Slope failure characteristics and stabilizationmethods

H. (Joanna) Chen and S.H. Liu

Abstract: This paper presents numerical and laboratory experiments to investigate slope failure characteristics andcommonly used slope stabilization methods. Using an improved distinct element method, the interparticle adhesiveforce is incorporated with a modified numerical model to account for the effect of suction. The model is validatedthrough laboratory tilting box tests. Calculated slope failure angles are consistent with experimental observations.Different patterns of slip surface are also identified. Furthermore, the modified numerical model quantifies themicromechanical characteristics of the interparticle network and their evolutions during shear deformation. The calcula-tions show that the maximum ratio of shear stress to normal stress takes place when the contact plane coincides withthe mobilized plane, whereas the minimum value occurs when it is parallel to the directions of principal stresses. Onthis basis, we propose the optimal installation angle of soil nails along the minor principal stress (σ3) direction. The ef-fectiveness of this approach is evaluated through tilting box tests. Two commonly used slope surface stabilization meth-ods are also experimentally investigated.

Key words: distinct element method, tilting box test, slip surface, optimal installation angle of soil nails.

Résumé : Cet article présente des études numériques et des expériences en laboratoire pour étudier les caractéristiquesde rupture de talus et les méthodes couramment utilisées pour la stabilisation des talus. Au moyen d’une méthodeaméliorée d’éléments distincts, la force d’adhésion entre les particules est incorporée dans un modèle numérique modi-fié pour tenir compte de l’effet de succion. Le modèle est validé par des essais d’inclinaison de boîte en laboratoire.Les angles de rupture de talus calculés sont consistants avec les observations expérimentales. Différents schémas desurface de rupture ont été identifiés. De plus, le modèle numérique modifié quantifie les caractéristiques micromécani-ques du réseau interparticule et leurs évolutions durant la déformation en cisaillement. Les calculs montrent que le rap-port maximum de la contrainte de cisaillement sur la contrainte normale est atteint lorsque le plan de contact coïncideavec le plan mobilisé, alors que la valeur minimale se produit lorsque ce plan est parallèle aux directions des contrain-tes principales. Sur cette base, nous proposons l’angle optimal d’installation des clous de sol dans la direction de lacontrainte principale mineure (σ3). L’efficacité de cette approche est évaluée au moyen des essais de boîte inclinée. Onétudie aussi expérimentalement deux méthodes de stabilisation des surfaces de talus communément utilisées.

Mots-clés : méthode d’éléments distincts, essai de boîte inclinée, surface de glissement, angle optimal d’installation declous de sol.

[Traduit par la Rédaction] Chen and Liu 391

Introduction

Landslides are natural disasters that often originate insteep slopes. Expanding urbanization and changing land-usepractices have increased the frequency of their occurrence.Despite improvements in recognition, prediction, and mitiga-tive measures, natural landslides and engineered slope fail-ures still exert a heavy social, economic, and environmentaltoll (e.g., McConnell and Brock 1904; Cruden and Varnes1996; Chen and Lee 2000; Crosta et al. 2004). Fundamentalaspects in the study of landslide- and slope-failure-related

problems include triggering and runout mechanisms, mobil-ity analysis, and countermeasure approaches. As slopes con-sist of native or transported earth materials, engineeringproperties and behaviours are quite variable and unpredict-able to precise limits. Attention to this subject is being em-phasized in theoretical study and geotechnical engineeringpractices.

Various slope stabilization methods exist in geotechnicalengineering practices that correspond to different field con-ditions and economic considerations. For example, soil nail-ing is a method of construction that reinforces the existingground (such as slopes and retaining walls). This is becausethe nails develop tension when the ground deforms laterallyin response to ongoing excavation. Soil-nailing technologyhas been widely adopted in soil excavation and slope andretaining wall stabilization because of its cost effectiveness,rapid construction, and revision flexibility in constructionprocess. Attention to soil–nail interaction has been largelybrought to the pullout behavior of nails in sandy clay(Chai and Hayashi 2005), in loose fills with fine gravels

Can. Geotech. J. 44: 377–391 (2007) doi:10.1139/T06-131 © 2007 NRC Canada

377

Received 22 March 2005. Accepted 13 November 2006.Published on the NRC Research Press Web site at cgj.nrc.caon 3 May 2007.

H.J. Chen.1 Golder Associates Ltd, 1000, 940–6th AvenueSW, Calgary, AB T2P 3T1, Canada.S.H. Liu. College of Water Conservancy and HydropowerEngineering, Hohai University, Nanjing, China.

1Corresponding author (e-mail: Joanna_Chen@golder.com).

(Junaideen et al. 2004), and in loose to medium dense sand(Schlosser et al. 1992; Luo et al. 2000; Hong et al. 2003). Inthese cases nail installations are horizontal. The frictional re-sistance at the soil–nail interface is regarded as the majorcontribution to the soil mass stabilization (Shewbridge andSitar 1990; Jewell and Pedley 1992; Raju et al. 1997). Insome cases, the inclination angles of nails are within 10°–20° of the horizontal direction (Prior 1992; Barley 1993;Kim et al. 1995). A recent study (Güler and Bozhurt 2004)on two full-scaled nailed structures with upward and down-ward installations suggested that the soil-nailed structureswith nails installed at angles above horizontal give better re-sults with regards to the factor of safety. To the best knowl-edge of the authors, the optimal installation angle has rarelybeen studied in the literature.

Experimental and numerical modelling are the two impor-tant components in the study of slope failure characteristics.Experimental investigations usually deliver macroscopicinformation for slope failure patterns and measurable param-eters. As a soil mass consists of discrete particles, micro-scale interaction among particles significantly influences themacromechanical behavior of soil mass. The distinct ele-ment method (DEM), which was originally designed for re-search into the micromechanical behavior of granularassemblies that were subject to generalized motion (Cundall1971), has been vastly improved since its original inceptionand has been successfully applied to simulate themicrobehaviour of interacting particles (e.g., Cundall andStrack 1979; Rothenburg and Bathurst 1989; Cundall 2000).Conventional DEM generally deals with dry granular parti-cles exclusive of pore-water pressure. It is noted that slopefailures typically occur following heavy rainfall. Rainfall in-filtration perceivably results in major changes in soil suction.Conventional DEM modelling when incorporated withinterparticle adhesive forces may account for the effect ofsoil suction. It helps us to understand slope failure mecha-nisms under different boundary conditions, such as rainfall-induced slope failures.

In this paper, an interparticle adhesive force is incorpo-rated into the conventional DEM to account for the influenceof capillary menisci among particles. This improved DEM isvalidated through laboratory tilting box tests simulating theslope failure process under plane-strain – plane-stress condi-tions. Calculated results quantify the micromechanical char-acteristics of the interparticle network and the evolution ofparticles during shear deformation. On this basis, we de-signed a series of tilting box tests to investigate some com-monly applied slope-stabilization measures, with emphasison the installation angle of the nails.

The improved distinct element model

The DEM is a numerical technique in which individualparticles are represented as rigid bodies. Tracing the move-ment of individual particles, the interaction of assemblies ofdisc (two-dimensional) or spherical (three-dimensional) par-ticles, is described as a transient problem with states of equi-librium contact forces and displacements of the stressedassemblies developing whenever the internal forces are bal-anced. In two dimensions, a particle has three degrees offreedom (two translational and one rotational). A particle

may be in contact with the neighboring particles or structureboundaries. Particles are in contact only when the distancebetween the particle centers is not larger than the sum oftheir radii. If the displacement increments of two individualdiscs over a very small time interval, ∆t, are represented as(∆xi, ∆yi, ∆ϕi) and (∆xj, ∆yj, ∆ϕ j ), the relative displacementincrements of the two individual particles at contact may beexpressed as

[1] ∆ ∆ ∆ ∆ ∆u x x y yi j ij i j ijN = − + −( ) cos ( ) sinα α

∆ ∆ ∆ ∆ ∆u x x y yi j ij i jS = − − + −( ) sin ( )α

× + +cos ( )α ϕ ϕij i i j jr r∆ ∆

where ∆uN and ∆uS are the normal and tangential displace-ments along the contact plane, respectively, ∆uN is positivefor compression and ∆uS is positive for counterclockwise ro-tation, ri and rj are the radii of the two particles, and (xi, yi)and (xj, yj) are the Cartesian coordinates of the particle cen-troids.

The global unit vector e = (cos αij , sinαij ) is defined as

[2]sin ( )/

cos ( )/

α

αij j i ij

ij j i ij

y y R

x x R

= −

= −

normalized by the distance Rij = [(xi – xj)2 + (yi – yj)

2]1/2.Contact between two particles, or a particle and a bound-

ary, is modeled by the elastic spring and viscous dashpots inboth the normal and tangential directions (suffixed with Nand S, respectively). The increment of the normal contactforce, ∆eN, is caused by the relative displacement increment,∆uN, and can be calculated via an elastic force –displacement law:

[3] ∆ ∆e k uN N N=

where kN is the normal stiffness. The relative velocity∆ ∆u tN/ leads to the dynamic normal contact force, dN,

[4] dut

N NN= η ∆

∆

where ηN is the normal damping. The total normal contactforce between two particles is given by the summation of thestatic and dynamic components

[5a] [ ] [ ] [ ]f e dt t tN N N= +

in which

[5b] [ ] [ ] [ ]e e e d dt t t tN N N N Nand= + =−∆ ∆

There is no extension force at the contact surface when[eN]t < 0 or [eN]t = [dN]t = 0.

Likewise, the total tangential contact force between twoparticles may be written as

[6a] [ ] [ ] [ ]f e dt t tS S S= +

where

[6b] [ ] [ ] [ ]e e e e k ut t t t tS S S S S S= + = +− −∆ ∆∆ ∆

[6c] [ ]d d du

ttS S S S

S= = η∆∆

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378 Can. Geotech. J. Vol. 44, 2007

In the tangential direction, the particle slides if the tangentialforce reaches the Coulomb friction limit. Therefore,

[7a] [ ] [ ] [ ]e d et t tS S N0, if 0= = <

[7b] [ ] [ ] [ ] [ ]e e e dt t t tS N S Ssign and 0,= × =µ

if S N[ ] [ ]e et t> µ

where the friction coefficient, µ = µtan φ , with φµ being theinterparticle friction angle.

Once the normal and tangential forces are determined foreach contact, they are projected onto the x and y directions.The summation of the force components over all contactsand the resultant moment [Mi]t are given by

[8a] [ ] ( [ ] cos [ ] sin )F f f m gxi tj

t ij t ij i x= − + +∑ N Sα α

[8b] [ ] ( [ ] sin [ ] )F f f m gyi tj

t ij t ij i y= − − +∑ N S cosα α

[8c] [ ] ([ ] )M r fi t ij

t= − ∑ S

where mi and (gx, gy) represent the mass of a particle and thecomponents of gravitational acceleration, respectively.

In unsaturated soils with a low degree of saturation, waterpartially occupies the voids of soil particles and capillarymenisci build up between adjacent particles. Water attachesto the surface of some particles, as shown in Fig. 1a. Thecurved water–particle interface produces surface tension (T),which in turn generates suction (s) and interparticle adhesiveforce (PS) perpendicular to the contact plane between adja-cent particles (Fig. 1b). Assuming that the shape of the liq-uid bridge is a toroid characterized by radii r and b, suctionacross the liquid water bridge and the interparticle adhesiveforce are calculated in a 2D manner (Ohashi and Matsuoka1995; Han et al. 2004) by

[9a] s u u T r b= − = −a w 1 1( / / )

[9b] P u u b T bS a w2 2= − +( ) ( )π π

where ua and uw are the pore-air and pore-water pressures,respectively, and r and b are the radii of the meniscus andthe capillary water cylinder at its center. The radii r and bcan be expressed geometrically in term of the radius of parti-cle R and the angle of capillary water retention, β, by b =R(tan )β β+ −1 sec and r R= −( )secβ 1 .

We incorporate the interparticle adhesive force betweentwo adjacent particles by

[10]

[ ] cos

[ ] sin

[ ]

F P

F P

M

xip

t ijj

ij

yip

t ijj

ij

ip

t

=

=

=

∑

∑

S

S

0

α

α

and add it to eq. [8] for the total net forces. Newton’s secondlaw was applied to trace the motion of a particle resultingfrom the contact forces and momentum, and the accelera-tions are given by

[11] [ ][ ] [ ]

; [ ][ ]X

F Fi t

X t Xp

t

ii t

i t

imMI

= + =i i ϕ

where Xi = (xi, yi), F = (Fx, Fy), and Ii and ϕi represent themoment of inertia and angular displacement of a particle, re-spectively. The velocity and displacement can be integratedusing an explicit central difference scheme.

The mean stress is calculated from the interparticle con-tact forces by (Christoffersen et al. 1981)

[12] σij i jl F V=

∑

Ω

where Ω is the calculation domain, V is the volume of thedomain, li is the length of the vectors connecting the centersof contacting particles, and Fj is the contact force. Theabove procedure has been formulated in a computer pro-gram, GRADIA (Yamamoto 1995), which was validatedthrough the comparisons with the experimental tests con-ducted in the next section.

Tilting Box Test (TBT)

The slope-failure characteristics were investigated throughthe observation of the movement of an assembly of alumi-num rods contained in a titling box. As sketched in Fig. 2,the titling box was rectangular: 82 cm in length and 30 cmin both height and width. The front and back walls of thetilting box were removable to allow for an adjustable width.The front wall was transparent (glass) for the convenience ofobservation. Driven upwards by an electric motor, the boxcould be adjusted gradually to a maximum inclination of60°. An assembly of aluminum rods was used to construct aslope inside the tilting box. The rod assembly can stand upunder its own weight without any external support and sub-sequently no frictional resistance would be produced on thefront or back wall of the tilting box. The movement of thealuminum rods could be traced visually by placing a markon the front surface of the constructed slope.

Two assemblies of cylindrical aluminum rods (50 mmlong) were used. The first assembly comprised a mixturewith diameters of 5.0 and 9.0 mm (henceforth, type I). Thesecond assembly had diameters of 1.6 and 3.0 mm (hence-forth, type II). The weight ratio of type I rods refers to theratio of the weight of the 9.0 mm rods to that of the 5.0 mmrods. The weight ratio of type II rods is defined as ratio ofthe weight of the 3.0 mm rods to that of the 1.6 mm rods.The proportions of the larger and smaller rods for type I andtype II were the same as their weight ratio, 3:2. These twotypes of mixed assemblies had the same specific gravity of2.69, a void ratio of 0.201, and a dry density of 21.6 kN/m3.The diameters of type I and type II rods were in the sizerange of fine gravel and medium to coarse sand, respec-tively. The specific gravity was close to that of quartz chips(about 2.65).

Testing in a dry stateThe type I assembly was arranged to construct a slope in-

side the tilting box whose front and back walls were re-moved after the setup. Colour lines were drawn on the frontsurface of the rods so that their movement could be easilyobserved and traced as the box was gradually tilted at a con-stant angular speed of 1°/min. The failure process of the dryaluminum-rod slope is shown in Fig. 3. It was observed thatthe particle movement began along the slope surface, gradu-

© 2007 NRC Canada

Chen and Liu 379

ally developing to a certain depth, and eventually shaped asa shallow slip plane beneath the slope surface. The failureangle was defined to be the inclination of the slope whenvisible initial movement of the rods occurred. It was re-

corded as 24.5° in this case. The mean failure depth wasaround 3.0 cm (case A1). The above test procedures were re-peated on the type II rods in a dry state (case B1). The fail-ure angles ranged between 24.0° and 26.6°. The failurepattern was similar to case A1. Comparisons were madewith some previous laboratory tests by Matsuoka et al.(1999) using materials such as Toyoura sand (0.10–0.30 mm, e0 = 0.71), glass beads (0.355–0.60 mm, e0 =0.62), and crushed sand (0.42–2.0 mm, e0 = 0.82) in drystates. A similar failure pattern was shown in these testswhere the failed body always formed a shallow slip planerather than a circular arc.

Testing in a moist stateType I and type II assemblies were submerged with wa-

ter in a bucket. The wetted rods were taken out of waterand constructed to a slope inside the tilting box. A film ofwater was readily visible around some rod surfaces, but nofree water was present. Similar test procedures were carriedout in the TBT of A2 and B2, in which the water content(w) was equal to 1.4%. The rods were observed to movewhen the box was inclined up to 29.5° (about 5° higherthan the relevant one in the dry state). As shown in Fig. 4(type II), the slip surface exhibited a circular arc as com-monly observed in cohesive soil slopes. The maximum fail-ure depth was around 10 cm. The failure angles of test

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380 Can. Geotech. J. Vol. 44, 2007

Fig. 1. (a) Water attached to aluminum rods, capillary menisci buildup (after Ohashi and Matsuoka 1995). (b) Sketch of theinterparticle adhesive force due to the surface tension of capillary water.

Fig. 2. Setup for the titling box tests.

cases A1, A2, B1, and B2 using aluminum rods are summa-rized in Table 1. The above testing procedures were ap-plied to Toyoura sand (w = 2.9%), which was wetted in thesimilar way. The front and back walls of the tilting boxwere adjusted to the maximum width of 30 cm and their in-ner sides were lubricated so as to minimize the friction be-tween the walls and the testing materials. The failureangles ranged from 48.2° to 48.7°, considerably higherthan the dry state angles of 33°–36°. The failure slip sur-

face showed a circular arc. We recognized that the slipplane with shallow depth occurred in dry conditions with-out cohesion, while the circular slip surface with shallowdepth took place in moist conditions.

Numerical validations

The proposed numerical model was validated through thesimulation of the above TBT on type I aluminum rods. As

© 2007 NRC Canada

Chen and Liu 381

Fig. 3. Sequence of the failure process of the dry aluminum rod slope (type I): (a) → (b) → (c).

shown in Fig. 5, the initial particle distributions for the sim-ulations were created and digitized based on the exact ar-rangements of the rods in the above tests in terms of rodsize, distribution, and total number.

Slope failures in a dry stateThe input parameters of the DEM simulations of type I

rods in a dry state are listed in Table 2, corresponding to theproperties of the rod assembly used in the experiments. Theinterparticle adhesive force, PS, was equal to 0. The stiffnessand the damping parameters are based on the contact theoryof two elastic discs by considering the stress level possiblyapplied on rod particles; the interparticle friction angle, φµ =16°, was obtained from the frictional tests on the aluminumrods. These parameters have been used to simulate biaxialcompression test, simple- and direct-shear tests on an assem-bly of aluminum rods (Yamamoto 1995; Liu and Matsuoka2003; Liu et al. 2003). The computed failure angle was 25°,within the ranges measured from the conducted TBT (caseA1). To exclude the boundary effect, the midportion alongthe slope surface with a length of 60 cm was analyzed. Forclarity, the mid-slope had a grid at every 10 cm parallel to

the slope surface with 9 mm in depth (see Fig. 6). The meandisplacement of the particles within a mesh represents thegross movement in this region. During shear deformation,the cohesionless assemblies exhibited a continuous changein the evolution of interparticle forces. Figure 6a shows thecalculated particle displacements at failure with the inter-particle contact information along the mobilized plane. It isseen that the particles move almost parallel to the slope sur-face, similar to the simple-shear deformation with a shallowdepth. Corresponding to the relevant depth of the region, thestatistical distribution of the mean mobilized friction anglesis shown in Fig. 6b, calculated by

[13] tan

sin( )

cos( )

φφ

φmo

mo,

mo,

=+

+

=

=

∑

∑

f

f

ii

n

i i

ii

n

i i

1

1

θ

θ

µ

µ

in which θ is the interparticle contact angle defined as theangle between the contact plane and the plane parallel to theslope surface, f is the interparticle contact force, φµmo is the

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382 Can. Geotech. J. Vol. 44, 2007

Case Material StateSlopelength (cm)

Slope angleat failure (°)

A1 Type I assembly: 9 and 5 mm aluminum rods mixed ina 3:2 proportion

Dry, moist (w = 1.4%) 80–86 23.0–25.0

A2 Type I assembly: 9 and 5 mm aluminum rods mixed ina 3:2 proportion

Dry, moist (w = 1.4%) 80–86 29.0–29.5

B1 Type II assembly: 3 and 1.6 mm aluminum rods mixedin a 3:2 proportion

Dry, moist (w = 1.4%) 80–86 24.0–26.5

B2 Type II assembly: 3 and 1.6 mm aluminum rods mixedin a 3:2 proportion

Dry, moist (w = 1.4%) 80–86 29.0–29.5

Table 1. Tilting box tests using aluminum rod assemblies.

Fig. 4. Failure pattern of the moist aluminum rod slope (type II).

interparticle mobilized friction angle, and i is the particlecontact number. The calculated mean mobilized friction an-gle within the deformed area was between 22° and 25°.

The orientation of principal stresses was calculated byeq. [12] and is shown in Fig. 6c. At peak state, the majorprincipal stress was roughly inclined to the slope surface atan angle of 32.5°. The internal friction angle of granular ma-terial follows the common definition, φ = tan–1(τ/σN), whereτ is the shear stress and σN is the normal stress. The internalfriction angle of the aluminum rod system herein was ob-tained from direct shear tests, ranging between 22° and 24°.The angle between the mobilized plane and the major princi-pal stress was equal to (π /4 – φ/2), ranging from 33° to 34°in the present case. This value approaches the angle betweenthe major principal stress and the slope surface. Subse-quently, the mobilized plane parallels with the slope surface,and the particles within the midportion of the slope movealong the slope surface. The calculation agrees with the ex-perimental observations that the slip plane parallels the slopesurface. The number of the particle contact with respect toan angle, α, can be recorded during the shearing, where α isthe inclination between the particle contact normal directionand the mobilized plane. As illustrated in Fig. 6c, the fre-quency distribution of the contact orientation, M(α), tends toa preferred direction that gradually rotates with the increaseof shear stress more rapidly than other directions. This pre-ferred direction coincides with the major principal stress

axis. It agrees with similar observations in simple-shear testson photoelastic rods by Oda and Konishi (1974a, 1974b).

Shearing deformation also leads to the change of the num-bers of interparticle contacts. With respect to the possiblerange of contact angle θ, the number of interparticle contactsN(θ) was monitored during the slope-tilting process. Fig-ure 7 shows the normalized frequency distribution of thenumber of interparticle contacts, N(θ)/Nmax, parallel to theslope surface in accordance with Fig. 6. It was noted that thedistribution shifts to the right side as the slope angle in-creases, suggesting that the number of particle contacts in-creases in the positive zone of θ. We further define thefrequency distribution for the newly generated contact nor-mal stresses as Ng(θ) and for those have just disappeared asNd(θ). As was evident in Fig. 8, Nd(θ) is concentrated in thenegative zone of θ and Ng(θ) is more frequent for positive θ.This suggests that the number of interparticle contacts in-creases with the tilting of the slope angle, and the inter-particle contact angle is effective to the resistance ofshearing.

The change of the interparticle contact angle along themobilized plane (parallel to the slope surface) is traced inFig. 9 during the tilting of the slope until failure. The solidcurve represents the ratio of shear stress to normal stress onthe contact plane. The contact angle along the mobilizedplane is observed proportional to this ratio, suggesting thatthe frictional law on the contact plane controls the move-ments of particles on the mobilized plane. The maximumvalue of this ratio takes place when the contact plane coin-cides with the mobilized plane (θ = 0), and the minimumvalue occurs when it is parallel to the directions of principalstresses. This scenario agrees with the information conveyedin Fig. 6. This information is meaningful to the design ofslope-stabilization measures including the optimal installa-tion angle of soil–nails and will be discussed in the Experi-mental study section.

It is noteworthy that the change of interparticle frictionmay have a limited influence on the internal friction angle;the global internal friction angle increases with the inter-particle angle at a very small value, but is essentially con-stant for a larger value of interparticle angle (e.g., Skinner1969; Cambou et al. 1993; Oger et al. 1998).

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Chen and Liu 383

Parameter Value

Normal stiffness, kN (N/m2) 9.0×109

Shear stiffness, kS (N/m2) 3.0×108

Normal damping, ηN (N s m–2) 7.9×104

Shear damping, ηS (N s m–2) 1.4×104

Interparticle friction angle, φµ (°) 16Density of particles, ρ (kg/m3) 2700Time increment, ∆t (s) 2×10–7

Interparticle adhesive force, PS (N) 0–0.2

Table 2. Input parameters for the distinct elementmethod (DEM) simulations.

Fig. 5. Initial particle distribution in the distinct element method (DEM) simulation, reproducing the initial distribution of the type Iassembly in Fig. 1.

Slope failures in a moist stateThe adhesive force between particles is introduced by the

surface tension of water where capillary menisci build upbetween adjacent particles. The adhesive force at each con-tact point among particles may vary depending on the size,shape, and pore-water state inside the voids of soils. To sim-ulate the performed TBT on type I in moist conditions (case

A1), PS was made constant for simplicity in the present cal-culation. The moisture content of the wetted rods was 1.4%,which is equivalent to a degree of saturation of 0.185, pro-vided that the specific gravity is 2.65 and that the void ratiois 0.201. Referenced to Han et al. (2004), the possible maxi-mum value of the capillary force of sand is around 0.5 N,and the capillary force rapidly decreases to zero when thedegree of saturation increases to 0.34. In the current case, PSis taken as 0.2 N and other input parameters are the same asthose listed in Table 2. The calculated slope failure angle of30° matches with the value from the TBT of case A1. Thefailure-depth distribution and the particle movements areshown in Fig. 10, where the slip surface is circular as ob-served in the TBT (case A2).

Furthermore, the values of PS decrease from 0.2 to 0 Nwith an interval of 0.05 N. The slope angle was set as 25°.For a given PS, typical patterns of particle movements arepresented in Fig. 11. The displacements of particles alongthe slope surface increase with decreasing PS. For PS = 0,equivalent to the dry state without cohesion, the slope failed.The slope-failure angles are consistent with the experimentalmeasurements. Corresponding to different values of PS inmultiple runs, the ratio FS = tanφ/tanφmo were computed,where φmo is the distribution of the mean mobilized frictionangles related to the failure depth according to eq. [13], and

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384 Can. Geotech. J. Vol. 44, 2007

Fig. 7. Variation of contact angles on planes parallel to the slopesurface during the tilting of the box until failure; solid line, be-fore titling; dashed line, tilting to the slope angle of 25°.

Fig. 6. Numerical simulations of the dry aluminum rod slope at failure (failure angle = 25°): (a) particle displacement; (b) mean mobi-lized friction angles corresponding to the relevant depth; and (c) frequency distribution, M(α), of particle contacts along the contactnormal direction and orientation tendency of principal stresses.

φ is the internal friction angle of the slope materials (alumi-num rods, φ = 22°–24° obtained from direct-shear tests). It isapparent that PS plays an important role in FS, which in acertain sense may be considered as a safety measure forslopes.

When rainfall infiltrates dry soils, rainwater leads to atemporary change in soil suction in slopes above groundwa-ter level. Within the infiltrated area, only a certain amount ofwater enters the soils during a storm and only a limited zoneof soil is wetted. In thick mantle soils, the shear stress of the

upper zone is reduced, but the deeper soil is relatively unaf-fected. Slope failures in this situation commonly occurwithin a certain depth. This is especially true in some re-gions where many rainfall-induced slope failures are usuallyminor in volume and shallow in depth (Chen and Lee 2004),although in slope stability analysis, the failed body has beencommonly assumed as a complete rigid body failure withcircular slip surface. As illustrated in Fig. 12a, a shallowfailure occurred in the slope and the trees inclined towardsthe major descendent direction of the slope rather than itscrest. Only if the failed body is assumed rigid and the failureplane is assumed circular may the tree incline towards theslope crest (see Fig. 12b).

Soil suction can be found in a slope that lies above thewater table. The meniscus formed between adjacent soil par-ticles by the soil suction creates a normal force between theparticles, which bonds them in a temporary way. By the timethe residual water content of soil is reached, the increase inmatric suction contributes a significant component to theshear strength. Thus, the soil suction, if it can be reliedupon, may enhance the slope stability. Nevertheless, soilsuction also provides an attractive force for free water. Whena slope failure is shallow and results simply from a gradualdecrease of suction, the soil dilates as a low net stress is ap-plied. In the shearing zone, dilation causes the reduction ofpore-water pressure, which increases the effective stress andin turn strengthens the soil mass. On the other hand, dilationalso leads to a higher void ratio. The effective stress in-creases until the negative excess pore-water pressure is dissi-pated by water flowing into the expanding void, and thisserves to lower the soil strength. If the lowering of the soilstrength has a magnitude larger than the increment causedby dilation, the soil becomes brittle (Chen et al. 2004). Astable slope under normal conditions may become unstablebecause of boundary condition changes, such as a sufficientincrease of pore-water pressure. The volumetric deformationthat the soil suffered is caused by the soil structure rear-rangement and the occurrence of local shearing of grains inresponse to the suction reduction, which is in turn affectedby the change of suction and the applied external force. Therelationship of interparticle adhesive force with suction isbeyond our current study.

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Fig. 8. Particle contact information for disappearance and generation on the planes parallel to the slope surface.

Fig. 9. Variation of the interparticle contact angle along the mo-bilized plane during the tilting of the slope until failure (circularplots) and their fitting with the ratio of the shear stress to thenormal stress on the contact plane (solid curve).

Experimental study of slope-stabilizationmethods

Optimal installation angle of soil nailsThe DEM calculations in the previous seciton reveal that

the frictional law on the contact plane governs the movementof particles on the mobilized plane. The minimum ratio ofthe shear stress to normal stress takes place when the contactplane is parallel to the principal stresses. For the aluminumrod assemblies in the present study, the major principalstress at peak state is inclined to the slope surface at 32.5°(see Fig. 6). Bearing this in mind, we designed two series ofTBT for testing the optimal installation angle of nails.

In the first series of tests, the type II rod assembly wasused to construct a slope inside the tilting box. Five piecesof thin aluminum sheet were inserted perpendicular to theslope surface (case D1), acting as nails in the 2D manner.

Each aluminum sheet was 10 cm long and 5 cm wide. Theinserted depth was 10 cm. The surface of the aluminumsheet was rough so as to achieve a higher shear resistance.Under similar tilting procedures, the measured failure anglewas between 27° and 29° (Fig. 13). Another series of TBTwas conducted with the same aluminum sheets, but installedalong the σ3 direction (case D2, same insert depth). Asshown in Fig. 14, the angle between the aluminum sheetsand the slope surface was 57.5° (= 90° – 32.5°). The failureangle was now between 29° and 32°, higher than that of caseD1. The above experimental results are summarized in Ta-ble 3.

The shear resistance predominantly consists of two com-ponents: the one arising from the frictional sliding betweenparticles and another from interlocking between particlesand nails (Luo et al. 2000). In the above experimental set-tings, when shear failure takes place between particles, aconsiderable degree of interlocking between particles has tobe overcome owing to the rough surface of the nails. Withthe increase of tilting, the particles being sheared around thenails tend to slide and roll, resulting in dilation in the vicin-ity of a nail because of the loose state of the particles andthe low magnitude of confining pressure. The surroundingparticles restrict such a tendency, leading to an increase ofnormal stress on the surrounding surface of the nail. Theshear resistance on the interface between the nail and theparticles is essentially governed by the dilation behavior ofthe particles (Xanthako 1991). On the other hand, the appar-ent friction coefficient diminishes with increasing normalstress. When the tilting angle continues to increase, theparticles around the nails will collapse (move) beyond themaximum frictional resistance. The particle volume thencontracts rather than dilates, and the dilation effect on theapparent friction might completely vanish (Luo et al. 2000).If the nails are installed along the σ3 direction with the mini-mum shear to normal stress ratio, the interparticle contactplane is parallel to the principal stresses. As the frictionallaw on the contact plane controls the movements of the par-ticles on the mobilized plane, the maximum frictional resis-tance could be achieved. Moreover, the reinforced materialsshould be placed in the most extensible direction where thereinforced materials might develop maximum tensile defor-

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Fig. 10. Failure depth distribution and the particle movements of the moist aluminum rod slope (type II, PS = 0.2 N).

Fig. 11. Interparticle cohesive force, PS, decreasing from 0.2 to0.0 N.

mation. Therefore, it is expected that placing the nails alongthe direction of the minor principal strain would be the mosteffective way to stabilize slopes.

These primary laboratory tests aimed to qualitatively ana-lyze the installation angle of the nails. The aluminum sheetswere inserted into the slope model without any grouting. Inpractical installation, soil nails are generally steel bars thatcan resist tensile and shear stresses and bending moment.Once the nails are in place, the structures are sprayed withshotcrete and covered with precast textured panels. Cementgrouting is injected during the installation of some types ofnails (such as grouted nails and jet-grouted nails). Thesemethods would further increase the pullout resistance of thecomposite, and the nails are corrosion-resistant. Due to thevariety of field materials and the complexity of the interac-

tion mechanism between the apparent friction and dilatancy,further research work is being conducted on this subject.

Slope-surface stabilizationThe experimental and numerical simulations in the previ-

ous section also show that the failure pattern in a dry slopeis basically a slip plane roughly parallel to the slope surface.In a moist state without free water, the failure slip surfaceshows a circular arc. In both cases, the failure depths areshallow. We, therefore, considered stabilizing the mantlesoils along the slope surface so as to minimize the move-ment of the soil particles.

The TBT were carried out using the type II aluminumrods to construct a slope inside the titling box. Ten strips ofgum tape (15 cm × 2.5 cm) were, respectively, pasted on the

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Fig. 12. (a) Shallow failure along the descendent slope direction and (b) when the failed body was assumed as rigid and the failureplane was assumed as circular, the tree inclined towards the slope crest.

front and the back faces of the slope along the descendentdirection of the slope without any restraint at the toe (caseC1). The length of the slope surface with gum tape was75 cm (about 85% of the full slope-surface length of 86 cm),including the minor interval between two strips of gumtapes. The slope failure was triggered by tilting the box at anangular speed of 1°/min. Failure began locally around theslope toe and extended backwards to the mid-slope portion(Fig. 15). In a dry state, the mean slope failure angle wasabout 27°–29°, slightly higher than that without the stickygum-taped stabilization (24°–26.5°) described in the DEMsection (case B1). The failure depth was shallow, in therange of 2–3 cm. Failure occurred along a slip plane ratherthan in a circular arc. In the sense of force analysis, onecould imagine the sliding body as a sandwich, confined bythe upper reinforced material and the slope beneath the slipsurface. Frictional resistance exists for any relative move-ment along the upper and lower interfaces of the slidingbody, which increases slope stability, although the effect ofthe frictional resistance may not be very significant.

As for the failure initiated in the toe area, we conductedanother series of TBTs to evaluate the influence of thedownslope retaining wall together with the slope-surface sta-bilizing measures. Ten strips of gum tape were pasted, re-

spectively, on the front and back faces of the slope along thedescendent direction, as in case C1, except that a thick blockwas installed at the slope toe where a small portion of theslope was cut (case C2). There was no obvious gap betweenthe slope and the downslope block. The failure began withthe sliding of the reinforced cover, followed by the move-ment beneath the cover. It is surprising that the slope-failureangle increased up to 31°–32° (Fig. 16). This is substantiallylarger than the previous tests with only the gum-taped stabi-lizing surface (case C1, 27°–29°) or without any surface-stabilizing measures (case B1, 24°–26.5°).

Using rock, coarse stone, or boulders as rigid cover onsoil slope surfaces, riprap is one of the commonly used sta-bilization methods in engineering practice. Its effectivenesscan be enhanced with native plant species and re-establishedvegetations. A filter layer under the riprap is necessary to re-lieve the hydrostatic pressure inside the slope, to distributethe weight of the riprap, to prevent settling, and to preventfine materials in the slope from being removed by hydraulicaction. The filter material can be fabric, gravel, crushedstone, or small rock. Besides, riprap provides slope surfaceerosion control that will improve the slope stability. In someregions, the practice of upgrading loose fill slopes is to re-compact the top layer of mantle soil to 95% of the maximum

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Fig. 13. Photo at failure: five pieces of thin aluminum sheets, simulating soil nails, were inserted perpendicular to slope surface (insertdepth, 10 cm).

Fig. 14. Photo at failure: five pieces of thin aluminum sheets, simulating soil nails, were inserted along the σ3 direction (insert depth,10 cm).

dry density (Chen et al. 2004). Recompaction has beenproven effective in stabilizing fill slopes; static liquefactionof the fill would be very unlikely, although it could not becompletely ruled out. It is noted that the experiments alsoshow that most of the failures begin at the slope toes. Re-taining walls constructed at the toe of a slope may mitigateand (or) prevent small size or secondary landslips that oftenoccur along the toe portions. For large-scale earth move-ment, however, crib walls might be more effective than theconventional reinforced concrete retaining walls.

Concluding remarks

The incorporation of interparticle adhesive force wascoded into the conventional DEM to account for the effect ofsuction. This improved DEM was validated through labora-

tory tilting box tests in which slope failure was simulatedusing aluminum rod assemblies. The simulations agree withthe laboratory test results that the failure pattern of a dryslope largely shows a slip plane parallel to the slope surface,but a circular slip surface in a moist slope. Both failures areshallow in depth. Furthermore, the numerical simulationsreveal microscopic information such as particle movement,including the interparticle force and contact angle, the mobi-lized friction angle, the principal and contact normalstresses, and the development of contact angle along the mo-bilized plane. The interparticle network shows that the maxi-mum ratio of shear stress to normal stress takes place whenthe interparticle contact plane coincides with the mobilizedplane, and the minimum value of this ratio occurs when thecontact plane is parallel to the directions of principalstresses. This paper shows that the micromechanical charac-

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Fig. 15. Photo at failure: 10 strips of gum tape (15 cm × 2.5 cm) were pasted on the front and back faces of the slope along the de-scendent slope direction; no restraint at the slope toe.

Table 3. Tilting box tests using type II aluminum rods in a dry state.

teristics of granular materials in shear deformation are perti-nent to the design of slope stability measures. On this basis,the effectiveness of slope surface and soil–nail stabilizationmethods has been experimentally evaluated. Specifically, weshowed that the optimal installation angle of soil nails isalong the minor principal stress direction so that the rein-forced material might develop maximum tensile deforma-tion.

Acknowledgements

The authors are grateful to Professor H. Matsuoka of theNagoya Institute of Technology, Nagoya, Japan, for his per-sistent guidance and inspiration to the study reported herein.The following financial supports are deeply appreciated bythe authors: the Japan Society for the Promotion of Science(JSPS) for H. Chen, and the National Natural Science Foun-dation of China (grant 10672050) and Hohai University,P.R. China (grant 2084/4040110) for S.H. Liu.

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