Abstract 1 Introduction - vsb.czfast10.vsb.cz/science/mm2006/docs/kralik_1.pdfwhere M, C and K are:...

MODELOVÁNÍ V MECHANICE OSTRAVA, ÚNOR 2006

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SAFETY AND RELIABILITY ANALYSIS OF DAMPING DEVICES UNDER IMPACT LOADS FROM CONTAINER FALL

ANALÝZA BEZPEČNOSTI A SPOĽAHLIVOSTI TLMIČOV OD RÁZOVÉHO ZAŤAŽENIA PRI PÁDE KONTAJNERA

Juraj Králik1

Abstract This paper presents the transient dynamic analysis of nuclear power plants building with impact loads. Finite element idealization of building structure is used in space. The steel tubular damper system is proposed for dissipation of the kinetic energy of the container free fall. The experimental results of the shock-damper basic element behavior under impact loads are presented. The sensitivity and probabilistic analysis of damping devices was realized in the AntHILL and ANSYS software.

1 Introduction In recent time of permanent demands for increasing of active and passive nuclear power plants safety the question of estimation of the technological equipment resistance after certain operation time is very actual. Calculation of the containment structure, including personnel access doors, equipment hatches and penetrations and isolation valves shall be based with sufficient margin on design basis events and test conditions. All penetrations through the containment should meet the same design requirement as the containment structure itself [1, 2 and 4].

1 Juraj Králik, doc.Ing.Ph.D., STU Bratislava, Faculty of Civil Engineering, Department of Structural Mechanics, Radlinského 11, Bratislava 813 68 ([email protected])

Fig.1


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They should be protected against reaction forces stemming from pipe movement or accidental loads such as jet forces, pipe whip and missiles. According to the principles of the European Concrete Code (EC No.2) three types of load combinations can be considered. The first type of combination is that which corresponds to the serviceability limit state. The second type of combination is the fundamental ultimate limit state and is used to verify the structural integrity with normal safety factor on the load and on the material. It is used for primary and secondary ruptures, normal operating conditions and normal operating conditions in combination with the operating basis earthquake. The third type of combination is the accidental ultimate limit state. It is used to verify the structural integrity for external hazard of low probability (airplane crash, SSE) and simultaneous LOCA and seismic events. The same is true for the building structure resistance on extreme loads such as in a case of small or middle accidents, like the loads from external man-induced events from external explosion or air plane crash [1] associated with design basis broken pipe or missile or the container free fall. We considered [2, 4] one from presented loads cases, the impact loads according to free fall of container in the time of the nuclear fuels exchange. The simulation of a load-bearing structure true behavior is considering the 3D space interaction [3, 9, 10 and 14], the interaction between the structure and the soil and interaction between the structure and the fluid in the deactivate basin [1, 8]. The load-bearing structure complex analysis for different kind of loads was provided with software ANSYS 5.5. The building of a power block was idealized with a discrete model, consists of the solid elements (SOLID 45), shell elements (SHELL43), beam elements (BEAM4), linear actuator elements (LINK11), mass elements (MASS21), solid fluid elements (FLUID80). The overall model has 20 840 elements and 15 600 nodes.

Fig.2 Calculation model of NPP building


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Fig.3 Geometric characteristics of the container C30


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2 Formulation of dynamic equations The dynamic equation at time is obtained through discretization of a structure model with finite elements and with the approximation of a displacement function:

M r C r K r f.. . .

n n n n+ + = , (1) where M, C and K are: the mass matrix, the damping matrix and the stiffness matrix and rn is a displacement vector and fn- global load vector at time tn.

( )r r r r. . .. ..

n 1 n n n1 t+ = + − +

δ δ ∆ , r r r r rn 1 n n n n 1t12

t+ += + + −

+

. .. ..∆ ∆β β 2 , (2)

where the parametersβ, δ are determined by the direct integration accuracy and stability. This method is conditionally stable [3] for β = 1/4 and δ = 1/2, what responds to the assumption of the average constant acceleration in time. After the substitution of the eq. (2) to (1) the dynamic equation will be as follows:

( )a a a a a a a ao 1 n 1 n 1 o n n n 1 n n nM C K r F M r r r C r r r+ + = + + + + + +

+ + 2 3 4 5

. .. . .. (3)

, , , , ,o 1 2 3 4 521 1 1 ta a a a 1 a 1 a 2t t t 2 2

δ δ δβ β β β β β

∆= = = = − = − = − ∆ ∆ ∆

3 Free fall loading of container TK-C30 The hall crane transports the nuclear fuel in the steel container TK - C30 under ceiling plate at +18,90m . The cylinder container has diameter 2285mm, height 4367mm and weight 85t. In the case of accident the container can fall to the containment plate. The accident scenario was defined by the technologic engineer. Two possibilities tracks were defined (see fig.3) 1. Track - at line 31, 32, 33, 37, 38, 36, 39, 41 2. Track - at line 31, 32, 33, 34, 35, 36, 39, 41

Fig.4 The proposed way of the container transport under containment plate


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We proposed three levels of container fall: 1. Fall on the plate at level +18,90m from height 200 mm (point 31,32,33,34,35,37,38) 2. Fall on the plate at level +18,90m from height 3670 mm (point 36) 3. Fall on the plate at level +7,30m from height 15270mm (point 41) The impact loads can be defined from equality of kinetic energy Ek of container weight mo before impact and potential energy Ep of the plate deformation in moment of maximal impact effect

Ek = Ep, ook wmE &21

= , max21 kwE p = , (4)

where ow& is the velocity of container fall in the moment of the plate-container contact, wmax is maximal amplitude of displacement of the plate, k is stiffness of plate (defined from FEM model of structures). The velocity of the fall is oo ghw 2=& , (5) where ho is the height of free hall. The longtime of the impact tr and the amplitude of force Fmax can be considered as the impact loads in the form of half wave as follows

k

mt or π= , k

mwkF oo ..max = , (6)

In the case of the fall of container into the basin we must consider two phases of the fall - firstly the fall above water surface (ho) and secondly underwater (h1). Moreover the kinematics' energy of the fall on the basin bottom is

221 21

21

oook wmwmE && −= , (7)

and potential energy of deformation is

( )kvkkvop hhAghAghghmkwE −ρ−ρ−+= 22max 21

21 , (8)

where wmax is the velocity of the impact to the basin bottom (alias to the water surface), hv (alias hk) is the height of the basin water (alias container). The total impact longtime can be considered as half wave from the equation of the vibration in the form ( ) ( ) ( ) 0=ρ++ tgAwtkwtwmo && (9)

Point (CSYS) Height [mm] Force impact [MN] Period [s] 15119(CS31) 200 56.347 0.0093878 4143(CS32) 200 54.731 0.0096649 15156(CS33) 200 52.951 0.0099898 15165(CS34) 200 50.777 0.0104180 15382(CS35) 200 42.716 0.0123840 15335(CS37) 200 40.819 0.0129590 10826(CS38) 200 52.071 0.0101590 10064(CS39) 200 63.443 0.0083377 15535(CSA0) 200 38.738 0.0136550 10827(CS36) 3670 277.65 (56.197)* 0.0081613 15498(CS41) 14000 52.765 (30.866)* 0.0100250

* Force impact after damping effect

Tab.1 Impact loads from the container fall


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3.1 Soil - Structure interaction The dissipation of energy in the soil, as well as the soil deformation during vibration of structure has the influence for total damping. The soil can be modeled by finite elements or boundary elements [3, 7, 9, 10 and 14]. In the power block building loading case, caused by the container falling and continuous steam pressure the boundary damping elements are accurate enough and thus create a realistic model. Recently the soil under the foundation plate is consolidated. The soil is characterized by layers of loess, loam and sand gravel. Based on geophysical reflex and refract research the velocity of longitudinal and transverse waves in the soil were found. For the shear waves is valid ρν /Gs = , where ρ is soil density. Under the assumption that the foundation plate is acting as a rigid body, the soil stiffness can be considered according to Barkan [14]

k k G1

abx y H= = −. µα , ( )k 2 1 G abz V= + µ α , (10)

where a, b, are the foundation plate width and length and the coefficients αh, αv can be determined according to Richart [14],

α µρV

b

a

14

mr

=−

3 , ( )α

µµ ρH

b

a32 1mr

=−−

7 83 , (11)

where r aba = π is the equivalent foundation radius, mb is a foundation mass and ρ is the soil density.

Mo- del

Author Lumped SSI

Translatalong X

Translatalong Y

Translatalong Z

Rocking about X

Rocking about Y

Torsion about Z

M1 STN 730036 Spring 15-30 15-30 30-60 - - - Damping - - - - - -

M2 PN-80/B-03040 Spring 24 24 35 - - - Damping - - - - - -

M3 Schmidtbauer spring 17,87 17,87 39,71 - - - damping 0,826 0,826 2,705 - - -

M4 Mean modulus spring 28,83 28,83 50,48 - - - damping 1,332 1,332 3,438 - - -

M5 ASCE 4/86 spring 15,57 15,57 19,83 1,579.108 1,228.108 1,584.108 damping 0,718 0,718 1,350 2,441.106 1,834.106 0,562.106

M6 Woods spring 16,31 16,31 20,81 1,327.108 1,197.108 1,584.108 damping 0,751 0,751 1,417 625,2 544,6 109,9

M7 Pais, Kausel -1) spring 16,34 16,34 21,67 1,766.105 1,846.105 2,491.105 damping 0,758 0,754 1,476 2731 2758 2229

M8 Pais, Kausel -2) spring 34,67 34,67 52,47 5,416.104 4,926.104 6,471.104 damping 1,492 1,492 3,332 780,7 686,0 1137,0

M9 Meek, Veletson spring 16,05 16,05 20,71 2,528.104 2,279.104 2,910.104 damping 0,741 0,741 1,417 390,8 340,5 7619

M10 Apsel, Luco spring 19,42 19,42 23,18 3,728.104 3,401.104 4,692.104 damping 0,897 0897 1,578 576,5 508,0 9676

M11 Gazetas -1) spring 33,45 33,45 51,75 5,172.104 4,699.104 6,153.104 damping 2,145 2,145 2,221 334,9 286.7 6421

M12 Tassoulas, Gazetas spring 27,49 27,49 46,09 2,788.104 2,532.104 3,977.104 damping 1,183 1,183 2,926 401,8 352,6 8911

M13 Gazelas -2) spring 49,85 49,85 34,97 2,256.104 2,001.104 2,065.104 damping 2,301 2,301 2,382 348,9 299,0 6419

Tab. 2 Dynamic stiffness of the spring [Mpa/m] and damping [Mpa.s/m]


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4 The damping modeling Damping of a vibration structure corresponds to a mechanical energy dissipation, usually changed to thermal energy. In the case of reinforced concrete structures it is a viscous damping in the concrete in the uncracked compression zone and a damping due to friction between the reinforcement and concrete in the cracked tension zone. According to [3, 4] in the case of extreme load in the reinforced concrete structures it is possible to consider the damping ratio in extent 7-10 % of the critical damping. The soil vibration is damped due to plastic deformation. Damping soil property under the foundation plate is considered according to [14] with the value of

c c 0 288x yH

= =,α

, c 0 425yV

=,α

(12)

In the linear analysis it is used the Rayleigh damping model, which is proportional to the stiffness matrix. The damping matrix in the dynamic equation (1) can be expressed as C M K= +α αo 1 , (13) where the coefficient α0, (α1) is decisive for the damping of a lower (higher) natural frequencies. The Rayleigh damping coefficients can be determined from the solution of the conditional equation:

ξξ

ω ωω ω

αα

m

n

m m

n n

o

1

12

=

11

, (14)

where ωn, ωm are the minimum and maximum natural frequencies from the structure decisive natural frequencies and ξn, ξm are the values of the damping ratio of the critical damping. As it was shown, the damping ratio is different in the reinforced concrete structure, as well as in the soil and will be more outstanding in the mechanical system extremely loaded parts. The system ANSYS enables to cover the true behavior of such a structure through introducing of so called material damping, which can be defined particularly for each element.

5 Solution of impact response In the case of refueling, during the reactor shutdown, it is manipulated with 85t heavy containers above the reactor building ceiling. If the suspension is released during this operation, the container can fall down on the ceiling or in the spent fuel storage pond [1]. For complex structure checking up of this situation were chosen 3 different ways and 10 places in the ceiling structure and in the pond [2]. During the load modeling were used the technical parameters, given from the operator. Container free fall was modeled as an impact load [1]. The impulse intensity and its duration are expressed from the condition of equality of the kinetic energy of a free falling body and deformation potential energy of the load- bearing structure and the container. The time interval of impulse acting responds to 1/2 of the impulse period. For example [2], in the case of container falling from the height 0,20m (3,67m) the speed at the moment of contact with the ground is reaching 1,98m/s (8,49m/s), which corresponds to the impulse intensity 40,8-64,8MN (277,6MN) in the period 0,009-0,013s (0,008s) depending on the stiffness of reinforced plate in the point of impact. Maximum internal forces exceed the bearing capacity of the ceiling plate for about 8%


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due to the impulse intensity 277,6MN in the time impulse 0,008s. In the case of the falling from the height 1,0m above the water surface in the basin the intensity impulse is equal to 428,5MN in the period 0,01s. The bearing capacity of the basin bottom was exceeded more than 19,4x.

Fig.5

Fig.6

Relative capacity [ %]

Impact in the point

Load Case

Element

Localization

bending shearing

36 26 20261 20265 Plate at level +18,9m (fall 3670mm)

108,10 -

38 28 20092 20185 Plate at level +18,9m (fall 200mm)

29,39 74,28

36 26 Section 20463 Circular wall (fall 3670mm)

101,49 53,12

36 46 12501 Section Circular wall (fall 3670mm)

79,54 105,60

38 48 12585 20459 Circular wall (fall 200mm)

23,55 41,83

31 21 20378 20378 Wall at axis 18 (fall 200mm)

14,15 87,90

41 51 21056 11979 Basin bottom at +7,3m (fall 14270mm)

1942,05 -

Tab. 3 Design check of the reinforced structures


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The second effect of the containment fall in the case of the crane accident is the vibration response of the structure. Six steam generators in the containment are suspended with four steel linkages in the containment plate at level +18,90m (Fig.6).

Fig.7 Scheme of the anchor of the steam generators

The behavior of the velocity and acceleration peaks in the characteristic point of the reinforced containment plate due to container fall is presented in Fig.7. The results from the dynamic analysis of the container fall during the transport show that the peak accelerations are 3-5times higher than in the case of earthquake.

0

0.03

0.06

0.09

0.12

0.15

1 3 5 7 9Container t ransport way

Vel

ocity

[m/s]

LC35LC37LC40LC41

0

5

10

15

20

25

1 3 5 7 9Container t ransport way

Acc

eler

atio

n [m

/s^2]

LC35LC37LC40LC41

Fig. 8 Velocity and acceleration peaks in the points of the containment plate

During the reconstruction of the nuclear power plants buildings the systems of the damping devices were proposed as the optimal solution of the NPP safety. In this solution the minimization of the kinetic energy with the plasticity absorption by the damping devices from the pipe elements was proposed.


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6 Design of damping device Kinetic energy of the free fall container can be dissipated with the plastic energy of damping devices from the tubes in one or two layers both. This type of damping devices was used in Germany.

Fig.9 Force-dilatation diagram Fig.10 Deformation of tube damper

The efficiency of this damping system was experimentally attested in Bundesanstalt für Materialprufung (BAM) in 1976.

The carrying capacity of the tube devices is defined by

Fm = α.σF.2bd2/(Ds-a), (15)

where α is parameter reliability (α = 1,1), σF - stress yield (σF = 350MPa), b - length of tube, d - thickness of tube, Ds - diameter of tube, a - highness. The maximal plastic deformation of tube can be used as 0,85Ds and the maximal diameter dilatation is a = 1,5Ds. Two layer damping devices from tubes 2 x 24 x 219/20 - 150mm were proposed for dissipate the kinetic energy Ek = 256,7kNm (free fall from high 3670mm ) with the efficiency η = 113,7%.

Fig.11

Type Diameter of pipe Ek [MNm] Ep [MNm] η[%]

Free fall from height 3670mm T1 1x18 x 219/18 – 460mm 2,813 2,718 95,5 T2 2 x 24 x 219/20 - 150mm 2,567 2,917 113,7

Free fall from height 15270mm T3 1x24 x 219/32 - 460mm 10,796 11,452 112,8 T4 2 x 52 x 219/25 - 160mm 10,592 10,535 100,5

Tab. 4 Design of the damping devices


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Z VÝŠKY 4000 MM

REZ B - B' M1:20

B B'

TLMIČ T2 - PRE PÁD KONTAJNERA C30


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7 Probability and sensitivity analysis of damping device The methodology of the probabilistic analysis of the damping device efficiency results from the requirements [11, 15] and experiences from their applications. In this case the direct simulation method MONTE CARLO [11] to solve the reliability of the damping devices was used. The probability of the loss capacities in the case of the plasticity deformation of the steel pipes under container impact hence it will be calculated from the probability of no accomplishment condition of reliability SF, Pf = P(SF < 0) , (16) where the reliability condition is defined by [11] in form

SF = Ep - Ek ≥ 0, various in the form relative SF = Ep / Ek -1 ≥ 0 (17) where Ep is the potential energy of the plasticity capacity of structure, Ek kinetic energies of the impact load. The probabilistic analysis of the damping device reliability to absorb the kinetic energies of the container fall was realized by simulation of design check using the direct method MONTE CARLO under system AntHILL and ANSYS.

The probabilistic analysis of the accident due the transport way of the container above containment plate results from uncertainty of material and geometry properties, load level, non linear deformation and design condition.

On the base of mentioned inaccuracy of input data for probabilistic analysis of the loss damping capacities of the steel pipes were determined their mean values and standard deviations, variable constant for normal distribution. The discrete histograms of the AntHILL program were used (tab.5).

Variable Variable coefficient

Bounded histogram

Mean value Standard deviation

CovarianceCoV

Fy - yield stress of struct. steel [MPa] Fyvar ST355 392 30,07 0,077

m – container mass [t] mvar DEAD1 85 3,12 3,674

h - fall distance [m] hvar N1-10 3,67 15,27 0,13 0,57

0,038 0,038

hn – depth of basis [m] hnvar N1-10 14,27 0,54 0,037 D – diameter of pipe [mm] Dvar N1-01 219 0,80 3,443

b - length of pipe [mm] bvar N1-10 46 18 1,72 0,63

3,712 3,513

t – thickness of pipe [mm] tvar N1-10 28 1,04 37,338 c – width of U beam + plate [mm] cvar N1-05 77 1,44 18,680

a – height of U beam [mm] avar N1-05 80 1,41 17,596 S – area of container [m2] Svar N1-10 4,10 0,13 3,120 hk– height of container [m] hkvar N1-05 3,917 0,06 0,016

Table 5 Parameters for the random variable

The calculation of the impact response and sensitivity analysis of the damping devices affectivity was considered in the ANSYS program. Four types of the damping devices with various geometry of steel pipes in one and two layers were analyzed (tab.4). The damping devices (types T1 and T2) were designed for free fall of container on the containment plate. Type T1 is satisfying in the case of


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70% effectivity of the impulse damping, T2 for 80% effectivity. The damping devices (types T3 and T4) were designed for free fall of container on the basin bottom. Type T4 is satisfying in the case of 90% effectivity of the impulse damping.

Effectivity Pf - Probability of the damping device failure of damping in % T1 T2 T4

60 0,0 0,0 0,0 70 0,000089 0,0 0,0 80 0,007303 0,000032 0,0 90 0,083356 0,002333 0,000007 100 0,320213 0,030070 0,000818

Table 6 Probability analysis of the damping devices failure

The sensitivity analysis of the damping devices were realized in the ANSYS program. The results from this analysis show that the effectivity of the damping devices depends firstly on the material properties of steel – strength and thickness of pipes, secondly on the variability of the container mass and height of free fall.

Fig.12

8 Conclusion This paper deals with the problem of the analysis of the buildings of nuclear power plants in the case of their resistance to the possible accident during the transport of container C30 [2] with the nuclear fuel. Depending on the importance of these buildings there was provided not only numeric analysis, but also experimental mea-surement [2, 8]. The dynamic transient analyses from the container falling during the accident simulation were realized using the system ANSYS. During the container falling simulation is the influence of the load-bearing structure vibration very significant for the bearing capacity of the steam generator suspensions, anchored in the ceiling.


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During the reconstruction of the containment structure was designed the damping devices from steel pipes. The panel on the flooring plate was reinforced to reduce the effects of the container falling on the structure. The damping devices were designed in accordance with results of attests of Bundesanstalt für Materialprufung (BAM). The kinetic energy was dissipated in the plastic deformation of the steel tubes. The probability and sensitivity analysis of the effectivity of the damping devices were realized in the program AntHILL and ANSYS.

The uncertainties of the loads level (container mass, height of free fall), the geometric and material properties (steel strength, geometric characteristic of pipe segments) and other influences following the inaccuracy of the calculated model and numerical methods were taken in the account in the 106 direct MONTE CARLO simulations.

In accordance with the probability and sensitivity analysis the reconstruction project of the protection of the NPP building before the crane accident due to transport of the container C30 was proposed.

Table 7

Acknowledgements This paper was supported by Grant Agency ME SR VEGA 1/2136/05.

References [1] BANKASH,M.,Y.,H.: IMPACT AND EXPLOSION. ANALYSIS AND DESIGN. OXFORD

LONDON 1993. [2] CESNAK,J.-KRÁLIK,J.: POSÚDENIE ÚNOSNOSTI ŽELEZOBETÓNOVÝCH KONŠTRUKCIÍ

TRANSPORTNEJ TRASY PREPRAVY ŤAŽKÝCH BREMIEN REAKTOROVEJ SÁLY OBJ.800 JE-V2, PRO-REK, BRATISLAVA 2001.

[3] CLOUGH,R.,W.-PENZIEN,J.,: DYNAMICS OF STRUCTURES, MC GRAW-HILL, INC. 1993.

[4] IAEA : GUIDELINES FOR WWER 440/213 CONTAINMENT EVALUATION, REP. IAEA, MARCH 1995.


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[5] JANAS,P,-KREJSA,M.: NUMERICAL PROBABABILISTIC CALCULATION WITH CUT OFF HISTOGRAMS, IIITH INTERNATIONAL CONFERENCE, RELIABILITY OF STRUCTURES, 2002, PP.33-38, ISBN 80-02—01489-8.

[6] JCSS-OSTL/DIA/VROU-10-11-2000, PROBABILISTIC MODEL CODE, PART 1 BASIS OF DESIGN, WORKING MATERIAL, HTTP://WWW.JCSS.ETHZ.CH/, 2001.

[7] KANICKÝ,V.,SALAJKA,V.: SOME REMARKS TO THE APPLICATION OF PROFESSIONAL FEM-BASED PROGRAMS. IN: NUMERICAL METHODS IN CONTINUUM MECHANICS, PROCEEDING OF THE INTERNATIONAL SCIENTIFIC CONFERENCE, SEPTEMBER 19-22, 1994, HIGH TATRAS, STARÁ LESNÁ - SLOVAKIA, STR.345-352.

[8] KRÁLIK,J.,CESNAK,J.: NUMERICAL AND EXPLOSION ANALYSIS OF NUCLEAR POWER PLANT BUILDINGS, IN. PROC. ASIA-PACIFIC CONFERENCE ON SHOCK & IMPACT LOADS ON STRUCTURES, JAN.,1996, SINGAPORE.

[9] KRÁLIK,J. ET ALL: STRUCTURAL SOIL INTERACTION UNDER SEISMIC LOAD FROM EARTHQUAKE AND EXPLOSION FOR NON-LINEAR CONCRETE AND SOIL STRAIN-STRESS BEHAVIOUR, VEGA 1/3606/99 SVF STU BRATISLAVA, 1999.

[10] KRIŠTOFOVIČ,V.-TÓTHOVÁ,D.: DYNAMIC INTERACTION OF HIGH-RISE STRUCTURES WITH THE SUBSOIL. RESEARCH REPORTS SVF A4/7-1. KOŠICE, SVF TU KOŠICE, 1993.

[11] MAREK,P.-BROZZETTI,J.-GUŠTAR,M.: PROBABILISTIC ASSESSMENT OF STRUCTURES USING MONTE CARLO SIMULATION, BACKGROUND, EXERCISES AND SOFTWARE, ITAM ACADEMY OF SCIENCES OF THE CZECH REPUBLIC, GLOS S.R.O., SEMILY CZECH REPUBLIC, PRAHA 2001.

[12] MELCER, J.- MARČOKOVÁ, M.: SOME CONSIDERATIONS ON THE CREATION OF COMPUTING MODELS. STUDIES OF UNIVERSITY OF TRANSPORT AND COMMUNICATIONS IN ŽILINA, CIVIL ENGINEERING SERIES, VOL. 20, EDITING CENTRE, VŠDS, ŽILINA, 1996, PP.73-90.

[13] MRÁZIK, A., TEÓRIA SPOĽAHLIVOSTI OCEĽOVÝCH KONŠTRUKCIÍ, VEDA SAV BRATISLAVA, 1986.

[14] RICHART,F.,E.-WOODS,R.,D.-HALL,J.,R.,: VIBRATIONS OF SOILS AND FOUNDA-TIONS, PRENTIC-HALL, ENGLEWOOD CLIFFS, 1994.

[15] ŘEŘICHA P.-ŠEJNOHA J.: PREDICTION OF THE LIFETIME OF NPP CONTAINMENT CONSIDERING VARIOUS ACCIDENT. IN: SPOLEHLIVOST KONSTRUKCÍ, OSTRAVA: DŮM TECHNIKY, 2004, S. 7-10. ISBN 80-248-0573-1.

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