**9. Non-mandatory assumptions**

172 Earthquake Engineering

SASSI model.

on used in SSI analysis.

harmonic wave in the same sample.

Both SHAKE results – profiles of wave velocities/damping and surface motion – are further

Theoretically a wide range of nonlinearities can be described by strain-dependent properties. However, these properties should be transient, i.e. they should vary from one time point to another during one seismic event. In the Seed's approach these properties in each soil layer are established once for the whole event duration (changing not from time to time, but from one linear run to another one). So, in fact soil properties depend not on the instant transient strains, but on some "effective" strains (in practice - on some portion of the maximal strain over the duration). In fact, Seed provided a tool to extrapolate the results of the lab test with harmonic excitation of the soil sample to another situation with non-

Nowadays seismologists are ready to provide more sophisticated approaches to the soil description. They can model accelerations in the soil more accurately with truly transient soil properties. But in the SSI problems (e.g., in SASSI or CLASSI) one will need linear soil

The result of SHAKE is obtained for horizontally-layered soil without structure. So, they say, that it contains "primary" non-linearity. The same equivalent strain-dependent properties can be further applied in the SSI problems to account for the "secondary" nonlinearity caused by structure, but the result will spoil horizontally-layered geometry of the soil. As we know, that will spoil CLASSI model and create additional problems in

That is why modern standards (e.g., ASCE4-98) require the consideration of the primary non-linearity, but do not require consideration of the secondary non-linearity of the soil.

Looking at soil-structure system, one can find nonlinearities not only in soil, but at the contact surface. Even if both soil and structure are modeled by linear systems, they may have various contact terms. Most often full contact is assumed – it does not spoil linearity. However, soil tension (unlike soil compression) is very limited, and that may cause a) uplift of the base mat from the soil, b) separation of the embedded basement walls from the soil.

Base mat uplift may be estimated if linear "full contact" vertical forces over contact surface Q are compared to the static vertical forces caused by structural weight. In practice the full uplift is seldom met, but rocking of the structure can cause dynamic tension near the edges of the base mat. This "partial" dynamic uplift usually occurs for stiff soils and sizable structures. Does it change the response motion considerably? Today they believe that if the area of partial dynamic uplift is less than 1/3 of the total contact area, one can neglect this

Separation of vertical embedded walls is treated as follows. In the upper half of the embedment depth (but only up to 6 meters from the surface) they break soil-structure

uplift and still use SSI linear model with full contact.

contact completely. Below this level they assume full contact.

with "effective" soil properties, so SHAKE still remains the best "pre-SSI" processor.

So, basic assumptions currently used in the SSI analysis are a) linearity of the soil, of the structure and of the soil-structure contact; b) horizontal layering of the soil (except some limited volume near the structure).

There are two other assumptions - not mandatory, but usually used in the SSI analysis. The first assumption is the rigidity of the soil-structure contact surface. Usually base mats are not extremely rigid, but they are considerably enforced by rather dense and thick shear walls, so in fact their behavior is almost rigid. Standards ASCE4-98 allow the treatment of base mats of the NPP structures as rigid ones. However, SASSI can treat flexible base mats as well. Different parameters of structural seismic response show different sensitivity to the flexibility of the base mat. Some examples are presented in the author's reports in SMiRT-21 [25,26].

The second assumption is about seismic wave field in the soil without structure. Usually, one starts from the three-component acceleration recorded on the surface of the soil (in some "control point", as they say). As we saw, in SSI problem one needs to know the motion of a certain soil volume (at least the soil motion in the nodes of the future contact surface). So some additional assumptions are introduced. The most common assumption "is vertically propagating body seismic waves in horizontally-layered medium". This assumption means, that three components of the acceleration in the control point are produced by three separate vertically propagating waves: vertical acceleration is a result of the P-wave, two horizontal accelerations are the result of two S-waves in main coordinate vertical planes. Each wave can be analyzed separately by SHAKE, providing seismic motion of any point in depth. Another consequence of this assumption is that seismic motion depends on vertical coordinate, but not on the horizontal coordinates: every horizontal plane in the free field moves "rigidly".

Again, this assumption is not mandatory. In SASSI one can set up other assumptions linking the whole wave field to the control point motion. However, as SHAKE (usually used as a preprocessor for SASSI) implements that very assumption, most often this assumption is accepted for the whole SSI problem.

### **10. Some examples of the SSI effects in practice**

Concluding the chapter, the author should like to give some practical examples. One of recently built NPPs was analyzed for different soil and excitation models. Let us look at the acceleration response spectra on the elevation +21.5 m.

The first comparison is for rigid soil and flexible soil (without embedment). As we remember, rigid soil means the absence of the SSI effects. Flexible soil in this case was of medium type. Structure was one of the NPP buildings. One and the same three-component seismic excitation (corresponding to the standard spectra described in RG1.60) was applied to the surface of the rigid and flexible soil. In the first case this very motion became the response motion of the base mat; in the second case, the response motion of the base mat was modified by the SSI effects. The comparison of the floor response spectra (enveloped over 8 corner nodes of the floor slab, smoothed and broadened 15% each side in the frequency range) at the structural level +21.5 m is shown in Fig. 14.

Soil-Structure Interaction 175

DA2 emb DA2 surf

**Enveloped and broadened spectra with 2% damping along Oz, g**

0 5 10 15 20 25 30  **Frequency, Hz**

**Figure 15.** Comparison of enveloped broadened spectra with 2% damping at the level +21.5 m for sitespecific excitation for surface and embedded structures; spectral accelerations are shown along

0 0,5 1 1,5 2 2,5 3 3,5

On the other hand, for higher frequencies there may appear spectral accelerations for the embedded structure greater than those for the surface structure (see Fig.14a). Still the overall effect of the small embedment is considered conservative; that is why standards ASCE4-98 [1] allow neglecting the embedment, if the embedment depth is less than 30% of the equivalent radius of the basement. Interesting to note that in the sample shown in Fig.15, this limit is almost met (10.4 m of embedment versus 34.7 m of equivalent radius).

Concluding the chapter about soil-structure interaction (SSI), the author should like to give

1. At the very beginning one should estimate the importance of SSI and decide whether it should be considered at all. The answer depends on the soil data (wave velocities in the soil, first of all), base mat size/embedment and inertia of the structure. For civil structures most often SSI can be omitted (i.e. structure can be analyzed using a platform model with platform kinematical excitation given by seismologists and without soil

2. If SSI is to be considered, one should examine whether some simple assumptions can be applied. Main assumptions: homogeneous half-space or a layer underlain by rigid rock as a soil model (depends on real-world geotechnical data), surface base mat, rigid base mat. General recommendation is as follows. One should start with the simplest model allowed by standards. Only if the results seem overconservative, one should try to go to more sophisticated models, accounting to various specific SSI effects. Usually there is a

trade between the complexity of the model and the conservatism of the results.

Nevertheless, the difference in the spectral shape in Fig.15 is dramatic.

DA2 emb DA2 surf

horizontal axis Ox (a) and vertical axis Oz (b)

0 5 10 15 20 25 30 **Frequency, Hz**

**Enveloped and broadened spectra with 2% damping along Ox, g**

several recommendations to engineers.

**11. Conclusions** 

0 0,5 1 1,5 2 2,5 3 3,5

springs).

We see the considerable difference in the spectral shape: SSI effects form the main spectral peak, but for high frequency range (here - after 5 Hz) spectral accelerations with SSI are less than without SSI. As to the maximal accelerations (we see them in the right part of the spectral curves), SSI effects may decrease them (see Fig.14b) or not. It sometimes depends on the height of the floor considered.

**Figure 14.** Comparison of enveloped broadened spectra with 2% damping at the level +21.5 m for excitation RG1.60 for rigid and flexible soil; spectral accelerations are shown along horizontal axis Ox (a) and vertical axis Oz (b)

The second comparison is for surface and embedded base mats. Site-specific threecomponent seismic excitation is "applied" at the free surface of two flexible soil foundations: first, real soil foundation; second, the same soil foundation without upper 10.4 meters of soil (corresponding to the embedment depth of the structure). The comparison of the response spectra is shown in Fig.15 in the same format as in Fig.14.

We see that the embedment considerably impacts the first spectral peaks, decreasing spectral accelerations. The physical reason is that the mass of the "outcropped soil" for the embedded basement in fact is subtracted from the mass of the basement when inertial loads are developed for the platform model of "inertial interaction" in the moving coordinate system placed on the platform.

**Figure 15.** Comparison of enveloped broadened spectra with 2% damping at the level +21.5 m for sitespecific excitation for surface and embedded structures; spectral accelerations are shown along horizontal axis Ox (a) and vertical axis Oz (b)

On the other hand, for higher frequencies there may appear spectral accelerations for the embedded structure greater than those for the surface structure (see Fig.14a). Still the overall effect of the small embedment is considered conservative; that is why standards ASCE4-98 [1] allow neglecting the embedment, if the embedment depth is less than 30% of the equivalent radius of the basement. Interesting to note that in the sample shown in Fig.15, this limit is almost met (10.4 m of embedment versus 34.7 m of equivalent radius). Nevertheless, the difference in the spectral shape in Fig.15 is dramatic.
