NUREG-1750

Assessment of Soil 

Amplification of 

Earthquake Ground 

Motion Using the 

"CARES" Code 

Version 1.2 

U.S. Nuclear Regulatory Commission 

Office Nuclear Reactor Regulation 

Washington, DC 20555-0001
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NUREG-1750

Assessment of Soil 

Amplification of 

Earthquake Ground 

Motion Using the 

"CARES" Code 

Version 1.2 

Manuscript Completed: September 2001 

Date Published: September 2001 

Prepared by 

R. Pichumani 

Division of Engineering 

Office of Nuclear Reactor Regulation 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001
ABSTRACT

This report describes the results of two 

studies to assess the soil amplification of 

earthquake ground motion by varying three 

parameters pertinent to the soil and rock 

supporting nuclear power plant structures. 

Both studies used version 1.2 of the 

computer code CARES, Version 1.0 of 

which was developed by Brookhaven 

National Laboratory for the U.S. Nuclear 

Regulatory Commission. The model is a 

single layer of soil overlying a rock half

space. In the first study, the input 

earthquake ground motion (corresponding 

to the Regulatory Guidel.60 spectrum) was 

specified at the rock level. The parameters 

varied in the first study were: the shear 

wave velocity of the soil stratum, the 

thickness of the soil stratum, and the shear 

wave velocity of the rock half-space 

underlying the soil stratum. The study 

analyzed the effects of varying each 

parameter on the motion at the ground 

surface and at 40 feet (ft) below the ground 

surface. Three values of soil layer thickness 

were considered: 50 ft, 100 ft, and 200 ft. 

Three values of the shear wave velocity of 

the soil stratum were considered, 1000 ft per 

second (fps), 2000 fps, and 3000 fps. The 

three shear wave velocities of the rock were 

5000 fps, 7500 fps, and 10000 fps. The 

results of the first parametric study show 

significant shifts in the frequency at which 

the maximum spectral acceleration occurs 

when the soil thickness is varied from 50 ft 

to 200 ft and when the shear wave velocity 

of the soil stratum is varied from 1000 fps to 

3000 fps.

No frequency shifts are seen when the 

shear wave velocity of the rock medium is 

varied from 5000 fps to 10000 fps, but 

significant changes in the maximum spectral 

amplitude of acceleration are observed for 

the 100 ft and 200 ft thick soil layer. The 

second parametric study used the seismic 

ground motion specified by a rock site

specific spectra input at the rock outcrop, 

varying only the thickness of the soil layer 

and the shear wave velocity of the soil layer. 

A comparison of the results of the two 

parametric studies shows that the shapes of 

the spectral responses for both types of 

ground motion input are quite similar to the 

corresponding cases of soil thickness and 

soil shear wave velocity. However, the 

spectral amplitudes obtained for the site

specific rock spectra input are lower than 

the corresponding values for the Regulatory 

Guide (R.G)1.60 input because the 

amplitudes of the input spectral 

accelerations of the site-specific rock 

spectra are lower than those of the R.G. 

1.60 spectra at all frequencies larger than 

approximately 0.18 Hz, even though the 

peak ground acceleration (PGA) of the site

specific rock spectra was set at 0.3g by 

scaling the actual PGA of 0.24g by a factor 

of 1.25 to match the 0.3g PGA of the R.G. 

1.60 spectra.

iii
CONTENTS

Page 

ABSTRACT iii

ACKNOWLEDGMENTS 

ABBREVIATIONS 

1. INTRODUCTION 

2. OVERVIEW OF CARES CODE 

3. PARAMETRIC STUDIES AND RESULTS 

4. SUMMARY 

5. CONCLUSION 

6. REFERENCES 

TABLES 

FIGURES

xi 

xii 

1 

2 

4 

7 

8 

9 

10 

14

APPENDIX: "CARES - Computer Analysis for Rapid Evaluation of Structures," 31 

Version 1.2, a theoretical report and user manual prepared by Carl J. Costantino, 

Charles A. Miller, Ernest Heymsfield, and Anshi Yang (ADAMS Accession No. ML012670418).

V
TABLES 

1. Parametric Variation of Soil Properties for Regulatory Guide 1.60 Spectrum (PGA 0.3g) 

Input at Rock Outcrop 

2. Combinations of Parameters for Studying the Effects of Soil and Rock Properties on 

Amplification for Regulatory Guidel.60 Input 

3. Parametric Variation of Soil Properties for Site-Specific Rock Spectra (PGA 0.24g Scaled 

by 1.25)(VR = 10,000fps) 

4. Combinations of Parameters for Studying the Effects of Soil and Rock Properties on 

Amplification for Site-Specific Rock Spectra (VR = 10,OOOfps)

vii
FIGURES 

1. Effect of Soil Thickness, H, on Amplification at Ground Surface (Vs = 2000fps; 

V, = 1 0,000fps) for R.G. 1.60 Input 

2. Effect of Soil Thickness, H, on Amplification at Depth of 40 ft (V,= 2000fps; 

VR= 10,000fps) for R.G.1.60 Input 

3. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Ground Surface 

(H = 100ft; VR= 10,000fps) for R.G.1.60 Input 

4. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Depth of 40 ft 

(H = 100ft; V,= 10,000fps) for R.G.1.60 Input 

5. Effect of Rock Shear Wave Velocity, VR, on Amplification at Ground Surface 

(H = 100ft; Vs= 2000fps) for R.G. 1.60 Input 

6. Effect of Rock Shear Wave Velocity, VR, on Amplification at Depth of 40 ft 

(H = 100ft; V, = 2000fps) for R.G. 1.60 Input 

7. Effect of Soil Thickness on Amplification at Ground Surface (Vs= 1000fps; VR= 

.10,000fps) for R.G. 1.60 Input 

8. Effect of Soil Thickness on Amplification at Depth of 40 ft (V,= 1000fps; VR= 10,0OOfps) 

for R.G. 1.60 Input 

9. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Ground Surface 

(H = 50ft; V,= 10,000fps) for R.G. 1.60 Input 

10. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Depth of 40ft (H = 50ft; 

VR= 10,000fps) for R.G. 1.60 Input 

11. Effect of Rock Shear Wave Velocity, VR, on Amplification at Ground Surface 

(H = 50ft; Vs= 1000fps) for R.G. 1.60 Input 

12. Effect of Rock Shear Wave Velocity, VR, on Amplification at Depth of 40 ft (H = 50ft; V,= 

1000fps) for R.G. 1.60 Input 

13. Effect of Soil Thickness, H, on Amplification at Ground Surface (Vs = 3000fps; 

V, = 10,000fps) for R.G. 1.60 Input 

14. Effect of Soil Thickness, H, on Amplification at Depth of 40 ft (Vs= 3000fps; V, = 

10,000fps) for R.G. 1.60 Input 

15. Effect of Soil Shear Wave Velocity on Amplification at Ground Surface 

(H = 200ft.; V,= 1 0,000fps) for R.G. 1.60 Input 

16. Effect of Soil Shear Wave Velocity on Amplification at Depth of 40 ft (H = 200ft; V,= 

10,000fps) for R.G. 1.60 Input 

17. Effect of Rock Shear Wave Velocity on Amplification at Ground Surface (H = 200ft; Vs= 

3000fps) for R.G. 1.60 Input 

viii
18. Effect of Rock Shear Wave Velocity on Amplification at Depth of 40 ft (H = 200ft; V, = 

3000fps) for R.G. 1.60 Input 

19. Effect of H on Amplification at Ground Surface (Vs = 1000fps, V, = 10,000fps) for Rock 

Site-Specific Spectra Input 

20. Effect of H on Amplification at Depth of 40 ft (Vs = 1 000fps, V, = 1 0,000fps) for Rock Site

Specific Spectra Input 

21. Effect of H on Amplification at Ground Surface (Vs = 2000fps, VR = 10,OOOFPS) for Rock 

Site-Specific Spectra Input 

22. Effect of H on Amplification at Depth of 40 ft (V, = 2000fps, V, = 10,000fps) for Rock Site

Specific Spectra Input 

23. Effect of H on Amplification at Ground Surface (Vs = 3000fps, V, = 10,000fps) for Rock 

Site-Specific Spectra Input 

24. Effect of H on Amplification at Depth of 40 ft (V, = 3000fps, V, = 1 0,000fps) for Rock Site

Specific Spectra Input 

25. Effect of V, on Amplification at Ground Surface (H = 50ft, VR = 10,000fps) for Rock Site

Specific Spectra Input 

26. Effect of V, on Amplification at Depth of 40 ft (H = 50ft, VR = 10,000f ps) for Rock Site

Specific Spectra Input 

27. Effect of V, on Amplification at Ground Surface (H = 1 00ft, VR = 10,000fps) for Rock Site

Specific Spectra Input 

28. Effect of Vs on Amplification at Depth of 40 ft (H = 100ft, VR = 10,000fps) for Rock Site

Specific Spectra Input 

29. Effect of V. on Amplification at Ground Surface (H = 200ft, V, = 10,000fps) for Rock Site

Specific Spectra Input 

30. Effect of V, on Amplification at Depth of 40 ft (H = 200ft, VR = 10,000fps) for Rock Site

Specific Spectra Input 

31. Comparison of R.G.1.60 Spectrum With Rock Site-Specific Spectrum (with PGA of 0.3g 

for both input spectra)

ix
ACKNOWLEDGMENTS

This parametric study to assess the soil amplification of earthquake ground motion was 

performed using the computer code CARES, Version 1.2. Version 1.0 of CARES was originally 

developed by Brookhaven National Laboratory (BNL) for the Office of Nuclear Regulatory 

Research (RES), U.S. Nuclear Regulatory Commission (NRC), and published in July 1990 

(NUREG/CR-5588, Volumes 1, 2, and 3). Herman Graves III of RES was the NRC Project 

Manager in charge of developing the original CARES code. CARES Version 1.2 was the result of 

modifications and additions made to Version 1.0 by Carl J. Costantino, Charles A. Miller, Ernest 

Heymsfield, and Anshi Yang for the Office of Nuclear Reactor Regulation (NRR), U.S. NRC. The 

author acknowledges the support and advice of Robert Rothman, Goutam Bagchi, Eugene Imbro, 

and Kamal Manoly of the Office of NRR.

xi
ABBREVIATIONS

ADAMS Agency Wide Documents Access and Management System 

BNL Brookhaven National Laboratory 

fps Feet per second 

ft Feet 

g Acceleration due to gravity 

H Thickness 

IMSL A graphics plotting software program 

NRC U.S. Nuclear Regulatory Commission 

NRR (Office of) Nuclear Reactor Regulation, U.S. NRC 

RES (Office of) Nuclear Regulatory Research, U.S. NRC 

R.G. Regulatory Guide 

ROC Rock outcrop 

v Version 

VR Shear wave velocity of Rock 

VR5 VR = 5000 fps 

V,7.5 VR = 7500 fps 

VR10 V, = 10,000 fps 

Vs Shear wave velocity of soil 

V'1 Vs = 1000 fps 

V,2 Vs = 2000 fps 

V,3 V, = 3000 fps

xii
1. INTRODUCTION

To perform the seismic analysis of a structure, an appropriate seismic demand is needed. 

Seismic demands are generally in the form of earthquake time histories or earthquake ground 

motion spectra. The demands should reflect the seismic hazard at the site of the structure with a 

level of conservatism appropriate to the function of the structure. Seismic demands can be 

developed by using theoretical numerical models or empirical earthquake data or a combination 

of the two. The seismic demand should be based on the magnitude of the earthquake and its 

distance from the site, the geology between the sources and the site, and the conditions at the 

immediate site. For sites founded on soils, there is often not enough strong-ground-motion data 

available from similar sites to make a statistically robust estimate of the seismic demand. In such 

cases, it is common to estimate the seismic ground motion at the site by assuming that the site 

geology is rock. The rock ground motion is then used as input to a computer model of the soil 

column, which represents the actual geology at the site, to obtain the seismic demand to be used 

for the design or analysis of the civil structure. The study reported here investigated the 

sensitivity of the seismic hazard using the computer code CARES (Computer Analysis for Rapid 

Evaluation of Structures), version 1.2 (Ref. 1), by performing two sets of parametric evaluations 

of the effects of the properties of the soil and the underlying rock that support the structures. Two 

kinds of seismic ground motion input (one specified by Regulatory Guide (R.G.) 1.60 spectrum, 

the other specified by a site-specific rock spectrum) were applied at the rock outcrop, and the 

results of the soil amplification of the earthquake ground motion were compared for both cases of 

seismic hazard.

1
2. OVERVIEW OF CARES CODE

Background 

During the late 1980s, the CARES computer program was developed for the Nuclear Regulatory 

Commission (NRC) by Brookhaven National Laboratory. The first version of the CARES code 

(Ref. 2) was designed for use on a small personal computer (PC) and was intended to provide 

the NRC staff with the capability to rapidly evaluate the seismic response of simplified structural 

stick models of nuclear power plant structures. This capability enabled the staff to quickly check 

the validity and/or accuracy of the analytical data received from applicants for nuclear power plant 

licensing actions. These data were typically obtained from numerical studies performed with 

large state-of-the-art computer packages for structural analysis and were difficult to assess. By 

performing simplified analytical model studies, the staff could evaluate the sensitivity of computed 

responses to variations in a host of controlling parameters to confirm the results of studies done 

with the larger computers. 

Since the original development, the staff has validated the usefulness of the CARES concept by 

applying it to a number of problems. The CARES code has been modified to operate on the Sun 

SPARC workstations. The code is modular, which allows the user to access various capabilities in 

an interactive fashion. The code has three primary functions (Refs. 1 and 2): 

a. A free-field computational algorithm allows the analysis of the seismic response of a 

layered soil column subjected to upwardly propagating horizontal shear waves developed 

by a given input seismic motion. The input motion can be specified by a target response 

spectrum appropriate tor a given earthquake magnitude at a given distance from the 

source or by an actual accelerogram at a given location in the soil column. The algorithm 

computes the motion at various locations in the soil column for the input seismic motion as 

well as the final stress and strain conditions developed in each soil layer. 

b. From the ground motions generated in the free-field analysis module above, the 

seismic response of a structure embedded in or supported by the soil can be determined. 

c. A variety of postprocessing capabilities allow the generation of other parameters of 

interest in the dynamic response (soil motions at any depth of interest to the user, 

in-structure response spectra, etc.) and plotting of results. 

The capability to easily perform simplified analyses at one's desk on a PC has proved to be a 

valuable asset. As always, however, advances in the state of the art of seismic response 

calculations made it desirable to expand the capability of the CARES code. In addition, the staff 

wanted to tackle bigger problems with CARES because the new structural stick models in the 

advanced reactor programs were significantly larger than the models used in the original CARES 

development. The CARES code was therefore extended and modified to satisfy these new 

objectives, resulting in CARES version (v) 1.1. 

A version of CARES v 1.1 designated as CARES v 1.2, was developed to run on Sun SPARC 

workstations, which operate in the UNIX environment. CARES v 1.2 (Ref. 1) runs only on the 

SPARC workstation, although it can be made operational on other machines with minor 

reprogramming. To further utilize the capabilities of the workstation, CARES v 1.2 modifies and 

extends to take advantage of the plotting capability of CARES v 1.1, i.e., the IMSL plotting 

software appropriate to the Sun workstation. On-line plots of computed results can be obtained in 

this new version and then be saved or printed.

2
Two major changes were incorporated in CARES v 1.1 to extend the capability of the code. The 

first change allowed the inclusion of a rock outcrop model within the soil column formulation. 

Second, extended soil modulus degradation models were incorporated to keep pace with recent 

developments. In CARES v 1.2, the computations have been extended to include calculation of 

tau/sigma stress ratios for soil liquefaction evaluations. Improvements have also been added to 

the soil degradation specification in the code, as has the code's ability to output initial and final 

soil properties in the convolution calculations. 

Program Modules 

The CARES code performs three separate functions: the free-field analysis, the structural (or soil

structure interaction) analysis, and the ancillary or pre- and post-processing analyses of ground 

motion time histories or spectra. In the original PC-based version, CARES v 1.0, the program 

essentially had a single "general manager," which allowed the transfer of data between any and 

all of the individual modules directly accessed by the code. This was no longer possible with the 

greatly expanded capability of v 1.1. Each of the free-field and structural modules were 

significantly larger, making the use of a single General Manager impractical. Therefore, CARES v 

1.1 was divided into modules. V 1.2 maintains the separate modules and has a common 

input/output file format to allow easy communication between the modules. The modules are 

labeled CRSSOIL, CRSSTRUC, CRSPOST, and CRSPLOT. Data transfer is accomplished by 

using data files generated by each module and stored on the disk. Data entry is described in 

Section 3 of Ref. 1 and can be easily performed using the machine prompts for interactive 

operation of the code.

3
3. PARAMETRIC STUDIES AND RESULTS

Two parametric studies were performed by varying the significant properties of the foundation 

materials for two kinds of seismic ground motion input (i.e., one specified by R.G. 1.60 spectra, 

the other by site-specific rock spectrum) applied at the rock outcrop. Three parameters were 

varied in the first study: 

1. the thickness, H, in feet (ft), of the soil layer 

2. the shear wave velocity of the soil layer, V, 

3. the shear wave velocity of the rock underlying the soil stratum, V, 

Table 1 lists the values of these three parameters that were varied in this study. For each of the 

three values of thickness, H, of the soil stratum (50 ft, 100 ft, and 200 ft), three values of V, (1000 

fps, 2000 fps, and 3000 fps) and three values of VR (5000 fps, 7500 fps, and 10000 fps) were 

used; so there were 27 computer analyses. In all 27 runs, the seismic ground motion was input 

at the rock outcrop as the spectral acceleration value of the R.G. 1.60 spectrum with a peak 

ground acceleration (PGA) of 0.3g, and convolved up through the soil stratum using the 

CRSSOIL segment of the CARES code. 

In the second parametric study, nine analyses (varying Vs and H as with the R.G. 1.60 input, but 

keeping V, constant) were performed using a site-specific rock spectra input for seismic ground 

motion at the rock outcrop with a PGA of 0.24g scaled by 1.25 to match the 0.3g PGA of The 

R.G. 1.60 spectrum. 

Results for R.G. 1.60 Input 

The convolution analyses of seismic ground motion for the 27 combinations of the three 

parameters provided the ground motions at the ground surface of the soil and at a depth of 40 ft 

below the ground surface with the input seismic ground motion specified at the rock outcrop 

(ROC). One general finding is that the maximum motions at the ground surface are larger than 

40 ft below the ground surface for all combinations of the three parameters. However, the 

amplitudes and the frequency of maximum amplitude at these elevations differed significantly for 

various values of the three parameters considered in this study. 

These observations are confirmed by the results of additional postprocessing of the basic output 

data from the 27 cases. The additional postprocessing was done to illustrate the effects of the 

three parameters (H, Vs, and V,) on the amplifications and frequency characteristics of the ground 

motions at the two depths. Table 2 shows the combinations of the parameters used in these 

postprocessing computer runs. The effects are shown in Figures 1 through 18. 

Figures 1 and 2 show the effects of using the three values of soil thickness, H, on the amplitude at 

the surface and 40 feet below the surface. The two figures show that the frequency dramatically 

decreases as the soil thickness increases from 50 ft to 100 ft and to 200 ft, keeping V, at 2000 fps 

and V, at 10000 fps. Figure 1 shows that the maximum spectral amplitude of acceleration at the 

ground surface increases from about 3.3g to about 3.65g as the soil layer thickness increases 

from 50 ft to100 ft, but decreases from about 3.65g to about 2.9g as the soil layer thickness 

increases from 100 ft to 200 ft. Figure 2 shows similar increase in frequency and decrease in 

spectral amplitude in the response spectra at 40 ft below the ground surface.

4
Figures 3 and 4 show frequency shifts in the maximum spectral acceleration when the soil shear 

wave velocity, Vs, is varied from 1000 fps to 3000 fps, keeping the thickness of the soil layer, H, at 

100 ft and the rock shear wave velocity, VA, at 10000 fps. The frequency at which the maximum 

spectral amplitude of acceleration occurs increases with increasing values of the soil layer shear 

wave velocity, V,. The spectral amplitude increases as Vs increases from 1000 fps to 2000 fps, 

but decreases when Vs increases from 2000 fps to 3000 fps. 

Figures 5 and 6 show the effect of using rock shear wave velocities of 5000, 7500, and 10000 fps 

and keeping the soil layer thickness at 100 ft and the soil layer shear wave velocity at 2000 fps. In 

this case, the maximum spectral amplitude of accelerations increases significantly with increasing 

values of rock shear wave velocity, both at the ground surface and 40 ft below the ground surface. 

However, there are no frequency shifts for any of the three values of rock shear wave velocity. 

Figures 7 and 8 show the effect of the soil thickness 50 ft, 100 ft, and 200 ft with soil and rock 

velocities of 1000 fps and 10,000 fps, respectively. The frequency at which maximum spectral 

amplitude of acceleration occurs decreases with increasing soil thickness, as in the case of 

V,=2000 fps and V,=10,000 fps (Figs.1 and 2). The maximum spectral amplitude at the ground 

surface for a 50 ft thick soil layer is significantly higher (about 3.4g) than for the 100 ft thick soil 

(about 2.1 g). 

Figures 9 and 10 show the effect of varying the values of soil shear wave velocity (Vs) from 1000 

fps to 2000 fps and 3000 fps for a 50 ft thick soil layer overlying a rock half-space with the shear 

wave velocity of the rock (V,) at 10,000 fps. The frequency at which the maximum spectral 

amplitude of accelerations occurs increases with increasing Vs as in the case of 100 ft thick soil in 

Figures 3 and 4; however, the maximum spectral amplitude decreases with increasing V, contrary 

to the case of 100 ft thick soil. 

Figures 11 and 12 show the effect of using V, values of 5000 fps, 7500 fps, and 10,000 fps, 

keeping the soil layer thickness at 50 ft and V, at 1000 fps. There is no change in the frequency 

at which the maximum spectral amplitude of acceleration occurs. The shapes of the spectral 

curves are similar. There is an increase in the maximum spectral amplitude at the ground surface 

from about 3g for V, = 5000 fps to about 3.5g for V, =10000 fps, as seen in Figure 11. Figure 12 

shows similar results for 40 ft below the ground surface, with maximum spectral amplitudes 

increasing from about 1.5g for V, = 5000 fps to about 1.7g for V, = 10000 fps. 

Figures 13 and 14 show the effect of soil thickness on spectral acceleration when the soil shear 

wave velocity is 3000 fps and the rock shear wave velocity is 10000 fps. Comparing the spectral 

curves shown in Figure 13 with those in Figure 7 (which gives the results for V,=1000 and V, = 

10000 fps), the following are noted: 

1. The frequencies at which the maximum spectral amplitude of accelerations 

occurs decrease with increasing soil thickness in both cases (for V, = 1000 fps and 

Vs= 3000 fps). However, the frequency at which the maximum spectral amplitude 

occurs for Vs= 3000 fps and H = 50 ft is about 12 Hz, whereas the corresponding 

frequency for soil with Vs = 1000 fps is about 3 Hz. Similar decreases in the 

frequencies at which the maximum acceleration occurs are also noted for H = 100 ft 

and 200 ft. 

2. The maximum spectral amplitude for the soil layer with V, = 1000 fps (in Figure 

7) is significantly higher for H=50 ft than the corresponding amplitude for the soil 

layer with V,= 3000 fps (Figures 7 and 13). However, the maximum spectral

5
amplitudes for the 100 ft and 200 ft thick soil strata are higher for the higher velocity 

soil than the corresponding amplitude for the lower velocity soil. 

Figures 15 and 16 show the effect of using the soil shear wave velocities, Vs, of 1000 fps, 2000 

fps, and 3000 fps for a soil thickness of 200 ft and a rock shear wave velocity of 10000 fps. 

Comparing the spectral curves in Figures 15 and 16 (for H = 200 ft) with those in Figures 3 and 4 

(for H = 100 ft) shows that the maximum spectral amplitude of accelerations occurs at lower 

frequencies for H = 200 ft than for H = 100 ft. Furthermore, the maximum spectral amplitudes for 

the 100 ft thick soil are larger for V, = 1000 fps and 2000 fps than the corresponding amplitudes 

for the 200 ft thick soil. However, the maximum spectral amplitude for the 200 ft thick soil (with V, 

= 3000 fps) is larger (about 3.05g) than the corresponding amplitude (about 2.85g) for the 100 ft 

thick soil (with V, = 3000 fps), as seen in Figures 3 and 15. 

Figures 17 and 18 show the effect of using values of rock shear wave velocity, V,, of 5000 fps, 

7500 fps, and 10000 fps for soil layer thickness of 200 ft and Vs = 3000 fps. The variations in rock 

shear wave velocities from 5000 fps to 10000 fps produce negligible change in the frequencies at 

which the maximum spectral amplitudes occur both at ground surface and at 40ft below ground 

surface. However, the maximum spectral amplitude at ground surface is about 50% larger for rock 

with V, = 10000 fps than for rock with V, = 5000 fps (Figure 17). Similar (qualitative) phenomena 

are also seen in Figure 5 and 6 for a 100 ft thick soil stratum with minor variations in frequency 

and amplitudes. 

Results for Site-Specific Rock Spectra 

Table 3 lists the values of the soil parameters, H and V., that were combined in the second 

parametric study. Figures 19 through 30 show the results of the nine computer analyses 

performed using a site-specific rock spectrum input at the rock outcrop and varying the soil 

thickness and soil shear wave velocity (as with the case of R.G. 1.60 input), but keeping the rock 

shear wave velocity constant at 10,000 fps. These figures illustrate the effects of the two 

parameters (H and Vs) on the amplifications and frequency characteristics of the ground motions 

at the ground surface and at 40 ft below the ground surface. Table 4 shows the combinations of 

the parameters used in postprocessing the results of the second parametric study. 

Comparing the ground motions due to site-specific rock spectra input at the rock outcrop shown in 

Figures 19 through 30 with the corresponding results obtained using the R.G.1.60 input shows 

that the shapes of the spectral responses for both types of ground motion input (with a PGA of 

0.3g) are quite similar for the corresponding cases of soil thickness and the soil layer shear wave 

velocity. However, the maximum amplitudes of the spectral response accelerations for the site

specific rock spectra input are lower than the corresponding response values for the R.G. 1.60 

spectra. The explanation may be that (as seen in Figure 31) the amplitudes of the input spectral 

accelerations of the site-specific rock spectra are lower than those of the R. G. 1.60 spectra at all 

frequencies larger than approximately 0.18 Hz, even though the PGA of the site-specific rock 

spectrum was set at 0.3g by scaling its actual PGA of 0.24g by a factor of 1.25 to match the PGA 

of 0.3g of the R.G. 1.60 spectrum.

6
4. SUMMARY

Two parametric studies were performed by varying the significant properties of the foundation 

materials for two kinds of seismic ground motion input (i.e., one specified by Regulatory Guide 

1.60 spectrum, the other by a site-specific rock spectrum) applied at the rock outcrop. The studies 

examined the effects of varying three parameters of the soil and rock on the amplitude of ground 

motion response spectra due to seismic ground motion. Three parameters were varied in the first 

study: 

1. thickness of the soil layer 

2. shear wave velocity of the soil layer 

3. shear wave velocity of the underlying rock half-space 

This study analyzed the effects of varying each parameter on the response spectra at the ground 

surface and at 40 feet below the ground surface. The thicknesses of the foundation soil were 50 

ft, 100 ft, and 200 ft. Three values of the shear wave velocity of the soil were considered: 1000 

fps, 2000 fps, and 3000 fps. The values of the shear wave velocity of the rock were 5000 fps, 

7500 fps, and 10000 fps. The results of the parametric study show significant shifts in the 

frequency at which the maximum spectral amplitude of acceleration occurs when the soil thickness 

is changed and also when the shear wave velocity of the soil layer is varied. No frequency shifts 

are seen when the shear wave velocity of the rock is varied from 5000 fps to 10000 fps, but 

significant changes in the maximum amplitude of the spectral acceleration are observed for soil 

thicknesses of 100 ft and 200 ft. The changes in the amplitude are not as significant for the 50 ft 

thick soil stratum as for the deeper soil strata. 

The second study used the seismic ground motion specified by a rock site-specific spectrum input 

at the rock outcrop, varying only the thickness of the soil layer and the shear wave velocity of the 

soil layer. The shear wave velocity of the rock stratum underlying the soil layer was kept constant 

at 1 0,000fps. The values of the other two soil parameters in this second parametric study were 

the same as in the first set. 

A comparison of the results of the two parametric studies shows that the shapes of the spectral 

responses for both types of ground motion input (with a PGA of 0.3g) are quite similar for the 

corresponding cases of soil thickness and the soil shear wave velocity. However, the maximum 

spectral amplitudes obtained for the site-specific rock spectra input are lower than the 

corresponding values for the Regulatory Guidel.60 input, because the amplitudes of the input 

spectral accelerations of the site-specific rock spectra are lower than those of the Regulatory 

Guidel1.60 spectra at all frequencies larger than approximately 0.18 Hz, even though the PGA of 

the site-specific rock spectrum was set at 0.3g by scaling its actual PGA of 0.24g by a factor of 

1.25 to match the 0.3g PGA of the Regulatory Guidel.60 spectrum.

7
5. CONCLUSION

The type of the seismic ground motion input spectrum does not affect the response of the soil 

layers overlying the rock stratum. Both types of ground motion input have similar qualitative 

effects on the frequencies and spectral amplitudes of ground motion. However, the quantitative 

values of the response spectral amplitudes in the case of the site-specific rock spectra are lower 

than for the Regulatory Guidel.60 spectra. The reason is that the amplitudes of the input spectral 

accelerations of the site-specific rock spectra are lower than those of the Regulatory Guidel.60 

spectra at all frequencies larger than approximately 0.18 Hz, even though the PGA of the site

specific rock spectra was set at 0.3g by scaling the actual PGA of 0.24g by a factor of 1.25 to 

match the 0.3g PGA of the Regulatory Guidel.60 spectra.

8
6. REFERENCES

1. CARES - Computer Analysis for Rapid Evaluation of Structures, Version 1.2, report prepared 

by Carl J. Costantino, Charles A. Miller, Ernest Heymsfield, and Anshi Yang. (ADAMS Accession 

No. ML012670148). 

2. CARES (Computer Analysis for Rapid Evaluation of Structures), Version 1.0, NUREG/CR-5588, 

Vols. 1 through 3 prepared by J. Xu, A.J. Philippacopoulas, C.A. Miller, and C. J. Costantino, 

Brookhaven National Laboratory, for U.S. Nuclear Regulatory Commission, July 1990.

9
Table 1. Parametric Variation of 

Outcrop

Soil Properties for R. G. 1.60 Spectrum (PGA 0.3g) Input at Rock

Run No. Depth of soil, ft Soil Shear Wave Velocity Rock Shear Wave Velocity 

1 100 2000 7,500 

2 100 2000 10,000 

3 100 2000 5,000 

4 200 2000 7,500 

5 200 2000 10,000 

6 200 2000 5,000 

7 50 2000 7,500 

8 50 2000 10,000 

9 50 2000 5,000 

10 50 1000 7,500 

11 50 1000 10,000 

12 50 1000 5,000 

13 100 1000 7,500 

14 100 1000 10,000 

15 100 1000 5,000 

16 200 1000 7,500 

17 200 1000 10,000 

18 200 1000 5000 

19 50 3000 7,500 

20 50 3000 10,000 

21 50 3000 5,000 

22 100 3000 7,500 

23 100 3000 10,000 

24 100 3000 5,000 

25 200 3000 7,500 

26 200 3000 10,000 

27 200 3000 5,000

10
Table 2: Combinations of Parameters to Study the Effects of Soil and Rock Properties on 

Amplification for R.G. 1.60 Input 

S. No. Computer Run Nos. for Soil thickness, Soil Shear Wave Rock Shear Wave 

amplifications @ 0 ft and H (ft) Velocity, Vs (fps) Velocity, Vr (fps) 

40ft 

1 1 and 2 (using Runs 2, 50, 100, 200 2000 10000 

5, and 8)* 

2 3 and 4 (using Runs 2, 100 1000, 2000, 3000 10000 

14, and 23) 

3 5 and 6 (using Runs 3, 100 2000 5000, 7500, 10000 

1, and 2) 

4 7 and 8 (using Runs 11, 50,100,200 1000 10000 

14, and 17) 

5 9 and 10 (using Runs 50 1000, 2000, 3000 10000 

11, 8, and 20) 

6 11 and 12 (using Runs 50 1000 5000, 7500, 10000 

12, 10, and 11) 

7 13 and 14 (using Runs 50, 100, 200 3000 10000 

20, 23, and 26) 

8 15 and 16 (using Runs 200 1000, 2000, 3000 10000 

17, 5, and 26) 

9 17 and 18 (using Runs 200 3000 5000, 7500, 10000 

27, 25, and 26) 1 1 1 

* Output of amplifications from the computer runs 1 through 27 shown in parentheses here and is 

used in CRSPLOT to plot the effects of various combinations of soil and rock properties on soil 

amplifications in Figures 1 through 18.

11
Table 3: Parametric Variation of Soil Properties for Site-Specific Rock Spectra (PGA 0.24g scaled 

by 1.25 to match the R. G. 1.60 PGA of 0.3g) 

Run Depth of Soil (H), ft Vs, fps Remarks 

Nos. 

1 50 1000 VR = 1 0,000fps for all 

runs in this set. 

2 100 1000 

3 200 1000 

4 50 2000 

5 100 2000 

6 200 2000 

7 50 3000 

8 100 3000 

9 200 3000

12
Table 4: Combinations of Parameters to Study the Effects of Soil and Rock Properties on 

Amplification for Site-Specific Rock Spectra (V, = 10,000fps) 

S. Soil Thickness H, ft Soil Shear Wave Remarks 

No. Velocity, Vs, fps 

1 50,100, 200 1000 Effect of Soil thickness for Vs=1 000 

fps 

2 50 1000, 2000, 3000 Effect of Vs for H=50 ft 

3 50,100, 200 2000 Effect of Soil thickness for Vs=2000 

fps 

4 100 1000, 2000, 3000 Effect of Vs for H=100 ft 

5 50,100, 200 3000 Effect of Soil thickness for Vs=3000 

fps 

6 200 1000, 2000, 3000 Effect of Vs for H=200 ft

13
FIGURES

14
z 

LI 

U

10.1 100 101 102

FREQUENCY (Hz) 

Figure 1. Effect of Soil Thickness, H, on Amplification at Ground Surface 

(V,=2000fps; V,=1 0,000fps) for R.G. 1.60 Input

4.0

z 

0 

U 

U 

0.

10-1 100 101 102 

FREQUENCY (Hz) 

Figure 2. Effect of Soil Thickness, H, on Amplification at Depth of 40 ft 

(Vs=2000fps; V,=10,000fps).for R.G. 1.60 Input

15
2: 

0 

U 

U. 

C-) 

Ct)

FREQUENCY (Hz) 

Figure 3. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Ground Surface 

(H=1 00ft; V,=1 0,000fps) for R.G. 1.60 Input

4.0 

3.0 

.1± 

U 2.0 

U 

C..) 

S 1.0

0.0

10-' 100 101 102 

FREQUENCY (Hz) 

Figure 4. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Depth of 40 ft 

(H=1 00ft; VR=1 0,000fps) for R.G. 1.60 Input

16
4.0

3.0 

z 

0 

[ 1. 0 

l/ 

10 

q 

0 

0 

0.0

10-' 100 10110 

FREQUENCY (Hz) 

Figure 5. Effect of Rock Shear Wave Velocity, VR, on Amplification at Ground Surface 

(H=1 00ft; V,=2000fps) for R.G. 1.60 Input 

4.0. 

Damping = 5.00% 

INPUTRG.3g 

40FT VR5 

40FT VR7.5 

z 3.0

z S .0 

40FT VR 10 -B

U ,. 

'" I 

< n 10A/_A 

A. 

t

102

FREQUENCY (Hz)

Figure 6. Effect of Rock Shear Wave Velocity, VR, on Amplification at Depth of 40 ft 

(H=100ft; Vs=2000fps) for R.G. 1.60 Input

17
10-1 10o 10' 102 

FREQUENCY (Hz) 

Figure 7. Effect of Soil Thickness on Amplification at Ground Surface 

(VS=1000fps; V,=10,000fps) for R.G. 1.60 Input

10-, 10o 10' 102 

FREQUENCY (Hz) 

Figure 8. Effect of Soil Thickness on Amplification at Depth of 40 ft 

(V1=1000fps; VR=10,000fps) for R.G. 1.60 Input

18

4.0

z 

L)

3.0

2.0' 

1.0

0.0

z 

0 

U 

U 

,

U 

Lu
z 

0 

U 

U 

(±1

FREQUENCY (Hz) 

Figure 9. Effect of Soil Shear Wave Velocity, V., on Amplification at Ground Surface 

(H=50ft; V,=10,000fps) for R.G. 1.60 Input

U 

U 

w 

04 

COO

10-1 100 10' 102 

FREQUENCY (Hz) 

Figure 10. Effect of Soil Shear Wave Velocity, Vs, on Amplification at Depth of 40 ft 

(H=50ft; VR=10,000fps) for R.G. 1.60 Input

19
4.0

0 

c-.) 

C,.) U 

U

10-' i0 10' 102 

FREQUENCY (Hz) 

Figure 11. Effect of Rock Shear Wave Velocity, VR, on Amplification at Ground Surface 

(H=50ft; V3=1000fps) for R.G. 1.60 Input

U 

0 

U

IV) 100 10' 102

FREQUENCY (Hz) 

Figure 12. Effect of Rock Shear Wave Velocity, V,, on Amplification at Depth of 40 ft 

(H=50ft; Vs=1 000fps) for R.G. 1.60 Input

20

, ^
1o 

a 0 

U

10-1 100 101 

FREQUENCY (Hz) 

Figure 13. Effect of Soil Thickness, H, on Amplification at Ground Surface 

(V8=3000fps; VR=1 0,000fps) for R.G. 1.60 Input

4.0

z 

0 

U 

U 

-J

3.0 

2.0 

1.0

0.0

102

102

FREQUENCY (Hz) 

Figure 14. Effect of Soil Thickness, H, on Amplification at Depth of 40 ft 

(Vs=3000fps; V,=10,000fps) for R.G. 1.60 Input

21
4.0

z 0 

2J 

C-) 

C-) 

2 

U

10-1 100 10! 

FREQUENCY (Hz)

102

Figure 15. Effect of Soil Shear Wave Velocity on Amplification at Ground Surface 

(H=200ft; VR=1 0,000fps) for R.G. 1.60 Input

4.0

0 

,a 

z 

C-) 

U 

U 

IVl

FREQUENCY (Hz) 

Figure 16. Effect of Soil Shear Wave Velocity on Amplification at 40ft Below Ground Surface 

(H=200ft; VR=10,000fps) for R.G. 1.60 Input

22
z 

0 

U U ,-:

102

FREQUENCY (Hz) 

Figure 17. Effect of Rock Shear Wave Velocity on Amplification at Ground Surface 

(H=200ft; V,=3000fps) for R.G. 1.60 Input

4.0 

3.0 

z 

0 

H 

U 

V 1.0

0.0

FREQUENCY (Hz) 

Figure 18. Effect of Rock Shear Wave Velocity on Amplification at 40 ft Below Ground Surface 

(H=200ft; Vs=3000fps) for R.G. 1.60 Input

23
z 

.2 

C-) 

2 

U 

U~ 

r0)

10-1 100 10, i02 

FREQUENCY (Hz) 

Figure 19. Effect of H on Amplification at Ground Surface (Vs=1000fps, VR=10,000fps) 

for Rock Site-Specific Spectra Input

z 

0 

U 

0) 

,2 

r,)

4.0 

3.0 

2.0 

1.0

0.0

10-, 10o 10' 102

FREQUENCY (Hz) 

Figure 20. Effect of H on Amplification at Depth of 40 ft (Vs=1000fps, VR=10,000fps) 

for Rock Site-Specific Spectra Input

24

• ^
z 

U 

U 

0-

10-1 100 101 102 

FREQUENCY (Hz) 

Figure 21. Effect of H on Amplification at Ground Surface (Ve=2000fps, VR=10,000fps) 

for Rock Site-Specific Spectra Input

,a z 

0 

U 

UJ 

,. 

0•

10-' 100 I0o 102

FREQUENCY (Hz) 

Figure 22. Effect of H on Amplification at Depth of 40 ft (Vs=2000fps, VR=10,000fps) 

for Rock Site-Specific Spectra Input

25
4.0

S3.0 

0 

S2.0 

U 

L'n 1.0 

FREQUENCY (Hz) 

Figure 23. Effect of H on Amplification at Ground Surface (Vs=3000fps, V,=1 0,000fps) 

for Rock Site-Specific Spectra Input

40

3.0 

0 

U 2.0 

U 

.j 1 . 

1.) 1.0

0.0

102

FREQUENCY (Hz) 

Figure 24. Effect of H on Amplification at Depth of 40 ft (Vs=3000fps, V,=10,000fps) 

for Rock Site-Specific Spectra Input

26
4.0

z 

0 

fLI 

U

FREQUENCY (Hz) 

Figure 25. Effect of V, on Amplification at Ground Surface (H=50ft, VR=10,000fps) 

for Rock Site-Specific Spectra Input

z 

0 

U 

U 

U 

cj~

10-' 100 101 102 

FREQUENCY (Hz) 

Figure 26. Effect of Vs on Amplification at Depth of 40 ft (H=50ft, VR=10,000fps) 

for Rock Site-Specific Spectra Input

27
4.0

z 

ci)

10"1 100 10' 102 

FREQUENCY (Hz) 

Figure 27. Effect of V, on Amplification at Ground Surface (H=100ft, VR=10,000fps) 

for Rock Site-Specific Spectra Input

4.0 

- 3.0 

z 

0 

r 2.0 

U 

1.0 

0.0

10-, 100o 10 

FREQUENCY (Hz)

102

Figure 28. Effect of V, on Amplification at Depth of 40 ft (H=100ft, VR=10,000fps) 

for Rock Site-Specific Spectra Input

28
z 

~L1 

U 

U•

101 100 10, 102 

FREQUENCY (Hz) 

Figure 29. Effect of V, on Amplification at Ground Surface (H=200ft, VR=10,000fps) 

for Rock Site-Specific Spectra Input

4.0

z 

U U•

10-1 100 10' 102

FREQUENCY (Hz)

Figure 30. Effect of V, on Amplification at Depth of 40 ft (H=200ft, V,=10,000fps) 

for Rock Site-Specific Spectra Input

29
4.0

S3.0 

z 

,-.1 

U 2.0 

U 

C~1.0 

,.0

to-, t0o 10, 10, 

FREQUENCY (Hz) 

Figure 31. Comparison of R.G. 1.60 Spectrum with Rock Site-Specific Spectrum 

(with PGA of 0.3g for both input spectra)

30
APPENDIX: "CARES - Computer Analysis for Rapid Evaluation of Structures, Version 1.2," 

A Report prepared by Carl J. Costantino, Charles A. Miller, Ernest Heymsfield, and Anshi Yang. 

(The report is in ADAMS Documentation Accession No. ML01 2670418).

31
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER 

(2-89) (Assigned by NRC, Add Vol., Supp., Rev., NRCM 1102. 

3201, 3202 BIBLIOGRAPHIC DATA SHEET and Addendum Numbers, if any.) 

(See instructions on the reverse) 

2. TITLE AND SUBTITLE NUREG-1750 

Assessment of Soil Amplification of Earthquake Ground Motion Using the "CARES" Code 

Version 1.2 3. DATE REPORT PUBLISHED 

MONTH - YEAR 

September 2001 

4. FIN OR GRANT NUMBER 

5. AUTHOR(S) 6. TYPE OF REPORT 

R. Pichumani Technical 

7. PERIOD COVERED (Inclusive Dates) 

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor, 

provide name and mailing address.) 

Division of Engineering 

Office of Nuclear Reactor Regulation 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (IfNRC, type 'Same as above;, if cntractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

and mailing address.) 

Same as above

10. SUPPLEMENTARY NOTES

11. ABSTRACT (200 words or less) 

This report describes the results of two studies to assess the soil amplification of earthquake ground motion by varying three 

parameters pertinent to the soil and rock supporting nuclear power plant structures. In the first study, the input earthquake 

ground motion (corresponding to the Regulatory Guidel.60 spectrum) was specified at the rock level. The study analyzed the 

effects of varying each parameter on the motion at the ground surface and at 40 feet (ft) below the ground surface. The results 

of the first parametric study show significant shifts in the frequency at which the maximum spectral acceleration occurs when 

the soil thickness is varied from 50 ft to 200 ft and when the shear wave velocity of the soil stratum is varied from 1000 fps to 

3000 fps. No frequency shifts are seen when the shear wave velocity of the rock medium is varied from 5000 fps to 10000 fps, 

but significant changes in the maximum spectral amplitude of acceleration are observed for the 100 ft and200 ft thick soil 

layer. The second parametric study used the seismic ground motion specified by a rock site-specific spectra input at the rock 

outcrop. A comparison of the results of the two parametric studies shows that the shapes of the spectral responses for both 

types of ground motion input are quite similar to the corresponding cases of soil thickness and soil shear wave velocity. 

However, the spectral amplitudes obtained for the site-specific rock spectra input are lower than the corresponding values for 

the Regulatory Guide (R.G)1.60 input because the amplitudes of the input spectral accelerations of the site-specific rock 

spectra are lower than those of the R.G. 1.60 spectra at all frequencies larger than approximately 0.18 Hz, even though the 

peak ground acceleration (PGA) of the site-specific rock spectra was set at 0.3g by scaling the actual PGA of 0.24g by a factor 

of 1.25 to match the 0.3g PGA of the R.G. 1.60 spectra.

12. KEY WORDS/DESCRIPTORS (List words or phreses that will assist researchers in locating the report.) 13. AVAILABILITY STATEMENT 

soil amplification unlimited 

soilamplficaion14. SECURITY CLASSIFICATION 

earthquake ground motion input _4.SEUR ____ASIFCA _O 

site-specific spectra (This Page) 

soil shear wave velocity unclassified 

rock shear wave velocity (This Report) 

unclassified 

15. NUMBER OF PAGES 

16 PRICE

NRC FORM 335 (2-89)
on Printed recycled 

ipaper 

Federal Recycling Program
ASSESSMENT OF SOIL AMPLIFICATION OF EARTHQUAKE GROUND MOTION USING 

THE "CARES" CODE VERSION 1.2

SEPTEMBER 2001

UNITED STATES 

NUCLEAR REGULATORY COMMISSION 

WASHINGTON, DC 20555-0001 

OFFICIAL BUSINESS 

PENALTY FOR PRIVATE USE, $300

NUREG-1750