SEISM

ABSTRA

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1 INTRO

Variouresponsecompresconcretethrough DruckerChina. Hresponse

One oconcreteparametedevelopmapplied t

In thisseismic 1 Doctor, 2 Professo3 Professo4 Professo

MIC DAMDIFFE

ACT

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or, China Instior, China Instior, China Insti

MAGE ANERENT M

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am-foundatioomputation b

models consiDrucker-Pra

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mplete nonle element mnsidering coonsidering daue to energy

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1

LURE ANAL MOD

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linear dynammethod in thontraction joam and foun

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plastic modeken as an exmodels of fouamage mode

mic response

uring the recan isotropic ge of an arcture of the cd the extendmpare the seial rotating s

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ynamic propeusing differe

Hydropower nd Hydropownd Hydropownd Hydropow

NALYSISELS OF F

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mic analysis he time domoint openingndation, andto the far fieproblem andd enormousomposition msed for coml. The studyample. The rundation, anl for dam an

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Research, Beier Research, Ber Research, Ber Research, B

OF ARCFOUNDA

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model of amain is prese

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method is intmparison, incl

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orce model;

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ijing, guoss@Beijing, lideyuBeijing, tujin@Beijing, chenh

CH DAM WATION

arch dam-fouented. In thig, nonlinear ring boundaron are includmaterial modon work is troduced accluding elastii arch dam s that differege of dam-fon is close to t

foundation

the seismicllows for tened seismic fe model wasc damage mangshan arch

to study the

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WITH

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material ry model

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needed, cordingly. ic model, in China nt failure

oundation the actual

radiation

c damage nsion and failure of s verified odel, and h dam in e seismic

terial like echanical with the

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2

comparative investigations are taken. The seismic damage process of Shapai dam-foundation system is investigated by using damage model applied to dam-foundation system. As comparative studies, the seismic damage process of dam-foundation system is investigated by using damage model for dam, using Drucker-Prager elastoplastic and elastic model for rock mass. Since the computation is enormous, parallel computation is introduced in this paper and all computing work is completed by the parallel finite element program developed by China Institute of Water Resources and Hydropower Research.

2 Time domain dynamic equation

Dynamic equation after finite element discretization：

MU CU KU F (1)

Where, M , C and K are the mass, damping and stiffness matrixes respectively，and F , U , U andU are the load, acceleration, velocity and displacement vectors respectively. For large scale nonlinear dynamical calculations, the decoupled explicit integration algorithm is more efficient. Thus, this paper adopts the decoupled explicit numerical integration format which combines the center differential and unilateral differential method as:

n n 1n dt

U UU

,

n 1 n n 1n 2

2

dt

U U U

U. (2)

The discrete dynamic equation at time step n+1 is written as:

2 2

n 1 n n 1 n n n 1 n2 MU M U U KU C U U Fdt dt dt (3)

If the diagonal lumped mass matrix M is used, the equation is solved explicitly.

3 Foundation radiation damping

For the seismic response of the dam, since foundation is infinite with respect to the dam, the seismic analysis of dam is actually to simulate the wave propagation of the open system consisting of infinite foundation and dam, which includes both the vibration of dam generated by the input wave and the scattering wave to the foundation generated by the dam as vibration source. The energy gradually escapes as the scattering wave transmits to the foundation due to the geometric spreading and damping dissipation. In the actual calculation, it is impossible to simulate the scattered wave dissipation process of infinite foundation, and the foundation can be only taken a limited range. Theoretically, as long as the scope of foundation meets the need of 2L CT , where C is the velocity of foundation

and T is the seismic wave duration，the dissipation effect can be included. In static analysis, the foundation far away from the dam could take a larger size grid, but in dynamic analysis oversized grid could not be taken due to the limit of the wave length. Thus, if the scope of foundation is taken by

/L CT 2，considerable computing would be brought and difficulty to apply to engineering practice. If a smaller range of foundation is taken，the scattered wave which was supposed to spread to foundation would reflect back to dam and seismic response of dam would be amplified. The effect that energy spreads to foundation is equivalent to damping, so called ‘foundation radiation damping’. In order to simulate the effect of ‘foundation radiation damping’, in the context of a limited range of foundation, the concept of artificial boundary is proposed to simulate the effect of infinite foundation to near –field wave.

Global artificial boundary and local artificial boundary are two main boundaries. Global artificial boundary5,6 is based on the frequency domain and coupled equation is formed in space domain. To solve the coupled equation, cumbersome and enormous computation is needed. The nonlinearity of foundation can’t be considered due to the frequency domain. Thus, the local artificial boundary which is a decoupled method in space and time domain is proposed. The local artificial boundary includes

Authors should be written like A.Mehmet and M.Ahmet 3

displacement artificial boundary and stress artificial boundary. Transmitting boundary7 belongs to displacement artificial boundary which has second –order accuracy, but the phenomenon of numerical instability may occur and usually requires repeatedly trial. Viscous-spring artificial boundary8 belongs to stress artificial boundary, which needs to impose external force and spring-damping system on the boundary. The boundary nodes and internal nodes use a uniform format to solve and the algorithm has first order accuracy and good stability.

The viscous-spring artificial boundary is used in the present paper. This boundary condition is applied at the far –end boudanry of the foundation in 3D space given as :

n nK u C u , 1 s sK v C v , 2 s sK w C w (4)

Where and are the normal and shear tractions; u , v , and w are the displacement of normal and two shear components; u , v , and w are the velocity of normal and two shear components; nK

and sK are the spring coefficient of normal and shear components; nC and sC are the damping

coefficient of normal and shear components; K and C are given as:

n

EK

r2 ,

s

GK

r2 (5)

n pC c, s sC c (6)

Where r is the distance from wave source to boundary; E is modulus of elasticity; G is shear modulus of elasticity; is density ; pc is pressure wave velocity; sc is shear wave velocity; pc and

sc are given as:

p

(1 )

(1 )(1 2 )

Ec

,

s 2(1 )

Ec

(7)

Where is Poisson’s ratio.

4 The contact nonlinearity of contraction joints

Contraction joints are an important aspect of seismic response of arch dam. During the construction process, the placement of arch dam concrete is divided into several dam sections as a section of 20m width. After concrete cools to the steady temperature and contraction joints grouting between dam sections, dam sections combines into a whole model to resist water load. Under the static load, contraction joints work in compression. During earthquake, the arch tensile stress generated overcomes the arch compressive stress under static load and then contraction joints open. Pacoima arch dam in America has experienced the Richter 6.6 earthquake and dam itself is not damaged, but the opening and closing of contraction joints has obviously occurred. The contact nonlinearity caused by contraction joints attracts the attention of scholars.

Contact problem has clearly physical concept, mainly including opening, closing and slipping of contact surface, and easy to determine the constraint condition. The point is to get appropriate numerical solution method aiming to the discontinuous nonlinear problem.

The contact model can be divided into two categories aiming to the different treatment of constraint condition. One is contact force model based on the nonlinear boundary condition, taking Lagrange multiplier method as representative, and Lagrange multiplier represents the unknown contact force. Another is represented as penalty function. The introduction of contact stiffness into model is to meet the contact boundary constraint condition. To meet the condition of no embedding between contact surface, penalty function method needs to introduce greater stiffness. Theoretically, there still exists embedded distance, and there is a certain sensitivity to the stiffness value. In the contact force model, applying the unknown force as the contact force to the contact interface is to meet the constraint

4

condition, and there is no problem of artificially assumed stiffness. The Lagrange multiplier method is used in this paper.

The contact surface constraint condition:

a. Opening condition B A n

s

0 0

0

u u n

b. Closing condition

B A n

n 1 n 1 n 1B A B A s n

0 0

u u n

u u t u u t

c. Slipping condition

B A n

n 1 n 1 n 1B A B A s n

0 0

u u n

u u t u u t

Where, the location of point A and B is Au and Bu ; n is the direction vector from A to B; s is

shear contact force; n is normal contact force; is friction coefficient; t , n 1t is the current step and

previous step.

From (3), A M ， 2 2n n 1 n n n 1 n2 F M U U KU C U U Fdt dt dt ， n 1U U ，the

equation can be written as:

AU F (8)

The equation including contact force can be given as:

AU F Bλ (9)

Where, B is contact constraint matrix, λ is contact force vector.

Contact constraint equation can be given as:

T B U γ (10)

Where, γ is displacement constraint vector.

From (9) and (10), contact force equation is given as:

l Cλ DU (11)

Where lλ is contact force vector in the local coordinate system, C is flexibility matrix , DU is displace vector .C and DU are given as:

T 1 T TC TB A B T , T 1 l DU TB A F γ (12)

Where lγ is displace constraint vector in the local coordinate system, T is coordinate system transformation matrix.

The flexibility matrix of contact force equation C is full matrix due to added mass considering the effect of dynamic water pressure, normal contact force and shear contact force are coupled each other. The modified Gauss-Seidel iterative method solving normal contact force and shear contact force alternatively is used to solve the equation.

5 Damag

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e with PGA oe 5.

hang Cuiran) ts, and degreld is modeledof dam is takng the cross

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150

Authors should be written like A.Mehmet and M.Ahmet 9

Figure 8 tw f Figure 9 w D

The rock material parameters are taken as: density 32600kg/ m , original elastic modulus

0 11GP aE , Poisson ratio 0.23 , friction angel 47.73 , cohesive stress 2.0MPac ,

dynamic tensile strength t 0 2 cos 1 sin 1.55MPaf c , F 107 N mG . The parameters of

viscous damping boundaries of the foundation are taken as: 7 3n 1.61 10 N mK ,

6 3n 5.76 10 N s mC , 7 3

s 0.65 10 N mK , 6 3n 3.41 10 N s mC . Figure 10 and Figure 11

show the adjusted function of cracking displacement to the degradation tensile strength tw f and to

the damage variable w D .

Figure 10 tw f Figure 11 w D

The shear strengths of contraction and induced joints are taken as: f=1.1, c=1.1MPa. The tensile

strength of contraction joints and induced joints are zero and half of the tensile strength of concrete, respectively.

Damage model for concrete and rock: Figure 12 shows that the dam is basically not damaged even near the bottom pedestal, but the

jointed foundation rock body is damaged, as the tensile strength and fracture energy of the cracked foundation rock body are less than those of the dam concrete.

0 50 100 150 200 2500

1

2

3

4

5

f t/M

Pa

w/m

GF=296N/m

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0

D

w/m

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

f t/M

Pa

w/m

GF=107N/m

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0

D

w/m

‐Dt

Damadamaged

age model for near the botto

Figure 13

Upstream da

Downstream

Upstream

Downstre

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om pedestal an

Damageable

m surface

m dam surface

m dam surface

eam dam surfac

ure 12 DamagDrucker-Pragnd the jointed

model for dam

can

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e

10

ge of jointed fger elastoplastd foundation ro

m with Druker

Crown ntilever section

undation

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foundation roctic model for rock is damage

r-Prager mode

ck masses rock: Figure 1ed in the plasti

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Conclusi

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REFERE

1 Cemodels, E

2 Zhheterogen

3 Pacracking

4 Hadam-foun13(6) 135

5 CWCEE. M

mage model fodue to stress

comparing all more appropria

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ENCES

ervera M, OlEarthq.Eng. Sthong H, Linneity of concran J, Zhang Canalysis of coariri-Ardebili ndation-reserv50032 (24 pag

Chopra A K, eMadrid, 8.

Authors s

or concrete andconcentration

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atively compte element m

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odel for dam,t numerical avolution bothdation rock muake.

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iver J, and Ftruc. Dyn., 24

n G, Li X anete, Soil Dyn.C, Xu Y and oncrete dams, M A and Mir

voir system usges). et al(1922). M

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aria R(1995),4 1225-1245. nd Li J (201 Earthq. Eng. Jin F(2011),

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model for eval

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11), Seismic 31(12) 1678- A comparatirthq. Eng. 31(2013), A compelement and v

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with elastic fou

both considerinpai arch dam d

analysis modn is presenteg damage mocess of dam-flastoplastic ans are drawntion rock maes will be dam

luating the d

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aluation of co

failure mode-1689. ive study of t(11) 1594-160parative studyviscous bound

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del of arch daed. The seismodel applied foundation syand elastic mn: asses should bmaged earlie

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am-foundatiomic damage p

to dam-founystem is inve

model for rock

be considereer than the da

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lty of experimstigation is n

via continuum

crete dams co

procedures fo

tability of couInt. J. Struct.

f arch dams . P

11

tly pedestal.

ete and hquake.

on process ndation estigated k mass.

ed. The am

rock

mental needed.

m damage

onsidering

or seismic

upled arch Stab. Dy.

Proc. 10th

12

6 Dominguez J, et al(1992). Model of the seismic analysis of arch dams including interaction effects . Proc. 10th WCEE. Madrid, 8.

7 Tu J(1999), Nonlinear seismic response analysis of high concrete dam–foundation system with cracked surface, Ph.D. Thesis, China Institute of Water Resources and Hydropower Research.

8 Liu J B, Lu Y D(1998), A direct method for analysis of dynamic soil-structure interaction. China Civil Engineering Journal, 31(3):55-64.

9 J. Lee and G. L. Fenves(1998), Plastic-damage model for cyclic loading of concrete structures, J. ENG. MECH-ASCE. 124(8) 892-900.

10 J. Lubliner, J. Oliver, S. Oller and E. Onate(1989), A plastic-damage model for concrete, Int. J. Solids. Struct. 25(3) 299-326.