Flow-like landslides, such as flow slides and debris avalanches, have caused serious infrastructure damage and casualties for centuries. Effective numerical simulation incorporating accurate soil mechanical parameters is essential for predicting post-failure landslide mobility. In this study, smoothed particle hydrodynamics (SPH) incorporating soil ring shear test results were used to forecast the long-runout mobility for a landslide on an unstable slope in China. First, a series of ring shear tests under different axial stresses and shear velocities were conducted to evaluate the residual shear strength of slip zones after extensive shear deformation. Based on the ring shear test results, SPH modeling was conducted to predict the post-failure mobility of a previously identified unstable slope. The results indicate that the landslide would cut a fire service road on the slope after 12 s and cover an expressway at the foot of that slope after 36 s. In the model, the landslide would finally stop sliding about 38 m beyond the foot of the slope after 200 s. This study extends the application of the SPH model from disaster simulations to predictive analysis of unstable landslide. In addition, two sets of comparative calculations were carried out which demonstrate the robustness of the SPH method.

Flow-like landslides triggered by intense earthquakes or rainfall, such as debris and rock avalanches, have caused serious infrastructure damage and casualties for centuries (Wang et al., 2005; Okada et al., 2007). This kind of landslide is commonly high speed and has a long runout distance. For example, a large landslide in southern Italy in February 2010 had a runout distance of 1.2 km and necessitated the evacuation of nearly 2300 people. This landslide was triggered by heavy and prolonged rainfall between August 2009 and February 2010 (Gattinoni et al., 2012). The 2009 Shiaolin landslide in Taiwan, induced by a cumulative rainfall of nearly 1700 mm from Typhoon Morakot, buried Shiaolin Village and resulted in more than 400 people dead and missing (Tsou et al., 2011). Numerical simulations that incorporate accurate soil mechanical parameters are a powerful tool for simulating landslide runout distances; these simulations can provide fundamental reference information for landside disaster mitigation (Žic et al., 2015; Yerro et al., 2016).

Overview of the Dafushan landslide.

The main numerical methods for simulating landslides are the discrete element methods and the continuum methods (Lu et al., 2014; Wu et al., 2017). Using a discrete element method, such as the distinct element method (DEM) or discontinuous deformation analysis (DDA), the nonphysical parameters cannot be determined exactly (Huang et al., 2014). However, continuum methods based on grids, like the finite element method (FEM) and the finite difference method (FDM), have the shortcomings of grid distortion and low accuracy for the numerical analysis of a landslide with a long runout. Recently, a new numerical method has been used to overcome these limitations, namely the smoothed particle hydrodynamics method (SPH) (Bui et al., 2008). This method is in the framework of continuum methods. SPH is a pure Lagrangian, meshless hydrodynamics method, and it is capable of simulating flow deformation, free surfaces, and deformation boundaries (Liu and Liu, 2003). Several studies have demonstrated the efficiency of the SPH method for the large deformation analysis post landslide. Huang et al. (2014) provided a general view of SPH applications for solving large deformation and failure problems such as dam breaks, slope failure, and soil liquefaction flow. Pastor et al. (2009) applied a depth-integrated, coupled SPH model successfully to simulate catastrophic flow-like landslides that occurred in southern Italy in 1998. Cascini et al. (2014) proposed an SPH model to represent two actual flow-type events accurately. Cuomo et al. (2016) used SPH to simulate flow-like landslides (debris flows and debris avalanches) and discussed the influence of bed entrainment on landslide propagation. Hu et al. (2015) conducted two- and three-dimensional SPH numerical simulations of flow-like landslides triggered by the 2008 Wenchuan earthquake in China and proposed that the SPH method is well suited for modeling free surfaces, moving interfaces, and extensive deformation.

Geology and soil at the Dafushan landslide.

Study into the residual shear strength property of slip zones under large shear deformation is essential to landslide long-runout mechanism explanations (Tika and Hutchinson, 1999; Wen et al., 2007). Because the physical sample displacement using conventional laboratory shear tests, like direct shear tests and triaxial shear tests, is limited to about 10 mm (Casagli et al., 2006; Okada et al., 2007; Van Asch et al., 2007), the shear behavior for large shear displacements cannot be assessed by these methods (Dai et al., 2016). Ring shear tests, which can impart extremely large shear strains, may be the ideal laboratory tool for extensive shear deformation testing (Okada et al., 2007; ASTM Standard D7608-10, 2010). Several studies have applied ring shear tests to study the residual shear strength of soils (Wang et al., 2005; Fukuoka et al., 2007; Li et al., 2013; Hoyos et al., 2014). For example, Fukuoka et al. (2007) applied a newly developed ring shear test to study shear zone development during large displacements. That study pointed out that a ring shear test is the most appropriate test for studying long-travel landslides. Kimura et al. (2014) studied the effect of the shearing rate on the residual strength of landslide soils using ring shear tests. Zhang et al. (2011) used ring shear tests to study the transform mechanism of the slide–debris flow under large deformations. Li et al. (2017) explored the residual strength of silty sand under different degrees of over consolidations and different shear rates using ring shear tests.

This study presents an effective numerical simulation method, namely SPH, that incorporates accurate soil mechanical parameters derived from ring shear tests. The aim is to predict the downslope flow after slope failure of a previously identified unstable slope and thereby provide basic information for landside disaster mitigation. First, this paper describes the geomorphological and geological setting, hydrogeology and rainfall, and triggering factors of the landslide examined for this case study. These descriptions are based on detailed fieldwork. Next, a series of ring shear tests under several different normal stresses and shear rates were performed to identify the shear strength of the landslide soil. Finally, an SPH-based numerical simulation of the landslide was run to predict the extent of the landslide and track the slide velocity at different times.

The Dafushan landslide, located in the Panyu District, Guangzhou city,
southern China, was selected for this case study (Fig. 1a). The slope is primarily
composed of Cretaceous silty mudstone, conglomerate, and sandstone overlain
by Quaternary silty clay (Yu et al., 2017) (Fig. 1b). The landslide is
creeping from the northeast to the southwest covering an area of about
70 m

Photograph of the GCTS SRS-150 Residual Ring Shear Testing System and an image of the GCTS software interface.

The ground was first found to be unstable in May 2013. This instability was manifested mainly by cracks in the ground surface and cracks in the road that lies around the mountain. The road was built for fire response services in May 2011. The relevant departments repaired the damaged road immediately to guarantee the normal operation of the road. However, additional evidence of instability was found in the middle of August 2013 after a period of intense rainfall. The road was damaged again, and the trees up the hill began to tilt. Based on preliminary field investigation, the main factors that triggered the landslide were deduced.

Rainfall is the main supply source of groundwater in the study area. The average annual rainfall is 1635.6 mm. Most of the rain falls between April and September; this rainfall accounts for 81 % of the yearly precipitation. In the rainy season, the groundwater level rises significantly and reduces the shear strength of the soil. Combined with the rainfall flushing effect on the slope surface, the stability of the slope is decreased significantly.

The shallow part of the landslide is mainly composed of silty clay (Fig. 2) and a strongly weathered mudstone soil with a low shear strength. These materials soften and disintegrate when wet; thus, the slope is stable in the dry season but shows signs of instability in the rainy season.

Human engineering activities impaired the natural stability of the slope. Two examples include (a) a cut that was made in the slope in order to build the fire service road and (b) the heavy high-voltage power line tower that increases the downward pressure on the slope (Fig. 1d).

A GCTS Residual Ring Shear Testing System (model SRS-150) produced by
Geotechnical Consulting and Testing Systems (GCTS) in 2012 in the USA was
used for the ring shear tests conducted for this study (Fig. 3). The SRS-150
is a fully automated electropneumatic and servo-controlled testing system
used for determining the residual strength of continuously sheared soil.
Shear torques of up to 820 Nm can be applied, consolidation stress can be up
to 1000 kPa, and unlimited angular rotation is allowed (Hoyos et al., 2014;
Dai et al., 2016). The unit is capable of applying shearing rates of 0.001 to
360

A schematic illustration of a sample in the apparatus is shown in Fig. 4. For testing granular materials, the device accepts ring-shaped samples with a 150 mm outer diameter and a 100 mm inner diameter. The sample is sheared by rotating the upper half of the testing unit and keeping the lower half motionless. Two types of shearing modes, either a shear speed control mode or a shear torque control mode, can be chosen.

Schematic cross sections of the ring shear apparatus shown in Fig. 3.

The samples studied were samples of the silty clay soil from the Dafushan landslide shown in Fig. 2b. The soil's physical properties are listed in Table 1.

Physical properties of a soil from the Dafushan landslide.

A series of ring shear tests were performed to determine the physical
properties of the landslide soil after it had been extensively sheared. The
saturated soil sample was first consolidated under normal stress, and then
it was sheared to a residual state under naturally drained conditions using
the shear speed control mode of the ring shear test system. For these tests,
normal stresses of 50, 100, 200, 300, and 400 kPa were used to consolidate
the soil samples, and different shear rates (1, 5, 10, 20

Consolidation stresses, shearing rates, and saturations for soil specimens subjected to laboratory ring shear tests.

Shear stress–angular displacement curves for the landslide soil at a
shear rate of 5

Figure 5 shows the relationships between shear stress and angular
displacement under a shear rate of 5

The residual strength envelope of the soil can be illustrated by plotting the shear stress against axial stress, as shown in Fig. 6.

Residual strength envelopes for the landslide soils;

Cohesion and internal friction for landslide soils at peak and residual shear strengths calculated from the Mohr–Coulomb criterion

Based on the Mohr–Coulomb criterion, the peak and residual shear strengths of the landslide soil were obtained and are listed in Table 3. Because the main trigger for the Dafushan landslide was heavy rain, the residual strength of saturated soil is used for the numerical simulation presented in Sect. 4 of this paper.

Figure 7 shows the relationships between shear stress and angular
deformation under a normal stress of 200 kPa at shear rates of 1, 5, 10, and
20

Shear stress–angular displacement curves for saturated landslide soil under 200 kPa axial stress.

Differences in shear strengths and angular displacements for saturated landslide soil at different shearing rates.

To analyze the relationship between the residual shear strength of the
saturated soil and the shear strain rate, the residual shear stress–shear
strain rate curve can be drawn (Fig. 8). The formula for calculating the
shear strain rate is

As shown in Fig. 8, the residual shear strength of the saturated soil as
determined by these experiments increases linearly with shear strain rate.
This result agrees with the results reported by Li et al. (2013) and Dai et
al. (2016). This relationship is similar to the behavior of a viscous fluid
and can be expressed by Eq. (2):

Residual shear stress–shear strain rate curves for the saturated landslide soil.

Flow chart for the SPH numerical simulation used in this study.

Smoothed particle hydrodynamics is a mesh-free and fully Lagrangian method based on fluid dynamics. In Lagrangian models, the coordinates move with the medium being modeled. The continuous medium is discretized into a series of arbitrarily distributed discrete elements (called particles), and field variables (like energy, velocity, density, or any other variable) for each particle can be calculated in the form of SPH (Dao et al., 2013; Huang and Dai, 2014).

Longitudinal section of the SPH numerical model of the Dafushan landslide. The particles representing the slide mass are shown in red, and the particles representing the fixed boundary are shown in blue.

Predicted results in Dafushan landslide with different calculating parameters.

Parameters used in the SPH simulation of the Dafushan landslide.

The SPH method is built on interpolation theory with two essential
approximations. These approximations are smoothing and the particle (Huang
et al., 2014). The smoothing approximation, also known as kernel
approximation, describes a function in a continuous form as an integral
representation. The particle approximation means that the value of a
function for a particle can be determined by the average value of all the
particles in the support domain. The smoothing and the particle
approximations can be expressed, respectively, by the following two
equations:

The Navier–Stokes equations in a computational fluid dynamics framework are
used as governing equations in this study. The equations of continuity and
motion in the SPH version can be expressed as

Predicted results in Dafushan landslide with different calculating parameters.

The Bingham model has been proven as one of the most effective models for
runout simulation of flow-like landslides (Marr et al., 2002; Moriguchi et
al., 2009). In this paper, the Bingham flow model is also adopted as the
constitutive model for the Dafushan landslide in this study. The
relationship between shear stress and strain rate can be written as

For this study, the concept of equivalent viscosity was adopted to better
integrate the Bingham model into the SPH framework. The equivalent viscosity
can be expressed as

Longitudinal profiles showing the results of the SPH forecasting
model. The panels represent the outline of the Dafushan landslide from the
time the slide is initiated at

A flow chart for the SPH numerical simulation is shown as Fig. 9. Details about how the calculations are carried out can be found in Huang et al. (2014). The accuracy of the SPH program in landslide modeling was also fully validated in Huang et al. (2014).

Velocity curve of the front and rear edges of the Dafushan landslide as predicted by the SPH model.

Previous studies have been conducted on the verification analysis of landslides, which proves the accuracy of SPH model is relatively high (Huang et al., 2012; Hu et al., 2015). The error of slide distance can reach 4.6 % (Huang et al., 2012). Meanwhile, this study extends the application of the SPH model in combination with accurate soil parameters derived from ring shear tests to predictive analyses of unstable landslides. In addition, two sets of comparative calculations were carried out which demonstrate the robustness of the SPH method.

Based on a terrain model derived from an unmanned aerial vehicle and structure from motion (Yu et al., 2017), an SPH simulation of the failure process of the Dafushan landslide was conducted. Figure 10 is a longitudinal section of the model slide, with the particles in the slide mass shown in red, and the boundary particles shown in blue. The soil particles in the model can be deformed in both the vertical and horizontal directions under gravitational force in the vertical direction.

Displacement curve of the front and rear edges of the Dafushan landslide as predicted by the SPH model.

Table 5 lists the parameters used in the SPH simulation of the landslide. The
shear strength parameters listed in Table 5,

Figures 12a–f show the flow process of the Dafushan landslide predicted by
the SPH simulation. In Fig. 12, the solid black line represents the bed on
which the mass slides, and the red dashed line represents the SPH-modeled ground
surface. At time

Because this SPH simulation is a Lagrangian method, it can track the velocity
and displacement of each particle accurately. The velocity and displacement
curves for the front and rear edges of simulated landslide are shown in
Figs. 13 and 14. As shown in Fig. 13, the velocity of the front edge increases
rapidly after slope failure begins and reaches three velocity peaks as the
slide passes the three steps labeled A, B, and C shown in Fig. 10. The speed
of the front and the times after initiation that it reaches these three steps
are 5.23 m s

According to Fig. 14, the maximum flow distances of the front and rear
edges are up to 95.4 m and 12.3 m, respectively. The front edge of the slide
will destroy the fire service road about 10–12 s after the slide starts and reach
the highway at

In this study, the SPH method incorporating soil mechanical parameters
derived from ring shear tests is used to predict the flow of a potential
landslide that could develop on an unstable slope in Guangzhou city, China.
This study provides basic information for landside disaster mitigation. The
conclusions are the following.

Under the same shear rate, soil shear strength increases with increasing axial stress. For the conditions used in this study, under high axial stress (> 200 kPa) the soil exhibits strain softening.

During ring shear tests, as the shear rate increases, the residual shear strengths increase slightly, but the peak shear strengths decrease as the angular displacements at peak shear strength increase significantly.

An SPH-based numerical simulation of the potential Dafushan landslide
conducted to predict the scope of the landslide and track the slide velocity
at different times shows that the landslide would cut the fire service road at

The data are available from the authors upon request.

MY undertook the work and wrote the manuscript under the supervision of YH. WD and HC helped with test data collection and numerical analysis.

The authors declare that they have no conflict of interest.

This work was supported by the National Key R&D Program of China (grant no. 2017YFC1501304); the National Natural Science Foundation of China (grant nos. 41625011 and 41807293); the Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education, Tongji University (grant no. KLE-TJGE-B1704); the Fundamental Research Funds for National University, China University of Geosciences (Wuhan) (grant no. CUGL170806); and the National Key Technologies R&D Program of China (grant no. 2012BAJ11B04). Edited by: Mario Parise Reviewed by: two anonymous referees