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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

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

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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



Carlos Lam

Geotechnical Engineer, Geotechnical Engineering Office, Civil Engineering and



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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.


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.


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.


Jack Yiu

Associate, Arup, Level 5, Festival Walk, 80 Tat Chee Avenue, Kowloon Tong, Kowloon,

Hong Kong.


Ken K.S. Ho

Deputy Head, Geotechnical Engineering Office, Civil Engineering and Development

Department, Hong Kong SAR Government


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W.K. Pun

Head, Geotechnical Engineering Office, Civil Engineering and Development Department,

Hong Kong SAR Government


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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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