XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ th INTERNATIONAL SCIENTIFIC CONFERENCE VSU' CALCULATION OF FLOOR RESPONSE SPECTRA. CASE STUDY FOR THE MAIN EQUIPMENT OF A 5 MW STEAM TURBINE Stoyan Andreev Risk Engineering Ltd. Abstract: The current paper presents the calculation of floor response spectra for the main equipment of a thermal power plant, situated in an area with high design peak ground acceleration. Dynamic time-history analyses are performed, using artificial ground motion records, compatible with BDS EN 998-/NA. The dynamic soilstructure interaction is taken into account by introducing frequency-independent lumped spring and dashpot, defined with varying soil properties. The calculated response spectra for the equipment support locations are enveloped and broadened, so they could be used as a seismic design basis by the equipment's manufacturer. Keywords: Earthquake Engineering, Floor Response Spectra, Soil-Structure Interaction, Time-History Seismic Analysis, Turbine Foundation Reconstruction. Introduction In - Risk Engineering Ltd. replaced a 55 years old steam turbine at Sofia TPP with a new one having a net capacity of 5 MWe. This required a reconstruction of the existing turbine foundation, including removal of RC walls to fit the condensing boiler heater, construction of a new massive RC girder supporting the turbine front bearings (#), and enlargement of the RC girder supporting the turbine rear bearings (#). Steam turbine foundations are relatively stiff structures, so their seismic response is determined mostly by the dynamic soil-structure interaction and the hysteretic soil behaviour, especially for soft soils. The non-linear hysteretic behaviour of the foundation RC structure has a lesser, but also considerable effect on the floor response spectra.. Background for the Analyses The main purpose of the performed analyses was obtaining the floor (in-structure) response spectra for the equipment supports and this determines the applied simplifications and assumptions... Structural Modelling The original structure was built with concrete grade BM5, which is equivalent to grade C/5 in EC. For the reconstruction concrete grade C/5 is used. Reinforcement (rebars and structural steel sections) is added only in the mass density of the RC. The concrete material parameters are calculated according to ref. [], see Table. MSc, Structural Engineer, Vihren Str, Buxton 68, Sofia, Bulgaria, Stoyan.Andreev@RiskEng.bg
XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ th INTERNATIONAL SCIENTIFIC CONFERENCE VSU' Table. Concrete material parameters Concrete grade Density, t/m Poisson s ratio E ci, MPa E c, MPa G c, MPa C/5.5. 7 95 965 C/5.5. 55 65 A detailed finite element model is developed using SAP []. In the model X- direction is horizontal, parallel to the turbine axis, Y-direction is horizontal, transverse to the turbine-generator axis and Z-direction is vertical. Equipment is modelled as lumped masses. Floor response spectra are calculated for the locations of the equipment, see Fig.. Fig.. FE model of the turbine-generator foundation The foundation mat is x6 meters in size, embedded meters in the ground. It is assumed to be rigid [5]. The total height of the structure is.6 meters. The total mass of the structure, including the equipment is approximately 65 tons The behaviour factor of the structure in the reconstruction design is given as q=.5. The used relations between q, the ductility ratio μ, the effective period of the structure T eff and the initial period of the fixed base structure T are given in ref. [] and []. The modal analysis shows that initial natural period of the structure with a fixed base is.6 sec. It is calculated that μ=.6 and T eff =.7 sec. The effective material damping for a given ductility ratio is calculated according to equations in ref. [] and []. For μ=.6 the calculated effective damping is ξ eff =9.%. To adjust the fixed base period the bending stiffness of the structural members is decreased by 6% and the shear stiffness is decreased by %... Soil-Structure Interaction In the analyses the soil is represented with a 6 DOFs lumped spring-dashpot []. It is assumed that the clay layer is thick and uniform for the considered depth m. According to EC8 this is a type C soil with shear wave velocity V S, =8 6 m/s [8]. The uncertainties in the soil stiffness are treated as given by ref. [5] a best estimated (BE) value for the initial shear modulus G max is assumed, and lower (LB) and upper (UB) values are calculated by dividing or multiplying the BE value by a factor of. The strain softening of the soil due is considered with shear wave velocity reduction factor n=.6, as given in ref. []. The reduced shear wave velocity is noted as V s,r. Corresponding soil hysteretic damping is calculated using shear strain damping relations after Ishibashi and Zhang for G eff and PI= [6]. The soil properties are given in Table.
XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ th INTERNATIONAL SCIENTIFIC CONFERENCE VSU' Table. Initial and effective soil parameters Variation Density, Poisson s V s,, G max, G t/m V ratio m/s MPa s,r, m/s eff, Damp, MPa % BE..5 55. 5 6.8.9 LB..5 8 6.8 8..9 UB..5 6 59. 6 9..9 The spring and dashpot constants are calculated with equations developed by Richard et al [5], [7]. For uniform soil layer they are frequency-independent, see Tables and. Table. Lumped spring stiffness Variation K rx, K ry, K rz, K ψx, K ψy, K t, MN/m MN/m MN/m MNm/rad MNm/rad MNm/rad BE 59 65 5 689 57 LB 766 8 5 5 85 585 UB 68 68 68 5 78 Table. Lumped dashpot constants Variation C rx, C ry, C rz, C ψx, K ψy, K t, MN.s/m MN.s/m MN.s/m MNm.s/rad MNm.s/rad MNm.s/rad BE 6,7 8,5 8, 7 5 78 LB 5,9 7, 57, 75 55 UB 5,8 5,,8 5 6.. Seismic input The target free-field spectra are the elastic response spectra from EC8/NA with importance factor of., soil factor. and reference ground acceleration.g [8]. For the analyses a set of three statistically independent ground motions is generated using the program SIMQKE-II. The time step of the records is. sec. The envelope shape is based on the Compound model of Jeninngs et al. [9]. The total length of the records is sec with a sec strong motion part. The PGA is approximately.8g for horizontal and.g for vertical direction. The compatibility between the artificial ground motions and the target spectra is evaluated according to ref. [5]. The comparison between the target spectra and the spectra of the generated ground motions is shown in Fig...5 Acc X Acc Y Target.9*Target.5 5 5.5 Acc Z Target.9*Target.5 5 5 Fig.. Seismic input: Horizontal directions; Vertical direction
XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'.. Dynamic Analyses and Calculation of Floor Response Spectra Linear modal time-history analyses are performed for the three soil conditions. In each case vibration modes up to at least 5 Hz are calculated with a procedure using Ritz vectors. Composite modal damping is applied, including soil damping, dashpot viscous damping and RC material damping []. The procedure for calculating design floor response spectra is given in Commentary to ref. [5].. Analytical Results The two fundamental horizontal mode shapes for BE soil are shown in Fig.. Fig.. Predominant mode shapes: Y-direction @.85 Hz; X-direction @. Hz The modal mass participation ratios of the predominant modes are given in Table 5 Table 5. Modal Mass Participation Ratios of the Predominant Modes Mode Freq, Hz UX, % UY, % UZ, % RX, % RY, % RZ, %.85. 76.. 98.5. 6.. 78.8... 7.8..99..... 7. 6.69..... 5. 5 7.9.6. 98.... 6 9.55.....5. 7.8...7. 8.. 8.....5.. The predominant modes in all three principal directions are determined by the SSI. The first mode in Y-direction at is pure rocking and has the lowest natural frequency at.85 due to the large (.5:) aspect ratio of the foundation mat. The relatively high centre of masses compared to the Y-direction mat size also contributes for this response. In X- direction the predominant mode is sliding-rocking and due to the larger mat size in this direction the frequency is higher. Hz. The Z-direction predominant mode is translational and governed by the SSI.
XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ th INTERNATIONAL SCIENTIFIC CONFERENCE VSU' The calculated -damping envelope raw (not broadened) floor response spectra for turbine supports # and # are shown in Fig. 5. Both locations are shown in Fig.. X-dir. Y-dir. Z-dir. X-dir. Y-dir. Z-dir..5 5 5.5 5 5 Fig. 5. Enveloped raw floor response spectra, damping: Turbine support #; Turbine support # The strong influence of the foundation s large aspect ratio is clear in the raw response spectra the Y-direction spectrum has the highest spectral accelerations for the lowest frequency range (.-.5 Hz). The spectra for turbine supports # and # are similar with some difference around.5 Hz the predominant frequency for UB soil. The torsion response at.99. In X-direction the effect of the structural response is more pronounced there is a peak in the spectral accelerations for turbine support # with values about % higher for the predominant frequencythe DFRS for the condensing boiler heater have smaller values due to its lower location. Design floor response spectra (DFRS) for horizontal directions at Turbine supports # and # are shown in Fig. 6 and 7. % % % % % %.5 5 5.5 5 5 Fig. 6. DFRS, X-direction: Turbine support #; Turbine support #
XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ th INTERNATIONAL SCIENTIFIC CONFERENCE VSU' 5 % % % 5 % % %.5 5 5.5 5 5 Fig. 7. DFRS, Y-direction: Turbine support #; Turbine support # Conclusion A set of three statistically independent ground motion records compatible with the response spectra and PGA given by EC8/NA is developed. Detailed FE model of the foundation structure is developed, using the FEA code SAP. Three linear dynamic analyses of the considered turbine foundation have been performed using equivalent stiffness and damping to account for soil-structure interaction, hysteretic soil behaviour and ductile response of the RC structure. The seismic response of the system is determined by the aspect ratio of the foundation the predominant mode shape is rocking in Y-direction. The peak spectral acceleration for turbine and generator supports in Y-direction is higher than the peak acceleration in X-direction. The two turbine supports have different peak spectral accelerations in X-direction due to the structural response of the foundation. DFRS are developed as seismic design basis for the main equipment of the TPP unit. Acknowledgement The author wishes to thank Dr Marin Kostov and Mr Georgi Varbanov for their expert guidance during this project, and to Ms Nina Koleva for her assistance in the calculation of artificial ground motions and DFRS. REFERENCES [] Comite Euro-International Du Beton. CEB-FIP Model Code 99, 99. [] Computers and Structures inc. CSi Analysis Reference Manual, Berkeley,. [] Iwan W.D. Estimating inelastic response spectra from elastic spectra, Earthquake Engineering and Structural Dynamics, Vol. 8, 98, pp. 75-88. [] FEMA. Improvement of Nonlinear Static Seismic Analysis Procedures, 5. [5] ASCE -98. Seismic Analyses of Safety-Related Nuclear Structures, 997. [6] Ishibashi I., Zhang X. Unified Dynamic Shear Moduli and Damping Ratios of Sand and Clay, Soils and Foundations, Vol., No., pp. 8-9. [7] Richart F.E., et al. Vibrations of Soils and Foundations, Prentice-Hall, 97. [8] BDS EN 998-/NA. National Annex to Eurocode 8, Part, (in Bulgarian) [9] Jennings P.C., Housner G.W., Tsai N.C. Simulated Earthquake Motions, EERL Report, California Institute of Technology, 968.