**3.1. Instrumental method of seismic microzonation**

40 Earthquake Engineering

On basis of the given maps it is necessary to make up the maps of seismic microzonation (SMZ) of cities and large settlements of each certain subject of the Russian Federation with the usage of the most modern standard methods and tools, but in scale 1:10 000. The probabilistic maps of SMZ were first developed in the Center of Geophysical Investigations of Vladikavkaz Scientific Center RAS and RNO-A. Such maps of SMZ are direct and reliable

Besides, it is necessary to note that at usage of the traditional units of macroseismic intensity the boundaries between different zones are characterized by sharp changes, which obviously do not correspond to the real situation of monotonous change of intensity for homogenous soil conditions of the investigated territory. No doubt, it will form evident inaccuracies at the assessment of the level of seismic hazard of this or that territory. The practical usage of artificial intensity subdivision, for example, in the form of 7.2 or 8.3 points is not validated enough from the theoretical point of view. So, firstly, it is not usually explained how these fractional assessments are obtained and, secondly, the following transition to the acceleration units (obviously, according to foreign data, as there are no acceleration records for forming reliable correlation in Russia), undoubtedly, forms considerable inaccuracy and it is hardly ever physically proved because of the formality of

On the other hand, at seismic influence assessment at earthquake - proof design engineers use the acceleration values, (strictly speaking, conveniently) corresponding to specified intensities. Thus, it's assumed that design acceleration a = 0.1 g corresponds to the intensity 7 earthquake, 0.2g – to the intensity 8, 0.4g – to the intensity 9 etc. At the same time, network of digital stations dislocated on the Southern Caucasus installed in source zones of Spitak (Armenia, 1988), Racha (Georgia, 1991), Barisakho (Georgia, 1992), Baku (Azerbaijan, 2000), Gouban (Georgia, 1991), Tbilisi (Georgia, 2002) and other earthquakes collected seismic records for formation of database of accelerations for Caucasus. Namely it makes possible to design maps of the seismic hazard independently in units of PGA. Such maps for the territory of North Ossetia for exposition of 50 years with exceedance probability 1%, 2%, 5%, 10% in scale 1:200 000 were created (Fig. 6). It is obvious that at changing of smoothering step it is possible to obtain smooth variations of accelerations directly used as design impacts.

In contrast to the maps of general seismic zoning (GSZ) with a scale of M 1: 8000000 and, at the best, with the scale M 1:2500000 obtained maps of both types on a scale 1:200000 can be

Thus, these materials allow assessing seismic hazard on a detailed level, according to the known formulas to calculate the macroseismic field of seismic effects on a scale that may

Seismic microzonation (SMZ) actually is final stage of seismic hazard assessment. SMZ results are direct foundation for earthquake-proof construction. In the process of seismic

base of earthquake-proof design and object construction.

the parameter of «intensity» itself.

referred to the DSZ type maps.

provide a reliable basis for SMZ.

**3. Seismic microzonation of territory** 

Instrumental method is the main SMZ method. Exactly it urges to solve a problem of forming earthquake intensity forecast. At the same time the calculation method, which allows to model any definite conditions of area and influence features, is often characterized by more reliability. It has great importance to soil thickness with high power. Combined usage of both methods significantly increases results validity.

#### *3.1.1. Seismic microzonation on basis of strong earthquakes instrumental records*

It is supposed at usage of strong earthquakes records for SMZ purposes, that at some strong seismic influence the observing soil behavior is adequate to the display of their potential seismic hazard at future strong earthquakes (Nikolaev, 1965). This fact was the reason of stimulation of a number of large international scientific-research projects on organization of long-term instrumental observations with the help of powerful measurement systems in the Earth's different regions with high seismic activity for the purpose of obtaining the strong movements of soils, which are the base of buildings and constructions (the groups SMART-1 and SMART-2 on the Taiwan island etc.).

At the same time, presence of unit record of a real strong seismic influence at its inestimable value for SMZ often can't give the adequate forecast of soil behavior at a next following strong earthquake. This problem can be solved by creation of a number of records of seismic influences, generated by hazardous for the zoned territory active fractures, i.e. by zones of possible earthquake source (PES).

#### *3.1.2. Seismic microzanation with the help of weak earthquakes records*

In the connection of the fact that strong earthquakes occur seldom, the intensity increments, as a rule, are assessed by records of weak earthquakes, when a linear dependence between the dynamic stress and the deformation takes place.

Soil conditions considerably change (fig. 8) the right shape of the original undistorted signal, incident from the crystal foundation. Complex shapes of isoseisms pointed out to the undoubtful link between the earthquake display intensity and soil conditions (Reiter, 1991).

Increase of the soil thickness depth (alluvium) considerably changes the character of earthquake records (Reiter, 1991) in the process of approaching the city (fig. 8).

Calculation of intensity increment with the help of weak earthquakes is realized by the formula (Medvedev, 1962; Recommendations on SMZ, 1974, 1985):

$$
\Delta \mathbf{I} = \mathbf{3} \,\text{J} \mathbf{l} \mathbf{g} \mathbf{A}\_i \,/\ A\_{0\prime} \tag{5}
$$

Assessment of Seismic Hazard of Territory 43

<sup>0</sup> 2lg / , *<sup>i</sup> I= A A* (7)

<sup>0</sup> 3,3lg / , *Δ <sup>i</sup> I= A A* (8)

microseism on their origin to the purely natural phenomena is not quite correct. Numerous artificial sources, influence degree of which can't be controlled, undoubtedly, take part in

Intensity increment for strong earthquakes on microseism is calculated by the formula

where *Ai* <sup>0</sup> *,A* are the maximum amplitudes of microvibrations for investigated and etalon

Impossibility of the compliance of necessary standard conditions of microseism registration and large spread in values of maximum amplitudes limit the usage of microseism for calculation of soil intensity increment. The above mentioned causes the application of

Spectral features for different sites are estimated by means of H/V-rations (Nakamura, 1989).

The intensity increment ΔI of the soils of the zoned territory is calculated by the formula (Medvedev, 1962; Recommendations on SMZ, 1974, 1985) at usage of weaker explosions:

Execution of powerful explosions on the territory of cities, settlements or near the responsible buildings is connected with large and often insurmountable obstacles (technical and ecological problems, safety problems, labouriousness and economical expediency) and practically isn't

where Ai, A0 are vibrational amplitudes of the investigated and etalon soils.

used nowadays. This leads to the wide spreading of nonexplosive vibration sources.

their forming along with the natural sources (fig. 8.6).

microseism tool only in complex with other instrumental tools.

**Figure 9.** Microseisms records (10.07.1996, Voronezh Region, Russia)

*3.1.5. Seismic microzonation using explosive impact* 

(Recommendations on SMZ, 1974, 1985):

soils.

where *Ai* <sup>0</sup> *,A* are the amplitudes of investigated and etalon soils vibrations.

The usage of tool in the form of registration of strong and weak earthquakes needs the organization of instrumental observations in a waiting mode.

**Figure 8.** Scheme of California earthquake in Koaling sity

#### *3.1.3. Seismic microzanation with the help of weak earthquakes records*

In the connection of the fact that strong earthquakes occur seldom, the intensity increments, as a rule, are assessed by records of weak earthquakes, when a linear dependence between the dynamic stress and the deformation takes place.

Calculation of intensity increment with the help of weak earthquakes is realized by the formula (Medvedev, 1962, Recommendations on SMZ, 1974, 1985):

$$
\Delta \mathbf{I} = \mathbf{3}\_{\prime} \mathbf{3} \mathbf{l} \mathbf{g} \mathbf{A}\_{i} / A\_{0 \prime} \tag{6}
$$

where *Ai* <sup>0</sup> *,A* are the amplitudes of investigated and etalon soils vibrations.

The usage of tool in the form of registration of strong and weak earthquakes needs the organization of instrumental observations in a waiting mode.

#### *3.1.4. Seismic microzonation using microseisms*

The results of microseisms observations (Kanai, 1952) are used as subsidiary instrumental tool of SMZ. Predominant periods are determined at that in order to assess resonance properties of soils and amplitude level of microvibrations. Strictly speaking, the reference of microseism on their origin to the purely natural phenomena is not quite correct. Numerous artificial sources, influence degree of which can't be controlled, undoubtedly, take part in their forming along with the natural sources (fig. 8.6).

Intensity increment for strong earthquakes on microseism is calculated by the formula (Recommendations on SMZ, 1974, 1985):

$$
\Delta I = 2 \lg A\_i / A\_{0i} \tag{7}
$$

where *Ai* <sup>0</sup> *,A* are the maximum amplitudes of microvibrations for investigated and etalon soils.

Impossibility of the compliance of necessary standard conditions of microseism registration and large spread in values of maximum amplitudes limit the usage of microseism for calculation of soil intensity increment. The above mentioned causes the application of microseism tool only in complex with other instrumental tools.

Spectral features for different sites are estimated by means of H/V-rations (Nakamura, 1989).


**Figure 9.** Microseisms records (10.07.1996, Voronezh Region, Russia)

#### *3.1.5. Seismic microzonation using explosive impact*

42 Earthquake Engineering

Increase of the soil thickness depth (alluvium) considerably changes the character of

Calculation of intensity increment with the help of weak earthquakes is realized by the

The usage of tool in the form of registration of strong and weak earthquakes needs the

In the connection of the fact that strong earthquakes occur seldom, the intensity increments, as a rule, are assessed by records of weak earthquakes, when a linear dependence between

Calculation of intensity increment with the help of weak earthquakes is realized by the

The usage of tool in the form of registration of strong and weak earthquakes needs the

The results of microseisms observations (Kanai, 1952) are used as subsidiary instrumental tool of SMZ. Predominant periods are determined at that in order to assess resonance properties of soils and amplitude level of microvibrations. Strictly speaking, the reference of

<sup>0</sup> 3,3lg / , *Δ <sup>i</sup> I= A A* (5)

<sup>0</sup> 3,3lg / , *Δ <sup>i</sup> I= A A* (6)

earthquake records (Reiter, 1991) in the process of approaching the city (fig. 8).

where *Ai* <sup>0</sup> *,A* are the amplitudes of investigated and etalon soils vibrations.

formula (Medvedev, 1962; Recommendations on SMZ, 1974, 1985):

organization of instrumental observations in a waiting mode.

**Figure 8.** Scheme of California earthquake in Koaling sity

the dynamic stress and the deformation takes place.

*3.1.3. Seismic microzanation with the help of weak earthquakes records* 

formula (Medvedev, 1962, Recommendations on SMZ, 1974, 1985):

organization of instrumental observations in a waiting mode.

*3.1.4. Seismic microzonation using microseisms* 

where *Ai* <sup>0</sup> *,A* are the amplitudes of investigated and etalon soils vibrations.

The intensity increment ΔI of the soils of the zoned territory is calculated by the formula (Medvedev, 1962; Recommendations on SMZ, 1974, 1985) at usage of weaker explosions:

$$
\Delta \mathbf{I} = \mathbf{3}\_{\prime} \mathbf{3} \mathbf{l} \mathbf{g} \mathbf{A}\_{i} / A\_{0 \prime} \tag{8}
$$

where Ai, A0 are vibrational amplitudes of the investigated and etalon soils.

Execution of powerful explosions on the territory of cities, settlements or near the responsible buildings is connected with large and often insurmountable obstacles (technical and ecological problems, safety problems, labouriousness and economical expediency) and practically isn't used nowadays. This leads to the wide spreading of nonexplosive vibration sources.

#### *3.1.6. Seismic microzonation using nonexplosive impulse impact*

The features of SMZ methods development led to the situation when the tool of elastic wave excitation with the help of low-powered sources (for example, hammer impact with m = 8– 10 kilograms) has become the most wide spread in the CIS countries, in order to determine S- and P-wave propagation velocities in soils of the typical areas of territory. Velocity values are used in order to calculate the intensity increment using the tool of seismic rigidities by S.V.Medvedev (Medvedev, 1962; Recommendations on SMZ, 1974, 1985):

$$
\Delta I = 1,67 \lg \left( \rho\_0 V\_0 / \rho\_i V\_i \right),
\tag{9}
$$

Assessment of Seismic Hazard of Territory 45

where f0, fi are predominant frequencies of etalon and investigated soils.

[Zaalishvili, 1986]:

**Figure 10.** Surficial gasodinamical pulse source (SI-32)

the help of the formula (Zaalishvili, 1986):

*3.1.7. Seismic microzonation using vibration impact* 

results on the formulas (9) and (11) were practically similar (Zaalishvili, 1986).

Intensity increment was determined by the following formula (Zaalishvili, 1986):

where fwa0, fwai are weight-average vibration frequencies of etalon and investigated soils.

Weight-average vibration frequency of soils was calculated at that on the formula

where Ai and fi are the amplitude and the corresponding frequency of vibration spectrum.

At usage of a vibration source (fig. 10) the calculation of intensity increment is realized with

The developed tool was used at SMZ of the territories of cities Tbilisi, Kutaisi, Tkibuli, single areas of the Bolshoy Sochi city. The tools' feature consists in the fact that it allows to assess soil seismic hazard without any preliminary investigations: at realization of direct measurements of soil thickness response on standard (vibration or impulse) influence. Later the formula was successfully used at SMZ of the sites of Novovoronezh Nuclear power-

where Si and S0 are the squares of vibration spectra of investigated and etalon soils.

plant (NPP) with the help of an impulsive source (Zaalishvili, 2009).

A.B.Maksimovs' tool didn't find wide distribution, as frequency differences of soil vibrations with sharply different strength properties (at usage of traditional for the seismic exploration of small depths low-powered sources) were insignificant and the calculation

2 2

0 0 wa0 wa 0.8 lg / *Δ ii i I = ρ V f ρ V f* (12)

св *ii i f Af A* (13)

<sup>0</sup> 2lg / , *Δ <sup>i</sup> I= S S* (14)

where ρ0V0 and ρiVi is the product of the soil consistency and P-wave (S-wave) velocity – seismic rigidities of the etalon and the investigated soil accordingly.

The intensity increment, caused by soil watering, is calculated by the formula

$$
\Delta I = K \,\mathrm{e}^{-0.04h\_{\mathrm{GL}}^2} \tag{10}
$$

where K = 1 for clay and sandy soils; К = 0,5 for large-fragmental soils (with sandyargillaceous filler not less than 30%) and strongly weathered rocks; К = 0 for largefragmental firm soils consisting of magmatic rocks (with sandy-argillaceous filler up to 30%) and weakly weathered rocks; hGL is the groundwater level.

The simplicity and immediacy of practical application of S.V.Medvedevs' tool, which is called the tool of the "intensities", led to its widespread in CIS countries and countries of Eastern Europe, Italy, USA, India, and Chile in 1970-es. The tool of the "intensities" was advantageously different from other tools by the immediacy, simplicity in initial data obtaining and its processing and independence from seismic regime of the territory. It to a certain extent hampered the development and making up of new tools. Unfortunately, the calculation results of predicted values of intensity increment are often quite incorrect as data of macroseismic observations of destructive earthquake consequences shows (Shteinberg, 1964, 1965, 1967; Poceski, 1969; Stoykovic and Mihailov, 1973).

By means of the special investigations it was determined that the reliability of calculated intensity increments considerably increases at usage of modern powerful impulsive energy sources (fig. 9).

The lowering of final results quality is to a certain extent caused by the fact that in the tool of "intensities" the seismic effect dependence in soils on frequency or "frequency discrimination" of soils (Shteinberg, 1965) and also the origin of typical "nonlinear effects" at strong movements isn't taken into account. A.B.Maksimov tried to remedy this deficiency by developing the tool, where frequency peculiarities of soils were taken into account (Maksimov, 1969):

$$
\Delta I = 0.8 \,\mathrm{kg} \,\rho\_0 V\_0 f\_0^2 \, / \,\rho\_i V\_i f\_i^2 \tag{11}
$$

where f0, fi are predominant frequencies of etalon and investigated soils.

44 Earthquake Engineering

sources (fig. 9).

(Maksimov, 1969):

*3.1.6. Seismic microzonation using nonexplosive impulse impact* 

S.V.Medvedev (Medvedev, 1962; Recommendations on SMZ, 1974, 1985):

seismic rigidities of the etalon and the investigated soil accordingly.

and weakly weathered rocks; hGL is the groundwater level.

1964, 1965, 1967; Poceski, 1969; Stoykovic and Mihailov, 1973).

The intensity increment, caused by soil watering, is calculated by the formula

The features of SMZ methods development led to the situation when the tool of elastic wave excitation with the help of low-powered sources (for example, hammer impact with m = 8– 10 kilograms) has become the most wide spread in the CIS countries, in order to determine S- and P-wave propagation velocities in soils of the typical areas of territory. Velocity values are used in order to calculate the intensity increment using the tool of seismic rigidities by

> 0 0 1,67 lg ( / ), *i i I VV*

where ρ0V0 and ρiVi is the product of the soil consistency and P-wave (S-wave) velocity –

where K = 1 for clay and sandy soils; К = 0,5 for large-fragmental soils (with sandyargillaceous filler not less than 30%) and strongly weathered rocks; К = 0 for largefragmental firm soils consisting of magmatic rocks (with sandy-argillaceous filler up to 30%)

The simplicity and immediacy of practical application of S.V.Medvedevs' tool, which is called the tool of the "intensities", led to its widespread in CIS countries and countries of Eastern Europe, Italy, USA, India, and Chile in 1970-es. The tool of the "intensities" was advantageously different from other tools by the immediacy, simplicity in initial data obtaining and its processing and independence from seismic regime of the territory. It to a certain extent hampered the development and making up of new tools. Unfortunately, the calculation results of predicted values of intensity increment are often quite incorrect as data of macroseismic observations of destructive earthquake consequences shows (Shteinberg,

By means of the special investigations it was determined that the reliability of calculated intensity increments considerably increases at usage of modern powerful impulsive energy

The lowering of final results quality is to a certain extent caused by the fact that in the tool of "intensities" the seismic effect dependence in soils on frequency or "frequency discrimination" of soils (Shteinberg, 1965) and also the origin of typical "nonlinear effects" at strong movements isn't taken into account. A.B.Maksimov tried to remedy this deficiency by developing the tool, where frequency peculiarities of soils were taken into account

2 2

0 00 0.8 lg / *Δ i ii I = ρ V f ρ V f* (11)

 

2

(9)

GL 0,04 e *<sup>h</sup> ΔI=K* (10)

A.B.Maksimovs' tool didn't find wide distribution, as frequency differences of soil vibrations with sharply different strength properties (at usage of traditional for the seismic exploration of small depths low-powered sources) were insignificant and the calculation results on the formulas (9) and (11) were practically similar (Zaalishvili, 1986).

Intensity increment was determined by the following formula (Zaalishvili, 1986):

$$
\Delta I = 0.8 \,\mathrm{kg} \,\rho\_0 V\_0 f\_{\mathrm{wa}0}^2 / \rho\_i V\_i f\_{\mathrm{wa}i}^2 \tag{12}
$$

where fwa0, fwai are weight-average vibration frequencies of etalon and investigated soils.

Weight-average vibration frequency of soils was calculated at that on the formula [Zaalishvili, 1986]:

$$f\_{\rm ca} = \sum A\_i f\_i \bigwedge \sum A\_i \tag{13}$$

where Ai and fi are the amplitude and the corresponding frequency of vibration spectrum.

**Figure 10.** Surficial gasodinamical pulse source (SI-32)

#### *3.1.7. Seismic microzonation using vibration impact*

At usage of a vibration source (fig. 10) the calculation of intensity increment is realized with the help of the formula (Zaalishvili, 1986):

$$
\Delta I = \mathsf{2lgS}\_i / \mathsf{S}\_{0\prime} \tag{14}
$$

where Si and S0 are the squares of vibration spectra of investigated and etalon soils.

The developed tool was used at SMZ of the territories of cities Tbilisi, Kutaisi, Tkibuli, single areas of the Bolshoy Sochi city. The tools' feature consists in the fact that it allows to assess soil seismic hazard without any preliminary investigations: at realization of direct measurements of soil thickness response on standard (vibration or impulse) influence. Later the formula was successfully used at SMZ of the sites of Novovoronezh Nuclear powerplant (NPP) with the help of an impulsive source (Zaalishvili, 2009).

**Figure 11.** Vibration source (SV-10/100)

#### *3.1.8. Seismic microzonation on basis of taking into account soil nonlinear properties*

The comparison of the absorption and nonlinearity indices with the corresponding spectra of soil vibrations shows that at higher absorption the spectrum square prevails in LF field and at high nonlinearity it prevails in HF field of the spectrum. In other words, the presence of absorption is displayed in additional spreading of LF spectrum region, and the presence of nonlinearity – in spreading of HF range.

All the mentioned allowed to obtain the formula for calculation of intensity increment on basis of taking into account nonlinear – elastic soil behavior or elastic nonlinearity (at usage of vibration source) [Zaalishvili, 1996]:

$$
\Delta \mathbf{I} = \mathbf{3} \text{ lg } \mathbf{A} \mathbf{f}\_{\text{wai}} / \mathbf{A} \mathbf{0} \mathbf{f}\_{\text{wai}0} \tag{15}
$$

Assessment of Seismic Hazard of Territory 47

spectrum of soil vibrations, caused by near emitter, the HF component, which quickly attenuates with distance (fig. 11, b), predominates. In case of influence by distant emitter to the soil surface, the LF component predominates in the spectrum of vibrations (fig. 11, c). In other words, at nonlinear-elastic deformations the main energy is concentrated in the HF range of spectrum and at nonelastic – in the LF range. The signal spectrum has the

Elastic linear and nonlinear vibrations are characterized for the given source by the constancy of the real spectrum square, which is the index of definite source energy value, absorbed by soil (which is deformed by the source). The analysis of strong and destructive earthquake records and also the analysis of specially carried out experimental influences showed that at nonelastic phenomena spectra square of corresponding soil vibrations is not the constant value. It can decrease and the more it decreases, the less the soil solidity and the

**Figure 12.** Investugation of site spectral features by means of GSK-6M seismic source: a) experiment

At usage of vibratory energy source, the whole number of new formulas (Zaalishvili, 2009) in order to assess soil seismic hazard with taking into account the values of their

where (Sri)n,d and (Sr0)n,d are the squares of real spectra of investigated and etalon soils in

Δ*I* = 2,4 lg [(*S*r*<sup>i</sup>*)n(*S*r0)d */* (*S*r*<sup>i</sup>*)d(*S*r0)n], (17)

Δ*I* = 3,3 lg *(Ai f*aw*<sup>i</sup>*)n (*A*<sup>0</sup> *f*aw0)d /(*Ai f*aw*<sup>i</sup>*)d (*A*0 *f*aw0)n, (18)

scheme; b) record of second source impact; c) record of first source impact

nonelasticity were obtained:

near and distant zones of the source.

symmetrical form in the far and practically linear-elastic zone.

greater the influence value (Zaalishvili, 2009).

where Aifwai, A0fwa0 is the product of spectrum amplitude on weight-average vibration frequency of investigated and etalon soils.

The formula (14) characterizes soil nonlinear–elastic behavior at the absence of absorption.

If the impulsive source is used at SMZ than the formula will have the form (Zaalishvili, 2009):

$$
\Delta \mathbf{I} = \mathbf{2} \text{ lg } \mathbf{A} \mathbf{f}\_{\text{wai}} / \text{ A} \mathbf{f}\_{\text{wai}}.\tag{16}
$$

#### *3.1.9. Seismic microzonation on basis of taking into account soil inelastic properties*

As soil liquefaction and uneven settlement of the constructions are observed at strong earthquakes (Niigata, 1966; Kobe, 1995), the most actual problem of SMZ is to assess possible soil nonelasticity adequately and physically proved at intensive seismic influences.

In order to assess directly nonelasticity of soil, the special scheme of the realization of experimental investigations (fig. 11, a) with gas-dynamic impulsive source GSK-6M (with two oscillators) was used. Selected location of the longitudinal profile allowed to influence alternately by two emitters from adjoining and somewhat far radiation zones. In the spectrum of soil vibrations, caused by near emitter, the HF component, which quickly attenuates with distance (fig. 11, b), predominates. In case of influence by distant emitter to the soil surface, the LF component predominates in the spectrum of vibrations (fig. 11, c). In other words, at nonlinear-elastic deformations the main energy is concentrated in the HF range of spectrum and at nonelastic – in the LF range. The signal spectrum has the symmetrical form in the far and practically linear-elastic zone.

46 Earthquake Engineering

**Figure 11.** Vibration source (SV-10/100)

of nonlinearity – in spreading of HF range.

of vibration source) [Zaalishvili, 1996]:

frequency of investigated and etalon soils.

2009):

*3.1.8. Seismic microzonation on basis of taking into account soil nonlinear properties* 

The comparison of the absorption and nonlinearity indices with the corresponding spectra of soil vibrations shows that at higher absorption the spectrum square prevails in LF field and at high nonlinearity it prevails in HF field of the spectrum. In other words, the presence of absorption is displayed in additional spreading of LF spectrum region, and the presence

All the mentioned allowed to obtain the formula for calculation of intensity increment on basis of taking into account nonlinear – elastic soil behavior or elastic nonlinearity (at usage

where Aifwai, A0fwa0 is the product of spectrum amplitude on weight-average vibration

The formula (14) characterizes soil nonlinear–elastic behavior at the absence of absorption.

*3.1.9. Seismic microzonation on basis of taking into account soil inelastic properties* 

If the impulsive source is used at SMZ than the formula will have the form (Zaalishvili,

As soil liquefaction and uneven settlement of the constructions are observed at strong earthquakes (Niigata, 1966; Kobe, 1995), the most actual problem of SMZ is to assess possible soil nonelasticity adequately and physically proved at intensive seismic influences. In order to assess directly nonelasticity of soil, the special scheme of the realization of experimental investigations (fig. 11, a) with gas-dynamic impulsive source GSK-6M (with two oscillators) was used. Selected location of the longitudinal profile allowed to influence alternately by two emitters from adjoining and somewhat far radiation zones. In the

ΔI = 3 lg Aifwai / A0fwa0**,** (15)

ΔI = 2 lg Aifwai / A0fwa0**.** (16)

Elastic linear and nonlinear vibrations are characterized for the given source by the constancy of the real spectrum square, which is the index of definite source energy value, absorbed by soil (which is deformed by the source). The analysis of strong and destructive earthquake records and also the analysis of specially carried out experimental influences showed that at nonelastic phenomena spectra square of corresponding soil vibrations is not the constant value. It can decrease and the more it decreases, the less the soil solidity and the greater the influence value (Zaalishvili, 2009).

**Figure 12.** Investugation of site spectral features by means of GSK-6M seismic source: a) experiment scheme; b) record of second source impact; c) record of first source impact

At usage of vibratory energy source, the whole number of new formulas (Zaalishvili, 2009) in order to assess soil seismic hazard with taking into account the values of their nonelasticity were obtained:

$$\Delta I = 2,4 \lg \left[ (S\_{\rm ri})\_{\rm n} (S\_{\rm r0})\_{\rm d} / (S\_{\rm r0})\_{\rm d} (S\_{\rm r0})\_{\rm h} \right] \tag{17}$$

where (Sri)n,d and (Sr0)n,d are the squares of real spectra of investigated and etalon soils in near and distant zones of the source.

Δ*I* = 3,3 lg *(Ai f*aw*<sup>i</sup>*)n (*A*<sup>0</sup> *f*aw0)d /(*Ai f*aw*<sup>i</sup>*)d (*A*0 *f*aw0)n, (18)

where (Ai fawi)n,d and (A0 faw0)n,d are the amplitudes and weight-average frequencies of investigated and etalon soils in near and distant zones of the source.

In case of powerful impulsive source usage the offered formulas will have a form:

$$
\Delta \mathbf{I} = \mathbf{1}\_{\mathsf{L}} \mathsf{Z} \left[ \lg \left< \mathbf{S}\_{\mathsf{H}} \right> \mathbf{\hat{n}} \left< \mathbf{S}\_{\mathsf{H}} \right> \mathbf{\hat{n}} \left< \mathbf{\hat{S}}\_{\mathsf{H}} \right> \mathbf{\hat{n}} \left< \mathbf{S}\_{\mathsf{H}} \right> \mathbf{\hat{n}} \right] \mathbf{\hat{n}} \tag{19}
$$

Assessment of Seismic Hazard of Territory 49

**Figure 13.** Instrumental stress-sstrain curve, showing property of soil bimodularity

*3.2.1. Equivalent linear model. SHAKE and EERA programs* 

correspond to the deformation levels in each layer.

*3.2.2. IM model. NERA program* 

the programs SHAKE (Schnabel et al., 1972) and EERA (Bardet et al., 2000).

etc.).

The solution of the given nonlinear problem for soils in the analytic form is based, as a rule, on considerable assumptions due to the complication of adequate taking into account behavior features of such complex system as the soil (Bonnet & Heitz, 1994). Therefore the numerical solution of nonlinear problems on the modern stage of knowledge is the most proved if the data of field or laboratory investigations is taken into account in these or those connections. Thus, the correlations, which are determined by the experimental investigations, are the basis of the solution of calculation nonlinear problems. In other words calculation programs for the solution of calculation nonlinear problems essentially are analytical-empirical. The most adequate programs are exactly like these (SHAKE, NERA

Equivalent linear model is one of the first models, which take nonlinear soil behavior into account. Equivalent linear approximation consists in modification of the model of Kelvin– Voight (for taking some types of nonlinearity into account) and, for example, is realized in

Equivalent linear model is based on the hypothesis that shear modulus G and attenuation coefficient ξ are the functions of shearing strain γ (fig. 18.1). In the programs SHAKE and EERA (Equivalent-linear Earthquake site Response Analyses) the values of shear modulus G and attenuation coefficient ξ are determined (in the process of iteration) so that they

In 2001 realization principle, which was used in the program EERA, was applied in the programming of NERA (Nonlinear Site Response Analysis) (Bardet, Tobita, 2001), which allows to compute soil thickness nonlinear reaction on seismic influences. The program is based on the medium model, offered by Iwan (1967) and Mroz (1967), which is often called the IM model for short. As it is shown in the fig. 18.2, the model supposes the simulating of nonlinear curves strain-deformation, using a number of n mechanical elements, which have different stiffness kj and sliding resistance Rj, where R1 < R2 < … < Rn. Initially the residual stresses in all elements are equal to zero. At monotonically increasing load the element j

where (SРi)бд and (SР0)бд are the squares of real spectra of investigated and etalon soils in near and distant zones of the source;

$$
\Delta \mathbf{I} = \mathbf{2} \lg \left[ \left< (A \circ f\_{\mathbf{u} \circ \mathbf{i}}) \mathbf{a} \left( A \mathbf{0} f\_{\mathbf{u} \circ \mathbf{0}} \right) \mathbf{a} \right> \left< A \circ f\_{\mathbf{u} \circ \mathbf{i}} \right> \mathbf{a} \left( A \mathbf{0} f\_{\mathbf{u} \circ \mathbf{0}} \right) \mathbf{a} \right] \tag{20}
$$

where (Ai fawi)n,d and (A0 faw0)n,d are the amplitudes and weight-average frequencies of investigated and etalon soils in near and distant zones of the source.

The formulas (17) and (18) are true only for loose dispersal soils. The formulas (17) and (18) were used at SMZ of the territory of Kutaisi city. Besides, with the help of the formulas (19) and (20) nonelastic deformation properties of soils in full-scale conditions on the site of Novovoronezh NPP-2 were defined more exactly (Zaalishvili, 2009). The formulas were obtained on basis of physical principle, which underlies the scheme, applied at the assessment of soil looseness measure (Zaalishvili, 1996, Nikolaev, 1987).

### **3.2. Calculational method of seismic microzonation**

Calculational method of SMZ is used in order to analyse features of soil behavior with introduction of definite engineering–geological structure characteristics of investigated site as initial data: values of transverse wave velocities, index of extinction, modulus of elasticity, power of soil layers, their consistency etc. Calculational method includes thinlayer medium, multiple-reflected waves, finite-difference method, finite-elements analysis (FEA) and other techniques.

One can take nonlinear soil properties into account in the problems of earthquake engineering by means of instrumental and calculation methods. The instrumental method of SMZ is the main method. Nevertheless it is quite often necessary to solve such problems using calculational method, which allows to model practically any conditions, which are observed in the nature. At the same time the practice reqirements lead to the necessity of calculation of soil vibrations for the conditions of their nonlinear-elastic and nonelastic deformations. At the solution of such problem it is assumed that elastic half-space behaves as linear-elastic medium and the covering soil displays strong nonlinear properties at intensive seismic or dynamic influences (Bonnet & Heitz, 1994).

Instrumental stress-sstrain dependences can be used, for example one obtained for plastic clay soil shown in fig. 12. The conception of the so-called soil bimodularity, offered by A.V.Nikolaev (Nikolaev, 1987, Zaalishvili, 1996; 2000) is taken into account in the given dependence. Considerable differences in behavior of "weak" soils at compression and dilatation lie in the base of the phenomenon. Such soil is characterized at dilatation by quite small shear modulus.

**Figure 13.** Instrumental stress-sstrain curve, showing property of soil bimodularity

The solution of the given nonlinear problem for soils in the analytic form is based, as a rule, on considerable assumptions due to the complication of adequate taking into account behavior features of such complex system as the soil (Bonnet & Heitz, 1994). Therefore the numerical solution of nonlinear problems on the modern stage of knowledge is the most proved if the data of field or laboratory investigations is taken into account in these or those connections. Thus, the correlations, which are determined by the experimental investigations, are the basis of the solution of calculation nonlinear problems. In other words calculation programs for the solution of calculation nonlinear problems essentially are analytical-empirical. The most adequate programs are exactly like these (SHAKE, NERA etc.).

#### *3.2.1. Equivalent linear model. SHAKE and EERA programs*

Equivalent linear model is one of the first models, which take nonlinear soil behavior into account. Equivalent linear approximation consists in modification of the model of Kelvin– Voight (for taking some types of nonlinearity into account) and, for example, is realized in the programs SHAKE (Schnabel et al., 1972) and EERA (Bardet et al., 2000).

Equivalent linear model is based on the hypothesis that shear modulus G and attenuation coefficient ξ are the functions of shearing strain γ (fig. 18.1). In the programs SHAKE and EERA (Equivalent-linear Earthquake site Response Analyses) the values of shear modulus G and attenuation coefficient ξ are determined (in the process of iteration) so that they correspond to the deformation levels in each layer.

#### *3.2.2. IM model. NERA program*

48 Earthquake Engineering

and distant zones of the source;

(FEA) and other techniques.

small shear modulus.

where (Ai fawi)n,d and (A0 faw0)n,d are the amplitudes and weight-average frequencies of

where (SРi)бд and (SР0)бд are the squares of real spectra of investigated and etalon soils in near

where (Ai fawi)n,d and (A0 faw0)n,d are the amplitudes and weight-average frequencies of

The formulas (17) and (18) are true only for loose dispersal soils. The formulas (17) and (18) were used at SMZ of the territory of Kutaisi city. Besides, with the help of the formulas (19) and (20) nonelastic deformation properties of soils in full-scale conditions on the site of Novovoronezh NPP-2 were defined more exactly (Zaalishvili, 2009). The formulas were obtained on basis of physical principle, which underlies the scheme, applied at the

Calculational method of SMZ is used in order to analyse features of soil behavior with introduction of definite engineering–geological structure characteristics of investigated site as initial data: values of transverse wave velocities, index of extinction, modulus of elasticity, power of soil layers, their consistency etc. Calculational method includes thinlayer medium, multiple-reflected waves, finite-difference method, finite-elements analysis

One can take nonlinear soil properties into account in the problems of earthquake engineering by means of instrumental and calculation methods. The instrumental method of SMZ is the main method. Nevertheless it is quite often necessary to solve such problems using calculational method, which allows to model practically any conditions, which are observed in the nature. At the same time the practice reqirements lead to the necessity of calculation of soil vibrations for the conditions of their nonlinear-elastic and nonelastic deformations. At the solution of such problem it is assumed that elastic half-space behaves as linear-elastic medium and the covering soil displays strong nonlinear properties at

Instrumental stress-sstrain dependences can be used, for example one obtained for plastic clay soil shown in fig. 12. The conception of the so-called soil bimodularity, offered by A.V.Nikolaev (Nikolaev, 1987, Zaalishvili, 1996; 2000) is taken into account in the given dependence. Considerable differences in behavior of "weak" soils at compression and dilatation lie in the base of the phenomenon. Such soil is characterized at dilatation by quite

Δ*I* = 1,2 [lg (*S*r*<sup>i</sup>*)n (*S*r0)d / (*S*r*<sup>i</sup>*)d (*S*r0)n]**,** (19)

Δ*I* = 2 lg [(*Ai f*aw*<sup>i</sup>*)n (*A*<sup>0</sup> *f*aw0)d / (*A i f*aw*<sup>i</sup>*)d (*A*<sup>0</sup> *f*aw0)n], (20)

In case of powerful impulsive source usage the offered formulas will have a form:

investigated and etalon soils in near and distant zones of the source.

investigated and etalon soils in near and distant zones of the source.

assessment of soil looseness measure (Zaalishvili, 1996, Nikolaev, 1987).

**3.2. Calculational method of seismic microzonation** 

intensive seismic or dynamic influences (Bonnet & Heitz, 1994).

In 2001 realization principle, which was used in the program EERA, was applied in the programming of NERA (Nonlinear Site Response Analysis) (Bardet, Tobita, 2001), which allows to compute soil thickness nonlinear reaction on seismic influences. The program is based on the medium model, offered by Iwan (1967) and Mroz (1967), which is often called the IM model for short. As it is shown in the fig. 18.2, the model supposes the simulating of nonlinear curves strain-deformation, using a number of n mechanical elements, which have different stiffness kj and sliding resistance Rj, where R1 < R2 < … < Rn. Initially the residual stresses in all elements are equal to zero. At monotonically increasing load the element j

deforms until the transverse strain τ reaches Rj. After that the element j keeps positive residual stress, which is equal to Rj.

The equation, describes dynamics of soil medium, is solved by the method of central differences.

#### *3.2.3. Calculation of nonlinear absorptive ground medium vibrations using multiple reflected waves' tool of seismic microzonation*

Let's suppose that we have the seismic wave, which falls on the soil thickness surface. Let's assume that soil thickness is nonlinear absorptive unbounded medium with the density and S-wave propagation velocity vS. At small deformations the value of shear modulus G will be maximum for the given soils:

$$\mathbf{G} = \mathbf{G}\_{\text{max}} = \rho \mathbf{v}\_{\text{S}}^{\text{2}} \tag{21}$$

Assessment of Seismic Hazard of Territory 51

(24)

max max

*G G*

where G is the current shear modulus, is normal stress.

1 exp 0.0145

2

of Tbilisi city, was chosen as the accelerogram, given into the bedrock.

1,3 <sup>2</sup>

0.333 0.586 1.547 1

On basis of the given ratios and introduced by us ratios for determination of necessary indices (normal stress, deformation etc), nonlinear version of the program ZOND was worked out. From the database of strong motions AGESAS, which was formed by us (Zaalishvili et al., 2000), the accelerogram, which was recorded on rocks in Japan, with the characteristics (magnitude, epicentral distance, spectral features etc.) similar to the territory

The analysis of the results of linear and nonlinear calculations models of definite areas of Tbilisi city territory confirms the adequacy of calculations to the physical phenomena, which were obtained in soils at intensive loads (fig. 13) (Zaalishvili, 2009). With the increase of seismic influence intensity the nonlinearity display increases. Absorption grows simultaneously. Hence the resulting motion at quite high influence levels can be lower than the initial level. It corresponds to the fact, which is known on the results of analysis of strong earthquake consequences, which happened in recent yares (for example, Northridge

**Figure 14.** Results of calculations using multiple reflected waves' tool in linear (a) and nonlinear

a) b)

*3.2.4. Calculation of nonlinear soil response using FEM tool of seismic microzonation* 

(FEM) in the following way (Zaalishvili, 2009).

The problem of the determination of soil massif response on dynamic influence with taking soil nonlinear properties into account can be solved by usage of finite element method

*PI G G*

Seismic energy absorption is calculated by the formula

earthquake, 1994).

(b) cases.

At the deformation increase the value G remains constant at first but at reaching some value (which is definite for each material or soil) the value G considerably changes, i.e. the soil begins to display its nonlinear properties. At the continued deformation increase the growth of stresses decelerates and then can remain unchanged until material destruction or hardening, i.e. until structural condition change.

As the main soil index, which characterizes its type and behavior at intensive loads, the value of plasticity PI was chosen. The parameters, which are necessary for calculations, are determined on basis of empirical ratios (Ishibashi, Zhang, 1993):

$$k\left(\mathcal{Y}, PI\right) = 0.5 \left\{ 1 + \tanh\left[ \ln \frac{0.000102 + n\left(PI\right)}{\mathcal{Y}} \right]^{0.492} \right\} \tag{22}$$

where

$$n(P\_I) = \begin{cases} 0.0 & \text{for} \quad PI = 0, \\ 3.37 \cdot 10^{-6} PI^{1.404} & \text{for} \quad 0 < PI \le 15, \\ 7.0 \cdot 10^{-7} PI^{1.976} & \text{for} \quad 15 < PI \le 70, \\ 2.7 \cdot 10^{-5} PI^{1.115} & \text{for} \quad PI > 70 \end{cases},$$

$$d = 0.272 \left\{ 1 - \tanh \left[ \ln \left( \frac{0.000556}{\mathcal{I}} \right)^{0.4} \right] \right\} \text{e}^{-0.0145PI^{1.3}}.$$

Then the change of shear modulus is determined on basis of the ratio

$$\frac{G}{G\_{\text{max}}} = k(\gamma, PI)(\sigma)^d \tag{23}$$

where G is the current shear modulus, is normal stress.

Seismic energy absorption is calculated by the formula

50 Earthquake Engineering

differences.

where

residual stress, which is equal to Rj.

will be maximum for the given soils:

*reflected waves' tool of seismic microzonation* 

hardening, i.e. until structural condition change.

*k PI* 

*n P*

*I*

determined on basis of empirical ratios (Ishibashi, Zhang, 1993):

, 0.5 1 tanh ln

deforms until the transverse strain τ reaches Rj. After that the element j keeps positive

The equation, describes dynamics of soil medium, is solved by the method of central

Let's suppose that we have the seismic wave, which falls on the soil thickness surface. Let's assume that soil thickness is nonlinear absorptive unbounded medium with the density and S-wave propagation velocity vS. At small deformations the value of shear modulus G

> <sup>2</sup> *GG v* max *<sup>S</sup>*

At the deformation increase the value G remains constant at first but at reaching some value (which is definite for each material or soil) the value G considerably changes, i.e. the soil begins to display its nonlinear properties. At the continued deformation increase the growth of stresses decelerates and then can remain unchanged until material destruction or

As the main soil index, which characterizes its type and behavior at intensive loads, the value of plasticity PI was chosen. The parameters, which are necessary for calculations, are

0.492

6 1.404 7 1.976 5 1.115

 

0.4 0.000556 0.0145 0.272 1 tanh ln e . *PI <sup>d</sup>* 

( , )( ) , *<sup>G</sup> <sup>d</sup> k PI*

 

max

*<sup>G</sup>*

Then the change of shear modulus is determined on basis of the ratio

 

0.0 PI 0, 3.37 10 f 0 15, 7.0 10 f 15 70, 2.7 10 f 70 ;

0.000102

*for PI or PI*

*PI or PI PI or PI*

*n PI*

1.3

(23)

(21)

(22)

*3.2.3. Calculation of nonlinear absorptive ground medium vibrations using multiple* 

$$\xi = 0.333 \frac{1 + \exp\left(-0.0145PI^{1.3}\right)}{2} \left[ 0.586 \left(\frac{G}{G\_{\text{max}}}\right)^2 - 1.547 \frac{G}{G\_{\text{max}}} + 1 \right] \tag{24}$$

On basis of the given ratios and introduced by us ratios for determination of necessary indices (normal stress, deformation etc), nonlinear version of the program ZOND was worked out. From the database of strong motions AGESAS, which was formed by us (Zaalishvili et al., 2000), the accelerogram, which was recorded on rocks in Japan, with the characteristics (magnitude, epicentral distance, spectral features etc.) similar to the territory of Tbilisi city, was chosen as the accelerogram, given into the bedrock.

The analysis of the results of linear and nonlinear calculations models of definite areas of Tbilisi city territory confirms the adequacy of calculations to the physical phenomena, which were obtained in soils at intensive loads (fig. 13) (Zaalishvili, 2009). With the increase of seismic influence intensity the nonlinearity display increases. Absorption grows simultaneously. Hence the resulting motion at quite high influence levels can be lower than the initial level. It corresponds to the fact, which is known on the results of analysis of strong earthquake consequences, which happened in recent yares (for example, Northridge earthquake, 1994).

**Figure 14.** Results of calculations using multiple reflected waves' tool in linear (a) and nonlinear (b) cases.

#### *3.2.4. Calculation of nonlinear soil response using FEM tool of seismic microzonation*

The problem of the determination of soil massif response on dynamic influence with taking soil nonlinear properties into account can be solved by usage of finite element method (FEM) in the following way (Zaalishvili, 2009).

Soil medium is represented in the form of two-dimensional massif, which is approximate by triangular finite elements. The net, which consists of triangular elements, allows to describe quite accurately any relief form and form of the layer structure of soil massif with its physics-mechanical parameters. Within finite elemet the soil is homogeneous with inherent to it characteristics, which vary in time depending on influence intensity. Earthquake accelerogram of horizontal or vertical direction, which is applied, as a rule, to the foundation of soil massif, is used as the influence. Soil is in the conditions of plane deformation and is considered as an orthotropic medium. Axes of the orthotropy coincide with the directions of main strains.

Assessment of Seismic Hazard of Territory 53

the tendency of the increase of seismic vibration intensity from foundation to the top remains. The increment of seismic intensity for the relief mesoforms is about 0.3 degree. It was shown that weak hilly relief, with the inclinations less than 10°, does not influence on

The investigations of S.V.Puchkov and D.V.Garagozov (Puchkov, Garagozov, 1973) showed that at vibrations of mountain range, composed by volcanic tuf, the amplitude of seismic vibrations in S-waves increases on the height 15 m in 1.46 times in comparison with the foundation. For the massif, composed by loamy sand and loams on the same height marks the vibrational amplitude increased in 1.8 times for p-waves and in 3.2 times

Slope steepness considerably influences on the increment of seismic intensity. The increase of slope steepness, composed by incoherent gravel-pebble and sabulous-loamy grounds is conductive to the sharp worsening of engineering-geological and seismic conditions of the territory. So, for example, it is determined that slope steepness more than 19°–15° (for dry sandy-argillaceous and gravel-pebble differences) produces the intensity increment up to 1 degree and at variation of slope steepness from 10° to 40° the amplitudes of seismic

It is known that the increase of slope steepness from 40° to 80° produces the increment of

The correlation analysis of the dependence of seismic intensity increment on true altitude, slope steepness and relief roughness showed that the main factors, which change the value of seismic intensity, are the first two indices [Puchkov, Garagozov, 1973]. It conforms well to the investigation results of V.B.Zaalishvili, who introduced the new parameter of the relief

Later the data analysis allowed to offer us (I.Gabeeva & V.Zaalishvili) the empirical formula for the possible amplification calculation K and intensity increment ∆I, which are caused by

0.1 0.68lg *K = R* (26)

where R= H is the relief coefficient; is the relief slope angle, degree; H is height, m.

seismic intensity equal to 1.5 degree (Zaalishvili, Gogmachadze, 1989).

the seismic vibrations intensity.

vibrations increase approximately in 2.5 times.

coefficient (Zaalishvili, Gogmachadze, 1989) (fig. 14).

the relief (Zaalishvili, 2006):

**Figure 15.** Relief coefficient R

for S-waves.

The problem of nonlinear dynamics of soil massif is solved by means of the consecutive determination of mode of deflection of the system on the previous step. The system is linearelastic on each step.

#### **3.3. Instrumental-calculational method of seismic microzonation**

In recent years a new «instrumental-calculational» method of SMZ (per se simultaneously having the features of both instrumental and calculational method) which includes tool of «instrumental-calculation analogies» has been developed in Russia in recent years (Zaalishvili, 2006). Its usage is based on direct usage of modern databases of strong motions.

As a basis at realization of tool instrumental database of strong movements, registered in definite soil conditions, is used. As a result of given database with the help of numerical calculations it is possible more or less safety to forecast behavior of these or those soils (or their combination) for strong (weak) earthquakes with typical characteristics for the investigated territory (magnitude, epicentral distance, focus depth etc.).

#### **3.4. Relief influence on the earthquake intensity in SMZ problems**

Morphological and morphometric features of relief meso- and macroforms influences on seismic intensity increment.

On basis of the analysis of numerous macroseismic observations the consequences of strong earthquakes, which took place on the territory of the former USSR, S.V.Puchkov and D.V.Garagozov offered the empirical formula for the intensity increment calculation (∆I) depending on relief feature (Puchkov, Garagozov, 1973):

$$
\Delta I = 3.31 \text{g} \left( \text{W}\_{\text{gr}} \,/\text{W}\_{\text{et}} \right) + 3.31 \text{g} \left( \text{W}\_{\text{top}} \,/\text{W}\_{\text{f}nd} \right) \tag{25}
$$

where Wgr, Wet are the accelerations of vibratory motion on soil and etalon; Wtop, Wfnd are the accelerations on the top of mountain construction and its foundation.

It was determined as a result of the instrumental and theoretical investigations that for the microrelief the increment of seismic intensity increases from the foundation of mountainshaped feature to its top and can reach approximately 1.8 degree. For the locality mesorelilef the tendency of the increase of seismic vibration intensity from foundation to the top remains. The increment of seismic intensity for the relief mesoforms is about 0.3 degree. It was shown that weak hilly relief, with the inclinations less than 10°, does not influence on the seismic vibrations intensity.

The investigations of S.V.Puchkov and D.V.Garagozov (Puchkov, Garagozov, 1973) showed that at vibrations of mountain range, composed by volcanic tuf, the amplitude of seismic vibrations in S-waves increases on the height 15 m in 1.46 times in comparison with the foundation. For the massif, composed by loamy sand and loams on the same height marks the vibrational amplitude increased in 1.8 times for p-waves and in 3.2 times for S-waves.

Slope steepness considerably influences on the increment of seismic intensity. The increase of slope steepness, composed by incoherent gravel-pebble and sabulous-loamy grounds is conductive to the sharp worsening of engineering-geological and seismic conditions of the territory. So, for example, it is determined that slope steepness more than 19°–15° (for dry sandy-argillaceous and gravel-pebble differences) produces the intensity increment up to 1 degree and at variation of slope steepness from 10° to 40° the amplitudes of seismic vibrations increase approximately in 2.5 times.

It is known that the increase of slope steepness from 40° to 80° produces the increment of seismic intensity equal to 1.5 degree (Zaalishvili, Gogmachadze, 1989).

The correlation analysis of the dependence of seismic intensity increment on true altitude, slope steepness and relief roughness showed that the main factors, which change the value of seismic intensity, are the first two indices [Puchkov, Garagozov, 1973]. It conforms well to the investigation results of V.B.Zaalishvili, who introduced the new parameter of the relief coefficient (Zaalishvili, Gogmachadze, 1989) (fig. 14).

Later the data analysis allowed to offer us (I.Gabeeva & V.Zaalishvili) the empirical formula for the possible amplification calculation K and intensity increment ∆I, which are caused by the relief (Zaalishvili, 2006):

$$K = -0.1 + 0.681 \lg R \tag{26}$$

where R= H is the relief coefficient; is the relief slope angle, degree; H is height, m.

**Figure 15.** Relief coefficient R

52 Earthquake Engineering

with the directions of main strains.

elastic on each step.

seismic intensity increment.

Soil medium is represented in the form of two-dimensional massif, which is approximate by triangular finite elements. The net, which consists of triangular elements, allows to describe quite accurately any relief form and form of the layer structure of soil massif with its physics-mechanical parameters. Within finite elemet the soil is homogeneous with inherent to it characteristics, which vary in time depending on influence intensity. Earthquake accelerogram of horizontal or vertical direction, which is applied, as a rule, to the foundation of soil massif, is used as the influence. Soil is in the conditions of plane deformation and is considered as an orthotropic medium. Axes of the orthotropy coincide

The problem of nonlinear dynamics of soil massif is solved by means of the consecutive determination of mode of deflection of the system on the previous step. The system is linear-

In recent years a new «instrumental-calculational» method of SMZ (per se simultaneously having the features of both instrumental and calculational method) which includes tool of «instrumental-calculation analogies» has been developed in Russia in recent years (Zaalishvili, 2006). Its usage is based on direct usage of modern databases of strong motions.

As a basis at realization of tool instrumental database of strong movements, registered in definite soil conditions, is used. As a result of given database with the help of numerical calculations it is possible more or less safety to forecast behavior of these or those soils (or their combination) for strong (weak) earthquakes with typical characteristics for the

Morphological and morphometric features of relief meso- and macroforms influences on

On basis of the analysis of numerous macroseismic observations the consequences of strong earthquakes, which took place on the territory of the former USSR, S.V.Puchkov and D.V.Garagozov offered the empirical formula for the intensity increment calculation (∆I)

where Wgr, Wet are the accelerations of vibratory motion on soil and etalon; Wtop, Wfnd are the

It was determined as a result of the instrumental and theoretical investigations that for the microrelief the increment of seismic intensity increases from the foundation of mountainshaped feature to its top and can reach approximately 1.8 degree. For the locality mesorelilef

*ΔI= W W W W* 3,3lg / +3,3lg / gr et top *fnd* (25)

**3.3. Instrumental-calculational method of seismic microzonation** 

investigated territory (magnitude, epicentral distance, focus depth etc.).

depending on relief feature (Puchkov, Garagozov, 1973):

accelerations on the top of mountain construction and its foundation.

**3.4. Relief influence on the earthquake intensity in SMZ problems** 

The analysis of the experimental data shows that intensity increment can vary at that independently of the type of rocks, from 0 to 1.5 degree.

Assessment of Seismic Hazard of Territory 55

change. Seismic intensity increment in the given case is formed by the wave interference and

Thus, at the execution of SMZ works in the mountain regions or under the conditions of billowy relief, it is necessary to pay special attention to the influence of surface or underground relief on the intensity forming. It is necessary to continue the investigations in order to obtain statistically proved ratio for the calculation of intensity increment, caused by

If we consider 5% DSZ map as basis for seismic microzonation so seismic intensity of 8

Then, maps of seismic microzonation of cities must be created. According to the above mentioned maps of detailed zoning the maps of seismic microzonation with probability 1%,

Though, that definitions of the word «zoning» are similar, actually they are quite different in essence. Unlike the maps of detailed seismic zoning, which give seismic potential (Mmax) and source features, the maps of seismic microzonation give assessments of soil condition influence (sands, rocks, pebbles, clays etc., their combination; watering; relief (as underground as surface); spectral distribution of incoming wave; predominant vibration frequencies on city square etc.) on forming of future earthquake intensity. As a rule, the scale of such maps is 1:10 000, in order to have the opportunity of taking them into account at building. Maps can be more detailed (1:5000 etc.) but this makes no sense as the type and physical condition of soils in space on the territory site can change fast. The most important thing is to assess intensity of possible earthquakes on areas with typical soil conditions for

Maps of seismic microzonation can be made up for the certain territories (cities and settlements, as a rule). It is impossible to make them up in entire format because of the necessity of geological conditions knowledge on larger territories, which are mostly not built up. We often don't have such data even for the modern cities! It's practically impossible because the resources will be lost for nothing! And absurdity! In the other words there is no the microzonation map even for the territory of North Ossetia let alone the whole

Maps of seismic microzonation do not only show the place of earthquake-proof building up, but they also show on what intensity this or that building must be calculated and designed: on 6, 7, 8 or 9 points. And sometimes even on 10 points (for very soft grounds!). And this suggests investments of different financing for the realization of antiseismic measures (thicker armature, more connections etc.). Seismic risk can considerably be reduced at building-up zones with 7, 8 and 9 point of the calculated intensity by adequate site development on the territory of city, for example, as social losses will be minimal, though

can be 1.5–2.0 degree (Bugaev & Kharlov, 1977; Bondarik et.al., 2007).

**3.5. Seismic microzonation of Vladikavkaz city** 

corresponds to etalon grounds for whole territory.

2%, 5% or 10 %, correspondingly, were made up.

buildings will be damaged in this or that extent.

relief.

city territory.

Northern Caucasus.

Finally, let's try to assess the amplification of vibrational amplitude, which is caused by relief, with the help of the calculation method of FEM (Zaalishvili, 2006).

The algorithm for the calculation of seismic reaction of soil thickness for the twodimensional model was developed for this purpose (fig. 15) (Zaalishvili, 2009). The results of the executed earliear investigations were used for the program testing (Puchkov, Garagozov, 1973). Mountain structure had the form of frustum of a cone with the height 30 m and slope angle of the generatrix 30º. The element maximum size was equal to 5 m, Swave propagation velocity was 300 m/s, the density 1800 kg/m3. The seismic influence was applied to the foundation of soil thickness in the form of instrumental accelerogram, modeling the vertically propagating SH wave.

It was determined that the vibrational amplitude considerably chances with the relief. The given dependence at that is various for the displacements, velocities and accelerations. The largest value of the amplification is observed for displacements and the maximum ratio of vibrational amplitudes, for example, in the point C to the point A, is 2.1 and for the point D – 3.2. It well satisfies the results of experimental observations where the ratio in the point C for the S-wave is equal to 2.3 and in the spectral region the maximum values are 1.8 (at T = 0.4 s) and 3.2 (at T = 0.7 s) for P- and S-waves accordingly. Spectral analysis also shows the resonance increase of vibrational amplitudes in the top part of the slope on the frequency 1.6 Hz (i.e. T=0.6 s).

**Figure 16.** Final elements analysis (FEA) application example: a) Variation of amplitudes of displacement, velocity and acceleration along surface; b) calculational model; c) seismograms, calculated in points A, B, C, D.

Considerably fewer investigations are dedicated to the influence of the underground relief on the intensity. On the data of B.A.Trifonov (1979) the underground and buried topography of the rocks influences on seismic vibrations intensity, if the surface slope exceeds 0.3. At the vee couch of the rocks, which are covered by sedimentary thickness, the ratio between wave length and the sizes of vee stripping influences on seismic intensity change. Seismic intensity increment in the given case is formed by the wave interference and can be 1.5–2.0 degree (Bugaev & Kharlov, 1977; Bondarik et.al., 2007).

Thus, at the execution of SMZ works in the mountain regions or under the conditions of billowy relief, it is necessary to pay special attention to the influence of surface or underground relief on the intensity forming. It is necessary to continue the investigations in order to obtain statistically proved ratio for the calculation of intensity increment, caused by relief.

## **3.5. Seismic microzonation of Vladikavkaz city**

54 Earthquake Engineering

The analysis of the experimental data shows that intensity increment can vary at that

Finally, let's try to assess the amplification of vibrational amplitude, which is caused by

The algorithm for the calculation of seismic reaction of soil thickness for the twodimensional model was developed for this purpose (fig. 15) (Zaalishvili, 2009). The results of the executed earliear investigations were used for the program testing (Puchkov, Garagozov, 1973). Mountain structure had the form of frustum of a cone with the height 30 m and slope angle of the generatrix 30º. The element maximum size was equal to 5 m, Swave propagation velocity was 300 m/s, the density 1800 kg/m3. The seismic influence was applied to the foundation of soil thickness in the form of instrumental accelerogram,

It was determined that the vibrational amplitude considerably chances with the relief. The given dependence at that is various for the displacements, velocities and accelerations. The largest value of the amplification is observed for displacements and the maximum ratio of vibrational amplitudes, for example, in the point C to the point A, is 2.1 and for the point D – 3.2. It well satisfies the results of experimental observations where the ratio in the point C for the S-wave is equal to 2.3 and in the spectral region the maximum values are 1.8 (at T = 0.4 s) and 3.2 (at T = 0.7 s) for P- and S-waves accordingly. Spectral analysis also shows the resonance increase of vibrational amplitudes in the top part of the slope on the

**Figure 16.** Final elements analysis (FEA) application example: a) Variation of amplitudes of displacement, velocity and acceleration along surface; b) calculational model; c) seismograms,

Considerably fewer investigations are dedicated to the influence of the underground relief on the intensity. On the data of B.A.Trifonov (1979) the underground and buried topography of the rocks influences on seismic vibrations intensity, if the surface slope exceeds 0.3. At the vee couch of the rocks, which are covered by sedimentary thickness, the ratio between wave length and the sizes of vee stripping influences on seismic intensity

independently of the type of rocks, from 0 to 1.5 degree.

modeling the vertically propagating SH wave.

frequency 1.6 Hz (i.e. T=0.6 s).

calculated in points A, B, C, D.

relief, with the help of the calculation method of FEM (Zaalishvili, 2006).

If we consider 5% DSZ map as basis for seismic microzonation so seismic intensity of 8 corresponds to etalon grounds for whole territory.

Then, maps of seismic microzonation of cities must be created. According to the above mentioned maps of detailed zoning the maps of seismic microzonation with probability 1%, 2%, 5% or 10 %, correspondingly, were made up.

Though, that definitions of the word «zoning» are similar, actually they are quite different in essence. Unlike the maps of detailed seismic zoning, which give seismic potential (Mmax) and source features, the maps of seismic microzonation give assessments of soil condition influence (sands, rocks, pebbles, clays etc., their combination; watering; relief (as underground as surface); spectral distribution of incoming wave; predominant vibration frequencies on city square etc.) on forming of future earthquake intensity. As a rule, the scale of such maps is 1:10 000, in order to have the opportunity of taking them into account at building. Maps can be more detailed (1:5000 etc.) but this makes no sense as the type and physical condition of soils in space on the territory site can change fast. The most important thing is to assess intensity of possible earthquakes on areas with typical soil conditions for city territory.

Maps of seismic microzonation can be made up for the certain territories (cities and settlements, as a rule). It is impossible to make them up in entire format because of the necessity of geological conditions knowledge on larger territories, which are mostly not built up. We often don't have such data even for the modern cities! It's practically impossible because the resources will be lost for nothing! And absurdity! In the other words there is no the microzonation map even for the territory of North Ossetia let alone the whole Northern Caucasus.

Maps of seismic microzonation do not only show the place of earthquake-proof building up, but they also show on what intensity this or that building must be calculated and designed: on 6, 7, 8 or 9 points. And sometimes even on 10 points (for very soft grounds!). And this suggests investments of different financing for the realization of antiseismic measures (thicker armature, more connections etc.). Seismic risk can considerably be reduced at building-up zones with 7, 8 and 9 point of the calculated intensity by adequate site development on the territory of city, for example, as social losses will be minimal, though buildings will be damaged in this or that extent.

In the next stage we should carry out SMZ. It should be noted that as a basis the maps of different probability of exceedance will be used and as the initial intensity, the value of which corresponds directly to the intensity of the sites, composed by average soils or characterized by average soil conditions and, therefore, the maps will be referred to the 7, 8 or 9 points (and similarly for acceleration). The zones, composed by clay soils of fluid consistency, which can be characterized by liquefaction at quite strong influences, are marked by the index 9\*. Intensity calculation here supposes the usage of special approaches in the form of direct taking soil nonlinearity into account (Zaalishvili, 2000). The usage of relevant methods and techniques of SMZ will allow to obtain the correspondent maps of SMZ.

Assessment of Seismic Hazard of Territory 57

It must be noted that usage of the maps with high time exposition i.e. maximal magnitude (maximal intensity) for given territory (for return period of 50 years and exceedance probability 2% or 1%) physical nonlinearity of soils necessarily must be taken into account

Unlike small-scale М 1:8 000 000 seismic hazard map of the territory of Russia (GSZ) maps of DSZ in scale 1:200 000 allow taking into account features of specific seismic sources (faults) directly. But the main thing is that such scale zoning is suitable for quite large territories. So it's seen that alignment of faults of different constituent entities of the Russian

Analysis and consequent account of initial accelerograms transformation will become the basis for site effect analysis at strong seismic loadings (fig. 17) (Zaalishvili et al., 2010).

Methods of such modeling are based on accordance of spectral properties of modeled and real earthquake. In a whole modeling accuracy depending on the purposes of total motion usage and what characteristics defining structural system behavior must be

**Figure 18.** Synthetical accelerograms for different source locations: a – western part of fault; Sb – middle part of fault; c – eastern part of fault; d – scheme of sources of scenarios earthquakes

Earthquake source that is a region of rupture can be considered as point source only for much larger distances than fault size. At close distances effects of finite fault size become more significant. Those phenomena are mainly connected with finite rupture velocity,

with the help of developed tools (Zaalishvili, 2009).

reproduced.

Federation of Northern Caucasus make a good sense (fig.7).

**4. Specified seismic fault and design seismic motion** 

Thus for maps with probability of exceedance 1%, 2%, 5% and 10% one can obtain corresponding maps of SMZ with probability of exceedance 1%, 2%, 5% and 10%, i.e. probabilistic maps of SMZ (Fig. 16).

For each of the zoning subject the probabilistic map of the seismic microzonation with location of different calculated intensity (7, 8, 9, 9\*) zones is developed (the zones, composed by clay soils of fluid consistency, which can be characterized by liquefaction at quite strong influences, are marked by the index 9\*). The maps in accelerations units show the similar results.

**Figure 17.** The maps of seismic intensity microzonation for probabilities of 5% (a) and 2% (b) for the central part of Vladikavkaz city territory (Zaalishvili et al., 2010).

Such maps of SMZ except of mentioned developments are also based on materials of local network of seismic observations "Vladikavkaz". Network was organized for the first time on the urbanized territory of the Northern Caucasus in July 2004. Stations are located on the sites with different typical for the city soils (clays of medium-hard and liquid consistence, gravels with filling material of less than 30% and more than 30%, and their assembly).

It must be noted that usage of the maps with high time exposition i.e. maximal magnitude (maximal intensity) for given territory (for return period of 50 years and exceedance probability 2% or 1%) physical nonlinearity of soils necessarily must be taken into account with the help of developed tools (Zaalishvili, 2009).

Unlike small-scale М 1:8 000 000 seismic hazard map of the territory of Russia (GSZ) maps of DSZ in scale 1:200 000 allow taking into account features of specific seismic sources (faults) directly. But the main thing is that such scale zoning is suitable for quite large territories. So it's seen that alignment of faults of different constituent entities of the Russian Federation of Northern Caucasus make a good sense (fig.7).

### **4. Specified seismic fault and design seismic motion**

56 Earthquake Engineering

SMZ.

probabilistic maps of SMZ (Fig. 16).

In the next stage we should carry out SMZ. It should be noted that as a basis the maps of different probability of exceedance will be used and as the initial intensity, the value of which corresponds directly to the intensity of the sites, composed by average soils or characterized by average soil conditions and, therefore, the maps will be referred to the 7, 8 or 9 points (and similarly for acceleration). The zones, composed by clay soils of fluid consistency, which can be characterized by liquefaction at quite strong influences, are marked by the index 9\*. Intensity calculation here supposes the usage of special approaches in the form of direct taking soil nonlinearity into account (Zaalishvili, 2000). The usage of relevant methods and techniques of SMZ will allow to obtain the correspondent maps of

Thus for maps with probability of exceedance 1%, 2%, 5% and 10% one can obtain corresponding maps of SMZ with probability of exceedance 1%, 2%, 5% and 10%, i.e.

For each of the zoning subject the probabilistic map of the seismic microzonation with location of different calculated intensity (7, 8, 9, 9\*) zones is developed (the zones, composed by clay soils of fluid consistency, which can be characterized by liquefaction at quite strong influences,

are marked by the index 9\*). The maps in accelerations units show the similar results.

**Figure 17.** The maps of seismic intensity microzonation for probabilities of 5% (a) and 2% (b) for the

a) b)

Such maps of SMZ except of mentioned developments are also based on materials of local network of seismic observations "Vladikavkaz". Network was organized for the first time on the urbanized territory of the Northern Caucasus in July 2004. Stations are located on the sites with different typical for the city soils (clays of medium-hard and liquid consistence, gravels with filling material of less than 30% and more than 30%, and their assembly).

central part of Vladikavkaz city territory (Zaalishvili et al., 2010).

Analysis and consequent account of initial accelerograms transformation will become the basis for site effect analysis at strong seismic loadings (fig. 17) (Zaalishvili et al., 2010).

Methods of such modeling are based on accordance of spectral properties of modeled and real earthquake. In a whole modeling accuracy depending on the purposes of total motion usage and what characteristics defining structural system behavior must be reproduced.

**Figure 18.** Synthetical accelerograms for different source locations: a – western part of fault; Sb – middle part of fault; c – eastern part of fault; d – scheme of sources of scenarios earthquakes

Earthquake source that is a region of rupture can be considered as point source only for much larger distances than fault size. At close distances effects of finite fault size become more significant. Those phenomena are mainly connected with finite rupture velocity, which causes energy radiation of different fault parts in different times and seismic waves are interference and causes directivity effects (Beresnev & Atkinson, 1997, 1998).

Assessment of Seismic Hazard of Territory 59

Usage of maps of detailed seismic zoning in units of accelerations at seismic microzonation level is possible only for calculation method giving results in units of accelerations. Today traditional instrumental method of seismic microzonation does not allow obtaining intensity increments in accelerations due to traditional orientation on macroseismic intensity indexes. The exclusion is the case of investigation of strong earthquakes accelerations when instrumental records are obtained (in presence of accelerometer) (Zaalishvili, 2000). At the

On the other hand in recent years a new instrumental-calculation method was developed (Zaalishvili, 2006). New method is based on selection from database (including about 5000 earthquake records) soil conditions which are the most appropriate to real soil conditions of the investigated site. Then the selection of seismic records with certain parameters or their intervals follows (magnitude, epicentral distance, and source depth). Then maximal amplitudes are recalculated for given epicentral distances. Absorption coefficient can be

Thus, a new complex method of seismic hazard assessment providing probability maps of seismic microzonation, which are the basis of earthquake-proof construction, is introduced.

Considered procedures on the level of possible seismic sources zones exploration, maps of detailed seismic zoning and seismic microzonation may differ from described above. So paleoseismological investigations like «trenching» (Rogozhin, 2007), which allow determining more reasonable the recurrence and other features of seismic events realization

Today, we have conditions for detailed seismic zoning maps development like the above mentioned but for all the territory of the Northern Caucasus on basis of the modern achievements of engineering seismology. It will give us a possibility to develop probabilistic maps of seismic microzonation with the help of powerful nonexplosive sources, methods

Thus algorithm of seismic hazard assessment of the territory taking into account multiple factors forming seismic intensity was considered. Forms of typical seismic loadings for firm soils are given, which will be changed from site to site in dependence of differences in ground

Aptikaev, F.F. et al. (1986) Methodological recommendations on detailed seismic zoning. *Questions of engineering seismology*. Issue 27. Moscow, 1986. 184-212. (in Russian)

conditions (engineering-geological, geomorphological and gidrogeological conditions)

Undoubtedly such approach significantly increases physical validity of final results.

taking into account physical soils nonlinearity (Zaalishvili, 2009).

*Center of Geophysical Investigations of RAS, Russian Federation* 

same time investigations are conducted and the problem supposed to be solved.

calculated by attenuation model for given region.

are also possible when it is necessary.

**Author details** 

V. B. Zaalishvili

**5. References** 

Let's compare amplitude spectra of obtained design accelerograms with spectrum of real earthquake from considered fault. Data analysis (fig. 18 and fig. 19) shows that spectra of calculated and real earthquakes in a whole are similar in their main parameters.

It must be noted that spectrum of vertical component of real earthquake is closer to design spectra. The last fact is quite obvious and is explained by proximity to earthquake source. Indeed, close earthquakes in general are characterized by predomination of vertical component. Record of TEA station (located in theater) was selected due to its location on dense gravel and has a minimal distortions caused by soil conditions.

Analysis of spectrum of weak earthquake shows that peaks are observed on 1.3 and 5.6 Hz (Fig. 18). In spectra of synthesize accelerograms mentioned amplitudes are also observed. At the same time medium response on strong earthquake, undoubtedly, differ from weak earthquake response (Fig. 19) (Zaalishvili, 2000).

**Figure 19.** Spectra of design accelerograms at different source locations of earthquake М=7,1: 1 – western part of fault; 2 – middle part of fault; 3 – eastern part of fault

**Figure 20.** Spectra of accelerograms of weak earthquake with epicenter in the zone of Vladikavkaz fault. (25.08.2005 10:25 GMT, H = 8 km M= 2.5).

Usage of maps of detailed seismic zoning in units of accelerations at seismic microzonation level is possible only for calculation method giving results in units of accelerations. Today traditional instrumental method of seismic microzonation does not allow obtaining intensity increments in accelerations due to traditional orientation on macroseismic intensity indexes. The exclusion is the case of investigation of strong earthquakes accelerations when instrumental records are obtained (in presence of accelerometer) (Zaalishvili, 2000). At the same time investigations are conducted and the problem supposed to be solved.

On the other hand in recent years a new instrumental-calculation method was developed (Zaalishvili, 2006). New method is based on selection from database (including about 5000 earthquake records) soil conditions which are the most appropriate to real soil conditions of the investigated site. Then the selection of seismic records with certain parameters or their intervals follows (magnitude, epicentral distance, and source depth). Then maximal amplitudes are recalculated for given epicentral distances. Absorption coefficient can be calculated by attenuation model for given region.

Thus, a new complex method of seismic hazard assessment providing probability maps of seismic microzonation, which are the basis of earthquake-proof construction, is introduced. Undoubtedly such approach significantly increases physical validity of final results.

Considered procedures on the level of possible seismic sources zones exploration, maps of detailed seismic zoning and seismic microzonation may differ from described above. So paleoseismological investigations like «trenching» (Rogozhin, 2007), which allow determining more reasonable the recurrence and other features of seismic events realization are also possible when it is necessary.

Today, we have conditions for detailed seismic zoning maps development like the above mentioned but for all the territory of the Northern Caucasus on basis of the modern achievements of engineering seismology. It will give us a possibility to develop probabilistic maps of seismic microzonation with the help of powerful nonexplosive sources, methods taking into account physical soils nonlinearity (Zaalishvili, 2009).

Thus algorithm of seismic hazard assessment of the territory taking into account multiple factors forming seismic intensity was considered. Forms of typical seismic loadings for firm soils are given, which will be changed from site to site in dependence of differences in ground conditions (engineering-geological, geomorphological and gidrogeological conditions)
