1. XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ’2014
14th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'2014
CALCULATION OF FLOOR RESPONSE SPECTRA. CASE STUDY FOR
THE MAIN EQUIPMENT OF A 35 MW STEAM TURBINE
Stoyan Andreev1
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 1998-1/NA. The dynamic soil-
structure 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
1. Introduction
In 2012-2013 Risk Engineering Ltd. replaced a 55 years old steam turbine at Sofia
TPP with a new one having a net capacity of 35 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 (#1),
and enlargement of the RC girder supporting the turbine rear bearings (#2).
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.
2. 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.
2.1. Structural Modelling
The original structure was built with concrete grade BM150, which is equivalent to
grade C12/15 in EC2. For the reconstruction concrete grade C20/25 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. [1], see Table 1.
1
MSc, Structural Engineer, 10 Vihren Str, Buxton 1618, Sofia, Bulgaria, Stoyan.Andreev@RiskEng.bg

2. XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ’2014
14th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'2014
Table 1. Concrete material parameters
Concrete grade Density, t/m3
Poisson’s ratio Eci, MPa Ec, MPa Gc, MPa
C12/15 2.5 0.2 27000 22950 9605
C20/25 2.5 0.2 30000 25500 10625
A detailed finite element model is developed using SAP2000 [2]. 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. 1.
Fig. 1. FE model of the turbine-generator foundation
The foundation mat is 21x6 meters in size, embedded 2 meters in the ground. It is
assumed to be rigid [5]. The total height of the structure is 10.6 meters. The total mass of
the structure, including the equipment is approximately 1165 tons
The behaviour factor of the structure in the reconstruction design is given as q=1.5.
The used relations between q, the ductility ratio μ, the effective period of the structure Teff
and the initial period of the fixed base structure T0 are given in ref. [3] and [4].
The modal analysis shows that initial natural period of the structure with a fixed base
is 0.136 sec. It is calculated that μ=1.63 and Teff=0.147 sec.
The effective material damping for a given ductility ratio is calculated according to
equations in ref. [3] and [4]. For μ=1.63 the calculated effective damping is ξeff=9.0%.
To adjust the fixed base period the bending stiffness of the structural members is
decreased by 16% and the shear stiffness is decreased by 20%.
2.2. Soil-Structure Interaction
In the analyses the soil is represented with a 6 DOFs lumped spring-dashpot [2].
It is assumed that the clay layer is thick and uniform for the considered depth – 30 m.
According to EC8 this is a type C soil with shear wave velocity VS,30=180–360 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 Gmax is assumed, and lower (LB) and upper (UB) values
are calculated by dividing or multiplying the BE value by a factor of 2.
The strain softening of the soil due is considered with shear wave velocity reduction
factor n=0.6, as given in ref. [4]. The reduced shear wave velocity is noted as Vs,r.
Corresponding soil hysteretic damping is calculated using shear strain–damping relations
after Ishibashi and Zhang for Geff and PI=20 [6]. The soil properties are given in Table 2.

3. XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ’2014
14th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'2014
Table 2. Initial and effective soil parameters
Variation
Density,
t/m3
Poisson’s
ratio
Vs,30,
m/s
Gmax,
MPa
Vs,r, m/s
Geff,
MPa
Damp,
%
BE 2.0 0.45 255 130.1 153 46.8 12.9
LB 2.0 0.45 180 64.8 108 23.3 12.9
UB 2.0 0.45 360 259.2 216 93.3 12.9
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 3 and 4.
Table 3. Lumped spring stiffness
Variation
Krx,
MN/m
Kry,
MN/m
Krz,
MN/m
Kψx,
MNm/rad
Kψy,
MNm/rad
Kt,
MNm/rad
BE 1539 1615 2311 25000 168900 105700
LB 766 804 1151 12500 84450 52850
UB 3068 4608 4608 50000 337800 211400
Table 4. Lumped dashpot constants
Variation
Crx,
MN.s/m
Cry,
MN.s/m
Crz,
MN.s/m
Cψx,
MNm.s/rad
Kψy,
MNm.s/rad
Kt,
MNm.s/rad
BE 36,7 38,5 81,3 170 2445 783
LB 25,9 27,2 57,4 120 1725 553
UB 51,8 54,3 114,8 240 3450 1106
2.3. Seismic input
The target free-field spectra are the elastic response spectra from EC8/NA with
importance factor of 1.4, soil factor 1.2 and reference ground acceleration 0.23g [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 0.01 sec. The envelope
shape is based on the Compound model of Jeninngs et al. [9]. The total length of the
records is 40 sec with a 22 sec strong motion part. The PGA is approximately 0.38g for
horizontal and 0.32g 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. 3.
0
0.5
1
0.5 5 50
SA,g
Frequency, Hz
Acc X
Acc Y
Target
0.9*Target
a)
0
0.5
1
0.5 5 50
SA,g
Frequency, Hz
Acc Z
Target
0.9*Target
b)
Fig. 3. Seismic input: a) Horizontal directions; b) Vertical direction

4. XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ’2014
14th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'2014
2.4. Dynamic Analyses and Calculation of Floor Response Spectra
Linear modal time-history analyses are performed for the three soil conditions. In
each case 20 vibration modes up to at least 50 Hz are calculated with a procedure using
Ritz vectors. Composite modal damping is applied, including soil damping, dashpot
viscous damping and RC material damping [2]. The procedure for calculating design floor
response spectra is given in Commentary to ref. [5].
3. Analytical Results
The two fundamental horizontal mode shapes for BE soil are shown in Fig. 4.
a) b)
Fig. 4. Predominant mode shapes: a) Y-direction @ 2.85 Hz; b) X-direction @ 4.41 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, %
1 2.85 0.0 76.4 0.0 98.5 0.0 6.0
2 4.41 78.8 0.0 0.2 0.0 74.8 0.0
3 4.99 0.0 0.2 0.0 0.1 0.0 71.4
4 6.69 0.0 0.0 0.0 0.0 0.0 5.4
5 7.94 0.6 0.0 98.4 0.0 1.0 0.0
6 9.55 11.1 0.0 0.0 0.0 2.5 0.0
7 11.84 3.2 0.1 0.7 0.0 8.2 0.0
8 12.01 0.0 22.2 0.0 0.5 0.0 1.4
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
2.85 due to the large (3.5:1) 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 – 4.41 Hz. The Z-direction predominant mode is
translational and governed by the SSI.

5. XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ’2014
14th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'2014
The calculated 5%-damping envelope raw (not broadened) floor response spectra for
turbine supports #1 and #2 are shown in Fig. 5. Both locations are shown in Fig. 1.
0
1
2
3
0.5 5 50
SA,g
Frequency, Hz
X-dir.
Y-dir.
Z-dir.
a)
0
1
2
3
0.5 5 50
SA,g
Frequency, Hz
X-dir.
Y-dir.
Z-dir.
b)
Fig. 5. Enveloped raw floor response spectra, 5% damping: a) Turbine support #1; b)
Turbine support #2
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 (2.0-3.45 Hz). The spectra for turbine supports #1 and #2 are
similar with some difference around 3.45 Hz – the predominant frequency for UB soil. The
torsion response at 4.99.
In X-direction the effect of the structural response is more pronounced – there is a
peak in the spectral accelerations for turbine support #2 with values about 40% 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
#1 and #2 are shown in Fig. 6 and 7.
0
1
2
3
4
0.5 5 50
SA,g
Frequency, Hz
2%
3%
5%
7%
10%
a)
0
1
2
3
4
0.5 5 50
SA,g
Frequency, Hz
2%
3%
5%
7%
10%
b)
Fig. 6. DFRS, X-direction: a) Turbine support #1; b) Turbine support #2

6. XIV МЕЖДУНАРОДНА НАУЧНА КОНФЕРЕНЦИЯ ВСУ’2014
14th INTERNATIONAL SCIENTIFIC CONFERENCE VSU'2014
0
1
2
3
4
5
0.5 5 50
SA,g
Frequency, Hz
2%
3%
5%
7%
10%
a)
0
1
2
3
4
5
0.5 5 50
SA,g
Frequency, Hz
2%
3%
5%
7%
10%
b)
Fig. 7. DFRS, Y-direction: a) Turbine support #1; b) Turbine support #2
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
SAP2000. 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
[1] Comite Euro-International Du Beton. CEB-FIP Model Code 1990, 1993.
[2] Computers and Structures inc. CSi Analysis Reference Manual, Berkeley, 2010.
[3] Iwan W.D. Estimating inelastic response spectra from elastic spectra, Earthquake
Engineering and Structural Dynamics, Vol. 8, 1980, pp. 375-388.
[4] FEMA 440. Improvement of Nonlinear Static Seismic Analysis Procedures, 2005.
[5] ASCE 4-98. Seismic Analyses of Safety-Related Nuclear Structures, 1997.
[6] Ishibashi I., Zhang X. Unified Dynamic Shear Moduli and Damping Ratios of Sand
and Clay, Soils and Foundations, Vol.33, No.1, pp. 182-191.
[7] Richart F.E., et al. Vibrations of Soils and Foundations, Prentice-Hall, 1970.
[8] BDS EN 1998-1/NA. National Annex to Eurocode 8, Part 1, 2012 (in Bulgarian)
[9] Jennings P.C., Housner G.W., Tsai N.C. Simulated Earthquake Motions, EERL
Report, California Institute of Technology, 1968.