# 2Elements of Ssi Analysis

## 2ELEMENTS OF SSI ANALYSIS

Chapter 2 presents an overview of the elements of SSI and directs the reader to other chapters in this TECDOC for more in-depth and complete discussion.

The elements of SSI analysis are:

• Free-field ground motion – seismic inputSite configuration and modelling of soil properties
• Site response analysis
• Modelling of foundation and structure
• Methods of SSI analysis
• Uncertainties

Table 21 summarizes the elements of SSI with reference to chapters of the TECDOC where the element is addressed.

### 2.1FREE-FIELD GROUND MOTION

The term free-field ground motion denotes the motion that would occur in soil or rock in the absence of the structure or any excavation. Describing the free-field ground motion at a site for SSI analysis purposes entails specifying the point at which the motion is applied (the control point), the amplitude and frequency characteristics of the motion (referred to as the control motion and typically defined in terms of ground response spectra, and/or time histories), the spatial variation of the motion, and, in some cases, strong motion duration, magnitude, and other earthquake characteristics.

In terms of SSI, the variation of motion over the depth and width of the foundation is the important aspect. For surface foundations, the variation of motion on the surface of the soil is important; for embedded foundations, the variation of motion over both the embedment depth and the foundation width is important.

Free-field ground motion may be defined by site independent or site dependent ground response spectra.

• Site independent ground motion is most often used for performing a new reference design or a Certified Design (CD), which is to be placed on a number of sites with differing characteristics.
• Site specific ground motion is most often developed from a seismic hazard analysis (SHA) and is most often used for site specific design or assessments.

There are two stages in the development of the site-specific free-field ground motion and seismic input to the SSI analyses:

• Source to neighbourhood of the site. There are four basic approaches that are used to develop ground motion models that generate ground motions in the neighbourhood of the site: empirical ground motion prediction equations (GMPEs), point source stochastic simulations, finite-fault simulations (FFS), and the hybrid empirical method (HEM). These methods are generally implemented probabilistically and some are probabilistic by definition, e.g., point source stochastic simulations. This stage is referred to as seismic hazard analysis (SHA). These methods are discussed later in the TECDOC.

In the neighbourhood, means in the site vicinity, but not yet having site specific characteristics introduced into the ground motion definition, e.g., local geological or geotechnical properties, strain-dependency of soil properties, etc.

In the current state-of-practice, the location of the free-field ground motion in the neighbourhood, i.e., the SHA results, are most often derived at to the top of grade (TOG) at the site of interest or at a location within the site profile, such as on hard rock, a competent soil layer, or at an interface of soil/rock stiffness with a significant impedance contrast. U.S. NRC SRP Section 3.7.1 defines a competent soil layer as soil with shear wave velocity (Vs) of 305 m/s or greater. The EUROCODE defines a significant impedance contrast as a ratio of six for the shear modulus.

In the context of the “neighbourhood” this location is denoted the “control point”.

In this latter case, a site response analysis is performed to generate the ground motion for input to the SSI analysis.

• Local site effects. Given the free-field ground motion in the neighbourhood of the site, the next stage in defining the seismic input to the SSI analyses is to incorporate local site effects.

This may be achieved through site response analysis. In the broadest sense, the purpose of site response analysis is to determine the free-field ground motion at one or more locations given the motion at another location. Site response analysis is intended to take into account the wave propagation mechanism of the ground motion (usual assumption is vertically propagating P- and S-waves; however, other wave propagation mechanisms may need to be considered) and the strain dependent material properties of the media. Either convolution or deconvolution procedures may be necessary to do so.

-If the end product of the first stage of this definition process is ground motions at top of grade (TOG), then deconvolution may be required to generate seismic input for SSI analyses of structures with embedded foundations. Deconvolution may also be required to generate seismic input on boundaries of a finite element SSI model, e.g., nonlinear SSI model.

-If the end product of the first stage of this definition process is ground motions on a hypothetical or actual outcrop at depth or an in-soil location, convolution analysis will be performed.

The output from these “site effects” (or site response) analyses are the seismic input and soil material properties for the SSI analyses.

The details of the free-field ground motion and seismic input elements of the SSI analysis, along with the soil property definitions, are contained in:

• Chapter 3 – Site Configuration and Soil Properties
• Chapter 4 – Seismic Hazard Analysis
• Chapter 5 – Seismic Wave Fields and Free-Field Ground Motions
• Chapter 6 – Site Response Analysis and Seismic Input

NOTE to Team: This should be included here, moved to another section, or deleted???

Important considerations of defining the free-field ground motion that are discussed later in this TECDOC are:

a)Free field ground motions due to wave types propagated from source to site without distinct site specific features (such as, slanted layers, topographic effects, etc.) influencing the propagation, i.e., uniform site; for discussion purposes, vertically propagating shear and compressional waves;

b)Free-field ground motion due to natural geological and geotechnical characteristics that differ from “a” – slanted layers of soil and rock, hard rock intrusions (dykes), basins, etc.; topographic effects (hills,valleys etc.);

c)Free-field ground motion taking into account man-made features at the site, e.g., excavated soil and rock for construction purposes; construction of berms to support structures; etc.

d)Relationship between vertical and horizontal ground motion;

e)Effect of high water table on horizontal and vertical ground motion;

f)Incoherence of ground motion, especially for high frequencies;

g)Others to be identified.

### 2.2MODELING SITE CHARACTERISTICS AND SOIL MATERIAL BEHAVIOUR

#### 2.2.1In-situ soil profiles and configurations

NOTE to Team: This should be included here, moved to Chapter 3 or deleted???

Field investigations of a site are essential to defining its characteristics. As stated in IAEA SSG-9 [2-2], geological, geophysical, and geotechnical investigations should be performed on four spatial scales. The four spatial areas are regional (encompassing all important features outside the near regional area); near regional (an area composed of not less than a radius about the site of 25 km), site close vicinity (radius of less than 5 km), and site area. The first three scales of investigation lead primarily to progressively more detailed geological and geophysical data and information. The detail of these data is determined by the different spatial scales. The site area investigations are aimed at developing the geotechnical database. The data from these investigations and other sources are to be contained in a geological, geophysical, and geotechnical (GGG) database. To achieve consistency in the presentation of information, whenever possible the data should be compiled in a geographical information system (GIS) with adequate metadata information. The GGG database is complemented by a seismological database.

These investigations are feasible for new sites. However, the site area investigations may be difficult, but highly recommended, for existing sites with operating nuclear facilities.

[J1]

#### Soil material behaviour – construction features

The selection of material models for construction features of soil and rock is dependent on issues identified in Sub-section 2.2.2, but with the ability to better understand the placement and material characteristics of these man-made features.

Examples are:

• Excavation and engineered fill beneath basemats and backfill around structures.
• Construction of berms, break-waters, channel walls, etc.

### [J2]2.3MODELING SOIL, STRUCTURES, FOUNDATIONS

#### 2.3.1Modelling of soil for DBE and BDBE

NOTE to Team: This should be moved to Chapter 3, 6, or 7, or deleted???

The selection of material models for in-situ soil and rock is dependent on numerous issues:

• Soil characteristics – hard rock to soft soil.
• Strain level.
• Availability of soil material models for SSI analysis in candidate software to be used (linear, equivalent linear, nonlinear, elastic-plastic).
• Laboratory tests to define material property parameters (linear and nonlinear); correlation with field investigation results for excitation levels of interest.
• Phenomena to be modelled, e.g., dynamic response vs. soil failure.
• Risk importance of SSCs to be analyzed.

#### 2.3.2Modelling structures and SSI models

In general, one can categorize seismic structure analysis, and, consequently, the foundation and structure models, into multistep methods and single step methods. (see Figure 2-xx – to be created)

• In the multi-step method, the seismic response analysis is performed in successive steps. In the first step, the overall seismic response (deformations, displacements, accelerations, and forces) of the soil-foundation-structure is determined.

-The structure model of the first step of the multistep analysis represents the overall dynamic behaviour of the structural system but need not be refined to predict stresses in structural elements.

-The response obtained in this first step is then used as input to other models for subsequent analyses of various portions of the structure. In these subsequent analyses, detailed force distributions and other response quantities of interest are calculated.

-Many simple and sophisticated sub-structuring methods assume the foundation behaves rigidly, which is a reasonable assumption taking into account the stiffening effects of structural elements supported from the foundation (base mat, shear walls and other stiff structural elements).

-The second step analyses are performed to obtain: (i) seismic loads and stresses for the design and evaluation of portions of a structure; and (ii) seismic motions, such as time histories of acceleration and in-structure response spectra (ISRS), at various locations of the structural system, which can be used as input to seismic analyses of equipment and subsystems.

-The first step model is sufficiently detailed so that the responses calculated for input to subsequent steps or for evaluation of the first model would not change significantly if it was further refined.

-A detailed “second-step” model that represents the structural configuration in adequate detail to develop the seismic responses necessary for the seismic design of the structure or fragility evaluations is needed. Seismic responses include detailed stress distributions; detailed kinematic response, such as acceleration, velocity, and displacement time histories, and generated ISRS.

• In the single step analysis, seismic responses in a structural system are determined in a single analysis. The single step analysis is conducted with a detailed “second-step” model as introduced above.

Initially, the single step analysis was most often employed for structures supported on hard rock, with a justified fixed-base foundation condition for analysis purposes. Recently, with the development of additional computing power, single step analyses areperformed more frequently.

#### 2.3.3Modelling decisions to be made

All modelling decisions are dependent on the purpose of the analysis, i.e., for DBE design or for assessments (BDBE, DEC, or actual earthquake occurs and affects the nuclear installation.

Decisions concerning structure modelling should consider the following items:

• Multi-step vs. single step analysis – seismic response output quantities to be calculated
• Stress level expected in the structure

‒Linear or nonlinear structure behaviour.

• Lumped mass vs. finite element models. Is a lumped mass model representative of the dynamic behaviour of the structure for the purpose of the SSI analysis?
• Frequency range of interest – especially high frequency considerations (50 Hz, 100 Hz).

Decisions concerning foundation modelling should consider the following items:

• Multistep vs. single step analysis (overall behaviour or in-structure detailed seismic response – strain level);
• Piles and caissons.

‒Boundary conditions – basemat slab retains contact with soil/separates from underlying soil.

‒Pile groups – how to model.

• Behaving rigidly or flexibly.
• Surface-or near surface-founded.
• Embedded foundation with partially embedded structure.
• Partially embedded (less than all sides).
• Contact/interface zone for embedded walls and base mat (soil pressure, separation/gapping and sliding)

Decisions concerning SSI modelling should consider the following items:

• Direct or sub-structuring methods
• Purpose of the analysis – DBE design, BDBE assessment
• Strain level – equivalent linear or nonlinear soil and structure behaviour.
• Irregular soil/rock profiles.
• Probabilistic/deterministic.
• Embedment conditions (partial or full ).
• High water table.
• Structure-to-structure interaction.
• Other issues.

Chapter 7 Methods and Models for SSI Analysis and Chapter 8 Seismic Response Aspects for Design and Assessment address these and other issues.

### 2.4UNCERTAINTIES

#### 2.4.1Aleatory and epistemic uncertainties

Uncertainties exist in the definition of all elements of soil-structure interaction phenomena and their analyses:

In many cases, uncertainties can be explicitly represented by probability distributions of SSI analysis parameters, e.g., soil material properties, structure dynamic properties. In other cases, uncertainties in SSI analysis elements may need to be assessed by sensitivity studies and the results entered in the analysis by combining the weighted results.

In general, uncertainties are categorized into aleatory uncertainty and epistemic uncertainty (ASME/ANS [2-5]) with the following definitions:

“aleatory uncertainty: the uncertainty inherent in a nondeterministic (stochastic, random) phenomenon. Aleatory uncertainty is reflected by modelling the phenomenon in terms of a probabilistic model. In principle, aleatory uncertainty cannot be reduced by the accumulation of more data or additional information. (Aleatory uncertainty is sometimes called “randomness.”)”

“epistemic uncertainty: the uncertainty attributable to incomplete knowledge about a phenomenon that affects our ability to model it. Epistemic uncertainty is reflected in ranges of values for parameters, a range of viable models, the level of model detail, multiple expert interpretations, and statistical confidence. In principle, epistemic uncertainty can be reduced by the accumulation of additional information. (Epistemic uncertainty is sometimes also called “ parametricuncertainty”).

Randomness is considered to be associated with variabilities that cannot practically be reduced by further study, such as the source-to-site wave travel path, earthquake time histories occurring at the site in each direction.

Uncertainty is generally considered to be variability associated with a lack of knowledge that could be reduced with additional information, data, or models.

Aleatory and epistemic uncertainties are often represented by probability distributions assigned to SSI parameters. Further, these probability distributions are typically assumed to be non-negative distributions (for example lognormal, Weibull, etc.).

An input parameter to the SSI analysis may be represented by a median value (Am) and a double lognormal function (εR and εU) with median values of 1.0 and variability (aleatory and epistemic uncertainty) defined by lognormal standard deviations (βRand βU).

A = Amεrεu(2.1)

In some cases, it is advantageous to combine the randomness and modelling/data/parameteruncertainty into a “composite variability” as defined in ASME/ANS, 2013):

“composite variability: the composite variability includes the aleatory (randomness) uncertainty (βR) and the epistemic (modelling/data/parameter) uncertainty (βU). The logarithmic standard deviation of composite variability, βC, is expressed as:
(βR2 + βU2)1/2”

The same functional representation of Eqn. 2.1 typically defines the fragility function for SSCs in a SPRA.

Table 22 summarizes the concept of separation of epistemic and aleatory uncertainties.

#### 2.4.2Avoiding double counting of uncertainties

There can be a tendency to unintentionally account for the same or similar uncertainties in multiple aspects of the SSI analysis process. One reason for this is the multi-disciplinary nature of the process and the separation of responsibilities between disciplines and organizations: seismic hazard analysts develop the PSHA or DSHA models and results, geotechnical or civil engineers perform site response analyses, civil/structural engineers perform the SSI analyses developing the seismic demand for SSCs, mechanical/electrical/I&C and other engineering disciplines develop seismic designs and perform assessments for systems, components, equipment and distribution systems. This separation of tasks requires careful understanding of the uncertainties introduced and modelled in the “prior” steps to avoid double counting of such. This is especially true for the seismic hazard element’s affect on all other aspects in the seismic analysis and design chain.

More to be written on this topic.

#### 2.4.3Treating uncertainties in the SSI analyses: explicit inclusion and sensitivity studies

NOTE to Team: This should be moved to Chapter 3, 6, 7, 8 or remain here?

All aspects of the SSI analysis process are subject to uncertainties. The issue is how to appropriately address the issue in the context of design and assessments.

Some issues are amenable to modelling probabilistically:

• Earthquake ground motion

‒Control motion (amplitude and phase);

‒Spatial variation of motion

• – wave fields generating coherent ground motion;
• Random variation of motion – high frequency incoherent ground motion;
• Physical material properties (soil, structure dynamic characteristics).
• Physical soil configurations, e.g., thickness of soil layers).
• Water table level, including potential buoyancy effects.Others.

Some issues are amenable to sensitivity studies to determine their importance to SSI response:

• Linear vs nonlinear soil and structure material properties
• Sliding/uplift.
• Non-horizontal layering of soil.
• Use of 1D, 2D, or 3D modelling of wave propagation

### 2.5REFERENCES

[2-1]Johnson, J.J., “Soil-Structure Interaction,” Chapter 10, Earthquake Engineering Handbook, CRC Press, 2002.