2013-02 Soil Stability and Flow Slides in Unsaturated Shallow Slopes - Can Saturation Events Trigger...

8/10/2019 2013-02 Soil Stability and Flow Slides in Unsaturated Shallow Slopes - Can Saturation Events Trigger Liquefaction

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Buscarnera, G. & di Prisco, C. (2013). Geotechnique 63, No. 10, 801817 [http://dx.doi.org/10.1680/geot.11.P.097]

801

Soil stability and flow slides in unsaturated shallow slopes: can saturationevents trigger liquefaction processes?

G . B U S C A R N E R A a n d C . D I P R I S C O

This paper illustrates an application of the theory of material stability to the analysis of unsaturatedslopes. The main goal is to contribute to the understanding of rainfall-induced flow slides. For thispurpose, a coupled hydromechanical constitutive model is combined with a simplified approach forthe analysis of infinite slopes. Simple shear-test simulations are used to evaluate triggering perturba-tions and investigate the role of both initial suction and stress anisotropy in the activation of slopefailures. The numerical simulations clearly show that different mechanisms of activation can beoriginated. The onset of instability is detected by introducing appropriate stability indices for distinctmodes of failure: localised shear failure, static liquefaction and wetting-induced collapse. Criticalintervals of slope inclinations are identified, cautioning that the predicted failure mode may changedramatically depending on initial conditions, slope angle and material properties. The numericalsimulations demonstrate that, in particular circumstances, saturation of the pore space can be theunexpected result of a volumetric instability. According to this interpretation, a rainfall-induced flow

slide can originate from a complex chain process consisting of a sudden volume collapse, uncontrolledsaturation of the pores and, eventually, catastrophic liquefaction of the deposit.

KEYWORDS: constitutive relations; landslides; liquefaction; partial saturation; suction; theoretical analysis

INTRODUCTIONIn many parts of the world, geohazards pose serious threatsto territory, economy and human lives. During recent dec-ades, catastrophic events have been exacerbated by unpre-dicted climate changes and uncontrolled human activities(Cascini, 2005). The environment tends to be exposed tophenomena never experienced before, which now represent

systematic causes of massive economic loss. Within thiscontext, rapid landslides induced by rainfall represent acritical issue. These catastrophic events are characterised byrapid and unexpected activation, and are capable of mobilis-ing huge volumes of material over large areas (Chu et al.,2003;Olivares & Picarelli, 2003;Picarelli et al., 2008).

The compelling need to capture the physical causes ofsuch dramatic landslides requires a deep understanding ofthe phenomena involved, and advanced modelling strategies.This paper focuses on the study of landslides triggered byrainfall events, with the aim of investigating the mechanicsof these processes and modelling their activation. Particularemphasis is given to the study of those landslides in whichthe soil suffers a phase transition from solid to fluid (here

referred to as flow slides). Such transition is usuallyattributed to a liquefaction process (Castro, 1969; Lade,1992), which is schematically illustrated in Fig. 1. Depend-ing on the shearing scenario (either undrained or drained),different failure modes can take place, given that in aliquefiable deposit the shear perturbations leading to lique-faction (liq) are significantly lower than those associatedwith drained failures (sf). The main engineering implica-tion of such a variety of instability modes is the existence of

Manuscript received 29 July 2011; revised manuscript accepted 7December 2012. Published online ahead of print 27 February 2013.Discussion on this paper closes on 1 January 2014, for further detailssee p. ii.

Department of Civil and Environmental Engineering, NorthwesternUniversity, Evanston, USA. Department of Structural Engineering, Politecnico di Milano,Milan, Italy.

Soil

Bedrock

z

Shear perturbation ( )

n0

0

(a)

(b)

sf

liq

Shearstress,

Normal ef fective stress,n

In situ stress

Shear failure locus

Fig. 1. (a) Schematic representation of a shear perturbation

acting over a submerged infinite slope (9n is the in situ normaleffective stress); (b) possible failure modes: difference in externalperturbations needed to activate either drained shear failure(sf) or static liquefaction (liq)


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a multiplicity of safety factors. These considerations inspiredthe development of a wide spectrum of theories aimed atdifferentiating liquefaction from shear failure and evaluatingthe risk of flow slides in subaqueous sandy slopes ( Poulos etal., 1985;Sladen et al., 1985;di Prisco et al., 1995).

In the reminder of the paper this logic will be exported tothe case of sub-aerial slopes, for which a comprehensiveframework of interpretation is not yet available. The purpose

is to provide a consistent geomechanical explanation offailure processes in unsaturated deposits by answering threemajor questions.

(a) What is the amount of suction removal at which a slidecan take place?

(b) How and when can slope failures evolve into a flow-likemass movement?

(c) Are fully saturated conditions necessary to induceliquefaction, or can such collapses be initiated by theprior wetting process?

To address such problems, a novel methodology has beendeveloped, which is based on three cornerstones:

(a) the extension of the concepts of material stability to

unsaturated soils (Buscarnera & Nova, 2011;Buscarnera& di Prisco, 2012)

(b) their application to the simplified scheme of infinite slope(di Prisco et al., 1995; Buscarnera & di Prisco, 2011a,2011b;Buscarnera & Whittle, 2012)

(c) the use of a coupled hydromechanical constitutive modelfor unsaturated soils (Buscarnera & Nova, 2009).

The paper is thus aimed at applying the theory alreadydiscussed inBuscarnera & di Prisco (2011b) by employing asuitable constitutive relationship. The main goal of theinvestigation is to elucidate the mechanical processes in-volved in the triggering of flow slides in partially saturatedsoil slopes.

THEORETICAL BACKGROUNDSecond-order work and controllability for unsaturated soils

A generally accepted approach for identifying unstableconditions in solids is Hills criterion (Hill, 1958), accordingto which a sufficient condition for stability is the positivedefiniteness of the second-order work, d2W. This criterionprovides a physical interpretation for instability, given thatnegative values for d2W can correspond to a spontaneousburst in kinetic energy (Sibille et al., 2007), and can be usedfor studying the initiation of slope instabilities (Lignon etal., 2009). In unsaturated contexts, a critical task is toincorporate the mechanical implications of saturation pro-cesses. In fact, changes in the degree of saturation imply

additional energy contributions (Houlsby, 1997; Gray et al.,2010), and require the adaptation of second-order workmeasures. A strategy for this extension has been recentlysuggested by Buscarnera & di Prisco (2012), who showedthat under unsaturated conditions d2Wbecomes

d2W 12

_ij Sr_uwij 1 Sr _uaij

_ij12n _ua _uw _Sr

12_ij_ij

12_s _Sr

(1)

where ij is the total stress tensor, ij is the strain tensor, ijis Kroneckers delta, _uw and _ua are the pore water and poreair pressure rates respectively, Sr is the degree of saturation,

and n is the porosity. For Sr 1, the above expressionconverges to the usual definition of second-order work forsaturated media (i.e. d2W 1

2_9ij_ij, 9ij ij uwij being

the effective stress tensor). By rearranging equation (1) it is

also possible to identify incremental stress variables forsecond-order work analyses, as for instance

_ij _ij Sr_uwij 1 Sr _uaij

and

_s n _s n _ua _uw

The extended expression for d2W enables instability condi-tions for unsaturated geomaterials to be identified and linkedto the mathematical concept ofcontrollability (Nova, 1994;Imposimato & Nova, 1998; Buscarnera & Nova, 2011;Buscarnera et al., 2011). In order to describe this concept,consider a set of incremental hydromechanical constitutiverelations linking the control variables _ (i.e. the disturbanceapplied to the material) and the response variables _ (i.e.the outcome of the response of the material), as

_ X_ (2)

where X is the control matrix. If the hydromechanicalvariables in equation (2) are selected in accordance withequation (1), the loss of uniqueness and/or existence of theincremental response (i.e. detX 0) corresponds to a van-ishing second-order work (i.e. it violates Hills criterion).

The concept of controllability

(a) provides a further insight into the physical meaning ofequation (1)

(b) defines the failure mode mathematically (through theeigenvectors ofX)

(c) permits an intuitive definition of instability that encom-passes saturated (Imposimato & Nova, 1998) and unsaturated conditions (Buscarnera & Nova, 2011).

As will be expounded later, the most notable feature of thistheory is the ability to cope with latent instabilities, that is,

potential collapses that are contingent on specific boundary/control conditions (Nova, 1994; di Prisco et al., 1995;Buscarnera & Whittle, 2013).

Using second-order work principles in unsaturated infiniteslopes

The concepts of second-order work and controllability canbe used to elucidate the hydromechanical properties that canplay a role in the initiation of uncontrolled deformationprocesses. For this purpose, consider a reference systemassociated with an unsaturated infinite slope of a giveninclination (Fig. 2). By starting from the three-dimensionalstressstrain response of a material point (see the Appendix

for such a representation), it is possible to represent the

Soil

Bedrock

(out-of-plane coordinate)

Fig. 2. Reference system for unsaturated infinite slopes

802 BUSCARNERA AND DI PRISCO


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mechanical response of a point within the deposit as asimple shear deformation mode, having

_

__

_s

8>:

9>=>;

D11 D14 D17D41 D44 D47D71 D74 D77

24

35 __

_Sr

8>:

9>=>; D

_E (3)

The two vectors _ and _E are linked by a coupled constitu-

tive operator (matrix D) and collect the hydromechanicalvariables associated with the incremental energy input on aninfinite slope. In particular, _ is the incremental skeletonstress along the direction normal to the slope, and _ is theshear stress increment along the slope inclination, while _and _ are their work-conjugate kinematic counterparts.The hydraulic variables associated with changes in saturationconditions (i.e. _s and _Sr) are selected on the basis ofequation (1).

The loss of positive definiteness of d2W is governed bythe symmetry properties of D. By decomposing this matrixinto the sum of a symmetric part, Ds, and a skew-symmetricmatrix, Dsk, it can be shown that

d2W 12

_T

_E 12

_ET

Ds_E (4)

given that Hills criterion can be violated for the first timewhen detDs 0 (Imposimato & Nova, 1998). It interestingto observe that, since detDs < det D (Ostrowski & Taussky,1951), possible non-symmetries of D imply that Hills criter-ion can be violated before condition detD 0 is satisfied.As a result, stress-suction control conditions may not be themost critical combination of control parameters underpinningthe collapse of natural slopes, which thus suggests theexistence of unexpected failure modes. For simple shearconditions this concept is exemplified by the skew-sym-metric part, Dsk, which embodies the difference betweenmatrix D (whose singularity reflects suction-controlled fail-ure) and its symmetric part Ds (which reflects possible

violations of Hills criterion)

Dsk

0 D14 D41

2

D17 D712

D41 D142

0 D47 D74

2D71 D17

2

D74 D472

0

2666664

3777775 (5)

Alternative modes of failure are promoted by the differ-ence between terms [D14, D41] (reflecting non-associativityof the mechanical response) or between the pairs [D17, D71]and [D74, D47] (related to hydromechanical coupling). While[D14, D41] depend on the characteristics of the yield surfaceand the plastic potential, the other off-diagonal terms reflect

different behavioural properties: terms D17 and D47 repro-duce the inelastic effects of saturation paths (e.g. wetting-induced compaction), and terms D71 and D74 reproduceinstead the dependence of the retention curve on volumetricand shear strains respectively. At variance with the effect ofnon-associativity on material instabilities, which has beenwidely studied for several decades (Rudnicki & Rice, 1975;Bigoni & Hueckel, 1991; Lade, 1992; Nova, 1994), the roleof hydromechanical coupling still deserves special attention.Similar to the non-associativity of the plastic flow rule,hydraulic off-diagonal contributions must be assessed on thebasis of experimental evidence. In this work, the assump-tions for the hydromechanical contributions are motivated bythe geomechanical characterisation of some unsaturated soils

involved in recent flow slide events (Cascini & Sorbino,2004;Bilotta et al., 2005;Ferrari et al., 2012). These studiessuggest that, while suction effects can induce changes in thepreconsolidation stress of the collapsible deposits (terms D17

and D47), the effect of soil deformation on the retentioncurve is often negligible at shallow depths. It is worth notingthat these observations have implications that are comparableto the use of a non-associated flow rule (i.e. they exacerbatethe potential for instability), and may not apply to all classesof unsaturated geomaterials. For instance, if the water reten-tion curve depends significantly on the void ratio (termD716 0), compressive deformation can promote a shift of

the retention curve towards higher suctions (possibly havingbeneficial effects in terms of stability). At this point it isworth noting that, although consistent advances have beenproduced in describing the effect of volumetric strains onretention capabilities (Romero & Vaunat, 2000; Gallipoli etal., 2003), there is still little guidance for incorporating theeffect of shear strains (term D74). This fact complicatesevaluation of the interplay between retention properties andsoil stability. For these reasons, the effect of deformation onthe retention curve will not be accounted for in the follow-ing developments, thus using a simpler modelling strategy,one that is consistent with the limited geomechanical evi-dence available for collapsible unsaturated soils involved inflow slides.

APPLYING UNSATURATED SOIL MECHANICS TOSTABILITY OF SUB-AERIAL SHALLOW SLOPESStability indices for unsaturated shallow slopes

By following the strategy proposed by di Prisco et al.(1995), it is possible to derive stability indices in analyticalform and use them for the stability analysis of shallowdeposits. The extension of this procedure to unsaturatedslopes has recently been expounded in Buscarnera & diPrisco (2011b), and this paper is a numerical application oftheir analytical results. Hereafter, only some basic aspects ofthe theory are noted; the Appendixprovides a description ofthe mathematical strategy used by the authors to derive thestability indices. Two triggering mechanisms are investi-

gated: (a) a translational slide taking place under constantsuction (in this case permeability is assumed to be infinite);and (b) slope collapse initiated under water-content control(e.g. water-undrained shearing, water inundation, etc.). Thesefailure modes will be referred to as mode A and mode Brespectively.

Shear failure (mode A) can be considered the most usualform of material instability in slopes, and it is often thefailure mechanism included in conventional stability analysesfor unsaturated slopes (Ng & Shi, 1998; Gasmo et al.,2000). This mechanism is originated either by an increase inshear stresses or by a decrease in suction due to waterinfiltration. The former perturbation is conveniently repre-sented by a change in stresses at constant suction, and the

latter is often modelled through a decrease in suction atconstant total stresses. In both cases the control variablescoincide with those collected in the left-hand side of equa-tion (3). By following Buscarnera & di Prisco (2011b), astability index for this mechanism can be defined as

IAU D11D44 D14D41 (6)

where the subscript U stands for unsaturated conditions. Theabove expression has been obtained by excluding singular-ities in the retention curve (i.e. D776 0) and neglecting apossible role of strains in the retention behaviour (i.e.D71 D74 0). Under these assumptions, condition IAU 0coincides with the strain localisation criterion obtained bydiPrisco et al. (1995) for a saturated layer of an infinite slope,

IAS IAU (7)

where the subscript A refers to a shear failure mode, and Sstands for saturated conditions.

SOIL STABILITY AND FLOW SLIDES IN UNSATURATED SHALLOW SLOPES 803


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The second triggering mechanism (mode B) occurs whenthe water content is controlled. This mode is relevant eitherwhen water drainage is prevented by natural layering orwhen water inlets from a surrounding formation can bemodelled as a fluid volume injected into the pores (Buscar-nera & di Prisco, 2011b). In either cases, changes in suctionare no longer imposed, but are obtained as an outcome ofthe deformation of the porous medium. From a mathematical

viewpoint this analysis is similar to passing from stress-controlled to strain-controlled conditions, and influences theonset of bifurcation. The stability index associated withfailure of the slope under constant water content has anexpression that is very similar to shear failure,

IBU D11D44 D14D

41 (8)

where the modified terms D11 and D41 reflect the role of

hydromechanical coupling in the considered failure mechan-isms (i.e. they also depend on degree of saturation, porosityand coupling terms D77, D17 and D47). The derivations ofD11 and D

41, as well as their analytical expressions, are

given in the Appendix. Buscarnera & di Prisco (2011b)showed that when S

r 0 (i.e. when the role of solidfluid

coupling vanishes), IBU coincides with IAU, and the twoindices provide the same bifurcation mechanism. By con-trast, when Sr 1, the water-undrained deformation mode isnaturally associated with the initiation of static liquefaction.It is possible to expound this conceptual link by deriving thehydromechanical control matrix associated with the controlof total stresses and water content

__

_ew= 1 e

8>>>>>>>>>>>>>>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>;

D11 D12 D13 D14 D15 D16 D17

D21 D22 D23 D24 D25 D26 D27

D31 D32 D33 D34 D35 D36 D37

D41 D42 D43 D44 D45 D46 D47

D51 D52 D53 D54 D55 D56 D57

D61 D62 D63 D64 D65 D66 D67

D71 D72 D73 D74 D75 D76 D77

2666666666666664

3777777777777775

_

_

_

_

_

_

_Sr

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>;

(20)

The kinematic constraints deriving from the assumption of aninfinite slope can be used to simplify the above relations. Plane-strain conditions imply that _ _ _ 0, while the sym-metry along the axis implies _ 0: These kinematic constraintsare representative of a simple shear strain mode, and lead toequation (3).

The stability index for mode A can be obtained by considering anincremental loading path characterised by controlled changes instresses and suction (e.g. constant-suction shearing, constant-stresssuction removal). In this case the control variables coincide withthose collected in the left-hand side of equation (3). The theory oftest controllability therefore identifies the inception of a bifurcation

mode when the constitutive matrix inequation (3)is singular: that is,when

D77 D11D44 D14D41 0 (21)

in which conditions D71 D74 0 have been used.Mode B can be derived by modifying equation (3) to reproduce

water-undrained loading. If the drainage of the water phase isprevented, the evolution of both degree of saturation and suctiondepends on the overall mechanical response of the material. Underconstant water content, the constraint relating volumetric strains andsaturation index is given by

n _Sr Sr_ (22)

By expressing _ as a function of the increment in total normalstress and suction (i.e. _ _ Sr_s), the constitutive equationscan be reformulated as

__

D11 D14D41 D44

_

_

(23)

where

D11 D11Sr

n D17

Sr

nD77

(24)

D41 D41Sr

nD47 (25)

in which the hydraulic variables are eliminated by using theconstraint in equation (22). Equations (23) are complemented byn_s (Sr=n)D77_, which is needed for tracking the changes insuction during shearing. It is interesting to note that the stabilityindex associated with failure of the slope under constant water

content coincides with the determinant of the control matrix inequation (9).

NOTATIONaf shape parameter of the yield surfaceag shape paremeter of the plastic potentialaR shape parameter of the retention curveBp plastic compressibility parameterCh hydraulic parameter related to retention propertiesD hydromechanical constitutive matrix

Di j principal minors of the constitutive stiffness matrix_E hydromechanical strain vectore void ratio

ew water ratiofR soil water retention curve

G0 elastic shear modulusIAS stability index for shear failure (saturated soil)IAU stability index for shear failure (unsaturated soil)IBS stability index for liquefaction (saturated soil)

Saturation instability ( 1)activates liquefaction

Sr

1

0

|

|/

s

s0

Staticliquefaction

* 0IBS

2

(a)

Latent instability* 0IBU

Saturation instability ( 1)Sr

1

0

|

|/

s

s0

* 0IBS

2a

(b)

Latent instability* 0IBU

2b

Metastability Liquefaction

Zone ofpossible

metastableevolution

Fig. 19. Schematic representation of instability charts. (a) Stabi-lity chart for IBS 0 is entirely located below condition for

IBU 0; static liquefaction can be the ultimate consequence of a

wetting instability. (b) Stability chart for IBU 0 can be above thecondition forIBS 0 (interval 2a); evolution of wetting instabilitycan be characterised by condition of metastability (shaded areaindicates zone of possible metastable evolution)



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IBU stability index for liquefaction (unsaturated soil)Iij normalised stability indices

k elastic compressibilityMcf shape parameter of the yield functionMcg shape parameter of the plastic potentialMef shape parameter of the yield functionMeg shape parameter of the plastic potential

mf shape parameter of the yield functionmg shape parameter of the plastic potential

mR shape parameter of the retention curven porosity

nR shape parameter of the retention curvepr reference pressure for nonlinear elasticity

_pnet net stress incrementp 0s internal variable for isotropic hardening

qw rainfall infiltrationrsw hydraulic hardening parameter

Sr degree of saturationSrF degree of saturation at failure

s suction_s rate of smeared suctions perturbation of suction

ssf triggering suction perturbation for shear failureswc triggering suction perturbation for wetting collapses normalised triggering suction perturbation

ua pore air pressureuw pore water pressure

d2W second-order work per unit volumeX constitutive control matrixz vertical depth slope anglez vertical overburdenij Kroneckers deltaij total strain tensorpv volumetric plastic strainps deviatoric plastic strainseij elastic strain tensor

pij plastic strain tensor axis of the reference system (tangential to the slope) axis of the reference system (normal to the slope)s dilatancy hardening parameter

_ hydromechanical stress vectorij total stress tensor9ij effective stress tensor0ij skeleton stress tensor

_ij incremental skeleton stress9n in situ normal effective stress shear perturbation

liq triggering shear perturbation for liquefactionsf triggering shear perturbation for shear failure

vector of control variablesh hydraulic-softening parameter vector of response variables

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