Observed and calculated arching in the clayey silt of an earth dam

8/12/2019 Observed and calculated arching in the clayey silt of an earth dam

1/7

Observed and calculated arching in the clayey siltof an earth dam

Reza Imam, Assistant Professor, & Nariman Mahabadi, MSc StudentDepartment of Civil and Environmental EngineeringAmirkabir University of Technology, Tehran, Iran

ABSTRACTArching in the core of earth dams may result from the partial transfer of weight of the more flexible, fine-grained corematerials to the stiffer shell, filter, or abutment materials. This leads to a reduction in vertical stresses in the core,increasing the risk of hydraulic fracturing when the core is subjected to high water pressures during dam impoundment.In the current research, arching in the clayey silt core of a rockfill dam is examined based on both readings of daminstrumentation and finite element analyses of various dam sections. Since the wide rock valley of the dam variessubstantially in depth and shape along the dam longitudinal section, arching occurs differently at the various sections.Effects of cross section shape and height on arching is examined, and differences between measured and calculatedvalues are discussed with respect to the shape and height of the cross-sections analyzed.

RSUMVoilage dans le noyau des barrages en terre peuvent rsulter de la cession partielle du poids de la plus souple,

matriaux d'me grain fin la plus rigide enveloppe, un filtre, ou des matriaux de bute. Cela conduit une rductiondes contraintes verticales dans le noyau, ce qui augmente le risque de fracturation hydraulique lorsque le noyau estsoumis des pressions hautes eaux pendant la mise en fourrire du barrage. Dans la recherche actuelle, des votesdans le noyau de limon argileux d'un barrage en enrochement est examine en fonction des deux lectures del'instrumentation du barrage et les analyses par lments finis de sections diffrentes du barrage. Depuis la valle durock chelle du barrage varie considrablement en profondeur et la forme le long de la section longitudinale du barrage,des votes se produit diffremment diffrentes sections. Effets de la forme et la hauteur de coupe sur vote estexamin, et les diffrences entre les valeurs mesures et calcules sont discutes par rapport la forme et la hauteurde la croix-sections analyses.

1 INTRODUCTION

1.1 General

In earth dams, arching may occur due to differentialsettlements between various parts of the dam, especiallythe central core and the shells or the dam abutments. Asa result, the parts having higher vertical deformationtransfer some of their weight to the stiffer parts. This loadtransfer leads to the development of shear stresses at theinterfaces of the regions with different material properties,especially those with considerable contrast indeformability characteristics. Therefore, reductions in theamount of vertical and horizontal stresses at the lowerparts of the core occur and this in turn, increases thechances of fracturing due to high water pressures appliedto the core during dam impoundment. The more the coresettles compared to the shell, the greater will be the shearstresses that develop at the interfaces. Eventually, whilethe exterior parts of the core may remain attached to theshell through shear stresses, separation of the uppersection of the core from the lower section may occur(Shamsayi, 2004).

Upon application of hydraulic pressures, theaforementioned mechanisms can cause hydraulicfracturing and, eventually, piping in the dam core(Sharma, 1991). Some researchers even argue that usingsofter core materials which do not have enough shear

strength which cause suspension of these materials onthe shell might help decrease such risks (Knight et al.,1985).

1.2 The Doosti Dam

In the current research, arching in the clayey silt core ofthe Doosti dam in Northeastern Iran is examined basedon both readings of dam instrumentation duringconstruction, and finite element analysis of the variousdam sections. The Doosti dam is an earth and rockfilldam with silty clay core, located on the common border ofIran and Turkmenistan at the north 3575' latitude andeast 619' longitude. The dam height above its rockfoundation level is 79m at its deepest location; its crestlength is 655m; and, the dam width is 428 m at foundationand 15 m at crest elevations. The dam cross-section andzoning are shown in Figure 1.

The dam primary purpose is to supply water for the cityof Mashhad and for agriculture in the Sarakhs plain. Thedam water storage volume is approximately 1.25 billioncubic meters. As shown in Figure 1, the impermeable partof the dam includes a silty clay core with a permeability ofabout 7.5*10-6cm/s, placed on the intact foundationbedrock. The average plasticity index (PI) of the materialfound locally for the dam core was approximately 4,making it necessary to take into account provisions


2/7

required in the design and construction of low-plasticitycore dams.

In order to monitor the performance and behavior ofthe dam during its construction and long term utilization, acomprehensive instrumentation system consisting ofvarious devices such as total pressure cells, electrical andother types of piezometers, inclinometers, etc. was

designed and installed at various parts of the dam and itsfoundation.The dam has a stiff rockfill shell and rock abutments

and is, therefore, susceptible to arching and load transferto both its shell and abutments. Since the wide damvalley varies substantially in depth and shape at variouslocations along the dam longitudinal section, arching mayoccur differently at various transverse dam sections.Figure 2 shows a plan of the dam layout and the locationsof the six cross-sections at which numerical analyseswere performed and instrumentation readings wereexamined.

In the current study, arching ratio, which is the ratio ofthe actual vertical stress to the theoretical gravitationalstress expected due to weight of the overlying soil layers,

was determined at various depths along the centerline ofthe core in selected transverse sections using finiteelement modeling. Vertical stresses obtained from daminstrumentations are then compared with those obtainedfrom analysis, and possible causes of some observeddifferences between these values are discussed. Effectsof cross section shape and height on the potential forarching is also examined.

Figure 1. Typical cross section of the Doosti dam

2 NUMERICAL MODELLING

2.1 The Finite Element Model

In order to study the behavior of the Doosti dam duringconstruction, six sections of the dam were modeled by astep by step application of the soil layers in each section.Construction of the dams was carried out at an average

rate of 15 to 30 cm per day. However, in order to avoidexcessive increases in numerical modeling efforts, largerlayer thicknesses were used in the numerical modeling. Inthis respect, 2m thick layers were used for modeling thedam during construction. Due to the variable height of thedam at various sections, the number of layers wasdifferent, but the thickness of each layer was kept thesame and equal to 2 meters in all the sections.

Figure 2. Layout of the Doosti dam and locations of thesections selected

Except for its initial parts, the Doosti dam wasconstructed at an approximately similar time rate.Therefore, in numerical modeling of the consolidation andtime-dependent behavior of the dam, construction of eachlayer was assumed to be carried out at an average time of15 days. Boundary conditions of the model such asgeometrical conditions of the valley and the dam were

modeled such that they correspond to the actualconditions, as much as possible. Also, mesh generationwas performed automatically; and, due to the relativelycomplex geometries of the models, the meshing schemewas done using a combination of quadratic and triangularelements. Element dimensions were selected to be largerin the foundation and smaller in the areas near the dambody. Figure 3 presents the finite element models of thesix sections of the dam selected for analysis and Table 1provides a summary of specifications of these sections.

Table 1. Specifications of the selected cross sections

SectionFoundationelevation

(m)

Crestelevation

(m)

Number ofconstruction

stages

Constructiontime(day)

2-2 407 478 37 555

3A-3A 402 478 38 570

4A-4A 400 478 39 585

9-9 400 478 39 585

12-12 425 478 26 390

16-16 440 478 20 300


3/7

Figure 3. Finite element models of the dam cross-sections

2.2 Material Properties

Accuracy of prediction of earth dam deformations duringconstruction is strongly dependent on the quality ofrepresentation of the stress-strain relationships of thedam materials. In rockfill dams, actual stress-strainbehavior is controlled primarily by the properties of therockfill which depends mainly on its intact strength,method of placement and particle size distribution aftercompaction. The embankment height is a significantfactor as it determines the level of applied stresses withinthe embankment. Valley shape is also important inembankments constructed in narrow valleys due to theeffects of cross-valley arching and the resultant reductionin applied stresses. Typical stress-strain relationships ofrockfill materials obtained from field measurements duringconstruction show that this relationship is generally non-

linear, and has a general trend of decreasing secant (andtangent) modulus with increasing applied stress (Hunterand Fell, 2002).

Based on the above, the Duncan-Chang nonlinearhyperbolic constitutive model was used in the currentfinite element modeling. This model is widely applied inmodeling soil behavior and is based on the shape of thestress-strain curve obtained from drained triaxialcompression tests of both clay and sand, which can beapproximated by a hyperbola with a reasonable degree ofaccuracy. Therefore, the stress-strain relationship of thesoil is assumed to be nonlinear elastic, and the failurecriterion is based on the Mohr-Coulomb two parametermodel, with as the friction angle and c as the cohesion.

In the Duncan-Chang model, through using Eiand v

i

as the initial tangent Youngs modulus and tangentPoissons ratio, themodel describes the three importantcharacteristics of soils: non-linearity, stress-dependency,and inelastic behavior. Both E

iand v

iare stress path

dependent. At a given confining stress level, distinction ismade between a primary loading stiffness, E

iand an

unloading and reloading stiffness, Eur

.

The hyperbolic stress-strain curve is defined using thefollowing equation for the stress-dependent elastictangential modulus (E

t) at a given stress condition:

[1]

in which 1

and 3

are the major and minor principal

stresses, respectively; pais the atmospheric pressure; K is

a modulus number, which is a dimensionless parameterrepresenting Young's modulus; and, n is a modulusexponent, which governs the stress dependency of E

ion

3. The unloading and reloading behavior is defined

using Eq. 2:

[2]

in which Kuris a modulus number similar to Eibut used for

unloading and reloading, and other variables are asdefined before.

The material properties used in Duncan-Changmodeling of the Doosti dam are presented in Table 2.Original material properties were estimated using resultsof laboratory triaxial, consolidation and direct shear tests.These properties were later adjusted based on backanalyses of dam settlements recorded by inclinometers

Et = 1 Rf1 sin(1 3)2c cos + 23sin

2

K. Pa 3Pan


4/7

installed at various locations within the dam core and shell(Mahabadi, 2011).

Table 2. Material properties used in numerical analyses

Zone

(ton/m3) K Kur n RfC

(ton/m2)

Core 2.1 125 150 0.45 0.7 10 26

Filter 2.2 400 600 0.3 0.8 0 40

Rockfill 2.3 600 900 0.24 0.85 0 40

3 ANALYSIS RESULTS

3.1 Stresses and Strains

During the current study, several analyses for thedetermination of stresses and deformations in the dambody and clayey silt core were carried out. Contours of

settlements and stresses were obtained for all the sixsections shown in Figure 3. As an example, resultsobtained for the maximum section, Section 4A-4A areshown in Figure 4.

Figure 4(a) shows the calculated deformations at theend of construction. The figure shows that the maximumdeformations occur at about the middle height of the core.

Also, contours of vertical stresses and the occurrence ofarching may be observed clearly in Figure 4(b), whichshows that the vertical stresses in the core are smallerthan those in the adjacent areas within the shell.

The pore water pressures developed at the end ofconstruction are shown in Figure 4(c). These porepressures are produced due to consolidation of the soilsduring construction and, as can be seen from the figure,

are very small compared to the total vertical stressesdeveloped in the core. The low plasticity, clayey silt coreallows for a relatively rapid dissipation of the porepressures developed during consolidation of the core. Asa result, there is no significant difference between theeffective and total vertical stresses developed in the damat the end of construction.

3.2 Arching Ratios

The degree of arching in the core of earth and rockfilldams may be determined using the Arching Ratio (AR),which is defined at any point using the followingrelationship:

Arching Ratio = [3]

in which p is the vertical stress measured by the totalpressure cell at the current point, is the unit weight ofsoil and h is the height of soil above the current point.The AR is inversely proportional with the degree ofarching. A lower AR is an indication of greater arching.

Figure 4. Contours obtained for section 4A-4A: (a) Totaldeformations (m) (b) Total vertical stresses (kPa) (c) Porepressure (kPa) (d) Effective vertical stress (kPa)

Calculated variations of arching ratio with depth at theaxis of the Doosti dam core are shown in Figure 5 for thesix selected sections. A summary of the calculatedmaximum and minimum ARs at the end of construction isalso shown in Table 3.

As can be seen from Figure 5, minimum arching ratios,which correspond to the maximum amount of arching,range from about 0.64 to 0.66 at the various crosssections. These arching ratios occur at approximately aquarter height of the dam from the foundation.

Table 3. Summary of the calculated arching ratios

SectionMinimum arching ratio

Maximum archingratio

Quantity Location Quantity Location

2-2 0.64 H 0.97 Crest

3A-3A 0.66 H 0.96 Crest

4A-4A 0.65 H 0.97 Crest9-9 0.66 H 0.97 Crest

12-12 0.64 H 0.90 Crest

16-16 0.64 H 0.92 Crest

(a)

(b)

(c)

(d)


5/7

Figure 5. Calculated variations of arching ratio with depth at the axis of the Doosti Dam cross-sections

The lowest values of AR are obtained for sections 2-2,12-12 and 16-16, in which the cross-sections havesmaller widths and are supported by bedrock on theirsides. As a result, more pronounced arching effects areobserved in these sections. Compared to other sections,in these sections,ARs obtained in the dam crest are alsolower, indicating more pronounced arching effects.

Calculated maximum arching ratios, which correspond

to minimum arching effects, vary from 0.90 to 0.97 at thevarious cross-sections, and they occur at the dam crest inall the sections. Contact areas between the core and shellat elevations above the dam crest are not available and,as a result, shear stresses developed between the coreand shell are smaller, resulting in less hanging of the coreto the shell and less decrease in the vertical gravitationalstresses in the core in these locations.

4 MEASURED AND CALCULATED ARCHINGEFFECTS

In order to verify accuracy of the calculated verticalstresses and the corresponding calculated archingeffects, results of the numerical analyses are comparedwith stresses measured by the total pressure cellsinstalled in the core of the Doosti dam, as reported byToosab Consulting Engineering Company (2005). The

total pressure cells located in the largest section 4A-4Awere damaged. Therefore, calculated and measuredstresses are compared for cross sections 2-2, 3A-3A, 9-9,12-12 and 16-16. Figure 6 shows locations of the totalpressure cells installed in the aforementioned sections.The first number after the letters TPC refers to thesection in which the cell is installed.


6/7

Figure 6. Locations of the total pressure cells installed inthe dam core sections

Figure 7 shows comparisons between the observedand calculated total vertical stresses at the locations ofthe pressure cells. This figure indicates a good generalagreement between results of the numerical analyses andreadings of dam instrumentation. However, except forSection 16-16, in all other sections, measured stressesare somewhat higher than calculated stresses, indicatingthat actual arching effects are somewhat smallercompared to calculated effects in these sections.

Measured stresses indicate that arching effects aresmaller in the wider sections 2-2, 3A-3A and 9-9 andhigher in the narrower sections 12-12 and 16-16 such thatin the latter section, measured stresses are considerablysmaller than calculated stresses. It is noted that thecalculated stresses are obtained from two-dimensionalanalyses of the dam sections, which do not consider thecontributions of 3D effects to arching. It is likely that inthe narrower sections and, particularly, in the narrowSection 16-16 closest to the dam abutment, some 3Deffects lead to more pronounced arching and therefore,actual vertical stresses in the core are smaller thanstresses obtained from 2D analysis of the dam section.

The degree of influence of arching depends also on thelocation of the point under consideration within the dam

core, both laterally (i.e. how close it is relative to theshell/filter) as shown by Mahabadi (2011), and vertically,as shown in Figure 5. Figure 6 shows that the pressurecells are installed at various lateral and vertical locations.Some differences in the observed and calculated archingeffects may be attributed to factors that have not beenconsidered in the 2D numerical analyses of the damsections. Table 4 compares the minimum arching ratioscalculated and observed at the selected cross-sections.

Table 4. Comparison between calculated and observedminimum arching ratios at the end of construction

Instrument

Observed arching

ratio

Calculated arching

ratioTPC-2-2 0.67 0.64

TPC-3A-2 0.67 0.61

TPC-9-2 0.50 0.46

TPC-12-2 0.66 0.66

TPC-16-1 0.54 0.65

Figure 7. Total vertical stress in the core of dam sections

TPC-2-2 TPC-3A-2 TPC-9-2 TPC-12-2 TPC-16-2

Section 2-2

Section 3A-3A

Section 9-9

Section 12-12

Section 16-16

1


7/7

5- CONCLUSIONS

Finite element analysis of six transverse sections of theDoosti Dam showed that arching effects in the clayey siltcore of the dam vary with elevation within the core, widthof the section, and proximity of the rock abutments to thedam core. Highest arching effects were calculated at

about one fourth of the dam height from the foundation,and lowest effects were calculated at the dam crest.Arching effects appear to be more pronounced atnarrower sections and closer to the dam abutments where3D effects are present.

Vertical stresses measured by pressure cells installedin the dam core at various sections and elevations weregenerally in good agreement with calculated stresses.Therefore, it may be concluded that two dimensional finiteelement modeling of the dam behavior using non-linearelastic constitutive modeling of the dam material providesa relatively good estimation of vertical stresses, includingthe effects of arching on these stresses. However, some3D effects seemed to have influenced the measuredstresses at some sections, but they could not be

considered in the current 2D modeling. Except for thenarrow section nearest to the dam abutment, archingeffects obtained from measurements of total pressurecells were smaller than those obtained from theaforementioned calculations.

REFERENCES

Hunter, G. and Fell, R. 2002. The deformation behaviourof rockfill. UNICIV Report No. R-405, the University ofNew South Wales, School of Civil and EnvironmentalEngineering.

Knight, D.J., Davis, P.D., Naylor, D.J. 1985, Stress-strainbehavior of the Monavasu soft core rockfill dam:prediction, performance and analysis", Proceeding of15th. International Congress on Large Dams,Lausanne, 1985, 56, vol. I, PP. 1299-1326.

Mahabadi, N. 2011. Analysis of the behavior of Doostidam during construction and impounding andcomparison with results of instrumentation. MScthesis, Amirkabir University of Technology. Tehran,Iran.

Shamsayi, A., 2004. Design and construction of reservoirdams (in Persian). Vol. 2, Science and IndustryUniversity Publication, Iran.

Sharma H.D. 1991. Embankment Dams. published byRaju Primlani for Oxford and IBH publishing co.

Toosab Consulting Engineering Company. 2005. Thirdphase report of Doosti Storage Dam: Report of Dammonitoring to the end of construction, Report No.232093-2475-1, Mashad, Iran.

Documents

Observed and calculated arching in the clayey silt of an earth dam