influence of thermomechanics in the catastrophic collapse of planar landslides

Influence of thermomechanics in the catastrophiccollapse of planar landslides

Francesco Cecinato and Antonis Zervos

Abstract: Frictional heating has long been considered a mechanism responsible for the high velocities and long run-out ofsome large-scale landslides. In this work a landslide model is presented, applicable to large-scale planar landslides occurringin a coherent fashion. The model accounts for temperature rise in the slip zone due to the heat produced by friction, leadingto water expansion, thermoplastic collapse of the soil skeleton, and subsequently to an increase of pore-water pressure. Thelandslide model, comprising equations that describe heat and pore pressure diffusion and the dynamics of the moving mass,is used to analyse the evolution of the Jiufengershan planar landslide as an example. Further, its parameter space is system-atically and efficiently explored using a Taguchi parametric analysis in an attempt to quantify dominant parameters. It isshown that the process of sliding is dominated by the softening properties of the material, as expected, but also by the per-meability of the slip zone and the thickness of the sliding mass. It is worth noting that the latter two parameters do not entertraditional stability analyses of uniform slopes.

Key words: thermal pressurization, landslide dynamics, numerical analysis, thermo-mechanics, Taguchi methods, parametricstudy.

Résumé : Le réchauffement frictionnel a longtemps été considéré comme un mécanisme responsable des vitesses élevées etde la longue portée de certains glissements de terrain à grande échelle. Dans cet article, un modèle de glissement de terrainest présenté, qui est applicable aux grands glissements de terrain en plan se produisant de manière cohérente. Le modèletient compte de l’augmentation de la température dans la zone de glissement causée par la chaleur produite par la friction,qui à son tour cause l’expansion de l’eau, un effondrement thermoplastique du squelette du sol, et par la suite, une augmen-tation de la pression interstitielle. Le modèle de glissement de terrain comprend des équations qui décrivent la diffusion dela chaleur et des pressions interstitielles et la dynamique d’une masse en mouvement. Il est utilisé pour analyser l’évolutiondu glissement de terrain en plan Jiufengershan en tant que démonstration. De plus, son espace paramétrique est exploré sys-tématiquement et efficacement à l’aide de l’analyse paramétrique de Taguchi afin de quantifier les paramètres dominants. Ilest démontré que le processus de glissement est dominé par les propriétés de ramollissement du matériau, tel que prévu,mais aussi par la perméabilité de la zone de glissement et l’épaisseur de la masse glissante. Il est intéressant de noter queles deux derniers paramètres ne font pas partie des analyses de stabilité traditionnelles pour des pentes uniformes.

Mots‐clés : pressurisation thermique, dynamique des glissements de terrain, analyse numérique, thermomécanique, méthodesde Taguchi, étude paramétrique.

[Traduit par la Rédaction]

IntroductionFrictional heating has long been considered one of the pos-

sible key phenomena behind the rapid, substantial loss ofshear strength occurring in the slip zone of some large-scalelandslides, leading to unconstrained acceleration (Habib1975; Voight and Faust 1982). Pore pressure in soils in-creases with temperature due to thermal expansion and theeventual thermal collapse of the skeleton (Hueckel and Baldi1990; Hueckel and Pellegrini 1991; Modaressi and Laloui1997), especially under conditions of slow or no drainagelike the ones occurring in the rapidly deforming slip zone ofa landslide. Moreover, heating reduces the soil’s apparentoverconsolidation ratio, shrinks its elastic domain, and lowers

its peak stress ratio (Hueckel and Baldi 1990; Laloui and Ce-kerevac 2003). These processes lead to declining shear resist-ance at the slip zone, causing the sliding mass to accelerateand potentially making the difference between a relativelylow-impact event and a catastrophic one.The first comprehensive landslide model accounting for

frictional heating and thermal pressurization in the slip planeof a uniform slope was presented by Vardoulakis (2000,2002). However, the specialized constitutive law it used forthe soil cannot capture the full range of temperature-dependentsoil behaviour observed experimentally, and it cannot beeasily generalized to include the behaviour of the soil priorto failure or to model two- or three-dimensional problems.

Received 27 October 2010. Accepted 22 October 2011. Published at www.nrcresearchpress.com/cgj on 26 January 2012.

F. Cecinato* and A. Zervos. Faculty of Engineering and the Environment, University of Southampton, Highfield, SO17 1BJSouthampton, UK.

Corresponding author: Francesco Cecinato (e-mail: [email protected]).*Present address: ENI, E&P Division, Geomechanics Laboratory (LAIP), Via Maritano 26, 20097 S. Donato Milanese, Milan, Italy.

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Can. Geotech. J. 49: 207–225 (2012) doi:10.1139/T11-095 Published by NRC Research Press

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Cecinato et al. (2008, 2011) further developed Vardoula-kis’ (2002) model by adopting a more general constitutive as-sumption for the soil, applicable to a wider range of soils.This was done by adopting a thermoplastic Modified CamClay constitutive framework, in which strain-, strain-rate–,and thermal softening could be accommodated. It was shownthat contrary to what may have been expected, the introduc-tion of thermal softening did not lead to ill-posedness of thegoverning equations. It was also possible to determine thepressurization coefficient in terms of other, better-establishedmaterial parameters and state variables, rather than considerit an independent parameter.In this work, the model equations of Cecinato et al. (2011)

describing heat generation and diffusion, pore pressure gener-ation, and dissipation, and the thermomechanical behaviourof soil are outlined, in the framework of an infinite slope ge-ometry. The model is then employed to simulate as an exam-ple the collapse of the large-scale planar landslide ofJiufengershan (e.g., Chang et al. 2005), showing that realisticsliding velocity estimates can be obtained. A parametric anal-ysis is subsequently carried out, to identify the dominant pa-rameters (among different geometrical characteristics and soilproperties) that make an infinite slope prone to catastrophiccollapse. To improve the efficiency of the parametric studyand explore significant parameter combinations only, thestatistical-based Taguchi experimental design method (e.g.,Taguchi et al. 1989; Peace 1993) is adopted. Through thisprocedure the main factors that maximize the predicted slidevelocity, i.e., those exacerbating the catastrophic character ofthe slide, are identified and ranked.In the next section we present the soil constitutive model,

followed by the section on the formulation of the landslidemodel. In the section titled “Numerical example: the Jiufen-ghershan landslide”, the analysis of the Jiufengershan land-slide is discussed and in the section titled “Parametersgoverning catastrophic collapse” we describe a general para-metric study involving 13 parameters. The significance ofthermomechanical properties in particular is explored in thesubsequent section, followed by a summary of the conclu-sions.

Constitutive model

Thermoplastic behaviour of soilTemperature influences the behaviour of clays by causing

volume variations of the free water and by changing the ad-sorption forces in the structural water (Sulem et al. 2007).Such effects are reflected in volumetric strains caused byheating, which are mainly reversible and dilative if the soilis overconsolidated, and irreversible and contractive if thesoil is normally consolidated (Hueckel and Baldi 1990; La-loui et al. 2005). Another typical feature of clays is thermalsoftening, i.e., a reduction of the size of the elasticity domainof the soil as temperature increases (Laloui and Cekerevac2003).The first model on the thermal response of soils was pro-

posed by Campanella and Mitchell (1968) and formed the ba-sis for several subsequent constitutive studies; notablyHueckel and Borsetto (1990) described the thermoplasticityof saturated soils and shales, and more recently Laloui andCekerevac (2003) proposed a model to describe the volumet-

ric response of clay to heating, which was then extended to amulti-mechanism framework (Laloui et al. 2005; Laloui andFrancois 2009). Based on these ideas, Cecinato et al. (2011)described the development of a constitutive model of theCam Clay family able to capture the main features outlinedabove, in the context of a rapidly deforming clayey shearbandsubject to frictional heating. The core aspects of this modelare summarized here for completeness.The Modified Cam Clay model (Roscoe and Burland

1968) was adopted as it is a widely used model with clearadvantages when it comes to numerical implementation. Theyield surface is expressed in terms of the mean effectivestress p′ and the deviatoric stress q

½1� f ¼ q2 �M2p0ðs 0c � p0Þ

where M the critical state parameter, s 0c is the apparent pre-

consolidation stress, and associated plastic flow is assumed.The thermal softening–hardening response of the volumetric

behaviour of soil is described by the hardening rule proposedby Laloui and Cekerevac (2003) where s 0

c, corresponding tothe intersection of the yield surface with the mean effectivestress axis, is a function of temperature

½2� s 0c ¼ s 0

c0 expðeb3pvÞ½1� g logðq=qrefÞ�where s 0

c0 is the isothermal value of the preconsolidationstress, eb is the plastic compressibility, 3pv is the accumulatedvolumetric plastic strain, g is a material parameter represent-ing the rate of softening, and q and qref are the current andreference values of temperature, respectively.Another feature that has been observed in some clays is

thermal friction-softening, i.e., the dependence on tempera-ture of the friction angle at critical state, f0

cs. However, thereis no clear consensus in the literature, as both the existenceof this effect and its nature appear to be material-dependent(Marques et al. 2004; Laloui et al. 2005; Sulem et al. 2007).To allow for the possibility of thermal friction-softening,which may be a mechanism contributing to the destabiliza-tion of a sliding mass, the linear law proposed by Laloui etal. (2005) is adopted

½3� M ¼ Mref � egðq � qrefÞwhere Mref is the value of the critical state parameter at thereference temperature qref, and eg represents the rate of ther-mal friction-softening.

Thermal pressurization mechanismThermal pressurization due to frictional heating has been

studied in a number of different contexts (Sibson 1973; La-chenbruch 1980; Vardoulakis 2000, 2002; Wibberley andShimamoto 2005; Rice 2006; Sulem et al. 2007), while ex-perimental evidence for both rocks and soils is also available(Campanella and Mitchell 1968; Baldi et al. 1988; Sultan1997; Sultan et al. 2002; Ghabezloo and Sulem 2009). Thekey parameter governing thermal pressurization is the pres-surization coefficient lm, defined as the pore pressure in-crease due to a unit temperature increase in undrainedconditions. Its value depends on the material, the temperature,and the stress level. Different average values for lm have beenproposed for clay, ranging between 0.01 and 0.1 MPa/°C. Asshown in Cecinato et al. (2011), within the framework of the

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constitutive model presented above a gradual collapse of thesoil skeleton is predicted and it is possible to determine thepressurization coefficient lm as a function of the temperature,the void ratio, and the soil constants

½4� lmðqÞ ¼ �1

c

l� k

l

gk

ð1þ eÞq½1� g logðq=qrefÞ� � 2bs

� �

where c is the oedometric compressibility, which can be de-termined in terms of other material parameters; l and k arethe (dimensionless) slope of the normal-compression lineand the unloading–reloading line of the soil, respectively; eis the void ratio; and bs is the thermoelastic expansion coeffi-cient (Cecinato et al. 2011). The pressurization coefficient lmmust be positive to be physically meaningful.

The landslide model

The geometry of a considered landslide is divided into tworegions: the shearband, which is a thin zone where all defor-mation is localized and which is embedded in a thicker soillayer, and the overburden, which moves as a rigid block(Fig. 1). The thickness of the shearband is assumed constantand may be empirically related to the mean grain size of thegeomaterial (Vardoulakis 2002).The considered analysis starts at incipient failure, thus we

assume that the soil within the shearband has already reachedcritical state. Furthermore, plane strain conditions are as-sumed along the y-axis. The x-axis points in the direction ofmovement and the z-axis is taken perpendicular to it. A linearprofile of velocity within the shearband is assumed (Vardou-lakis 2001), while the bulk of the slide moves as a rigid bodywith a speed vd(t), where t is time. Velocity and accelerationalong the z-axis are considered negligible. The small, com-pared to the slide dimensions, thickness of the band allowsfor all variations in the direction of sliding to be neglected,so that temperature and pore pressure changes occur alongthe z-direction only.

Heat equationThe heat equation is derived from energy balance, and de-

scribes the evolution of temperature q within the shearband(Cecinato et al. 2008, 2011)

½5� @q

@t¼ Di

@2q

@z2þ Fi

vdðtÞd

where vd(t) is the velocity at the upper boundary of the shear-band, also corresponding to the sliding velocity of the rigidblock, and d is the shearband thickness. The coefficientsDi(q, u, g, _g ) and Fi(q, u, g, _g ) depend on pore pressureu, temperature q, and on the shear strain g and strain rate_g (Cecinato et al. 2011). Both thermal friction-softeningand displacement and velocity friction-softening of the soilin the shearband are taken into account (see Appendix A).Equation [5] is a diffusion-generation equation for the tem-

perature where the diffusivity coefficient Di varies nonli-nearly with temperature and pore pressure. Extensivenumerical experimentation showed Di to vary very little andto be positive for a wide range of values of the parametersinvolved (Cecinato et al. 2008; Cecinato 2009, 2011), there-

fore the problem remains well-posed from the mathematicalpoint of view.

Pore pressure equationThe pore pressure equation is derived from mass balance

considerations and Darcy’s law, and describes the time evolu-tion of excess pore pressures within the shearband and thesurrounding soil due to thermal pressurization and flow

½6� @u

@t¼ cv

@2u

@z2þ lm

@q

@t

where cv is the average consolidation coefficient

½7� cv ¼ kw

grwc

where c is the soil (oedometric) compressibility, g is the ac-celeration of gravity, rw is the pore-fluid density, and kw isDarcy’s permeability coefficient.

Dynamic equation of the sliding massTo complete the description of the phenomena, an equa-

tion for the dynamics of the sliding mass is needed. Here at-tention is given to planar sliding, appropriate for translationallandslides in which the rupture surface can be assumed, withreasonable approximation, parallel to the surface of the slope.The case of rotational sliding, which is an appropriate as-sumption for deep-seated slides where the slip surface can beapproximated as circular, is treated elsewhere (Cecinato et al.2011).Within the framework of an infinite slope geometry, shown

in Fig. 1, the slope is assumed uniform and of unlimited ex-tent. The slip plane is parallel to the surface of the slope atdepth H. A unit length of slope is considered and, for a givengeometry, gravity and seepage forces determine the safetyfactor in static analyses or the acceleration in post-failure, dy-namic analyses. Dynamic equilibrium of the unit length blockof Fig. 1 leads to the dynamical equation

½8� dvd

dt¼ g sinb� tzxðtÞ

gsH

� �

where vd is the velocity of the block, b is the slope angle, gsis the unit weight of the soil, and tzx(t) is the shear stress inthe shearband.The shear stress in the shear band, together with the block

velocity, provides the coupling between the shearband constit-utive model and the dynamical equation, and it can be ex-pressed according to a conventional Mohr–Coulomb frictionallaw as

½9� tzxðtÞ ¼ s 0nðtÞ tanðf0

csÞwhere f0

csðtÞ ¼ f0csðg; _g ; qÞ is the (potentially softening with

strain, strain rate, and temperature) friction angle ands 0nðtÞ ¼ s 0

n0 – u(t) is the current normal effective stress(where s 0

n0 is the initial normal effective stress). The lattercan be written in terms of the mean effective stress p′, underthe simplifying assumption that s 0

xx ¼ s 0yy (Cecinato et al.

2011), as

Cecinato and Zervos 209


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½10� s 0n ¼ 3

1� n

1þ n

� �p0

where p′ is the current mean effective stress and v is thePoisson’s ratio of the soil.Equation [8] can be adopted to interpret the dynamics of

the collapse of a planar landslide coupled with the shearbandgoverning eqs. [5] and [6]. The coupling variables are theslide velocity vd(t), the average pore pressure at the shear-band–block interface ud(t), and the friction anglef0csðtÞ ¼f0

csðg; _g; qÞ.

Outline of the numerical treatmentThe coupled eqs. [5], [6], and [8] were discretized using a

finite difference scheme and integrated numerically to deter-mine the evolution of temperature, excess pore pressure, andslide velocity with time. The heat and pore pressure equa-tions were discretized using a “forward-time centered-space”explicit finite difference scheme. Stability was ensured bycontrolling the size of the time-step on the basis of a vonNeumann–type stability analysis and numerical experimenta-tion. Equation [8] was discretized with a standard fourth-order Runge–Kutta scheme using the same time-step.The shearband is assumed to be embedded in a clay layer

of the same characteristics, whose thickness is much largerthan the shearband thickness, d. Shear straining and conse-quent heat production occur within the shearband only. Theextent of the spatial domain modelled was 10 times the thick-ness of the shearband and it was assumed to be uniform inhydraulic, thermal, and geotechnical properties. This distancewas assumed sufficiently large for the excess pore pressurethere to be considered zero and for the temperature to beequal to the ambient value.

Numerical example: the Jiufenghershanlandslide

Main features of the slideAs an example, the above model is applied to the case his-

tory of the landslide of Jiufengershan (Shou and Wang 2003;Wang et al. 2003; Chang et al. 2005). This particular landslidewas chosen because (i) it had, with good approximation andover a relatively long distance, a planar slip surface; (ii) a num-ber of field data are available which, although limited, are ad-equate for a first-approximation simulation; and (iii) there wasdirect field evidence for the development of both high temper-atures and high excess pore pressures in the course of sliding.The Jiufengershan landslide was triggered by the 1999

Chi-Chi earthquake in Taiwan. It affected weathered rockand soil materials, which quickly slid along the beddingplane, initially in a coherent manner and subsequently in aflow-like fashion (Chang et al. 2005), for a total displacementof 1 km. The slip surface developed along a pre-existing bed-ding fault, constituted of alternating beds of dark gray shaleand muddy sandstone. Bedding-parallel clay seams of 1–6 cm in thickness were found in the slip plane throughoutthe slope, with clear slickensides and dip-slip striations(Wang et al. 2003). The occasional presence of pseudotachy-lytes (glassy material resulting from rock melting) implies asliding velocity so high that, locally, the rock must havebeen heated to temperatures in excess of 1000 °C, presum-ably at locations of the slip plane where direct rock-to-rockcontact was possible (Chang et al. 2005). We can then rea-sonably expect similar sliding-induced heat production tohave taken place within the clay as well, although of a lowerorder of magnitude. Furthermore, there was field evidence ofpore-water pressurization in the shear zone, as adjacent rock

Fig. 1. Infinite slope geometry. The shearband (shaded) has negligible thickness compared to that of the overburden, i.e., H >> d. d, averageshearband thickness; H, slide thickness; hw, height of water table, W, weight of the unit length block; b, slope inclination with respect tohorizontal; s 0

zz, normal effective stress in the shearband; tzx; shear stress in the shearband.



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joints were recorded to be “filled with sheared mud” (Changet al. 2005). This is compatible with the occurrence of pore-water pressurization in the course of sliding.Based on the above observations, Chang et al. (2005) pro-

posed a simple block-on-slope model to simulate the land-slide dynamics accounting for thermal effects. To provide amore comprehensive understanding of the thermomechanicsof the landslide and of the extent to which different parame-ters of the problem could have affected it, the infinite slopemodel presented in the section titled “The landslide model”is employed to investigate the final collapse phase.

Choice of parametersThe available field data on the Jiufengershan slide, re-

ported by Shou and Wang (2003), Wang et al. (2003), andChang et al. (2005), are given in Table 1. In this table, pa-rameter d has been assigned a value of 1 cm as a reasonablemid-range value for the thickness of the shearband, whichwas found to vary between extremes of 1 mm and 10 cm(Chang et al. 2005). The water table height is assigned theaverage value hw = 30 m after Chang et al. (2005), implyingwithin the framework of an infinite slope geometry that theflow lines are assumed parallel to the slope.The reported field observations (Huang et al. 2001) sug-

gest that the slip occurred along the bedding plane separatingthe Changhuken formation (shale interbedded with thin sand-stone layers) and the Shihmen formation (thick sandstone).The presence of clayey layers with clear slip striations inter-calated between the aforementioned rock formations (Wanget al. 2003) suggests that the slip occurred at the interface be-tween rock and the clay seams, similarly to the Vajont case(Hendron and Patton 1985). It will be therefore assumed thatdeformation was localized within one of the clay layers.However, no information is available on the geotechnicalproperties of the clay. In this case the friction angle at criticalstate may be calculated through limit equilibrium conditionswith the field data of Table 1, resulting in f0

cs = 27.4° at in-cipient failure. By considering equilibrium of forces in the z-direction, the initial normal effective stress is calculated ass 0n = 0.876 MPa. In the absence of site-specific data, the

clay properties k, l, and G, defining the slope of the elasticrecompression line, the slope of the isotropic normal com-pression line, and the specific volume intercept of the criticalstate line, respectively, are assigned mid-range values from arange of known values for different clays (Schofield andWroth 1968; Wood et al. 1992). The thermomechanical prop-erties of the soil, namely the thermoelastic expansion coeffi-cient bs, the thermal diffusivity km, and the thermal constantCf, do not vary significantly for different types of soil (cf.Alexandre et al. 1999; Vardoulakis 2002) and are assignedtypical values (Cecinato et al. 2011). The reference tempera-ture qref can be set to 25 °C as reported by Chang et al.(2005), reflecting the climate of Taiwan. Water compressibil-ity is set to the average value of 4.9 × 10–4 MPa–1 (cf. Var-doulakis 2002).In the absence of direct measurements, the soil permeabil-

ity is set to a value kw = 10–11 m/s, representative of clayeysoils (cf. Vardoulakis 2002). The thermal softening parameterg is assigned the lower-mid-range value g = 10–2 (Cecinatoet al. 2011). Furthermore, as no information is available on

the friction-softening properties of the Jiufengershan soil, thefriction angle is set constant for a first-attempt simulation.The above-discussed parameters are summarized in Ta-

ble 2.

Numerical results and discussionIt should be noted that the thermomechanical landslide

model can interpret the final catastrophic acceleration phase;however, it cannot be employed to simulate the “stick–slipbehaviour” that is typical of co-seismic inertial displacements(Chang et al. 2005). Due to prolonged earthquake shaking(more than 30 s based on the available accelerogram records,cf. Huang et al. 2001), one may assume that the soil in theshearband reached failure in an undrained manner (Cecinato2009, 2011) while the temperature at the base of the slide in-creased, due to frictional heating, from the ambient value ofqref = 25 °C. A value of q0 = 45 °C (where q0 is the theshearband temperature at the onset of catastrophic collapse),as calculated by Chang et al. (2005) through a Newmark-type analysis (Newmark 1965) modified to include thermo-mechanical considerations, is adopted.The final collapse phase of Jiufengershan is simulated by

numerically integrating the landslide model of the section ti-tled “The landslide model” using the above parameter valuesand initial conditions. The initial velocity is set to zero andsliding is numerically initiated by a minute reduction of thefriction angle.Temperature and excess pore pressure isochrones were

produced for a time window of 20 s after initiation (Figs. 2and 3). It can be seen that after 10s from initiation, at the

Table 1. Field data of Jiufengershan slide.

Parameter Value

Unit weight of water, gw (N/m3) 9.81 × 103

Unit weight of the overburden, gs (N/m3) 24.525 × 103

Slope inclination, b (°) 20Slide thickness, H (m) 50Average shearband thickness, d (m) 1 × 10–2

Height of water table, hw (m) 30

Table 2. Choice of parameters for Jiufengershan slide.

Parameter Value

Slope of URL of clay, k 4.5 × 10–2

Slope of NCL of clay, l 0.17Specific volume intercept of clay, G (kPa) 3.2Soil (drained) Poisson’s ratio, n 0.3Compressibility of water, cw (MPa–1) 4.93 × 10–4

Reference temperature, qref (°C) 25Soil thermal diffusivity coefficient, km (m2/s) 1.45 × 10–7

Thermoelastic expansion coefficient, bs (°C–1) 7.41 × 10–5

Thermal constant, Cf (MPa/°C) 2.84Soil permeability, kw (m/s) 10–11

Thermal-softening parameter, g 10–2

Calculated friction angle at CS, f0cs (°) 27.4

Calculated initial normal effective stress, s 0n0

(MPa) 0.876



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shearband mid-plane q ≈ 55 °C and u ≈ 60 kPa. In bothgraphs, the flat profile of the isochrones within the shearbandfor t = 20 s reveals the asymptotic convergence to a steadystate for heat production: the temperature reaches a maximum

value qmax ≈ 134 °C as the shearband soil liquefies due tofull pressurization and the shear stress tends to zero. This isbest illustrated in Fig. 4, where the computed excess porepressure and shear stress at the shearband mid-plane are plot-

Fig. 2. Temperature isochrones for the catastrophic collapse phase of the Jiufengershan slide, with shearband thickness d = 1 cm.

Fig. 3. Excess pore pressure isochrones for the catastrophic collapse phase of the Jiufengershan slide, with shearband thickness d = 1 cm.



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ted against time: the weakening of shear resistance is closelyrelated to the rise of excess pore pressure, and the rates ofboth tend to zero after t = 18 s.In Fig. 5 the slide velocity and displacement are plotted

against time. At t = 10 s, a velocity of 0.9 m/s is reachedafter 1.5 m displacement. A rapid acceleration follows, suchthat only 10 s later (at t = 20 s) the landslide attains the cata-strophic velocity of 25 m/s.Field observations suggest that the maximum displacement

of the Jiufengershan slide was 1 km (Chang et al. 2005). Themaximum velocity reached by the slide was estimated byChang et al. (2005) to be about 80 m/s, at a stage when themass could have lost its integrity and moved in a flow-likefashion. Nevertheless, this later-stage evolution appears to bewell reproduced with the above-presented landslide model:by extending the simulations to a time of 40 s after initiation(Fig. 6), a velocity of about 80 m/s is calculated after a dis-placement of 1000 m.

Impact of friction-softening and shearband thicknessThe effects of possible material friction-softening and of a

thinner shearband in the Jiufengershan simulations are ex-plored hereafter. As an example it may be assumed that thestatic residual friction angle for the Jiufengershan clay isaround 10°, as is typical of soils with a significant clay frac-tion (Skempton 1985). For simplicity, the friction angle isallowed to decrease with displacement only, assuming forthe rate of static friction-softening — in the absence of betterinformation — the value reported in Vardoulakis (2002).Calculations were carried out for a total time window of

20 s. The resulting temperature and pore pressure isochrones

are very similar to those presented in the subsection titled“Numerical results and discussion”, but the effect of the rapiddecrease of friction with displacement is evident in the varia-ble slope of the shear stress plot (Fig. 7): an initial, verysteep branch due to friction-softening is followed by a rela-tively milder one, representing the continuation of the shearresistance weakening due to pressurization, towards theasymptotic attainment of a liquefied state after t = 12 s. Bycomparing the shear stress and excess pore pressure plots ofFig. 7 to those in Fig. 4 it can be seen that pressurizationnow occurs sooner, due to faster frictional heating (Fig. 8).In fact the velocity and acceleration are heavily affected bymaterial softening, as the slide reaches 500 m at a speed ofalmost 60 m/s 20 s after initiation (Fig. 9).The effect of the shearband thickness on the slide dynamics

is investigated by choosing for d the lower-range value of 1 mm(Chang et al. 2005), all other parameters being equal: more lo-calized shearing causes heating and pressurization to be moreconcentrated around the shearband mid-plane (Figs. 10 and11). Also, thermal pressurization happens faster, as in thiscase full pressurization is attained after only 8 s (Fig. 12).The acceleration is also higher, as velocity reaches about50 m/s at t = 20 s (Fig. 13).

Parameters governing catastrophic collapseThe general difficulty in finding a sufficient number of re-

liable geotechnical parameters from landslide case historiesbrings about a significant degree of uncertainty in the modelpredictions. To overcome this difficulty, the influence of eachof the different parameters on the response of the systemshould be assessed, to determine their relative importance

Fig. 4. Computed shear stress and excess pore pressure at the shearband mid-plane of the Jiufengershan slide as a function of time, withshearband thickness d = 1 cm.



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and allow prioritization of the field and laboratory measure-ments that deserve most attention. To meet this purpose, inthis section the landslide model is employed to carry out ageneral parametric study, with the aim of identifying themost important parameters that may make a slope prone tocatastrophic failure. This is done through a number of simu-lations where each relevant geometrical and geomechanicalproperty of the slide is varied independently within realisticranges.

Due to the wide variety of contexts in which landslides oc-cur, there is no unique definition of what constitutes a “cata-strophic” slide. Nevertheless, a criterion to formallydistinguish between catastrophic and noncatastrophic casescould still be established, based on the velocity reached by aslide after a certain distance. For example, one could con-sider as catastrophic any landslide that after 10 m of dis-placement reaches a velocity of 3 m/min (i.e., 0.05 m/s) ormore. The latter value constitutes the threshold velocity for

Fig. 6. Computed velocity and displacement of the Jiufengershan slide, plotted against time, with shearband thickness d = 1 cm. The verticaldashed line marks the reaching of 1 km of displacement, roughly corresponding to a velocity of 80 m/s.

Fig. 5. Computed velocity (vb) and displacement (xd) profiles of the Jiufengershan slide, with shearband thickness d = 1 cm.



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“very rapid” slides in the International Union of GeologicalSciences Working Group on Landslides (1995) velocity clas-sification; while 10 m can arguably — although rather arbi-trarily — be considered (in first approximation) a distancelarge enough for a slide to be noticed, but perhaps depending

also on the context, small enough to avoid major damage. Al-ternatively, one could use as a criterion of ranking how cata-strophic a landslide can be the velocity reached after 10 sfrom initiation, 10 s being a small enough value to save com-putational time, yet long enough for the development of ther-

Fig. 8. Computed temperature at the shearband mid-plane of the Jiufengershan slide as a function of time, in the case of a friction-softeningsoil, with shearband thickness d = 1 cm.

Fig. 7. Computed shear stress and excess pore pressure at the shearband mid-plane of the Jiufengershan slide as a function of time, in the caseof a friction-softening soil, with shearband thickness d = 1 cm.



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mal pressurization at least in the most catastrophic cases, asshown by previous calculations (see subsection titled “Choiceof parameters”, Vardoulakis 2002; Cecinato et al. 2011).

Choice of parametersAmong all the model parameters listed in the subsection

titled “Main features of the slide”, the following are chosen

for the parametric study: the slide thickness H and the slopeinclination b, which are basic geometrical quantities enteringclassical stability analyses, along with the shearband thick-ness d, introduced by the thermomechanical model. Of thegeotechnical properties of the soil we include k, l, and G,whose range is well established (see following subsection), andsoil permeability kw. The effects of material friction-softening

Fig. 10. Temperature isochrones for the Jiufengershan slide in the case of a thinner shearband (d = 1 mm instead of 1 cm).

Fig. 9. Computed velocity and displacement of the Jiufengershan slide, plotted against time for the first 20 s of catastrophic collapse, in thecase of a friction-softening soil, with shearband thickness d = 1 cm.



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will be taken into account through the critical state, residualstatic, and residual dynamic friction angles fcs, frs, and frd,respectively, as well as the static and dynamic softeningrates a1 and a2, respectively (cf. Appendix A). Finally we

include the material parameter g, to explore the impact ofthe thermoplastic softening mechanism.Model parameters that do not exhibit in nature a high var-

iability, or that are not expected to influence the results with

Fig. 12. Computed shear stress and excess pore pressure at the shearband mid-plane of the Jiufengershan slide as a function of time, in thecase of a thinner shearband (d = 1 mm instead of 1 cm).

Fig. 11. Excess pore pressure isochrones for the Jiufengershan slide in the case of a thinner shearband (d = 1 mm instead of 1 cm).



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their variation, are kept constant in the parametric study. Inparticular, the soil thermal properties bs, km, and Cf are as-signed an average value typical of clays (see subsection titled“Choice of parameters”), the Poisson’s ratio v is set equal to anaverage value of 0.3, and the rate of thermal friction-softeningeg is set to zero, due to the lack of information on this phe-nomenon and to its ascertained secondary importance whencompared with static and dynamic material friction-softening(Cecinato et al. 2011). The reference temperature qref is setto 20 °C. The compressibility of water cw, the unit weightof water gw, and the unit weight of the overburden gs, areassigned the same values as those listed in the subsectiontitled “Main features of the slide”, which can be consideredrepresentative of average conditions.

Choice of parameter rangeAfter selecting the variables to be examined in the para-

metric analysis, realistic ranges for them must be established.We consider 5 ≤ H ≤ 250 m, with 5 m being an arbitrary butreasonable lower-bound value and 250 m representing themaximum depth at which a slip plane has been detected indeep-seated slides (Petley and Allison 1997). The rangechosen for the slope inclination is 15° ≤ b ≤ 35° (cf. Ceci-nato 2009, 2011), while for the shearband thickness 0.3 ≤d ≤ 3 mm based on the observations by Vardoulakis (2002)that this value should be a few hundreds of micrometres.Based on the measured properties of typical clay soils (cf.Schofield and Wroth 1968; Wood et al. 1992), ranges 3 ×10–2 ≤ k ≤ 6 × 10–2, 9 × 10–2 ≤ l ≤ 2.6 × 10–1, and 2.8 ≤G ≤ 3.8 can be chosen. The ranges of characteristic frictionangles may be determined on the basis of available datafrom shear tests on clays (cf. Skempton 1985): 20° ≤ fcs ≤32°, 10° ≤ frs ≤ 20° and 4° ≤ frd ≤ 10°. Rates of friction-

softening, on the other hand, have very rarely been reportedin the literature; hence, we will select for both a1 and a2 abroad range, representing all possible scenarios spanningfrom the extremely slow to the very sudden softening case:10–5 ≤ a1 ≤ 103, 10–5 ≤ a2 ≤ 103. From the few availabledata on the friction-softening behaviour of clays (Skempton1985; Lehane and Jardine 1992; Tika and Hutchinson 1999)it may be deduced that a reasonable mid-range value for botha1 and a2 is 0.1, as proposed by Vardoulakis (2002) for theVajont clay. Permeability is assumed to vary as 10–13 ≤ kw ≤10–6 m/s, the upper-bound value representing fissured clays(cf. Powrie 1997) and the lower-bound one representing auniform clay whose permeability has decreased due to pro-longed shearing and consequent alignment of the platy par-ticles parallel to the direction of motion (Vardoulakis 2000).The range chosen for the parameter g of the thermoplasticmodel is 10–3 ≤ g ≤ 10–1, in agreement with the range ofexperimentally observed values (Laloui et al. 2008) whilstensuring the calculation of realistic values for the pressuriza-tion coefficient (cf. Cecinato et al. 2011).

Parametric analysis setupThe aim of the parametric analysis is to run one simulation

for each possible combination of the selected parameters, andanalyse the results to determine which factors are most influ-ential in causing large slide velocities. The set of values (lev-els) that each parameter can assume must be defined. Threelevels for each parameter are selected, namely the upperbound, the lower bound, and a mid-range value. This choiceis justified by the likelihood that the parameters investigatedwill have a more quantifiable effect in the results when theyare set to an extreme value, the mid-range setting being use-ful to evaluate any nonlinearity that may arise over each pa-

Fig. 13. Computed velocity of the Jiufengershan slide in the case of a thinner shearband (d = 1 mm instead of 1 cm).



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rameter’s range. The 13 parameters discussed in the subsec-tion titled “Choice of parameter range” are summarized inTable 3, along with the three selected levels denoted as“min”, “med”, “max”.The parametric study was set up using the concepts of “ex-

perimental design,” a branch of engineering statistics (e.g.,see NIST/SEMATECH 2003) that deals with deliberatelychanging one or more variables (the selected parameters) ina process (the landslide dynamic simulation), to observe theeffect that the changes have on a response variable (the calcu-lated velocity 10 s after slide initiation). Among the availabletypes of experimental design, the one that was found to bestsuit the problem at hand due to its robustness, flexibility, andsimplicity, is the Taguchi method (e.g., Taguchi et al. 1989,Peace 1993). With the current settings of 13 parameters andthree levels (Table 3), a Taguchi analysis needs only 27 sim-ulations (experiments) to be completed, followed by some ba-sic statistical analysis of the results. By contrast, with the“full factorial” method (i.e., running a simulation for eachone of the possible combinations of parameters) the numberof simulations needed would be 313 = 1 594 323.A fundamental step in Taguchi analysis is the definition of

a suitable “orthogonal array,” i.e., a two-dimensional matrixdefining the variable settings for each of the experimentsneeded. Each row of the matrix contains the list of settingsfor all parameters in one experiment. Each column corre-sponds to one of the variables and contains all the valuesthat this variable will be assigned during the experiments.The essential property of the orthogonal array is “statisticalindependence”: not only within each column an equal num-ber of occurrences for each level is present, but also the col-umns are mutually orthogonal, i.e., for each level within onecolumn, each level within any other column will occur anequal number of times as well. A given parameter has astrong impact on the output variable if the results associatedwith one of its levels are very different from the results asso-ciated with another one of its levels. Because, due to ortho-gonality, the levels of all other parameters occur an equalnumber of times for each level of this given parameter, theireffect will be cancelled out in the computation of the givenparameter’s effect. The estimation of the effect of any oneparticular parameter will then tend to be accurate and repro-ducible (Peace 1993).The Taguchi method requires that any interactions between

factors be accounted for, where these interactions are definedas the situations where two or more factors acting togetherhave a different effect on the output variable than the super-posed effects of each factor acting individually. To avoid thiscomplication, the parameters and the relative levels for theanalysis at hand were chosen (see subsection titled “Choiceof parameters”) with the aim of avoiding interactions. For ex-ample, the ranges of the three friction angles fcs, frs, andfrd, were chosen contiguous, but not overlapping. Moreover,the lower-bound level of the friction-softening rates a1 and a2was chosen very small, but not zero, which would otherwiserule out the effect of the residual friction angles, thus givingrise to an unnecessary interaction.For the above described 13-parameter, three-level Taguchi

analysis, the conventional orthogonal array “L27(313)” is read-ily available in the literature, and can be filled in with thefactors’ settings of Table 3 to finalize the parametric study

design. The resulting array is shown in Table 4, where a col-umn has been added at the extreme right to specify the out-put of the simulations for each row, i.e., the calculated slidevelocities after 10 s from triggering. These rather diverse ve-locity values constitute the “raw data” of the Taguchi para-metric study, to which some statistical post-processing needsto be applied to extract meaningful results. This is done inthe next section.

Parametric analysis results and discussionTo determine the combination of factors affecting the tar-

get variable the most, the velocity output values of Table 4were interpreted with a level average analysis (Peace 1993),consisting of (i) calculating the average simulation result foreach level of each factor, (ii) quantifying the effect of eachfactor by taking the absolute difference between the highestand lowest average results, and (iii) identifying the strong ef-fects, by ranking the factors from the largest to the smallestabsolute difference. Results are summarized in the responsetable (Table 5).The top five factors can be reasonably assumed as those

having a significant influence in the slide velocity, namely(i) the static friction-softening rate a1, (ii) the slope inclina-tion b, (iii) the soil permeability kw, (iv) the dynamic residualfriction angle frd, and (v) the slide thickness H. This choicewas validated by performing a reliability check (Peace 1993),consisting of calculating an estimate of the predicted re-sponse and comparing it with a confirmation run (Table 6)based on the above-selected levels of the dominant parame-ters (Cecinato 2009, 2011).The worst-case scenario for a planar slide is represented by

the parameter combination of Table 6: a potentially unstableslope is bound to be most catastrophic if the soil’s static soft-ening rate, the inclination, and the thickness of the slope arevery large, and the soil’s permeability and dynamic residualfriction angle are very small. Of these five properties, a1, b,and frd have not been introduced by thermomechanical con-siderations, thus constituting important factors in standardlandslide analyses as well. The strong influence of a1 andfrd is explained by observing that while thermal pressuriza-tion needs a certain time to cause significant effective stressreduction, material friction-softening fully develops withincentimetres of displacement after the initiation of movement(cf. subsection titled “Numerical results and discussion” andVardoulakis 2002). The slope inclination is understandablycrucial in the landslide dynamics as it determines the magni-tude of the driving force. On the other hand, parameters kwand H deserve more attention, as they have been introducedby the thermomechanical model and are not normally consid-ered in the analysis of infinite uniform slopes. kw is the mostimportant one of the two and it affects pore pressure diffu-sion: a low soil permeability implies poor dissipation of theexcess pore pressure within the shearband, thus promoting asustained reduction of shear resistance. Secondly, parameterH determines the level of stress, thus affecting the dissipationterm D (see subsection titled “Heat equation”): the larger His, the higher the effective stress and therefore the heat pro-duction, bringing about a higher pressurization rate thatcauses a quicker reduction of shear resistance.The above observations may be useful as guidance for

field investigations on potentially unstable large slopes: by



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measuring or estimating the aforementioned five key proper-ties, it may be possible to estimate whether or not the slopeis likely to evolve catastrophically. The slope’s inclinationand the depth of a potential slip plane may be easier to de-tect, while for a1 and frd it is necessary to collect samplesand run laboratory tests, more specifically dynamic ringshear tests such as those performed by Tika and Hutchinson(1999). Although in situ measurement of the permeability kwis possible, the presence of any fractures would lead to anoverestimation of its value and in turn to underestimation ofthermal pressurization. Moreover, the permeability of mostclays is likely to decrease as the soil approaches residualstate, due to the alignment of the platy particles parallel tothe direction of motion. Thus, to obtain more sensible infor-mation it might be appropriate to run a laboratory permeabil-ity test on a sample that has previously undergone prolongedshearing.

Significance of thermomechanical effectsThe analysis presented in the previous section involved 13

parameters that can be grouped into “thermomechanical” and“standard mechanical” parameters, depending on whether ornot they are relevant to a thermomechanical analysis only, asopposed to a standard stability analysis. Some of the thermo-mechanical parameters, namely the shearband thickness d andthe thermal softening parameter g, have been left out of thelist of key factors, as the level average analysis showed thattheir influence on model predictions is weak. However, incases where the standard mechanical parameters assume val-ues that minimize the velocity, such as moderate or absentfriction-softening and moderate slope angle, the thermome-chanical factors may yet have an important role in the poten-tial catastrophic evolution of a slide. To corroborate theobservations presented in the subsection titled “Parametricanalysis results and discussion”, it is useful to investigate thesignificance of the thermomechanical parameters in particu-lar. This procedure also makes it possible to assess whetherthese parameters can be decisive in making catastrophic aslide that a standard analysis would predict to be noncata-strophic. The analysis can be performed by means of a stand-ard four-parameter, three-level orthogonal array, where thethermomechanical factors kw, H, d, and g are varied within

the relevant ranges while the remaining nine factors of Ta-ble 3 are kept constant at mid-level values. To simulate aconservative scenario in terms of loss of resistance to move-ment, friction-softening is ruled out by setting a1 and a2 tozero. With these settings the role of thermomechanical phe-nomena in the catastrophic development of a slide can be ex-plored in isolation.Given the reduced number of experiments needed, longer

simulations could be run, hence the velocity reached by theslide after 10 m of displacement (cf. section titled “Parame-ters governing catastrophic collapse”) was here considered asoutput. The relevant orthogonal array is reported in Table 7.Next, a level average analysis was carried out, summarized

in Table 8, whose outcome confirms the results obtainedfrom the 13-parameter analysis. The resulting order of impor-tance (ranking) of the thermomechanical factors is (1) perme-ability, (2) slide thickness, (3) shearband thickness, and (4)thermal softening parameter. In fact, the thermomechanicalparameters alone can make the difference between cata-strophic and noncatastrophic evolution of a slide: simulations7, 8, and 9 in Table 7, in which permeability is high thus rul-ing out thermal pressurization, yield values of velocity after10 m that are below the threshold of 0.05 m/s defining “veryrapid” slides (see section titled “Parameters governing cata-strophic collapse”). In contrast, simulations 1–6 of Table 7can be regarded as cases of “thermomechanical collapse,” i.e.,cases in which the catastrophic evolution of the slide, whenthe velocity after 10 m exceeds the threshold considered, isbrought about by thermomechanical phenomena.It is worth observing that, due to the statistical nature of

the results, only about half of the parameters in the rankingcan be considered to have a significant effect (Peace 1993).By examining the results of the four-parameter analysis ofthis section in light of this criterion, we have confirmationthat the two properties that should be determined to assessthe danger of thermomechanical collapse are the permeabilityof the soil and the thickness of the slide. Both these have aclear physical meaning and are the easiest to quantify amongall thermomechanical parameters. The measurement of Himplies the detection of an existing rupture surface or a rea-sonable assumption, based on local geology and in situ con-ditions, of where a rupture surface would be expected to

Table 3. Parameters selected for the parametric study and their levels.

Level

Parameter Min Med MaxSlope inclination, b (°) 15 25 35Permeability, kw (m/s) 10–13 10–9 10–6

Slide thicknes, H (m) 5 130 250Slip zone thickness, d (mm) 0.3 1 3Thermal softening parameter, g 10–3 10–2 10–1

Critical state friction angle, fcs (°) 20 25 32Static residual friction angle, frs (°) 10 15 20Dynamic residual friction angle, frd (°) 4 8 10Static softening parameter, a1 10–5 10–1 103

Dynamic softening parameter, a2 10–5 10–1 103

Specific volume intercept, G 2.8 3.2 3.8Slope of k-line, k 3 × 10–2 4.5 × 10–2 6 × 10–2

Slope of l-line, l 9 × 10–2 1.7 × 10–1 2.6 × 10–1



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Table 4. Orthogonal array for the 13-parameter Taguchi analysis.

Ex-peri-mentNo. b kw H d g fcs frs frd a1 a2 G k l

Results: velocityafter 10 s (m/s)

1 15 1.00E–13 5 3.00E–04 1.00E–03 20 10 4 1.00E–05 1.00E–05 2.8 3.00E–02 9.00E–02 1.522 15 1.00E–13 5 3.00E–04 1.00E–02 25 15 8 1.00E–01 1.00E–01 3.2 4.50E–02 1.70E–01 17.943 15 1.00E–13 5 3.00E–04 1.00E–01 32 20 10 1.00E+03 1.00E+03 3.8 6.00E–02 2.60E–01 18.684 15 1.00E–09 130 1.00E–03 1.00E–03 20 10 8 1.00E–01 1.00E–01 3.8 6.00E–02 2.60E–01 17.245 15 1.00E–09 130 1.00E–03 1.00E–02 25 15 10 1.00E+03 1.00E+03 2.8 3.00E–02 9.00E–02 18.556 15 1.00E–09 130 1.00E–03 1.00E–01 32 20 4 1.00E–05 1.00E–05 3.2 4.50E–02 1.70E–01 2.327 15 1.00E–06 250 3.00E–03 1.00E–03 20 10 10 1.00E+03 1.00E+03 3.2 4.50E–02 1.70E–01 13.458 15 1.00E–06 250 3.00E–03 1.00E–02 25 15 4 1.00E–05 1.00E–05 3.8 6.00E–02 2.60E–01 0.859 15 1.00E–06 250 3.00E–03 1.00E–01 32 20 8 1.00E–01 1.00E–01 2.8 3.00E–02 9.00E–02 18.6910 25 1.00E–13 130 3.00E–03 1.00E–03 25 20 4 1.00E–01 1.00E+03 2.8 4.50E–02 2.60E–01 29.2511 25 1.00E–13 130 3.00E–03 1.00E–02 32 10 8 1.00E+03 1.00E–05 3.2 6.00E–02 9.00E–02 33.4512 25 1.00E–13 130 3.00E–03 1.00E–01 20 15 10 1.00E–05 1.00E–01 3.8 3.00E–02 1.70E–01 13.7513 25 1.00E–09 250 3.00E–04 1.00E–03 25 20 8 1.00E+03 1.00E–05 3.8 3.00E–02 1.70E–01 20.0214 25 1.00E–09 250 3.00E–04 1.00E–02 32 10 10 1.00E–05 1.00E–01 2.8 4.50E–02 2.60E–01 7.815 25 1.00E–09 250 3.00E–04 1.00E–01 20 15 4 1.00E–01 1.00E+03 3.2 6.00E–02 9.00E–02 33.3616 25 1.00E–06 5 1.00E–03 1.00E–03 25 20 10 1.00E–05 1.00E–01 3.2 6.00E–02 9.00E–02 4.00E–0517 25 1.00E–06 5 1.00E–03 1.00E–02 32 10 4 1.00E–01 1.00E+03 3.8 3.00E–02 1.70E–01 35.8518 25 1.00E–06 5 1.00E–03 1.00E–01 20 15 8 1.00E+03 1.00E–05 2.8 4.50E–02 2.60E–01 12.1519 35 1.00E–13 250 1.00E–03 1.00E–03 32 15 4 1.00E+03 1.00E–01 2.8 6.00E–02 1.70E–01 53.2520 35 1.00E–13 250 1.00E–03 1.00E–02 20 20 8 1.00E–05 1.00E+03 3.2 3.00E–02 2.60E–01 33.8921 35 1.00E–13 250 1.00E–03 1.00E–01 25 10 10 1.00E–01 1.00E–05 3.8 4.50E–02 9.00E–02 45.422 35 1.00E–09 5 3.00E–03 1.00E–03 32 15 8 1.00E–05 1.00E+03 3.8 4.50E–02 9.00E–02 1.1123 35 1.00E–09 5 3.00E–03 1.00E–02 20 20 10 1.00E–01 1.00E–05 2.8 6.00E–02 1.70E–01 0.6924 35 1.00E–09 5 3.00E–03 1.00E–01 25 10 4 1.00E+03 1.00E–01 3.2 3.00E–02 2.60E–01 48.3825 35 1.00E–06 130 3.00E–04 1.00E–03 32 15 10 1.00E–01 1.00E–05 3.2 3.00E–02 2.60E–01 34.5326 35 1.00E–06 130 3.00E–04 1.00E–02 20 20 4 1.00E+03 1.00E–01 3.8 4.50E–02 9.00E–02 45.5127 35 1.00E–06 130 3.00E–04 1.00E–01 25 10 8 1.00E–05 1.00E+03 2.8 6.00E–02 1.70E–01 2.58

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develop. The permeability kw can be estimated by specificpermeability tests. On the other hand, the shearband thick-ness has hardly ever been directly measured (e.g., see Mor-genstern and Tchalenko 1967; Vardoulakis 2002) andparameter g would require nonstandard thermally controlledtriaxial tests (Laloui and Cekerevac 2003). It may be con-cluded that, to assess whether a potentially unstable slope islikely to exhibit thermomechanical collapse, the depth of theslip plane and the permeability of the soil therein should beestimated or measured.It may be estimated, as guidance, that if the permeability

falls in the (lower) range 10–9 ≤ kw ≤ 10–13 m/s and thedepth in the (higher) range 130 ≤ H ≤ 250 m, the likelihoodof thermomechanical collapse increases; thus, the slide couldassume unexpectedly high velocities, despite possibly retain-ing its coherence of mass, and pose a higher threat than atraditional stability analysis would indicate.It should be finally remarked that while the thermome-

chanical model presented here is useful for estimating the or-der of magnitude of velocity that a catastrophically collapsingslide can reach after a certain displacement, it cannot be em-ployed to capture the timescale of the creeping motion thatsometimes precedes catastrophic collapse in large-scale,deep-seated landslides (e.g., see Veveakis et al. 2007, 2010).

ConclusionsIn this work, a new model for the final collapse of planar

landslides has been proposed, taking into account a pressur-ization phase due to frictional heating. It is based on themodel presented by Vardoulakis (2002) and a more generaland more realistic constitutive law for the soil. The governingequations of the model were integrated numerically and usedto analyse the Jiufengershan landslide, demonstrating thatrealistic predictions for the velocity of the slide can be ob-tained.A systematic investigation of the development of cata-

strophic failure in uniform slopes was then carried out. Itwas found that the most influential parameters in promotingcatastrophic collapse are (i) the static friction-softening ratea1, (ii) the slope inclination b, (iii) the soil permeability kw,(iv) the dynamic residual friction angle frd, and (v) the over-burden thickness H. The worst-case scenario is when a1, b,and H are very large and kw and frd are very low. Of theabove, the “thermomechanical parameters” kw and H are notnormally considered in standard stability analyses of uniformslopes. A second parametric study demonstrated that thermo-mechanical parameters alone can make the difference be-tween a relatively noncatastrophic event and a catastrophicone. Hence, further insight into the design of landslide risk-mitigation measures is gained if, in addition to the standardsite investigations, the permeability of the soil is measuredand the depth of an existing or expected failure surface ismeasured or estimated, respectively.

AcknowledgementsThe authors acknowledge the support of the UK’s Engi-

neering and Physical Sciences Research Council (EPSRC),grant number EP/C520556/1. Dr. Emmanuil Veveakis andthe late Professor Ioannis Vardoulakis are also gratefully ac-knowledged for fruitful discussions.T

able

5.Responsetableof

thelevelaverageanalysisforthe13-param

eter

Taguchianalysis.

Level

bk w

Hd

gfcs

frs

frd

a 1a 2

Gk

l

Min

12.14

27.46

15.15

20.22

18.93

19.06

21.53

27.81

7.09

16.77

16.05

25.02

21.95

Med

20.63

16.61

21.91

24.29

21.61

20.33

20.61

17.45

25.88

24.73

22.83

19.44

17.76

Max

29.48

18.18

25.19

17.74

21.70

22.85

18.78

16.98

29.27

20.75

22.05

17.79

22.53

Effectof

parameter

(Delta)

17.34

10.85

10.04

6.56

2.77

3.79

2.74

10.83

22.18

7.96

6.77

7.23

4.77

Ran

king

23

59

1211

134

16

87

10

Tab

le6.

Parameter

settingsfortheconfirmationrunof

the13-param

eter

Taguchianalysis.

Experim

ent

bmax

k w,m

inH

max

d med

gmed

fcs,m

edfrs,m

edfrd,m

ina 1

,max

a 2,m

edGmed

kmed

lmed

Result:velocity

vafter10

s(m

/s)

Con

firm

ation

run

351.00E–13

250

1.00E–003

1.00E–002

2515

41.00E+03

0.1

3.2

4.50E–0

21.70E–01

51.2



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Table 7. Orthogonal array for the 4-parameter Taguchi analysis.

ExperimentNo. kw H d G

Velocity at10 m (m/s)

1 1.00E–013 5 3.00E–004 1.00E–003 1.462 1.00E–013 130 1.00E–003 1.00E–002 6.023 1.00E–013 250 3.00E–003 1.00E–001 5.24 1.00E–009 5 1.00E–003 1.00E–001 0.825 1.00E–009 130 3.00E–003 1.00E–003 3.86 1.00E–009 250 3.00E–004 1.00E–002 1.977 1.00E–006 5 3.00E–003 1.00E–002 0.038 1.00E–006 130 3.00E–004 1.00E–001 1.62E–039 1.00E–006 250 1.00E–003 1.00E–003 1.23E–03

Table 8. Response table of the level average analysis for the 4-parameter Taguchi analysis.

Level kw H d g

Min 4.227 0.770 1.144 1.754Med 2.197 3.274 2.280 2.673Max 0.011 2.390 3.010 2.007Effect of parameter(Delta)

4.216 2.504 1.866 0.920

Ranking 1 2 3 4



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Appendix AIn critical state soil mechanics the parameter M is constant

and depends on the soil’s friction angle at critical state. How-ever, to account for the reduction of the friction angle ofclays when they reach the so-called residual state, the hyper-bolic strain- and strain rate–softening law proposed by Var-doulakis (2002) is adopted. Furthermore, we allow forpossible thermal friction-softening behaviour as described inthe subsection titled “Thermoplastic behaviour of soil”.Therefore, in the general case the critical state parameter M,which can be related to the friction angle at critical state f0

cs,is taken to depend on strain, strain rate, and temperature asper Cecinato et al. (2011)

½A1� Mðg; _g ; qÞ ¼ bMðg; _gÞ � egðq � qrefÞwhere the material friction-softening critical state parameterbM is expressed as (Cecinato 2009, 2011)

½A2� bM ¼ffiffiffi3

psin½arctanðbmÞ�

In the above, the friction coefficient bmðg; _gÞ follows thestatic and dynamic friction-softening law of Vardoulakis(2002)

½A3� bm ¼ mr þ ðmp � mrÞ1

1þ a1ðxd=dÞwhere

½A4� mr ¼ mrd þ ðmrs � mrdÞ1

1þ a2ðvd=dÞ



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mp is the initial value of friction coefficient, xd is the slidedisplacement, and d is the shearband thickness. The limitingvalues mrs and mrd are the static and dynamical residual fric-tion coefficients, respectively, while vd is the slide velocity,so that the (thickness-dependent) shear strain is g = xd/d andits rate _g ¼ vd=d. a1 and a2 are numerical factors defininghow quickly the static and dynamic coefficients, respectively,decrease with displacement and velocity.The critical state parameter Mðg; _g; qÞ is featured in the

heat eq. [5] via parameter Fi (Cecinato et al. 2011).

ReferencesCecinato, F. 2009. The role of frictional heating in the development

of catastrophic landslides. Ph.D. thesis, School of Civil Engineer-ing and the Environment, University of Southampton, South-ampton, UK.

Cecinato, F. 2011. Mechanics of catastrophic landslides. LambertAcademic Publishing, Saarbrücken.

Vardoulakis, I. 2002. Dynamic thermo-poro-mechanical analysis ofcatastrophic landslides. Géotechnique, 52(3): 157–171. doi:10.1680/geot.2002.52.3.157.



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influence of thermomechanics in the catastrophic collapse of planar landslides

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