Draft
Back-analysis of geophysical flows using 3-dimensional
runout model
Journal: Canadian Geotechnical Journal
Manuscript ID cgj-2016-0578.R1
Manuscript Type: Article
Date Submitted by the Author: 20-Jul-2017
Complete List of Authors: Koo, R.C.H.; Geotechnical Engineering Office, Kwan, J.S.H.; 12/F Civil Engineering and Development Department Building, Lam, Carlos; Geotechnical Engineering Office Goodwin, George; Hong Kong University of Science and Technology, Department of Civil and Environmental Engineering
Choi, Clarence; Hong Kong University of Science and Technology, Department of Civil and Environmental Engineering Ng, C.W.W.; Hong Kong University of Science and Technology, Department of Civil and Environmental Engineering Yiu, Jack; Ove Arup Foundation Ho, K.K.S; Geotechnical Engineering Office, Pun, W.K.; Geotechnical Engineering Office
Is the invited manuscript for consideration in a Special
Issue? : N/A
Keyword: equivalent internal friction angle, finite-element method, geophysical flows, geophysical flow case-study
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Back-analysis of geophysical flows using 3-dimensional
runout model
R.C.H. Koo, J.S.H. Kwan, C. Lam, G.R. Goodwin, C.E. Choi, C.W.W. Ng, J. Yiu,
K.K.S. Ho, and W.K. Pun
Raymond C.H. Koo (corresponding author)
Geotechnical Engineer, Geotechnical Engineering Office, Civil Engineering and
Development Department, Hong Kong SAR Government
E-mail: [email protected]
Telephone: +852 6078 3587
Julian S.H. Kwan
Chief Geotechnical Engineer, Geotechnical Engineering Office, Civil Engineering and
Development Department, Hong Kong SAR Government
E-mail: [email protected]
Carlos Lam
Geotechnical Engineer, Geotechnical Engineering Office, Civil Engineering and
Development Department, Hong Kong SAR Government
E-mail: [email protected]
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George R. Goodwin
MPhil student, Department of Civil and Environmental Engineering, Hong Kong University
of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
E-mail: [email protected]
Clarence E. Choi
Research Assistant Professor, Department of Civil and Environmental Engineering, Hong
Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
E-mail: [email protected]
Charles W.W. Ng
Chair Professor, Department of Civil and Environmental Engineering, Hong Kong University
of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
E-mail: [email protected]
Jack Yiu
Associate, Arup, Level 5, Festival Walk, 80 Tat Chee Avenue, Kowloon Tong, Kowloon,
Hong Kong.
E-mail: [email protected]
Ken K.S. Ho
Deputy Head, Geotechnical Engineering Office, Civil Engineering and Development
Department, Hong Kong SAR Government
E-mail: [email protected]
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W.K. Pun
Head, Geotechnical Engineering Office, Civil Engineering and Development Department,
Hong Kong SAR Government
E-mail: [email protected]
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Abstract:
Predicting the mobility and delineating the extent of geophysical flows remains a challenge
for engineers. The accuracy of predictions hinges on the reliability of input parameters of
runout models. Currently, limited field data for landslide case histories are available for
benchmarking the performance of runout models. Key rheological parameters, such as the
equivalent internal friction angle, cannot be measured directly using laboratory experiments,
and must instead be determined through back-analyses. A series of dynamic back-analyses
was carried out for notable landslide case histories in Hong Kong, accounting for the effects
of pore water pressure on the equivalent internal friction angle, using a three-dimensional
finite-element mobility model. The recorded and simulated run-out distances, as well as
lateral spreading, were compared. Results reveal that the back-analysed equivalent internal
friction angles resulting from open-hillslope failures and from channelised geophysical flows
are from 25° to 30°, and 15° to 20°, respectively. This is attributed to incised geophysical flow
channels having an elevated water head and higher degree of saturation compared to
open-hillside slope surfaces, wherein the induced elevated pore water pressure profoundly
lowers the equivalent internal friction angle. The back-calculated values may be useful for
finite-element-based design of mitigation measures.
keywords: equivalent internal friction angle; geophysical flows; finite-element
method; geophysical flow case-study
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Introduction
Channelised geophysical flows are a serious hazard in mountainous regions worldwide (Jakob
and Weatherly 2003). Remedial measures, such as reinforced concrete barriers, may be used
to arrest flows before they reach downstream facilities (Lo 2000). To effectively design such
remedial measures, engineers must estimate the likely velocity, depth, path and reach of the
flow (Choi et al. 2015). Hungr (1995) suggested that the key governing parameters required to
simulate the motion of geophysical flows are the internal friction angle and the parameters
that govern the basal rheology. (see also O’Brien and Julien 1985, 1988; Sosio et al. 2007;
2012; Hungr et al. 2007). (The energy dissipation term used in DAN is the Voellmy
turbulence coefficient (not necessarily due to turbulence within a flow: Sosio et al. 2012), but
there are other methods of implementing energy dissipation (see O’Brien 1993 and Iverson
and George 2014). However, it was also reported that not all of these properties can be
measured in laboratory experiments, and must instead be determined through numerical
back-analyses. In particular, the internal friction angle dictates the shear strength and energy
dissipation of the flow, which heavily affects flow-structure interaction (Mancarella and
Hungr 2010; Aaron and Hungr 2016; Ng et al. 2017). However, the internal friction angle is
not readily measurable during flows, and must be back-calculated. Many models are based on
the Savage-Hutter assumption, which assumes that the interior of the flow is governed by an
internal friction angle (Savage and Hutter 1989; Hutter et al. 2005). The internal friction angle
of the flow may be inferred using the results of numerical methods by comparing the actual
runout with that computed. Suitable models which can be used to implement the
Savage-Hutter assumption include depth-averaged methods (e.g. Hungr 1995; and Kwan and
Sun 2006), smoothed particle hydrodynamics (e.g. Huang et al. 2012), and constitutive
models in large-deformation finite-element packages (e.g. Li and Liu 2002). (Many other
numerical models are available (see Soga et al. 2016), but a comprehensive discussion is
beyond the scope of this paper.)
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Depth-averaged continuum models can assess flow kinematics for free-field conditions. Both
2D (e.g. DAN and 2D-DMM; Hungr 1995 and Kwan and Sun 2006 respectively) and 3D (e.g.
3D-DMM; Kwan and Sun 2007) versions exist. These depth-averaged models are based on
plastic theory and discretise the mass into a series of inter-connected vertical slices using a
Lagrangian formulation and solve the depth-averaged shallow water equations (McDougall
and Hungr 2004). The effects of pore water pressure and energy dissipation are lumped at the
base of the slices as shear forces. The internal friction angle only imparts shear strength to the
flow at the interfaces between slices. The value of the back-calculated internal friction angle
from studies such as Mancarella and Hungr (2010) and Aaron and Hungr (2016), which use
numerical methods based on Savage and Hutter (1989) is thus likely to be an overestimate.
This is because whilst the lateral pressure is considered, mesoscopic shearing of the flow
causing frictional energy losses is neglected (Kwan et al. 2015). It is assumed that frictional
losses only occur at the base of the flow: internal frictional shearing between grains is not
considered, and energy dissipation within the flow body in accounted for using a ‘turbulence’
term. The back-calculated basal friction angle must therefore be higher than the real value to
compensate for energy dissipation due to internal frictional shearing between grains. With the
exception of centripetal accelerations caused by terrain curvature, Savage-Hutter models also
neglect vertical momentum, although Denlinger and Iverson (2004) state that the change of
momentum in the z-direction is essential for stresses caused by irregular terrain.
Savage-Hutter models additionally assume that the lateral earth-pressure coefficients are
correlated with lateral displacement (as oppose to explicitly calculated in LS-DYNA). This
reduces the ability of the model to deal with abrupt topography changes, including interaction
with rigid structures such as barriers. Indeed, since impact cannot be directly modelled, the
computed velocity and flow depth at a barrier must be input separately into the hydrodynamic
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equation (Hübl et al. 2009) to calculate the impact force, which cannot capture typical
non-uniform loading profiles (Ng et al. 2017).
In smoothed particle hydrodynamics (SPH), geophysical flows may be modelled as an
effective fluid (Pastor et al. 2014; Soga et al. 2016; He et al. 2017). The internal stress state
may be modelled using the Savage-Hutter assumptions. The fluid is divided into discrete
particles, the motion of which is governed by Newton’s laws. These particles are assigned a
characteristic distance called the ‘smoothing length’. Properties such as velocity and density
are then interpolated between particles based on the smoothing length. However, an increase
in the number of particles leads to an increase in computation time. Modelling particles
sufficiently fine to interact realistically with complex 3D terrain problems may thus be
computationally impractical.
Large-deformation finite element methods that can model geophysical flows are also available
(e.g. LS-DYNA: Ng et al. 2017; and Di et al. 2007). The computational domain is discretised
using a mesh of elements. Eulerian (Li and Liu 2002) and Lagrangian (Ng et al. 2017)
treatments are available. The displacement, velocity, acceleration, stress and strain of the of
the elements considers Newton’s laws of motion and energy conservation principles.
Elements are free to move in any direction, whilst the finite element mesh is re-generated
every time step. A key advantage of this method is that the internal shear profile, and hence
shear strength, can be explicitly simulated in terms of the internal friction angle. (The internal
friction angle used in these finite-element methods is fundamentally different to that of the
Savage-Hutter family of models, since it does not simply govern earth pressure). This means
that impact can be explicitly modelled: the bending moment on a structure should be a
function of the stress profile of the impacting flow (Ng et al. 2017) rather than being assumed
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constant along the height of the structure. Furthermore, complex 3D geometries can be
handled by using a sufficiently fine mesh; the mesh size can be non-uniform to increase
computational efficiency.
In this study, LS-DYNA is used to back-analyse five well-documented case histories of
geophysical flows in Hong Kong. The aim is to establish a reliable range of equivalent
internal friction angles of dynamic geophysical flows for design use. The adopted numerical
method is first validated against data from laboratory experiments reported in the open
literature, after which selected case histories of geophysical flows in Hong Kong are
back-analysed to obtain the internal friction angles of the geological material. Back-analyses
were based on matching the simulated and actual run-out distances and, where appropriate,
the extent of lateral spreading and flow thickness. Comparison of velocities for the flows
considered in this study was also possible for Sham Tseng San Tsuen (case 4), where field
data was available. Values for key parameters have been adopted from the literature
throughout the case studies in this manuscript.
Numerical method
LS-DYNA is a general-purpose finite-element program developed by Livermore
Software Technology Corporation (Hallquist 2006). In geotechnical engineering, LS-DYNA
has been used to solve a wide variety of dynamic and high strain-rate problems, such as the
seismic performance of reinforced soil walls and the simulation of soil behaviour under blast
loading (An et al. 2011; Lee and Chang 2012; Xu and Zhang 2015). Recently, this software
has also been adopted to study the performance of barriers in resisting geophysical flows
(Huang et al. 2012; Kwan et al. 2015). Compared to the conventional depth-averaged
numerical models in which the flow mass is discretised into a series of inter-connected slices
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(Kwan and Sun 2006, 2007), the finite-element method can simulate explicitly the internal
shearing of the geophysical flow material. A finite-element model can also be used to study
the interaction between geophysical flows and structures such as buildings and rigid barriers.
Interaction depends on input parameters such as the internal and basal friction angles, as well
as the density of flow material (Ng et al. 2017).
Numerical procedure and modelling
Fig. 1 shows the steps followed during the finite-element analyses. The topographic
surface was generated using quadrilateral rigid shell elements with dimensions 2 m by 2 m,
which are solid planar surfaces. The geophysical source material was generated as a
hexagonal mesh, the elements of which represented the geophysical material. At the landslide
source location, a ‘lid’ (not shown) was constructed using rigid shell elements to retain the
source material. The topography of the ‘lid’ conformed to the topography. A container (not
shown) was also generated using shell elements to restrict the lateral movement of the
material at the source location. The container facilitates ‘dam-break’ conditions, wherein the
entire mass fails simultaneously; this may not reproduce realistic initiation conditions
(Iverson and George 2014), but is widely accepted for studying transportation (e.g. Iverson et
al. 2010) and impact mechanisms (e.g. Choi et al. 2015; Ashwood and Hungr 2016). The
extent of the container is nonetheless determined from records of the failure zone. Therefore,
at the start of the analysis, the material was contained between the topographic surface at the
bottom, the ‘lid’ at the top, and the container. In addition to these parts, an ALE mesh was also
built using solid elements measuring 5.0 by 5.0 by 1.5 (width by length by height). The
computational domain was made large enough to cover the entire possible run-out path of the
geophysical flow. To start the back-analysis, gravity was applied and the material was
released by lifting the ‘lid’ and the container together. The simulation terminated after the
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flow had come to rest.
The elasto-plastic Drucker-Prager model was adopted by LS-DYNA (Crosta et al. 2003),
with the two states (qφ and kφ respectively) separated by a yield surface. The internal friction
angle is calculated thus:
q� =6 sinϕ
√3(3 + sinϕ), k� =
6 cosϕ
√3(3 + sinϕ)
where φ is the friction angle of the material. In this model, the internal friction angle is
the sole calibration parameter for back-analysing flow cases of geophysical flows. The
internal friction governs the internal stresses and by extension deformation.
It should be noted that since pore water pressure is not explicitly considered in the
present back-analyses, the back-calculated internal friction angle is expressed in terms of total
stress. The arbitrary Lagrangian-Eulerian (ALE) formulation was used to model the flow as it
undergoes very large deformations during the flow process. ALE is a finite-element
formulation in which the computational system is not a priori fixed in space or attached to
material. The computational mesh inside the domains can move arbitrarily to optimise the
shapes of elements, while the interfaces of the domains can move along with materials to
precisely track the interfaces of a multi-material system.
During the flow process, the interface shear resistance (T) between the flow and the
ground surface was handled using Coulomb’s friction law: T = N tan ϕb, where N is the
normal force and ϕb is the basal (interface) friction angle. For geophysical flow case histories,
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a velocity-dependent damping force was also used in Voellmy models to account for
energy-dissipation following the work of Ayotte et al. (1999). The damping resistance is
expressed as (Kwan et al. 2015):
(1) � = �����
where R is damping resistance (in N), ξd is a damping coefficient (in m−1), m is the mass of
flow material (in kg), and v is flow velocity (in m/s). Eqn. (1) is essentially the turbulent term
in the Voellmy rheological model. For depth-averaged runout analyses, Hungr (1995)
expressed R as:
(2) � =����
�
where A is the basal area of a vertical slice (in m2), γ is the unit weight of the flow material (in
N/m), v is the flow velocity (in m/s), and ξ is a turbulence coefficient (in m/s2). It can be seen
that the lower the value of ξ, the higher the resistance. Eqn. (2) is only suitable for use with
depth-averaged analyses (e.g. DAN and 2d-DMM) in which the basal areas of individual
slices are known. For geophysical flow case histories where the turbulence coefficient (ξ) has
already been back-calculated, the damping coefficient (ξd) can be readily obtained using the
following expression, derived by equating Eqs. 1 and 2:
(3) �� =�
ℎ�
where g is acceleration due to gravity (9.81 m/s2) and h (in m) is the height of a vertical slice
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in a depth-averaged analysis.
The impact force is directly output from the model. The finite-element program searches for
intersections between the solid and shell elements. It then tracks the independent motions of
the contacting elements over a small time step. Any penetration of the flow material into the
barrier or channel base causes a normal interface reaction force which is distributed evenly to
both the flow and the shell elements (i.e. the barrier or channel base). The magnitude of the
force is proportional to the penetration and is calculated using an interface spring stiffness,
which is governed by the Young’s moduli of the flow and shell. Details about the ALE
formulation and the penalty coupling method are discussed in Olovsson and Souli (2008) and
Hallquist (2006).
Verification of numerical model
Experimental setup
Prior to the proposed back-analyses, the numerical method described was verified by
comparing results of finite-element simulations against controlled laboratory experiments
reported by Manzella (2008). The experiments were conducted to study the behaviour of
unconfined dry sand flows; Fig. 2(a) shows the experimental setup. The sand was contained in
a box 200 mm high by 400 mm wide by 650 mm long. The source volume was 5.2 × 10−6 m3.
The box was located at the top of a plane inclined at 37.5°. This plane was adjoined to another
plane inclined at 22.6°. The internal friction angle of the sand was taken as the internal
friction angle which was 34°. The basal interface friction was found to be 32° from a tilting
test. The density of the sand was 1,260 kg/m3. Table 1 summarises the values of the material
parameters including the assumed shear and elastic stiffnesses for loose sand which are
required for the numerical model.
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Specific details of numerical model
Fig. 2(b) shows the setup of the finite-element model. To build the model, the
topographical surface was constructed using 2 mm thick quadrilateral rigid shell elements.
The dimensions of the shell elements were 10 mm by 10 mm. Rigid shell elements were also
used to construct the release gate. The ALE mesh comprises regular tetrahedral solid elements
which are 20 mm cubes. As discussed in the previous section, Coulomb’s frictional model was
used to simulate the basal resistance experienced by the material. The additional damping
force (Eqn. (1)) was not applied as it only becomes significant for certain landslide types such
as rock avalanches (Hungr and Evans 1996) and channelised geophysical flows (Ayotte et al.
1999). The finite-element analysis was initialised by applying gravity (9.81 m/s2) and then
lifting the front gate to release the soil.
Model calibration
Fig. 3(a) shows an isometric view of the simulated final deposition profile of the sand.
The source area was placed above the slope. Material was generated within the source area
and allowed to pile up. The internal friction angle is larger than the inclination of the slope
onto which the material falls, hence the lack of flow. The extent of the deposition given by the
simulation is comparable with that from experiments as shown in Fig. 3(b). In Fig. 3(b), it can
be seen that the deposition at the centre is the thickest, at 0.1 m, and spreads about 0.005 m at
the edge. A noticeable difference between the two figures can be seen near the tail of the
deposition profile; this is due to the presence of a thin layer of dispersed sand that cannot be
simulated in the finite-element model.
Fig. 4 shows the simulated and measured deposition profiles across the transverse and
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the longitudinal directions labelled respectively as A-A and B-B. It can be seen that the
numerical model does not fully capture the deposition profile, though the extent of deposition
along these two directions is well reproduced. This can be attributed to the inability of the
continuum model to account for grain rearrangement or the compressibility of soil. This
comparison demonstrates that the finite-element method can nonetheless simulate the run-out
distance and deposition profile of flow material reasonably well if the basic material
parameters are known. This gives confidence to using the finite-element method to
back-analyse landslide case histories.
Back-analyses of landslide case histories
Introduction
Back-analyses of four notable landslide case histories in Hong Kong have been carried
out and the results are presented in this paper. These cases can be divided into two categories
based on their failure modes, namely, open hillslope failures and channelised geophysical
flows. Table 2 summarises some basic information including references to the landslide
investigation reports (Knill and GEO 2006a, 2006b; FMSW 2005; MGS 2008; AECOM
2012). The fifth case history, which is a channelised geophysical flow that occurred above Yu
Tung Road in 2008, has been back-analysed in Kwan et al. (2015) so only the key results are
presented. All landslide investigation reports have been published by the Geotechnical
Engineering Office (GEO) in Hong Kong and made available in the public domain. The
back-analysed parameters are summarised in Table 3 and the location of the case histories are
presented in Fig. 5. The five case histories, identified as Cases 1 to 5, are discussed
individually as follows.
Case 1–Open hillslope failure above Shum Wan Road
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The landslide that occurred above Shum Wan Road was the result of an open hillslope failure
involving a soil volume of around 26,000 m3 (Knill and GEO 2006a). The landslide occurred
on a 30° natural hillside during heavy rainfall on 13 August 1995. Fig. 6 shows an aerial
photograph of the landslide location. A back-analysis of this landslide has been carried out
using the depth-averaged program 3d-DMM and the results reported in Kwan and Sun (2007).
In this previous work, a reasonable match between numerical simulations and site
observations was obtained when a basal interface friction angle of 20° was used.
Using LS-DYNA to run several trials, an internal friction angle of 25° was found to give the
best agreement between the numerical results and field observations in terms of runout. The
runout is compared graphically with the back-analysed result from 3d-DMM (Kwan and Sun
2007) in Fig. 7(a), which shows the simulated flow locations at different times after the onset
of the event. At time t = 0 s, the flow mass is just starting to move. At t = 8 s, the flow has
substantially spread out, both longitudinally and laterally. Between t = 16 s and 30 s, the flow
mass splits into several section of different sizes in both the FEM model and the 3D-DMM
model. However, the flow in the 3D-DMM does not spread as far laterally for the FEM model.
This may be attributed to three reasons: (i) energy dissipation due to the internal friction angle
is not considered in the 3D-DMM model, allowing the flow to spread further; (ii) the fluid
elements in the 3D-DMM model tend to laterally disperse at the non-constrained edge
boundary in the particle-in-cell (PIC) analysis (Kwan and Sun 2007); and (iii) because the
mesh size for the 3D-DMM model is limited by the number of particles limited to each cell.
(The mesh size for the FEM model is much finer than for the 3D-DMM model.)
Furthermore, it can be seen that the zone affected by the landslide (denoted by the dotted line
in Fig. 7a) is considerably larger than the predicted extent of the debris flow at any given time.
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This is because the landslide-affected zone represents the boundary of the total eroded area
due to debris run-out, while the simulated debris extent is shown for a particular simulation
time. The total area affected by the geophysical flows as calculated using the two numerical
methods is shown in Fig. 7b. The total area affected by the predicted landslide as computed
using LS-DYNA was generally within the bounds of that demarcated by the real event.
However, results from 3D-DMM were again over-conservative due to the lateral dispersion of
the fluid elements at the non-constrained boundary. This again emphasises the need for using
‘true’ 3D models which can explicitly consider energy dissipation due to the internal friction
angle.
It should be noted that the physical meaning of the internal friction angle in not the same as in
previous studies such as Kwan and Sun (2007) since energy dissipation (governing flow
velocity and runout length) is governed by the empirical Voellmy damping parameter.
Nonetheless, it is expected that a back-analysed internal friction angle for models in the
Savage-Hutter family would be overestimated, since it governs the longitudinal spreading of
the flow (and hence the mobility). Simultaneously, the energy dissipation due to internal
frictional shearing is neglected. Thus, using the ‘true’ internal friction angle in Savage-Hutter
models should lead to an overestimate of the mobility; to correct for this, the internal friction
angle input parameter would have to be increased. A key advantage of LS-DYNA is thus that
explicit resolution of the interaction between flow material and structures allows a better
resolution of the internal friction angle, which is especially relevant to flow-structure
interaction. Flow energy dissipation that occurs during impact due to internal shearing (Song
2017) is considered, unlike the hydrodynamic equation which must be used to calculate
impact force if using the 3D-DMM model. Furthermore, the impact force on a rigid structure
from a geophysical flow is highly non-uniform (Ng et al. 2017). This non-uniform impact
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force is modelled by LS-DYNA, but cannot be considered using the hydrodynamic equation,
the latter leading to over-conservative solutions.
Case 2–Open hillslope failure above Fei Tsui Road
A man-made cut slope above Fei Tsui Road failed during heavy rainfall in 1995 (Knill and
GEO 2006b). Due to the failure, about 14,000 m3 of soil slipped, crossed the fenced-off level
ground and then ran onto Fei Tsui Road. Fei Tsui Road was built on the northern side of the
slope which had a maximum height of about 27 m and an overall slope angle of about 60°.
The flow was brought to stop after hitting a reinforced concrete building (a church) on the
other side of the road. Fig. 8 shows a photograph of the landslide scar and some of the
deposited material. The photograph was taken from the affected church building. The width
and length of the landslide scar were 33 m and 90 m respectively. The maximum thickness of
the flow at the toe of the slope was about 15 m.
The topographic surface and the external profile of the church building were generated using
rigid shell elements measuring 1 m by 1 m. An ALE mesh was generated using solid elements
measuring 1 m long by 1 m wide by 0.5 m high to cover the space of the possible landslide
trail.
Kwan and Sun (2007) used 3d-DMM with two different basal friction angles (ϕb) to
back-analyse this case history. At the source location, ϕb was taken as 22° due to the presence
of a kaolinite-rich layer which was identified after the landslide. A higher value of 35° was
used for the run-out path along Fei Tsui Road to take into account the higher interface
resistance. This angle was later found to be too high and has been revised to 30° for the
present analysis. The internal friction angle governs longitudinal spreading, whilst the basal
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friction angle governs translational movement. The two parameters are thus not directly
interchangeable. After several trials, an internal friction angle (ϕ) of 30° was found to give the
best agreement between the simulated and actual run-out distances and lateral spreading. The
revised friction angle is because of the interaction of the flow with the church, and by
extension flow energy dissipation that occurs during impact, is explicitly modelled by
LS-DYNA. This contrasts with 3D-DMM in which the impact force must be calculated using
the hydrodynamic equations using the open-channel velocity and flow depth. The calculated
basal friction angle for 3D-DMM is clearly overly conservative, thus justifying the use of
truly 3D models for modelling flows impacting structures.
Fig. 9a shows the extent of the geophysical flow on top of a topographic map of the affected
area. It can be seen that the flow material stopped at the southern corner of the church
building on the other side of the Fei Tsui Road with an estimated impact thickness of 5 m. A
cross-section of the deposited flow material is shown in Fig. 9(b) to compare the simulated
and actual flow depths. It can be seen that the finite-element results are in good agreement
with the field observation within 10% different of predicted flow thickness. The difference is
again due to the simplified assumption of homogenous properties, e.g. incompressible flow
with no particle rearrangement, for the geophysical flow in the numerical model. The run-out
distance is nonetheless consistent with field survey data, thus validating the back-analysed
equivalent internal friction angle. The site observation also showed that there was limited
water seepage from the deposited flow material, suggesting a relatively low initial water
content (Knill and GEO 2006b). This is likely the reason for the relatively high back-analysed
equivalent internal friction angle: the pore water pressure is likely relatively less within the
flow material itself.
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Case 3–Channelised geophysical flow in Kwun Yam Shan
A geophysical flow occurred on a natural hillside on Kwun Yam Shan in 2005 (MGS 2008).
Fig. 10 shows an aerial photograph of the scar and part of the flow trail. Approximately
1,000 m3 of soil became detached from the source area and developed into a geophysical flow
running down a stream course. The slope angle of the run-out path was initially between 30°
and 40° and gradually reduced to about 12° at the flow deposition zone. The flow material
travelled a total distance of 330 m down the run-out path before coming to rest.
Fig. 11 shows the finite-element model used for the back-analysis, with square rigid shell
elements with an area 1 m2. Following Kwan and Sun (2007), a basal friction angle of 15° and
a turbulence coefficient (ξ) of 500 m/s2 were adopted for this case history. The corresponding
damping coefficient (ξd) was computed as 0.01 m−1 using Eqn. (3). Following several trials,
an internal friction angle of 20° was found to give the best agreement between the simulated
and observed flow run-out distance.
Fig. 12 shows the simulated flow location at three different instances during the flow event.
Time zero refers to the onset of the event. The finite-element simulation shows that the flow
material would stop after reaching the two pre-existing boulder dams at around 41 s. The
post-landslide inspection revealed the same run-out distance (330 m) though the simulated
run-out time cannot be verified as there is no video of the event. Fig. 13 shows a cross-section
of the flow when it was passing through the sharp bend at chainage 220 m. In this plot, the
vertical axis represents the elevation in mPD (metres above principal datum) and the
horizontal axis represents the distance from the centreline of the local depression. It can be
seen that due to the sudden change of the flow direction, the back-analysis gives a
super-elevation of 7.1 m up the north-eastern (left on this plot) flank of the stream course.
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This compares well with the actual super-elevation of 6.8 m as revealed from the
post-landslide inspection (MGS 2008). These comparisons give confidence to the
back-analysed results.
Case 4–Channelised geophysical flow above Sham Tseng San Tsuen
On 23 August 1999, four small shallow failures occurred on the natural hillside above Sham
Tseng San Tsuen during a severe rainstorm (FMSW 2005). The flow had a volume of about
600 m3 and consisted of mainly decomposed granite (silty and gravelly sand) and in-situ
corestones. Fig. 14 shows an aerial photograph of the locations of the landslides, the flow trail
and the affected village buildings at the toe of the slope. The gradient was over 45° in places,
likely causing a fast, turbulent flow; the frontal velocity of the flowing material was estimated
to be up to 11 m/s (FMSW 2005).
Fig. 15 shows the finite-element model used. The topographic surface was generated using
shell elements measuring 1 m wide and 1 m long. Kwan and Sun (2007) back-calculated a
basal friction angle (ϕb) of 12° and a turbulence coefficient (ξ) of 500 m/s2 by matching the
total run-out distance. Unlike the previous case, no field data for the superelevation was
available, so no comparison could be made. Consideration of the flow frontal velocities at
selected locations later resulted in a change of these parameters to ϕb = 9° and ξ = 250 m/s2.
The damping coefficient (ξd) corresponding to the revised ξ was computed as 0.03 m/s2 using
Eqn. (3). This value is higher than the one obtained for case 3 (0.01 m/s2), probably due to the
higher flow turbulence caused by the steep slopes. The calibration constant that was most
sensitive the internal friction angle was runout distance. An internal friction angle of 15° was
found to give the best agreement between the simulated and estimated debris frontal velocities
as shown in Fig. 16, although it should be noted that back-analysed parameters may vary
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depending on the numerical model employed by the software. The observed reduction in flow
velocity after chainage 120 m was due to the rugged nature of the stream course and the
reducing slope gradient. This feature can be realistically reproduced in the finite-element
simulation since the topographic surface in the model was generated using site-specific survey
data collected before and after the landslide event. The reduction in debris flow velocity was
also simulated by Kwan and Sun (2007), although this was due primarily to a pre-defined and
non-varying basal friction angle. Since rugged terrain also tends to have a braking effect, a
back-calculated basal friction angle using the model presented in Kwan and Sun (2007) would
tend to be over-estimated.
Case 5–Channelised geophysical flow above Yu Tung Road
On 7 June 2008, 19 shallow landslides occurred on the natural hillside above Yu Tung Road in
Hong Kong. One of these, with an initial failure volume of 2,350 m3, developed into a
channelised geophysical flow with a total volume of about 3,500 m3. Fig. 17 shows an aerial
photograph of the catchment area and the flow path. Findings of the post-landslide
investigation are given in AECOM (2012).
Fig. 18 shows the horizontal chainage on the y-axis and time on the x-axis for four different
internal friction angles, specifically 5, 10, 15 and 20°. Field observations from video footage
of the event are also shown for comparison. The closest match was for the internal friction
angle of 15°. The reduction in flow velocity as the friction angle increases is expected as the
friction angle governs the energy dissipation characteristics of the flow.
This flow was previously back-analysed by Kwan et al. (2015) using depth-averaged and
finite-element models, so only the key results are summarised here. From the depth-averaged
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back-analyses, the basal friction angle (ϕb) and the turbulence coefficient (ξ) were found to be
8° and 500 m/s2 respectively. The corresponding damping coefficient (ξd) was 0.01 m−1. In
addition, from the finite-element analyses, the internal friction angle (ϕ) was found to be 15°.
The low basal and internal friction angles reflect the significantly high water volume fraction
within the geophysical flow, similar to results reported in Reid et al. (2011), wherein a higher
degree of saturation was correlated with faster and further runout. The internal friction angle
is explicitly modelled by LS-DYNA wherein it can take into account flow energy dissipation
that occurs during impact. This contrasts with conventional free-field runout model in which
the impact force is calculated using the open-channel flow velocity and depth. This justifies
the use of truly 3D models for modelling flows impacting structures”
Engineering applications
The back-analysed internal friction parameters are useful for engineers to use as input
parameters to explicitly model geophysical flows impacting structures using
three-dimensional large-deformation finite-element modelling. Using such finite-element
models to explicitly model impact can lead to less over-conservative structure design since
interaction between the structure and the flow can be explicitly modelled, capturing energy
losses due to shearing (Ng et al. 2017).
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Concluding remarks
Notable landslide case histories in Hong Kong have been back-analysed using the finite
element method to deduce the internal friction angle (ϕ) of the geophysical flow originating
from residual soil (decomposed tuff and granite) and colluvium. Computed results show that
the values of ϕ range between 25° and 30° for open hillslope failures and between 15° and 20°
for channelised geophysical flows. Incised flow channels have an elevated water head and a
higher degree of saturation compared to open-hillside slope surfaces since seepage into
channel beds occurs in a concentrated region. This suggests that the induced pore water
pressure is relatively higher, significantly lowering the equivalent friction angle. The basal
friction angle and the Voellmy turbulence coefficient are the other key parameters controlling
kinematic flow behaviour. The back-analysis of the equivalent internal friction angle is
reliable provided valid assumptions are made regarding the basal friction angle and turbulence
conditions.
Compared to previous similar studies, where only the basal friction angles and
turbulence coefficients were determined from depth-averaged analyses, the present study
represents an advance in our understanding of the equivalent internal friction angle of
geophysical flows. The water content of overridden soil differentiates the equivalent internal
friction angle between open-hillside failure and channelised geophysical flows. The new
findings should be useful for predicting the behaviour of geophysical flows and facilitating
the preliminary design of flow-resisting structures in landslide-prone areas.
Acknowledgements
This paper is published with the permission of the Head of the Geotechnical Engineering
Office and the Director of Civil Engineering and Development, Hong Kong SAR Government.
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The work described in this paper was supported by a grant from the Research Grants Council
of the Hong Kong SAR (T22-603/15N).
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Notation
A Basal area of a vertical slice
g Acceleration due to gravity
h Average flow thickness
hs Height of a vertical slice
m Mass of debris
N Normal force
NFr Froude number
R Damping resistance
v Debris velocity
α Impact pressure coefficient
γ Unit weight of debris
ξd Damping coefficient
ξ Turbulence coefficient
ϕ Internal friction angle
ϕb Basal friction angle
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List of figure captions Fig. 1. Numerical steps followed during back-analyses of landslide material. Fig. 2. Setup for deflected sand flow experiments reported by Manzella (2008) and the finite-element model in LS-DYNA. Fig. 3. Measured and simulated sand deposition areas in deflected flow experiments conducted by Manzella (2008). Fig. 4. Measured and simulated deposition profiles: (a) cross-section A-A; (b) cross-section B-B. Fig. 5. Locations of notable landslide case histories in Hong Kong Fig. 6. Aerial photograph of the Shum Wan Road Landslide Fig. 7. Simulated mobility of flow material at Shum Wan Road: (a) LS-DYNA and 3d-DMM results at various times; (b) LS-DYNA output at 30 s. Fig. 8. Photograph showing the scar and some of the material resulting from the landslide above Fei Tsui Road. Fig. 9. Simulation of Fei Tsui Road Landslide. Fig. 10. Aerial photograph of the scar and part of the flow trail of the Kwun Yam Shan geophysical flow. Fig. 11. Finite-element model of the Kwun Yam Shan geophysical flow. Fig. 12. Simulated flow trail of the Kwun Yan Shan geophysical flow.
Fig. 13. Cross-section of flow at chainage 220 m.
Fig. 14. Aerial photograph showing the landslide locations and the flow path above Sham Tseng San Tsuen. Fig. 15. Finite-element model of Sham Tseng San Tsuen geophysical flow. Fig. 16. Frontal velocity of the flowing material above Sham Tseng San Tsuen. Fig. 17. Aerial photograph of the catchment area and the flow path of Yu Tung Road geophysical flow.
Fig. 18: Parametric study of effects of internal friction angle on the horizontal chainage of the geophysical flow front as a function of time
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Table 1. Properties of materials used for deflected flow experiment
Material property Fine Hostun sand
Internal friction angle 34°
Base material Forex
Basal (interface) friction angle 32°
Source volume 52,000 mm3
(5.2 × 10−6
m3)
Bulk density 1,260 kg/m3
Shear modulus 5 MPa
Elastic modulus 10 MPa
Table 2. Landslide case histories back-analysed
Case No. Category Date Location Landslide
Investigation Report
1 Open Hillslope
Failure
13 August 1995 Shum Wan Road Knill and GEO
(2006a)
2 13 August 1995 Fei Tsui Road Knill and GEO
(2006b)
3
Channelised
Debris Flow
22 August 2005 Kwun Yam Shan MGS (2008)
4 23 August 1999 Sham Tseng San
Tsuen FMSW (2005)
5a 7 June 2008 Yu Tung Road AECOM (2012) a The back-analysis result of this case history can be found in Kwan et al. (2015); only the key findings are discussed.
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Table 3. Summary of soil parameters
Previous studies* This study
Case
No. Type Location
Basal friction
angle,
ϕb
(degrees)
Turbulence
coefficient,
ξ
(m/s2)
Damping
coefficient,
ξd
(m−1
)
Internal
friction angle,
φ (degrees)
Density Shear
modulus
(MPa)
Elastic
modulus
(MPa)
1 Open
Hillslope
Failure
Shum Wan Road 20 - - 25 2000 5 10
2 Fei Tsui Road 22 (scar)
30 (road)†
- - 30 2000 5 10
3
Channelised
Flow
Kwun Yam Shan 15 500 0.01 20 1900 5 10
4 Sham Tseng San
Tsuen 9 250 0.03 15 1900 5 10
5 Yu Tung Road 8 500 0.01 15 2000 5 10
* The back-analysed results for Cases 1-4 and Case 5 are given in Kwan and Sun (2007) and Kwan et al. (2015) respectively.
† The interface friction angle between debris and road surface material has been revised from 35° as reported in Kwan and Sun (2007) to 30° in the present study.
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Table 4. Debris impact pressure
Impact
maximum velocity (m/s)
Impact
Maximum thickness (m)
Impact pressure (kPa)
Case No. Location Finite-element
back-analysis
Field
observation
Finite-element
back-analysis
Hydrodynamic
equation (eq. (4))
α = 2.5
(Kwan, 2012)
1 Shum Wan
Road 14.0 3.0 500 980
2 Fei Tsui Road 3.8 4.5 69 75
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Fig. 1. Numerical steps followed during back-analyses of geophysical flow.
Generate material source
volume using solid elements
Apply gravity
Generate topography using rigid
shell elements
Use Lagrangian solver to
simulate flow mobility
Constitutive material models:
1) Drucker-Prager yield
criterion for internal shear
strength
2) Rheological model for flow:
• Coulomb’s law for
interface friction
• Velocity- dependent
resistance for flow
turbulence
Apply arbitrary Lagrangian-
Eulerian (ALE) rezoning
A numerical formulation for
remapping the solution from
distorted mesh to the smooth
mesh
Flow-structure interaction
Simulation output
Penalty coupling method to
provide contact force between
ALE-based solid elements and
rigid shell elements
Flow output:
• Internal shear strength
• Velocity
• Thickness
Rigid structure output:
• Impact pressure
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Fig. 2. Setup for deflected sand flow experiments reported by Manzella (2008) and the
finite-element model in LS-DYNA (redrawn and modified from orginal setup).
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Fig. 3. Measured and simulated sand deposition areas in deflected flow experiments
conducted by Manzella (2008) (redrawn from Manzella 2008).
(a) Isometric view (b) Plan view
Source area
B
B
A
A
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(a)
(b)
Fig. 4. Measured and simulated deposition profiles: (a) cross-section A-A; (b) cross-section
B-B.
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Fig. 5. Locations of notable landslide case histories in Hong Kong.
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Fig. 6. Aerial photograph of the Shum Wan Road Landslide.
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(a) LS-DYNA and 3d-DMM flow reach at various times
(b) Full extent of LS-DYNA and 3d-DMM flows
Fig. 7. Simulated mobility of flow material at Shum Wan Road.
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Fig. 8 Photograph showing the scar and some of the flow material resulting from the
landslide above Fei Tsui Road.
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(a) Extent of the landslide material on top of a topographic map of the affected area
(b) Cross-section of the deposited material
Fig. 9. Simulation of Fei Tsui Road Landslide.
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Fig. 10. Aerial photograph of the scar and part of the flow trail of the Kwun Yam Shan
geophysical flow.
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Fig. 11. Finite-element model of the Kwun Yam Shan geophysical flow.
Topography
Source
Two
pre-existing
boulder dams
dams
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Fig. 12. Simulated geophysical trail of the Kwun Yan Shan geophysical flow. (a)
Aerial view of three time instants; (b) cross-section at 0 s; (c) cross-section at 8 s; (d)
cross-section and 16 s
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Fig. 13. Cross-section of geophysical flow at chainage 220 m.
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Fig. 14. Aerial photograph showing the landslide locations and the geophysical flow path
above Sham Tseng San Tsuen.
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Fig. 15. Finite-element model of Sham Tseng San Tsuen geophysical flow.
Fig. 16. Frontal velocity of the flow above Sham Tseng San Tsuen.
Topography
Source
Location of
the squatter
dwellings
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Fig. 17. Aerial photograph of the catchment area and the geophysical flow path of Yu Tung
Road geophysical flow.
Fig. 18: Parametric study of effects of internal friction angle on the horizontal chainage of the
geophysical flow front as a function of time
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