**3. Brief history**

146 Earthquake Engineering

they are able to change the soil motion.

not show the signs of considerable SSI effects.

the development of these two fields of industry.

excitation taken from the free field).

neglecting SSI, when allowed.

that only part of them satisfies the conventional definition of SSI.

only when these interaction forces are able to change the basement motion as compared to the free-field ground motion (i.e. motion recorded on the free surface of the soil without structure). So, historically the conventional definition of SSI is different from simple occurrence of the interaction forces: these forces occur for every structure, but not always

This simple fact leads to the important consequences. If a structure can be analyzed as based on rigid foundation with free-field motion at it, then they use to say that "no SSI effects occur" (though structure is in fact moved by the interaction forces, and the same forces impact the foundation). Looking at the variety of the real-world situations, we can conclude

The ability of the interaction forces to change the soil motion depends, of course, on two factors: value of the force and flexibility of the soil foundation. The value of the interaction force may be often estimated via the base mat acceleration and inertia of the structure. For given soil site and given free-field seismic excitation the heavier is the structure, the more likely SSI effects occur. Usually most of civil structures resting on hard or medium soils do

From the inertial point of view, the heaviest structures we deal with are hydro-structures (like dams) and nuclear power plant (NPP) main structures – first of all, reactor buildings. So, the development of the SSI field in the earthquake engineering was historically linked to

From the soil flexibility point of view, for the given structure and given free-field seismic excitation the softer is the soil, the more likely SSI effects occur. Soil shear module is a product of mass density and square of the shear wave velocity. Mass density of soil in practice varies around 2,0 t/m3 in a comparatively narrow range, so the main characteristic of the soil stiffness is shear wave velocity Vs. Usually soil is considered "soft" when Vs is less than 300 m/s, and "hard" when Vs is greater than 800 m/s. If Vs is greater than 1100 m/s, they usually talk about "rigid" soil (no SSI effects – just rigid platform with a structure on it and

All these ranges are of course purely empirical. Obviously, one and the same soil can behave as rigid one towards very light and small structure (like a tent), and behave as a soft one

Sometimes to decide whether to account for SSI effects they compare the natural frequencies of the rigid structure on the flexible soil foundation with those of the flexible structure on a rigid foundation. If the lowest natural frequency of the first set is greater than the first dominant frequency of the second set two and more times, they do not consider SSI effects (e.g., see standards ASCE4-98 [1]). As SSI field is rather sophisticated, sometimes it is worth

However, one should keep in mind another situation, when SSI effects occur. In soft soils seismic wave may have moderate wavelength comparable to the size of structure, so that

towards heavy and rigid structure (like the NPP reactor building).

As SSI field combines structures' and soil modeling, the level of such modeling is generally lower than in the classical soil mechanics and in the structural mechanics standing alone.

For several decades (up to 1960-s) only soil flexibility was considered without soil inertia – springs modeled soil. At that time mostly the machinery basements were analyzed for the dynamic interaction with soil foundation (the largest of them probably being turbines). In fact, it was a quasi-static approach – the well-known static solution for rigid stamps, beams and plates on elastic foundation was applied at every time step. The model was so simple, that nobody even used the special term "SSI" at that time. The key question of such a simple approach appeared to be damping. The material damping measured in the laboratories with soil samples proved to be considerably less than the damping measured in the dynamic field tests with rigid stamps resting on the soil surface.

Soil-Structure Interaction 149

Some other scientists have greatly contributed to this field approximately at the same time

After the Three Miles Island and Chernobyl accidents there was a long pause in the nuclear energy development in the West (e.g., in 2012 US NRC issued a first permission for a new NPP block in last 33 years) and in Russia (due to the economic problems of 1990s), though in Asia they continued to build new blocks. SSI investigations went forward in South Korea, China, India. Nowadays, in spite of the Fukushima accident, nuclear industry goes forward. In parallel SSI was studied by hydro-engineers (for the dams design, first of all). However, this field separated from the "NPP field of SSI" about 40 years ago. The reason was that the SSI models usually applied in nuclear industry (horizontally layered soil, rigid or very stiff base mats) are often not applicable to the hydro-dams situations (rocky canyons, etc.). That is why both models and methods used in the SSI field usually are different in nuclear and

In last decades, civil structures are gradually increasing in size and embedment. Effects like SSI and SSSI from time to time are considered during the design procedures of such structures. Naturally, they are closer to the NPP practice than to the hydro-energy practice. The author has about 30 years of experience in nuclear industry, dealing with SSI problems.

Today there exist three approaches to SSI problems, namely "direct", "impedance", and "combined" ones. To understand them all, let us start from common general approach based

Let us call the problem with seismic wave, soil and structure "problem A" and start with completely linear soil-structure model. Let Q be some surface surrounding the basement in the soil and dividing the soil-structure model into two parts: the "external" part Vext and internal part Vint. Let *(-F)* be additional external loads distributed over Vint and specially tuned so, to provide zero displacements in Vint. Then "problem A" can be split in the sum of two wave pictures: "problem A1", including seismic excitation and loads *(-F),* and "problem

1. As in "problem A1" all displacements in the internal volume Vint are zero, the motion of Vint in "problem A2" is the same as in "problem A". Hence, if we are interested in the

2. As in "problem A1" all displacements in the internal volume Vint are zero, all the strains and internal forces in the internal volume Vint are zero, and the external loads *(-F)* must

3. As in "problem A1" all displacements, strains and internal forces in the internal volume Vint are zero, no forces are impacting Q from Vint (i.e., forces impacting Q from Vext are

So, the subsequent text will be based on the "NPP" approach to the SSI problems.

(J.Wolf [10,11], J.M..Roesset, E.Kausel [12] and J.Luco [4] should be mentioned).

hydro-industries.

**4. Basic superposition** 

on the superposition of the wave fields.

A2" including only loads *(F)* without seismic wave – see Fig.1.

be zero everywhere in Vint, except surface Q.

This simple superposition leads to a number of important conclusions.

motion of Vint only, we can substitute "problem A" with "problem A2".

The nature of this effect was discovered in 1930-40s (Reissner in Germany [3], Schechter in the USSR) and proved to be in inertial properties of the soil. Inertia plus flexibility always mean wave propagation. It turned out that in the field tests actual energy dissipation in the soil was composed of two parts: conventional "material" damping (the same as in laboratory tests) and so-called "wave damping". In the latter case the moving stamp caused certain waves in the soil, and those waves took away energy from the stamp, contributing to the overall "damping" in the soil-structure system. This energy was not transferred from mechanical form into heat (like in material damping case), but was taken to the infinity in the original mechanical form. In reality waves did not go to the infinity, gradually dissipating due to the material damping in the soil, but huge volumes of the soil were involved in this wave propagation. Even without any material damping in the soil this "wave damping" contributed a lot to the response of the stamp. In practice it turned out that the level of wave damping was usually greater than the level of material damping.

In parallel it turned out that when the base mat size is comparable to the wave length in the soil, not only damping, but stiffness also depends on the excitation frequency. This effect is invisible for comparatively small machine basements, but important for large and stiff structures.

To study these wave effects new soil-structure models with infinite inertial soil foundations should be considered. That was the moment (1960-s) when the very term "SSI" appeared [2,4,5]. It happened so, that NPPs were actively designed at that time, including seismic regions (e.g., California), and intensive research was funded in the US to study the SSI effects controlling the NPP seismic response. Earthquake Engineering Research Center (EERC) in the University of Berkley, California became a leader with such outstanding scientists as H.B.Seed and J.Lysmer on board [6].

The main result of these investigations was the development of new powerful tools to analyze more or less realistic models. The earlier SSI models considered homogeneous halfspace with surface rigid stamp. They could be treated analytically or semi-analytically for simple stamp shapes (e.g., circle).

In practice soil is usually layered. Layering can lead to the appearance of the new wave types and change the whole wave picture. Important achievements of 1960-70s enabled to move from the homogeneous half-space to the horizontally–layered medium in soil modeling [7,8]. However, the infinite part of the foundation, excluding some limited soil volume around the basement, still remains a) linear, b) isotropic, c) horizontally layered. These limitations are due to the methods of the SSI analysis. The final masterpiece of Prof. Lysmer was SASSI code [9], further developed by F.Ostadan, M.Tabatabaie, D.Giocel et al. This code combined finite element modeling of the structure and limited volume of the soil with semi-analytical modeling of the infinite foundation (see below). Limitations on the embedment depth and on the shape of the underground part have gone.

Some other scientists have greatly contributed to this field approximately at the same time (J.Wolf [10,11], J.M..Roesset, E.Kausel [12] and J.Luco [4] should be mentioned).

After the Three Miles Island and Chernobyl accidents there was a long pause in the nuclear energy development in the West (e.g., in 2012 US NRC issued a first permission for a new NPP block in last 33 years) and in Russia (due to the economic problems of 1990s), though in Asia they continued to build new blocks. SSI investigations went forward in South Korea, China, India. Nowadays, in spite of the Fukushima accident, nuclear industry goes forward.

In parallel SSI was studied by hydro-engineers (for the dams design, first of all). However, this field separated from the "NPP field of SSI" about 40 years ago. The reason was that the SSI models usually applied in nuclear industry (horizontally layered soil, rigid or very stiff base mats) are often not applicable to the hydro-dams situations (rocky canyons, etc.). That is why both models and methods used in the SSI field usually are different in nuclear and hydro-industries.

In last decades, civil structures are gradually increasing in size and embedment. Effects like SSI and SSSI from time to time are considered during the design procedures of such structures. Naturally, they are closer to the NPP practice than to the hydro-energy practice.

The author has about 30 years of experience in nuclear industry, dealing with SSI problems. So, the subsequent text will be based on the "NPP" approach to the SSI problems.
