Representativeness of Measurements in the Interpretation of Earth Dam Behaviour_Pagano, Sica, Desideri_2006

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Representativeness of measurements in theinterpretation of earth dam behaviour

Luca Pagano, Stefania Sica, and Augusto Desideri

Abstract: The representativeness of measurements monitored in earth dams is analysed to investigate how a givenmeasured quantity can be used to interpret the dams mechanical behaviour. Representativeness is evaluated on the ba-sis of spatial continuity of the measured quantity and the sensitivity of that quantity to natural mechanical nonhomo-geneity. The discussion is supported by results from case studies and numerical examples. The study is mainly focusedon pore-water pressure measurements. Spatial continuity of pore-water pressure is analysed with consideration of bothsaturation and drainage conditions. The paper discusses how pore-water pressure representativeness can vary over thelifetime of the dam.

Key words: earth dam, pore-water pressure, monitoring.

Rsum : On analyse la reprsentativit des donnes des mesures obtenues dans les barrages en terre pour tudiercomment une quantit donne mesure peut tre utilise pour interprter le comportement mcanique dun barrage. Lareprsentativit est value sur la base de la continuit spatiale de la quantit mesure et de sa sensibilit la non ho-mognit mcanique naturelle. La discussion est appuye par des rsultats dtudes de cas et des exemples numri-ques. Ltude se concentre principalement sur les mesures de la pression interstitielle. On analyse la continuit spatialede la pression interstitielle en considrant les conditions de drainage de mme que de saturation. Larticle discute com-ment la reprsentativit de la pression interstitielle peut varier au cours de la vie du barrage.

Mots cls : barrage en terre, pression interstitielle, mesures.

[Traduit par la Rdaction] Pagano et al. 99

Introduction

In the field of earth dams, monitoring of typical physicalquantities is a fundamental activity. Measuring internal and

boundary displacements, total stresses, pore-water pressures,and seepage is important, as it enables the carrying out of anumber of tasks (ICOLD 1982), such as characterizing thedams overall behaviour (e.g., Pagano et al. 1998), checkingthe behaviour of specific zones, obtaining information aboutthe in situ mechanical properties of the embankment soils(e.g., Marsal and Resendiz 1975), and finally, supporting thedifficult task of evaluating dam safety and efficiency (e.g.,Gould and Lacy 1993).

If the objectives outlined above are to be reached, variousmeasurements need to be interpreted by means of simple orcomplex models (e.g., Marsal 1958; Poulos et al. 1972;Alonso et al. 1988; Pagano et al. 2001). The first stages of the interpretative process often consist in rebuilding spatial

trends of measured quantities by extrapolating data taken at

measurement points. This is essentially based on the as-sumption that measurements are representative or, equiva-lently, that spatial trends of the physical quantities arecontinuous.

Figure 1 a shows settlement profiles measured in the coreof the Beliche Dam during the first 5 years of operation, notincluding settlements developed during construction. Themeasurements refer to three different verticals, monitored bycross arms installed inside the core during construction; thedegree of continuity of the settlements is high enough thateach trend will remain unchanged, even if some measure-ments are eliminated. In the case shown here and in themajority of cases, settlement measurements are highly repre-sentative.

Figure 1 b shows vertical strains at the same verticals and forthe same period as in Fig. 1 a . Vertical strains were obtained bydividing the settlement difference between two successive mea-surement points by their distance. Trends of the local strains

appear to be quite discontinuous2

and would change signifi -

Can. Geotech. J. 43 : 87 99 (2006) doi:10.1139/T05-093 2006 NRC Canada

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Received 13 January 2005. Accepted 9 September 2005. Published on the NRC Research Press Web site at http://cgj.nrc.ca on6 January 2006.

L. Pagano 1 and S. Sica. Dipartimento di Ingegneria Geotecnica, Universit degli Studi di Napoli Federico II, Via Claudio, 2180125 Napoli, Italy.A. Desideri. Dipartimento di Ingegneria Strutturale e Geotecnica, Universit di Roma La Sapienza, Via Montedoro, 2800196Roma, Italy1Corresponding author (e-mail: [email protected]).2Distances between pairs of successive cross-arm plates are high enough to ensure that in the differentiation of settlement withdepth, settlement differences ( S) are one order of magnitude as high as measurement accuracy ( A); the possible scatteringassociated with a bad S / A ratio should therefore be negligible.


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cantly if fewer measurements were considered. In the caseshown and in the majority of cases, local strain measurementsare less representative than settlement measurements.

Experience indicates that measurements of some quanti-

ties, such as displacements and seepage, typically show con-tinuous trends and are, therefore, representative. Conversely,measurements of other quantities, such as local strains andstresses, are often characterized by significant scattering thatmakes them poorly representative.

Scattering can be associated with inaccuracies, instrumentand acquisition system noise, and scale problems (when thesize of the zone where the measurement is taken is small,compared with the size of the soil particles). A main sourceof scattering can also be intrinsically related to the specificquantity that is measured. This issue will be addressed in theremainder of the paper.

An earth dam is made of one or more macroscopically

homogeneous zones, each containing randomnonhomogeneities, with location and properties undetect-able. Nonhomogeneities tend to make spatial trends of somemeasured quantities discontinuous. The influence of

nonhomogeneities in reducing continuity and representative-ness of measurements may vary according to the quantity athand, the instrument location, and the state of the soil wherethe measurement is carried out.

Some quantities, such as local strains and stresses, may bestrongly affected by even small nonhomogeneities such thatthe measurement at the point cannot be extended around thepoint.

Other quantities preserve a high degree of spatial continu-ity and representativeness, even in the presence of strongnonhomogeneities. This, for instance, is the case of displace-ments and seepage. Their enhanced continuity can be ex-plained within the framework of continuum mechanics, as

Fig. 1. The Beliche Dam: ( a ) settlements and ( b) vertical strains developed during operation along three cross arms located within thecore at the main cross section of the dam.


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they are integral functions of strains and water flow, respec-tively.

The theoretical example of Fig. 2 supports what is statedabove. It shows how a difference in sensitivity to mechanicalnonhomogeneity affects some typical monitored quantities.The example refers to a linearly elastic fill, which deformsas a result of the dead load. Nonhomogeneities sized 2 m 2 m are randomly introduced within the fill. They are arbi-trarily assumed to be less stiff than the fill. This effect, forexample, could be induced by a different compaction effort

or different physical properties of the placed material. In theanalysis carried out, the difference between the fill stiffness(Youngs modulus = 2000 MPa) and nonhomogeneity stiff-ness (Youngs modulus = 500 MPa) corresponds to stiffnessdiscontinuities measured by the down-hole technique at thecore midheight of the Camastra Dam (southern Italy). Fig-ure 2 indicates that nonhomogeneities render computed dis-tributions of stresses and strains strongly discontinuous(characterized by jumps). In contrast, settlement trendsmaintain continuity in presence of nonhomogeneities. Thelatter affect only the settlement gradients.

Representativeness of pore-water pressure measurementsmay change substantially during the life of the dam as a re-

sult of changes in saturation and drainage conditions. Thisissue will be addressed throughout the paper by interpretingpore-water pressure measurements carried out in two se-lected case histories.

In the following, the essential features of the two case his-tories are described, and the piezometric head measurementsare shown. Interpretation of measurements is then carriedout in a discussion of measurement representativeness.Finally, representativeness is used as a criterion to determinewhich physical quantities can be used as reference for the

observed behaviour within a back-analysis process.

Case histories of pore-water pressuredistribution

Representativeness of pore-water pressure is discussed onthe basis of the measurements taken for two earth dams thathave been in operation for many years.

The Beliche Dam was constructed in southeast Portugalbetween July 1983 and March 1985. Dam behaviour is welldocumented in several Laboratrio Nacional de EngenhariaCivil internal reports and summarized by Naylor et al.(1997). The dams cross section is shown in Fig. 3; its maxi-

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Fig. 2. (a ) Vertical stresses, ( b) vertical strains, and ( c) settlements computed along the vertical axis AA of the reported sample ge-ometry, containing mechanical nonhomogeneities.


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mum height is 54 m. The fine-grained core, founded on bed-rock, was compacted around the optimum of the standardProctor test. It is characterized by low plasticity (plasticityindex (PI) 10%) and by a permeability coefficient ( k ) of 10 8 m/s. The shells were constructed from two differentcoarse-grained materials. Weathered schists, characterizedby poor mechanical properties, were placed close to thecore, and a stiffer rockfill material constituted the outerzones. This geometry was intended to avoid core arching,

which might have caused hydraulic fracturing.The piezometric head, measured from construction until

the early stages of operation, is shown in Fig. 4 in terms of both time histories (Fig. 4 a ) and isochrones of spatial distri-bution (Fig. 4 b).

During construction, saturation of a given zone within thecore takes place soon after a few metres of overburden mate -rial is put in place, as indicated by positive pore-water pres-sures (piezometric heads higher than the piezometerelevation). After saturation, the dead load produces signifi-cant increments in pore-water pressure throughout the entireconstruction process. Piezometric heads at the central lineare observed to be higher than those at the lateral piezo-meters (Fig. 4 a ; Fig. 4 b, curve 1). This distribution is consis-tent with that predicted by simple behavioural models thatplace piezometric heads higher at the central piezometer as aresult of both maximum load and maximum distance fromdrainage boundaries.

After dam completion and before first impounding, piezo-metric heads decrease as the consolidation process takesplace (Fig. 4 a ; Fig. 4 b, curves 2, 3, and 57).

During and after the first impounding, piezometric headdistributions decrease from upstream to downstream consis-tently with the seepage process from upstream to down-stream (Fig. 4 a ; Fig. 4 b, curves 1214).

The Polverina Dam is a zoned earth dam 27.5 m high,

built in central Italy from March 1964 to November 1965.The dams cross section is shown in Fig. 5. The core is aclayey sandy silt (PI = 12%18%), compacted around theoptimum of the standard Proctor test. The permeability coef-ficient is between 5 10 11 and 1 10 10 m/s. The down-stream shell is made of sandy gravel (30% sand). Theupstream shell is made of sandy gravel near the core and acoarser material in the outer zone. Around the center of thevalley, foundation soils consist of a 20 m deep fluvial de-

posit, which lies on a marly bedrock. A lacustrine clayey siltdeposit (PI = 20%26%; k 10 10 m/s; compressibility in-dex ( C c) = 0.170.26) is included within the sandy gravellayer. It is around 8 m thick at the valley center but thenthins out and disappears toward the two abutments. A 0.5 mthick concrete cutoff wall provides water tightness inside thefoundation soils. The wall runs from the foundation level of the core down to the marls crossing the sandy gravel andclayey sandy silt.

The piezometric heads measured at the Polverina Damduring construction and the early stages of operation areshown in Fig. 6 in terms of both time histories (Fig. 6 a ) andisochrones of spatial distribution (Fig. 6 b). For this dam aswell, saturation of a given zone within the core takes placesoon after the addition of a few metres of overburden mate-rial. Significant increments in pore-water pressure were ob-served throughout the entire construction process. Duringthe early stages of construction, pore-water pressures werehigher in the upstream piezometer (Fig. 6 a ; Fig. 6 b, curve1), whereas from mid-construction they increased signifi-cantly on the downstream side, until they reached the highestvalue, at the end of the construction (Fig. 6 a ; Fig. 6 b, curve3). In this case, the observed behaviour is inconsistent withwhat might be expected. Pore-water pressures at the piezo-meter installed at the central line are expected to be higherthan those at the lateral piezometers, for the same reason as

Fig. 3. Beliche Dam: main cross section.


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discussed earlier for the Beliche Dam and because the rigidcutoff wall may attract stresses that generate further incre-ments in pore-water pressures.

After dam completion and before the first impounding,piezometric heads decrease progressively during the consoli -dation process (Fig. 6 a ; Fig. 6 b, curves 4 and 5).

During the first impounding, measurements indicate thatchanges induced by the rapid rise in the water table weremore significant at the downstream piezometer (Fig. 6 a ;Fig. 6 b, curves 6 and 7). Upstream increments were insteadexpected to be higher than downstream increments. In con-trast, some months after the complete impounding, the spa-tial distribution of the piezometric heads became consistentwith a typical upstreamdownstream seepage process, withmeasured piezometric heads decreasing from the upstreamto the downstream piezometers (Fig. 6 a ; Fig. 6 b, curve 10).

In short, at the Beliche Dam the spatial distribution of pore-water pressures is consistent with that expectedthroughout the entire dam life. At the Polverina Dam, thedistribution of pore-water pressure appears to be somewhatanomalous from the beginning of construction until the endof the trial fills, but a more typical trend was observed a fewmonths following the complete impounding.

Interpretation of pore-water pressuredistribution

General aspectsRepresentativeness of pore-water pressure measurements

due to a major or minor spatial continuity of the actual dis -tribution may change substantially during the life of the damas a result of changes in saturation and drainage conditions.When a soil is in an unsaturated state, negative values of pore-water pressure are strongly affected by the retentioncharacteristics of the soil. For this reason, small spatialchanges in grain-size distribution and (or) in compaction wa-ter content may produce significant scattering in negativepore-water pressure values. Poor representativeness of mea-surements may occur, especially when the water phase iscomposed of isolated menisci. If the water phase becomescontinuous, reequilibrium processes are likely to increasespatial continuity of pore-water pressures. This means that if a soil is in an unsaturated state, pore-water pressure mea-surements would have a point-based validity while the de-gree of representativeness increases with the increasingdegree of saturation.

Under saturated conditions, representativeness of positive

Fig. 4. Piezometric head measured across the core of the Beliche Dam during construction and the first stages of operation: ( a ) timehistories; and ( b) isochrones at the selected times indicated in ( a ).


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pore-water pressure measurements depends essentially onthe stage reached by the hydraulic reequilibrium processaround the measurement point.

Under nearly undrained conditions (rapid constructionprocess or quick and significant changes of the impoundinglevel), pore-water pressure changes are induced by totalstress increments. Mechanical nonhomogeneities may maketotal stress discontinuous (see Fig. 2 a ), so pore-water pres-sures may also result in discontinuous trends. Pore-waterpressure scattering may also be due to hydraulicnonhomogeneities in the period during which they producedifferent rates of hydraulic reequilibrium. Pore-water pres-sure differences may increase between zones characterizedby higher permeability, where reequilibrium rapidly takesplace, and zones characterized by lower permeability, wherereequilibrium is still inhibited.

Under nearly undrained conditions, pore-water pressurescattering produced by both mechanical and hydraulicnonhomogeneities may be relevant. Because at these stagesmeasurements are poorly representative, it is preferable not

to use few measurement points to rebuild the spatial distri-bution of pore-water pressure.Significant reequilibrium processes in the water phase

tend to relate pore-water pressure only to hydraulic proper-ties and boundary conditions and to reduce pore-water pres-sure sensitivity to mechanical nonhomogeneities, along withthe associated scattering. If the construction process is slow,if long consolidation periods occur after construction, or if changes in the impounding level are slow, pore-water pres-sures are expected to be influenced essentially by nonhomo-geneities in permeability. Under drained conditions,nonhomogeneities in permeability cannot produce disconti-nuities in the pore-water pressure distribution but only

changes in pore-water pressure gradients. Under suchconditions, measurements should therefore be sufficientlycontinuous to allow a rebuilding of spatial trends of pore-water pressures.

Sensitivity of pore-water pressure to mechanical

nonhomogeneitiesThe presence of mechanical nonhomogeneities and thesensitivity of pore-water pressure to the latter may be crucialin determining the degree of pore-water pressure representa-tiveness over the dam life. The two following examples pro-vide a deeper insight into factors enhancing pore-waterpressure sensitivity with regard to mechanical nonhomo-geneities during the construction and impounding stages.The dam geometry in Fig. 7 is analysed by assuming lin-early elastic behaviour for the fill materials. A coupled un-saturated approach is adopted for the vertical core (seeAppendix A for details), whereas an uncoupled approach isassumed for the shells. Nonhomogeneity is quite idealized,with a stiffer zone located inside the core. Its Youngs modu-

lus is four times as high as the core Youngs modulus. Thenonhomogeneity is placed nonsymmetrically with respect tothe core axis.

Differences between calculations carried out with andwithout nonhomogeneity are used to evaluate the sensitivityof pore-water pressures with regard to nonhomogeneity. Thecomparison between the homogeneous and the nonhomoge-neous cases is made along a horizontal axis placed justabove the mechanical nonhomogeneity (Fig. 7) at the end of a simulated construction process.

During construction of an earth dam, hydraulicreequilibrium processes are enhanced if the construction rateis low or if the permeability coefficient is high; for a given

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Fig. 5. Polverina Dam: main cross section.


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Fig. 6. Piezometric heads measured across the core of the Polverina Dam during construction and the first stages of operation: ( a ) timehistories; and ( b) isochrones at the selected times indicated in ( a ).

Fig. 7. Geometric scheme of a zoned earth dam, used for simulating construction and impounding stages under plane strain conditions.


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dam geometry and stiffness properties, a parameter that in-fluences hydraulic reequilibrium is the nondimensional ratiov / k between the average rate at which the fill level increases(v) ([ L / T ]) and the permeability coefficient ( k ) ([ L / T ]).

The construction process was simulated with different val-ues of the ratio v / k . Figure 8 shows pore-water pressures pre-dicted for six values of v / k . With increasing v / k , that is,moving toward undrained conditions, the pore-water pres-sure predicted for the nonhomogeneous case tends to divergemore and more from that computed for the homogeneouscase. Above a given threshold of v / k (v / k = 1 10 5), whennearly undrained conditions are reached, results remain un-changed. In contrast, the effects of nonhomogeneity tend todisappear progressively with decreasing v / k , thus enhancinghydraulic reequilibrium inside the core. Pore-water pressuredistributions of the homogeneous and nonhomogeneouscases are equal for a second threshold of v / k (v / k = 7 10 3),below which nonhomogeneity does not induce any apprecia-ble effect.

The case of v / k = 1 105 is also analyzed during the im-pounding stages, which are simulated by assuming that theimpounding level rises up instantaneously, just after con -struction, and does not change with time (Fig. 9). Significantdifferences in pore-water pressures between the nonhomoge-neous and the homogeneous cases arise at the end of con-struction (Fig. 9 a ). Discrepancies persist during the early

stages of impounding (Fig. 9 b, curves b and c). Subse-quently, pore-water pressure changes indicate that with timehydraulic reequilibrium reduces pore-water pressure sensi -tivity to nonhomogeneity, until distributions obtained withand without nonhomogeneity nearly coincide (Fig. 9 b,curves d and e).

The above examples clearly show that sensitivity to me-chanical nonhomogeneity depends on the degree of hydrau-lic reequilibrium, which during construction is essentiallycontrolled by the ratio v / k .

The Polverina and Beliche damsThe above discussion helps to explain why difficulties en-

countered in interpreting pore-water pressures measured atthe Polverina Dam ( v / k = 2 10 4) were greater than thoseencountered in interpreting pore-water pressure measure-ments at the Beliche Dam ( v / k = 2 10 2).

For the Polverina Dam, the v / k value of two orders of magnitude greater than that of the Beliche Dam (the greatervalue is essentially related to the lower permeability coeffi-cient) could inhibit the reequilibrium processes substantially,producing nearly undrained conditions. During construction,complex stress distributions and evolution are likely to oc-cur, as a result of nonhomogeneities inside the core due tothe presence of the rigid cutoff wall and to the mechanicalinteraction between core and stiffer filters, which may also

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Fig. 8. Pore-water pressure distributions computed at the end of construction in the core along a horizontal axis under different drain-age conditions: ( a ) in the presence of a dishomogeneity in the core; and ( b) under the hypothesis of a homogeneous core.


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be nonhomogeneous. Nearly undrained conditions in thecore could have made actual pore-water pressures dependenton complex stress distributions. As highlighted before, under

such conditions even hydraulic nonhomogeneities may haveenhanced the complexity of the pore-water pressure distribu-tion. Simple behavioural models seem therefore to be unsuc-cessful in interpreting measurements. During the life of thedam, significant reequilibrium processes make pore-waterpressures progressively insensitive to mechanical nonhomo -geneities. Predictions provided by simple behavioural mod-els become consistent with the distribution and evolution of pore-water pressure. In short, from the beginning of con-struction until the end of the trial fills, the piezometric headdistribution appears to be somewhat anomalous, but then ittakes on a more predictable trend. Rather than assuming thatmeasurement reliability changes over time, it seems morereasonable to consider an increase in representativeness of

the data with time.For the Beliche Dam, the low construction rate and thehigh permeability render possible significant hydraulicreequilibrium processes; pore-water pressures are then repre-sentative, and their distributions are always consistent withwhat might be expected.

Representativeness and back analysis

The interpretation of measurements may require morecomplex approaches based on mathematical and numericalmodelling of the problem. Model parameters are determined

either from results of laboratory tests carried out on the con-struction materials or from back analyses of the observedbehaviour. A back-analysis procedure requires a reference

period, within which results from analysis prediction are ad- justed to those coming from dam monitoring. As previouslypointed out, the models typically adopted for the analysesusually assume that wide zones of the dam are made of ho-mogeneous material so that inside each zone all physicalquantities are characterized by a continuous distribution. Asa consequence, these models may succeed only in interpret-ing representative measurements.

From the above discussion, it emerges that measurementsof total stresses or local strains may not be appropriate asreference quantities because of their poor representativeness;boundary and internal settlement measurements should in-stead be strongly considered in simulating dam behaviour.

Pore-water pressure measurements should be consideredas reference data in a back-analysis process, essentiallywhen hydraulic reequilibrium processes make these mea-surements representative.

To clarify these concepts, some results of the back analy-sis of the Polverina Dam are presented. The discretized ge-ometry of the dam shown in Fig. 10 was adopted to predictpiezometric heads and settlements of the Polverina damthrough a back-analysis procedure. The dam is made of dif-ferent zones, each considered homogeneous. The mathemati-cal model used for the back analysis is that described inAppendix A. The modified Cam clay model was adopted todescribe the mechanical behaviour of the silt layer in the

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Fig. 9. Pore-water pressure distributions computed in the core along a horizontal axis for v / k = 1 105 (a ) at the end of construction;and ( b) during the impounding stages, in the presence of core nonhomogeneity and under the hypothesis of a homogeneous core.


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foundation soil and the core. For the remaining zones, anelastic perfectly plastic nondilatant soil behaviour wasadopted, assuming a Drucker yield surface.

Figure 11 shows predicted versus measured piezometricheads in terms of both time histories (Fig. 11 a ) and isoch-rones (Fig. 11 b).

Referring to pore-water pressures, Fig. 11 shows how con-sistency between measurements and predictions was ne-

glected during construction and until the first impounding,as measurements were considered to be poorly representa-tive during this period. In Fig. 11 b, measured and computedvalues are in poor agreement (see curves 28). A fair agree-ment was instead obtained some months after the first im-pounding, when hydraulic reequilibrium processes renderedthe pore-water pressure distribution more continuous and thepore-water pressure measurements more representative

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Fig. 10. Finite-element mesh used for the Polverina Dam.

Fig. 11. Measured versus computed piezometric heads of the Polverina Dam during construction and early stages of operation: ( a ) timehistories; and ( b) computed (dashed lines) and measured (continuous lines) isochrones at the selected times indicated in ( a ).


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(Fig. 11 b, curve 10). In the back-analysis work, this wasfound to be the key to obtaining a satisfactory agreement be-

tween predicted and measured pore-water pressures over the30 years of dam operation (Fig. 12).

Figure 12 shows that modern analysis tools could interpretobservations quantitatively, even if a number of factors (deadload during construction, consolidation process, impoundingconditions) affect measurement evolution and spatial distri-bution. This, however, is possible only if measurements arerepresentative and factors affecting predictions are the sameas those affecting measurements.

Conclusions

The mechanical behaviour of earth dams can essentiallybe characterized by interpreting monitored physical quanti-ties. Assessments of measurement reliability and measure-ment interpretation are two different aspects of the sameactivity, which consists in comparing measurements with theexpected behaviour provided by a mathematical model. Lack of measurement reliability or anomalous dam behaviour isoften invoked when inconsistencies between the predictedand the observed behaviour occur. Malfunctioning of instru-ments, drawbacks during instrument installation, or inaccu -racy during the carrying out of measurements often representsthe source of such inconsistencies. However, inconsistenciesmay derive from the inadequacy of the interpretative processas well.

The measurement of displacements and seepage is charac-terized by high representativeness, with spatial trends that

are similar to those predicted by behavioural or mathemati-cal models. Stress and strain measurements may be discon-tinuous and therefore poorly representative.

Pore-water pressures may be poorly representative underlow degrees of saturation or under nearly undrained condi-tions; their representativeness rises with increasing degreesof saturation and enhancement of hydraulic reequilibriumprocesses. For these reasons, pore-water pressure representa-tiveness may change over the lifetime of the dam. The engi-neer should make the effort to characterize these stateconditions in order to understand representativeness, beforeattempting to interpret measurement trends.

The analysis of the representativeness of measured quanti-ties can help in determining the number of instruments re-quired to characterize the actual distribution of a givenquantity. Since they are characterized by poorly representa-tive measurements, stresses and local strains in any stateconditions of the soil, together with pore-water pressures instrongly unsaturated or nearly undrained conditions, shouldbe experimentally detected on the basis of many measure-ment points; in contrast, settlements and seepage in any stateconditions of the soil and pore-water pressures when signifi-cant reequilibrium processes take place can be detected onthe basis of a few measurement points because these quanti-ties are characterized by highly representative measure-ments.

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Fig. 12. Measured versus computed piezometric heads of the Polverina Dam during construction and operation.


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Measurements that are less representative or, in otherwords, more sensitive to mechanical nonhomogeneity tendto be sensitive even to the nonhomogeneity caused by thepresence of the measurement instrument itself and to differ-ences in compaction that typically characterize soil placedaround the instrument. Poor representativeness and unreli-ability may be related to each other.

The assessment of measurement representativeness is fun -damental in establishing which monitoring data should beused in back-analysis processes and which periods should bechosen to obtain satisfactory agreement between predictionsand observations. The first step is to evaluate the representa-tiveness of the available monitoring data, because only rep-resentative quantities should be involved in a back-analysisprocess.

Acknowledgements

The authors with to thank the Registro Italiano Dighe(RID) for its financial support for this research project, and,in particular, engineers Angelica Catalano, Vincenzo

Chieppa, and Claudia Russo for their fruitful discussion andsuggestions. The valuable comments of Prof. SebastianoRampello are also gratefully acknowledged.

References

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Gould, J.P., and Lacy, H.S. 1993. Seepage control in dam rehabili-tation. In Proceedings of the Geotechnical Practice in Dam Re-

habilitation, North Carolina State University, 2528 April 1993.ASCE Geotechnical Special Publication No. 35, pp. 240255.ICOLD. 1982. Automated observation for the safety control of

dams. International Commission on Large Dams, CIBG ICOLD,Paris, France. Bulletin 41, pp. 120.

Marsal, R.J. 1958. Analisis de asentamientos en la presa PresidenteAleman. Instituto de Ingenieria, National Autonomous Univer-sity of Mexico, Mexico City, Mexico, Oaxaca, No. 5.

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Naylor, D.J., Maranha, J.R., Maranha das Neves, E., and VeigaPinto, A.A. 1997. A back-analysis of Beliche Dam.Gotechnique, 47(2): 377381.

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Geoenvironmental Engineering, ASCE, 124 (10): 923932.Pagano, L., Silvestri F., and Vinale, F. 2001. A back-analysis of

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Appendix A. Coupled approach used for theanalyses

The coupled unsaturated approach adopted in this work consists of the following set of governing equations:(i) equilibrium; ( ii) water continuity equation (with a vari-

able degree of saturation, Sr); (iii ) equation of water reten-tion characteristic curve; and ( iv) soil skeleton stressstrainrelationship.

In this approach, air pressure is assumed to be equal to theatmospheric value, so the continuity equation of air does notneed further consideration.

The ABAQUS code and the finite-element technique were

used to discretize the spatial problem, and the finite-difference technique was adopted to discretize the problemin the time domain.

The soil skeleton constitutive law is defined within amonotensorial Bishop-based approach, following the sugges-tion by Schrefler (1991) to define the effective stress compo-nents:

[A1] ij = ij ij Sruw

where ij represents total stress components; ij = 1 for i = j;ij = 0 for i j; Sr is the degree of saturation; and uw is thepore-water pressure.

The approach requires that initial conditions in terms of

pore-water pressure, effective stress components, degree of saturation, and void ratio be defined.During the simulation of the construction stages, horizon-

tal element layers are progressively activated. All layer acti-vations develop in three steps.

In the first step, the elements of the layer are introducedin an undeformed shape, with the proper initial conditionsbut without weight. Initial conditions consist of null totalstress components ( ij(0)) and an initial negative pore-waterpressure, uw(0) , representing, with the initial degree of satura-tion, the soil state after compaction. Initial conditions interms of effective stress components ( ij ( )0 ) are defined inaccordance with eq. [A1], as

[A2] ij ( )0 = ij Sr(0) uw(0)

In the second step, the dead weight of the layer is appliedin a very short time.

In the third step, consolidation is allowed over a periodconsistent with that obtained from the actual embankmentconstruction curve.

During both the second and third steps, pore-water pres-sure boundary conditions at the top of the activated layer areforced to stay at the uw(0) value, in order to avoid hydraulicinconsistency when the subsequent layer is activated with itsinitial conditions at uw(0) .

On the lateral boundaries of the region where a coupledanalysis is assumed, a seepage surface is adopted during

construction. This is applied by forcing a dependency of wa-ter velocity normal to the boundary ( vwb) on pore-water pres-sure values ( uwb) (Pagano 1997):

[A3 a ] vwb = 0 if uwb < 0

[A3 b] vwb = k *uwb if uwb 0

where k * is a constant that influences the flow rate normal tothe boundary.

When pore-water pressure at the boundary is negative,eq. [A3 a ] forces that boundary to be impermeable.

When water pressure at the boundary pore tends to as-sume a value that exceeds the zero value, eq. [A3 b] forces

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water velocity at the boundary, vwb , to increase proportion-ally, causing a lowering of the pore-water pressure down toalmost zero. Such lowering occurs if k * is large, comparedwith k / wc, where k is the permeability of the medium; w isthe specific water weight; and c is a characteristic lengthscale (Pagano 1997).

During the impounding stages, known pore-water pressure

values are applied along the wet boundary of the regionwhere the analysis is assumed coupled. A seepage surface isinstead applied on the dry boundary.

References

Pagano, L. 1997. Steady state and transient unconfined seepageanalysis for earthfill dams. In Proceedings of the VIII ABAQUSUsers Conference, Milan, 46 June 1997. Hibbitt, Karlsson,and Sorensen, Inc. pp. 577585.

Schrefler, B.A. 1991. Recent advances in numerical modelling of geomaterials. Meccanica, 26: 9399.

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