Picarelli,
L: Soil characterization from monitoring over steep slopes in layered
granular volcanic deposits, Proceedings of the 2nd Italian Workshop on
Landslides, Naples, 28–30 September 2011, edited by: Picarelli, L., Greco, R.,
and Urciuoli, G., Cooperativa Universitaria Editrice Studi, Fisciano,
147–153, 2012.
Li, X. S.: Modelling of hysteresis response for arbitrary wetting/drying paths,
Comput. Geotech., 32, 133–137, 2005.Marino, P., Comegna, L., Damiano, E., Olivares, L., and Greco, R.:
Monitoring the hydrological balance of a landslide-prone slope covered by
pyroclastic deposits over limestone fractured bedrock, Water, 12, 3309, 10.3390/w12123309, 2020.
Mualem, Y.: Hysteretical models for prediction of the hydraulic conductivity
of unsaturated porous media, Water Resour. Res., 12, 1248–1254, 1976.
Pham, H. Q.: An engineering model of hysteresis for soil–water
characteristic curves, MSc thesis University of Saskatchewan, Canada, 2002.
Pirone, M., Papa, R., Nicotera, M. V., and Urciuoli, G.: Evaluation of the
hydraulic hysteresis of unsaturated pyroclastic soils by in situ
measurements, Proced. Earth Plan. Sci., 9, 163–170, 2014.Rianna, G., Comegna, L., Pagano, L., Picarelli, L., and Reder, A.: The role
of hydraulic hysteresis on the hydrological response of pyroclastic silty
covers, Water, 11, 628, 10.3390/w11030628, 2019.
Tami, D., Rahardjo, H., and Leong, E. C.: Effects of hysteresis on
steady-state infiltration in unsaturated slopes, J. Geotech. Geoenviron. Eng.,
130, 956–966, 2004.
Tarantino, A.: A water retention model for deformable soils,
Géotechnique, 59, 751–762, 2009.
Thornthwaite, C. W.: An approach toward a rational classification of climate,
Geogr. Rev., 38, 55–94, 1948.
Topp, G. C., Davis, J. L., and Annan, A. P.: Electromagnetic determination of
soil water content: measurement in coaxial transmission lines, Water Resour.
Res., 16, 574–582, 1980.
van Genuchten, M. T.: A closed-form equation for predicting the hydraulic
conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892–898, 1980.
Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E., and Clifton, A. W.: Model for
the prediction of shear strength with respect to soil suction, Can.
Geotech. J., 33, 379–392, 1996.
Wheeler, S. J., Sharma, R. S., and Buisson, M. S. R.: Coupling of hydraulic
hysteresis and stress–strain behaviour in unsaturated soils,
Géotechnique, 53, 41–54, 2003.
Yang, C., Sheng, D., and Carter, J. P.: Effect of hydraulic hysteresis on
seepage analysis for unsaturated soils, Comput. Geotech., 41,
36–56, 2012.