seizmic analysis of the leŠĆe dam including water-dam-soil …

Seizmic analysis of the Lesce dam including water-dam-soil dynamic interaction.

V International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2013

S. Idelsohn, M. Papadrakakis and B. Schrefler (Eds)

SEIZMIC ANALYSIS OF THE LEŠĆE DAM INCLUDING WATER-DAM-SOIL DYNAMIC INTERACTION

JURE RADNIĆ, ALEN HARAPIN AND MARINA SUNARA*

University of Split, Faculty of Civil Engineering, Architecture and Geodesy Matice hrvatske 15, 21 000 Split, Croatia

e-mail: [email protected]

Key words: Lešće dam, seismic analysis, water – dam – soil dynamic interaction.

Abstract. Structures that are in direct contact with fluid (for example: dams, water tanks, off shore structures, pipelines, water towers, etc.) are often present in engineering practice. Numerical models for real simulations of these structures have to include the simulation of the fluid-structure dynamic interaction. The results of seismic analysis of Lešće dam are presented, which include the water-dam-soil dynamic interaction. The main nonlinear effects of concrete, reinforcement, soil and water, as well as change of the system geometry (large displacements), are modeled. Three different scaled earthquakes and harmonic base excitation, with a maximum acceleration of 0.15g, are considered. Performed analysis confirms sufficient safety of the dam, compared to current regulations and seismic activity of the area.

1 INTRODUCTION

The Lešće dam, as part of namesake hydropower plant, was the first dam built in Croatia (Fig. 1). It is situated on Gojačka Dobra river, a tributary of Kupa, at the end of the canyon near the town of Generalski stol, downstream of Hydropower plant Gojak. The dam is 52.5 meters high and the crest length is 176.4 meters. Its bottom thickness is 35 meters and its top thickness 4 meters. The dam created an accumulation lake length of about 12.61 km and surface area of 146 ha.

Figure 1: Hydropower plant and dam Lešće

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J. Radnić, A. Harapin and M.Sunara.

2

The dam was constructed of 12 concrete blocks, with an average width of 14.7 m. Blocks are founded on the solid rock, with different and relatively large founding depth at the bottom of the existing river bed (Fig. 2). The dam was designed [1,2] in accordance with regulations applicable at that time and calculated on the appropriate seismic actions: (i) for the operating period of 200 years, earthquake type "e1" with maximum acceleration 0.08g, and (ii) for the operating period of 1000 years, earthquake type "e2" with a maximum acceleration of 0.1g.

176.4 14.5

1 2 3 4 5 6 7 8 9 10 111 2

53.0

5:1

189.00

34.99°R=6.20 m

t=1.95 ml=3.78 m

a=

Dam

axi

s

0.71

136.00

LINE OF NATURAL TERRAIN

29.4

5 :1

5.3

143.80

149.18Gal

lery

axi

s54.2

Figure 2: Longitudinal section on the dam crest Figure 3: Cross-section through the dam's block no. 7

This paper discusses only the dam block no.7, 14.5 m wide, with cross section shown in Figure 3. Block is differently buried into the ground and it’s assumed that it has the extreme stresses and strains compared to all others blocks. It is also assumed that, as the most unfavorable condition, the height of the block along its entire length is equal to maximum height of dam, and direct contact of water with the dam base is possible (the maximum possible water pressure at the bottom of the dam). According to the current map of seismic areas of Croatia, HPP Lešće site is located in earthquake area with the maximum expected peak ground acceleration of 0.141g for return period of 475 years [3].

Acting of three real earthquakes on the dam is analyzed: “Ston”, “Banja Luka” and “Petrovac” [4], as well as the harmonic base acceleration. The influence of the simultaneous horizontal and vertical components of base acceleration was included. All excitations are scaled to a maximum acceleration of 0.15g. It should be noted that the adopted computational base acceleration is significantly higher than the one on which the dam was originally calculated. The period of harmonic base accelerations is calculated to correspond to the first period of free oscillations of water-dam-soil coupled system.

2 BASIC CHARACTERISTICS OF THE USED NUMERICAL MODELPreviously developed numerical model, described in detail in papers [5-9], is used for static and dynamic analysis of Lešće dam. The model can simulate fluid-structure dynamic interaction, as well as all main non-linear effects of concrete and ground rock (yielding in compression, cracks occurrence and propagation in tension, tensile and shear stiffness of cracked materials), reinforcement (yielding in compression and tension) and water

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(cavitation). Also, the effect of hydrostatic and hydrodynamic water pressure in structure cracks, as well as geometric non-linearity (large displacements), is simulated.

In displacement formulation for the structure and displacement potential formulation for the fluid, behavior of the fluid-structure system (structure in this context includes the dam and surrounding soil) in dynamic load conditions can be expressed with two second order differential equations:

(b)cf+f=f+f+f

(a)s=s+s+sffψKψCψM

fuKuCuM

&&&

&&&(1)

which define dynamic equilibrium of system, where:

( )duQρf

ψ Qf&&&& +=

= T

fcf

cs(2)

In the above equations Ms, Cs and Ks represent mass, damping and stiffness matrices for structure, whilst Mf, Cf and Kf represent same matrices for fluid. Vectors uuu &&& ,, represent structure’s displacements, velocities and accelerations, and ψψψψψψψψψψψψ &&& ,, are displacement potential and its associated derivations. Q is the interaction matrix between structure and fluid. System of equations (1) in matrix form can be expressed as:

+

−−

−

cf

csT

ff

ss

f

s

f

s

fT

f

s =0

+0

0+

0ff

dQρfdMf

ψu

KQK

ψu

CC

ψu

MQρM

&&

&&

&

&

&&

&&(3)

Fluid-structure interaction contact interface with fluid and structure elements is shown in Fig. 4. Interaction matrix Q includes only the contact interface integration and is defined as:

∫iΓ

ipjTuiij dΓn )( NNQ r= (4)

Matrices Nui and Npj represent shape functions matrices for structure and water (fluid), where nr represents normal unit vector on interaction contact interface. It should be noted that the second derivation of displacement potential ψ&& represents dynamic water pressure on that position.

Figure 4: Water-structure contact interface and unit norm vector

The system of equations (1) and (3) is solved by so-called partitioned scheme approach. Each field is solved separately, including interaction forces on the interaction contact interface between fluid and structure for every increment of the imposed load and every iteration step. The process is repeated until convergence criterion is obtained.

Water (f) Structure (s)

fcsfcf

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This approach allows the use of previously developed models for each separate field, with additional calculations of the interaction forces only. Thus, in the fluid-structure interaction model, all non-linear effects of material and geometry, that are present in a particular field, can also be simulated in the coupled problem. Flow chart for the solution of the fluid-structure coupled problem is given in Fig. 5.

Soil-structure interaction is modeled indirectly by contact elements on the contact interface. In fact, by applying the appropriate material model for contact elements, various effects in the contact surface can be simulated, such as: separating, embedment and sliding.

Figure 5: Flow chart for the solution of the fluid-structure coupled problem

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7 THE RESULTS OF ANALYSIS As previously mentioned, this paper considers only the dynamic analysis of the dam

block no. 7 (Fig. 3). Numerical discretization of the analyzed coupled system is shown in Fig. 6. Adopted values of the basic material parameters are shown in Table 1, and adopted base ground acceleration is shown in Figure 7. Reinforcement is embedded around opening (gallery) in the body of the dam (rods Φ16 mm on spacing of 25 cm).

251.4 m

31.4 120.0 100.0

76.0

35.7

40

.3

16.3

24.0

Figure 6: Spatial discretization of water-dam-soil system

(i) Earthquake ‘’Ston’’ (ii) Earthquake ‘’Banja Luka’’

(iii) Earthquake ‘’Petrovac’’ (iv) Harmonic ground acceleration

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9 10 11 12 13

[m/s

2 ]

t [s]

horizontal direction

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9 10 11 12 13

[m/s

2 ]

t [s]

vertical direction

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9 10 11

[m/s

2 ]

t [s]

horizontal directionn

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9 10 11

[m/s

2 ]

t [s]

vertical direction

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

[m/s

2 ]

t [s]


-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

[m/s

2 ]

t [s]

vertical direction

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9

[m/s

2 ]

t [s]


Tp=8 s

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

0 1 2 3 4 5 6 7 8 9

[m/s

2 ]

t [s]

vertical direction

Tp=8

Figure 7: Adopted base acceleration

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The 2D model for spatial discretization is adopted, which is proved for reliable modeling of gravity dams. First, the initial stress-state and displacement state of the system for gravitational loads is solved. Then, a dynamic analysis is performed. Computational accelerations according to Fig. 7 are applied to the model (Fig. 6) as prescribed base accelerations on the bottom of the dam. In the conventional analysis, excitation is applied as acceleration of boundary restrained nodes. Therefore, according to this approach, ground acceleration on model shown on Fig. 7 should be applied to the bottom of the considered part of ground, which will result in significantly more unfavorable state of the dam. The difference in calculated dam’s top horizontal displacement, according to on which level earthquake (“Ston”) is applied, is shown in Fig. 8. It can be concluded that, if “Ston” earthquake acts on the considered part of ground the dam will be collapsed at the end of earthquake.

Table 1. Adopted main material characteristics Main material characteristics

Dam

Con

cret

e

Ec = 32 000 MPa … Modulus of elasticity Gc = 13 333 MPa … Shear modulus υc=0.2 … Poisson’s coefficient fcc = 30 MPa … Compression strength fct = 3.0 MPa … Tensile strength εcc = -0.0035 … Limit compression strain εct = 0.00188 … Limit tension strain

Rei

nfor

cem

ent

Es = 210 000 MPa … Modulus of elasticity fs = 560 MPa … Tensile strength εss = 0.01 … Limit tension strain

Soil

(bas

e ro

ck) Et = 25 000 MPa … Modulus of elasticity

Gt = 10 416 MPa … Shear modulus υt=0.2 .. … Poisson’s coefficient ftc = 3.0 MPa … Compression strength ftt = 0.3 MPa … Tensile strength εtc = -0.0035 … Limit compression strain εtt = 0.00024 … Limit tension strain

Wat

er Ew = 2 045 MPa … Modulus of elasticity ρw = 1 000 kg/ m3 … Sound velocity c=1430 m/s … Mass density

Figure 8: The dam’s top horizontal displacement for a “Ston” earthquake in function of earthquake level

application

Some results of the analysis are presented in Fig.9-Fig.20. It is clearly shown that earthquake “Ston” has the most unfavorable effects on the dam. The presented displacements and stresses under dynamic load oscillate around the initial static values.

Horizontal displacement of the dam’s crest is shown in Fig. 9. They are relatively small (due to the high stiffness of the dam) and tend to initial displacement from gravitational loads.

Vertical stresses at the bottom of the upstream side of the dam are shown in Fig. 10. Tensile stresses caused by dynamic excitation do not exceed the tensile strength of concrete, so the cracks do not occur. When dynamic excitation ends, stresses in concrete tend to the initial stress value.

Fig. 11 shows vertical stresses in soil below the dam on the upstream side (contact between dam and foundation rock). Cracks on the joint appear after vertical tensile stresses occurred. When dynamic excitation ends, stresses in the soil tend to initial compressive stress value.

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7

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0 2 4 6 8 10 12 14 16 18 20

Hor

izon

tal d

ispl

acem

ent o

f the

top

of th

e da

m (m

)

Time (s)

earthquake ''Ston''earthquake ''Banja Luka''earthquake ''Petrovac''harmonic excitation

x..

u

Figure 9: Horizontal displacement of the top of the dam

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0 2 4 6 8 10 12 14 16 18 20

Vert

ical

str

esse

s at

the

botto

m o

f the

ups

trea

m

side

of t

he d

am(M

Pa)

Time (s)

earthquake ''Ston''

earthquake ''Banja Luka''

earthquake ''Petrovac''

harmonic excitation

x..

C1

Figure 10: Vertical stresses in concrete at the bottom of the upstream side of the dam

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0 2 4 6 8 10 12 14 16 18 20

Vert

ical

str

esse

s in

soi

l bel

ow th

e da

m o

n th

e up

stre

am s

ide

(MPa

)

Time (s)

earthquake ''Ston''



harmonic excitation

x..

S1

Figure 11: Vertical stresses in soil below the dam on the upstream side

Vertical stresses at the bottom of the downstream side of the dam are shown in Fig. 12, and vertical stresses in soil below the dam on the downstream side in Fig. 13. It is obvious that vertical stresses are always compressive and trend to initial compressive stress value after the excitation ends.

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-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0 2 4 6 8 10 12 14 16 18 20Ve

rtic

al s

tres

ses

at th

e bo

ttom

of t

he d

owns

trea

m

side

of t

he d

am(M

Pa)

Time (s)

earthquake ''Ston''



harmonic excitation

x..

C2

Figure 12: Vertical stresses in concrete at the bottom of the downstream side of the dam

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0 2 4 6 8 10 12 14 16 18 20

Vert

ical

str

esse

s in

soi

l be

low

the

dam

on

the

dow

nstr

eam

sid

e(M

Pa) Time (s)

earthquake ''Ston''



harmonic excitation

x..

S2

Figure 13: Vertical stresses in soil below the dam on the downstream side

Fig. 14 shows the stresses in reinforcement on the bottom of the gallery, which are relatively low. The maximal principal stresses (σ11, σ22) in the dam, registered in time steps of maximal displacement, are shown on Fig. 15. It can be noted that they are also relatively low.

-15.0

-10.0

-5.0

0.0

5.0

10.0

0 2 4 6 8 10 12 14 16 18 20

Stre

sses

in re

info

rcem

ent o

n th

e bo

ttom

of t

he

galle

ry(M

Pa)

Time (s)

earthquake ''Ston''



harmonic excitation

x..

Figure 14: Stresses in reinforcement on the bottom of the gallery

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(ii) earthquake ''Ston'' (ii) earthquake ''Banja Luka'' (iii) earthquake ''Petrovac'' (iv) harmonic excitation Displacement acrosssurca of accumulation

(ii) earthquake ''Ston'' (ii) earthquake ''Banja Luka'' (iii) earthquake ''Petrovac'' (iv) harmonic exscitation

Displacement toward accumulation

Figure 15: Principal stresses σ11 i σ22 in dam

Deformations of the dam at some time steps for “Ston” earthquake, with the cracks on the surface of the joint between dam and the base rock, are shown in Figure 16 (red line indicates the length of the open horizontal crack).

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10

t=0,1 s t=0,2 s t=2,0 s t=2,2 s

t=4,7 st=5,5 s t=10,0 s t=12,0 s

Figure 16: Deformation and the crack state of the dam in some time steps for “Ston” earthquake

Fig. 17 shows the hydrodynamic forces on the dam. It is evident that its value is about 25% of hydrostatic force for the harmonic base acceleration. Position of hydrodynamic force in relation to the dam height is shown in Fig. 18. It oscillates around a point which is positioned about 40% of the dam height, which is close to the result for the rigid structures [5].

-250.0

-200.0

-150.0

-100.0

-50.0

0.0

50.0

100.0

150.0

0 2 4 6 8 10 12 14 16 18 20

The

tota

l hyd

rody

nam

ic fo

rce

on th

e da

m(M

N)

Time

earthquake ''Ston''earthquake ''Banja Luka''earthquake ''Petrovac''harmonic excitation

hydrostatic force

x..

Sd

Figure 17: The total hydrodynamic force on the dam

Hydrodynamic pressures at the bottom of the dam are shown in Fig. 19. The maximal hydrodynamic pressure is about 25% of hydrostatic pressure. Cavitation in water is not registered under the considered excitations.

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2 4 6 8 10 12 14 16 18 20

The

posi

tion

of th

e hy

drod

ynam

ic fo

rceξ

/ H

Time (s)

earthquake ''Ston''



harmonic excitation

x..

H

Figure 18: The position of the hydrodynamic force

-550.0

-450.0

-350.0

-250.0

-150.0

-50.0

50.0

150.0

250.0

0 2 4 6 8 10 12 14 16 18 20

Hyd

rody

nam

ic w

ater

pre

ssur

e on

the

botto

m o

f the

da

m(k

Pa)

Time (s)

earthquake ''Ston''

earthquake ''Banja Luka''earthquake ''Petrovac''harmonic excitation

hydrostatic pressure

x..

p

Figure 19: Hydrodynamic water pressure on the bottom of the dam

4 CONCLUSIONS Previously developed, tested and reliable numerical model for static and dynamic

analysis of water-soil-structure coupled system [5-9] was used for the analysis of Lešće dam. The model simulates all main nonlinear effects of water, concrete, reinforcement and soil. The dam block no. 7, which is probably the least favorable of all blocks of the dam, was analyzed. The analysis determines sufficient security and stability of the block, even for possible earthquake actions with a maximum acceleration of 0.15 g. Of all possible non-linearity, only the elevation of the dam bottom of the foundation rock is present. It is expected that other dam blocks also have sufficient security and stability for the same maximum base acceleration. With respect to the all considered dynamic excitations, earthquake “Ston” showed the most unfavorable effects.

REFERENCES [1] The main design of gravitational concrete Lešće dam, static and dynamic calculation,

IGH Zagreb, (1991/1996) (in Croatian)

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[2] The work design of gravitational concrete Lešće dam, The dam body and program of concreting, Elektroprojekt d.d. Zagreb, (2000), (in Croatian)

[3] Seismic maps of territory of Republic of Croatia, http://seizkarta.gfz.hr/karta.php, 27.03.2012.

[4] European Strong-Motion Data, http://www.isesd.hi.is/ESD_Local/frameset.htm, 30.03.2012.

[5] J. Radnić, Fluid-structure dynamic interactions including cavitation, Građevinar, (1987) 7:269-275. (in Croatian)

[6] J. Radnić, Numerical model for dynamic analysis of concrete gravity dams, Izgradnja, (1990), 12:5-14. (in Croatian).

[7] J. Radnić, A. Harapin, Fluid srtucture interaction including water pore pressure in cracks, IV Congress DHGK, (1996), 429-436. (in Croatian).

[8] Radnić J., Harapin A., Brzović D.: “WYD method for an eigen solution of coupled problems”, 2nd International Conference on Advanced Computational Engineering and Experimenting, Eds. A. Öchsner, L. da Silva; Barcelona, Espana, July, (2008), 237-246.

[9] Brzović D., Šunjić G., Radnić J., Harapin A.: „Numerical Model for Fluid-Structure Coupled Problems under Seismic Load“, Research monograph: Materials with Complex Behaviour II, A. Öchsner et al. (Eds.), Berlin: Springer-Verlag,(2012), 175-198.

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seizmic analysis of the leŠĆe dam including water-dam-soil …

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