SEISMIC EFFECTS ON 

SOIL-STRUCTURE INTERACTIONS 

Prepared for

U.S. Nuclear Regulatory Commission 

Contract NRC–02–07–006 

Prepared by 

Sui-Min (Simon) Hsiung 

Asadul H. Chowdhury 

Center for Nuclear Waste Regulatory Analyses 

San Antonio, Texas 

September 2011
ii 

CONTENTS 

Section Page 

FIGURES ...................................................................................................................................... iii 

TABLES ....................................................................................................................................... iv 

EXECUTIVE SUMMARY .............................................................................................................. v 

ACKNOWLEDGMENTS .............................................................................................................. vii 

1 INTRODUCTION ............................................................................................................ 1-1

 1.1 Background ........................................................................................................ 1-1 

 1.2 Objective and Scope .......................................................................................... 1-2 

2 THEORETICAL BACKGROUND OF SOIL-STRUCTURE 

 INTERACTION ANALYSIS ............................................................................................ 2-1 

2.1 Theory ............................................................................................................................ 2-1 

2.2 Background for SASSI 2000 Computer Code .................................................... 2-1 

2.2.1 Formulation ........................................................................................................ 2-1 

2.2.2 Site Response Analysis ...................................................................................... 2-4 

 2.2.2.1 Free-Field Displacements ................................................................. 2-4 

 2.2.2.2 Boundary Conditions ........................................................................ 2-5 

 2.2.2.2.1 Transmitting Boundary .................................................... 2-5 

 2.2.2.2.2 Viscous Boundary ........................................................... 2-6 

2.2.3 Impedance Matrix Determination........................................................................ 2-7 

3 SEISMIC HAZARDS AND SITE RESPONSE ................................................................ 3-1 

3.1 Seismic Hazards ................................................................................................ 3-1 

3.2 Spectral Matching of Input Time Histories .......................................................... 3-1 

3.3 Site-Specific Soil Model ...................................................................................... 3-2 

3.4 Free-Field Ground Acceleration Time Histories ................................................. 3-6 

4 SOIL-STRUCTURE INTERACTION ANALYSES .......................................................... 4-1 

 4.1 Model of a Hypothetical Waste Handling Facility ............................................... 4-1 

4.1.1 Facility Description .................................................................................. 4-1 

4.1.2 Structural Model...................................................................................... 4-1 

 4.2 Soil Model ........................................................................................................... 4-1

4.3 Input Ground Motions ......................................................................................... 4-3 

5 RESULTS AND DISCUSSIONS .................................................................................... 5-1 

 5.1 Effects of Soil Geometry ..................................................................................... 5-1 

5.2 Effects of Soil Material Variation......................................................................... 5-6 

5.3 Comparison Set A and B Ground Motion Effects ............................................. 5-13 

5.4 Potential Effects of Soil-Model Parameters ...................................................... 5-15 

6 CONCLUSIONS ............................................................................................................. 6-1

7 REFERENCES ............................................................................................................... 7-1 
iii 

FIGURES 

Figure Page 

2-1 Substructures I [2-1(b)], II [2-1(c)], and III [2-1(d)] of a Total Soil-Structure 

Interaction System [2-1(a)] for Soil-Structure Interaction Analysis ........................... 2-2 

2-2 Two-Dimensional Plane-Strain Soil Model for Impedance Matrix Calculation ......... 2-8 

2-3 Axisymmetric and Three-Dimensional Soil Model 

 for Impedance Matrix Calculation ............................................................................. 2-9 

3-1 Schematic of the Site Showing the Relative Location Points A, B, C, D, and E ....... 3-2 

3-2 Six Deaggregation Earthquake Response Spectra Representing the 

 5 × 10−

4 Hazard Level .............................................................................................. 3-3 

3-3 Geologic Profiles Used for Site-Response and Soil-Structure 

 Interaction Analyses ................................................................................................. 3-5 

4-1 Full and Cutaway Views of the Hypothetical Waste Handling Facility ...................... 4-2 

5-1 Envelope Spectral Responses at Tower-Top for Set A Ground Motions for 

 the Nine Geologic Profiles ........................................................................................ 5-1 

5-2 Envelope Operating Floor Spectral Responses for Set A Ground Motions for 

 the Nine Geologic Profiles ........................................................................................ 5-2 

5-3 Envelope Spectral Responses for Set A ground Motions for 

 the Nine Geologic Profiles ........................................................................................ 5-3 

5-4 Envelope Spectral Responses for Set B Ground Motions for the Nine 

Geologic Profiles Except the Ground Motion that Results High Spectral 

Acceleration in the 45–60 Frequency Range ........................................................... 5-5 

5-5 Mean Tower-Top Spectral Responses for Set A and B Ground Motions for 

 the Nine Geologic Profiles ........................................................................................ 5-7 

5-6 Median Tower-Top Spectral Responses for Set A Ground Motions for 

 the Nine Geologic Profiles ........................................................................................ 5-8 

5-7 Envelope Tower-Top Spectral Responses for Set A and B Ground Motions 

for the Three Soil Conditions .................................................................................... 5-9 

5-8 Mean Tower-Top Spectral Responses for Set A and B Ground Motions for 

 the Three Soil Conditions ....................................................................................... 5-10 

5-9 Envelope Tower-Top Spectral Responses of Group 1 Geologic Profiles for 

 Set A and B Ground Motions for the Three Soil Conditions ................................... 5-12 

5-10 Envelope Tower-Top and Operating Floor Spectral Responses for Set A and 

B Ground Motions .................................................................................................. 5-14 

5-11 Mean Tower-Top and Operating Floor Spectral Responses for Set A and B 

 Ground Motions ...................................................................................................... 5-16 

5-12 Effects of Soil-Model Layer Thickness on Structural Responses ........................... 5-17 

5-13 Effects of Number of Half-Space Layers on Basemat Spectral Responses ........... 5-19 

5-14 Effects of Number of Half-Space Layers on Tower-top Spectral Responses ......... 5-20 

5-15 Combined Effects of Subdivision Options and Number of Half-Space Layers 

on Structural Responses ........................................................................................ 5-21 
iv 

TABLES 

Table Page 

3-1 Characteristics of Earthquake Used for Generating Spectrally 

Matched Acceleration Time Histories Representing 5 × 10−4

 Annual 

 Exceedence Frequency ................................................................................................. 3-4 

3-2 Density, Shear-Wave Velocities for Each Unit of the Nine Geologic Profiles ................. 3-5 
v 

EXECUTIVE SUMMARY 

U.S. Nuclear Regulatory Commission (NRC) regulations, including 10 CFR Part 63, require 

safety review of nuclear facilities license applications for naturally occurring hazards. The 

assessment of seismic hazard and its impact on nuclear and other critical facilities is 

important to NRC, the license applicants for nuclear facilities, self-regulators such as the 

U.S. Department of Energy and the U.S. Department of Defense, and owners of non-nuclear 

facilities. Depending on the relative characteristics of a structure and geological medium such 

as natural soil, natural soft or hard rock, or engineered foundation system, the effects of 

interaction between the structure and geological medium under seismic load may be significant 

depending on the response of both the structure and the geological medium. The key 

characteristics of the structure and the site geological condition include, among others, weight of 

the structure and its dynamic properties, variations of geologic profile and geotechnical 

properties of the geological medium, and dynamic properties of the geological medium. 

The objective of this report is to present a detailed overview of work performed by the Center for 

Nuclear Waste Regulatory Analyses (CNWRA®) supporting the NRC high-level waste repository 

safety program (Hsiung, et al., 2006, 2007). This report summarizes the soil-structure 

interaction analyses of a hypothetical waste handling facility at Yucca Mountain, Nevada, a 

seismically active site, for which six deaggregation earthquake response spectra on a 

hypothetical reference rock outcrop corresponding to the 5 × 10−4

 annual exceedence frequency 

are available (Bechtel SAIC Company, LLC, 2004). The waste handling facility is located on an 

alluvium soil of varying thickness, which is above soft rock units of varying thicknesses and 

depths relative to the reference rock outcrop. The soil-structure interaction analyses were 

performed using two sets of free-field ground motions. One set of ground motions was from 

Bechtel SAIC Company, LLC (2004) and the other set was developed by CNWRA. 

Bechtel SAIC Company, LLC (2004) developed free-field response spectra at the top of 

alluvium soil by conducting a ground response analysis with the six deaggregation response 

spectra for the reference rock outcrop as the input. The design-basis response spectrum at the 

top of the alluvium soil was then developed by enveloping these free-field response spectra. 

Bechtel SAIC Company, LLC (2004) further developed nine acceleration time histories 

corresponding to this design-basis response spectrum. The CNWRA developed 24 acceleration 

time histories on the reference rock outcrop by spectrally matching the six deaggregation 

response spectra Bechtel SAIC Company, LLC (2004) developed and then performed ground 

response analyses to calculate the free-field acceleration time histories on the top of the 

alluvium soil considering variations of geologic profiles and soil materials. Thus, the 

Bechtel SAIC Company, LLC generated nine acceleration time histories corresponding to a 

single design-basis response spectrum and the CNWRA generated free-field acceleration time 

histories corresponding to the six deaggregation response spectra developed by Bechtel SAIC 

Company, LLC (2004). 

This report assesses the effects of geologic profile and soil material variations on the seismic 

structural responses at various locations of the waste handling facility. This report also 

compared the structural responses of the waste handling facility calculated by CNWRA using 

the Bechtel SAIC Company, LLC (2004) acceleration time histories and the CNWRA generated 

acceleration time histories. 

The soil-structure interaction analysis results of the hypothetical waste handling facility reported 

herein showed significant influence of the geologic profiles of the foundation medium and their 

geotechnical and dynamic properties on the seismic structural response of the facility. The 
vi 

simplistic assumption of a homogeneous and isotropic medium representing a geological 

medium with complex and highly heterogeneous geologic profiles and material properties may 

not provide reasonable results for the seismic response of a facility supported by that type of 

geological medium. The soil-structure interaction analysis results show that a facility with a 

large footprint resting on a complex and heterogeneous geological medium needs to be 

designed for a broadened design response spectrum. The soil-structure interaction analysis 

results could also identify the segments of the heterogeneous foundation medium that could be 

improved by engineered measures to reduce the effect of soil-structure interaction on the 

seismic response of the facility that would result in a more efficient and economical design. 

Comparison of the results of soil-structure interaction analyses conducted using the free-field 

acceleration time histories CNWRA developed and those generated by Bechtel SAIC Company, 

LLC shows reasonable agreement. The bounding acceleration responses of the operating floor 

at a height of 8.2 m [27 ft] and the top of the facility at a height of 25.6 m [84 ft] show general 

agreement except at some isolated frequencies. In developing the free-field acceleration time 

histories, CNWRA explicitly modeled the alluvium soil and each geologic stratum with the 

specific material properties provided in Bechtel SAIC Company, LLC (2004), whereas the 

free-field acceleration time histories Bechtel SAIC Company, LLC developed were based on site 

response analyses that used statistically processed homogenized material properties for the 

entire geological medium. 

REFERENCES 

Bechtel SAIC Company, LLC. “Development of Earthquake Ground Motion Input for Preclosure 

Seismic Design and Postclosure Performance Assessment of a Geologic Repository at 

Yucca Mountain, NV.” MDL–MGR–GS–000003. Rev. 01. Las Vegas, Nevada: Bechtel SAIC 

Company, LLC. 2004. 

Hsiung, S.M., A. Ghosh, and A.H. Chowdhury. “Site Response and Soil-Structure Interaction 

Analyses—A Progress Report.” San Antonio, Texas: Center for Nuclear Waste Regulatory 

Analyses. 2007. 

Hsiung, S.M., S.H. Gonzalez, and A.H. Chowdhury. “Site Response and Soil-Structure 

Interaction Analyses—A Progress Report.” San Antonio, Texas: Center for Nuclear Waste 

Regulatory Analyses. 2006. 
vii 

ACKNOWLEDGMENTS

This knowledge capture report was prepared to document a detailed overview of the 

work performed by the Center for Nuclear Waste Regulatory Analyses (CNWRA®) for the 

U.S. Nuclear Regulatory Commission (USNRC) under Contract No. NRC–02–07–006. The 

activities reported here were performed on behalf of the USNRC Office of Nuclear Material 

Safety and Safeguards, Division of High-level Waste Repository Safety. This report is an 

independent product of the CNWRA and does not necessarily reflect the view or regulatory 

position of USNRC. 

The authors thank D. Pomerening for technical review, D. Pickett for programmatic review, 

and E. Pearcy for his editorial review. The authors also appreciate L. Selvey for her 

administrative support. 

QUALITY OF DATA, ANALYSES, AND CODE DEVELOPMENT

DATA: CNWRA-generated hand calculation results are contained in this report. Sources of 

other data should be consulted for determining the level of quality for those data. 

ANALYSES AND CODES: ProShake® Version 1.11 (EduPro Civil Systems, 2001) was used 

for one-dimensional equivalent-linear site response analyses. EZ-FRISKTM Version 7.20 

(Risk Engineering, Inc., 2005) was used to spectrally match acceleration time histories with 

response spectra. SASSI 2000, Revision 1 (Lysmer, et al., 1999) was used for soil-structure 

interaction analyses. These codes are controlled under the CNWRA quality assurance 

program. Analyses described in this report are documented in CNWRA Scientific Notebooks 

No. 726 (Hsiung, 2005). 

REFERENCES

EduPro Civil Systems. “ProShake.” Version 1.11. Sammamish, Washington: 

EduPro Civil Systems. 2001. 

Hsiung, S.M. “Soil-Structure Interaction Analyses.” Scientific Notebook No. 726. 

San Antonio, Texas: Center for Nuclear Waste Regulatory Analyses. 2005. 

Lysmer, J., F. Ostandan, and C.C. Chin. “SASSI 2000—A System for Analysis of Soil-Structure 

Interaction, User’s Manual.” Rev. 1. Berkeley, California: University of California. 1999. 

Risk Engineering, Inc. “EZ-FRISK.” Version 7.20. Golden, Colorado: Risk Engineering, Inc. 

2005. 
1-1 

1 INTRODUCTION 

1.1 Background 

Appropriate consideration of seismic hazard and its impact on nuclear and other critical facilities 

is important to the U.S. Nuclear Regulatory Commission (NRC), the license applicants for 

nuclear facilities, other federal agencies such as the U. S. Department of Energy and the 

U.S. Department of Defense, and owners of non-nuclear critical facilities. Design of nuclear 

facilities to account for the seismic hazard is an important step to ensure operational safety and 

health and safety of the public. 

Most civil engineering structures involve direct contact with the ground. When subjected to 

earthquake ground motions, the structural response and the ground displacements are not 

independent of each other. In an earthquake, seismic waves are transmitted from the 

bedrock through the soil medium to a structure of interest. The seismic waves excite the 

structure, which in turn modifies the input free-field ground motion. This difference in ground 

motion is due to interaction between the soil geological medium including soil and the 

superstructure, also known as soil-structure interaction. 

Damage observed in several earthquakes such as the 1985 Mexico City earthquake 

(Resendiz, 1986; Avilés and Pérez-Rocha, 1998), the 1995 Kobe earthquake (Mylonakis, 

et al., 2000), and the 1999 Ji-Ji Taiwan earthquake (Earthquake Engineering Field Investigation 

Team, 2011) has shown that the seismic behavior of a structure is influenced by the responses 

of the structure, its foundation, and the ground. In general, the response of the structure is 

dependent on the properties of the soil, characteristics of the dynamic excitation, type of 

foundation of the structure, and the physical characteristics of the structure. For example, soft 

soil sediments could lead to elongation of the period of seismic waves resulting in the structure 

resonating with the long period ground vibration (Mylonakis, et al., 2000). The failure of soil 

may further aggravate the seismic response of the structure (Earthquake Engineering Field 

Investigation Team, 2011). Avilés and Pérez-Rocha (1998) identified the significant soilstructure interaction effects of an extended alluvial valley (Valley of Mexico) on medium- and 

long-period structures. 

The soil-structure interaction effects between the structure and its geological medium under 

seismic load become more prominent for heavy structures (e.g., nuclear power plants, high-rise 

buildings, elevated highways, and other infrastructures). Whereas the conventional design 

approach of not considering soil-structure interaction may be acceptable for light structures, it is 

prudent to include soil-structure interaction as an integral part of the design process for heavy 

structures. Once seismic hazard assessment is completed and a design-basis response 

spectrum is determined, soil-structure interaction analysis should be the next step for design 

and performance analysis of heavy structures. This step will develop appropriate seismic input 

for structural analysis, design, and qualification of critical structures, systems, and components. 

If the seismic input for analysis of the structures—especially the systems and components to be 

located within the structures—is not appropriately developed, the performance of their intended 

safety functions may not be assessed adequately. As discussed previously, to develop 

reasonable seismic input for structural analysis, appropriate consideration of the parameters 

such as the variability of geology and geotechnical and dynamic properties of geological 

medium, characteristics of the dynamic excitation, and the physical characteristics of 

the structure is essential. 
1-2 

Analysis of soil-structure interaction includes two major parts: (i) free-field ground motion or site 

response to seismic waves, in the absence of the structure, propagating through the earth to the 

ground surface and (ii) interaction between the structure, including systems and components 

located within the structure, and the geological medium using the free-field site-response data 

developed in part (i). 

1.2 Objective and Scope 

In this report, the Center for Nuclear Waste Regulatory Analyses (CNWRA®) documents its 

independent analyses conducted previously (Hsiung, et al., 2006, 2007) on the effects of the 

complex site subsurface geological medium on soil-structure interaction of a hypothetical waste 

handling facility at Yucca Mountain, Nevada. The complexity involves large variability in 

geologic units, including spatial variation of thicknesses and dynamic properties of geologic 

units. The soil-structure interaction analyses also assess the proposed seismic design-basis 

spectrum for the site of interest through comparing the responses of the critical structures 

resulting from the ground motions for the design-basis spectrum with the structural responses 

subjected to the ground motions developed separately at the same hazard level for the 

same site. In addition, this report discusses the potential effects of the soil-model assumptions 

used in the soil-structure interaction analyses. 

The computer code SASSI 2000 (A System for Analysis of Soil-Structure Interaction) 

(Lysmer, et al., 1999a) was used to investigate the seismic responses of a hypothetical waste 

handling facility. The input free-field acceleration time histories include two sets of ground 

motions. All of them correspond to the 2,000-year return period (i.e., annual exceedance 

frequency of 5 × 10−4

). The first set of ground motion time histories were developed by 

CNWRA. In developing the free-field ground motion time histories, one-dimensional site 

response analyses were performed using the computer code ProShake® (EduPro Civil 

Systems, 2001). The second set of ground motion time histories were from Bechtel SAIC 

Company, LLC (2004). 
2-1 

2 THEORETICAL BACKGROUND OF SOIL-STRUCTURE

INTERACTION ANALYSIS 

2.1 Theory 

Soil-structure interaction problems can be analyzed using the substructuring approach by 

subdividing the problem into simpler subproblems. The subproblems may be solved individually 

and the results combined to provide a complete solution using the principle of superposition. 

Because superposition is used to obtain the solution, the substructuring method is limited to the 

linear domain (Lysmer, et al., 1999a). 

Conceptually, the substructuring methods for soil-structure interaction analysis can be 

categorized into four types depending on the interaction at the soil and structure interface 

(Lysmer, et al., 1999a). These methods include (i) rigid boundary, (ii) flexible boundary, 

(iii) flexible volume, and (iv) substructure subtraction. All methods require site-response 

analysis, soil-impedance calculation, and structural response analysis. In addition, the rigid and 

flexible boundary methods require performing scattering analysis for the soil-structure 

interaction evaluation. 

The SASSI 2000 computer program (Lysmer, et al., 1999a) was selected for the independent 

soil-structure interaction analyses the CNWRA staff conducted. This program uses the 

substructuring method to approach a soil-structure interaction problem and solves the problem 

in the frequency domain. The program includes both the flexible volume and substructure 

subtraction techniques (Lysmer, et al., 1999a). Users can specify which technique to use. For 

the analyses presented in this report, the flexible volume method was used. 

The current version of SASSI 2000 has two major limitations: (i) the site should consist of 

horizontal soil layers (Lysmer, et al., 1999a) and (ii) the analytical method the program uses 

solves linear problems only. 

2.2 Background for SASSI 2000 Computer Code 

2.2.1 Formulation 

Both the flexible volume and substructure subtraction methods in SASSI 2000 use the concept 

of partitioning the soil-structure system [Figure 2-1(a)] into three substructures [Figure 2-1(b), 

(c), and (d)] (Lysmer, et al., 1999b). Substructure I consists of the free field, Substructure II is 

made of the excavated soil volume, and Substructure III consists of the structure itself including 

the basement. The term basement is used here to mean any portion of a structure below grade. 

A basement can be a complicated structure or a basemat, as the term is used later in this report 

in the context of soil-structure interaction. In the flexible volume method, the interaction 

between the free field (Substructure I) and the excavated soil volume (Substructure II) occurs at 

the boundary and within the excavated soil volume, and the soil-structure interactions between 

Substructures II and III and Substructures I and III occur at the interfaces with the basement of 

Substructure III (Lysmer, et al., 1999b). 
2-2 

g

Figure 2-1. Substructures I [2-1(b)], II [2-1(c)], and III [2-1(d)] of a Total System [2-1(a)] for 

Soil-Structure Interaction Analysis (Modified From Lysmer et al., 1999b) 
2-3 

In the frequency domain, the equation of motion for each substructure in Figure 2-1 may be 

expressed as (Lysmer, et al., 1999b) 

ሾܥሿሼܷሽ ൌ ሼܳሽ (2-1)

where ሾܥሿ is complex frequency-dependent dynamic stiffness matrix, ሼܷሽ is complex 

displacement matrix, and ሼܳሽ is complex load matrix. 

At a specific frequency ߱, 

ሾܥሿ ൌ ሾܭሿ െ ߱ଶሾܯሿ

(2-2)

ሼܷሽ ൌ ൛ܷൟ݁ି௜ఠ௧

(2-3)

ሼܳሽ ൌ ቄܳቅ ݁ି௜ఠ௧ (2-4)

where ሾܭሿ is stiffness matrix, ሾܯሿ is mass matrix which is a combination of one-half lump mass 

matrix and one-half consistent mass matrix, ൣܷ൧ is displacement matrix in the time domain, and 

ቂܳቃ is load matrix in the time domain due to the seismic excitations. 

A lump mass matrix is a mass matrix formed by assuming the total element mass is directly 

apportioned to nodal freedom, ignoring any cross coupling and the consistent mass matrix is a 

mass matrix derived using the same shape functions as those for the stiffness matrix. 

Combining the substructures, the equation of motion used for solving a soil-structure problem 

used in the SASSI 2000 can be expressed as follows. 

CCX CXC

CX C X

C C

U

U

U

XU X U

XU X U

ii

III

ii

II

ii iw

II

iw is

III

wi

II

wi ww

II

ww

si

III

ss

III

i

w

s

ii i iw w

wi i ww w

−+ −+

−+ − +









































=

′ + ′

′ + ′





















0

0 0

(2-5)

where superscripts ܫܫ and ܫܫܫ are types of substructures shown in Figure 2-1, subscript ܫ is for 

nodes at the interface between the soil and the structure, subscript w is for nodes within the 

excavated soil volume, subscript ݏ is for nodes for the structure excluding the basement, ൣܺ௙௛൧ is 

the impedance matrix representing the dynamic stiffness of the foundation at the interaction 

nodes where subscripts ݂ and ݄ represent either ݅ or ݓ, and ൛ܷ௙

ᇱ

ൟ is the matrix of free-field 

motions where subscript ݂ represents either ܫ or ݓ. 

This formulation applies to both two- and three-dimensional soil-structure interaction problems. 

Notice that Substructure I is not included in Eq. (2-5), implying that it is sufficient to assess the 

interaction response of a structure based only on the free-field motions within the depth of the 

basement (Chen, et al., 1981). 
2-4 

The subproblem in the flexible volume method used in SASSI 2000 includes 

(i) Determining ൛ܷ௙

ᇱ

ൟ by conducting site response analysis 

(ii) Solving for ൣܺ௙௛൧ by performing the impedance analysis 

(iii) Solving the linear equation of motion to obtain the transfer functions that will be used to 

determine structural responses. 

Thus, to analyze the site response, the free-field displacements at the interaction points at 

the soil-layer interface are calculated. Through the impedance analysis, the impedance matrix 

or the dynamic stiffness for the excavated soil volume at the interaction points will be 

determined. SASSI 2000 performs structural analyses using the finite element method as 

defined in Eq. (2-5) for both Substructures II and III. 

2.2.2 Site Response Analysis 

The site response analysis is performed using SASSI 2000 for a horizontally layered soil system 

with a semi-infinite halfspace. The equations of motion are formulated such that the 

displacements are solved at the interfaces of soil layers. The displacements in each soil layer 

are assumed to vary linearly with the thickness of the soil layer. SASSI 2000 can calculate the 

free-field displacements resulting from a combination of plane-wave fields including body 

waves, such as compressive (P-), vertically propagating shear (SV-), and horizontally 

propagating shear (SH-) waves, and surface waves, such as Rayleigh and Love waves. 

2.2.2.1 Free-Field Displacements 

To solve for the free-field displacements ൛ܷ௙

ᇱ

ൟ at the interaction nodes (Figure 2-1) including 

those within the excavated soil volume in the flexible method, Substructure I [Figure 2-1(b)] is 

used (Lysmer, et al., 1999b). SASSI 2000 requires that all interaction nodes be placed at the 

soil layer interfaces. 

The equation of motion of a layered soil system for the incident P- and SV-waves is 

(Lysmer, et al., 1999b; Chen, et al., 1981; Udaka, 1975) 

൫ሾܣሿ݇ଶ ൅ ൣܤ൧݇ ൅ ሾܩሿ െ ߱ଶሾܯሿ൯ሼܷሽ ൌ ൜ 0

ܲ௕

ൠ (2-6)

where ሾܣሿ and ሾܩሿ are constant matrices for each soil layer and are a function of layer thickness, 

Lame’s constant, and shear modulus of the soil layer; ൣܤ൧ is the constant matrix for each soil 

layer and is a function of Lame’s constant and shear modulus of the soil layer; ሼܲ௕ሽ is the load 

matrix for the forces at the interface between the layered soil system and the half space; and 

݇ is the eigenvalue or wave number. The load matrix ሼܲ௕ሽ and wave number k can be 

determined if the information regarding the incidence angle of the wave and the nature of the 

wave field is provided. 
2-5 

The equation of motion of a layered soil system for the SH-waves takes the form (Lysmer, et al., 

1999b; Chen, et al., 1981) 

൫ൣܣ൧݇ଶ ൅ ൣܩ൧െ߱ଶൣܯ൧൯ሼܷሽ ൌ ൜ 0

ܲ௕

ൠ (2-7)

where ൣܣ൧ and ൣܩ൧ are constant matrices for each soil layer and are a function of layer thickness 

and shear modulus of the soil layer and ൣܯ൧ is the mass matrix of each soil layer. 

The equation of motion of a layered soil system for the Rayleigh waves can be generalized as 

(Chen, et al., 1981; Waas, 1972) 

ሺሾܣሿ݇ଶ ൅ ݅ሾܤሿ݇ ൅ ሾܩሿ െ ߱ଶሾܯሿሻሼܸሽ ൌ 0 (2-8)

where ሾܤሿ is constant matrix for each soil layer and is a function of Lame’s constant and shear 

modulus of the soil layer and ሼܸሽ is associated eigenvectors (mode shapes). 

The equation of motion of a layered soil system for the Love waves can be generalized as 

(Chen, et al., 1981; Wass, 1972) 

൫ൣܣ൧݇ଶ ൅ ൣܩ൧െ߱ଶൣܯ൧൯ሼܸሽ ൌ 0 (2-9)

Note that for a soil system with n-number of horizontal layers, the matrices in the equation of 

motion for the SV- and P-waves [Eq. (2-6)] contain 2 (n + 1) × 2 (n + 1) elements. In the 

matrices in the equation of motion for the SH-waves [Eq. (2-7)] contain (n + 1) × (n + 1) 

elements. In the matrices in the equation of motion for the Rayleigh waves [Eq. (3-8)], each 

matrix contains 2 n × 2 n elements. The matrices in the equation of motion for the Love waves 

[Eq. (2-9)] contain n × n elements (Lysmer, et al., 1999b; Chen, et al., 1981). 

After solving the equations of motion for displacements ሼܷሽ at the soil-layer interfaces, 

displacements along the horizontal direction can be determined using (Lysmer, et al., 1999b) 

ሼܷሺݔሻሽ ൌ ߜሼܷሽ݁ି௜௞௧ (2-10)

where ݔ is the horizontal distance from the defined control-point location (an input by 

SASSI 2000 user) where the input control motion is applied and ߜ is the mode participation 

factor which can be obtained from the input control motion at the frequency of interest. 

2.2.2.2 Boundary Conditions 

2.2.2.2.1 Transmitting Boundary 

To correctly transmit the seismic energy in the horizontal direction, SASSI 2000 implemented 

transmitting boundaries. Formulation of the transmitting boundary for two-dimensional problems 

adopted in SASSI 2000 was developed by Waas (1972) using the eigenvalues and eigenvectors 

obtained from solving the equation of motion for the Rayleigh waves [Eq. (2-8)]. The formulated 

force-displacement relationship for two-dimensional problems in the frequency domain for a 

layered soil system takes the form of 

ሼܲሽ ൌ ሾܴሿሼܷሽ (2-11)
2-6 

where ሼܲሽ is force matrix and ሾܴሿ represents the dynamic stiffness matrix of the semi-infinite 

layered region beyond the transmitting boundary and (Lysmer, et al., 1999b) 

ሾܴሿ ൌ ݅ሾܣሿሾܸሿሾܭሿሾܸሿିଵ ൅ ሾܦሿ (2-12)

where ሾܦሿ is a constant matrix and a function of Lame’s constant and shear modulus of a 

soil layer. 

Using the eigen-solutions for Rayleigh and Love waves [Eqs. (2-8) and 2-9)], a 

force-displacement relationship similar to Eq. (2-12) for a layered soil system in an 

axisymmetric condition may be obtained. However, the analytical solution for the dynamic 

stiffness matrix ሾܴሿ for the axisymmetric problems appears to be more complicated than that for 

the two-dimensional problems. In the axisymmetric case, the radius (distance from the central 

axis to the transmitting boundary) of the axisymmetric model is an important parameter in 

formulating the dynamic stiffness matrix (Lysmer, et al., 1999b). The transmitting boundary 

formulation for the axisymmetric problems is also used as the transmitting boundary formulation 

for the three-dimensional problems in SASSI 2000. 

2.2.2.2.2 Viscous Boundary 

The bottom boundary of the layered soil system in SASSI 2000 may be modeled as a rigid 

(fixed) boundary or a halfspace. The halfspace may be represented by several soil layers with 

variable thicknesses and a viscous boundary at the bottom (Lysmer, et al., 1999a). The rigid 

boundary tends to reflect some seismic energy back to the system and may, in turn, result in 

some erroneous natural frequencies that affect the overall response (Lysmer, et al., 1999a). 

Simulation of a halfspace will reduce the energy reflection problems and greatly improve the 

accuracy of the impedance calculation. 

In SASSI 2000, the halfspace option is selected by specifying the number of sublayers to 

represent the halfspace. SASSI 2000 requires a minimum of four sublayers to simulate a 

halfspace. The total thickness of the sublayers specified for the halfspace is a function of 

frequency of interest and shear velocity of the halfspace. The thickness of each sublayer is a 

function of total thickness, number of sublayers, and thickness of the soil layer above the 

halfspace (Lysmer, et al., 1999b). 

The viscous boundary consists of two dashpots per unit area of the boundary (Lysmer and 

Kuhlemeyer, 1969; Lysmer, et al., 1999b)—one for P-wave damping and the other for 

shear-wave damping. The damping coefficients for the dashpots can be expressed as 

(2-13) ௣ܸߩ ൌ௣ ܥ

and 

ܥ௦ ൌ ߩܸ௦ (2-14)

where ܥ ௣is damping coefficient for P-waves, ܥ௦ is damping coefficient for shear waves, ߩ is 

mass density of the halfspace, ܸ௣ is P-wave velocity for the halfspace, and ܸ௦ is shear-wave 

velocity for the halfspace. 
2-7 

2.2.3 Impedance Matrix Determination 

As with the flexible volume method, the impedance matrix ൣܺ௙௛൧ needs to be calculated by all 

interaction nodes in the excavated soil volume, as shown in Eq. (2-5) and Figure 2-1(c). The 

impedance matrix can be obtained by inverting the compliance matrix at each frequency of 

interest. The compliance matrix is a collection of the displacements responding to a unit 

harmonic force acting at the interaction nodes defined in the excavated soil volume. More 

specifically, the elements in the i

th column of the impedance matrix are the displacements of the 

interacting degree-of-freedom induced by a unit harmonic force acting at the i

th degree-offreedom (Lysmer, et al., 1999b). To determine the compliance matrix, a soil column consisting 

of a single column of loaded interaction nodes (Figures 2-2 and 2-3) is used in the SASSI 2000. 

This soil column includes two transmitting boundaries for two-dimensional problems and a 

cylindrical transmitting boundary for axisymmetric and three-dimensional problems. The 

displacement responses at the interaction nodes (shown as the loaded interaction nodes in 

Figures 2-2 and 2-3) and the boundary nodes in the soil model can be determined by solving 

the following equations of motion (Lysmer, et al., 1999b) and successively applying the unit 

loads to the interaction nodes on the center line of the model. 

൤

௟௖ܥ ௖௖ܥ

൜൨ܴ௟௟ ൅ ܥ ௖௟ܥ

ܷ௖

ܷ௟

ൠ ൌ ቄ

ܳ௖

0 ቅ (2-15)

where subscript ܿ is index referring to the degree-of-freedom for the interaction nodes along the 

center line, subscript ݈ is index referring to the degree-of-freedom for the nodes along the 

transmitting boundary, ሾܥሿ is dynamic stiffness matrix which takes the form of Eq. (2-2), and ሼܳ௖ሽ

is load matrix (for each load case, this matrix has only one non-zero element corresponding to 

the applied unit load). 

The solution for the compliance or displacement matrix for a single column of the interaction 

nodes can be used as the compliance matrix for the remaining columns of interaction nodes. 

As discussed previously, once the displacement matrix for all interaction nodes is obtained, this 

matrix can be inverted to determine the impedance matrix used to solve Eq. (2-5). 
2-8 

Figure 2-2. Two-Dimensional Plane-Strain Soil Model for Impedance 

Matrix Calculation (Modified From Lysmer, et al., 1999b) 
2-9 

Figure 2-3. Axisymmetric and Three-Dimensional Soil Model 

for Impedance Matrix Calculation (Modified From Lysmer, et al., 1999b) 
3-1 

3 SEISMIC HAZARDS AND SITE RESPONSE

3.1 Seismic Hazards 

Ground motion results for the probabilistic seismic hazard analyses were developed for a 

hypothetical reference rock outcrop at Yucca Mountain, referred to as Point A in Figure 3-1 

(Stepp, et al., 2001). Point A in Figure 3-1 is located on the same rock unit and at the same 

elevation as Point B, which represents the proposed repository horizon. The only difference 

between Points A and B is that Point A is an outcrop site. Within the proposed surface facilities 

site, Point D refers to locations southwest of the Exile Hill fault splay with alluvium thickness of 

at least 15 m [49 ft] and Point E refers to the area on the west side for which the alluvium is 

approximately 4.6 m [15 ft] thick or less (Bechtel SAIC Company, LLC, 2004). 

At Point A, six deaggregation earthquake response spectra were generated for each hazard 

level in the 10−3

 to 10−7 annual exceedence frequency range for both vertical and horizontal 

components of ground motion (Bechtel SAIC Company, LLC, 2004). Bechtel SAIC Company, 

LLC developed these deaggregation earthquake response spectra based on the deaggregation 

of the probabilistic seismic hazard analyses and divided them equally into two groups. The 

three response spectra in the first group represent the 1–2 Hz structural response frequency 

range, while the response spectra in the second group represent the 5–10 Hz structural 

response frequency range. The response spectra of the three deaggregation earthquakes in 

each group were developed by first deaggregating the probabilistic seismic hazard with respect 

to magnitude only to obtain the 5th, mean, and 95th percentile magnitudes. The site-to-source 

distances corresponding to these magnitudes were obtained by deaggregating the probabilistic 

seismic hazard with respect to distance only and selecting the corresponding distances for the 

5th, mean, and 95th percentile (Bechtel SAIC Company, LLC, 2004). 

In this report, one set of free-field ground accelerations used for the soil-structure interaction 

analyses were developed by CNWRA by performing site response analyses using these six 

deaggregation earthquake response spectra representing the 5 × 10−4 annual exceedence 

frequency (Figure 3-2). Detailed discussion on developing this set of free-field ground 

accelerations are provided in the following three sections. The second set of ground motions 

used in the soil-structure interaction analyses is from Bechtel SAIC Company, LLC (2004) and 

is discussed in Section 4.3 of this report. 

3.2 Spectral Matching of Input Time Histories 

Before free-field acceleration time histories can be generated, site response analyses are 

required to propagate the accelerations from Point A in Figure 3-1. These accelerations should 

be consistent with the six deaggregation earthquake response spectra (Table 3-1) representing 

the 5 × 10−4 annual exceedence frequency at the reference rock outcrop location. To calculate 

the acceleration time histories corresponding to the deaggregation earthquake response spectra 

representing the 5 × 10−4 annual exceedence frequency, CNWRA used the recorded 

acceleration time histories of 24 earthquakes to spectrally match the six deaggregation 

earthquake response spectra. These time histories were from the European Strong-Motion 

Database (2006) and McGuire, et al. (2001). These earthquakes were chosen because they 

have magnitudes, distances, and faulting styles similar to the deaggregation earthquakes. 

Three to six spectrally matched acceleration time histories were developed for each 

deaggregation response spectrum shown in Figure 3-2. 
3-2 

Figure 3-1. Schematic of the Site Showing the Relative Location Points 

A, B, C, D, and E [Note: PSHA = Probabilistic Seismic Hazard Analysis] 

(Modified From Stepp, et al., 2001) 

The 24 spectrally matched acceleration time histories were developed using EZ-FRISKTM 

Version 7.20 (Risk Engineering, Inc., 2005). A convergence tolerance criterion was used for 

spectral matching to ensure the maximum deviation of the matched spectrum from the target 

response spectrum was 0.01. 

3.3 Site-Specific Soil Model 

To generate the free-field acceleration time histories at the ground surface necessary for 

soil-structure interaction analyses of the hypothetical waste handling facility, all 24 spectrally 

matched acceleration time histories were used as inputs to the site response analyses. 

Considering the potential effects of spatial variations (both thicknesses and dynamic properties 

of geologic units), nine site-specific geologic profiles and three sets of shear wave (S wave) 

velocities were used for the soil-structure interaction analyses. Among the nine geologic 

columns (profiles), four (RF13, RF14, RF16, and RF17) were from Bechtel SAIC Company, LLC 

(2002) and the remaining five (SF01, SF02, SF03, SF04, and SF05) were extracted from a 

three-dimensional geological model representing the site built by CNWRA using the 

EarthVisionTM software (Dynamic Graphics, Inc., 2002). 

The lithologic information and thickness of each lithologic unit for these nine geologic profiles 

are shown in Figure 3-3. Differences in unit thicknesses for the nine geologic profiles are 
3-3 

Figure 3-2. Six Deaggregation Earthquake Response Spectra Representing the 

5 × 10−4

 Hazard Level 

substantial. Consequently, these nine geologic profiles should be sufficient to evaluate the 

significance of geologic spatial variations on the seismic response of the hypothetical waste 

handling facility assumed to be located at the site with this type of geological medium. 

Three sets of S-wave velocities selected to investigate the potential effects of soil stiffness on 

dynamic structural responses were average, average minus one standard deviation (lower 

bound), and average plus one standard deviation (upper bound) S-wave velocities. These 

S-wave velocities along with the densities of the geologic profile are given in Table 3-2. For 

convenience, the geologic profiles with the average S-wave velocity (Bechtel SAIC Company, 

LLC, 2002) are referred to as average soils, the geologic profiles with the average minus one 

standard deviation S-wave velocity are referred to as soft soils, and the geologic profiles with 

the average plus one standard deviation S-wave velocities are referred to as stiff soils.

These nine geologic profiles and three sets of dynamic properties were used in the site 

response analyses to develop free-field ground acceleration time histories for the soil-structure 

interaction analyses. 

0.010

0.100

1.000

0.1 1.0 10.0 100.0 Frequency, Hz

Spectral Acceleration, g

5th Percentile, Structural Response Frequency 1-2 Hz

Mean, Structural Response Frequency 1-2 Hz

95th Percentile, Structural Response Frequency 1-2 Hz

5th Percentile, Structural Response Frequency 5-10 Hz

Mean, Structural Response Frequency 5-10 Hz

95th Percentile, Structural Response Frequency 5-10 Hz
3-4 

Table 3-1. Characteristics of Earthquakes Used for Generating Spectrally Matched 

Acceleration Time Histories Representing 5 × 10−4

 Annual Exceedence Frequency

Earthquake Station Mw

Epicentral 

Distance, 

km [mi]

DOE Deaggregation 

Response Spectrum 

Matched

Umbria Marche 1, Italy 

(aftershock) 

Nocera UmbraBiscontini 5.5 10 [6.2] 5th Percentile, 

Structural Response 

Coalinga 1, California Transmitter Hill 5.2 10.4 [6.5] Frequency 1–2 Hz 

Coalinga 2, California Anticline Ridge FreeField 5.2 11 [6.8] 

Kozani 1, Greece Kozani-Prefecture 6.5 17 [10.6] Mean, Structural 

Response Frequency 

1–2 Hz 

Umbria Marche 3, Italy 

(aftershock) 

Borgo-Cerreto Torre 6 25 [15.5] 

South Iceland 1, Iceland 

(aftershock) 

Hveragerdi-Church 6.4 24 [14.9] 

South Iceland 2, Iceland 

(aftershock) 

Selfoss-City Hall 6.4 15 [9.3] 

Izmit 1, Turkey HeybeliadaSenatoryum 7.6 78 [48.5] 95th Percentile, 

Structural Response 

Vrancea 1, Romania Vrancioaia 7.2 49 [30.4] Frequency 1–2 Hz 

Izmit 2, Turkey Gezbe-Tubitak 

Marmara Arastima 

Merkezi 

7.6 47 [29.2] 

Vrancea 2, Romania Petresti-Foscani 7.2 75 [46.6] 

Umbria Marche 2, Italy 

(aftershock) 

Nocera UmbraBiscontini 5.3 8 [5.0] 5th Percentile, 

Structural Response 

Coalinga 3, California Oil City 5.8 8.2 [5.1] Frequency 5–10 Hz 

Coalinga 4, California Anticline Ridge Pad 5.2 11 [6.8] 

Valnerina, Italy Cascia 5.8 5 [3.1] Mean, Structural 

Response Frequency 

5–10 Hz 

Friuli, Italy (aftershock) Tarcento 6 12 [7.5] 

South Iceland 3, Iceland Thjorsarbru 6.5 15 [9.3] 

Bingol, Turkey Bingol-Bayindirlik 

Murlugu 6.3 14 [8.7] 

Parkfield, California Temblor pre-1969 6 16 [9.9] 

Helena, Montana Carroll College 6 5 [3.0] 

Montenegro, Yugoslavia Hercegnovi NoviO.S.D. Pavicic School 6.9 65 [40.4] 95th Percentile 

Structural Response 

Kocaeli, Turkey Gezbe 7.4 17 [10.5] Frequency 5–10 Hz 

Kozani 2, Greece Kozani-Prefecture 6.5 17 [10.5] 

Tabas, Iran Dayhook 7.3 12 [7.5] 
3-5 

Depth Below Grade, ft

-700

-600

-500

-400

-300

-200

-100

0 RF13 RF14 RF16 RF17 SF01 SF02 SF03 SF04 SF05

Quaternary Alluvium

Pre-Rainier Mesa

Tuff Unit X

Post-Tiva Canyon

Crystal-Rich 

Tiva Canyon

Upper Lithophysal 

Tiva Cayon

Middle Nonlithophysal

Tiva Canyon

Lower Lithophysal 

Tiva Canyon

Figure 3-3. Geologic Profiles Used for Site-Response and Soil-Structure Interaction 

Analyses [1 ft = 0.3048 m] 

Table 3-2. Density, Shear-Wave Velocities for Each Unit of the Nine Geologic Profiles

Unit Unit Weight,

kg/m3 [pcf] 

S-Wave Velocity, m/s [ft/s] 

Average − 1 SD Average‡ Average + 1 SD‡ 

Quaternary Alluvium 1,852 

[115.6] 

559 

[1,834] 

712 

[2,336] 

865 

[2,838] 

Pre-Rainier Mesa Tuff 1,816 

[113.4] 

781 

[2,563] 

1,011 

[3,318] 

1,238 

[4,063] 

Tuff Unit X 1,572 

[98.16] 

946 

[3,105] 

1,063 

[3,489] 

1,180 

[3,873] 

Post-Tiva Canyon Tuff 1,789 

[111.7] 

809 

[2,653] 

1,017 

[3,335] 

1,224 

[4,017] 

Crystal-Rich Tiva 

Canyon Tuff 

1,855 

[115.8] 

781 

[2,563] 

1,010 

[3,313] 

1,238 

[4,063] 

Upper Lithophysal 

Tiva Canyon Tuff 

2,070 

[129.2] 

757 

[2,483] 

1,132 

[3,713] 

1,506 

[4,942] 

Middle Nonlithophysal 

Tiva Canyon 

2,321 

[144.9] 

1,117 

[3,666] 

1,583 

[5,193] 

2,048 

[6,720] 

Lower Lithophysal 

Tiva Canyon 

2,207 

[137.8] 

1,234 

[4,050] 

1,639 

[5,378] 

2,044 

[6,706] 

Lower Nonlithophysal 

Tiva Canyon* 

2,127 

[132.8] 

1,528 

[5,012] 

1,894 

[6,213] 

2,260 

[7,415] 

†SD: standard deviation 

‡Data from Gonzalez, S., A. Ghosh, J. Stamatakos, K. Murphy, and L. McKague. “Review of Scientific Analysis 

Document—Geotechnical Data for a Potential Waste Handling Building and for Ground Motion Analyses for the 

Yucca Mountain Site Characterization Project.” Scientific Notebook No. 644. San Antonio, Texas: Center for 

Nuclear Waste Regulatory Analyses. 2004. 

*Unit used as a half-space in the site-response and the soil-structure interaction analyses
3-6 

3.4 Free-Field Ground Acceleration Time Histories 

To generate the free-field acceleration time histories at the ground surface for soil-structure 

interaction analyses, ProShake® Version 1.111 (EduPro Civil Systems, 2001) was used to 

perform the one-dimensional equivalent-linear site-response modeling. The equivalent-linear 

model approximates nonlinear site response by iteratively adjusting the stiffness and damping 

parameters of the soil or rock layers until they are compatible with the strain levels induced by 

the earthquake loading (Kramer, 1996; Lo Presti, et al., 2006). ProShake calculates the 

response of a horizontally layered soil deposit overlying a uniform half-space subjected to 

vertically propagating shear waves (Schnabel, et al., 1972). The 24 spectrally matched 

acceleration time histories were used as inputs to the site response analyses for each geologic 

profile shown in Figure 3-3 with the three S-wave velocity sets listed in Table 3-2. 

To conduct the site-response analyses, the upper mean alluvium and upper mean tuff shear 

modulus reduction and damping curves in Bechtel SAIC Company, LLC (2004) were used as 

inputs to the site-response models. The upper mean alluvium and upper mean tuff shear 

modulus reduction and damping curves were selected for the calculations because the 

site-response modeling results presented in Bechtel SAIC Company, LLC (2004) indicate that 

this combination of curves generally produced larger ground motions than other combinations of 

curves. These modeling results also show that, depending on frequency, alluvium thickness is 

an important factor. 
4-1 

4 SOIL-STRUCTURE INTERACTION ANALYSES 

4.1 Model of a Hypothetical Waste Handling Facility 

4.1.1 Facility Description 

For the soil-structure interaction analyses, a SASSI (Lysmer, et al., 1999a) model simulating a 

hypothetical waste handling facility (Figure 2-1) was developed. This facility consists of 

(i) A ground floor area 64 m [210 ft] long in the east-west direction and 47.1 m [154.5 ft] 

wide in the north-south direction 

(ii) An operating floor located at the northern portion of the facility at a height of 8.2 m [27 ft] 

above the ground floor 

(iii) A partial mezzanine floor located at the northeast portion of the facility and located 

13.7 m [45 ft] above the ground floor 

(iv) A rooftop at 19.5 m [64 ft] above the ground level 

(v) An enclosed rectangular tower located at the southeast corner of the facility with its 

rooftop at the 25.6-m [84-ft] level 

Figure 4-1 shows the top and cross-sectional views of this hypothetical facility. The basemat of 

this hypothetical facility is 3.05 m [10 ft] thick, and the top of the basemat is at ground level. 

The thickness assumed for the east-west walls is 1.37 m [4.50 ft], south-north walls is 1.52 

m [5.00 ft], north outer wall is 1.22 m [4.00 ft], operating and mezzanine floors is 0.38 m 

[1.25 ft], roof at the 19.5 m [64 ft] level is 0.99 m [3.25 ft], and roof at the 25.6 m [84 ft] Level is 

0.76 m [2.50 ft]. 

4.1.2 Structural Model 

The hypothetical waste handling facility was modeled as a three-dimensional structure. 

The SASSI structural model consisted of 9,101 nodes and 5,132 elements. Out of the 

5,132 elements, 594 elements represent the excavated soil and 4,538 elements represent the 

structure. For the element nodes located above grade, six degrees of freedom of motions were 

permitted. The structure was assumed to be made of concrete with a unit weight of 2,403 kg/m3

[150 pcf]. The Young’s modulus and Poisson ratio assumed for the concrete were 24,821 MPa 

[5.184 × 105

 ksf] and 0.2, respectively. 

The excavated soil was modeled using eight-node rectangular solid elements. Most solid 

element dimensions were controlled by the physical dimensions of the components of the 

structure above. Otherwise, the maximum dimension was set to ensure accurate transmission 

of the seismic waves. 

4.2 Soil Model 

The soil-structure interaction analyses were conducted using the nine different geologic profiles 

shown in Figure 3-3. For each geologic profile, the soil-structure interaction analysis considered 
4-2 

(a) Full View 

(b) Cutaway View With Outer Walls and Roofs Removed 

Figure 4-1. Full and Cutaway Views of the Hypothetical Waste Handling Facility 
4-3 

three soil stiffness variations. Each layer in a geologic profile was subdivided into smaller 

layers as necessary to satisfy the maximum permissible layer thickness recommended in the 

SASSI 2000 computer program to adequately transmit the waves. The maximum thickness 

permissible for a soil layer should be small enough to capture the particle motion associated 

with high frequency vibrations (e.g., Ofoegbu and Gute, 2002). Lysmer and Kuhlemeyer (1969) 

show that a better than 10-percent solution accuracy can be obtained if the layer thickness is 

less than or equal to (i) one-eighth of the shortest wavelength of interest if either lumped or 

consistent mass matrix is used in the analysis or (ii) one-fifth of the shortest wavelength of 

interest if a mixture of the lumped and consistent mass matrix is used in the analysis. 

The SASSI 2000 computer program calculates the mass matrices using a combination of half 

consistent mass matrix and half lump mass matrix (Lysmer, et al., 1999b). Consequently, in 

determining the maximum soil-layer thickness, it is sufficient to use the recommended one-fifth 

of the shortest wavelength of interest. Lysmer, et al. (1999b) indicate that larger soil layer 

thickness can be used in soil zones with higher S-wave velocities. 

To be effective, if a soil-layer thickness exceeds the permissible thickness, the soil layer should 

be subdivided into several sublayers. The same maximum permissible thickness should also be 

applicable to the finite element model of the structure sharing the interaction nodes with the 

surrounding soil. Given that the largest element dimension used in the soil-structure interaction 

analyses was 3.89 m [12.75 ft], the cutoff frequency was approximately 29 Hz for the soft soil 

cases, 37 Hz for the average soil cases, and 45 Hz for the stiff soil cases. 

For each geologic column, five extra layers and a set of viscous dashpots were added at the 

bottom of the column to simulate the half space condition. In the SASSI 2000, the total 

thickness of the added layers is 1.5 times the shear-wave length of the half space (Lysmer, 

et al., 1999a,b). The choice of this thickness is intended to minimize the potential effects of the 

fundamental mode Rayleigh waves because this fundamental mode decays rapidly with depth. 

In addition, at the surface, the Rayleigh wave essentially vanishes after a distance of 1.5 times 

wavelengths (Lysmer, et al., 1999b). The material properties used in this study for the extra 

layers were the same as those for the layer located at the bottom of the column (Table 3-2). 

4.3 Input Ground Motions 

As discussed previously, the free-field acceleration time histories CNWRA developed using the 

24 spectrally matched acceleration time histories (Section 3.2) for the soil profiles, including 

consideration of soil property variations through site-response modeling, were used as the input 

ground motions for soil-structure interaction analyses. 

Besides the free-field acceleration time histories generated from the 24 spectrally matched 

acceleration time histories, the five sets of free-field acceleration time histories developed in 

Bechtel SAIC Company, LLC (2004) for the design-basis response spectrum at Point D/E of 

Figure 3-1 were also used in the soil-structure interaction analyses. The design-basis response 

spectrum was consistent with the hazard level of 5 × 10−4

 annual exceedence frequency. In 

developing the design-basis response spectrum for seismic design, Bechtel SAIC Company, 

LLC (2004) used a one-dimensional equivalent-linear approach similar to that of CNWRA to 

calculate site responses of the soil and rock beneath the site. The design-basis response 

spectrum represents the envelope of the individual site response analyses results. An important 

distinction between the site response analyses approach CNWRA used and that Bechtel SAIC 

Company, LLC used was that CNWRA considered lithology when developing velocity, density, 

and layer thickness profiles (see Figure 3-3 and Table 3-2); whereas, Bechtel SAIC Company, 
4-4 

LLC incorporated randomized velocity/thickness (Hsiung, et al., 2005). Each set of the 

acceleration time histories consists of two horizontal and one vertical acceleration time history 

except Set 4, which consists of only one horizontal and one vertical acceleration time history. 

All nine horizontal acceleration time histories were used as the free-field ground motions for the 

soil-structure interaction analyses presented in this report. 

For convenience, the input ground motions using the free-field acceleration time histories 

generated from the 24 spectrally matched acceleration time histories are referred to as Set A 

ground motions and the input ground motions using the nine free-field acceleration time 

histories developed in Bechtel SAIC Company, LLC (2004) are referred to as Set B 

ground motions. 

The input ground motions were specified at the ground surface and applied to the soil-structural 

model along the east-west direction. A uniform damping of 4 percent was assumed for the 

structure and basemat. 
5-1 

5 RESULTS AND DISCUSSIONS

Three primary factors control soil-structure interactions: (i) soil geometry (geologic profile 

geometry), (ii) soil material property, and (iii) ground motion. Generally, the influence of these 

three factors is complex. It is often difficult to evaluate the effects of one factor on the dynamic 

response of a given structure independent of the others. The structural response results from 

the soil-structure interaction analyses discussed in the following sections are measured along 

the horizontal east-west direction. For convenience, the terms “soil profiles” and “geologic 

profiles” are used interchangeably in this chapter. 

5.1 Effects of Soil Profiles 

As discussed previously, nine geologic profiles were considered in these soil-structure 

interaction analyses. The wide variation in thickness of each unit or layer in the nine geologic 

profiles (Figure 3-3) should be sufficient to allow qualitative assessment of the potential 

influence of spatial variation of geological medium on dynamic structural responses. Figure 5-1 

shows the envelope structural responses at the tower-top level of the hypothetical waste 

handling subjected to the Set A earthquake ground motions developed from the six 

deaggregation response spectra by CNWRA. The tower top discussed here is the rooftop of the 

tower located at the southeast corner of the facility at the 25.6-m [84-ft] level. The envelope 

response spectra discussed in this section represent the largest spectral acceleration at each 

frequency from the results of the soil-structure interaction analysis cases for a geologic profile 

of interest. 

Figure 5-1. Envelope Spectral Responses at Tower-Top for Set A Ground Motions for the 

Nine Geologic Profiles 
5-2 

Figure 5-1 indicates that geologic profile (spatial) variations at the hypothetical surface facility 

site could cause significant variation in spectral responses of the hypothetical waste handling 

facility. The soil-structure system under investigation appears to exhibit two types of responses 

to seismic ground motions. For the first type (type 1), the response spectral acceleration peaks 

are in the frequency range of 5–14 Hz. For the second type (type 2), the response spectral 

acceleration peaks are in the frequency ranges of 9–17 Hz with much larger spectral amplitudes 

than those observed for the first type. The type 2 responses are the results of the soil-structure 

system resonance. The type 2 responses may be observed for the hypothetical waste handling 

facility located on the RF14, RF17, SF01, and SF03 (Group 2) geologic profiles, but not 

observed at any in-structure locations of the hypothetical waste handling facility for the RF13, 

RF16, SF02, SF04, and SF05 (Group 1) geologic profile cases. It appears that the 

soil-structure system resonates with the Group 2 geologic profiles for Set A ground motions in 

the 9–17 Hz frequency range. Similar observations can also be made for the spectral 

responses at the operating floor level, which is at a height of 8.2 m [27 ft] above the ground floor 

with smaller spectral acceleration amplitudes (Figure 5-2). 

The effects of geologic variations on spectral responses at the tower top and on the operating 

floor for the hypothetical waste handling facility subjected to Set B ground motions developed in 

Bechtel SAIC Company, LLC (2004) show the same behavior as observed for Set A ground 

motions (Figure 5-3). The tower top and operating floor resonate with Group 2 geologic profiles 

for the Set B ground motions in the 9–17 Hz frequency range. As expected, the spectral 

Figure 5-2. Envelope Operating Floor Spectral Responses for Set A Ground Motions for 

the Nine Geologic Profiles 
5-3 

(a) Tower Top 

(b) Operating Floor 

Figure 5-3. Envelope Spectral Responses for Set B Ground Motions for the 

Nine Geologic Profiles 
5-4 

acceleration peaks for the operating floor are smaller than those at the tower top. For the 

Set B ground motion case, the SF03 geologic profile produces the largest spectral response in 

the 9–17 Hz frequency range; it is the RF14 geologic profile for the Set A ground motions. 

For the Set B ground motion cases, two other soil-structure resonances with large local spectral 

acceleration peaks can also be observed on the tower top [Figure 5-3(a)] at the 25–30 Hz and 

45–65 Hz frequency ranges for the RF14 geologic profile case. The resonance behavior at the 

25–30 Hz frequency range can also be observed for the SF03 geologic profile case with 

relatively smaller spectral acceleration amplitude. The local spectral peak in the 25–30 Hz 

frequency range exists also for the cases related to the Set A ground motion cases, however, 

with negligible acceleration values (Figure 5-1). The resonance at the 45–65 Hz frequency 

range for the Set B ground motion case is not shown in the results of the Set A ground motion 

cases and has a high spectral amplitude of 15.75 g. This particular high spectral amplitude is 

associated with one time history in the Set B ground motion group. If the results for the time 

history that caused this high local peak are removed from Figure 5-3(a), a local spectral peak in 

the 45–65 Hz frequency range still exists, however, with a much smaller spectral amplitude 

(Figure 5-4). Examining the response spectral results for the RF14 geologic profile cases, it 

was found that more than half of the acceleration time histories in the Set B ground motion 

group produced resonance in the 45–65 Hz frequency range, with local spectral peaks ranging 

from 3.5–6.9 g besides the 15.8 g case mentioned previously. To understand why the tower of 

the hypothetical waste handling facility resonates at the 45–65 Hz frequency range with this 

high acceleration peak for only the RF14 geologic profile and the Set B ground motions, 

understanding the natural frequencies of the structure and the associated modal participation 

factors may offer valuable insights. 

The thickness of the Quaternary Alluvium top soil unit alone does not appear to explain the 

phenomena of the seismic responses of the hypothetical waste handling facility on Group 2 

geologic profiles that are different from those on Group 1 geologic profiles. As shown in 

Table 3-2, the Quaternary Alluvium unit has the lowest S-wave velocity. The S-wave velocity for 

the Pre-Rainier Mesa, Tuff Unit X, Post-Tiva Canyon, crystal-rich Tiva Canyon, and Upper 

Lithophysal Tiva Canyon tuff units are approximately 35 to 74 percent higher than those of the 

Quaternary alluvium. The S-wave velocities for the geologic units beneath the Upper 

Lithophysal Tiva Canyon tuff unit are more than twice those of the alluvium unit. 

The thickness of the alluvium unit for Group 1 geologic profiles varies from 9.1 to 27.7 m 

[29.8 to 90.9 ft], with the thinner alluvium unit from the SF05 geologic profile and the thicker one 

from the SF02 geologic profile. The alluvium thickness for Group 2 geologic profiles varies from 

20.5 m [67.1 ft] for the SF03 geologic profile to 42.9 m [140.7 ft] for the SF01 geologic profile 

(Figure 3-3). Notice there is overlap between the two thickness ranges. For example, the 

alluvium thickness is 26.1 m [85.5 ft] for the RF13 geologic profile, 27.7 m [90.9 ft] for the SF02 

geologic profile, and 21.8 m [71.5 ft] for the SF04 geologic profile. These thicknesses are larger 

than the alluvium thickness {20.5 m [67.1 ft]} associated with the SF03 geologic profile. 

However, the resonance structural responses found at the tower top and on the operating floor 

in the 9–17 Hz frequency range for the SF03 geologic profile are not observed for the RF13, 

SF02, or SF04 geologic profiles (Figures 5-1 and 5-2). Therefore, even though the thickness 

range for Group 2 geologic profiles is relatively larger than that for Group 1 geologic profiles, 

alluvium thickness does not seem to be the only factor that causes the soil-structure system 

with the geologic profiles in these two groups to respond differently. 
5-5 

Among the nine geologic profiles, the Pre-Rainier Mesa Tuff unit is present only in the RF17 

geologic profile. According to Figures 5-1 and 5-2, this unit does not appear to have a strong 

effect on soil-structure interaction. Table 3-2 shows that the Pre-Rainier Mesa Tuff, Tuff Unit X, 

Post-Tiva Canyon Tuff, and the Crystal-Rich Tiva Canyon Tuff units beneath the alluvium soil 

appear to have similar S-wave velocities. The total thickness of these four units varies from 

16.7 to 44.6 m [54.7 to 146.3 ft] for the Group 1 geologic profiles and from 52.8 to 117.5 m 

[173.2 to 385.6 ft] for Group 2 geologic profiles (Figure 3-3). The total thickness of the four units 

in Group 2 geologic profiles is greater than that in Group 1 geologic profiles. Furthermore, the 

total thickness of these four units and the alluvium unit in Group 2 geologic profiles is greater 

than that in Group 1 geologic profiles. The largest total thickness is 63.0 m [206.6 ft] for the 

Group 1 geologic profiles and the smallest thickness for Group 2 geologic profiles is 77.4 m 

[253.8 ft]. The combined effect of the alluvium unit and the four units immediately beneath it 

appears to be responsible for the soil-structure resonance behavior observed for Group 2 

geologic profiles. 

A thicker alluvium unit or a thicker combined first five units does not necessarily cause a higher 

resonance response in the 9–17 Hz frequency range for Group 2 geologic profiles. For Group 2 

geologic profiles, the thickness of the alluvium unit is 42.9 m [140.7 ft] for the SF01 geologic 

profile, 31.0 m [101.8 ft] for the RF14 geologic profile, 28.2 m [92.4 ft] for the RF17 geologic 

profile, and 20.5 m [67.1 ft] for the SF03 geologic profile (Table 3-2). Even though the alluvium 

unit for the SF01 geologic profile is the thickest among the four geologic profiles, the largest 

peak spectral accelerations observed for the tower top and operating floor are with the RF14 

Figure 5-4. Envelope Spectral Responses for Set B Ground Motions for the Nine 

Geologic Profiles Except the Ground Motion that Results High Spectral Acceleration in 

the 45–60 Frequency Range 
5-6 

geologic profile for the Set A ground motion case. For the Set B ground motion case, the 

largest tower and operating floor peak spectral accelerations are from the SF03 geologic 

profile, for which the thickness of the alluvium unit is the thinnest among the four Group 2 

geologic profiles. 

Figure 5-5 shows the mean response spectra at the tower top for both Set A and Set B ground 

motions. Similar observations made for the envelope in-structure response spectra are also 

applicable to the mean response spectra. Notice that the mean response spectra are much 

smaller than the corresponding envelope response spectra with the Group 2 geologic profiles 

for the Set A ground motion case. This observation suggests that a large number of the 

acceleration time histories in Set A ground motions generated small spectra accelerations in the 

9–17 Hz frequency range for Group 2 geologic profiles. The median tower top spectral 

response plot in Figure 5-6 supports this observation. Figure 5-6 indicates that more than half 

of Set A ground motions generate smaller spectral response in the 9–17 Hz frequency range for 

Group 2 geologic profiles, such that the median is smaller than the mean as shown in 

Figure 5-5(a). 

The mean response spectra on the operating floor also exhibit structural resonances in the 

9–17 Hz frequency range with much smaller acceleration amplitudes than those at the tower 

top. Additionally, for the Set A ground motion case, the amplitudes of the mean resonant 

response spectra on the operating floor for the Group 2 geologic profiles are not any larger than 

other mean response spectra for the Group 1 geologic profiles. 

The envelope and mean in-structure response spectra for the nine geologic profiles represent a 

broadened structural response (Figures 5-1, 5-2, 5-3, and 5-5) (i.e., the frequency content 

containing the spectral acceleration peaks for the resulting envelope has been widened). In 

other words, soil profile variation has a broadening effect on the structural response spectra. 

The broadening effect of soil profile variation on the in-structure response spectra is observed 

for all earthquake input conditions. For the individual response spectra in the envelope, the 

response spectra corresponding to a geologic profile may be considered to have a spectrum 

shift with respect to the response spectra of another geologic profile if the frequency contents 

for the spectral acceleration peaks are not the same. For example, the response spectra for the 

SF01 geologic profile shift to a higher frequency range relative to the response spectra for the 

RF13 geologic profile because the frequency content for the latter is lower. 

As discussed previously, the soil-structure interaction analyses results suggest that, if the 

hypothetical waste handling facility were to be located on the Group 2 geologic profiles, it would 

experience high spectral accelerations at a number of resonant frequencies. These high 

seismic responses may be reduced if necessary through several engineering measures. These 

measures include (i) avoiding locating the structure in areas with a subsurface geological 

medium similar to those of Group 2 geologic profiles, (ii) conducting ground improvements in 

areas with a subsurface geological medium similar to those of Group 2 geologic profiles, and 

(iii) modifying the design of the structure to change natural frequencies to prevent or 

mitigate resonance. 

5.2 Effects of Soil Material Variation 

Figure 5-7 compares the envelope structural seismic responses caused by Sets A and B ground 

motions at the tower top resulting from soil material variations. The envelope response spectra 

discussed in this section represent the largest spectral acceleration for all nine geologic profiles 

at each frequency from the results of the soil-structure interaction, analysis cases under a 
5-7 

(a) Set A Ground Motions 

(b) Set B Ground Motions 

Figure 5-5. Mean Tower-Top Spectral Responses for Set A and B Ground Motions for the 

Nine Geologic Profiles
5-8 

particular soil material condition of interest. Note that the soft soil referred to in the caption of 

the figure used the average minus one standard deviation S-wave velocities as input as 

discussed in Section 3.3 of this report, the average soil used the average S-wave velocities, and 

the stiff soil used the average plus one standard deviation S-wave velocities. In the previous 

section, the structural resonance behavior was discussed for Group 2 geologic profiles in the 

9–17 Hz frequency range. This observation needs to be conditioned based on the 

results shown in Figure 5-7. According to Figure 5-7, resonance behavior is only for the 

soft and average soil conditions and not for the stiff soil condition, irrespective of the soil 

profile variations. 

The two soil-structure resonances with large spectral acceleration peaks at frequency ranges of 

25–30 Hz and 45–65 Hz for Set B ground motions, as discussed in the previous section, are 

also shown in Figure 5-7(b). Figure 5-7(b) indicates that, for Set B ground motions, the 

resonance at the 25–30 Hz frequency range is related to the average soil condition and the 

resonance in the 45–65 Hz frequency range is associated with the stiff soil condition. As 

discussed previously, the resonance in the 25–30 Hz frequency range is specific to the RF14 

and SF03 geologic profiles, while the resonance in the 45–65 Hz frequency range is specific to 

the RF14 geologic profile only. The spectral acceleration responses for Set A ground motions 

also exhibit the resonance behavior [Figure 5-7(b)] with much smaller spectral acceleration 

amplitude compared to those for the Set B ground motion case. The resonance behavior in the 

45–65 Hz frequency range is not observed for any geologic profiles subjected to the Set A 

ground motions. 

The two resonances at the high frequency ranges (higher than 20 Hz) mentioned in the previous 

paragraph are not obvious from the results of mean tower-top response spectra (Figure 5-8). 

Figure 5-6. Median Tower-Top Spectral Responses for Set A Ground Motions for the 

Nine Geologic Profiles
5-9 

(a) Set A Ground Motions 

(b) Set B Ground Motions 

Figure 5-7. Envelope Tower-Top Spectral Responses for Set A and B Ground Motions for 

the Three Soil Conditions 
5-10 

(a) Set A Ground Motions 

(b) Set B Ground Motions 

Figure 5-8. Mean Tower-Top Spectral Responses for Set A and B Ground Motions for the 

Three Soil Conditions 
5-11 

The mean response spectra for both Set A and B ground motions show type 2 resonant 

behavior in the 9–17 Hz frequency range for the soft and average soil conditions. This resonant 

behavior is not apparent in the mean response spectra for the stiff soil condition for either 

ground motion set. In addition, the spectral acceleration peaks at the resonant frequency 

ranges are the highest for the soft soil condition and smallest for the stiff soil condition. This 

trend is not as clear for the envelope tower-top spectral acceleration peaks subject to the Set B 

ground motions, for which the spectral acceleration peaks for the soft and average soil 

conditions are comparable [(Figure 5-7(b)]. 

Consistent with the observation on the effects of spatial variation of areal geology, the structural 

systems located on the Group 1 geologic profiles show no resonance responses at the tower 

top for all soil material conditions. For these cases, the frequency contents of the spectral 

acceleration peaks tend to shift to the higher frequency range as the soils become stiffer 

(Figure 5-9). In addition, the spectral acceleration peaks are higher for the relatively stiffer soils. 

This trend is consistent irrespective of the geologic profiles used and free-field ground motions 

applied. This observation is consistent with the common understanding that the structural 

response of a stiffer soil-structure system generally has a higher frequency content than that of 

a softer system. It should also be noted that, for the Group 1 geologic profiles, the response 

spectral acceleration amplitudes are higher when the soil is stiffer. 

In the case of seismic responses generated by the Set A ground motions, the response spectral 

peaks are comparable for the average and soft soil conditions [Figure 5-9(a)]. This result may 

reflect the differences in how the Set A and B ground motions were developed. As discussed in 

Section 4.3, the free-field acceleration time histories used in the soil-structure interaction 

analyses for the Set B ground motions were generated by Bechtel SAIC Company, LLC (2004) 

using the design-basis response spectrum at Point D/E of Figure 3-1 corresponding to the 

hazard level of 5 × 10−4

 annual exceedence frequency. The Set A ground motions, on the other 

hand, were developed using the six deaggragation response spectra at Point A/B of Figure 3-1 

corresponding to the same hazard level of 5 × 10−4

 annual exceedence frequency by spectral 

matching. The spectrally matched time histories were then propagated from Point B through the 

nine geologic profiles under the three soil condition sets to the ground surface to generate 

free-field acceleration time histories at the surface. Because of the effects of specific soil 

conditions (including both variability of areal geology and soil materials), the resulting 

free-field ground motions were conditioned by the variations of soil profiles and stiffness. As 

a result, the free-field acceleration ground motion input for each soil-structure interaction 

analysis case was different. For the Set B ground motions, on the other hand, the same 

acceleration time history was used for all geologic profiles and soil material conditions in the 

soil-structure interaction analyses. 

The observed spectrum shift caused by the variation of soil materials (stiffness) broadens 

the response spectrum envelope at the tower top, similar to that observed from soil 

profile variation. This broadening effect is an important characteristic of a complex and 

heterogeneous geological medium. In this study, the complex and heterogeneous geological 

medium is represented by the nine geologic profiles and three sets of soil material conditions. 

For a facility with a large footprint on such a complex and heterogeneous geological medium, its 

design needs to be based on a broadened design response spectrum to properly include spatial 

variability of geological medium. 

The soil-structure interaction analysis results show that the dynamic structural response 

observed for the tower top also occurs in other in-structure locations. The two types of 

structural responses and the broadening effect caused by the variation of soil stiffness typically 
5-12 

(a) Set A Ground Motions 

(b) Set B Ground Motions 

Figure 5-9. Envelope Tower-Top Spectral Responses of Group 1 Geologic Profiles for 

Set A and B Ground Motions for the Three Soil Conditions 
5-13 

found at the tower top are also observed on the operating floor with only relatively smaller 

spectral acceleration amplitudes. 

The results for the soil material effects provide additional information to identify regions at the 

site where the grounds could be improved or avoided to reduce effects of soil-structure 

resonance. For example, the tower-top spectral response envelopes for Set A and B ground 

motions in Figure 5-7 suggest that only when a structure is to be built on the soft and average 

soils, ground improvements may need to be considered. There is no need for ground 

improvement when the structure is to be built on a location with stiff soil. 

5.3 Comparison of Set A and B Ground Motion Effects 

Figure 5-10 displays the response spectral envelopes at the tower top and on the operating floor 

subjected to both Set A and B ground motions. The envelope response spectra discussed in 

this section represent the largest spectral acceleration at each frequency from the results of all 

soil-structure interaction analyses cases, including all geologic profiles and soil material 

conditions of interest. Both tower-top and operating floor response spectral envelopes for the 

Set B ground motions appear to slightly shift to a higher frequency range relative to the 

response spectral envelope for the Set A ground motions. As a result, the response spectral 

acceleration amplitudes for the Set A ground motion case are slightly larger than those for the 

Set B ground motion case at the frequencies lower than approximately 11 Hz. In other words, 

the envelope response spectra for the Set B ground motions developed from the design-basis 

response spectrum corresponding to the hazard level of 5 × 10−4

 annual exceedence frequency 

do not appear to bound the envelope spectra for the Set A ground motions developed using the 

six deaggragation response spectra. Recognizing the uncertainties associated with the 

modeling approaches and the complex geological medium present, the difference between the 

two envelopes at frequencies below 11 Hz can be considered small; therefore, the two 

envelopes are in a reasonable agreement in this frequency range. 

At frequencies higher than 11 Hz, the Set B ground motions produced much larger spectral 

accelerations than the Set A ground motions in several frequency ranges. As discussed in 

Section 5.2, there are two resonances with large spectral acceleration peaks at frequencies 

higher than 20 Hz. The first resonance in the 25–30 Hz frequency range for the Set B ground 

motion case is related to the RF14 and SF03 geologic profiles under the average soil condition. 

The tower top experienced a resonance in the 45–65 Hz frequency range only when the 

structure was located on the RF14 geologic profile with a stiff soil for Set B ground motions. 

The Set A ground motion case does display the first resonance in the analysis results. 

However, the magnitude is not as pronounced as for the Set B ground motion case. For the 

operating floor, the spectral accelerations are slightly larger for the Set B ground motion case at 

frequencies higher than 11 Hz and the resonances at the two frequency ranges of 25–30 Hz 

and 45–65 Hz are negligible. Therefore, it can be concluded that the in-structure response 

spectral envelopes for the Set B ground motions are in a broad agreement with those for the 

Set A ground motions at frequencies higher than 11 Hz, with the tower-top envelope of Set B 

ground motions clearly bounding the tower-top envelope of Set A ground motions. In other 

words, the design-basis response spectra are appropriate for design of structure and generating 

in-structure response spectra for structural analysis, design, or qualification of systems and 

components in the structure if the envelope structural response spectra are intended to be used 

for these purposes. 
5-14 

(a) Tower Top 

(b) Operating Floor 

Figure 5-10. Envelope Tower-Top and Operating Floor Spectral Responses for Set A and 

B Ground Motions 
5-15 

Figure 5-11 shows the mean tower-top and operating floor response spectra for both Set A and 

B ground motions. The mean response spectra at the tower top for both Set A and B ground 

motions clearly reflect the dominance of Group 2 geologic profiles for both soft and average soil 

conditions; the mean response spectra peak in the 9–17 Hz frequency range. Such dominance 

is not as clear for the mean operating floor response spectra. The mean response spectra 

associated with the Set B ground motions appear to envelope the response spectra for the 

Set A ground motions at frequencies larger than 0.4 Hz, and the differences between the two at 

frequencies smaller than 0.4 Hz are negligible. If the mean in-structure response spectra were 

to be used as seismic input for structural analysis, design, and qualification of the systems and 

components located within the structure analyzed, the design-basis response spectrum is more 

than sufficient for all frequencies of interest. 

5.4 Potential Effects of Soil-Model Parameters 

As discussed in Section 4.2, two soil-model parameters potentially affect the soil-structure 

interaction results: allowable soil-model-layer thickness and number of half-space layers. The 

allowable soil layer thickness used in the soil-structure interaction analysis should not be larger 

than one-fifth of the shortest wavelength of interest (Lysmer, et al., 1999a,b). Lysmer, et al. 

(1999b) further suggest that the maximum model-layer thicknesses can be different for geologic 

units with different S-wave velocities. Inclusion of the half-space is intended to minimize the 

potential effects of Rayleigh waves. SASSI 2000 simulates the half-space by adding extra 

layers to the bottom of a geologic profile with a total thickness 11⁄2 times the shear wavelength of 

the half space. SASSI 2000 also allows users to select the number of half-space layers for the 

soil-structure interaction analysis. Lysmer, et al. (1999a) suggest that, for many practical cases, 

10 extra half-space layers are sufficient. This section is intended to develop a better 

understanding of the influence of model-layer thickness and number of half-space layers on 

dynamic structural responses for the soil-structure system studied in this report. The results are 

valuable to inform conducting similar soil-structure interaction analyses. 

In this investigation, the RF17 geologic profile is used to evaluate the potential effects of 

allowable layer thickness. This geologic profile, along with the RF14 geologic profile, is used to 

assess the potential effects of the number of half-space layers. The allowable model-layer 

thickness for the alluvium unit is the smallest because its S-wave velocity is the smallest among 

the geologic units (Table 3-2). The RF17 geologic profile is subdivided into 39 thinner layers for 

the case satisfying the allowable layer thickness for the respective unit and 52 thinner layers for 

the case meeting the allowable layer thickness for the alluvium unit. For the RF14 geologic 

profile, only one subdivision is used. This subdivision ensures that the subdivided model layer 

has a thickness consistent with the allowable layer thickness for the alluvium unit for all 

geologic units. 

Figure 5-12 presents the spectral response results for the two soil-model layer subdivision 

alternatives. In general, the effects of layer subdivision alternatives (39 sublayers versus 

52 sublayers in total) on the spectral responses at the basemat are relatively small, while the 

effects are more pronounced on the in-structure responses. In addition, the effects are larger at 

higher elevations than of lower elevations of the structure. The subdivision option with the 

sublayer thickness meeting the allowable layer thickness of each unit (39 sublayers in total) 

produces relatively larger in-structure spectral response at higher frequencies than the option 

with the sublayer thickness for all geologic units meeting the allowable layer thickness for the 

alluvium unit (52 sublayers in total), irrespective of the number of half-space layers used. 
5-16 

(a) Tower Top 

(b) Operating Floor 

Figure 5-11. Mean Tower-Top and Operating Floor Spectral Responses for Set A and B 

Ground Motions 
5-17 

(a) Basemat 

(b) Tower Top 

Figure 5-12. Effects of Soil-Model Layer Thickness on Structural Responses 
5-18 

Figure 5-13 compares the effects of the number of half-space layers on the spectral responses 

at the basemat for the RF14 and RF17 geologic profile cases. The effects of the number of 

half-space layers are small for response spectra at the basemat, irrespective of the geologic 

profiles used, except in the frequency range where the resonant behavior was observed. In that 

frequency range, the response spectra with 5 half-space layers are the largest among the three 

options for both RF14 and RF17 geologic profiles. The difference between 10 half-space layers 

and 20 half-space layers is almost negligible for all cases. 

The effects of the number of half-space layers on response spectra are much greater on 

in-structure response spectra than the basemat (Figure 5-14). Similar to the basemat, the 

response spectra with 5 half-space layers are the largest among the three options in the 

resonant frequency ranges for the RF14 geologic profile and at frequencies higher than 9 Hz for 

the RF17 geologic profile. The response spectra for the 20 half-space layer case are the 

smallest among the three options at all frequencies greater than 6 Hz. As with the observation 

for the basemat, the difference in the tower-top response spectra between the cases with 

10 and 20 half-space layers is negligible. This observation agrees with the suggestion Lysmer, 

et al. (1999a) made that 10 extra half-space layers are sufficient for most engineering cases. 

Given that both soil-model layer subdivisions and number of half-space layers have effects on 

the structural spectral responses, it may be worthwhile to determine which factor dominates. 

Figure-5-15 shows that the subdivision option with the model-layer thickness meeting the 

allowable layer thickness of the respective unit (39 sublayers in total) and more half-space 

layers (20 layers) produces larger in-structure spectral responses than the option with the 

model-layer thickness meeting the allowable layer thickness for the alluvium unit (52 sublayers 

in total) and fewer half-space layers (5 layers). This result suggests that the model-layer 

subdivision may have more pronounced effects than the half-space layer option. The difference 

in effects between the subdivision options and number of half-space layers on the spectral 

responses at the basemat cannot be clearly determined; however, the difference is small. 

In summary, for the hypothetical waste handling facility studied, the in-structure spectral 

response results are larger using the subdivision option with the model-layer thickness meeting 

the allowable layer thickness for each corresponding unit than using the subdivision option with 

the model-layer thickness meeting the allowable layer thickness of the alluvium unit. The 

response spectra for the former, in general, bound those for the latter. Similar observations 

may also apply to the use of half-space layers; the cases with fewer half-space layers may 

potentially result in conservative in-structure spectral responses relative to the cases with more 

half-space layers. Effects of both subdivision options and the number of half-space layers on 

basemat response spectra are substantially smaller than those on the in-structure response 

spectra and, therefore, may be ignored. 
5-19 

 

(a) RF14 Geologic Profile 

(b) RF17 Geologic Profile 

Figure 5-13. Effects of Number of Half-Space Layers on Basemat Spectral Responses
5-20 

(a) RF14 Geologic Profile 

(b) RF17 Geologic Profile 

Figure 5-14. Effects of Number of Half-Space Layers on Tower-top Spectral Responses
5-21 

(a) Basemat 

(b) Tower Top 

Figure 5-15. Combined Effects of Subdivision Options and Number of Half-Space Layers 

on Structural Responses
6-1 

6 CONCLUSIONS 

The effects of complex and heterogeneous geological media on soil-structure interaction of a 

hypothetical waste handling facility at Yucca Mountain were investigated using the SASSI 

computer code. The investigation includes spatial variations of geologic profiles and soil 

material conditions. This report compared the dynamic structural responses using the Set B 

acceleration time histories developed consistent with the design-basis response spectrum at the 

soil top for the site of interest with the Set A acceleration time histories generated by spectrally 

matching the deaggregation response spectra at the reference rock outcrop of the same site. 

The Set A ground motions were developed by CNWRA whereas the Set B ground motions were 

from Bechtel SAIC Company, LLC (2004). The investigation conducted in this report included 

nine geologic profiles to capture a wide variation in thicknesses of geologic units at the site to 

permit qualitative assessment of the potential effects of spatial variability of complex site 

geology. Three sets of soil material conditions (soft, average, and stiff) defined based on 

S-wave velocities of the geologic units were also analyzed to examine the potential influence 

of uncertainty associated with the S-wave velocity measurements. 

The soil-structure interaction analysis results showed soil-structure resonance at the top of a 

rectangular tower located at one corner of the hypothetical waste handling facility roof, 25.6 m 

[84 ft] above the ground floor, and on the operating floor at the 8.2-m [27-ft] level. This 

resonance, with sharp spectral acceleration amplitude increase in the frequency range of 9–17 

Hz, was observed for four of the nine geologic profiles irrespective of the set of ground motions. 

For other geologic profiles where the resonant behavior was not observed, the response 

spectral acceleration peaks were reported in the 5–14 Hz frequency range. 

A resonance in the 45–65 Hz frequency range with the response spectral acceleration peaks 

ranging from 3.5–15.75 g was observed for various acceleration time histories in the Set B 

ground motions. This resonance behavior with high response spectral peaks is specific to the 

RF14 geologic profile under the stiff soil condition. The presence (or absence) and thickness 

variations of the geologic units in the RF14 geologic profile are not any different from other 

geologic profiles used to explain this behavior. 

The soil-structure interaction analyses results yield valuable information on how a structure 

sitting on the ground with a complex geological medium reacts to ground motions. The 

results could be used to identify regions of a site where the soil-structure interaction may be 

too large to be tolerable for performance of the structure, including the systems and 

components in the structure. These insights are valuable for selecting alternatives to mitigate 

the complex geological effects on dynamic structural performance and result in a more efficient 

and cost-effective design. Many engineering measures are available to improve performance. 

For example, if the structure footprint is sufficiently small or the available site area is large 

enough, the structure could possibly be located in areas where the structural resonance 

behavior is less pronounced. Ground improvements to increase soil stiffness may prove to be 

effective as well because the soil-structure analysis results show that the resonant behavior is 

less pronounced when the structure is located on stiffer ground. The soil-structure interaction 

analyses could be used to assess the effectiveness of various ground improvement techniques 

provide input for cost estimation. Such information is helpful for decisionmaking on selecting 

reasonable techniques for ground improvement. 

Besides the resonant behavior, the soil-structure interaction analyses also highlight the need for 

the structure to be designed for a broadened design spectrum. The soil-structure interaction 

analysis results showed that, with a complex geology, the variation of geologic profiles results in 
6-2 

shifts in frequency contents of the spectral acceleration peaks and different soil material 

conditions tend to produce spectral acceleration peaks with different frequency contents. This 

shift in frequency contents of the spectral acceleration peaks suggests a broadened response 

spectra curve could be developed to account for the spatial geological variability to ensure 

reasonable consideration of possible seismic effects. 

Based on comparison of the soil-structure interaction analysis results from the Set A and Set B 

ground motions, the response spectral acceleration envelopes at various locations of the 

hypothetical waste handling facility for both Set and A and B ground motions are in a broad 

agreement even though at some frequencies the spectral accelerations for Set A ground 

motions are larger. The differences are not significant considering the uncertainties associated 

with modeling assumptions, the approaches used, and complex site geology. The mean 

response spectra from the Set B ground motions, on the other hand, bound those from the Set 

A ground motions at various locations of the hypothetical waste handling facility with a large 

margin. Because the Set B ground motions were developed consistent with the design-basis 

response spectrum, the design-basis response spectrum appears to be reasonable for 

structural analyses, design, and qualification of systems and components in the hypothetical 

waste handling facility. 

In performing the soil-structure analyses using the SASSI computer code, it is important that the 

layer thickness used in the soil model should, at least, be smaller than or equal to the allowable 

soil layer thickness for each corresponding soil-layer unit. The allowable thickness is one-fifth of 

the wavelength of interest. Using the allowable soil-layer thickness determined based on the 

smallest S-wave velocity among the geologic units in the geologic profile is preferable to using 

the allowable thickness based on each corresponding geologic unit. However, the latter 

appears to yield conservative results relative to the former. 
7-1 

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