Deep-seated landslides are an important and widespread natural hazard within
alpine regions and can have significant impacts
on infrastructure. Pore water pressure plays an important role in determining
the stability of hydrologically triggered deep-seated landslides. Based on
a simple tank model structure, we improve groundwater level prediction by
introducing time lags associated with groundwater supply caused by snow
accumulation, snowmelt and infiltration in deep-seated landslides. In this
study, we demonstrate an equivalent infiltration calculation to improve the
estimation of time lags using a modified tank model to calculate regional
groundwater levels. Applied to the deep-seated Aggenalm landslide in the
German Alps at 1000–1200

Deep-seated landslides in the European Alps and other mountain environments pose a significant hazard to people and infrastructure (Mayer et al., 2002; Madritsch and Millen, 2007; Agliardi et al., 2009). It has long been recognized that pore water pressure (PWP) changes by precipitation play a critical role for hydrologically controlled deep-seated landslide activation. The rise in PWP causes a drop of effective normal stress on potential sliding surfaces (Bromhead, 1978; Iverson, 2000; Wang and Sassa, 2003; Rahardjo et al., 2010). The estimation of pore water pressure is of great significance for anticipating deep-seated landslide stability. In past years, geotechnical monitoring systems have revealed PWP changes related to rainfall and snowmelt events (Angeli et al., 1988; Simoni et al., 2004; Hong et al., 2005; Rahardjo et al., 2008). Generally, two ways are employed to estimate the groundwater changes: (1) depending on the precise information of permeability and infiltration of material, the Green and Ampt model is generally used to describe groundwater infiltration and water table changes (producing PWP) in saturated material (Chen and Young, 2006). The Richards equation (Weill et al., 2009) with the Van Genuchten equation (Schaap and Van Genuchten, 2006) or the Fredlund and Xing (1994) method show better performance in the evaluation of infiltration and groundwater table in unsaturated material. Traditional deterministic models have advantages due to their explicit physical and mechanical approaches, but they require accurate knowledge, testing and monitoring of soil physical parameters, which are often not available with sufficient accuracy. For example, the widely used Richards equation with the Van Genuchten method needs soil suction tests under variable moisture content, saturated water content, residual water content and the pore-size distribution of materials, which are difficult to achieve for complex landslides with multiple reworked materials. (2) Empirical–statistical models employ optimization or fitting parameters in their model structure. Tank and other models need historical monitoring data to train parameters (Faris and Fathani, 2013; Abebe et al., 2010). Such empirical models, because of their simple conceptualized structure, do rely to a smaller degree on explicit physical and mechanical approaches. However, they can avoid the problems induced by the uncertainty of material parameterization and its spatial arrangement in the landslide mass. They can, therefore, be applied to a wide range of different landslide settings and we estimate that for more than 90 % of all landslides no explicit parameters on soil suction are available. As one of the most common empirical models, tank models typically describe infiltration and evaporation in shallow soil materials (Ishihara and Kobatake, 1979). They are based on the water balance theory, which means they account for flows into and out of a particular drainage area. Multi-tank models involving two or three tank elements have been developed to better estimate groundwater fluctuations within shallow landslides induced by heavy rainfall (Michiue, 1985; Ohtsu et al., 2003; Takahashi, 2004; Takahashi et al., 2008; Xiong et al., 2009).

Details of simple tank model and multi-tank model
applied in deep-seated landslides.

Figure 1a shows the work mode of a simple tank model.

From the Eqs. (3) to (5), there are seven unknown (

In this study, we introduce a simple method to estimate time lags by a modified standard tank model which predicts changes in pore water pressure. The innovation of our approach is to calculate equivalent infiltration before it enters the tank. The equivalent infiltration deals with the infiltration time lag, including snow accumulation and snowmelt in deep-seated landslides, based on a simple tank model structure. We hypothesize and provide quantitative evidence that, compared to a simple tank model, our modified model has a higher accuracy and physical meaning by controlling equivalent infiltration, including snow accumulation and snowmelt; compared to a multi-tank model our modified model is more robust and reliable. The prediction of precipitation type is very difficult because the vertical height of snow flakes is not easily calculated without advanced technology (Czys et al., 1996; Ahrens, 2007). Thus, in our study the judgment of precipitation type still uses the widely used statistic model. For the snowmelt calculation we used empirical equations to make the process earlier, because sophisticated models which can calculate the snowmelt precisely are quite complex and require several physical parameters, including topography, precipitation, air temperature, wind speed and direction, humidity, downwelling short-wave and long-wave radiation, cloud cover and surface pressure (Garen and Marks, 2005; Herrero et al., 2009; Lakhankar et al., 2013). In addition, compared to the original tank model without considering the snowmelt, we emphasized the tank model coupling the function of snowmelt (we just choose the simple snowmelt module). We apply our model to the Aggenalm landslide, where predicted PWP changes can be tested against piezometric borehole monitoring data. The monitoring network design and installation, as well as detailed monitoring data, and the introduction of monitoring devices have been described previously in detail (Thuro et al., 2009, 2011a, b, 2013; Festl et al., 2012). It should be pointed out our aim is only to estimate the local pore water pressure in deep-seated landslides. The relation between landslide movement and the groundwater table is not the focus of this study. The landslide movement is complex and time dependent and material strength is also very important. It has been hypothesized that deep-seated landslide velocity, although linked to pore-pressure-induced changes in effective stress, is also governed by rate-induced changes in shear strength of the materials, caused by changing mechanical properties during shear deformation (Lupini et al., 1981; Skempton, 1985; Angeli et al., 1996; Picarelli, 2007) and/or consolidation and strength regain during periods of rest (Nieuwenhuis, 1991; Angeli et al., 2004).

The Aggenalm landslide is situated in the Bavarian Alps in the Sudelfeld region near Bayrischzell (Fig. 2).

During the alpine orogeny, the rock mass was faulted and folded into several large east–west-oriented synclines, of which the Audorfer synclinorium is responsible for the nearly slope-parallel bedding orientation of the rock mass in the area of the Aggenalm landslide (Fig. 3).

Geological profile of the Aggenalm landslide (Festl, 2014).

The Aggenalm landslide is underlain by Late Triassic well-bedded limestones (Plattenkalk, predominantly Nor), overlain by Kössen layers (Rhät, predominantly marly basin facies) and the often more massive Oberrhät limestones and dolomites (Rhät) (Fig. 3). The marls of the Kössen layers are assumed to provide primary sliding surfaces and are very sensitive to weathering as they decompose over time to a clay-rich residual mass (Nickmann et al., 2006). The landslide mechanism can be classified as a complex landslide dominated by deep-seated sliding with earth flow and lateral rock spreading components (Singer et al., 2009). A major activation of the landslide occurred in 1935, destroying three bridges and a local road. Slow slope deformation and secondary debris flow activity have been ongoing since this time.

The Aggenalm is exposed to a sub-continental climate with a pronounced summer
precipitation maximum and an annually changing share of 15–40 % of the
mean annual precipitation that fall as snow. Abundant snow cover restricts
freezing of the top to a few tens of centimetres, allowing water penetration in cracks. Due to the all-year humid climate (see Fig. 4; nearby meteorological stations
such at the Brünnsteinhaus, the Sudelfeld (Polizeiheim) and the
Tatzelwurm indicate mean annual precipitation of 1594, 1523 and
1660

Mean monthly precipitation (1931–1960 and 1961–1990) for the Brünnsteinhaus, the Sudelfeld (Polizeiheim) and Tatzelwurm meteorological stations (data from Germany's National Meteorological Service, DWD).

Monitoring data for this study are derived from a rain gauge and
humidity sensor (alpEWAS central station) and a PWP
sensor installed in boreholes close to the assumed shear zone
(B4, 29.4

Figure 5 demonstrates the successive changes from the original tank model (Ishihara and Kobatake, 1979; Michiue, 1985; Ohtsu et al., 2003; Uchimura et al., 2010) to our modified model.

Design of the modified tank model.

Figure 5a shows the basic concept of the original tank model, the
daily change in the groundwater table height

If groundwater supply illustrated in Fig. 5b is incorporated in the
tank model, the daily change in groundwater table height

Incorporating snowmelt, Eq. (3) should be written as

Snow accumulation and snowmelt produces our time lag 1 controlled by
ambient temperature. Long infiltration paths which can take 1 or more days
to reach the water table in deep-seated landslide masses cause time lag 2
(Fig. 5c). The infiltration in

Schematic diagram of water infiltration from the surface to the groundwater table for a time lag 2 of 2 days.

The workflow chart of the modified tank model with respect to the original model. Time lags from snow accumulation, snowmelt and infiltration are highlighted in blue.

The antecedent precipitation index (API) can reduce this time lag 2 by
estimating the current water content of the ground affected by previous
precipitation (Chow, 1964). This is equivalent to the infiltration
calculations of some authors (Suzuki and Kobashi, 1981; Matsuura et al.,
2003, 2008) who define equivalent infiltration as

Thus, PWP can be linearly correlated to groundwater levels as
Eq. (11).

We assume that Quaternary deposits control the hydraulic properties of
the tank model (tank interior with soil/rock in Fig. 5). The fractured
limestone and dolomite control the water flow from higher to lower
elevations (groundwater inflow and drainage in Fig. 5). The marly
Kössen beds are treated as impermeable layers (thin, low porosity
and high normal stress above). As this is a regional groundwater table
estimation, we can use the modified tank model to simulate the
groundwater table changes induced by precipitation. We ignore surface
run-off flow resulting from snowmelt and heavy rainfall as (1) the
slope angle is less than 15

In order to determine an appropriate value of

The linear relationship between daily change of pore water pressure
(

Thus,

A threshold temperature under which the precipitation falls as snow is a key
factor for a snow accumulation model. However, diagnosis of precipitation is
difficult, and there are no parameters with which the type of precipitation
can be accurately determined (Wagner, 1957; Koolwine, 1975; Bocchieri, 1980;
Czys et al., 1996; Ahrens, 2007). The most common approach is to derive
statistical relationships between some predictors and different precipitation
types (Bourgouin, 2000). We select a statistical model (empirical formula)
based on hundreds of observation samples in Wajima, Japan, between 1975 and
1978 to estimate precipitation types (Matsuo and Sasyo, 1981). The threshold
of relative humidity calculated by

One of the most popular methods employed to forecast snowmelt is to correlate
air temperature with snowmelt data. Such a relation was first used for an
alpine glacier by Finsterwalder and Schunk (1887) and has since then been
extensively applied and further refined (Kustas et al., 1994; Rango and
Martinec, 1995; Hock, 1999, 2003). Recently, the most widely accepted
temperature index model is that of Hock (2003). The approach of daily melt
assumes the form

Estimation of the PWP using the original tank model and our
modified tank model (snowmelt

Estimation of the change of PWP using the original tank model
and our modified tank model (snowmelt

As shown in Fig. 10, our modified tank model and original tank model considering no time lag are used to estimate the change of PWP in summer. Both the original and modified tank model do reasonable estimate changes in PWP during summer. The original model, however, generally overestimates the PWP curve. The modified model matches the measurement curve better due to the infiltration time lag 2.

Evaluation of original and modified tank model.

The original model without snow accumulation and snowmelt failed to accurately estimate PWP during spring, as the change of PWP without time lag 1 caused by the original model to overestimate PWP from days 12 to 33 (Fig. 11). The modified tank model better reflects the peak of snowmelt (days 33–37) and matches the measurement curve well in consideration of time lag 1. The deviation derives from the naturally limited accuracy of snow accumulation and snowmelt models.

Figure 12 indicates evaluation index of original and modified tank model including correlation, root mean square error (RMSE) and relative error.

As shown in Fig. 13, modified tank model simulated the PWP levels in whole monitoring period.

Long-term consistency simulation of PWP using the modified tank model throughout the entire monitoring period (4 March 2009–23 April 2011).

In order to evaluate the performance of the modified tank model with respect to heavy rainfall and snowmelt, we introduce the standard Nash–Sutcliffe (1970) efficiency (NSE), which is the most widely used criterion for calibration and evaluation of hydrological models with observed data. NSE is dimensionless and is scaled onto the interval [inf. to 1.0]. NSE is taken to be the “mean of the observations” (Murphy, 1988) and if NSE is smaller than 0, the model is no better than using the observed mean as a predictor.

The modified tank model describes the fluctuation of PWP reasonably well,
especially during heavy rainfall days such as days 23 to 26 (43

We found a better correlation between measurements and our modified tank
model with 0.86 (RMSE: 0.97) than the original tank model in which all
precipitation was assumed to be rainfall and snowmelt was not considered with
0.04 (RMSE: 5.4) during snowmelt period. It has to be pointed out that the
snowmelt estimation is still not very precise, as the temperature index model
is relatively simple (Garen and Marks, 2005; Herrero et al., 2009; Lakhankar
et al., 2013). Also, we do not consider surface run-off due to the high
permeability of surface deposits. Our modified tank model, however, provides
a useful estimation of increased PWP in creeping landslide masses several
tens of metres deep. The NSEs of the original tank model and modified tank
model during the snowmelt season are

Compared to the simple tank model, our modified tank model improves the prediction ability by introducing the equivalent infiltration method to reduce the infiltration time lags. Compared to the recent multi-tank model researches (Ohtsu et al., 2003; Takahashi, 2004; Takahashi et al., 2008; Xiong et al., 2009), our modified tank model does not require complicated algorithms and several observation boreholes to optimize the parameters. It is a straightforward approach. The model integrates the snow accumulation–snowmelt model, which is not considered in other tank model researches. We present a flexible approach since the model can simulate groundwater table at least 2 years continuously without obvious accumulative error, unlike permeability-based numerical models or optimization parameter-based models that need refreshment at times (Takahashi et al., 2008; Xiong et al., 2009).

The naturally inevitable drawback for any “empirical model” is that it is physically not explicit. The presented model would need further adjustments for permafrost regions, with heavily frozen soils, for very steep slopes, with significant surface run-off and for very heterogeneous slopes, with complex fractured rock masses. However, it seems well suited for large mountain landslides on moderately inclined slopes in alpine conditions with significant snow accumulations.

Pore water pressure is one of the important dynamic factors in deep-seated slope destabilization and our modified tank model could help to anticipate critical states of deep-seated landslide stability a few days in advance by predicting changes in pore water pressure. In this paper, we propose a modified tank model for the estimation of increased pore water pressure induced by rainfall or snowmelt events in deep-seated landslides. Compared to the original tank model, we simulate the fluctuation of PWP more accurately by reducing the time lag effects induced by snow accumulation, snowmelt and infiltration into deep-seated landslides. In this modified model, a statistical method based on temperature and humidity controls precipitation type and a snowmelt model based on the temperature index method governs melting. Here we demonstrate a modified tank model for deep-seated landslides which includes snow accumulation, snowmelt and infiltration effects and can effectively predict changes in pore water pressure in alpine environments.

All data are available upon request from the corresponding author.

The authors declare that they have no conflict of interest.

The authors thank the support from the China Scholarship Council and monitoring data from project “alpEWAS”, especially John Singer for providing pore pressure data and supervising earlier stages of this project. This work was supported by the German Research Foundation (DFG) and the Technische Universität München within the funding programme Open Access Publishing. Edited by: Thomas Glade Reviewed by: two anonymous referees