Alonso 2003

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Influenceofrainfallonthedeformationandstabilityofaslopeinoverconsolidatedclays:acasestudyARTICLEinHYDROGEOLOGYJOURNALJANUARY2003ImpactFactor:1.71DOI:10.1007/s10040-002-0245-1Source:OAI

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Hydrogeology Journal (2003) 11:174192 DOI 10.1007/s10040-002-0245-1

Abstract The behaviour of an instrumented unstableslope in a profile of weathered overconsolidated clay hasbeen analysed. Available field investigation data and lab-oratory tests were integrated in a coupled hydromechani-cal model of the slope. Particular attention was given tothe unsaturated soil conditions above the water table andto the influence of the rainfall record. Recorded pore-wa-ter pressures helped to identify the hydrogeological con-ditions of the slope. The coupled model was used tocompute slope deformations and the variation of safetywith time. Actual rainfall records were also integratedinto the analysis. Comparison of measurements and cal-culations illustrate the nature of the slope instability andthe complex relationships between mechanical and hy-draulic factors.

Rsum Une pente instable dans un profil dargile alt-re sur-consolide a t instrumente et son comporte-ment a t analys. Des donnes disponibles obtenueslors dtude sur le terrain et des essais en laboratoire ontt intgrs dans un modle coupl hydromcanique dela pente. Une attention particulire a t porte aux con-ditions du sol non satur au-dessus de la nappe et lin-fluence de la succession de pluies. Les pressionsenregistres de leau dans les pores ont permis didenti-fier les conditions hydrogologiques de la pente. Le mo-dle coupl a t utilis pour calculer les dformationsde la pente et la variation de scurit au cours du temps.Les enregistrement de pluies relles ont t galementintgrs lanalyse. La comparaison des mesures auxcalculs illustre la nature de linstabilit de la pente et les

relations complexes entre les facteurs mcaniques et hy-drauliques.

Resumen Se ha analizado el comportamiento de una la-dera instable que fue instrumentada en un perfil de arci-llas meteorizadas sobreconsolidadas. Se ha integrado losdatos disponibles de investigaciones de campo y ensayosde laboratorio en un modelo hidromecnico acoplado dela ladera, prestando una atencin especial a las condicio-nes del suelo no saturado por encima del nivel fretico ya la influencia de los registros de lluvia. Los registros depresin del agua han ayudado a la identificacin de lascondiciones hidrogeolgicas de la ladera. El modelo aco-plado ha servido para calcular las deformaciones de laladera y el cambio de la seguridad con el tiempo, inte-grando tambin los datos reales de lluvia. La compara-cin entre valores medidos y calculados ilustra la natura-leza de la inestabilidad de la ladera y las complejas rela-ciones que se establecen entre factores mecnicos e hi-drulicos.

Keywords Overconsolidated clays Slope instability Expansion Flow Unsaturated soil Suction Safetyfactor

Introduction

In December 1982 a large flowslide in overconsolidatedclays caused the destruction of three suburbs of the cityof Ancona in eastern Italy. The area, which is located inthe southwest region of the city, has been, in the yearsfollowing the disaster, under close observation as a poten-tial slide area. Soil profiles were established and the pattern of slope movements and water pressure fluctua-tions were established (Franchini and Callari 1988; Baldelli et al. 1992). In 1991, a project financed by theEuropean Programme on Climatology and Natural Hazards (EPOCH) was awarded to several European in-stitutions with the purpose of analysing the stability ofslopes in overconsolidated clays in the context of Medi-terranean climates. A slope close to the sliding area,which affected Ancona in 1982, herein referred to as theVilla Blasi slope, was selected as an experimental site toperform a number of interrelated studies. Ten boreholeswere drilled along the slope, samples were taken for labo-

Received: 13 September 2002 / Accepted: 29 November 2002Published online: 17 January 2003

Springer-Verlag 2003

E. E. Alonso () A. GensDepartment of Geotechnical Engineering and Geosciences,Universidad Politcnica de Catalunya,C/ Jordi Girona 13, 08034 Barcelona, Spaine-mail: [email protected].: +34-93-4016866, Fax: +34-93-4017251C. H. DelahayeUniversidad de San Juan, Argentina

Influence of rainfall on the deformation and stability of a slope in overconsolidated clays: a case studyE. E. Alonso A. Gens C. H. Delahaye

175


ratory testing, and inclinometers and electric piezometersprovided field data in the period October 1992October1993. Rainfall in the area was also recorded. All these ac-tivities were described in a project final report (Baldelli etal. 1994). It was the responsibility of the authors of thispaper to identify the characteristics of the unsaturated up-per levels of the slope, perform controlled suction tests,and construct a model of the response of the slope to rain-fall. Additional analyses performed after the EPOCH pro-ject was formally finalised have led to an improved un-derstanding of the mechanisms of slope motion and its re-lationship with rainfall and the hydraulic characteristicsof the clay strata. This paper provides an account of allthis work. Geological and geotechnical field data, as wellas hydraulic and mechanical properties measured in sam-ples have been integrated into a coupled hydromechanicalmodel of the slope. The computed evolution of the slope,subjected to the rainfall action, was compared with fieldmeasurements. The question of safety has also been ad-dressed, and the evolution of the safety factor and its rela-tionship with the rainfall record and the hydraulic proper-ties of the soil was analysed. This work, which extendedover a number of years, has provided a better insight intothe role of suction, environmental actions and soil hetero-geneity on slope stability.

This case examines the stability of a slope in overcon-solidated clays. For such slopes, a number of issues areoften raised: the appropriate soil strength in safety esti-mations, the related question of progressive failure, andthe effect of clay permeability and pore pressure dissipa-tion. Early classical work concerning the delayed failureof slopes in overconsolidated clay was reported bySkempton (1964) and Bjerrum (1967). Later, Vaughanand Walbancke (1973) realised that pore-water dissipa-tion could extend over decades due to the low in-situpermeability of some natural formations. This explaineddelayed failures associated with cuts and excavations.The persistence of transient water changes is also ob-served when negative pressures are induced in the slope(Bromhead 2000).

Undisturbed overconsolidated clays are brittle materi-als with marked peak strengths. Progressive failuremechanisms, well documented in Cooper (1996), lead toa reduction of the available in-situ strength. The impor-tant practical problem of selecting the design strength islargely unresolved and it has been addressed by severalauthors (Chandler 1984; Cancelli and Chinaplia 1993;DElia et al. 1998; Leroueil 2001). A review of currentconstitutive models to describe the mechanical behaviourof overconsolidated clays and soft clayey rocks is givenin Kavvadas (2000). Advances in modelling progressivefailure are reported in Potts et al. (1997).

In reactivated slides the relevant in-situ strength isclose to residual values. A discussion of factors affectingresidual strength and the role of discontinuities (beddingplanes, in particular) is given in Alonso (2000). The re-duction of friction induced by leaching and other phy-sico-chemical actions has been raised in this referenceand in Frydman et al. (1996) and DiMaio (1996).

A significant feature of the analysis presented is theuse of a coupled hydromechanical model which may re-late slope displacements and safety assessments with wa-ter-pressure evolution, both for positive and negative(suction) values. This is believed to be a common situa-tion in nature.

The purpose of this paper is to analyse the conditionsleading to the instability of the Villa Blasi slope. Atten-tion will be focused on rainfall and on the role played bythe heterogeneous distribution of soil permeability andstrength. These factors are believed to control the stabili-ty of the slope and its evolution in time.

Geomechanical Characteristics of the Slope

The slope is located in clay sediments of Plio-Pleisto-cene age. The undisturbed, jointed base material is cov-ered by eluvialcolluvial deposits which reach thickness-es of 10 m. A longitudinal profile of the slope is shownin Fig. 1, where the location and depth of the boringsperformed in 1992 are also indicated. Figure 2 shows thedetailed boring record of borehole C. The transition be-tween the upper, weathered brown layers and the greyclay substratum was easily identified. Three layers wereidentified when all the field data were analysed: a Plio-cene substratum (layer ), described as blue Ancona clay(a stiff, blue silty clay with sandy inclusions), an inter-mediate sedimentary layer (layer ), described as brownAncona clay (a stiff, brown silty clay with sandy inclu-sions), and a surface layer (layer ), which is describedas a remoulded brown Ancona clay (see Fig. 1). The sur-face layer is rich in organic matter and it is partly ox-

Fig. 1 Slope profile showing the position of boreholes and thestratigraphic sequence

176


idised. Soil movements take place in the upper brownlayers (, ) but not in the blue substratum.

Soil mineralogy was essentially constant across thedifferent layers. Carbonates (mostly calcite) account for22% of the total mineral content. Quartz and, to a lesserextent, feldspar, oligoclase, plagioclase and mica werealso present. The dominant clay minerals includemontmorillonite, illite, chlorite and dolomite (61, 73, 8and 7% of the clay fraction, on average).

Most of the geotechnical tests were performed onsamples taken from layer (brown Ancona clay), sincethe slope deformations were concentrated in that layer.

Soil in layers and are classified as inorganic claysand silts of high plasticity (CH and MH; wL=5264%;PI=2534%; clay fraction=4055%; a small proportionof sand sizes=18%). Natural water content in layers and was close to the plastic limit and varied in therange 2132%. The specific particle weight was in therange s=27.227.8 kN/m3. High overconsolidation verti-cal stresses (23 MPa for layer , and 34 MPa for lay-er ) were measured in oedometer tests.

Clay strength was investigated by drained and un-drained, isotropically consolidated samples of intact aswell as reconstituted specimens. Figure 3 shows the de-viatoric stresses (Fig. 3a) and recorded volume change(Fig. 3b) measured in triaxial tests conducted on isotrop-ically consolidated, undisturbed samples taken from the horizon (Baldelli et al. 1994). Specimens failed in abrittle mode along a well-defined plane. A significantbrittleness and dilatant behaviour at peak and post-peakconditions was measured. Stiffness for an axial strain of1% increased from 14 to 29 MPa when the confiningstress increased from 50 to 250 kPa (the average estimat-ed confining stress for the layer is around 100 kPa).

Fig. 2 Stratigraphy of borehole C. Sampling and physical charac-teristics

Fig. 3a, b Isotropically consolidated drained triaxial compressiontest on intact sample. Borehole A7, depth 9.50 m

Fig. 4 Strength envelopes for natural and reconstituted samples.Also shown are the strength laws adopted for layers , and .TX Triaxial tests, DS direct shear tests

177


Direct shear tests were also run on intact specimens. Asummary of the strength envelopes is given in Fig. 4. Forthe intact samples, peak and post-peak values are repre-sented. Bounds limiting the scatter of data are plotted.The data plotted in Fig. 4 show that intact samples oflayer had a significant brittleness. For a confiningstress n=300 kPa, an average brittleness index IB=0.40was measured.

In the case of direct shear tests, the strength data atthe end of the test are also identified as residual in thefigure (a friction value close to res=10 is derived fromthese tests). Envelopes are shown to be curved with a ze-ro (true) effective cohesion. The post-peak strength, asmeasured in triaxial tests, comes close to the remouldedvalues.

Suction-controlled Oedometer TestsSuction-controlled experiments had two objectives: (1)to determine the influence of suction changes on volu-metric deformation, and (2) to determine the influence ofsoil suction on permeability. Three samples from layer were subjected to the stress paths shown in Fig. 5(tests 24). They imply sequences of suction-controlled

drying/wetting (and a saturated loading/unloading appli-cation after a suction cycle, in test 2) at a constant verti-cal stress of 0.09 MPa, equal to the overburden verticalstress.

The variation of void ratio as a function of suction forthe three tests is shown in Fig. 6. The closed cycles re-veal a hysteretic behaviour, although very limited irre-versible strains are measured. Deformation is small be-low a suction s=0.11 MPa. Beyond this value, suction-in-duced deformations are higher.

The water volume change of the specimens, for eachstep of suction change, was interpreted through the Rich-ards flow equation (Richards 1931) to derive permeabil-ity values. The derived values of water permeability withsuction for the three specimens are shown in Fig. 7. Per-meability reduces 1.5 orders of magnitude when matricsuction increases from 10 to 500 kPa. No definite hyster-esis effect could be identified. Finally, a water retentioncurve was measured using a filter paper method (see, forinstance, Sibley and Williams 1990 for a description ofthis test). The relationship is shown in Fig. 8. A low airentry value (~2030 kPa) was measured. Moderate suc-tion values (100 kPa) induce a significant desaturation ofthe soil.

Fig. 5 Stress paths in plane (s=papw: matric suction; p=vpa:net vertical stress) for tests 2, 3 and 4

Fig. 6 Measured changes in void ratio as suction cycles are ap-plied

Fig. 7 Measured variation of water permeability with suction

178


Modelling the Villa Blasi Slope

The results of in-situ investigations performed on theVilla Blasi slope (Franchini and Callari 1988; Baldelli etal. 1992, 1994) have confirmed that the deformation pro-cess of the slope is essentially limited to an upper thick-ness of 23 m. The measured deformations are attributedto changes in suction and effective stresses as the waterflow regime in the slope changes due to climatic condi-tions. Hydraulic monitoring led to the identification oftwo different hydraulic regimes within the slope, definedas follows.1. A deep flow regime, which is characterised by a

phreatic level nearly constant in both wet and dry sea-sons. The phreatic surface was detected at depthswhich vary in the range 412 m. A flow regime ap-proximately parallel to the slope surface is consistentwith observations.

2. A surficial flow regime, directly controlled by rain-fall. Positive and negative pore-water pressures weremeasured during the year within the upper few met-res.

Given this background, it was decided to study the re-sponse of the slope through a finite-element modelwhich could handle flow under saturated/unsaturatedconditions, and the mechanical interaction associatedwith changes in soil suction. The authors have developedin the past two decades a series of models of increasingcomplexity to deal with these coupled problems (Lloretand Alonso 1980; Alonso et al. 1988; Olivella et al.1994, 1996). The general approach is to solve the conti-nuity equations for air and flow coupled with mechanicalequilibrium conditions. Improved understanding of themechanical and hydraulic behaviour of the unsaturatedsoils has resulted in updated constitutive equations,which explain the evolution of the computational toolsdescribed in the quoted references.

The model used to describe the Villa Blasi slope isdescribed in the Appendix. It may be described as amodel of medium complexity as far as the mechanicalcharacterisation of the soil and the effect of suction isconcerned. In fact, it was realised that the success of themodelling exercise was closely related to a reasonableunderstanding of the hydraulic regime and the influenceof the heterogeneity of the soil profile. The model de-scription given in the Appendix provides the set of basicequations to be solved and the necessary constitutiveequations (water and air motion equations, definition ofpermeability and water retention, and the non-linearelastic model for stress-strain behaviour).

Reference should be made to the Appendix to inter-pret the set of constitutive parameters used in the analy-sis and, in particular, the sensitivity studies reported be-low.

The discretisation of the slope is shown in Fig. 9. Thearea covered by the F.E. mesh extends 308.5 m horizon-tally. The highest and lower levels of the slope surfaceare 113 and 60 m respectively. The lower horizontalboundary is located 20 m below the lowest point of theslope surface. Three materials are distinguished. The in-terfaces follow the actual positions identified in borings.In total the mesh has 648 four-noded, linear quadrilateral

Fig. 8 Water retention curve obtained by means of the filter papermethod

Fig. 9 Finite-element mesh

179


elements. The mesh is denser at the free surface and inthe vicinity of material interfaces where high flow gradi-ents are expected. Also indicated in Fig. 9 are the posi-tions of instrumented boreholes. The letters P and I, atthe beginning of each borehole identification number, in-dicate the presence of piezometers and inclinometers re-spectively. Two thick columns (PC and IB) around theposition of boreholes C and B are also indicated. Somemodelling details, presented below, refer to these twozones.

The computations have been organised in three phas-es: (1) definition of equilibrium conditions, (2) analysisof rainfall infiltration, and (3) deformation analysis andevaluation of safety factors. They are further describedbelow.

1. Equilibrium conditions. The aim of this phase is toget an equilibrated state of stress within the slope anda reference water pressure distribution consistent withpiezometric data on 1 October 1992. These equilibri-um conditions are the initial conditions for phase 2.This date was also the initiation for displacementanalysis. In fact, the period of observations consid-ered in the paper extends from 1 October 1992 to 31October 1993. During this period, observed changesin piezometer readings and deformations in inclino-meters were associated with rainfall changes.

2. Rainfall infiltration. Two different cases, leading todifferent boundary conditions, have been considered. Controlled infiltration. In this case the intensity of

rainfall, I, is smaller than the maximum water flow,Qi, which can infiltrate through the slope surface.Then, the inflow is controlled by the rain intensity.A prescribed flow boundary is adopted: Qi=I.

Flooded slope: If rainfall intensity I>Qi only part ofthe rainfall infiltrates. The infiltration depends onthe computed permeability and degree of saturationof the slope surface. A boundary condition for aflooded slope (s=papw=0) was applied at thesurface of the slope.

The following methodology was applied to the availablerainfall records (which correspond to the nearby villageof Posatora): average uniform monthly flow rates werecomputed. These flows were imposed as flow boundaryconditions at the slope surface. If a positive pore-waterpressure (pw>0) was computed at the slope surface(which is an indication that the rainfall rate was largerthan the infiltration capacity of the soil), the boundarycondition was changed to s=0.

3. Deformation analysis and evaluation of safety factors.The model provided time records of slope deforma-tions in parallel with the flow analysis. Local safetyfactors were determined by comparing, at some se-lected points within the slope, available shear strengthand existing shear stress. Details of the procedure aregiven below.

Soil ParametersSoil parameters were derived from laboratory tests. Mostof the specimens tested were taken from layer and con-sequently the derived parameters correspond to that lay-er. Parameters for the upper and lower layers were basedon the basic set for layer . In fact, the state surface forvoid ratio, the water retention curve, and the relative per-meability were accepted to be represented by commonlaws for the three layers. Layer differences were as-signed to saturated (or intrinsic) permeabilities and toshear-strength laws. Soil parameters are shown in Table 1.

The state surface for void ratio was approximated onthe basis of the suction-controlled oedometer tests. Theanalytical expression suggested by Lloret and Alonso(1985) was fitted to measured values (Fig. 10). The ana-lytical expression given by Bourgeois (1986) was usedfor the water retention curve (Fig. 8). The variation ofwater permeability with suction was derived from mea-sured values (Fig. 7). Figure 11 shows the resulting vari-ation of water relative permeability with degree of satu-ration. A symmetrical relationship was adopted for airrelative permeability (Fig. 11). Analytical expressionsare given in the Appendix.

The shear-strength data (Fig. 4) were approximatedwith piece-wise linear approximations for increasing

Fig. 10 State surface for void ratio. Sections along constant suc-tion values

Fig. 11 Relative permeabilities for air and water

180


Tabl

e1

Soil

para

met

ers (

*

:v

p a)

Rel

atio

nshi

pPa

ram

eter

Laye

rEq

uatio

n Fi

gure

(App

endix

)

Void

ratio

stat

e d

0.64

620.

6462

0.64

62Eq

.21

Fig.

10su

rface

(line

ar law

)a

(kPa1

)

7.58

10

5

7.

58

10

5

7.58

10

5

b(kP

a1)

6.

45

10

5

6.45

10

5

6.

45

10

5

c(kP

a1)

1.61

10

7

1.61

10

7

1.61

10

7

Deg

ree

of sa

tura

tion

S ri

0.12

0.12

0.12

Eq.1

5Fi

g.8

stat

e su

rface

(Bou

rgeoi

s)S r

s1.

01.

01.

0A w

1.0

1.0

1.0

B w0.

70.

70.

7C w

(kPa1

)1.

65

10

31.

65

10

31.

65

10

3

Wat

er p

erm

eabi

lity

Kw

s(m

/s)10

9

10

610

9

- 10

7

10

9Eq

.11

Figs

.7, 1

1(Ja

cqua

rd)A w

1.0

1.0

1.0

B w0.

960.

960.

96C w

(kPa1

)5.

16

10

15.

16

10

15.

16

10

1

Air

perm

eabi

lity

(Brun

)K

as

(m/s)

10

12

10

910

12

10

10

10

12Eq

.9Fi

gs.7

, 11

A a1.

01.

01.

0B a

0.

96

0.96

0.

96C a

(kP

a1)

5.16

10

1

5.16

10

1

5.16

10

1

Non

-line

ar e

lasti

c

0.30

0.30

0.30

Eqs.

23, 2

4m

ode

l (mo

del1

)Sh

ear s

treng

th

*

=0

100

kPa

100

400

kPa

>40

0 kP

a

*=

010

0 kP

a10

040

0 kP

a>

400

kPa

Eqs.

26, 2

7Fi

g.4

(plan

ar fai

lure

c (kP

a)0

532

,500

144,

700

532

,500

144,

700

env

elop

e)

()24

.542

3219

4232

19b

()s

20kP

as

20kP

as

20kP

ab

=

b=

b

=

s>20

kPa

s>20

kPa

s>20

kPa

b=

/2

b=

/2

b=

/2

181


confining stresses (see data for layers and in Ta-ble 1). The shear strength adopted for layer corre-sponds to the lower limit of the peak strength data re-corded in triaxial tests.

The lower limit of the remoulded sample strength(based on triaxial testing) was selected as the relevantstrength for the upper layer, which undergoes a pro-cess of natural reworking. The saturated strength param-eters for layer are therefore c=0, =24.5.

The effect of partial saturation is added by means ofthe apparent cohesion intercept, c, which increases withsuction (Fig. 12). To ensure consistency with the saturat-ed strength expression, the variation of c with s (angleb) was made equal to for suctions in the vicinity ofzero (s20 kPa). At higher suctions, a value of b=/2was adopted. This choice is an approximation based onpublished experimental results on the influence of suc-tion on shear strength (Fredlund and Rahardjo 1993).

Equilibrium Conditions of the Slope

Boundary conditions for the discretised geometry of theslope are established as marked in Fig. 13 for water flow,air flow and mechanical conditions. The water table is asurface of zero air and water pressure. Water pressures aswell as air pressures at the lateral boundaries increaselinearly below the phreatic surface, since suction ismaintained at zero under saturated conditions. The upperand lower boundaries for water flow had a zero pre-scribed flow. Air flow was also nil at the lower bound-ary, and the atmospheric condition (zero air pressure)was applied at the upper boundary. Two lower fixedpoints and zero normal displacements at the lateral and

lower boundaries define the mechanical boundary condi-tions.

Initial conditions for this initial phase of calculationare, however, more difficult to establish. There is no in-formation on the in-situ stress state. Oedometer test re-sults, discussed above, indicate that the pre-consolida-tion stress values of layers and vary between 23 and34 MPa respectively. Based on this information, an ide-alised geological sequence deposition under a N.C.state and erosion of overlying layers has been simulat-ed. The mesh used in this analysis is shown in Fig. 14.The initial block of soil has a vertical dimension which

Fig. 12 Variation of apparent cohesion with suction

Fig. 13ac Boundary conditions for a flow of water, b flow of air,and c mechanical analysis

Fig. 14 Mesh for the calculation of initial stress state

182


provides a vertical stress v=4 MPa at the lower limit ofthe discretisation. Vertical stresses at the highest andlower levels of the slope are 1.74 and 2.8 MPa. All thesevalues are believed to be reasonable in view of oedome-ter results. The horizontal stresses were derived from thecondition K0=0.52 obtained in triaxial testing of rem-oulded samples (Baldelli et al. 1992). For modelling pur-poses, an elastoplastic hyperbolic model with parametersc=95 kPa and =27 was used. These values correspondto peak strength values measured in triaxial and direct

shear experiments, as illustrated in Fig. 15. The initialblock of soil represented in Fig. 14 was excavateduntil the actual slope geometry was recovered and a setof initial stresses was computed.

Introducing this calculated distribution of initialstresses and the assumed initial values of water (and air)pressures, a calculation was performed using the bound-ary conditions given in Fig. 13. The computed finalphreatic surface (Fig. 16) was very close to actual pi-ezometer readings at the location of boreholes C and A(upper and centre parts of the slope). The shallow watertable measured at the lower levels (borehole E) in Octo-ber 1992 could not be reproduced. Some surface re-charge at the lower level of the slope would have beenrequired to reproduce the observations at borehole E.However, most of the slope and, in particular, the centralsections (BD) are correctly modelled. The pattern of the

Fig. 15 Hyperbolic model used to generate the initial stress state

Fig. 16 Calculated phreatic surface

Fig. 17 Initial steady state. Flow velocity field in section PC

Fig. 18 Computed initial stresses. Intensity and direction of mainstresses are shown

183


stationary computed flow is illustrated in Fig. 17 for thecentral section PC. Downward flow above the water ta-ble is restricted due to the reduction of water permeabili-ty in the unsaturated soil.

Computed principal stresses for the same central por-tion of the slope are given in Fig. 18. Large K0 values arepredicted in upper levels. As expected, K0 reduces withdepth.

Computed deformations were set to zero at thisstage, since it marked the beginning of inclinometerreadings.

Rainfall Infiltration

Probably the greatest uncertainty concerning materialproperties of the slope lies in the field values of perme-ability. There were available, however, detailed piezome-ter records during 13 months 1 October 1992 to 31 Oc-tober 1993. These data provided an opportunity to refine

the hydraulic model of the slope. To do so, several caseswere defined (cases ad, fh, j and k) by varying the per-meability of layers and . The permeability of the sub-stratum layer was kept constant. The adopted perme-abilities are given in Table 2. Note that case a corre-sponds to a homogeneous slope.

Permeability to air was changed in similar propor-tions as permeability to water. However, air flow plays aminor role in this problem.

Computed suction was zero below the phreatic line,and above it the air pressure was essentially zero. In-stalled piezometers are of two types: open tube (Casa-grande), and electrical piezometers. The open tubes wereinstalled in deep borings (A, B, C, D, E) at depths of1014 m and they record fluctuations in the water table.Electrical piezometers were installed at shallower depths(2.804 m) within the layer and were able to record(small) negative water pressures as well as positive val-ues.

The imposed rainfall record, following the criteriadiscussed above, is shown in Fig. 19. Some comparisonsof piezometer readings and calculations are shown inFigs. 20, 21 and 22 for the piezometers C (Casagrande;depth=9.80 m), P5699 (electrical; depth=2.80 m), and

Table 2 Rainfall infiltrationanalysis. Cases analysed Case Saturated water permeability kws (m/s) Number of different materials

Layer Layer Layer Steady state (phase A) 109 109 109 1a 109 109 109 1b 108 109 109 2c 107 109 109 2d 106 109 109 2f 108 108 109 2g 107 108 109 3h 106 108 109 3j 107 107 109 2k 106 107 109 3

Fig. 19 Rainfall record at Posatora

Fig. 20 Comparison of measured and calculated piezometer read-ings (piezometer C). Depth of measuring chamber: 9.80 m

184


P5698 (electrical; depth=3.15 m). Similar comparisonswere made for all the recorded piezometers. In all casesthe water pressure is expressed as a depth from the sur-face. When this depth exceeds the position of the sensor,the pore-water pressure is negative and the correspond-ing suction may immediately be derived. Note that in thecase of shallow piezometers, suctions are often comput-ed for some combinations of layer permeability. Somesuction values were also recorded at some particulartimes.

The general computed trend during the 13-month pe-riod was a general elevation of the deep water table(Fig. 20). This trend was essentially followed by calcula-tions except for a drop of water level recorded in the fi-nal reading. This is an unexpected fact in view of therainfall record, which provides a substantial average rainin excess of 80 l/m2 for the 13th month. It is clear that

some combination of layer permeabilities leads to a bet-ter reproduction of actual piezometer records. It is alsointeresting to observe the pattern of computed waterpressure predictions as permeability varies among thethree layers. There are permeability combinations whichlead to the strongest response of the slope in terms ofthe intensity of the generated water pressure at a particu-lar point. This comment is illustrated in Fig. 23, which isa plot of the computed response of piezometer P5699,350 days after the initial date. The combination K=107 m/s and K=108 m/s leads to the maximum pres-sure (positive) at the point considered. More or less per-vious and layers result in lower water elevations. Itmay be concluded that a particular sequence of perme-abilities is a critical one for a given rainfall record. Thereare no easy rules to predict such a critical profile of per-meabilities because the computed water pressure is theresult of several phenomena: infiltration flow, flow trans-port parallel to the slope, and (changing) storage capaci-ty of the soil. In fact, the critical situation identifiedfor a particular heterogeneity is probably not an absoluteconcept since it may change with the initial conditions.Nevertheless, this result stresses the relevance of soilpermeability and its distribution within the slope to gen-erate critical stability conditions for a given slope geom-etry, material properties and a given rainfall record.

The nine cases solved were rated from worst to bestfor each of the piezometer records available, in terms of

Fig. 21 Comparison of measured and calculated piezometer read-ings (piezometer P5699). Depth of sensor: 2.80 m

Fig. 22 Comparison of measured and calculated piezometer read-ings (piezometer P5698). Depth of sensor: 3.15 m

Fig. 23 Computed depth of water level at piezometer P5699 forthe time t=350 days after the beginning of the prediction exercise(1 October 1992). Depth of sensor: 2.80 m

185


its proximity to the actual measurements. This procedureof model fitting leads to identifying cases h, j or k as theoptimum ones. The worst representation was given bymodel a, the uniform slope. Figures 24 and 25 show thecomputed evolution of pore-water pressures in the soilprofile at borehole C for the cases h (K=106 m/s;

K=108 m/s, and K=109 m/s) and j (K=107 m/s;K=107 m/s, and K=107 m/s).

In case h, the strong transition of permeabilities be-tween the upper layers and leads to an accumulationof water at their interface. Positive pore-water pressuresat this interface are computed some time after the actionof rainfall. In case j, layers and have the same per-meability (107 m/s), and a suction is maintained at thisinterface throughout the modelled time period. This caseleads to a smoother variation of pore pressures at depth.The rain infiltration modifies substantially the downwardflow of water (Fig. 26), if compared with the initial state.The upper soil levels, which have approached saturation,carry increased flows toward the slope toe.

Given these results, the mechanical analysis was lim-ited to cases h, j and k, since it became clear that a tran-sition of permeabilities from higher values at the surfaceand lower values at depth was required to match piezom-eter readings.

Deformation Analysis and Evaluation of Safety Factors

Calculated deformations will now be compared withslope displacements measured in inclinometer B (upperpart of the slope: section IB in Fig. 9). The reference ze-ro reading for the inclinometer was taken on 22 Septem-ber 1992, a few days before the initial time for calcula-tions (1 October 1992). Computed displacements for oneof the reference cases selected (case h) are shown inFig. 27. Maximum surface displacements are small, inthe order of a few millimetres. A comparison of the mea-sured evolution of horizontal displacements and calculat-ed ones at a point near the surface (depth=0.30 m) atborehole B is shown in Fig. 28. The three reference cases(h, j, k) provide similar results (Fig. 27). The agreementis acceptable during the first 7 months. Sometime later,the upper part of the slope experiences a sudden motionwhich is not captured by the deformation model. The

Fig. 24 Computed pore pressures in vertical profile C (case h:K=106 m/s, K=108 m/s, and K=109 m/s)

Fig. 25 Computed pore pressures in vertical profile C (case j:K=107 m/s, K=107 m/s, and K=109 m/s)

Fig. 26 Computed water velocity field at section PC (case h:K=106 m/s, K=108 m/s, and K=109 m/s) at t=288 days (15 July 1993)

Fig. 27 Computed vertical profile of slope displacements at bore-hole B (case h)

186


displacement profile along depth (Fig. 29) shows thatthis sudden motion essentially displaces the upper re-worked layer . It seems that, at the interphase betweenthe and layers, a distinct shear surface has developed(or it was already formed). The non-linear elastic modelis obviously not able to reproduce this behaviour. In-stead, it provides the pattern of deformation associatedwith the soil volume change as suction changes as a re-sult of rainfall. Figure 30 is, in this regard, a deformedmesh of the slope for case h (the other reference casesprovide very similar results). The clay expansion, whichresults in increasing displacements as the slope surface isapproached, also induces downward components ofmovement. These downward displacements are small (afew millimetres) but they have consistently been mea-sured. No information on vertical displacements was,however, available.

An additional insight into the problem is gained fromanother perspective. Local safety factors have been com-puted as a ratio of shear strength and existing shearstress. For an infinite slope the classical expression for aplanar failure is:

(1)

where d is the depth below surface, the total specificweight, and the slope angle (11). The analysis per-formed provides pw as a function of time for every pointwithin the slope, and therefore Eq. (1) may be computed.

Since stresses (x, y, xy) are also known from theF.E. analysis, an alternative to Eq. (1) may be computedas follows:

The evolution of vertical profiles of local safety factorshas been represented in Figs. 31 and 32 for a homogene-ous slope at borehole C (centre of the slope). In this casea common failure envelope adopted for layer (seeFigs. 4 and 12) is assumed for the whole slope. The per-meability profile corresponds to case h. The FEM-basedsafety factor is smaller, within the upper layer (and,specifically, at the critical interphase with layer ), thanthe infinite slope-based value. A minimum safety factoris computed at the interface. However, absolute val-ues are high, far from explaining failure. Consider, how-ever, the heterogeneous case in which soil strength oflayer is approximated by the remoulded strength val-ues, given also in Figs. 4 and 12. The profiles of localsafety factors (FE-based calculations) are given inFig. 33 for case h, and in Fig. 34 for case j. Safety fac-tors in the upper reworked layer reach low values atsome particular times. The interphase between and layers is a critical surface, since it marks the change inpermeability and shear strength. Minimum safety factorsare computed at this interphase.

The choice of a remoulded strength for the layerand, in particular, for the interphase may be justified

Fig. 28 Computed and measured horizontal displacements of theslope at a point located 0.30 m (0.36 m) below the surface at bore-hole B

Fig. 29 Computed and measured profiles of horizontal displace-ments at borehole B

Fig. 30 Computed deformation of the slope 335 days after the ini-tial state (case h)

F c d pdisw

( ) = + ( )

cos tan

sin cos2

FFEM( ) =

c px y x y xy w

x yxy

++( )

( )

( )

2 2 2 2

2 2 2

cos sin tan

sin cos

(2)

187


on the basis of the physical processes taking place at theupper weathered layer. Inclinometer readings (Fig. 29)show that displacements are concentrated in the layerand therefore, the interphase will undergo largeshear strains or even a distinct shear surface, as men-tioned above. This natural remoulding effect reduces thesoil strength. As a result, strength parameters determinedin remoulded specimens may be appropriate for stabilityevaluation (as the computed safety factors tend to sug-gest). The presence of sand lenses in and layers mayalso have some effect. When sand lenses are continuous,they tend to channel the internal flow within the slopeand they may reach transient high pressures as a result ofexternal recharge (heavy rainfall in the area). Then, ef-fective stresses and available strength will drop to criti-cal values. However, measured pore-water pressures inpiezometers, recorded over a significant time period, donot show abnormally high values. Nevertheless, the de-

Fig. 32 Profiles of local safety factors (based on FE computa-tions) at borehole C (case h, homogeneous strength)

Fig. 33 Profiles of FE-based local safety factors at borehole C(case h, heterogeneous strength)

Fig. 34 Profiles of FE-based local safety factors at borehole C(case j, heterogeneous strength)

tailed characterization of the hydrological regime of aheterogeneous slope, such as the Villa Blasi slope, can-not be performed on the basis of available data and it isprobably an unrealistic proposition in most situations.

If a point within the upper layer is selected, the in-fluence of climate (rainfall) is better appreciated whenthe computed local safety factor is plotted with time.This is shown in Fig. 35 for a point at a depth=2.15 m atthe position of borehole C (central zone of the slope).Equations (1) and (2) are represented for the base hy-draulic cases (h, j, k). FE-based safety factors are con-sistently lower than their infinite slope-based counter-parts. This is explained by the significant influence ofthe method followed to find initial stresses, hopefullycloser to real conditions. The fluctuating rainfall recordmay be followed in Fig. 35. The safety factor decreasesin correspondence with the wet season, and it increaseswhen the rainfall inflow decreases. This is the reason for

Fig. 31 Profiles of local safety factor (based on an infinite slopeanalysis) at borehole C (case h, homogeneous strength)

188


the increase in safety factor observed after a dry seasonin January 1993. The maximum computed fluctuation insafety factor (FE-based, heterogeneous strength distribu-tion), once the initial transient period is discarded, isaround F=0.6 at a depth of 2.15 m. Larger fluctuations(shown in Fig. 35) are computed for other circumstances.Presumably extreme rainfall events may take the slope toa limiting failure condition (F=1) in the case plotted inFig. 35. The steady but slow decrease in safety factor ob-served in the figure follows the reduction in suction inthe upper layer.

The effect of an extreme rainfall event was finally inves-tigated. The hypothesis is now that the intensity of rain is, atall times, larger than the infiltration capacity. This conditionis simulated by flooding the slope. A zero water pressure isthen applied as a boundary condition in the upper slopeboundary. This condition was maintained for 61 days.

The evolution of water pressures in the slope at sec-tion C is shown in Fig. 36 for the reference case h.Shortly after 24 h of continuous rain, a perched water ta-ble develops over the interphase between layers and .A hydrostatic positive pore-water pressure develops inlayer after a week of rain. Suction in the layer pro-gressively decreases and extensive zones develop posi-tive pore-water pressures with time. The elevation of thedeep water table also increases beyond the first week.This evolution of water pressures is matched by parallelchanges in safety factor (FE-based, heterogeneousstrength distribution) (Fig. 37). Safety factors lower than1 are computed at the interface for times beyond thefirst seven days of flooding. Lower values are computedat higher levels. However, the layer of undisturbedbrown clay remains stable even after 2 months of surfaceflooding.

Discussion and Conclusions

Two deformation mechanisms may be identified in theslope analysed: a creep-type displacement which was de-tected along the full depth of the soil investigated (around12 m), and a surface planar slide. The first mechanism isinterpreted as a deformation associated with volumechanges of the overconsolidated clays as the water pres-sures change in time as a reaction to rainfall events. Pore-water pressures in the slope do not follow a simple mod-el. A rather deep but fluctuating water table affects theclay substratum. However, water pressures at the uppertwo weathered layers are controlled by the atmosphericweather. Positive or negative water pressures are recordedat different positions or times during the year. A fairly

Fig. 35 Evolution of local safety factors at a depth of 2.15 m,borehole C. Infinite slope and FE-based cases homogeneous andheterogeneous strength and three hydraulic base cases are repre-sented

Fig. 36 Profiles of water pressure for a permanent slope flooding.Case h

Fig. 37 Profiles of FE-based local safety factor. Heterogeneousstrength distribution. Case h

good agreement between computed and measured waterpressures is achieved when the three identified layers arecharacterised by three different permeabilities.

An interesting conclusion of the sensitivity analysisperformed regarding the influence of heterogeneous dis-tribution of permeability is that the critical situation of agiven slope (in the sense of reacting with the maximumdevelopment of water pressures) for a given climaticrecord is obtained for a given combination of layer per-meabilities. From another perspective, this result also in-dicates that, given a soil profile and geometry and its as-sociated permeabilities and additional water flow param-eters, there exist rainfall records which lead to a maxi-mum reaction of the slope in terms of pore-water pres-sure development. Permeability and water retention aretherefore fundamental properties in slope stability analy-sis, a fact often overlooked in engineering analyses.

The analysis performed indicated that downward aswell as heave displacements are to be expected in theslope. Only lateral displacements, as recorded in in-clinometers, were, however, available. Slopes in expan-sive natural clays are often known to present stabilityproblems. A primary cause for this situation is probablyassociated with downward displacements which resultfrom the cyclic expansion/shrinkage induced by suctionchanges as a consequence of weather changes. The up-per layers undergo the maximum suction and volumetricdeformation changes, and they are prone to develop theupper sliding mechanism identified also in the slopeanalysed. Probably, as deformation accumulates, peakstrengths are attained and, eventually, remoulded andeven residual strength conditions develop. Weatheringmechanisms result also in a change in permeability,which is stronger the closer to the surface. In fact, thewater pressures recorded are consistent with a decreaseof permeability with depth. One of the acceptable soilpermeability profiles is the sequence (106, 108, 109 m/s) for the three clay layers identified from top tobottom. It has been shown that permeability transitionslead to peak pressures computed at the interphases (see,for instance, Fig. 24). Both effects strength degrada-tion due to accumulated straining, and peak water pres-sures (positive or negative) may well result in the de-velopment of a sliding surface at an interface. Thisseems to be the case for the Villa Blasi slope, where theupper horizon of remoulded weathered clay is appar-ently sliding on its contact with the underlying, weath-ered, brown Ancona clay.

The coupled hydromechanical model used to analysethe slope is unable to reproduce the sliding mechanismbut it has been used to compute local sliding safety fac-tors. This type of analysis also provides interesting infor-mation, which is always useful in slope stability analy-sis. Two procedures have been used to derive local safetyfactors. Both share the hypothesis of infinite slope,which is considered acceptable in this case. In the firstprocedure, local safety factors are computed followingthe classical expression for infinite slope as a ratio ofavailable shear strength and shear stress in equilibrium

with the overburden weight. Water pressures (positiveand negative), required for strength calculations, are giv-en by the FE analysis. In the second approach, bothstresses and pore pressures, derived from the hydrome-chanical analysis, are the input for the safety factor. Rel-evant differences were found for the two types of analys-es, a result which highlights the importance of an ade-quate estimation of initial stresses in slope stability cal-culations.

The computed distributions and evaluations of localsafety factor illustrate also the singularity of the inter-phase between the upper reworked layer and the un-derlying brown clay layer . Minimum safety factors areconsistently found at this position. However, under theimposed rainfall history measured in one year, failureconditions are not found at this interphase if the strengthparameters of the weathered layer (lower envelope ofpeak resistances) are adopted for the whole profile.

If the strength of the upper layer is reduced to valuesmeasured for reconstituted samples (c=0; =24.5),safety factors at the interphase drop to values closeto 1.5 at the end of the rainfall period analysed. Addi-tional analyses, which attempt to simulate extremeweather conditions (heavy and prolonged rainfall), indi-cate that a failure along the interphase is possible even ifthe strength parameters are maintained at the measuredremoulded values. Probably, this was the case for a firstsliding in the past history of the slope. Then, strengthvalues would be even reduced and would be closer to re-sidual conditions. Under these circumstances, normalrainfall records could trigger additional sliding, as shownby the inclinometer readings during the period October1992 to October 1993.

Once a planar sliding surface has developed, the con-ceptual model of slope motion is simple in principle: theupper reworked layer slides on top of a critical surface atresidual or near-residual conditions. Even in this case,however, the periods of activity are dictated by the suc-tion changes in the upper few metres which depend criti-cally on the slope geometry, flow boundary conditions,rainfall record, flow parameters (permeability, water re-tention properties) and its spatial variation. The problemmaintains its complexity and shows the dependence ofslope safety on climate, geometry and a number of con-stitutive parameters.

The case record analysed illustrates the relationshipsamong the various factors controlling slope stabilityalong a heterogeneous clay profile. It also points to thedifficulties encountered in practice and the need for ac-curate, comprehensive and long records of behaviour insitu. Modern computational methods, which couple me-chanical and hydraulic conditions under saturated or un-saturated conditions, are powerful tools to interpret fieldperformance.

Acknowledgements The authors are thankful to the support pro-vided by the EU through the EPOCH Project EPOC-CT90-0033,Physical Processes in the Mediterranean Climates and RelatedSlope Instabilities in Overconsolidated Clayey Soils, coordinatedby Professor Scarpelli.

189


where Kas, Ag, a, Aa, Ba and Ca are constants, and a isthe viscosity of the air.

Water. Water flow is described by a generalization ofDarcys law:

(10)where Kw is the coefficient of permeability and w thespecific weight of water (assumed constant).

Several empirical expressions have been given for theKw(papw) or Kw(Sr, e) relationship. Jacquard (1988)proposed:

(11)

To combine the effects of void ratio and saturation, Lloret and Alonso (1980) proposed to use a product ofthe variation of permeability with void ratio proposed byLambe and Whitman (1968), and the variation with de-gree of saturation proposed by Irmay (1954):

(12)

In Eqs. (11) and (12), Kws, Aw, Bw, Al, Sru, Kow and areconstants. Finally, a state equation is required to describethe degree of saturation (or, alternatively, water content).

(13)In Lloret and Alonso (1985), several expressions for Fwere proposed on the basis of experimental data. Thefollowing equation describes the variation of degree ofsaturation with applied stress and suction:

(14)where a, b, d are constants, and the relevant stress(mean or vertical for isotropic or oedometric cases).

Changes in water retention induced by external load-ing are small in front of changes induced by suction. Inseepage problems in unsaturated soil, several relation-ships between water suction and moisture content havebeen proposed. Among them:

(15)

where Aw, Bw, Cw, Ew, Fw, Sri and Srs are constants (VanGenuchten 1980, Bourgeois 1986).

Mechanical behaviour. A practical stress-strain relation-ship which may take properly into account the relevantbehaviour of partially saturated soils is:

(17)

190


Appendix

Mathematical Formulation of the Flow-deformationModelContinuity and equilibrium equations Continuity of the air mass filling the soil voids

(3)

Continuity of the water mass filling the soil voids

(4)

Mechanical equilibrium

(5)

where a, w are air and water mass densities, n the soilporosity, Sr the degree of saturation, and H Henrys con-stant. Vectors va and vw refer to air and water velocities (inthe Darcy sense). pa is the air pressure, pw the water pres-sure, ij the total stress, bi the body forces, xi the systemcoordinates, and ij the Kroneckers symbol. Note that theequilibrium is formulated in terms of net stresses (excessof total stresses over air pressure). When the soil becomessaturated, pa=pw, suction s=papw becomes zero and theclassical formulation in effective stresses is recovered.

The displacement vector (u), and the air and waterpressures (pa and pw) are chosen as basic variables of theproblem. To solve the basic equations (3), (4) and (5) interms of these basic variables, a set of constitutive andmotion equations are necessary.

Constitutive and motion equationsAir. It is assumed that the air behaves as an ideal gas.Density and pressure are related as follows:

(6)where T (K) is the absolute temperature, R the gas con-stant, M the molecular weight of air, and is the com-pressibility of air.

Motion of air can be described by a generalization ofDarcys law:

(7)where Ka is the coefficient of permeabilitiy and a thespecific weight of air.

The coefficient of permeability varies strongly with Srand, to a lesser extent, with the void ratio (e). Typicalspecific expressions proposed by Yoshimi and Osterberg(1964) for Ka versus e and Sr, and by Brun (1989) for Kaversus (papw) are:

(8)

(9)

(16)

t div a a r r a wn S H S H1 0 +( )[ ] + +( )[ ] =v v

w r w wnSt

( )+ ( ) =div v 0

a a aMRT p p= =

where * are the net stresses:

(18)

and mt=[1, 1, 1, 0, 0, 0]. are the total strains:

(19)

and o are the volumetric strains induced by suctionchanges. The terms of the constitutive tangent matrix Dmay depend on stress level and macrostructural suction.Volumetric changes induced by suction changes may bedescribed by means of different methods. A suitable ex-pression for computational purposes is:

(20)The terms in vector hs will depend on macrostructuralsuction and stress level. Coefficients of matrix D and hsmay be defined through a constitutive model.

An approximate procedure to obtain matrix D andvector hs is to use the concept of state surface for voidratio (Matyas and Radhakrishna 1968). This surface pro-vides the variation of classical void ratio (e) with ap-plied total stress and suction for a given experimentalprocedure (oedometric or triaxial conditions, in mostcases). For instance, for isotropic or oedometric stressconditions, the following expressions have been suggest-ed for these state surfaces (Lloret and Alonso 1985):

(21)

(22)where a, b, c and d are constants, and is the relevantstress which defines the stress state. The state surfacegiven by Eqs. (21) or (22) does not consider explicitlythe influence of deviatoric stresses on volumetric changeinduced by suction changes.

Coefficients of matrix D may be defined through anon-linear elastic model. The tangent compressibilitymodulus Kt is (for isotropic test conditions) obtainedfrom Eqs. (21) or (22). The shear modulus (Gt) can beobtained assuming a constant Poissons ratio (model 1)or from a hyperbolic shear stressshear strain law (mod-el 2).

(23)

(24)

(25)

G0 and Rf are parameters of the hyperbolic model (Duncan and Chang 1970). (13) is the deviatoricstress, and (13)f is the deviatoric stress at failure.Note that the stiffening effect of suction increase hasbeen introduced in Eq. (25), through the initial G modu-lus, by means of a linear relationship with parameter M.This is in accordance with some experimental evidence(Brull 1980).

The effect of suction on shear strength is taken intoaccount via an extended Mohr-Coulomb criterion (Fred-lund et al. 1978; Gens 1993) for a planar failure enve-lope:

(26)(27)

where f is the shear stress at failure, n the total normalstress acting on the failure plane, c the effective cohe-sion, the effective internal friction angle, c the appar-ent cohesion, and b the apparent friction angle to ac-count for the increase of strength with suction. However,as pointed out by Escario and Sez (1986), the angle bshould be a function of suction. In particular, b ass0 to ensure consistency with the saturated strengthenvelope. b was made dependent on suction, as ex-plained in the text.

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en

nd a p b p pa a w=

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nd a p b p p pa a w at=

= + ( ) + +( )1 log log+ ( ) +( )c p p p pa a w atlog log

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Alonso 2003

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