ML19323E350
| ML19323E350 | |
| Person / Time | |
|---|---|
| Site: | South Texas  |
| Issue date: | 05/16/1980 |
| From: | HOUSTON LIGHTING & POWER CO. |
| To: | |
| Shared Package | |
| ML19323E348 | List: |
| References | |
| NUDOCS 8005230425 | |
| Download: ML19323E350 (200) | |
Text
{{#Wiki_filter:O C' SEISMIC ANALYSIS OF CATEGORY I STRUCTL"RES AN ALTERNATE COMPARATIVE ANALYSIS USI.VG THE " ELASTIC HALF-SPACE MET 9CD" 8005230
.. .. ___ =. .. .- _ . _ . . ;
- f TABLE OF CONTE.VIS I
SECTION TITLE PAGE
1.0 INTRODUCTION
. . . . ... . . . . . . . . .. .. . . 1 2.0 OBJECTIVES . . . . . . . . . .. . . . . . . . . . .. 1 3.0 TECHNICAL DESCRIPTION . . . .. . . . . . . . ... . 2 3.1 CONSTRUCTION OF MATHEMATICAL MODEL . . . . . . . . . . 2 3.2 COMPUTATION OF INPUT MOTIONS . . . . . . . . . . . . . 6 3.3 GENERATION OF FLOOR RESPONSE SPECTRA . . . . . . . . . 8 4.0
SUMMARY
OF RESULTS . . . . . . . . .. . . . . . . . . 9
5.0 CONCLUSION
. . . . . ... . . . . . . . . . . . . . . 10
6.0 REFERENCES
. . . . . ... . . . . . . . . . . . . . . 10 i
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LIST OF FIGU2ES FIGURES TITLE 1 Reactor Containment Building Mathematical Model 2 Response Spectra of Horizontal Support Motion and Control Motion of Reactor Containment Building 3 Response. Spectra of Horizontal Support Motion and Control Motion of Fuel Handling Building 4 Floor Response Spectra for Reactor Containment Building 4.1 Coo;ainment Shell, EL 153'-0", N-S Direction, 2% damping 4.2 Ccatainment Shell, EL 153'-0", N-S Direction, 4% damping 4.3 Containment Shell, EL 68'-0", N-S Direction, 2% damping 4.4 Containment Shell, EL 68'-0", N-S Direction, 4% damping 4.5 Internal Structure, EL 68'-0", N-S Direction, 2% damping 4.6 Internal Structure, EL 68'-0", N-S Direction, 4% damping 4.7 Internal Structuta, EL 19'-0", N-S Direction, 2% damping 4.8 Internal Structure, EL 19'-0", N-S Direction, 4% damping 4.9 Internal Structure, EL 32'-0", N-S Direction, 2% damping 4.10 Internal Structure, EL 32'-0", N-S Direction, 4% damping 4.11 Containment Shell, EL -13'-3", N-S Direction, 2% damping 4.12 Containment Shell, EL -13'-3", N-S Direction, 4% damping 4.13 Containment Shell, EL 153'-0", E-W Direction, 2% damping i 4.14 Containment Shell, EL 153'-0", E-W Direction, 4% damping 4.15 Containment Shell, EL 68'-0", E-W Direction, 2% damping , 4.16 Containment Shell, EL 68'-0", E-W Direction, 4% damping 4.17 Internal Structure, EL 68'-0", E-W Direction, 2% damping 4.18 Internal Structure, EL 68'-0", E-W Direction, 4% damping 4.19 Internal Structure, EL 19'-0", E-W Direction, 2% damping 4.20 Internal Structure, EL 19'-0", E-W Direction, 4% damping 4.21 Internal Structure, EL 32'-0", E-W Direction, 2% damping 4.22 Internal Structure, EL 32'0", E-W Direction, 4% damping 4.23 Containment Shell, EL -13'-3", E-W Direction, 2% damping 4.24 Containment Shell, EL -13'-3", E-W Direction, 4% damping 4.25 Containment Shell, EL 153'-0", Vertical Direction, 2% damping 4.26 Containment Shell, EL 153'-0", Vertical Direction, 4% damping 4.27 Containment Shell, EL 68'-0", Vertical Direction, 2% damping 4.28 Containment Shell, EL 68'-0", Vertical Direction, 4% damping 4.29 Internal Structure, EL 68'-0", Vertical Direction, 2% damping 4.30 Internal Structure, EL 68'-0", Vertical Direction, 4* aamping 4.31 Internal Structure, EL 19'-0", Vertical Direction, 2*. damping 4.32 Internal Structure, EL 19'-0", Vertical Direction, 4*. damping 4.33 Internal Structure, EL 32'-0", Vertical Direction, 2*. damping 4.34 Internal Structure, EL 32'-0", Vertical Directio'n, 4*. damping 4.35 Containment Shell, EL -13'-3", Vertical Direction, 2*. damping 4.36 Containment Shell, EL -13'-3", Vertical Direction, 4*.
- damping 5 Floor Response Spectra for Fuel Handling Building 4
5.1 Fuel Handling Bldg., EL -29'-0", N-S Direction 2*. damping s
; 5.2 Fuel Handling Bldg., EL -29'-0", N-S Directica, 4*. damping 5.3 Fuel Handling Bldg., EL 4'-0", N-S Direction, 2*. damping 5.4 Fuel Handling Bldg. , EL 4'-0", N-S Direction, 4*. damping 5.5 Fuel Handling Bldg., EL 30'-0", N-S Direction, 2*. damping 5.6 Fuel Handling Bldg., EL 30'-0", N-S Direction,4*. damping 5.7 Fuel Handling Bldg., EL 48'-0", N-S Direction, 2*, damping 5.8 Fuel Handling Bldg., EL 48'-0", N-S Direction, 4* damping 5.9 Fuel Handling Bldg., EL 68'-0", N-S Direction, 2% damping 5.10 Fuel Handling Bldg., EL 68'-0", N-S Direction, 4*, damping 5.11 Fuel Handling Bldg., EL 119'-0", N-S Direction, 2% damping 5.12 Fuel Handling Bldg., EL 119'-0", N-S Direction, 4% damping 5.13 Fuel Handling Bldg., EL -29'-0", E-W Direction, 2% damping 5.14 Fuel Handling Bldg. , EL -29'-0", E-W Direction, 4% damping 5.15 Fuel Handling Bldg., EL 4'-0", E-W Direction, 2*. damping 5.16 Fuel Handling Bldg., EL 4'-0", E-W Direction, 4*. damping 5.17 Fuel Handling Bldg., EL 30'-0", E-W Direction, 2*. damping 5.18 Fuel Handling Bldg., EL 30'-0", E-W Direction, 4% damping 5.19 Fuel Handling Bldg., EL 48'-0", E-W Direction, 2*. damping 5.20 Fuel Handling Bldg., EL 48'-0", E-W Direction, 4% damping 5.21 Fuel Handling Bldg., EL 68'-0", E-W Direction, 2* damping 5.22 Fuel Handling Bldg., EL 68'-0", E-W Direction, 4*. damping 5.23 Fuel Handling Bldg., EL 119'-0", E-W Direction, 2*. damping 5.24 Fuel Handling Bldg., EL 119'-0", E-V Direction, 4% damping 5.25 Fuel Handling Bldg., All Elevations, Vertical Direction, 2% damping 5.26 Fuel Handling Bldg., All Elevations, Vertical Direction, 4% damping 6 Floor Response Spectra for Diesel Generator Building 6.1 Diesel Gen. Bldg., EL 82'-0", N-S Direction, 2". dsmping 6.2 Diesel Gen. Bldg., EL 55'-0", N-S Direction, 2*. damping
-111.
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6.3 Diesel Gen. Bldg., EL 100'-0", E-W Direction, 2% damping 6.4 Diesel Gen. Bldg. , EL 82'-0", E-W Direction, 2% damping 6.5 Diesel Gen. Bldg., EL 55'-0", E-W Direction, 2% damping 6.6 Diesel Gen. Bldg., EL 100'-0", Vertical Direction, 2% damping 6.7 Diesel Gen. Bldg., El 55'-0", Vertical Direction, 2% damping 6.8 Diesel Gen. Bldg., EL 100'-0", N-S Direction, 2% damping 7 Floor Response Spectra for Mechanical Electrical Auxiliary Building 7.1 M.E. Aux. Bldg., EL 85'-0", N-S Direction, 2% damping 7.2 M.E. Aux. Bldg., EL 69'-6", N-S Direction, 2% damping 7.3 M.E. Aux. Bldg., EL 35'-0", N-S Direction, 2% damping 7.4 M.E. Aux. Bldg., EL 51'-0", N-S Direction, 2% damping 7.5 M.E. Aux. Bldg., EL 85'-0", E-W Direction, 2% damping 7.6 M.E. Aux. Bldg., EL 69'-6", E-W Direction, 2% damping 7.7 M.E. Aux. Bldg., EL 51'-0", E-W Direction, 2% damping 7.8 M.E. Aux. Bldg., EL 35'-0", E-W Direction, 2% damping 7.9 M.E. Aux. Bldg. , All Elevations, Vertical Direction, 2% damping i l } l
-iv-1
LIST OF TABLES TABLE NO. TITLE 1 Frequency-Dependent Stiffness and Damping Coefficients Based on Novak's Approach 2 Dynamic Stiffnesses for a Half-Space 0
-v- l I
l
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1.0 INTRODUCTION
During February 1975, a meeting was held among representatives of the NRC, HL&P, B&R, Woodward-Clyde Consultants (WCC), and
- EDS, Inc., to discuss the Soil-Structure Interaction (SSI) analysis approach to be used on the South Texas Project.
Design criteria were finalized at the meeting and subsequently documented (Ref. 1). Soil-Structure Interaction analysis was then performed using the Finite Element Method (FEM) as agreed upon. In April 1979, the NRC requested that a comparison be made between results from the FEM and the Elastic Half-Space Method (EHM). In May 1979, it was decided that a confirmatory analysis using the EHM would be performed to verify the FEM results. On September 18, 1979, HL&P, B&R, and WCC presented to the NRC for approval tentative procedures for the SSI analysis using the EHM (Ref. 2). Houston Lighting and Power stated that this analysis would be performed by the EHM model using Kausel's approach (Ref. 10), i.e., for deeply embedded structures {the Reactor Containment Building (RC3) and the Fuel Handling Building (FHB)}, the response spectra in Regulatory Guide 1.60 would be defined at the ground level and then modified to take into account the effect of deep embedment (Kinematic Interaction). The NRC stated that they would need to evaluate the results of the analysis, where Kausel's approach results in significant reductions in the response spectra, before making any judgments on the acceptability of the analysis (Ref. 3). To this end, the confirmatory analysis was performed, and the results are presented herein. 2.0 OBJECTIVES The objectives of this report are: o To present justifications for using Kausel's approach to account for Kinematic Interaction of deeply embedded structures, o To present results of the confirmatory analysis using the EHM to support the results obtained using the FEM, and o To provide a documentary base for obtaining approval to use the FEM results in the final design. 4
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3.0 TECHNICAL DESCRIPTION The outline of the procedures used to perform the EHM analysis was described in a memo from Mr. E. A. Turner of HI.&P to Mr. D.B. Vassallo of the NRC, dated August 8, 1979 (Ref. 2). In the EHM, a mathematical model was first constructed to represent the soil / structure system. The input motions to the base of the system were then computed. The response spectra were finally generated by applying the calculated input motions to the mathematical model. The technique and justification for the use of the method follow. 3.1 CONSTRUCTION OF MATHEMATICAL MODEL In this study, the superstructures were represented by three-dimensional lumped mass models identical to those used in the FEM. The foundation soil was represented _y a set of springs and dashpots. The integrated mathematical model for the RC3 is shown in Figure 1 as an example. The spring and damping coefficients were computed using Novak's approach (Ref. 4 through 7 and 16), which assumes that the force-displacement relations due to the soil underneath the embedded structures are identical to the force-displacement relations of the structures as if the side soil were completely removed. The effect of the side soil is then treated independently. Thus, the dynamic interaction of an embedded foundatiou consists a of two contributions: one from the half-space underneath the foundation and the other from the side soil. The set of equations used to compute the overall stiffness and damping coefficients based on Novak's approach is shown in Table 1. The dynamic stiffness coefficients for a half-space were computed from the expression (Ref. S): Kh=K {k (1 + 2iS) + ia,c (1 + i$)} where:
)
.(=staticstiffnesscoefficients k,c = stiffness functions a, = wr,/V, = dimensionless frequency w = 2nf = circular frequency 1
t r, = radius of foundation Vs = shear. wave velocity i =Q-l , and
$ = material (hysteretic) damping of the soil.
l This equation accounts for both the radiation and material damping. Values of K , k, and c for horizontal and vertical r translations, rotation, and torsion are summarized in Table 2. The dynamic stiffnesses for the side soil were computed as follows: for horizontal translation, the dimensionless dynamic stiffness, S , was derived from the expression: S (a,,v) = S y (a,,v) + i S 2 (*o' V) I ( ( ' { 'f3 (a ) H y ( ) (x,) + H2 (*o) Hy (2) (, )
= 2na V H
o (2) (ao ) H,s (2) (x o) + H (2) (x ) H, (2) (, ) o o . o
, where:
S y = frequency-dependent spring function S 2
= requency-dependent damping function ;
q -
= (1-2v)/2(1-v)
X o o a, = w r,/V, V, = shear wave velocity of side soil v = Poisson's Ratio of side soil i I H (2)(a,), H /2) (x,) = second Hankel functions of order n i
=
i f -1
For vertical translation, the dimensionless dynamic stiffness, Sy , was derived from the expression: Sy (a,) = Syy+iSw2 where: J1 (a,) J, (a,) + Y1 (a,) Y, (a,) Swl = 2na J o o o o S = J, 2 (a ) + Y, 2 (, ) J,(a,) = Bessel functions of the first kind of order n 1 Y" (a ) = Bessel functions of the second kind of order n (or Neumann's functions of order n) For rotation, the dimensionless dynamic stiffness, S,, was derived from the expression: S, (a,) = S,7 + i S o2 i where: J, (a,) J1 (a,) + Y, (a,) Y (a,) S =n 1-a o J 2 (a,) + Y 2 (a,) 1 _ 1 S 4 02 = J 1 (a,) + Yy 2 (, ) . For torsion, the dimensionless dynamic stiffness S q, was derived from the expression: S (a,) = S y+iS 2 1 4 4
where:
= 2n J, (a,) J1 (a,) + Y, (a,) Yg (a,)
S 2-a J1 2 (, ) 7 2 (, ,) 4 Jt 2 (, 9) , y 2 (39) J An examination of the equations in Tables 1 and 2 indicates that an equivalent shear modulus of soil rather than the shear modulus of each soil layer underneath the foundation was required. The equivalent shear moduli of soil underneath the foundations
, were computed by considering the stiffnesses of a soil mass to a a depth equal to one diameter or one long dimension of the foundation, assuming that stresses in the soil mass due to an applied load at the bottom of the foundation spread out with a depth below the foundation at the rate of 2 vertical to 1 horizontal. Based on these assumptions, the equivalent shear modulus was computed by weighting these effects using the expression:
l i 2 h I i i=1 a. 1 G = eq h I i i=1 a Gg where: h1 = thickness of ith soil layer underneath the foundation Gg = shear modulus of ith soil layer a.' = area of stress influence of a horizontal plane passing through the center of ith soil layer n = number of soil layers underneath bottom of the foundation to a depth equal to one diameter or one long dimension of the foundation
..~s
The equivalent shear modulus for side soil layers was computed by: m I j=1 h) Gd g = eq m I h j=1 3 where:
- h. = thickness of jth side soil layer J
G. = shear modulus of ith side soil layer J m = number of side soil layers 3.2 COMPUTATICN OF INPUT MOTIONS For the surface structures, the input motions were the time histories simulating the Regulatory Guide 1.60 Design Response Spectra. Since the application of the EHM was not in the NRC Standard Review Plan, other sources were researched for acceptable methods of analysis. The three-step lumped spring method, including the Kinematic Interaction analysis as described by Kausel et al. (Ref.10) and summarized in a report by the ASCE Ad Hoc Group on Soil-Structure Interaction (Ref. 9), was used for the deeply embedded structures. This repor:, titled
" Analysis for Soil-Structure Interaction Effects for Nuclear Power Plants" and prepared by experts in this specialized area, describes the theoretical basis and formulations of the method. It was issued by the ASCE committee for review and comment by professionals in governmental agencies, universities, and A/E firms in 1975 and 1976 and was approved by the executive committee of the Structural Division cf ASCE in early 1979.
The report provides a set of formulae to calculate, from the ground surface motion, a set of translational and rotational motions to be used as input base-excitations to the integrated mathematical model constructed as described in Section 3.1. The formulas used in the report are as follows: 6-
Translation: _ _
, F(0) )
f j , if f < 0.7 f,,
.. 1 Cos(n2 f nj u(t) = IIT h
> F(0) 0.453 , if f 1 0.7 f i a
Rotation: [ n f 3
.F(0) f /R - , if f <n f 0.257 l( 1 - Cos ia/
.. )
0(t) = IFT I F(G) 0.257/R , if f 1 f where: u = Translational acceleration time history
'd=rotationalaccelerationtimehistory(oispositive clockwise)
F(0) = Fourier components of the horizontal control motion at the finished grade in the free-field 0 = 2 n f = circular frequency f "= fundamental shear beam frequency of the soil column
'bove .he foundation level' R = radius of the foundation mat IFT = Inverse Fourier Transformation i
i i
The above procedure has been shown to yield satisfactory results for a wide range of embedment depths (Ref.10). The detailed theoretical description of this technique is in a paper by Kausel et al. (Ref. 10), submitted to Mr. D.B. Vassallo of the NRC from Mr. E.A. Turner of HL&P on August 8,1979 (ST-HL-AE-366: SEN: V-0100). This paper was presented at the 4th International Conference on Structural Mechanics in Reactor Technology in September 1977. Professor Kausel, who is the Senior Author of the paper, is our consultant in this Kinematic Interaction analysis effort to assure the correct application of the technique. An independent study by Luco et al., (Ref. 11) resulted in relationships si.milar to those given by the above two equations which relate the motions of a rigid foundation to the free-field ground surface motion. D'Appolonia Consulting Engineers, under contract to the NRC, investigated SSI due to embedment effects. Among the papers discussing the embedment effects, the one by Kausel et al., (Ref. 10, submitted by HL&P to the NRC) was specifically reviewed. D'Appolonia, in their final report (Ref. 12) tn :he NRC in 1979 titled " Seismic Input and Soil-structure Inte action," concluded that the motion computed using the two equations cited here would he more accurate for the lumped parameter (EKM) input than the surface motion. It is noted that for horizontal excitation, the peak acceleration for the Operating Basis Earthquake (OBE) at the South Texas Project site is 0.050 g. In the analysis presented here, the peak OBE ground motion at the finished grade was increased to 0.067 g (Ref. 17) to satisfy the requirement of peak acceleration at the foundation level in the free field, an increase of 34 percent, before applying Kausel's Kinematic Interaction Analysis Technique. The base excitations resulting from the Kinematic Interaction Analysis consist of both translational and rotational motions. The response spectra from the calculated translaticeal motion alone envelop the 60 percent design response spectra (corresponding to 0.03 g peak acceleration for the OBE), and in some frequency ranges, the spectral magnitudes exceed those of the design response spectra corresponding to 0.05 g peak acceleration. Figures 2 and 3 show the comparison of these response spectra. For vertical excitation, the peak acceleration for the OBE at the STP site is 0.033 g (2/3 of the horizontal peak acceleration) in the free field. For the analysis in the vertical direction, all the buildings were subjected to the free field time-histories. I l 3.3 GENE'4ATION OF FI.00R RESPONSE SPECTRA Using the mathematical models constructed as described in Section 3.1 and the input base excitations computed as described in Section 3.2, a set of floor response spectra were obtained at strategic locations in the RCB, the FHB, the Diesel Generator Building (DGB), and the Mechanical-Electrical Auxiliaries Building (MEAB). These response spectra were then superimposed on those obtained using the FEM for comparison. For the DGB and the MEAB, whose response spectra from the FEM generally envelop those from the EHM, only 2 percent damping floor response spectra were generated. For the RCB and the FHB, whose spectral responses from the EEM slightly exceed those from the FEM in a small frequency range, both 2 percent damping and 4 percent damping floor response spectra were generated for comparison. The superimposed spectra are shown in Figures 4, 5, 6, and 7 for the RCB, the FH3, the DGB, and the MEAB, respectively, and the results are discussed in Section 4.0. 4.0
SUMMARY
OF RESUI.TS For the MIAB, Figures 7.1 through 7.9 show that the response spectra obtained using the FEM are consistently higher than those obtained using the EHM. For the DGB, Figures 6.1 through 6.8 show that the response spectra obtained using the FEM in general envelop those obtained using the EHM except in a very small frequency range in the east-west direction (see Fig. 6.3). In this range, say from 1 to 3 Hz, the maximum increase of results using the EHM was about 20 percent but corresponding to a small increase from i 0.35 g to 0.42 g, an increase of 0.07 g which is an insignificant amount. For the RCB, Figures 4.1 through 4.24 show that the horizontal responses obtained using the FEM are generally higher than those obtained using the EHM except for small frequency ranges from 2 to 3 Hz in both directions. In this range, the EHM responses are greater than the FEM responses by up to 70 percent, but the increases diminish rapidly near 3 Hz. These increases are mainly due to the conservatism introduced by utilizing Kausel's approach as shown in Fig. 2. This figure shows that for frequencies lower than 2 Hz, the responses from Kausel's approach are up to 100 percent higher than those from the sixty percentile design spectrum. Without the conservatism associated with the approach in the low frequency ranges, the responses from the FEM would conceivably be compatible with or greater than those obtained from the EHM for the entire frequency
.g.
i l l range. In the vertical direction for both the shell and the internal structure, the responses calculated frcm the EHM are higher in the frequency range from 2 to 5 Hz but are lower in the remaining frequency range (see Figures 4.25 through 4.35). Even in the frequency range where the EHM results are higher than the FEM results, the differences are less than 20 percent. For the FHB, Figures 5.1 through 5.24 show that the EHM results exceed the FEM results only in the frequency range 0.8 Hz to 2 Hz in the east-west and the north-south directions. Even in this range, the maximum increase of response was within 10 percent. In the vertical direction (see Figures 5.25 and 5.26), the response spectra from the FEM envelop those from the EHM in the entire frequency range. It is noted that in the low frequency range, say less than 5 Hz, the responses from both the FEM and the EHM correlate well for the surface structures. The analysis techniques for deeply embedded structures using the FEM involved similar , procedures to those used for the surface structures, while the ' analysis technique using the EHM, which is also acceptable to the industry, involved additional approximations, assumptions, and formulae for deeply embedded structures. Much literature has commented that the FEM is a more appropriate method of treating deeply embedded structures with layered foundation soil as is the case for the South Texas Project. The FEM used in the FEM analysis is a plane strain, 2-dimensional one. The energy between buildings is confined and, therefore, can not propagate in all directions and dissipate as it will in actuality. This, and the conservative measures introduced in smoothing and plotting the response spectra from the FEM results, are j believed to be the basic reasons for the discrepancies between I the two response spectra.
5.0 CONCLUSION
The EHM technique utilized in analysis of South Texas Project Category I structures is well documented in the ASCE Design Manual (Ref. 9) and has gained acceptance throughout the industry. Results from the EHM are therefore acceptable for 1 structural design. I Results from EHM analysis tend to be conservative. This observation is due to the following factors: a) A design response spectrum has been specified for the soil site which l is rich in all frequency component contents, b) Elastic analysis j method was utilized in the analysis, c) Peaks of the floor l response spectra were widened by + 15 percent, and d) The low i damping values specified in Regulatory Guide 1.61 have been used. In addition to the above conservatisms, the use of FEM results provide an additional design margin as the response spectra from the FEM generally envelop those from the EHM as discussed in Section 4, provided that extra conservatism in the low frequency ranges are removed. The majority of our safety related piping and equipment has fundamental frequencies above 7 Hz. In this range the FEM results are consistently higher than the EHM results. Therefore, the use of the FEM results in the design will provide a sufficiently adequate safety margin. Furthermore, in our design of structures and the qualification of safety related piping or equipment, we have committed in the FSAR to use envelop response spectra for subsystems on multiple supports and minimum material strength values. In conclusion, based on the above discussion, the FEM results alone should be utilized in the final Design.
6.0 REFERENCES
- 1. Minutes of Meeting with the NRC Regarding South Texas Project; Lockets STN-50-498 and 499, Memo from E. Douglas Schwantes of WCC, Correspondence No. ST-VL-MS-0337, G-127138-100 (February 18, 1975).
- 2. Soil-Structures Interaction Analysis Procedures for Category I Structures of the South Texas Project; Memo from E.A. Turner of HL&P to D.B. Vassallo of VRC, Correspondence No. ST-HL-AE-366, SFN: V-0100 (August 8, 1979).
- 3. Summary of Meeting to Discuss Soil-Structure Interaction Analysis, from E. A. Licitra of NRC to HL&P (October 11, 1979).
- 4. Novak, M. "Effect of Soil on Structural Response to Wind and Earthquake," Earthquake Engineering and Structural Dynamics, Vol. 3 (1974), 79-96.
- 5. Novak, M. and Beredugo, Y.O. " Vertical Vibrations of Embedded Footings," Journal of Soil Mechanics and # andation Engineering Division. ASCE, Vol. 98, No. SM12 (December 1972).
- 6. Beredugo, Y.0. and Novak, M. " Coupled Horizontal and Rocking Vibration of Embedded Footings," Canadian Geotech-nical Journal (November 1972), 477-497.
- 7. Novak, M. and Sachs, K. " Torsional and Coupled Vibrations of Embedded Footings," International Journal of Earthquake g;gineering Sr-,.-tjural Dynamics, Vol. 2, No. 1 (July-Sept. 2.
- 8. Lysmer, J. " Foundation Vibration with Soil Damping,"
(Paper to be submitted to ASCE Specialty Conference: Civil Engineering and Nuclear Power, Knoxville, Tennessee, September 1980).
- 9. " Analyses for Soil-Structure Interaction Effects for Nuclear Power Plants" (Report by the Ad Hoc Group on Soil-Structure Interaction - I.M. Idriss, Chairman -
Nuclear Structures and Materials Committee of the Struc-tural Division of ASCE) .
- 10. Kausel, E. et al. " Dynamic Analysis of Embedded Structures,"
Fourth International Conference on Structural Mechanics in Reactor Technology (San Francisco, Sept. 1977) Paper No. K2/6.
- 11. Luco, J.E. et al. " Dynamic Response of Three-Dimensional Rigid Embedded Foundations," NSF Report EN-76-22632 (University of California, San Diego,1978).
- 12. " Seismic Input and Soil-Structure Interaction" (D'Appolonia Consulting Engineer's Final Report, No. NUREG/CR-0693, Prepared for U.S. Nuclear Regulatory Commission).
- 13. Veletsos A.S. and Wei, Y.T. " Lateral and Rocking Vibration of Footings," Journal of the Soil Mechanics and Foundations Division ASCE, Vol. 97, No. SM9 (September 1971), 1227-1248.
- 14. Veletsos, A.S. and Verbic, B. " Basic Response Functions for Elastic Foundations," Journal of the Engineering Mechanics Division, ASCE, Vol. 100, No EM2 (April 1974), 189-202.
- 15. Kausel, E. and Ushijima, R. " Vertical and Torsional Stiffnesses of Cylindrical Footings," MIT Publication No.
R79-6 (1979).
- 16. " Computations of Springs and Damping Coefficients for Category I Structures, South Texas Project, Units 1 and 2" (heport by Woodward-Clyde Consultants for Brown &
Root, Inc. , April 1980) TPNS-Y310XR1398CWC.
- 17. " Support Motions for Reactor Containment Building and Fuel Handling Building, South Texas Project, Units 1 and 2" (Report by Woodward-Clyde Consultants for Eroun &
Root, Inc. , April 1980) TPNS-Y310XR1399CWC. TABLE 1 FREQUENCY-DEPENDENT STIFFNESS AND DAMPIllG COEFFICIENTS BASED ON HOVAK'S APPROACII Type of Vibration Stiffness Coefficient Damping Coefficient
*llorizontal Translation k xx
=k yy
= Gr o 'Cx 1 + GES--6S x l_ c .= c = N2 C "
6S x2 xx yy w . x2 + G
- Vertical Translation k = Gr o
C 6S c =b C 8 6S zz _ zl + G z1 zz w _ z2 + u z 2, 3 - 3 - 3 -
- Rotation k = Gr 8 65 --- S c =NL C "
6S S 44 o .C41 + T $ 1 +CSS3 0 xl_ _ 44 e . 42 + C 42 + O2L-G 3 x 2_
*llorizontal Translation = Gr E S c =c = E22 " b2 S
-Rotation Coupling k@=kYi X -G 2 x 1, x4 y4 w ,
G-* x2_ 3 Torsion E8-- = S il-- U" 6S k - Gr C 6S c C cc o _Cl+ G cl_ (t e C2 + G c2_ where C = spring coefficients for the half-space x1, C41, Cz1, Ccl S = spring coef ficients for the overlying layer x1, S41, Szl, SC1 C = danping coefficients for the half-space x2, C42, C2.2, Cc2 S ,S ,S ,S = damping coefficients for the overlying layer ro - radius of foundation G = shear modulus of the soil underneath the foundation C, - shear modulus of the overlying layer g = embedment depth 6
= g/r = relative embedment o
- Rotation is positive clockwise.
llorizontal translation is positive to the right and vertical translation is positive upward. l l
i s. TABLE 2 DYNAMIC STIFFNESSES FOR A IIAI.F-SPACE Stiffness Functions j o c(2) Type of Vibration Static Stiffness (2) , K ,, k(2) - (Ref. 13) llorizontal Translation BGr o Vel (etsosRef. 13) Veletsos 2-v and Wei (1971) and Wei (1971) Vertical Translation 4Gr o Veletsos and . Veletsos and . 1-v Verbic (1974) Verbic (1974) (1:e l . 14) (Ref. 14) 3 (Ref. 13) Rotation 8Cr o Veletuos Vele(tsosRe f . 13) 3 (1-v) and Wei (1971) and Wei (1971) Torsion (I) 16Cro 1.-0.133a a <3. 0.3a / (2tao ) o O o 0.6 a >3. o-l G = shear modulus sa - 2nf = circular f requency v - Poisson's ratio V, - shear wave velocity r - radius of foundation. 13 - nuiterial (hysteretic) damping of the soil o a = D
To i -
W V a (1) From Kausel and Ushijima (1979) (Ref. 15) (2) Dynamic Stiffness Kh ~K h [k (1 + 2 id) + fa c (1 + 16)) luite : Values of k and c are given in tabular form in Refs. 13 & 14 as functions of f requency
eh p*O A uce. t9' Oj z e oo ~u cas A y 2 A -. ama ai~c,~u. as i ,oris 93*00- t noces u ano a avi zzao assa. g 1.
;,ig ,ag,irmurtuv ~u casun jo o@ Note: Actual Elevations are -15.0 ft.
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