Foreword

Fine-grained deposits extensively outcrop in Mediterranean countries where slow moving slides and earthflows are very usual slope movements. In particular, they are widespread along the Apennines chain in Italy (Picarelli et al. 1998), often located along the banks of rivers. Due to both river erosion and/or precipitations, they may be active over hundreds of years with an average rate of a few centimetres per year (Picarelli and Russo 2004). However, even though their annual cumulative displacement fluctuates around a practically constant value, the rate measured over much shorter time lengths is quite variable, showing peaks in the wet season and deceleration during the dry season. This behaviour depends on pore pressure fluctuations, which govern the shear stress level, and are in turn governed by weather conditions.

The risk posed by slow moving landslides is very low being a natural condition for some populations living in marginally stable areas, but people are well aware that long-term cumulative movements can eventually damage or put out of work roadways, railways, bridges, pipelines or tunnels (Kalteziotis et al. 1993; Picarelli et al. 1999; Urciuoli and Picarelli 2008; Mansour et al. 2010). Therefore, land managers should assess the long-term performance of structures and lifelines involved in slope movements and decide what to do. A new and intriguing problem today is to account for the influence on slope movements of ongoing climate changes, which in the long-term could play a crucial role.

Main features of slow landslides in fine-grained soils and problems posed to land management

Slow slope movements typically involve fractured rocks and fine-grained deposits. In fractured rocks, slow slope deformations can cover very long time spans during the so-called pre-failure stage (Leroueil et al. 1996), while in fine-grained soils long-lasting slope movements typically feature the post-failure stage until a stable morphological configuration is attained (active slides and earthflows).

The behaviour of active landslides in fine-grained deposits is governed by both a high shear stress level (ratio \( \frac{\tau }{{{\tau_{{\lim }}}}} \) of the shear stress, τ, to the shear strength, τ lim), which fluctuates around unity, and the viscous nature of the soil. In fact, even though a small increase in the stress level could trigger a significant acceleration, this is balanced by increase in the shear strength as a function of the displacement rate (Ledesma et al. 2009; Ranalli et al. 2010). Since many slides and earthflows are essentially translational and their cumulative displacement over long time length is small, the overall state of stress globally does not significantly change during movement, thus the main driving cause is the pore pressure fluctuation which affects the stress level (Picarelli et al. 2004). As a matter of fact, the most of studies on this topic are concentrated around the relationship between pore pressures and displacement rates.

According to data obtained from site investigations (Bertini et al. 1984; Mandolini and Urciuoli 1999; Ledesma et al. 2009), the relationship between pore pressure and displacement rate is non-linear and non-reversible. In particular, during the phase of pore pressure increase, the gradient in the displacement rate increases as well; however, for the same pore pressure, the rate of movement during the phase of pore pressure decrease seems to be less than during the phase of pore pressure increase. According to Bertini et al. (1986) such a different behaviour should be due to the different role that primary creep plays in the two phases of pore pressure increase and decrease.

In any case, the peaks of velocity are generally compatible with the normal working conditions of many infrastructures and lifelines. However, for structures which are sensible to even small displacements, the question of what to do in the long time is crucial and land managers must establish if and when measures for landslide stabilization or structure reinforcement have to be undertaken.

Often stabilization measures consist in reshaping of the slope morphology, in drainages or in retaining works, but experience (and even theoretical considerations) suggests that a complete stop of movement is rarely attained in the short time. In this case, the main problem is to establish if even a strong decrease in the displacement rate, which is anyway rather low even without any stabilization measure, may be a significant goal of the design (Picarelli and Russo 2004; Russo et al. 2004). For these reasons, a correct land management approach should consider the magnitude of the long-term displacement in order to decide if some reinforcement of involved structures or the scheduling of a periodic maintenance of them could be a better measure than expensive stabilization works.

Finally, it is worth to mention that in some geomorphological situations slow slope movements may experience a sudden and significant acceleration. This is the case of first-time landslides triggered by progressive failure whose pre-failure stage, featured by slow movements, may be very long, or the case of slow earthflows that can be suddenly reactivated by undrained loading (Hutchinson and Bhandari 1971).

The mechanics of earthflows has been carefully investigated in the past (Picarelli 2000; Comegna et al. 2007). Experience and monitoring suggest that their rapid initial post-failure stage is due to the building up of positive excess pore pressures induced by continuing alimentation which causes temporary instability conditions, but in the very long term, after dissipation of excess pore pressures and natural stabilization of the source area leading to a stop in the alimentation process, the earthflow takes the features of a slow translational slide driven only by high shear stress levels associated with pore pressure regime and, possibly, with river erosion. The active stage of these landslides can last many tens of years (Picarelli et al. 2005) and living with them is then a must, but an as precise as possible assessment of their future behaviour and movement becomes necessary for land management.

All these considerations highlight how delicate is the problem of living with active slides, which requires not only the use of sophisticated criteria of analysis and prediction, but also a sound judgement. Ongoing climatic changes make such a problem even more complicated.

The conceptual chain linking future climatic scenarios to landslide behaviour

A way to forecast the possible evolution of slope movements as a function of weather conditions may more and more rely on the coupling of meteorological forecasting or of long-term climate scenarios with analysis of the slope behaviour based on the effects of the ground-atmosphere interaction on the pore pressure regime. In fact, the development of sophisticated sensors and numerical codes for both weather forecasting and slope behaviour assessment encourages researchers in meteorology, in climatology and in geotechnics to join their efforts coupling their expertise. This is the reason for which CMCC (Euro-Mediterranean Centre for Climate Changes) and AMRA (Analysis and Monitoring of Environmental Risks) joined their efforts to this goal (Schiano et al. 2007; Schiano et al. 2009).

The basic idea is to couple the forecasting of weather parameters with the analysis of the slope behaviour. In principle, the same general approach may be used for short-term or long-term weather forecasting, or even for future climatic scenarios. Short-term predictions should help in the protection of human lives and of critical goods, especially within areas subjected to rapid catastrophic landslides. Long-term forecasting or climatic scenarios allow to plan the land use and the maintenance of man-made works.

Weather forecasting carried out by global models allows to predict the synoptic situation all over the world. Such models do not have enough spatial/temporal resolution to solve mesoscale phenomena (Holton 2004) that often are the main causes of intense rain. Therefore, in order to increase the spatial and temporal resolution of the global weather forecast some downscaling has to be provided. This is the main reason for the development of limited area models running with a higher spatial resolution, typically 7 km (Doms and Schattler 2002) or even 2.8 km (Baldauf et al. 2007). However, often also these last resolutions are not sufficient for specific applications (Meissner et al. 2009). For this reason, it is necessary to set up a statistical downscaling algorithm which can provide the values of the atmospheric variables at a spatial resolution of about hundreds of meters (Schiano et al. 2009).

The approach for the assessment of climatic scenarios is carried out through regional models (Solomon et al. 2007), such as COSMO-CLM (Rockel et al. 2008), which perform the dynamic downscaling of the data generated by climatic global models (e.g. ECHAM). Regional models provide data at a spatial resolution of about 10 km, time resolution of about 6 h, on time scales up to a century. It is worth mentioning that they work on a probabilistic approach thus the results are treated with statistical techniques.

This paper is focused on the effects of climate changes, showing that the present knowledge can help for the management of land and man-made works.

The case study

The Basento river valley is a well-known landslide prone area. Mainly relict, quiescent and active earthflows are located within a long corridor which embraces both banks of the river posing heavy problems to old and new settlements, infrastructures and lifelines (Iaccarino et al. 1995).

The behaviour of an earthflow located along the banks of the Basento river will help to discuss a methodology for the assessment of possible scenarios of landslide behaviour accounting for the presumable climate changes in the examined area. The earthflow involves a very deep deposit of highly fissured tectonized clay shales (Varicoloured Clays) covered by a thin layer of top soil: its source area is located at an elevation of 800 m a.s.l.; the debris spreads 1,100 m downslope until an elevation of 619 m (Vassallo and Di Maio 2008); the average slope angle is 10°. The accumulation zone is located in the alluvial plain of the Basento river (Fig. 1). Laboratory tests performed on samples taken from a nearby earthflow body located on the same slope (Di Maio et al. 2010) show that the clay shales present a clay fraction very close to 50 % and a liquidity limit in the range 60–80 % (Fig. 2). The peak shear strength envelope of samples taken from the earthflow body is characterized by a cohesion c′ = 50 kPa and a friction angle φ′ = 14°, while the residual strength is featured by a friction angle φ′res = 10°.

Fig. 1
figure 1

Landslide, weather stations WS 1 and WS 2 and verticals I3 and S1

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Fig. 2
figure 2

Stratigraphic column along the vertical I3 (after Vassallo and Di Maio 2006): a top soil; b grey silty clay with calcareous and marly fragments; c basal formation

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Weather parameters are available thanks to a couple of weather stations located in the same area (WS 1 and WS 2, Fig. 1) which provide continuous information about precipitations, temperature and relative humidity. In particular, the following data are available:

  • daily rainfall readings from 1916 to 2007, measured at the station WS 1 located at an elevation of 811 m a.s.l., about 5 km West from the landslide area;

  • daily highest, lowest and mean temperature from 1924 to 2007 obtained at the same station (WS 1);

  • rainfall, air temperature and relative humidity measured every 20 min from January, 2005, to December, 2007, at the station WS 2 (elevation 659 m a.s.l.) about 4 km West from the landslide area.

As typical of Italian peninsula, more than 60 % of the total yearly rainfall falls during autumn and winter. Moreover, the peak temperature, T, generally exceeds 30 °C during summer, dropping below 0 °C in winter. The lowest daily relative humidity, RH, fluctuates around 43 %, while the highest value is over 90 %.

Due to stabilisation of the source area the earthflow today appears very close to a stable final configuration, but very slow movements are still active as a function of pore pressure fluctuations and erosion (Vassallo et al. 2012). In particular, back-analysis confirms that the operative shear strength along the slip surface is very close to the residual value.

Some data about monitoring are reported in Figs. 3 and 4 (Vassallo and Di Maio 2006; Vassallo and Di Maio 2008). In particular, Fig. 3 reports the water levels measured through a couple of Casagrande piezometers installed in the accumulation area, and available displacement profiles measured in the track just upslope (Fig. 1). The two piezometers are located at depths of 15 and 34 m in the same borehole (S1). Available data cover the period January 2005–May 2008, showing significant pore water pressure fluctuations at the shallowest depth, and a practically constant value at the highest depth (Fig. 3b): this last is due to the time required for propagation with depth of changes of hydraulic conditions occurring at the ground surface (Kenney and Lau 1977); on the other hand, the different hydraulic response of the shallowest piezometer is due to the lowest depth of installation and to higher soil permeability, probably due to some cracking and fissuring, of shallower soils. Due to the type of piezometers and hydraulic conductivity of soil (Table 1), the time lag is reasonable and does not play an important role on quality of measurements.

Fig. 3
figure 3

Results of monitoring (Vassallo and Di Maio 2006, 2008): a displacement profiles obtained by the inclinometer I3; b total head values drawn by pore pressures measured in borehole S1 through Casagrande piezometers

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Fig. 4
figure 4

Comparison of water levels measured at a depth Z = 15 m (blue points) with cumulative displacement (a) and mean displacement rate (b) at the slip surface level (red points)

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Table 1 Geotechnical parameters adopted in the analysis
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Data concerning displacements cover the period March 2005–July 2006, showing that the slip surface in the track is located at a depth of 10 m from the ground surface (Fig. 3a). The rate of movement is about 2 cm/year and is clearly governed by cumulative rainfall over time intervals in the range of 3–4 months (Di Rosario 2008). Even with some difference from point to point, data from monitoring are quite consistent; in particular, the magnitude of displacements slowly decreases moving downslope.

Figure 4 shows the cumulative displacement at the depth of the slip surface and the mean velocity against the piezometric level. The displacement rate is essentially governed by pore pressure, changing as the groundwater level changes. In particular, in the time interval between December 2005 and March 2006, when the groundwater level in the landslide body was approaching the ground surface, the landslide clearly accelerated (Fig. 4b). In that period, the local average displacement rate was about 3 mm/month, compared to 1 mm/month displayed before and after that time interval.

Further data about landslide monitoring are reported by Di Maio et al. (2010) and by Vassallo et al. (2012).

Expected effects of climate changes

Climate scenario for the next 50 years

Global Climate Models are characterized by a resolution of about 100 km, which in general is too coarse for impact studies, while Regional Climate Models can be used for simulations with a spatial resolution of about 10 km over a time interval up to a century. Through such resolutions, land morphology is better described than with global models, that over/under-estimate valley/mountain elevations leading to errors in precipitation analysis. For the purposes of this paper, the Regional Climate System COSMO-CLM has been employed (Rockel et al. 2008) which exploits a non-hydrostatic model for the simulation of atmospheric processes. The model is developed by the European Consortium “CLM-Community”.

The non-hydrostatic modelling (Pielke 1984) provides a good description of the convective phenomena which are generated by vertical movement (through transport and turbulent mixing) of energy (heat), water vapour and momentum. Convection can redistribute significant amounts of moisture, heat and mass on small temporal and spatial scales. Furthermore, convection can cause severe precipitations (as thunderstorms or clusters of thunderstorm). The adopted spatial resolution in COSMO-CLM simulations is 8 km, thus convection represents a sub grid scale phenomenon and has to be parameterized (Steppeler et al. 2003). In COSMO-CLM, different convection schemes are implemented. For the special application considered in this paper, the Tiedtke scheme (Tiedtke 1989) has been adopted. In particular, a simulation of the climate in the Mediterranean area for the time period 1965–2100 has been performed. Such simulation exploits the IPCC scenario 20C3M, which describes the twentieth century climate using historical Greenhouse Gas Concentrations, for the period 1965–2000, and the IPCC-A1B emission scenario (Nakićenović et al. 2000), for the period 2000–2100. These scenarios drive the simulation performed by the CMCC-MED global coupled model (Gualdi et al. 2008; Scoccimarro et al. 2010), which is featured by a spatial resolution of about 80 km. In turn, CMCC-MED provides the initial and boundary conditions for the COSMO-CLM regional model (Fig. 5) using a special interpolation tool called INT2LM (Schattler 2011).

Fig. 5
figure 5

Procedure adopted to obtain a reliable climate scenario for the examined case, starting from a global model

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In order to test the capability of the model to capture the basic climate features, it has been validated through a comparison of observed temperature at 2-m elevation above the ground level and of daily precipitation values with the analogous variables obtained from the COSMO-CLM regional model. Such a comparison concerns the period 1971–2000 because of the availability of a large dataset of satellite observations from the Climate Research Unit (CRU). The CRU monthly mean global gridded dataset with 0.5° resolution (about 60 km) has been used as a reference (Mitchell and Jones 2005). Figure 6 shows the averaged 2-m temperature distribution in the period 1971–2000 for winter season. Globally, there is a good agreement between observed and simulated data, even if in the regions characterised by a complex orography, the resolution of CRU data is not sufficient to draw definitive conclusions. Figure 7 shows the averaged daily precipitation distribution for winter season. CRU data (Fig. 7a) show intense precipitations in the Alpine space and in Slovenia and Croatia area that are generally well reproduced by COSMO-CLM (Fig. 7b).

Fig. 6
figure 6

Two-meters temperature distribution, averaged on the period 1971–2000 (winter season): a CRU dataset; b COSMO-CLM simulation output

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Fig. 7
figure 7

Daily precipitation distribution, averaged on the period 1971–2000 (winter season): a CRU dataset; b COSMO-CLM simulation output

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Concerning the examined case, even though many atmospheric variables are computable, only those that have important relations with landslide behaviour (rainfall, temperature, relative humidity and wind speed) have been considered. All the variables are obtained by solving the differential equations implemented in the COSMO-CLM regional model. Simulated data come from a proper calibration associated with monitoring. In particular, a comparison between simulations and readings carried out over the time interval 2005–2007, shows a good agreement between yearly cumulative and calculated rainfall: in fact, the measured yearly rainfall in 2005, 2006 and 2007 is respectively 766, 612 and 582 mm, while the corresponding calculated values are 788, 653 and 707 mm, with an overestimation ranging between 3 and 21 %. Since daily values display a higher error, some sensitivity analyses have been performed in order to evaluate the influence of the distribution of the total precipitation over the year on the calculated pore pressures. Based on the historic data, three distributions, respectively recorded in 1931, in 1920 and in 2004, have been accounted for: the first one is an extreme case characterised by more than 70 % of the yearly cumulative rainfall, P cum , fallen during the first half of the year; the second one is an opposite case, with less than 30 % of the cumulative rainfall fallen during the same time interval (Fig. 8); finally, the distribution recorded in 2004 (cumulative rainfall during the first 6 months equal to 46 % of the total) is very similar to the average distribution from 1916 to 2007. The results of the pore pressure simulations for the three assumed distributions are considered in “Potential effects of future climate scenarios on the landslide behaviour” section.

Fig. 8
figure 8

Yearly distribution of precipitations in the century

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Going back to the other climate parameters, the analysis of data shows that the computed highest and lowest temperature and lowest relative humidity have been overestimated, while the highest relative humidity has been underestimated. Such mismatches have been statistically rectified in the post-processing phase by the “quantilebased” bias correction scheme proposed by Wood et al. (2004), which essentially rescales the calculated data to match the observations, giving the results reported in Figs. 9 and 10. Such a method is considered efficient leading the median differences to zero.

Fig. 9
figure 9

Measured and calculated daily highest (a) and lowest (b) temperature between 2005 and 2007

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Fig. 10
figure 10

Measured and calculated daily highest (a) and lowest (b) relative humidity between 2005 and 2007

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Once calibrated as described above, the model provides the climate scenario depicted in Figs. 11, 12, 13, and 14 that report also historic data measured by the weather stations present in the investigated area (Fig. 1), except the wind speed due to the absence of readings. Figure 11 shows that the general trend of the yearly cumulative precipitation in the last century is characterised by a clear decrease in the order of about 2.5 % per decade. Such a trend is confirmed by the climatic scenario, suggesting higher fluctuations in the yearly cumulative values compared to those measured until 2007. Historic data about average lowest and highest temperature show respectively an increase of 0.05 and 0.04 °C per decade (Fig. 12). The expected values in the next 50 years present an increasing trend with a gradient of about 0.3 °C per decade. Finally, Fig. 13 reports the trends in highest and lowest relative humidity. Both values show a very gentle decrease. On the whole, such values are slightly different from the general trend in the Italian area (Brunetti et al. 2006), that is characterized by a decrease in yearly cumulative rainfall (0.5 % per decade) and increase in the mean temperature (about 0.1 °C per decade).

Fig. 11
figure 11

Measured yearly cumulative rainfall and corresponding values expected until 2060 based on the climate scenario (COSMO-CLM)

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Fig. 12
figure 12

Measured yearly highest (T max) and lowest (T min) mean temperature and corresponding values expected until 2060 based on the climate scenario (COSMO-CLM)

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Fig. 13
figure 13

Measured yearly mean relative humidity RH and corresponding values expected until 2060 based on the climate scenario (COSMO-CLM)

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Fig. 14
figure 14

Daily wind speed expected until 2060 based on the climate scenario (COSMO-CLM)

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Such a climate scenario has been adopted to establish the boundary conditions for the assessment of the future groundwater conditions in the investigated area and to forecast future landslide movements.

Analysis of the long-term landslide behaviour

In order to provide a rational methodology to assess the impact of future climate changes on the long-term behaviour of active landslides in the examined area, some simulations have been carried out using previous case history as an example. Such approach includes different steps (Fig. 15):

Fig. 15
figure 15

Methodological approach adopted to assess the long-term landslide behaviour

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  1. a)

    calibration of a numerical model linking weather parameters and pore pressure regime;

  2. b)

    setting up of a reliable relationship between pore–water pressure and landslide movement;

  3. c)

    assessment of the long-time landslide behaviour based on the available climate scenario obtained by COSMO-CLM.

Numerical simulation of the groundwater regime

Simulations of pore pressures as a function of weather parameters have been performed by the FEM VADOSE/W code (Krahn 2004) which can analyse non-isothermal seepage problems. Considering the aims of the study and the strong computational effort, looking at the assessment of the slope behaviour in next 50 years, the analyses have been performed under 1D conditions that have been proven to provide reliable results. Moreover, the absence in the investigated site of a significant vegetative cover allows neglecting transpiration phenomena.

According to the adopted code, ground-atmosphere water exchanges are governed by three differential equations concerning: the hydraulic seepage, the heat transfer and the coupling of heat and mass equations. These include three unknown parameters: the pore-water pressure, u w, the pore-vapour pressure, u v and the temperature, T. Under the 1D assumption, transient flow in unsaturated soils is analysed through the Richards’ equation (1931) modified by Milly (1982) and Wilson (1990) to account for the vapour flow:

$$ {m_{\text{w}}}\frac{{\partial {u_{\text{w}}}}}{{\partial t}} = \frac{1}{{{\rho_{\text{w}}}}}\frac{\partial }{{\partial z}}\left( {{D_{\text{v}}}\frac{{\partial {u_{\text{v}}}}}{{\partial z}}} \right) + \frac{\partial }{{\partial z}}\left[ {{k_{\text{wz}}}\frac{{\partial \left( {z + \frac{{{u_{\text{w}}}}}{{{\rho_{\text{w}}}g}}} \right)}}{{\partial z}}} \right] $$
(1)

where

u w [pascal]:

water pressure

u v [pascal]:

vapour pressure

m w [per pascal]:

slope of the volumetric water content function

ρ w [kilogrammes per cubic metre]:

density of water

t [seconds]:

time

z [meters]:

elevation head

D v [kilogrammes per metre per second per pascal]:

vapour diffusion coefficient

k wz [metre per second]:

hydraulic conductivity in the vertical z-direction

g [metre per square second]:

gravity acceleration.

The adopted heat transfer equation is the one proposed by Fourier (1822) for conductive heat transfer with the inclusion of vapour transfer and convective heat transfer due to flowing water:

$$ {\lambda_{\text{t}}}\frac{{\partial T}}{{\partial t}} = \frac{\partial }{{\partial z}}\left( {{k_{\text{tz}}}\frac{{\partial T}}{{\partial z}}} \right) + \rho c{V_{\text{z}}}\frac{{\partial T}}{{\partial z}} + {L_{\text{v}}}\frac{\partial }{{\partial z}}\left( {{D_{\text{v}}}\frac{{\partial {u_{\text{v}}}}}{{\partial z}}} \right) $$
(2)

where

T [kelvin]:

temperature

λ t [joules per cubic metre per kelvin]:

volumetric heat capacity of soil

k tz [watts per metre per kelvin]:

thermal conductivity in the vertical z-direction

ρ [kilogrammes per cubic metre]:

bulk density of soil

c [joules per kilogramme per kelvin]:

mass specific heat capacity of soil

V z [metres per second]:

Darcy water velocity in vertical z-direction

L v [joules per kilogramme]:

latent heat of vaporization of water.

Heat and mass coupling is expressed by the Edlefsen and Anderson equation (1943),

$$ {u_{\text{v}}} = {u_{\text{vs}}} \cdot {h_{{{\text{r,air}}}}} $$
(3)

where

u vs [pascals]:

saturated vapour pressure of pure free water

h r,air :

relative humidity of air.

The boundary conditions required to establish the evaporative flux couple soil moisture and heat stress state at the ground surface with weather conditions. The atmospheric coupling is provided by the Penman–Wilson equation (Wilson 1990):

$$ AE = \frac{{\Gamma Q + \upsilon {E_{\text{a}}}}}{{\upsilon A + \Gamma }}, $$
(4)

where

AE [millimetres per day]:

actual vertical evaporative flux from soil surface

Γ [kilopascals per degree Celsius]:

slope of the u vs − T curve (saturated vapour pressure − temperature)

Q [millimetres per day]:

net radiant energy available at the soil surface

υ:

psycrometric constant

E a :

f(u) × P a × (B − A)

f(u) :

0.35(1 + 0.15 U a ), depending on wind speed, surface roughness and eddy diffusion

U a [kilometres per hour]:

wind speed

P a [kilopascals]:

vapour pressure in the air above the evaporating surface

B :

1/h r,air , inverse of the relative humidity of the air

A :

1/h r, inverse of the relative humidity of the soil surface.

The code calculates the net radiation at the ground surface, Q, based on weather input data at each daily time-step, i.e.: (1) highest and lowest temperature, (2) highest and lowest relative humidity of the air, (3) rainfall, (4) average wind speed.

In order to solve the governing equations, data about geotechnical and thermal soil properties are needed. These are expressed through two geotechnical functions, the permeability function and the characteristic curve, and two thermal functions, the thermal conductivity function and the volumetric heat capacity function (notice that thermal conductivity is the amount of heat that flows through a unit area of soil of unit thickness in unit time under unit temperature gradient, while the volumetric heat capacity is the amount of heat required to cause an increase of soil temperature by a unit degree).

The infiltration and evaporation processes have been simulated by a simple geotechnical model, in which a 1-m-thick top soil rests on a semi-infinite deposit of clay. This is a reasonable choice accounting for the nature of the subsoil, consisting of a thick deposit of uniform fine grained soils covered by a top soil, and for the type of soil parameters required (essentially hydraulic and thermal properties).

The adopted permeability function (Fig. 16a) is a function of the matric suction, u a−u w, through the expression proposed by Mualem (1976):

$$ {k_{\text{w}}} = \left\{ \begin{gathered} {k_{{{\text{ws}}\,}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right) \leqslant {\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)_{\text{e}}}\,\,\,\,\, \hfill \\ {k_{\text{ws}}} \cdot {\left[ {\frac{{\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)}}{{{{\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)}_{\text{e}}}}}} \right]^{{ - (2 + 5\lambda /2)}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right) > {\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)_{\text{e}}} \hfill \\ \end{gathered} \right. $$
(5)

where k ws is the saturated permeability, u a is the atmospheric pressure, (u a−u w)e is the air-entry value of suction and λ a dimensionless parameter which represents the slope of the characteristic curve. For this last (Fig. 16b), the following formulation has been adopted:

$$ {\theta_{\text{w}}} = \left\{ \begin{gathered} {\theta_{\text{ws}}} - {m_{\text{ws}}} \cdot \left( {u{}_{\text{a}} - {u_{\text{w}}}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right) \leqslant {\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)_{\text{e}}} \hfill \\ {\theta_{\text{wr}}} + \left( {{\theta_{{{\text{ws,aev}}}}} - {\theta_{\text{wr}}}} \right) \cdot {\left[ {\frac{{\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)}}{{{{\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)}_{\text{e}}}}}} \right]^{{ - \lambda }}}\,\,\,\,\,\,\,\,\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right) > {\left( {{u_{\text{a}}} - {u_{\text{w}}}} \right)_{\text{e}}} \hfill \\ \end{gathered} \right. $$
(6)

where θ w is the volumetric water content, θws is the saturated volumetric water content (u w = 0), m ws the saturated volumetric compressibility, θ wr the residual volumetric water content, θws,aev the volumetric water content for the air-entry value of suction (u a−u w)e. Equation [6] proposed by Brooks and Corey (1964) has been modified assuming the saturated volumetric compressibility, m ws, as the slope of the characteristic curve for suction lower than the air entry value.

Fig. 16
figure 16

Geotechnical functions adopted in the seepage analyses: a permeability function (derived from Mualem 1976); b characteristic curve (derived from Brooks and Corey, 1964)

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For the thermal conductivity of the soil, VADOSE/W adopts the Johansen method (1975) that is based on the volumetric water content function and the thermal conductivity of the mineral (Fig. 17a). For this last, a value of 130 kJ/(day m °C), typical of clays, has been adopted for both soils. Sensitivity analyses show that such a parameter plays a minor role compared to the geotechnical parameters

Fig. 17
figure 17

Thermal functions adopted in the analyses: a thermal conductivity function (derived from Johansen 1975); b volumetric heat capacity function (derived from de Vries 1963)

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For the volumetric heat capacity, the function reported in Fig. 17b has been adopted (de Vries 1963). Based on the VADOSE/W library, for the mass specific heat of the soil mineral, the typical value of 0.71 kJ/(kg °C) has been used for both soils.

The geotechnical parameters adopted in the analysis are reported in Table 1. The properties of the top soil come from personal experience and feeling of the authors. Adopted values along with the properties of the underlying formation, provide the best matching between calculated and measured piezometric levels. Regarding the Varicoloured Clays, a value of the saturated permeability of 1.00E−08 m/s has been assumed, accounting for the results of eight field falling head permeability tests performed at depths ranging between 14 and 34 m which provided values ranging between 2.60E−09 and 6.70E−08 m/s (Di Rosario, 2008). The saturated volumetric water content, θ ws, is equal to the average porosity.

A calibration of the model has been carried out based on the piezometric levels measured between 1 January 2005 and 31 December 2007, at a depth of 15 m using the weather parameters measured in the same period for the boundary conditions. The simulated water levels are reported in Fig. 18. Neglecting the values calculated in the first part of the examined period, which are clearly influenced by the initial conditions, the agreement between calculated and measured water levels is quite satisfactory (Fig. 18d). However, the reliability of the analysis has been tested through the efficiency criterion proposed by Willmot (1981):

$$ d = 1 - \frac{{\sum\limits_{{i = 1}}^n {{{\left( {{O_i} - {P_i}} \right)}^2}} }}{{{{\sum\limits_{{1 = 1}}^n {\left( {\left| {{P_i} - \overline O } \right| + \left| {{O_i} - \overline O } \right|} \right)} }^2}}} $$
(7)

where d is the index of agreement between observed and simulated values, O i and \( \overline O \) are respectively the observed and the corresponding mean values, P i are the simulated values. In this case, the index of agreement between observed and simulated piezometric levels is d = 0.8.

Fig. 18
figure 18

Net radiation (a), actual evaporation (b) and amount of infiltration (c) calculated at the ground surface; computed and measured piezometric level at a depth of 15 m (d)

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According to results of simulation, more than 90 % of total yearly cumulative rainfall infiltrates through the ground surface during 2006 and 2007 (Fig. 19). The lower value calculated for 2005 (only 76 % of yearly precipitation) is clearly influenced by the adopted initial conditions which assume a fully saturated topsoil causing a significant run-off during the initial computational steps. The figure also shows that the yearly effective infiltration is about 10–20 % of the total infiltration due to total evaporation in the year.

Fig. 19
figure 19

Measured cumulative precipitation, computed cumulative infiltration and computed cumulative evaporation

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Figure 20 shows the calculated mean moisture contents in the top soil and in the underlying deposit. It clearly shows that the fluctuations of the water content are much higher in the top soil than in the less pervious clays. In particular, only about 4 % of the cumulative effective infiltration through the ground surface can penetrate into this deposit. Differently from the topsoil, the degree of saturation of clay never drops below 100 %, any water content change being accommodated by a small change in the void ratio. Moreover, both the highest and the lowest value are attained with a delay of 2–3 months with respect to the corresponding highest and lowest values attained in the top soil respectively during the winter and summer seasons. Finally, the clay deposit is insensitive to peaks of water content in the top soil after summer rainstorms.

Fig. 20
figure 20

Mean moisture content θ W calculated within the top soil and the varicoloured clays

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Relationship between pore water pressures and landslide movement

Landslide movements have been calculated by an empirical expression between displacement rate and mobilised shear stress along the slip surface, which takes into account the viscous behaviour of this last. Vulliet (1986), who reviewed the literature on such a topic, proposed the following expression

$$ v = \frac{A}{{{{\left( {\frac{{{\tau_{{\lim }}}}}{\tau }} \right)}^n}}} $$
(8)

where v is the displacement rate, τ lim is the shear strength available along the slip surface, τ is the active shear stress, A and n are material parameters. Since the denominator of the Eq. [8] is directly related to the depth of the water level, h, the simplest power law

$$ v = \frac{a}{{{h^b}}} $$
(9)

has been used.

In the following analysis, the displacement rate, v, is expressed in millimetres per day, the depth of the water level, h, in metres, while the empirical material parameters a and b have been obtained through calibration of the expression based on the measured values of v. The parameters that provide the best matching between computed and measured cumulative displacements (Fig. 21a) depend on the trend of the piezometer level: the best values are: a = 0.010 mm/day and b equal to 0.20 and 0.62, respectively, for groundwater rising and lowering phases.

Fig. 21
figure 21

a Measured and computed cumulative displacements (red points) vs piezometric levels (blue points); b measured and computed mean velocities (red points and lines) vs piezometric levels (blue points); c computed rates of displacement as a function of the piezometric level

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The matching between calculated and measured displacements is quite good and reliable (Fig. 21a). In particular, the highest errors in the calibration are 0.9 mm on 9 December 2005 (overestimation) and 1.3 mm on 21 March 2006 (underestimation). On the other hand, considering the non cumulative values (Fig. 21b), the highest overestimation is 0.9 mm/month for the time interval 26 October–9 December 2005, and the highest underestimation is 1.4 mm/month between 15 March and 7 April 2005. Accounting for the time-scale, such approximation appears reasonable.

Figure 21c shows the rate of displacement calculated during phases of increasing or decreasing piezometer levels.

Potential effects of future climate scenarios on the landslide behaviour

The conceptual approach described above allows to depict a rational scenario of the potential impact of the expected climate changes on the landslide behaviour. Based on quantitative available climatic scenarios provided by the COSMO-CLM model, the numerical approach calibrated over the 2005–2007 time interval has been extended to the next 50 years in order to assess the potential effects of climate on the groundwater table and the consequent influence on movement rates and cumulative displacements.

As shown in “Climate scenario for the next 50 years” section, the COSMO-CLM model can predict with a reasonable approximation the total yearly rainfall, the average temperature and the air humidity but does not provide reliable data about daily precipitations which are required to assess pore pressure fluctuations. This problem cannot be neglected given that available scenarios seem to suggest a modification in the distribution of precipitations which should become less frequent and more intense. However, just to get more information about the potential error that can be caused by different distributions of the same annual precipitation over the year, further simulations of the piezometric regime from 2005 to 2007 have been carried out imposing different distributions of the total yearly precipitations, i.e. the distributions recorded in 1920 (when 70 % of cumulative precipitation fell in the second half of year), in 1931 (when 70 % of yearly precipitation fell instead in the first half of the year) and 2004 (when the yearly distribution was very close to the average distribution in the century). For the other daily climatic parameters (highest and lowest temperature and relative humidity, wind speed), the output of COSMO-CLM has been used, statistically corrected as explained in “Climate scenario for the next 50 years” section.

The results of such simulations are reported in Fig. 22a which shows that the differences in the calculated water levels are relatively small (even though not negligible) and can be considered acceptable accounting for the aims of this study; in particular, the observed landslide behaviour is well reproduced using the 1920 distribution. Based on the calculated values of the water level for the three examined cases, the total displacement from March 2005 to July 2006, should range between 2.2 cm (close to the measured value 2.5 cm) and 2.9 cm, depending on the adopted distribution (Fig. 22b). Once again, the results of the analysis can be considered reasonable.

Fig. 22
figure 22

Measured and calculated piezometric levels (a) and displacements (b) assuming different rainfall distributions

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The simulation covering next 50 years has been carried out adopting the 1920 and 2004 rain distributions, which provide the extreme values of the slope movement in the period 2005–2007 (notice that the 2004 distribution corresponds to the average in the century).

Figures 23 and 24 report the results of the analysis. Due to the expected decrease in precipitations and increase in temperature with a practically constant relative humidity the future average groundwater level should display a slow progressive reduction in the range 6–8 mm per decade (Figs. 23a and 24a), due to increasing evaporation (as shown transpiration effects should be negligible because of the poor plant cover). However the increasing oscillations in the yearly precipitation displayed by the available scenarios (Fig. 11) should lead to significant seasonal fluctuations in the groundwater level.

Fig. 23
figure 23

Effects of the climate scenario expected between 2010 and 2060 (yearly rainy distribution as in 1920): a piezometric level; b yearly rate of movement (red points) and cumulative rainfall (blue points); c cumulative displacement

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Fig. 24
figure 24

Effects of the climate scenario expected between 2010 and 2060 (yearly rainy distribution as in 2004): a piezometric level; b yearly rate of movement (red points) and cumulative rainfall (blue points); c cumulative displacement

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Combining pore pressures and landslide velocity through the empirical relationship discussed above, the future displacement rate should consequently decrease. Such a decrease should range in between about 1.5 mm/decade per decade (Fig. 23b) and 3 mm/decade per decade (Fig. 24b) for the two distribution scenarios, even though phases of moderate acceleration during winter and spring will take place every year due to water table rising. In spite of such changes in velocity, the cumulative displacement will follow a substantial linear trend. Depending on the adopted rainfall distribution, the total displacement over next fifty years should attain a value comprised between 77 and 86 cm. This will pose some problems to permanent infrastructures and lifelines present in the area that will require a continuous maintenance and periodic repair.

Such results demonstrate that in the case of slow landslides in clay the expected climatic changes should not play a relevant role due to the moderate decrease in the amount of annual precipitation and limited effect of temperature increase on evaporation and groundwater level. In any case, the global impact of climate changes should be favourable, at least in the considered climatic and geomorphological context.

Finally, it is worth to mention that further potential climate effects (as on river or superficial erosion caused by run-off) have not be taken into account. In such a respect, changing climatic conditions characterised by longer dry seasons followed by isolate intense thunderstorms could play a valuable role.

Summary and conclusions

According to all available data, the present phase of the human history seems to be characterised by some climatic changes. If such changes will persist according to the present apparent trend, during the next years they will lead to some consequences on hydrogeological phenomena and impact on human life. Presumably, the hazard will be different in different areas of the world, depending on local weather conditions and on the geomorphological and geotechnical characteristics of such areas.

Fortunately today, the available technological and scientific tools enable scientists to depict some scenarios of the incoming climate changes and land managers to adopt appropriate measures for risk mitigation. A methodology for a rational assessment of the possible effects of such climate changes has been proposed, exploiting the actual capability of researchers to set up reliable climate scenarios and to analyse the consequent slope behaviour. This last can be assessed by numerical methods conceived for the analysis of water exchanges at the ground-atmosphere interface as a function of weather parameters and empirical expressions relating pore pressures to landslide movement.

The potential future evolution of a slow landslide in stiff clays induced by potential changes in the groundwater regime has been examined bearing on the available climate scenarios, supported by an analysis of the present trends, and on a conceptual chain leading from the climatic scenario to the geotechnical analysis of the slope behaviour using a simplified model accounting for the slope-atmosphere interaction. The model has been tested using data regarding the behaviour of a landslide in Southern Italy over a 3-years monitoring period. Due to a slow but clear decrease in the cumulative rainfall which is being measured since almost a century, and to the expected increase in the average temperature, the global balance between infiltrated and evaporated water should cause a modest decrease in the piezometric levels thus to a decrease in the annual displacement.

For a more complete analysis of the potential consequences of climatic changes, an integrated research effort including also the assessment of potential changes in transpiration and erosion phenomena is needed.