3-d analysis with contaction joints

7/31/2019 3-D Analysis With Contaction Joints

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Engineering Structures 24 (2002) 757771

www.elsevier.com/locate/engstruct

Three-dimensional analysis of concrete dams including contractionjoint non-linearity

Malika Azmi a, Patrick Paultre b,*

a Department of Civil Engineering, Ecole Hassania des Travaux Publics, Casablanca, Moroccob Department of Civil Engineering, University of Sherbrooke, Sherbrooke, QC, Canada J1K 2R1

Received 4 April 2001; received in revised form 6 November 2001; accepted 28 December 2001

Abstract

In this study, a non-linear joint element was developed to represent the dynamic behaviour of vertical contraction joints inconcrete dams. This element can be used to describe partial joint opening and closing as well as tangential displacement. Jointopening and closure are governed by normal stress criteria; tangential displacement is governed by the MohrCoulomb frictioncriterion. This joint model was incorporated into a non-linear finite element analysis program for concrete dams. Validation of themodel was done on the Big Tujunga arch dam. The program was then used to study the effect of joint opening/closing on thebehaviour of the Outardes 3 gravity dam where potential joint movement was identified experimentally. The program can carryout energy analyses to evaluate the amount of energy dissipated in contraction joints during seismic events, in addition to dynamicand thermal analyses of concrete dams. 2002 Published by Elsevier Science Ltd.

1. Introduction

Concrete dams are not monolithic structures, butrather have discontinuities inherent to constructionphases, such as vertical contraction joints. These jointsrepresent planes of weakness in dams when they are sub-

jected to tensile and/or shear stresses. In spite of thesediscontinuities, linear dynamic analyses idealise concretedams as monoliths. Generally speaking, linear analysisengenders tensile stresses that are greater than contrac-tion joints can withstand. In reality, contraction jointsopen and close during earthquakes, releasing horizontaltensile stress and redistributing forces. A nonlineardynamic analysis of concrete dams accounting for con-traction joints would be more realistic and would makeit possible to determine the behaviour of the joints andtheir effect on dam stability and dynamic response. Thisis the objective of the finite element program developedin this study [2], which is based on ADAP-88 [7], acomputer program specifically designed for studyingarch dams with vertical contraction joints. This program,

* Corresponding author. Tel.: +1-819-921-7114; fax: +1-819-821-

7108.

E-mail address: [email protected] (P. Paultre).

0141-0296/02/$ - see front matter 2002 Published by Elsevier Science Ltd.

PII: S0 1 4 1 - 0 2 9 6 ( 0 2 ) 0 0 0 0 5 - 6

however, does not take into account tangential joint

movement.A number of studies have been conducted to include

contractionjoint behaviour in the dynamic analysis ofconcrete dams. Dowling and Hall [5] and Hall and Dow-ling [10] have presented a nonlinear finite-elementanalysis procedure for arch dams that takes into accountthe gradual opening and closing of vertical contraction

joints and horizontal cold joints. The joints are con-sidered as cracking planes; slip displacement is not auth-orised since the joints are represented by nonlinearsprings acting perpendicular to the plane of the joint.Fenves et al. [7,8] developed a nonlinear three-dimen-sional joint element and numerical analysis procedurefor calculating the nonlinear seismic response of archdams when the contraction joints open and close, but itonly considers movement perpendicular to the joint.Weber et al. [20] studied the nonlinear seismic behaviourof concrete arch dams, including the nonlinearity of ver-tical contraction joints and the joint at the damfoun-dation interface. They supposed that the joints wereadequately keyed against shear and, as a consequence,tangential displacement would not be introduced into the

joints. Fenves et al. [9] describe modifications to theADAP-88 program [7] to take into account tangentialdisplacement relative to contraction joints. The joint


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758 M. Azmi, P. Paultre / Engineering Structures 24 (2002) 757771

Nomenclature

Di Integration domain on internal degrees of freedom

De Integration domain on external degrees of freedom

Eb Modulus of elasticity of concrete

Ec Kinetic energyEd Viscous damping energy

Ee Elastic energyEf Modulus of elasticity of foundation rock

Eh Dissipated energy in the joints

Es Seismic energy

Et Total energy

f Dynamic forces in linear substructure

F Dynamic forces in the non linear substructure

(Fr, Fs, Fn) Local components of vector q

Fg Sliding force in the joint

Ft Shear forces resultant in the jointg Acceleration of gravity

k Stiffness matrix of linear substructureKn Normal stiffness of the joint

Kt Tangential stiffness of the joint

M Mass matrix of the nonlinear substructure

m Mass matrix of the linear substructure

P P(U,U) Restoring force vector in the joints

q Resistive force vector in the joint; force vector at the boundary of the linear substructureQ Force vector at the boundary of nonlinear substructuret Integration time step

u Acceleration vector in the linear substructureu Velocity vector in the linear substructure

u Displacement vector in the linear substructure

U

Acceleration vector in the non-linear substructureU Velocity vector in the non-linear substructure

u Displacement vector in the non-linear substructure

(vr, vs, vn) Local components of vector va Angle between the two directions of shearb, g Integration parameters for the Newmark integration methodm Friction coefficientf Angle of internal friction

element was modified without changing the behav-iour law to provide an approximate representation ofthe sliding force in the joint. Hohberg [11] developed a

joint element for the nonlinear dynamic analysis of arch

dams. His work focused on formulating the constitutive

model of the joint elements using penalty parameters as

elastic moduli. Recently Lau et al. [14] developed a jointelement that incorporates opening and sliding of joints

as well as nonlinear shear key effects and incorporatedit into the ADAP-88 program. The authors applied the

program to the analysis of an arch dam.

A literature review on the nonlinear seismic analysis

of concrete gravity dams [1,15,4,19,6,12] reveals that

most of the analyses carried out up to now deal with the

problem of the nonlinearity of concrete cracking or dam

reservoirfoundation interaction through two-dimen-sional analysis. Three-dimensional analysis, however, is

required in order to adequately represent the seismic

response of concrete gravity dams by including the non-

linearity of vertical contraction joints. Dynamic tests car-

ried out by Proulx and Paultre [17,16] on Outardes 3

gravity dam under summer and severe winter conditionsshowed evidence of vertical contraction joint move-

ments. This paper describes a parametric study on Out-

ardes 3 gravity dam to study the influence of contractionjoints openingclosing as well as shear sliding on theseismic response of the dam. As part of this researchprogramme, a joint element capable of modelling the

openingclosing and shear sliding of vertical contractionjoints in concrete dams was developed. Influence of joint


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759M. Azmi, P. Paultre / Engineering Structures 24 (2002) 757771

shear sliding on the seismic behaviour of an arch dam

is first presented. A parametric study on the seismicbehaviour of the Outardes 3 gravity dam is then

presented. Effects of cooling and warming of the dam

are also presented to study the effects of summer and

winter conditions. Effects of Ice cover on the reservoir

under winter conditions was not part of this research pro-gramme and is covered elsewhere [3]. However, it is

noted that this effect, which is part of a current research

programme, is significant and should not be neglected.

2. Constitutive joint model

A joint element was developed as part of this research

program and consists of a three-dimensional 8-node iso-parametric element with zero thickness that relates two

opposite finite elements. This nonlinear joint elementmodels the relative normal and tangential movement of

contraction joints in concrete dams. This element was

incorporated in the computer program Concrete Dam

Analysis Program (CDAP-92) which is a modified ver-sion of the computer program ADAP-88 developed at

the University of California at Berkeley by Fenves et al.

[7]. ADAP-88 has the capability of modelling the open-

ing and closing of joints in arch dams.

The relative displacement between two adjacent sur-

faces of the joint v with components (vr, vs, vn) withthe local coordinates (r, s, n) attached to joint element,

where r is directed according to the horizontal tangent,

s according to the vertical tangent, and n is normal to

the plane of the joint produces resisting stresses.These resisting stresses q in the joint are nonlinear func-

tions of v and depend on the state of the joint (open or

closed). The joint allows tensile strength qn and normal

stiffness Kn perpendicular to the joint, shear strength

qt and tangential stiffness Kt in the plane tangent to the

joint. When the joint is open, the normal component

Fn and the tangential component Ft of the resisting force

that develops in the joint element are nil. When the joint

is closed, the normal component is elastic with a stiff-ness Kn, while the tangential component is elastic with

a stiffness Kt in the direction r and Kt in the direction

s only if the resultant of the tangential forces Ft is less

than the sliding force Fg. The MohrCoulomb frictioncoefficient is used to determine the sliding threshold.When the tangential force Ft reaches the value of the

sliding force Fg, sliding occurs in the direction of Ft,

while the stiffness remains the same Kt in the direction

perpendicular to the direction of Ft (Fig. 1). The force

displacement relations representing the normal and tan-

gential behaviour of the joint are shown in Fig. 2.

3. Nonlinear analysis procedure

The substructure method was used to analyse and

model concrete arch dams with contraction joints. The

monoliths were considered as being linear substructures.A linear substructure can contain a number of adjacent

monoliths; each contraction joint is not necessarily

included in the finite element model. The joints betweenthe different substructures are modelled as nonlinear

elements. The joint elements constitute a single nonlin-

ear substructure in the finite element model. The equa-tions of motion for each linear substructure are formu-

lated separately. A linear substructure is connected to the

other linear substructures and the nonlinear substructure

to its boundaries. The linear substructures are then com-

bined with the nonlinear substructure using equilibriumand compatibility conditions at the boundaries. Iterations

are carried out in each time step to ensure system equi-

librium at the end of each time step [7].

3.1. Linear substructure

The equations of motion for a linear substructure are:

mu cu ku f q (1)

where u is the displacement vector related to the degrees

of freedom in the linear substructure; m, c, and k are

the mass, damping, and stiffness matrices, respectively;

f is the time-dependent loading vector; and q is the force

vector at the boundary of the substructure.

3.2. Nonlinear substructure

The nonlinear substructure comprises the set of con-

traction joints considered in the model. The equations of

motion of the nonlinear substructure are given by:

MU P(U,U) F Q (2)

where U is the displacement vector in the nonlinear sub-structure; M is the mass matrix, P P(U,U) is the

restoring force vector, which is a function of nonlinear

velocities and displacements; F is the time-dependent

load vector; and Q is the force vector on the boundary

of the nonlinear substructure.

The equilibrium between the nonlinear substructure

and the linear substructures yields the equation that links

the boundary forces:

Q q 0 (3)

where the summation bears on the set of linear substruc-

tures.


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Fig. 1. Flow chart of force computations at a joint.

Fig. 2. Normal and tangential forces at a joint.

4. Energy analysis

The occurrence of an earthquake imparts a quantity

of energy to a structure called seismic energy or

absorbed energy (Fig. 3). During an earthquake, part of

the absorbed energy is temporarily stored in the structureas kinetic energy and elastic strain energy; the remaining

absorbed energy is dissipated throughout the structurescomponents through damping and inelastic deformation.

Eventually, all energy absorbed by the structure should

dissipate. The equations required to determine the vari-ous energy quantities are derived from the relative

energy formulation presented by Uang and Bertero [18]

and are adapted to the substructure method used in the

present study.

Based on the equations of motion 1 defined above forlinear substructures, we have:

nsub

j 1

mjuj nsub

j 1

cjuj nsub

j 1

kjuj nsub

j 1

fj nsub

j 1

qj (4)

where nsub represents the number of linear substructures

in the complete system.

Combining this equation term-by-term with Eq. (2),

while taking into account Eq. (3), gives:

nsub

j 1

mjuj MU nsub

j 1

cjuj nsub

j 1

kjuj (5)

P nsub

j 1

fj FEq. (5) is valid for each time step and the different

expressions of incremental energy between the timesteps t and t t are derived as follows:

Ec D

i

nsub

j 1

mjujduj D

e

MU dU (6)

Ed D

nsub

j 1

cjujduj (7)

Ee D

nsub

j 1

kjujduj (8)


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Fig. 3. Ground motion for earthquake analysis of (a) Big Tujunga arch dam as scaled from San Fernando 1971 earthquake, Lake Hughes No. 12

records, and (b) Outardes 3 gravity dam as scaled from Imperial Valley 1940 earthquake, El Centro records.

Eh D

e

PdU (9)

Es D

i

nsub

j 1

fjduj D

e

FdU (10)

where stands for an incremental quantity, Ec is thekinetic energy; Ed is the viscous damping energy; Ee is

the strain energy; Eh is the hysteretic energy dissipated

in the joints; and Es is the seismic input energy.

The domain D represents the complete system, which

is divided into an internal domain Di, representing all

the internal degrees of freedom in the linear substruc-

tures, and an external domain De, representing all the

external degrees of freedom in the linear substructuresforming the degrees of freedom of the nonlinear sub-

structure. Using the above, kinetic and seismic input

energy can also be expressed as:

Ec D

nsub

j 1

mjujduj (11)

Es D

nsub

j 1

fjduj (12)

with the other expressions for energy unchanged.

Lastly, energy at time t t is obtained by adding

the quantity of incremental energy to the calculated

energy at time t as follows:

Ei(t t) Ei(t) Ei (13)

where i c,d,e,h,s.

If the sum of all the quantities of energy stored and

dissipated in the structure is referred to as total energy

and expressed as Et, then:

Et Ec Ee Eh Ed (14)

The error relative to the seismic input energy is calcu-

lated at each time step as:

e EsEt

Es

(15)

The kinetic energy and the elastic strain energy are

directly given at each time step by the following instan-

taneous equations:

Ec(t) nsub

1

2uT(t)mu(t) (16)

Ee(t) nsub

1

2uT(t)ku(t) (17)

Consequently, the kinetic and strain energies, at each

instant t, depend uniquely and respectively on the velo-


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city and displacement at the same instant, while the seis-

mic input energy Es, damping energy Ed, and hysteretic

energy Eh are calculated incrementally and cumulated at

the end of each time step. The trapezoid rule is used to

determine the value of the incremental quantity ofenergy between time t and t t.

5. Verification of the Big Tujunga arch dam

Big Tujunga is a concrete arch dam located in Big

Tujunga Canyon in Los Angeles, California. Its length

at the crest is 122 m; the height of the highest monolith

is 77 m above the rock foundation. Its thickness varies

from 22 m at the base to 2.50 m at the crest. The dam

was built in successive lifts 1.50 m in height, between7 vertical contraction joints spaced approximately every

15 m along the crest, forming a set of 8 monoliths. Three

contraction joints were introduced into the model: one

in the middle and one to each side of the median section.

Part of the rock foundation was introduced into the

model using finite elements. The reservoir was assumedto be full. Damreservoir interaction was taken intoaccount by a diagonalised consistent finite elementadded mass matrix representing the incompressiblewater impounded in the reservoir. This added mass

matrix was generated using the RESVOR computer pro-

gram [13]. The finite element mesh of the dam model isshown in Fig. 4. The foundation rock is modelled by one

layer of 80 three-dimensional solid elements to a depth

of 73 m which is approximately equal to the height of

the tallest monolith. The massless foundation model isstatically condensed to the degree-of-freedom at thedamfoundation rock interface. The material propertiesfor the concrete are: modulus of elasticity, 28 GPa, Pois-

sons ratio, 0.20, mass density, 2.46 t/m3; for the foun-

Fig. 4. Finite element mesh of Big Tujunga arch dam, adapted from

Fenves et al. [7].

dation rock: modulus of elasticity, 18 GPa, Poissonsratio, 0.32, mass density, 2.58 t/m3; for the water: mass

density, 1.0 t/m3. The normal and tangential stiffness

values used for the contraction joints in this study are

Kn 2 Kt 56 GPa/m. The angle of internal frictionused in the MohrCoulomb criterion is 35; the cohesion

is 4 MPa; and joint tensile strength is considered to benil. To simulate monolithic behaviour of the dam, a large

value was allocated to joint tensile strength. A viscous

damping percentage of 5% is used in the first and fifthmodes to represent Rayleigh damping in the dam.

The 1971 San Fernando earthquake was used as

ground motion in the seismic analysis of the Big

Tujunga Dam. Three components were selected: N21E

was applied across the canyons; N21W was applied in

the stream direction of the dam; and the vertical compo-nent of the earthquake was applied vertically. All accel-

eration components were scaled by the same factor

resulting in the N21E component being increased to 0.60

g. Solution for the static response of the damwaterfoundation is obtained before determining the nonlinear

earthquake response. The static loads considered here are

the weight of the dam, the temperature changes in the

dam and the hydrostatic pressure of the impounded

water. To simulate the construction sequence of the can-tilever monoliths each monolith is constructed inde-pendently and transfers its own weight to the foundation

before the contraction joints are effective two staticanalyses are performed for the gravity load on the dam.

In each analysis, gravity loads are applied to alternating

cantilevers by setting to zero the modulus of elasticity

of the remaining cantilevers. The hydrostatic waterpressure is then applied to the complete damfoundationrock model. Temperature change is finally applied to thecomplete structure. If any joints are opened, a nonlinear

analysis is performed to determine the equilibrium sol-

Fig. 5. Stream total displacement at the crest of Big Tujunga arch

dam at joint 2 caused by the scaled 1971 San Fernando earthquake

with full reservoir.


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Fig. 6. Envelope of openings of joints 1 and 2 of Big Tujunga arch dam in the stream direction caused by the scaled 1971 San Fernando earthquake


Fig. 7. Horizontal tangential relative displacement at the crest of

joints 1, 2 andt 3 of Big Tujunga arch dam in the stream direction

caused by the scaled 1971 San Fernando earthquake with full reservoir.

ution before applying the dynamic earthquake forces.

Optimum time step, t, for the numerical integration of

the equations of motion was determined considering the

following criteria: (i) convergence of the solution meas-

ured as a certain tolerance value of the strain energy

of the joints under static loads, (ii) optimal number of

Fig. 8. Vertical tangential relative displacement at the crest of joints

1, 2 and 3 of Big Tujunga arch dam in the stream direction caused by

the scaled 1971 San Fernando earthquake with full reservoir.

iterations in a given time step (2 to 10), (iii) total CPU

time for a complete analysis. Preliminary analyses with

varying time step indicated that a time step t

0.005 s satisfied all three criteria and was used in allsubsequent analyses.


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Fig. 9. Dynamic response of joint 2 at the crest of Big Tujunga dam caused by the 1971 San Fernando earthquake scaled to 0.30 g and 0.60 g


5.1. Influence of the tangential relative displacement

of the joints

The displacement of the crest at the centre of the dam

in the stream direction is depicted in Fig. 5. The

maximum displacement generated by the model with

joint opening and closing only was 10.8 cm at 1.85 s,compared to 10.6 cm at 2.04 s by the model including

shear sliding. These two values are nearly identical,although offset in time by 0.19 s.

The model contains three contraction joints labelled

1, 2, and 3 from right to left; joint 2 is located at the

middle of the dam. Fig. 6 represents the envelope of

maximum opening of the joints according to dam height.

The figure also shows the depth of joint opening

depending on dam height on the upstream and down-stream faces. The maximum opening of joint 2 is smaller

when shear sliding is allowed. The relative tangential

displacement of joints 1, 2, and 3 at the crest in the hori-

zontal and vertical directions is illustrated in Figs. 7 and

8 respectively. With respect to relative tangential dis-

placement, joint 1 evidenced more sliding than the othertwo joints: 120 mm in horizontal sliding and 8 mm in

vertical sliding. Tangential displacement assumes thatthe joints are not keyed against shear. When shear keys

are used, the maximum sliding value depends on the key

geometry. Fig. 9 shows the influence of the intensity ofthe earthquake on the dynamic response of the middle

joint (joint 2). The maximum opening of joint 2 was 10.5

mm at 0.30 g, compared to 30 mm at 0.60 g.


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5.2. Energy balance and energy dissipated in the

joints

The strain energy Ee, kinetic energy Ek, viscous damp-

ing energy Ed, hysteretic energy dissipated in the jointsEh, and seismic input energy Es were evaluated for a

period of 7.0 s at time steps of 0.005 s and are presentedin Fig. 10. About 15% of the total energy is dissipated

in nonlinear displacements in the contraction joints. Thisrepresents a nontrivial quantity compared to the linear

case, in which all the energy is dissipated through vis-

cous damping.

6. Application to the Outardes 3 gravity dam

Outardes 3 is a concrete gravity dam located on the

Riviere aux Outardes near Baie Comeau, Quebec. The

dam comprises 19 monoliths spaced at about 15 m and18 vertical contraction joints. All vertical joints are

ungrouted. Dam length at the crest is 288 m; the height

of the largest monolith is 80 m above the rock foun-

dation. Introducing three vertical contraction joints into

the finite element discretisation yields 993 nodes, 546three-dimensional elements, and 46 joint elements. The

reservoir was assumed to be full. Damreservoir interac-tion was taken into account by a diagonalised consistent

finite element added mass matrix as for the Big Tujungaarch dam. Forced vibration tests carried out on Outardes3 dam and finite element calibration have shown that thefoundation rockflexibility did not influence the dynamic

characteristics of Outrades 3 gravity dam and that thefoundation rock could be assumed to be rigid [17].

Further study with a nonlinear model confirmed this con-clusion. This allowed a more refined model of Outardes3 gravity dam with fixed base to be used to study theeffects of construction joints. The mesh of the dam is

Fig. 10. Energy dissipation in the Big Tujunga Dam during the 1971

scaled San Fernando earthquake with full reservoir.

Fig. 11. Finite element mesh of Outardes 3 gravity dam without foun-

dation rock.

represented in Fig. 11. The material properties for the

concrete are: modulus of elasticity, 28 GPa, Poissonsratio, 0.20, mass density, 2.40 t/m3; for the foundationrock: modulus of elasticity, 60 GPa, Poissons ratio,0.33, mass density, 3.0 t/m3; for the water: mass density,

1.0 t/m3. The penalty parameters for the contraction

joints are the same as for the Big Tujunga arch dam. A

viscous damping percentage of 5% is used in the firstand fifth modes to represent Rayleigh damping in thedam. The 1940 El Centro earthquake was used for

ground motion in the seismic analysis of the Outardes 3

Dam. The three components selected were two horizon-tal components (S00E and S90W) and the vertical

component. Again, all acceleration components were

scaled by the same factor resulting in the S00E compo-

nent being increased to obtain 0.60 g. The static loads

were applied prior to the earthquake forces. Construction

sequence of the cantilever monoliths was taken into

account similarly to Big Tujunga arch dam by applying

Fig. 12. Stream total displacement at crest of Outardes 3 gravity dam

near joint 2 under scaled NS component of 1940 El Centro earthquake



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Fig. 13. Maximum joint openings at the crest of joints 1, 2 and 3 of Outardes 3 gravity dam under scaled NS component of 1940 El Centro

earthquake with full reservoir.

gravity loads to alternating cantilevers in two load cases.

The hydrostatic water pressure for full reservoir was then

applied followed by temperature changes effects on the

complete structure. Again, if any joints are opened, anonlinear analysis is performed to determine the equilib-

rium solution before applying the dynamic earthquakeforces.

Four different models of the Outardes 3 Dam were

studied: one with three vertical contraction joints, one

with five, one with seven, and a monolithic model basedon the three-joint model in which the contractionjointtensile strength was assigned a large value.

6.1. Effect of the joints on the dynamic response of

the dam

In order to determine the influence of the dynamicbehaviour of the dams contraction joints, a comparisonwas made between the three-joint model and the mono-lithic model. According to Fig. 12, the maximum deflec-tion near the middle joint is 33 mm. Joint opening intro-

duces flexibility into the model that slightly lengthensthe vibration period.

The model contains three contraction joints labelled

joint 1, 2, and 3 from left to right; joint 2 is located at


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the middle of the dam. The maximum joint opening in

the normal direction computed at the crest of the

upstream and downstream faces is represented in Fig.

13. The maximum opening, occurring in joint 1, is 2.5

mm at the crest, both upstream and down. The maximumopening of the middle joint is 1 mm; 1.5 mm in joint 3.

The horizontal and vertical slip of joints 1, 2, and 3upstream and down at the crest are represented in Figs.

14 and 15 respectively. The maximum horizontal slip,

produced in joint 1, is 30 mm upstream and down.

Another comparison was developed with the maximum

tensile stress contour in the half of the dam between the

monolithic model and the three-joint model. The envel-

ope of maximum horizontal tensile stresses in the

Fig. 14. Tangential relative horizontal displacement at the crest of joints 1, 2 and 3 of Outardes 3 gravity dam under scaled NS component of

1940 El Centro earthquake with full reservoir.

upstream face is shown in Fig. 16. The envelope of

maximum vertical tensile stresses in the upstream face

is given in Fig. 17. On the upstream face in the mono-

lithic case, tensile stresses varied continuously from 0.2

MPa near the middle joint to 2.6 MPa near the left abut-ment. Therefore, the contraction joint, which normally

does not carry tensile stress, must transfer 0.4 MPa oftensile stress towards the crest and 0.8 MPa towards the

foundation. In the unlinked case in which the joints can

open, the discontinuity of tensile stresses around joint 1

is apparent. The joint transfers no more than 0.4 MPa

towards the foundation. Vertical tensile stresses (Fig. 17)

exhibit the same behaviour as in arch dams: vertical

stress contributes to the reduction of horizontal tensile


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Fig. 15. Tangential relative vertical displacement at the crest of joints 1, 2 and 3 of Outardes 3 gravity dam under scaled NS component of

1940 El Centro earthquake with full reservoir.

stress through a load transfer that balances internal

forces in the contraction joints.

6.2. Effect of temperature on joint behaviour

A thermal analysis of the Outardes 3 gravity dam wasconducted to demonstrate generally the impact of tem-

perature variation on joint behaviour in the structure.The dam was subjected to two different thermal loads

to approximate conditions in winter and summer. One

case represents a 15C increase in the structures tem-perature, simulating the average summer temperature;

the other represents a 15C decrease, simulating the

average winter temperature. The results from both cases

were compared to a control case in which temperature

variation did not figure into the statistical analysis. Thethree-joint model was used.

In the warming scenario, the Outardes 3 Dam behaved

monolithically; the joints remained closed due to the

compressive forces exerted on them generated by theexpansion of the concrete. As indicated in Fig. 18, the

maximum horizontal static stress was compressivethroughout the dam and joint 1 remained closed because

its displacement perpendicular to the crest was negative.

In the cooling scenario, the joints opened due to thetensile forces exerted on them generated by contraction

of the concrete. Joint 1 opened 10 mm under static load-

ing and 20 mm under dynamic loading. The maximum


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Fig. 16. Envelope of horizontal tensile stresses in MPa on the upstream face of Outardes 3 gravity dam under scaled NS component of 1940

El Centro earthquake with full reservoir.

Fig. 17. Envelope of vertical tensile stresses in MPa on the downstream face of Outardes 3 gravity dam under scaled NS component of 1940

El Centro earthquake with full reservoir.

horizontal static stress increased throughout the dam(Fig. 19).

6.3. Energy balance and energy dissipated in the

joints

Energy balance were carried out on the three-, five-,and seven-joint models. The calculations were based on

a duration of 7.0 s at time steps of 0.005 s. In all threemodels, nearly all the energy is dissipated through vis-

cous damping at the end of excitation. The energy dissi-

pated in the contraction joints as a percentage of total

energy is 0.38% in the three-joint model, 0.64% in the

five-joint model, and 0.76% in the seven-joint model.Based on these findings and the energy analysis, it can

be deduced that five joints are adequate for representingcontractionjoint behaviour in the Outardes 3 dam.

7. Conclusions

The analysis of the Big Tujunga dam demonstratedthat adding degrees of freedom in tangential directions

in contraction joints reduces maximum joint opening,especially in the upstream face. Significant horizontalslip was observed in the joints. The energy analysis of

the dam revealed that 15% of the total energy was dissi-

pated in the contraction joints, whereas 85% was dissi-

pated through damping in the structure as elastic and

kinetic energy. Further research must be carried out to


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Fig. 18. Envelope of horizontal tensile static stress in MPa on the downstream face and normal displacement dynamic response of joint 1 of

Outardes 3 dam with full reservoir and with the effect of warming by 15 C.

Fig. 19. Envelope of horizontal tensile static stress in MPa on the downstream face and stream total dynamic displacement response of joint 1

of Outardes 3 dam with full reservoir and with the effect of cooling by 15 C.

study shear-key size and impact on joint opening and

maximum joint slip, as well as to analyse the possible

effects of contractionjoint opening and sliding onmonolithic cracking.

The Outardes 3 gravity dam was selected to test the

model and to verify the dynamic behaviour of vertical

contraction joints in concrete gravity dams. In the case

of this dam, dynamic analysis revealed that joint opening

was not significant. On the other hand, joint sliding wasnontrivial in the up/downstream directions, especiallynear the shore. When the temperature increased in the

dam, the structure behaved monolithically. The expan-sion of the concrete generated compressive stresses,

forcing the joints to stay closed. Cooling, however, pro-

duced the opposite effect: the joints opened under static

loading due to the tensile stresses on contraction joints

generated by concrete contraction. Joint opening

increased under dynamic loading, reaching 20 mm in the

joint located on the left of the middle of the dam. The

energy analysis of the Outardes 3 dam also showed that

seismic energy was mainly dissipated through viscous

damping and that the optimal number of joints in thisdam is five. Further research is required to increaseknowledge about the behaviour of vertical contraction

joints in concrete gravity dams and to determine if this

nonlinearity must be a parameter in the analysis of

such dams.

References

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3-d analysis with contaction joints

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