The effect of preferential flow on the stability of landslides is studied through numerical simulation of two types of rainfall events on a hypothetical hillslope. A model is developed that consists of two parts. The first part is a model for combined saturated/unsaturated subsurface flow and is used to compute the spatial and temporal water pressure response to rainfall. Preferential flow is simulated with a dual-permeability continuum model consisting of a matrix domain coupled to a preferential flow domain. The second part is a soil mechanics model and is used to compute the spatial and temporal distribution of the local factor of safety based on the water pressure distribution computed with the subsurface flow model. Two types of rainfall events were considered: long-duration, low-intensity rainfall, and short-duration, high-intensity rainfall. The effect of preferential flow on slope stability is assessed through comparison of the failure area when subsurface flow is simulated with the dual-permeability model as compared to a single-permeability model (no preferential flow). For the low-intensity rainfall case, preferential flow has a positive effect on drainage of the hillslope resulting in a smaller failure area. For the high-intensity rainfall case, preferential flow has a negative effect on the slope stability as the majority of rainfall infiltrates into the preferential flow domain when rainfall intensity exceeds the infiltration capacity of the matrix domain, resulting in larger water pressure and a larger failure area.

Landslides are commonly triggered by rainfall events. Hydrological models can
be integrated with slope stability analysis methods to calculate the factor
of safety and predict the time and magnitude of landslides

The limit equilibrium method or infinite slope stability approach is
frequently integrated with Richards' equation

The strength reduction method ^{®}

The Darcy–Richards equation is the most widely used approach in current
software packages, but cannot effectively simulate preferential flow
resulting in rapid infiltration

Quantification of landslide triggering mechanisms is an essential step in
landslide forecasting. Some studies have shown that preferential flow is one
of the major mechanisms affecting the timing and location of landslides

Preferential flow and solute transport have been simulated at various scales
including the scales of pores, soil columns, hillslopes, and catchments

The objective of this study is to quantify the temporal and the spatial effect of preferential flow on slope stability, and to analyse its underlying hydrological mechanisms using numerical experiments of rainfall-induced shallow landslides. This paper is organised as follows. The subsurface dual-permeability hydrological model is described. The subsurface hydrological model is sequentially coupled with a soil mechanics model and a stress-field-based local factor of safety slope stability method (Sect. 2.2). The numerical experiments and parameterisation are discussed in Sect. 3. The hydrological and geotechnical results are given in Sect. 4. The influence of preferential flow on subsurface hydrological processes and consequent slope stability is discussed in Sect. 5 by comparing the results of single- and dual-permeability models.

The single-permeability model is described by one Richards' equation to
represent flow in a homogenous soil. The dual-permeability model divides the
flow domain into two overlapping and interacting continua, where two coupled
Richards' equations are used to describe the matrix flow and preferential
flow

The Brooks–Corey function is used to describe the hydraulic properties of both the matrix and
preferential flow domains

The total water content of the soil is the weighted average of the water contents of the two
domains:

The slope stability analysis is based on the local factor of safety approach

The local factor of safety

Structure of coupled dual-permeability model and soil mechanics model.

The influence of hydrology on slope stability is manifested in two ways. First, the unit weight function depends on the water content (Eq. 9). Second, the effective stress depends on the porewater pressure. In the dual-permeability model, the porewater pressure of the preferential flow domain is used in the computation of the effective stress.

Figure 1 summarises the structure of coupled dual-permeability and slope stability model. Two Richards' equations are coupled by the water exchange function. The hydrological results are sequentially coupled with a soil mechanics model without considering possible feedback of soil deformation on soil properties and the hydrological process.

In this study, COMSOL Multiphysics^{®} is used to develop a coupled hydrological
and slope stability model for both single-permeability and dual-permeability
subsurface flow

Computational mesh and boundary conditions.

Consider a slope of 23

The model domain is 42

Since the pressure head in the surface area can change drastically during rainfall, a very dense
mesh was used near the surface to accurately model the transient hydrological conditions. The mesh
density of the upper layer is approximately 0.25

Summary of parameters.

The volumetric ratio of the preferential flow domain

The soil hydraulic parameters are presented in Table 1. Preferential flow
plays an important role in the upper soil layer where there is an abundance
of macropores, but less so in the lower soil layer where macropores are
almost non-existent

Parameterisation of soil hydraulic properties for dual-permeability models is
difficult as the two conceptualised domains cannot be experimentally
separated. In this paper, the pragmatic approach of

The parameters of the soil mechanics model are also shown in Table 1. The
slope stability is a function of two parameters: the friction angle and the
effective cohesion. Decreasing the friction angle or increasing the effective
cohesion leads to a higher factor of safety. The friction angle is physically
constrained in a narrow range, and in this study is fixed. In numerical
modelling, effective cohesion

Intermittent and variable rainfall may significantly influence the pressure
response in the shallow layer soil, while the pressure response in the deeper
layer soil is driven by percolation and less dynamic to intermittent
rainfall. Two rainfall events are modelled: a low-intensity rainfall of
2

Flow component and water balance of study area.

Integrated fluxes for single-permeability model and
2

Integrated fluxes for dual-permeability model and 2

A schematic diagram of the subsurface flow components in the study area is shown in Fig. 3. Note that the study area is a small part of the model domain (Fig. 2). The main fluxes are the infiltration from rainfall (blue), the inflow/outflow along the left side and bottom (black), the seepage outflow along the surface (red), and the outflow along the right boundary (green).

Hydrological results for the single- and dual-permeability models are shown in Figs. 4 and 5,
respectively. The graphs on the left are results for the long-duration, low-intensity rainfall case
while the graphs on the right are results for the short-duration, high-intensity
rainfall. Integrated fluxes, as shown in Fig. 3, are reported in

Storage increase of single-permeability model and dual-permeability model.

For both models, all the rainfall infiltrates into the slope during the
beginning of the rain event and when the soil becomes saturated infiltration
decreases and saturation excess overland flow occurs. For the
single-permeability model and low-intensity rainfall overland flow starts
after 95

Water content distribution.

Water exchange rate distribution. Positive values (red): mean water exchange from preferential flow domain to matrix; negative values (blue): mean water exchange from matrix to preferential flow domain.

In the dual-permeability model (Fig. 5), the rainfall infiltration is divided over the two domains
and additional rainfall infiltrates into the preferential flow domain when the matrix domain reaches
infiltration capacity. Recall that the matrix domain is 90 % of the domain, and the
preferential flow domain is 10 % of the domain. A smaller fraction of rainfall infiltrates into
the preferential flow domain for the case of low-intensity rainfall (10–15 %) than for the case
of high-intensity rainfall (50–85 %). Overland flow starts after 80

The seepage outflow increases along the left, right, and bottom boundaries
during the rainfall event (Figs. 4c, d, and 5c, d) and is smaller than the
infiltration rate (storage is increasing). In the dual-permeability model and
the low-intensity rain, outflow along the surface boundary starts after
115

The integrated rainfall and water storage for the study area are shown for both models in Fig. 6. The water balance is obtained by integrating all flow components along the boundaries of the study area. The numerical water balance errors are between 2 and 3 %.

For all cases, the storage increase flattens out when the inflow decreases (Figs. 4 and 5). For the
high-intensity rainfall, the dual-permeability model stores 8 % less water than the
single-permeability model. The total storage after 150

For the dual-permeability model, the water exchange has a significant influence on the storage change in each domain. For the low-intensity rainfall, the storage in the preferential flow domain does not increase much after 6 h (Fig. 6). For the high-intensity rainfall, the storage in the preferential flow domain increases rapidly over the first 3 h as very little water infiltrates into the matrix domain due to the low infiltration capacity of the matrix. After 3 h, the preferential flow domain has almost reached full saturation and the large pressure difference between the preferential flow domain and matrix domain causes extensive water exchange (Fig. 5f).

The water content distribution in the study area is shown in Fig. 7 for both the single-permeability model (left-hand panels) and the dual-permeability model (centre and right-hand panels). The water exchange rate between the matrix and preferential flow domains of the dual-permeability model is shown in Fig. 8. The infiltration process of the dual-permeability model differs significantly from that of the single-permeability model.

The initial water content distribution in the matrix, as well as preferential flow domains, is similar for both models. During the rainfall events, the wetting front in the single-permeability model develops parallel to the surface and propagates downward. This holds for both low and high rainfall intensities (Fig. 7 left-hand column). The wetting front generally reaches the groundwater table at the toe of the slope first, after which the infiltrated water continuously enlarges the saturated area.

In the dual-permeability model, the combined effects of the preferential flow and the matrix flow show a more complicated response. For the low-intensity rainfall, infiltration is dominated by matrix flow, as 90 % of the subsurface consists of the matrix. Because the rainfall intensity is lower than the saturated conductivity of the matrix domain, on the surface boundary, 90 % of the rainfall infiltrates into the matrix domain and 10 % of the rainfall infiltrates into the preferential flow domain. The pressure difference between the two domains drives the water exchange at the matrix wetting front (Figs. 5e and 8a). Inside the flow domain of the slope, 10 % of matrix flow transferred to preferential flow due to water exchange in the soil. At first, water quickly reaches the soil layer interface by preferential flow where it transmits to the matrix, although this exchange flux is very small (Figs. 5e and 8a). After sufficient time (70 h), a much stronger matrix flow (taking about 80 % of the infiltrated rainfall) reaches the soil layer interface and generally reverses the water exchange direction (Fig. 5e). Overall, water exchange during low-intensity rainfall in the study area is dominated by flow from the matrix to the preferential flow domain (Fig. 8a and b).

For the high-intensity rainfall, the rainfall intensity is 8.4 times the matrix saturated hydraulic
conductivity. The percentage of infiltration into the matrix domain decreases from 90 to 50 %
within the first half hour, and continues to decrease to less than 20 % after 1.5

The local factor of safety is computed based on the computed water-pressure distribution
(Fig. 7). The distribution of the local factor of safety is shown in Fig. 9 for the initial
condition and after 150

A local factor of safety below 1 indicates a potential failure area. The area
with a

The size of the potential failure area is plotted vs. the cumulative rainfall in Fig. 10 for the two
different rainfall events and two sets of cohesion values. The results for the same cohesion values
(

The results for different cohesion values (

Final slope stability after the rainfall event (

Development of the failure area under different rainfall intensities and soil cohesion.

The slope stability result are directly related with subsurface hydrological results. For the low-intensity rainfall, the failure area for the single-permeability model is very similar in size and location to the dual-permeability model as the location of the water table is very similar in both models (Fig. 7). The initial condition of the dual-permeability model is slightly more stable than that of the single-permeability model, since the preferential flow domain has a higher drainage capacity and, consequently, a lower porewater pressure. In the case of low-intensity rainfall, the matrix flow dominates the groundwater recharge and, consequently, the slope instability. Furthermore, the porewater pressure in the preferential flow domain is very low due to its strong drainage capacity. As a result, the failure area calculated by the dual-permeability model under low-intensity rainfall is slightly smaller than that calculated by the single-permeability model (Fig. 10a). The location of the failure area is similar in the single- and the dual-permeability domain (Fig. 9).

For the high-intensity rainfall, the failure area is significantly larger for the dual-permeability model than for the single-permeability model as the perched water table in the preferential flow domain is much more extensive in the dual-permeability model as compared to the single-permeability model (Fig. 7). The regular wetting front of the single-permeability model does not reach the interface between soil layers, and the failure area is limited to the toe of the slope. For the dual-permeability model, the high-intensity rainfall results in a rapid infiltration through preferential flow, which quickly reaches the interface between soil layers, and increases the degree of saturation and pressure head of the deeper soil. Positive porewater pressure occurs in the preferential flow domain before the entire slope is fully saturated, and produces a larger failure area than in the equivalent single-permeability model.

The role of preferential flow in hydrology focuses mainly on the rapid
vertical infiltration of water and contaminant

Soil heterogeneity is one of the most difficult problems in both hydrology
and soil mechanics studies. As an alternative to the continuum approach used
here, preferential flow may be simulated by explicitly including fissures,
pipes, or fracture networks in discrete (or discontinuous) models. Several
field studies

Parameters setting of water exchange coefficients in different literature.

The dual-permeability model is a useful tool to simulate subsurface stormflow
and solute transport in a hillslope when the parameterisation is able to
capture the hydraulic characteristics of each domain

In this paper, flow in both domains is described with the Darcy–Richards
equation, which is valid when the macropores have a relatively small size,
and the macropore flow is still viscous

In the dual-permeability model, the two domains are in general not at
equilibrium. The parameterisation of the water exchange between the two
domains governs whether a dual-permeability model behaves as a
dual-permeability model or mimics the behaviour of a single-permeability
model. The water exchange is governed by the pressure difference between the
two domains and two parameters: the water exchange coefficient and the
average hydraulic conductivity between the two domains (Eq. 6). The average
hydraulic conductivity in turn is a function of the hydraulic conductivities
of the two domains, which are a function of the pressure head. The larger the
product, the quicker the two domains equilibrate. Specifically, the
sensitivity analysis of

The parameterisation of the water exchange used in this study was compared
with previous studies (see Table 2). Estimation of the water exchange
coefficient from physical measurements is very difficult. The most widely
used equation is

It may be seen from Table 2 that the magnitude of the product

In the dual-permeability model, the porewater pressure of the matrix and the
preferential flow domains are different and water flows from the domain with
a higher pressure to the domain with a lower pressure. Van der Spek et
al. (2013) showed that in the case of varved clays with a low hydraulic
conductivity of the soil matrix and a low density of fissures, the time delay
between water entering the fissure network and an increase in pressure in the
matrix is relatively large. This study concerns a system with a very high
density of macropores and consequently the numerical simulations show only
a small time delay for the pressure propagation from the preferential flow
domain to the matrix domain. The porewater pressure of the preferential flow
domain is used for the effective stress calculation in the slope stability
analysis, but failure time and area are only slightly different when the
matrix porewater pressure is used for the slope stability analysis. Field
evidence

This study is not the first to address the influence of preferential flow on
subsurface flow and slope stability. Preferential flow has an effect on
infiltration and drainage fluxes and as such influences the triggering
factors for rainfall-induced landslides. Moreover, storage capacity relates
to the pore distribution in a soil and controls the antecedent condition or
the cause of landslide occurrence

Parameterisation of a dual-permeability model is difficult in practice

The reverse is true, however, for high rainfall intensities, when the matrix reaches infiltration capacity early on. In these cases the preferential flow system dominates because water that cannot infiltrate into the matrix domain infiltrates into the preferential flow domain instead, resulting in a large pressure increase with a negative effect on slope stability. A much smaller pressure increase is simulated with a single-permeability model for the same high-intensity rainfall. Consequently, the stability is overestimated with a single-permeability model even when equivalent parameters are used.

A coupled dual-permeability and slope stability model was developed to simulate the influence of
preferential flow on subsurface hydrology and consequent slope failure area. The dual-permeability
model is able to simulate both preferential flow and matrix flow. The slope failure area was
determined with a local factor of safety analysis. Numerical experiments were carried out to study
the effect of rainfall events on slope stability with both a single-permeability (no preferential
flow) and a dual-permeability model. A 23

For low-intensity rainfall, the failure area of both models is similar when the cohesion of the upper and lower layers is equal, but the failure area is significantly larger in the single-permeability model as compared to the dual-permeability model when the cohesion of the upper layer is lower than the cohesion of the lower layer. During low-intensity rainfall, preferential flow has a positive effect on slope stability as it drains water from the matrix domain and decreases the water pressure.

For high-intensity rainfall, the failure area of the dual-permeability model is significantly larger than the single-permeability model whether the cohesion values of the two layers are equal or not. During high-intensity rainfall, the rainfall intensity is larger than the infiltration capacity of the matrix domain so that most of the rainfall infiltrates into the preferential flow domain. As a result, the water pressure increases very quickly in the preferential flow domain resulting in a much larger failure area than is the case for the single-permeability model.

In summary, two different effects of preferential flow on slope stability were identified with a coupled dual-permeability and soil mechanics model. Preferential flow has a positive effect on slope stability during low-intensity rainfall and a negative effect on slope stability during high-intensity rainfall. The magnitude of the effect is a function of the soil hydraulic properties and soil mechanical properties of a specific slope. Identification of parameter ranges for which this behaviour is significant requires further investigation.

The authors are grateful to both Jan Wienhöfer and the anonymous reviewer, and Editor Uwe Ehret for their extensive, profound and constructive comments and suggestions that substantially improved the quality of paper. The first author was financially supported by the China Scholarship Council for his PhD research with the project reference number of 2011671055. Edited by: U. Ehret