CONCRETE THERMAL STRAIN.pdf

8/10/2019 CONCRETE THERMAL STRAIN.pdf

1/34

Concrete Thermal Strain 345

CONCRETE THERMAL STRAIN, SHRINKAGE AND CRACKING ANALYSISFOR THE PANAMA CANAL THIRD SET OF LOCKS PROJECT

Vik Iso-Ahola, P.E. 1 Bashar Sudah, P.E. 2

Vincent Zipparro, P.E. 3

ABSTRACT

The Panama Canal Authority (ACP) has undertaken the Panama Canal ExpansionProgram to increase the Canals capacity in order to meet the continuous growth in thenumber of transits and vessel size. The expansion of the Canal involves the constructionof two new lock facilities, one on the Atlantic side and another on the Pacific side eachwith three chambers; the excavation of a new Pacific access channel to the new locks,and widening and deepening of the existing navigational channels and entrances; andincreasing the elevation of Gatun Lakes maximum operating level.

Two-dimensional and three-dimensional incremental finite element thermal analyseswere performed using ANSYS software to estimate the temperature distribution withinthe new lock walls, lock heads, crossunders, central connections, and chamber conduitswhich consist of reinforced mass concrete structures. The estimated temperatures fromthe finite element model were used to estimate the thermal strains and potential forcracking using procedures outlined in ACI 207. The overall evaluation was used todetermine optimal concrete placement temperatures, contraction joint spacing, and tocomply with the Employers Requirements regarding concrete temperature gradientlimitations. Potential for cracking due to drying shrinkage was also evaluated and crackdepths were estimated based on the anticipated moisture distribution within the concretestructures.

This paper presents the thermal strain, drying shrinkage strain, and cracking potentialanalyses that have been performed for the new lock walls, lock head structures, andrelated concrete structures for the Panama Canal Third Set of Locks Project. The resultsof these analyses were used as key inputs to concrete mixes and their placementtemperatures which are designed to withstand for 100 years the deleterious effects ofseawater and load cycling of hydrostatic pressures during filling & emptying of lockchambers.

INTRODUCTION

Completion of the new Pacific and Atlantic Lock Complexes for the Panama CanalExpansion Project (illustrated in Figure 1) includes construction of several massiveconcrete sections that consist of lock walls, lock heads, central connections, and

1 Principal Engineer, MWH Americas Inc., Walnut Creek, California, [email protected] 2 Structural Engineer, MWH Americas Inc., Walnut Creek, California, [email protected] 3 Design Engineer, Panama Canal Third Set of Locks Project, MWH Americas Inc., Chicago, Illinois,[email protected]


2/34

346 Innovative Dam and Levee Design and Construction

crossunders. These structures are being constructed using two different concrete mixtypes, a Structural Marine Concrete (SMC) mix and an Interior Mass Concrete (IMC)mix. A typical concrete section consists of IMC encapsulated by SMC facing. The SMCfacing is typically 60 cm thick while the IMC varies in thickness based on the geometryof the structures. A typical lock wall monolith (Figures 2 and 3 in the following section)

is approximately 18 meters wide, 30 meters high and 29 meters long. Each lock wallmonolith contains two 6.5 meter high culverts; the main and secondary culverts are 8.3and 7 meters wide, respectively. The culvert walls vary in thickness from 1.5 meters(center wall) to 4 meters. The wall stem thickness ranges from 12 meters at the bottom to2 meters at the top. The designed lift heights range from 2 meters (culvert) to 3.75 meters(wall stem), and are constructed with IMC and SMC facing. Another feature of the lockstructures include crossunders that provide utility and personnel access underneath thelock chambers and are constructed of SMC (Figure 4).

Figure 1. Artistic Rendering of the Panama Canal Third Set of Locks Project

The lock head structures (Figure 5) that house the lock chamber rolling gates areapproximately 38.4 meters high, 67 meters wide, and 20 meters in section length, withwall thicknesses varying from roughly 6.6 to 14 meters. Similar to the lock wallstructures, the lock head structures are constructed with IMC and SMC facing. The lockhead structures are designed with thick concrete sections that provide housing for therolling gates when they are in the open position, and protected dry bays that allow formaintenance and access to the gates, which are approximately 33 meters high by 58meters long and either 8 or 10 meters wide.

The culverts within the lock wall sections are part of the filling and emptying system thatroutes water from the lock chambers to either the Water Savings Basins (WSB) adjacent


3/34


to the lock structures (when they are used), or from Gatun Lake and chamber to chamberand to the Ocean when Lake to Ocean operations are used. Efficient routing of waterrequires a complex culvert geometry that includes curved conduits and connectionswhich result in thick concrete sections (Figures 6 & 7) constructed with IMC and SMCfacing.

Mix designs for the IMC and SMC utilize onsite materials, local cement and pozzolan,and imported silica fume to produce mixes that meet ACP temperature and durabilityrequirements, which stipulate a minimum 100-year life for the structures, including, butnot limited to, protection of the reinforcing steel for resistance against corrosion fromchloride (sea water) attack.

THERMAL CRACKING EVALUATION

In order to mitigate concrete cracking potential and meet ACP requirements fordurability, a thermal cracking analysis was performed in order to select the optimal

combination of concrete mixes and placement temperatures. Initially, a finite elementthermal evaluation was performed to consider various temperatures and placementscenarios. Thereafter, both mass and surface gradient analyses, including estimated straincomputations, were executed to perform the cracking evaluation. By combining theresults from the finite element model with simplified strain computations, estimates ofcracking potential for various combinations of mixes and placement temperatures were

provided as changing geometry (e.g. over-excavation), mix designs, and coolingconstraints were encountered during construction. The thermal studies were performed ingeneral accordance with ETL 1110-2-542 (USACE, 1997).

Thermal Finite Element Analysis

Finite element thermal analysis was performed to estimate time-dependent temperaturedistributions and peak temperatures at specific points in both the Pacific and Atlantic lockcomplexes to verify ACP requirements for concrete temperature differentials andthereafter as input into thermal strain computations.

Two-dimensional and three-dimensional finite element models for the incrementalthermal analyses were created to represent the typical geometry of the Pacific andAtlantic lock walls, lock heads, crossunders, central connections, and chamber conduits.Using the computer program ANSYS Version 12.1, these models were developed tosimulate phased construction of the concrete lifts, estimating the maximum temperaturerise at critical locations in the structures. Representative finite element models for eachstructure analyzed are presented in Figures 1 to 6 below.


4/34


Figure 2. Pacific Lock Wall Model Figure 3. Atlantic Lock Wall Model

Figure 4. Cross-under Model Figure 5. Lock Head Model

Figure 6. Central Connection Model Figure 7. Chamber Conduit Model

Material properties used in the finite element thermal models were selected fromlaboratory test results and typical values published for mass concrete mixes with

pozzolan and basalt aggregates, and are summarized in Table 1 below.


5/34


Table 1. Summary of Material Properties

Properties Units

InteriorMass

Concrete

(IMC)

StructuralMarine

Concrete

(SMC)Specific Heat ( C h) kJ / kgC 0.83 0.83Thermal Conductivity ( K ) kJ / mhC 3.74 3.74Density ( ) kg / m 3 2508 2523Diffusivity (h2) m2 / h x 10 -3 1.79 1.78Adiabatic Temperature Rise C 26.8 52.3Ultimate Compressive Strength ( F c) MPa 30.3 59.2Ultimate Modulus of Elasticity ( E c) GPa 38.9 43.3Coefficient of ThermalExpansion (CTE) mil/C 8.0 8.0

Adiabatic temperature rise curves were developed in the laboratory for typical SMC andIMC mixes used in the lock structures. These curves were used to develop the concreteheat generation functions used to simulate heat rise within the finite element model(Figure 8).

Figure 8. Adiabatic Temperature Rise Curves for Concrete

The average daily temperatures at the Pacific and Atlantic sites, including the effects ofthe diurnal cycle, were applied as ambient temperatures at the air-exposed boundaries of

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35 40 45 50

T e m p e r a t u r e R i s e

( C

)

Age (days)

Adiabatic Temperature Rise Curves

Structural Marine Concrete Interior Mass Concrete


6/34

350

the Fdiur

Figu(

Fig(

In ad

bouncoef ETL

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

T e m p e r a t u r e

( C

)

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

T e m p e r a t u r e

( C

)

EM modelsal cycles fo

re 9. Averaalboa Stati

re 11. Aver Gatun Stati

dition, a codaries, simuicient (film1110-2-365

Pacific46.4 kJ/h.22.9 kJ/h. Atlantic45.0 kJ/h.22.6 kJ/h.

33.134.0

34.4 34.2

26.627.2 27.5

27.8

22.4 22.7 22.9

23.8

JAN FEB MAR APR

BalboaDaily Maximum,

Average

30.5 30.631.2

31.7

23.9 24.2 24.3 24.7

26.5 26.7 27.0

27.4

JAN FEB MAR APR

GatunDaily Maximum,

Average

for every 4- both sites

e Ambientn Pacific

ge Ambienn Atlanti

vection bolating heat tcoefficient,(USACE, 1

m2 C (conm2 C (usin

m2 C (conm2 C (usin

31.9 31.5 31.6 31

27.126.8 26.7 26

24.2 24.0 23.8 23

MAY JUN JUL A

Station (1985 - 2inimum and Average Ai

ax Average A

31.7 31.531.0 3

24.6 24.3 24.2 2

27.2 27.0 26.7 2

MAY JUN JUL A

Station (1985 - 2inimum and Average Ai

M ax Ave rag e M in

Innov

hour time stre plotted i

emperatur Lock Site)

Temperatu Lock Site)

ndary condiansfer base) for the th

994). The r

rete exposeg plywood

rete exposeg plywood

.330.9 30.6 31.0

.5 26.3 26.1 26.1

.6 23.5 23.4 23.3

G SEP OCT NOV

005)r Temperatures

verage Min

1.231.7 31.6

30.9

4.1 24.0 23.9 23.8

6.7 26.6 26.5 26.3

UG SEP OCT NOV

005)r Temperatures

Average

tive Dam

ep. The av Figures 8 t

s Fig(B

res Fig(G

tion was apd on averagermal analysulting film

d to air, noormwork).

d to air, noormwork).

32.0

26.2

22.9

DEC

30.5

23.9

26.4

DEC

nd Levee

rage tempeo 11 below.

re 10. Diur lboa Statio

re 12. Diur atun Statio

lied at thee wind conses was calc coefficient

ormwork)

ormwork)

esign and

atures and

al Tempera Pacific

nal Temper Atlantic

oncrete air-itions. Theulated as de were calcu

onstructi

ormalized

ture Cycleock Site)

ture Cycleock Site)

exposedonvection

scribed inlated to be:

n


7/34

Con

Lift buteachwassnap

prese

Mas Oncefinitecracsecti

Straitempcrac

rete Ther

onfiguratioere generalsubsequentemoved frohot of peak

nted in Fig

Figure 13.

Gradient

the estimat element ming potentins.

s were coerature diffeing. The e

Tensile s

Strain ther

Where K

K c

E c

C

al Strain

and lift heiy placed inlift was plac

each lifttemperatur

re 13 belo

emperature

train Eval

ed temperatdels, massl, both in th

puted in acrentials wer uations use

ress = f t =

al = K R K f (C

= degree o

= degree o

= contracti

= sustaineoccurre

= differetempe

E = Coeffi

ghts used i3 meter liftsed on the pr n the 7th das generated

.

Distributio

ation

re distributradient stra

e longitudin

ordance wie used to ev to estimat

R K f c E c (E

TE) T

structural

foundation

n if there

modulusand for the

ce betweeature

ient of The

the models. The modelevious lift ay after placin the lock

Within Lo

ons withinin evaluatioal and trans

h ACI 207.aluate the p thermally i

. 5-2 in sec

eometry re

restraint ex

ere no restr

f elasticityduration in

n concrete

rmal Expan

varied fro inputs cont 7 day intement. A tyall after se

ck Wall Sec

he structur ns were per erse directi

R, where ptential for

nduced stra

ion 5.2 of

traint expre

pressed as a

int

of the concolved

peak temp

ion

structure tervatively avals and tha

pical heat dquenced pla

tion (at t=1

s were deteormed to cons of the a

eak temperahermally inn are prese

CI 207.2R)

ssed as a rat

ratio

rete at the

erature and

3

structure,ssumed that formworkstributioncement is

0 days)

mined in theck foralyzed cro

tures anducedted below.

io

ime when

final stab

1

e

s

c

e


8/34


Prior to computing mass gradient strains, age based compressive strength curves based onlaboratory data (Figure 14) were determined, which were then correlated to timedependent tensile capacity, creep, and modulus of elasticity functions. The correlationswere based on either published relationships or curve fit plots from correlated laboratorydata. Laboratory tested modulus of elasticity vs. compressive strength is presented in

Figure 15.

Figure 14. Estimated Compressive Strength of Concrete

Figure 15. Estimated Youngs Modulus vs. Compressive Strength of Concrete

0

10

20

30

40

50

60

70

80

1 10 100 1000

C o m p r e s s i v e S t r e n g t

h , f '

c ( M P a )

Age (days)

Estimated Compressive Strength

Interior Mass Concrete (183+77)

Structural Marine Concrete (300+56+19)

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45 50 55 60

Y o u n g

' s M o

d u l u s , E c

( G P a

)

Compressive Strength, f' c (MPa)

Estimated Modulus of Elasticity

Ec @ 25% of Ultimate Load




9/34


Using these time dependent properties, the sustained modulus (Schrader, 1985) of theconcrete was computed for the approximate time period that elapsed from peaktemperature to the stable mean annual temperature for select nodes in the FEM model.The sustained modulus was used to account for the change (increase) in modulus ofelasticity for the evaluated time periods, but also incorporates the effects of stress

relaxation due to creep, generally resulting in a net reduction in the elastic modulus.Thereafter, strain capacities for each concrete mix were computed using the sustainedmodulus (Table 2).

Table 2. Tensile Strain Capacity of Interior Mass and Structural Marine Concrete

From the ANSYS thermal model, temperature time histories were extracted to determinethe maximum temperatures generated in the concrete during construction at criticallocations. Figure 16 shows temperature time histories used to evaluate the Pacific LockWall.

Concrete AgeRange (days) Interior Mass Concrete Structural Marine Concrete

Initial Final E initial(GPa)Efinal

(GPa)Esustained(GPa)

StrainCapacity

(10 -6)

E initial(GPa)

Efinal (GPa)

Esustained(GPa)

StrainCapacity

(10 -6)0 1 0.0 9.9 4.7 57 0.0 24.7 11.0 921 3 9.9 18.3 12.9 50 24.7 37.0 28.2 773 7 18.3 25.3 19.3 54 37.0 42.4 35.8 957 14 25.3 32.9 25.0 67 42.4 43.6 38.6 119

14 28 32.9 38.9 30.1 82 43.6 43.3 38.7 14028 90 38.9 41.7 32.0 98 43.3 42.8 37.0 17190 180 41.7 42.3 33.6 100 42.8 42.8 36.9 174

180 365 42.3 42.5 33.1 104 42.8 42.8 36.1 180


10/34

354

Fig

The tdiffeduratnor differestr age oconcstrai

Whilmodigeo

K f fainter straiWall.

re 16. Te

emperatureential to thion from thalized to thentials wer int factorsf concrete (ete mixes.to check f

e maintainification facetric prope

ctors were colated fro calculatio

perature Ti

time histori average an peak temp mean annu used to calnd equationrom temper

The strain lir thermal cr

g a constanors, K R andties of each

alculated us tables deves is shown i

Innov

e Historiesthe Rig

s were useual ambienrature afteral temperatculate the sts from ACIature peak tmit of eachacking pote

coefficientK f were inpelement we

ing ACI 20loped by A Table 3 fo

tive Dam

for Pacificht Culvert

to estimatet temperatu placement tre was deteains in the207.2R. To mean annage range wtial at each

of thermalt as the onle used to d

.2R, EquatiI and refin

r the longit

nd Levee

ock Wallall

the maxime at each loo the pointrmined. Theconcrete ate allowableal) was the

as then conode.

xpansion, ty variable ptermine the

on 5-1, whild by Schradinal direct

esign and

ith Marine

m temperatcation. Ther

hen the sel temperatur ach locatiostrains for t determine

pared to the

e ACI 207.arameters.se modifica

e K R factorser. An exaon of the P

onstructi

Concrete in

ureeafter, theected nodee

usinghe selected

for thecalculated

2Rt each nodeion factors.

were ple of thescific Lock

n

,

e


11/34


Table 3. Mass Gradient Cracking Analysis (Pacific Lock Walls)

Surface Gradient Strain Evaluation

In addition to the mass gradient thermal strain evaluation, a surface gradient strainevaluation was performed. The surface gradient evaluation considered the potential fordevelopment of surface cracks during the critical period in the days immediately after

placement when the surface of the concrete cools and contracts more rapidly than thewarmer interior mass concrete.

Surface gradient strains were evaluated based on the difference between actualtemperatures throughout a given cross section and the concrete placement temperature.The critical point in surface gradient strain evaluations required determining where stressin the concrete is zero, or where it switched from tension (at the surface) to compression(beneath the surface). By plotting balanced temperature differences through a given

cross section (Figure 17), the depth at which this transition occurred was determined.This depth was subsequently used to calculate the strain modification factor, K R . for inputinto strain computations as defined in ACI 207.2R. For the surface gradient evaluation,age ranges during the curing process were used to determine the time dependent material

properties for input into the calculation of strain capacity. A similar process to the massgradient evaluation was then used to calculate the strain demand in the concrete andchecked against the computed strain capacity.

Base of Culverts 1.3 1.00 0.93 41.5 14.8 23 - 365 121 110.2 91% NoLeft Culvert Wall 4.8 1.00 0.48 59.1 32.4 6 - 180 196 124.3 63% NoRight Culvert Wall 4.8 1.00 0.55 60.1 33.4 7 - 180 192 147.5 77% NoLeft Culvert Wall 8.23 1.00 0.55 60.2 33.5 7 - 180 192 147.8 77% NoRight Culvert Wall 8.23 1.00 0.48 58.8 32.1 5 - 90 192 123.3 64% No

Top of Culverts 11.4 1.00 0.89 42.0 15.3 15 - 365 130 108.3 83% NoLower Part of Stem 18.4 0.41 0.35 45.4 18.7 29 - 365 116 21.8 19% No

Middle of Stem 25.9 0.11 0.35 46.1 19.4 19 - 365 125 6.0 5% NoTop of Stem 34.1 0.01 0.35 58.5 31.8 2 - 49 206 0.9 0% No

Strain Demand (LongitudinalDirection)

Modification Factors(Long. Direction)

K R K f Strain

(10-6)PercentStrain

CrackingLocationRel Elev

(m)Max T

(C)

T(C)

AgeRange(days)

StrainLimit

(10 -6)

Representative NodesTemperatureDifferential

Age DependentStrain Capacity


12/34

356

ThePaci

InitialTime

(days)

0124714285690

180(1) Te(2) Po

Figur

alculated sic Lock Wa

TableFinalTime

(days)

Einitial(GPa)

1 0.002 17.724 23.227 28.61

14 31.5428 32.4956 31.9090 30.89180 30.57365 30.40

eprature differencitive is tension and

17. Surfac

rface gradil are summ

4. Surface

Efinal(GPa)

CreepF(k) (

17.72 35.023.22 6.928.61 5.131.54 3.932.49 3.131.90 2.630.89 2.330.57 2.130.40 2.130.23 2.1

from the balancednegative is compress

Innov

e Gradient

nt strains arized in the

radient An

EsusMPa)

CompressiveStrength

(MPa)

8.2 14.2619.7 20.8424.5 30.2528.3 39.7129.6 51.3429.5 59.2428.6 65.8228.1 67.5727.4 68.4526.8 69.33emperature (zero stion

tive Dam

emperature

ross the firs table belo

alysis (FirstTensile

Strength(MPa)

H L/

1.01 0.4 41.60 0.39 42.48 0.48 33.41 0.61 34.59 0.75 25.42 0.78 26.12 0.93 16.31 1.1 16.40 1.33 16.50 1.45 1

ress temperature)

nd Levee

s Across C

t lift of the.

Lift of Left

H h/H Kr

5 1.00 0.936 1.00 0.948 1.00 0.920 1.00 0.904 1.00 0.883 1.00 0.889 1.00 0.856 1.00 0.834 1.00 0.792 1.00 0.78

esign and

ncrete Secti

eft culvert

Culvert Wa

T(1)

(C)

Incrementa T

(C)

2.52 2.529.77 7.2516.03 6.2617.71 1.6816.28 -1.439.34 -6.945.58 -3.763.48 -2.092.21 -1.270.83 -1.38

onstructi

on

all for the

ll)l

% Capacity Cracki

15% No Cra77% No Cra95% No Cra79% No Cra52% No Cra18% No Cra4% No Cra0% No Cra1% No Cra1% No Cra

n

g

ckckckckckckckckckck


13/34


14/34


Figure 19. Estimated Drying Shrinkage Strains with 14-Day Moist Cure Period

Figure 20. Estimated Drying Shrinkage Strains with 28-Day Moist Cure Period

In addition, the strain evaluation assumed a concrete splitting tensile strength equal to11%, and computed a sustained modulus using the modulus vs. compressive strengthcurve (Figure 15) in order to determine strain capacity and tensile strength.

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350

D r y i n g S h r i n

k a g e S t r a i n

( m i l l i o n t h s )

Sample Age (days)

Drying Shrinkage Strain (14-Day Moist Cure)

50% RH

60% RH

70% RH

80% RH

90% RH

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350

D r y i n g S h r i n

k a g e S t r a i n

( m

i l l i o n t h s )

Sample Age (days)

Drying Shrinkage Strain (28-Day Moist Cure)

50% RH

60% RH

70% RH

80% RH

90% RH


15/34


The strain and tensile stress induced by the drying shrinkage was then calculated acrossthe evaluated section at increasing increments of age and compared against the estimatedstrain capacity and tensile strength at the corresponding age. Strains were evaluated in 1cm intervals from the concrete surface to depths where strain capacity exceeded dryingshrinkage strain (thus no cracking). The drying shrinkage strain evaluation compared

differences in cracking for a 14-day moist cure period (required curing period) versus a28-day moist cure period. The comparative evaluation showed that, by extending thecuring period by 14 days to a total of 28 days, shrinkage strains and predicted crackingdepth was noticeably reduced. Results of the comparison are summarized in Tables 5and 6.

Table 5. Drying Shrinkage Cracking Analysis (14-Day Moist Cure)

Depth fromSurface

(cm)

Age Range(days)

DryingDuration

(days)

RelativeHumidity

(%)

Strain

(10-6)

IncrementalStrain

(10-6)

Esus(GPa)

IncrementalStress(MPa)

CumulativeStress(MPa)

PredictedTensile

Strength(MPa)

% ofCapacity

Crack /No Crack

14 - 28 0 - 14 79% 154 154 38.7 6.0 6.0 5.4 110% Crack

28 - 56 14 - 42 78% 261 107 38.0 4.1 10.0 6.1 164% Crack56 - 90 42 - 76 77% 311 50 38.0 1.9 11.9 6.3 189% Crack90 - 180 76 - 166 77% 331 20 36.9 0.7 12.7 6.4 198% Crack

180 - 365 166 - 351 76% 365 34 36.1 1.2 13.9 6.5 214% Crack14 - 28 0 - 14 91% 66 66 38.7 2.6 2.6 5.4 47% No Crack28 - 56 14 - 42 90% 118 52 38.0 2.0 4.5 6.1 74% No Crack56 - 90 42 - 76 89% 149 31 38.0 1.2 5.7 6.3 91% No Crack90 - 180 76 - 166 87% 187 38 36.9 1.4 7.1 6.4 111% Crack

180 - 365 166 - 351 85% 228 41 36.1 1.5 8.6 6.5 132% Crack14 - 28 0 - 14 94% 44 44 38.7 1.7 1.7 5.4 31% No Crack28 - 56 14 - 42 93% 83 39 38.0 1.5 3.2 6.1 52% No Crack56 - 90 42 - 76 92% 108 25 38.0 0.9 4.1 6.3 66% No Crack90 - 180 76 - 166 90% 144 36 36.9 1.3 5.5 6.4 85% No Crack

180 - 365 166 - 351 88% 182 38 36.1 1.4 6.8 6.5 105% Crack14 - 28 0 - 14 96% 29 29 38.7 1.1 1.1 5.4 21% No Crack28 - 56 14 - 42 95% 59 30 38.0 1.1 2.3 6.1 37% No Crack56 - 90 42 - 76 94% 81 22 38.0 0.8 3.1 6.3 49% No Crack90 - 180 76 - 166 92% 115 34 36.9 1.3 4.4 6.4 68% No Crack

180 - 365 166 - 351 90% 152 37 36.1 1.3 5.7 6.5 88% No Crack14 - 28 0 - 14 98% 15 15 38.7 0.6 0.6 5.4 11% No Crack28 - 56 14 - 42 97% 36 21 38.0 0.8 1.4 6.1 23% No Crack56 - 90 42 - 76 96% 54 18 38.0 0.7 2.1 6.3 33% No Crack90 - 180 76 - 166 94% 86 32 36.9 1.2 3.2 6.4 51% No Crack

180 - 365 166 - 351 92% 122 36 36.1 1.3 4.5 6.5 70% No Crack14 - 28 0 - 14 98% 15 15 38.7 0.6 0.6 5.4 11% No Crack28 - 56 14 - 42 97% 36 21 38.0 0.8 1.4 6.1 23% No Crack56 - 90 42 - 76 97% 41 5 38.0 0.2 1.6 6.3 25% No Crack90 - 180 76 - 166 95% 72 31 36.9 1.1 2.7 6.4 42% No Crack

180 - 365 166 - 351 93% 106 65 36.1 2.3 5.1 6.5 78% No Crack

Drying Shrinkage Strain (14-Day Moist Cure, Tensile Strength = 11% of Compressive Strength)

0

1

2

5

3

4


16/34


Table 6. Drying Shrinkage Cracking Analysis (28-Day Moist Cure)

SUMMARY AND CONCLUSIONS

Lock wall and Lock head structures for the Panama Canal Third Set of Locks projectwere analyzed for thermal stresses imposed during early placements of the massiveconcrete sections, providing guidance on mix design, placement temperature, andconfiguration to produce stress levels that minimized cracking in the critical water-

bearing structures. By combining the finite element thermal analysis with spreadsheet

based strain limit calculations, efficient re-evaluations were performed as additionalconcrete mix material property data was produced during construction. This methodologyallowed for quick judgments and changes to be made for concrete placementtemperatures, lift heights, and other recommendations during the fast-paced design-buildconstruction. Similarly, drying shrinkage cracking potential for air-exposed lock chambersurfaces was evaluated to determine cracking extent and provide recommendations forminimization the potential for cracking. The cracking potential evaluations ultimately

provided optimization of mix designs and construction methodology to produce concretedurable enough to meet stringent criteria for the projects 100 year design life.

REFERENCES

American Concrete Institute (ACI) September 2007, ACI 207.2R-07, Report on Thermaland Volume Change Effects on Cracking of Mass Concrete

Autoridad del Canal de Panama, 2005-2009, Temperatura Horaria Promedio, EstacionBalboa FAA, Periodo 2005-2009, Departamento de Ambiente, Agua y Energia, Divisionde Agua, Seccion de Recursos Hidricos

Depth fromSurface

(cm)

Age Range(days)

DryingDuration

(days)

RelativeHumidity

(%)

Strain

(10-6)

IncrementalStrain

(10-6)

Esus(GPa)

IncrementalStress(MPa)

CumulativeStress(MPa)

PredictedTensile

Strength(MPa)

% ofCapacity

Crack

28 - 56 0 - 28 79% 150 150 38.0 5.7 5.7 6.1 93% No Crack56 - 90 28 - 62 78% 186 36 38.0 1.4 7.1 6.3 112% Crack90 -180 62 - 152 77% 214 28 36.9 1.0 8.1 6.4 127% Crack

180 - 365 152 - 337 76% 237 23 36.1 0.8 8.9 6.5 137% Crack28 - 56 0 - 28 91% 64 64 38.0 2.4 2.4 6.1 40% No Crack56 - 90 28 - 62 90% 85 21 38.0 0.8 3.2 6.3 51% No Crack90 -180 62 - 152 87% 121 36 36.9 1.3 4.6 6.4 71% No Crack

180 - 365 152 - 337 85% 148 27 36.1 1.0 5.5 6.5 85% No Crack28 - 56 0 - 28 94% 43 43 38.0 1.6 1.6 6.1 27% No Crack56 - 90 28 - 62 93% 59 16 38.0 0.6 2.2 6.3 36% No Crack90 -180 62 - 152 91% 84 25 36.9 0.9 3.2 6.4 49% No Crack




180 - 365 152 - 337 93% 69 22 36.1 0.8 2.6 6.5 39% No Crack

4

5

Drying Shrinkage Strain (28-Day Moist Cure, Tensile Strength = 11% of Compressive Strength)

0

1

2

3


17/34


Autoridad del Canal de Panama, 2008, RFP-76161 - Design and Construction of theThird Set of Locks, Appendix A, Climatological Data from Balboa FAA, Volume VI-Reference Documents, Part 7 - Hydrometeorological Report, September 2008

Schn, J.H., 1996, Physical Properties of Rocks: Fundamentals and Principles ofPetrophysics, PermagonPress

Schrader, Tatro, 1985, "Thermal Considerations for Roller-Compacted Concrete", ACIJournal, March-April 1985

U.S. Army Corps of Engineers (USACE), 1994, ETL 1110-2-365, Engineering andDesign Nonlinear, Incremental Structural Analysis of Massive Concrete Structures, 31December 1994

U.S. Army Corps of Engineers (USACE), 1997, ETL 1110-2-542, Thermal Studies ofMass Concrete Structures, 30 May 1997

USBR (U.S. Bureau of Reclamation) 1981, A Water Resources Technical Publication,Engineering Monograph No.34, Control of Cracking in Mass Concrete Structures,Revised Reprint 1981

USBR, 1992, Concrete Manual, Pt. 2, A Manual for the Control of ConcreteConstruction, US Department of the Interior, Bureau of Reclamation, 1992.

URS Holdings, Inc., 2007, Table 4-42, Chapter 4, Category III Environmental ImpactStudy, Panama Canal Expansion Project, July 2007


18/34


19/34

Hydromechanical Analysis 363

HYDROMECHANICAL ANALYSIS FOR THE SAFETY ASSESSMENT OF AGRAVITY DAM

Maria Lusa Braga Farinha 1 Eduardo M. Bretas 2

Jos V. Lemos3

ABSTRACT

This paper presents a study on seepage in a gravity dam foundation carried out with aview to evaluating dam stability for the failure scenario of sliding along thedam/foundation interface. A discontinuous model of the dam foundation was developed,using the code UDEC, and a fully coupled mechanical-hydraulic analysis of the waterflow through the rock mass discontinuities was carried out. The model was calibratedtaking into account recorded data. Results of the coupled hydromechanical model werecompared with those obtained assuming either that the joint hydraulic aperture remains

constant or that the drainage system is clogged. Water pressures along thedam/foundation interface obtained with UDEC were compared with those obtained usingthe code DEC-DAM, specifically developed for dam analysis, which is also based on theDiscrete Element Method but in which flow is modelled in a different way. Resultsconfirm that traditional analysis methods, currently prescribed in various guidelines fordam design, may either underestimate or overestimate the value of uplift pressures. Themethod of strength reduction was used to estimate the stability of the dam/foundationsystem for different failure scenarios and the results were compared with those obtainedusing the simplified limit equilibrium approach. The relevance of using discontinuummodels for the safety assessment of concrete dams is highlighted.

INTRODUCTION

Gravity dams resist the thrust of the reservoir water with their own weight. The flowthrough the foundation, in the upstream-downstream direction, gives rise to uplift forces,which, in turn, reduce the stabilizing effect of the structures weight. Due to the greatinfluence that uplift forces have on the overall stability of gravity dams, the distributionof water pressures along the base of the dam should be correctly recorded, in operatingdams, and as accurately predicted as possible, using numerical models, at the design stageor for dams in which additional foundation treatment is required.

Stability analysis of gravity dams for scenarios of foundation failure is often based onsimplified limit equilibrium procedures. Equivalent continuum models of the rock massfoundation can be employed to assess the safety of concrete dams, complemented with

1 Research Engineer, Concrete Dams Department, LNEC National Laboratory for Civil Engineering, Av.Brasil 101, 1700-066 Lisboa, Portugal, [email protected] PhD, Graduate Student, Universidade do Minho, Departamento de Engenharia Civil, P-4800-058Guimares, Portugal, [email protected] Senior Research Engineer, Concrete Dams Department, LNEC National Laboratory for CivilEngineering, Av. Brasil 101, 1700-066 Lisboa, Portugal, [email protected].


20/34


interface elements to simulate the behaviour of joints, shear zones and faults along whichsliding may occur. More advanced analysis, however, is carried out with discontinuummodels which simulate the hydromechanical interaction, which is particularly importantin this type of structure. These models take into account not only shear displacements andapertures of the foundation discontinuities, but also water pressures within the dam

foundation. Discrete element techniques, which allow the discontinuous nature of therock mass to be properly simulated, are particularly adequate to assess the safety ofconcrete dams.

This study was carried out with data obtained from Pedrgo gravity dam (Figure 1), thefirst roller compacted concrete (RCC) dam built in Portugal, located on the RiverGuadiana. The dam is part of a multipurpose development designed for irrigation, energy

production and water supply (Miranda and Maia 2004). It is a straight gravity dam with amaximum height of 43 m and a total length of 448 m, of which 125 m are of conventionalconcrete and 323 m of RCC. The dam has an uncontrolled spillway with a length of301 m with the crest at an elevation of 84.8 m, which is the retention water level (RWL).

The maximum water level (MWL) is 91.8 m. The foundation consists of granite withsmall to medium-sized grains and is of good quality with the exception of the areaslocated near two faults in the main river channel and on the right bank, where thegeomechanical properties at depth are weak. The construction of the dam began in April2004 and work was concluded in February 2006. The controlled first filling of thereservoir ended in April 2006.

a

d

b

g

c

Figure 1. Pedrgo dam. Downstream view from the right side of the uncontrolledspillway and average position of the main sets of rock joints in relation to the dam.

In order to analyse seepage in some foundation areas and to interpret recorded discharges,a two-dimensional equivalent continuum model was developed, in 2006, in which themain seepage paths, identified with in situ tests, were represented (Farinha 2010; Farinhaet al. 2007). This model allowed recorded discharges during normal operation to beaccurately interpreted and thus it was used to calibrate the parameters of thediscontinuous hydromechanical model of Pedrgo dam foundation presented in this

paper. Analysis was carried out with the code UDEC (Itasca 2004), in which the mediumis represented as an assemblage of discrete blocks and the discontinuities as boundary


21/34


conditions between blocks. Water pressures along the dam/foundation interface obtainedwith UDEC were compared with those obtained using the code DEC-DAM, which is

being developed as part of a PhD thesis currently being written by the second author, forthe safety assessment of gravity dams. This code is also based on the Discrete ElementMethod but the flow is modelled in a different way. Results of the coupled

hydromechanical model were compared with those obtained with a simple hydraulicmodel, in which the joint hydraulic aperture remains constant. The method of strengthreduction was used to estimate the stability of the dam/foundation system for differentfailure scenarios, and the results were compared with those obtained using the simplifiedlimit equilibrium approach.

HYDROMECHANICAL DISCONTINUUM MODEL

Fluid flow analysis with both UDEC and DEC-DAM

The code UDEC allows the interaction between the hydraulic and the mechanical

behaviour to be studied in a fully-coupled way. Joint apertures and water pressures areupdated at every timestep, as described in Lemos (1999) and in Lemos (2008). It isassumed that rock blocks are impervious and that flow takes place only through the set ofinterconnecting discontinuities. These are divided into a set of domains, separated bycontact points. Each domain is assumed to be filled with fluid at uniform pressure andflow is governed by the pressure differential between adjacent domains. Total stresses areobtained inside the impervious blocks and effective normal stresses at the mechanicalcontacts.

Flow is modelled by means of the parallel plate model, and the flow rate per model unitwidth is thus expressed by the cubic law. The flow rate through contacts is given by:

l p

ak q j

= 3 (1)

where k j = a joint permeability factor (also called joint permeability constant), whosetheoretical value is 1/(12 ) being the dynamic viscosity of the fluid; a = contacthydraulic aperture; p = pressure differential between adjacent domains (corrected forthe elevation difference); l = length assigned to the contact between the domains. Thedynamic viscosity of water at 20C is 1.002 10 -3 N.s/m 2 and thus the joint permeabilityfactor is 83.3 Pa -1s-1. The hydraulic aperture to be used in Equation 1 is given by:

aaa += 0 (2)

where a0 = aperture at nominal zero normal stress and a = joint normal displacementtaken as positive in opening. A maximum aperture, a max, is assumed, and a minimumvalue, a res , below which mechanical closure does not affect the contact permeability.

The code DEC-DAM allows both static and dynamic analysis by means of the DiscreteElement Method, and has been used to investigate failure mechanisms of reinforced


22/34


gravity dams (Bretas et al. 2010). In both of the above-mentioned codes, the medium isassumed to be deformable and the flow is dependent on the state of stress within thefoundation. The main difference between both codes relies on the hydraulic-mechanicaldata model, mainly on the representation of block interaction. Regarding modelling of thehydraulic behaviour, DEC-DAM considers flow channels, where the flow rate is

determined, and hydraulic nodes, where water pressures are calculated. The flowchannels correspond to the mechanical face-to-face contacts, while the hydraulic nodescorrespond to the sub-contacts where the mechanical interaction between blocks takes

place. The main advantage of the approach used in DEC-DAM is that the mechanicalactions of the water are obtained from the integration of a trapezoidal diagram of water

pressures (rectangular diagrams are used in UDEC), allowing greater accuracy even whena coarse mesh is used. Both the above-mentioned codes allow the modelling of grout anddrainage curtains, which is necessary in order to study seepage in concrete damfoundations.

Model description

The discontinuous model developed to analyse fluid flow through the rock massdiscontinuities is shown in Figure 2. In a simplified way, only two of the five sets ofdiscontinuities identified at the dam site were simulated: the first joint set is horizontaland continuous, with a spacing of 5.0 m, and the second set is formed by vertical cross-

joints, with a spacing of 5.0 m normal to joint tracks and standard deviation from themean of 2.0 m. The former attempts to simulate the sub-horizontal set of discontinuitiesg) and the latter the sub-vertical set b), both of which are shown in Figure 1. Anadditional rock mass joint was assumed downstream from the dam dipping 25 towardsupstream, necessary to the stability analysis for failure scenarios of sliding alongfoundation discontinuities. The foundation model is 200.0 m wide and 80.0 m deep. Thedam has the crest of the uncontrolled spillway 33.8 m above ground level and the base is44.4 m long in the upstream-downstream direction. In concrete, a set of horizontalcontinuous discontinuities located 2.0 m apart was assumed to simulate dam lift joints.The UDEC model has 611 deformable blocks divided into 2766 zones, and 3451 nodal

points, and the DEC-DAM model has 611 deformable blocks.

200 m

80 m

33.8 m

Concrete:

unit weight = 2400 kg/m 3

Youngs modulus = 30 GPa

Poissons ratio = 0.2

Foundation blocks:

unit weight = 2650 kg/m 3

Youngs modulus = 10 GPaPoissons ratio = 0.2

Foundation discontinuities:

k n = 1 or 10 or 100 GPa/m

k s = 0.5 k n

= 30

Figure 2. Discontinuum model of Pedrgo dam foundation and material properties.


23/34


Both dam concrete and rock mass blocks are assumed to follow elastic linear behaviour,with the properties shown in Figure 2. Discontinuities are assigned a Mohr-Coulombconstitutive model, complemented with a tensile strength criterion. In a base run, a jointnormal stiffness ( k n) of 10 GPa/m, a joint shear stiffness ( k s) of 5 GPa/m, and a frictionangle ( ) of 35 were assumed at the dam lift joints, at the foundation discontinuities and

at the dam/foundation interface. Both at the dam lift joints and at the dam/foundationinterface cohesion and tensile strength were assigned 2.0 MPa. In rock joints, cohesionand tensile strength were assumed to be zero.

Figure 3. Block deformation (magnified 3000 times) due to dam weight, hydrostaticloading and flow.

To take into account the uncertainty in joint normal stiffness, new analysis was carriedout assuming rock masses with different deformability ( k n 5 times higher and 5 timeslower than that assumed in the base run). Using the following equation,

sk E E n R RM 111 += (3)

where E R is the modulus of deformation of the rock matrix, k n is the fracture normalstiffness, and s is fracture spacing, the rock mass in which the normal stiffness ofdiscontinuities is assumed to be 2 GPa/m has an equivalent deformability of 5 GPa, thatwith k n = 10 GPa/m an equivalent deformability of 8.33 GPa and the stiffest foundation,with k n = 50 GPa/m, an equivalent deformability of 9.6 GPa.

Sequence of analysis

Analysis was carried out in two loading stages. Firstly, the mechanical effect of gravityloads with the reservoir empty was assessed. In the UDEC model, an in-situ state ofstress with an effective stress ratio H/ V = 0.5 was assumed in the rock mass. The watertable was assumed to be at the same level as the rock mass surface upstream from thedam. Secondly, the hydrostatic loading corresponding to the full reservoir was applied to

both the upstream face of the dam and reservoir bottom. Hydrostatic loading was alsoapplied to the rock mass surface downstream from the dam. In this second loading stage,mechanical pressure was first applied, followed by hydromechanical analysis. In both


24/34


stages, vertical displacements at the base of the model and horizontal displacements perpendicular to the lateral model boundaries were prevented. Regarding hydraulic boundary conditions, joint contacts along the bottom and sides of the model wereassumed to have zero permeability. The drainage system was simulated assigning ahydraulic head along the drains equal to one third of the sum of the hydraulic head

upstream and downstream from the dam. On the rock mass surface, the head was 33.8 mupstream from the dam, and 5.0 m downstream. Figure 3 shows a detail of dam andfoundation deformation due to the simultaneous effect of dam weight, hydrostatic loadingand flow.

Hydraulic parameters

The model hydraulic parameters ( a 0 and a res ), which correspond to an equivalent permeability of the rock mass of 5.0 10 -7 m/s, were adjusted from a two-dimensionalequivalent continuum model previously developed, which had been calibrated taking intoaccount recorded discharges (Farinha et al. 2007). It was assumed that the grout curtain

was 10 times less pervious than the surrounding rock mass. The in situ borehole water-inflow tests performed (test procedures described in detail in Farinha et al. (2011)), led tothe conclusion that the main seepage paths crossed the drains at between 3.0 and 8.0 mdown from the dam/foundation interface. In order to simulate this area where the majorityof the flow is concentrated, it was assumed that the horizontal discontinuity located 5.0 m

below the dam/foundation interface was 8 times more pervious than the other rock massdiscontinuities, in the area underneath the dam and crossing the grout curtain .

In every run, with different joint stiffnesses, the same amax and a res were assumed and a0 was that which, in each analysis, led to the recorded discharge ( a0 = 0.1313 mm fork n = 50 GPa/m, a0 = 0.17 mm for k n = 10 GPa/m, and a0 = 0.4287 mm for k n = 2 GPa/mand a

res= 0.05 mm). In this way, the same situation is simulated with different models,

which enables comparison of water pressures and apertures along the base of the dam oralong other rock mass discontinuities.

RESULTS ANALYSIS

Fluid flow analysis

Results of fluid flow analysis carried out with the UDEC model, with the reservoir at theRWL, both with constant joint hydraulic aperture and taking into account thehydromechanical interaction are shown in Figures 4 and 5. Figure 4 shows the percentageof hydraulic head contours within the dam foundation (percentage of hydraulic head isthe ratio of the water head measured at a given level, expressed in metres of height ofwater, to the height of water in the reservoir above that level). In Figure 5, the linethickness is proportional to the flow rate in the fracture.When the coupling between stressand flow is taken into account, the loss of hydraulic head is concentrated at the groutcurtains area, below the heel of the dam, and the maximum water pressure is around10 % higher (Figure 4 a) and b)). Without drainage, the hydraulic head decreasesgradually below the base of the dam (Figure 4 c)).


25/34


a) b)

c)

a) constant joint aperture

b) hydromechanical interaction

c) hydromechanical interaction, without drainagesystem

Figure 4. Percentage of hydraulic head contours for full reservoir.

a) constant joint aperture

b) hydromechanical interaction

c) hydromechanical interaction, no drainage

system

max flow rate = 2.011E-05

each line thick = 3.000E-06





a) b)

c)

Figure 5. Flow rate for full reservoir (flow rate is proportional to line thickness; flowrates below 3.0 10 -6 (m 3/s)/m (0.18 (L/min)/m) are not represented).


26/34


Figure 5 shows that the majority of the flow is concentrated in the first two vertical jointsupstream from the heel of the dam, and that this water flows towards the drain, ortowards downstream in the foundation with no drainage system, along the joint of higher

permeability that crosses the grout curtain, which simulates the main seepage paths.When the hydromechanical interaction is taken into account, flow rates are higher at

lower levels and a higher quantity of water flows into the model through the secondvertical joint upstream from the heel of the dam, rather than through the first as is thecase in the run where joint aperture remains constant. This depends on the increase inwater pressure in a given vertical joint, which causes the closure of adjacent vertical

joints. The maximum flow rate is slightly higher when the interaction is taken intoaccount (it varies from around 1.21 to 1.25 (L/min)/m). The quantity of water that flowsthrough the model in the analysis with no drainage system and constant joint aperture is0.57 (L/min)/m. This increases by around 248 %, to 1.40 (L/min)/m, in the case of themost deformable foundation, and decreases by around 26 %, to 0.42 (L/min)/m, in thecase of the stiffest foundation.

Water pressures along the dam/foundation jointThe variation of water pressures along the dam/foundation joint is shown in Figure 6,along with a comparison of water pressures along the dam/foundation joint with both bi-linear and linear uplift distribution, usually used in stability analysis of dams with andwithout drainage systems, respectively. Results obtained with the foundations of differentdeformability are presented. In the hydraulic analysis in which the HM effect is not takeninto account, variations in uplift pressures along both the interface and the foundationdiscontinuities are the same regardless of the foundation deformability, because the jointhydraulic aperture remains constant. Figure 6 shows that variations in water pressures arehighly dependent on the pressure on the drainage line. Upstream from this line, water

pressures are higher for more deformable foundations. Downstream from the drainageline, on the contrary, water pressures are higher for stiffer rock masses. Along thedam/foundation joint, if all the drains are clogged, the highest water pressures areobtained with the stiffest foundation, and the lowest with the most deformable rock mass.

In the case of drained foundations, the water pressure curves are close to the bi-lineardistribution. In this case, computed water pressures between the heel of the dam and thedrainage line are lower than those given by the bi-linear distribution, whereas betweenthe drainage line and the toe of the dam they are higher, except for the most deformablefoundation. In the case of the stiffest foundations with no drainage system, calculateduplift pressures are lower than those obtained with the linear distribution, to a distance ofaround 8.0 m from the heel of the dam, and downstream from this point they areconsiderably higher. At the dam/foundation joint end close to the toe of the dam, UDECwater pressures are higher than those assumed with the linear distribution of pressures,due to the presence of the rock wedge downstream from the dam. For the mostdeformable foundation, the linear distribution of uplift pressures greatly overestimates

pressures along the base of the dam, with the exception of an area with a length of around6.0 m, close to the toe of the dam.


27/34


0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0

Distance from the heel along the base of the dam (m)

D o m a i n p r e s s u r e

( x 1 0 - 1

M P a )

bi-linear distributionof uplift pressures

linear distributionof uplift pressures

constant joint aperture constant joint aperture, no drainage system

HM interaction (kn = 2 GPa/m) HM interaction, no drainage system (kn = 2 GPa/m)

HM interaction (kn = 10 GPa/m) HM interaction, no drainage system (kn = 10 GPa/m)HM interaction (kn = 50 GPa/m) HM interaction, no drainage system (kn = 50 GPa/m)

Figure 6. Water pressure along the dam/foundation joint and comparison with both bi-linear and linear distribution of water pressures.

Figure 7 shows the comparison between water pressures along the dam/foundationinterface calculated with both UDEC and DEC-DAM, for the case of joint normalstiffness ( k n) of 10 GPa/m and of both operational and non-operational drainage systems.In the former case, there is an overall good match between the curves, except in thevicinity of the drain due to the small difference in the location assumed in the numerical

representation.

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0

Distance from the heel along the base of the dam (m)

D o m a i n p r e s s u r e

( x 1 0 - 1

M P a )

DEC-DAM, no drainage system

UDEC

DEC-DAM

UDEC, no drainage system

Figure 7. Water pressure along the dam/foundation joint, calculated with both UDEC andDEC-DAM.


28/34


STABILITY ANALYSIS

Strength reduction method

The UDEC model developed, with joint normal stiffness of 10 GPa/m, was used to assess

the stability of the dam/foundation system for the four different possible sliding failurescenarios shown in Figure 8. Scenarios a) and d) concern only the dam/foundation joint.Sliding along this interface is the most probable failure scenario in dam foundation rockmasses containing widely spaced discontinuities, none of which are unfavourablyoriented. Pedrgo dam is embedded in the foundation, and therefore the resistance tosliding is high. Scenario d) neglects the resistance of the rock wedge at the toe of thedam, in order to take into account a possible excavation downstream, close to the toe ofthe dam. Scenario b) involves both the dam/foundation joint and the rock mass jointdipping 25 towards upstream, which was purposely included in the model for stabilityanalysis. This hypothetical situation may simulate a combined mode of failure, where thefailure path occurs both along the dam/foundation interface and through intact rock, in

geology where the rock is horizontally or near horizontally bedded and the intact rock isweak (USACE 1994). In scenario c), sliding along the inclined rock mass joint is prevented, assuming that the behaviour of this joint is elastic.

a) dam/foundation interface b) dam/foundation interface and rock mass jointdownstream from the dam dipping 25 towardsupstream

c) dam/foundation interface, preventing slip on therock mass joint downstream from the dam dipping25 towards upstream

d) dam/foundation interface, neglecting theresistance of the rock wedge at the toe of the dam

Figure 8. Analysed failure modes.


29/34


Analysis was carried out with the method of strength reduction, typically applied infoundation design. An initial friction angle of 35 was assigned to the rock massdiscontinuities, dam foundation interface and dam lift joints, and zero cohesion and zerotensile strength were assigned to the dam/foundation joint, involved in the failure modes.The model was first run until equilibrium, then the fluid flow analysis was switched off

and, from this step, water pressures were kept constant. For each failure scenario, thefriction angle of the discontinuities highlighted in Figure 8 was gradually reduced untilfailure (the reduction coefficient was applied to tan ). The failure indicator was thehorizontal crest displacement. Analysis was carried out assuming that the reservoir was atthe RWL or at the MWL, and that the drainage system was either operational or non-operational. Stability analysis results are shown in Figure 9 and in Table 1. In Figure 9,friction angles in the x-axis are shown in reverse order, for ease of analysis.

a) b)

0.0

10.0

20.0

30.0

40.0

5.010.015.020.025.030.035.040.0

Friction angle (degrees)

H o r

i z o n

t a l d i s p l a c e m

e n t a t c r e s t

( m m

)

0.0

10.0

20.0

30.0

40.0

5.010.015.020.025.030.035.040.0


H o r

i z o n

t a l d i s p l a c e m

e n t a t c r e s t

( m m

)

c) d)

0.0

2.0

4.0

6.0

8.0

10.0

5.010.015.020.025.030.035.040.0


H o r

i z o n

t a l d i s p l a c e m e n

t a t c r e s t

( m m

)

2.0

4.0

6.0

8.0

10.0

20.025.030.035.040.0


H o r

i z o n

t a l d i s p l a c e m e n

t a t c r e s t

( m m

)

RWL, with drainage RWL, no drainage system RWL, failure MWL, with drainage MWL, failure

Figure 9. Variation in crest horizontal displacement due to reduction of the friction angleon highlighted joints, for the failures modes shown in Figure 7.

In the four analysed failure modes, the dam foundation system is unstable when thereservoir is at the MWL and the drainage system is non-operational, and therefore, thesesituations are not shown in Figure 9. For the same reservoir level, in both scenarios a) andc) the dam/foundation system remains stable when the drainage system is working

properly, while in scenario b), as shown in Figure 9, failure occurs for a friction angle ofaround 27.5 (safety factor F = 1.4). In scenario d) the dam is unstable for friction angleslower than 34.5 when the reservoir is at the MWL (F = 1.01).


30/34


Table 1. Comparison of friction angles for which failure occurs calculated with thehydromechanical model and with the limit equilibrium method.

Hupstream. (m)

Hdownstream (m)

Drainagesystem

River bottomdownstream

from the dam*

Friction angleLimit

equilibrium **UDEC

failure last stable

84.8 60.0 not operative 1) 27.8 34.2 34.5(RWL) 2) 11.1 - 22.6 18.4 19.3

operative 1) 21.2 21.3 22.42) 8.2 - 17.1 14.0 14.5

91.8 67.8 not operative 1) 45.6 unstable(MWE) 2) 27.8 - 40.6 unstable

operative 1) 32.4 34.5 34.72) 18.2 - 28.1 26.6 28.3

* Downstream from the dam the river bottom is: 1) at the same level as the dam/foundation interface(51.0 m) scenario d)

2) at its actual level (59.5 m) scenario b)** For failure scenario b), results are shown considering full passive force or only 1/3 of the passive force

Comparison of the UDEC results with those obtained using the limit equilibriummethod

Table 1 shows the comparison between the UDEC results and those from the equilibriummethod, for failure modes b) and d). In the analysis in which the stabilizing effect of therock wedge downstream from the dam is taken into account, the study was doneassuming either full development of passive pressure, which is improbable as it requireslarge structure displacements, or the development of one-third of the passive pressure,which is more realistic. Results show that the dam is stable when the reservoir is at theRWL, even when the drainage system is inoperative. When the reservoir is at the MWL,the safety factor is lower than 1 when: i) the drainage system is inoperative and theresistance from the rock wedge downstream from the dam is neglected (F = 0.69); and ii)the drainage system is inoperative and only one third of the passive force is considered inthe analysis (F = 0.82).

Failure mode d) is the only one which enables UDEC analysis to be verified, as the sameresults must be obtained for similar loads with both the UDEC and limit equilibriumanalysis. Indeed, when the reservoir is at the RWL and the drainage system is operativealmost the same friction angles were obtained (21.2 in the limit equilibrium analysis and

between 21.3 and 22.39 in the UDEC analysis). A difference as low as around 2 isobtained in similar conditions, but with the reservoir at the MWL (32.4 in the limitequilibrium analysis and between 34.47 and 34.73 in the UDEC analysis). However,when the drainage system is inoperative, the friction angles obtained in the UDECanalysis (34.21 - 34.47) are higher than that given by the limit equilibrium method(27.8). This difference can be explained by the higher uplift pressures obtained in theUDEC analysis, when compared with those given by the linear distribution of water

pressures between the reservoir and the tailwater, assumed in the limit equilibriumanalysis. This difference in water pressures is shown in Figure 10. A limit equilibriumanalysis carried out assuming a resultant of the uplift pressure 24 % higher than that


31/34


given by the linear distribution of water pressures would lead to the same friction angle atfailure as the UDEC analysis (assuming that in the UDEC model failure occurs for afriction angle of 34.3).

In the analysis in which it is assumed that downstream from the dam the reservoir is at its

actual level, the UDEC results are within the range of friction angles given by the limitequilibrium method, when only part or full passive force is considered, but are closer tothose obtained for one third passive force.

NPA

33.8 m

9.0 m

NPA

33.8 m

9.0 m

34.734.532.4operative(NME)

unstable45,6not operative67.891.8

22.421.321.2operative(NPA)

34.734.532.4operative(NME)

unstable45,6not operative67.891.8

22.421.321.2operative(NPA)

0.09 MPa

0.338 MPa

linear distribution of uplift pressures

hydromechanical model

RWL

Figure 10. Comparison between the UDEC results and those from the limit equilibriummethod.

CONCLUSION

This paper presents a study on seepage in Pedrgo dam foundation using a discontinuum

model, which was developed taking into account recorded data and information providedfrom tests carried out in situ . Analysis of seepage was done using both UDEC and DEC-DAM codes, which take into account the coupled hydromechanical behaviour of rockmasses. Stability analyses were carried out for different failure scenarios and withdifferent assumptions about uplift pressures and joint shear strength. Some of theanalyzed scenarios are highly unfavourable hypothetical situations, as in this dam theresistance to sliding is high. Results allowed us to quantify the influence of water

pressures on the stability of the dam. This result draws attention to the importance ofusing recorded water pressures for the sliding safety assessment of existing dams, asrecommended by the European Club of ICOLD (2004).

The uplift water pressure along the dam base is always of concern to the stability ofconcrete dams and is usually prescribed in design codes assuming a bi-linear upliftdistribution to account for the relief drains. The study presented here shows that resultsdepend mainly on the joint normal stiffness and on joint aperture. The comparison

between the results obtained with the codes UDEC and DEC-DAM showed that there is agood match between water pressures calculated along the dam foundation joint, with bothoperational and non-operational drainage systems.


32/34


Discontinuum models are difficult to apply in most practical cases, because jointing patterns are very complex and there is usually a lack of data on hydraulic properties ofthe discontinuity sets. Among these parameters are the orientation and spacing ofdiscontinuities, and the hydromechanical characterization data, namely joint normalstiffness, joint apertures and residual aperture, which is not readily available. However,

such models which simulate the hydromechanical interaction are relevant in stabilityanalysis, and the uncertainty in the different parameters, can be overcome by performingstability analysis assuming that each parameter may vary within a credible range.

Flow in fractured rock masses is mainly three-dimensional. However, in dam foundationsthe flow is mainly in the upstream-downstream direction, and therefore 2D analysis may

be considered adequate in most cases. For arch dams, 3D analysis is necessary, butcoupled fracture flow modelling of an arch dam foundation would imply representing anetwork of joints from various sets, which would be computationally prohibitive. Thealternative is to use 3D mechanical models, in which only the discontinuities involved in

possible failure modes are represented, and the water pressures are obtained from 3D

equivalent continuum models.In dam stability evaluation, the main advantage of using a 2D hydromechanicaldiscontinuum code instead of the limit equilibrium method is that it allows the study of awider range of failure modes. In addition, this type of code enables displacements to becalculated in seismic analysis, in contrast to what happens with the limit equilibriumapproach. This type of analysis is particularly useful when the foundation contains morethan one material or is made up of a combination of intact rock, jointed rock and shearedrock, as, in these cases, the overall strength of the foundation depends on the stress-straincharacteristics and compatibility of the various materials. It is also relevant in those casesin which controls of maximum displacement, needed to ensure proper function andsafety, may prevail over safety factor requirements. In 3D, discontinuum models are

particularly adequate for scenarios of foundation failure, as limiting equilibrium procedures, like those proposed by Londe (1973) , make basic assumptions about theforces acting on the independent volumes of rock that may become kinematicallyunstable, and are thus much simplified.

ACKNOWLEDGEMENTS

Thanks are due to EDIA, Empresa de Desenvolvimento e Infra-Estruturas do Alqueva,SA for permission to publish data relative to Pedrgo dam.

REFERENCES

Bretas, E.M., Lger, P., Lemos, J.V., and Loureno, P.B. 2010. Analysis of a gravity damconsidering the application of passive reinforcement. In Proceedings of the IIInternational Congress on Dam Maintenance and Rehabilitation, 23-25 November,Zaragoza 2010.

European Club of ICOLD 2004. Sliding safety of existing gravity dams Final Report.


33/34


Farinha, M.L.B. 2010. Hydromechanical behavior of concrete dam foundations. In situ tests and numerical modelling. Ph.D. thesis. IST, Technical University of Lisbon,Portugal

Farinha, M.L.B., Lemos, J.V., and Castro, A.T. 2007. Analysis of seepage in the

foundation of Pedrgo dam. In Proceedings of the 5th International Conference on DamEngineering. Lisbon, Portugal, 14-16 February 2007. LNEC, Lisbon, pp. 195-202.

Farinha, M.L.B., Lemos, J.V. and Maranha das Neves, E. 2011. Numerical modelling of borehole water-inflow tests in the foundation of the Alqueva arch dam. CanadianGeotechnical Journal, 48(1): 72-88.

Itasca 2004. UDEC Universal Distinct Element Code. Version 4.0. Itasca ConsultingGroup, Minneapolis, USA.

Lemos, J.V. 1999. Discrete element analysis of dam foundations. In Distinct Element

Modelling in Geomechanics. Edited by V.M. Sharma, K.R. Saxena and R.D. Woods.Balkema, Rotterdam, pp. 89-115.

Lemos, J.V. 2008. Block modeling of rock masses. European Journal of Environmentaland Civil Engineering, 12(7-8/2008), pp. 915-949.

Londe. P. 1973. Analysis of the stability of rock slopes. The Quarterly Journal ofEngineering Geology, 6(1), pp. 93-124.

Miranda. M.P., and Maia, M.C. 2004. Main features of the Alqueva and PedrgoProjects. The International Journal on Hydropower and Dams 11 (Issue Five, 2004): 95-99.

USACE 1994. Rock foundations. Engineer Manual 1110-1-2908. Washington, DC.


34/34