Chapter 2

The Definition of Seismic Actions

Seismic actions are calculated according to two schemes: the relevant different schemes of definition and seismic hazard.

Scheme 1. When setting seismological terms of two parameters, macro seismic intensity, I, and the average interval, TI, between earthquakes of this intensity, the calculation is reduced to the construction of seismic effects on the basis of statistical generalization of the available instrumental data, classified according to macro seismic intensity and, sometimes, categories of soil (p.2.1). The results obtained relate to conventional flat ground with a uniform basis. The influence of local geological conditions and terrain is taken into account in seismic zoning and is specified by the recommendations of Chapter 3.

Scheme 2. In this scheme, the risk assessment begins with the recognition provisions of the possible foci of strong earthquakes (p.2.2). With fixed parameters recognized by earthquake forecast, impact is carried out on the basis of the model (physical or numerical) solutions of the problem of fluctuations, the surface of half-space under the action of evolving dislocation, shear simulating the earthquake (p.2.3, p.2.4), or on the basis of statistical data about the connection parameters of the ground motion parameters of the hearth and hypocentral distance (p. 2.5).

Scheme 1 is carried out at all stages of design for facilities of all categories of responsibility.

Scheme 2 is performed for installations of category I and II stages of technical and/or detailed design in areas with possible macro seismic intensity not lower than seven points MSK. Description form or parameterization seismic effects should be selected based on specific calculation schemes used for evaluation of seismic stability of constructions or structures.

This seismic action can be specified by the following parameters:

Source seismological and geological characteristics of the area, presented in the manner and to the extent, are dependent on the schema of job impacts. These data depend on the extent of the study area, stage design, and penalties of the object.

The minimum information can be obtained from the map of seismic zoning, the evaluation of possible intensity earthquakes (usually in points MSK, MM or JMA), and the average interval between earthquakes of this intensity on medium soils. Also, you must know the category of soil foundation objects (loose, medium, or hard) and conditions of flooding.

To clarify, seismic effects can be used with the following additional seismological and geological data [132]:

Special attention should be paid to the detection of gravitational and hydrogeological anomalies. Gravitational anomalies are important as a possible indication of the location of the superdense matter and space origin [15]. The collapse of such substances is accompanied by a powerful impulse and can trigger an earthquake. Hydrogeological anomalies can form a zone of reduced normal stress in the soil skeleton and, therefore, increased risk of shear deformations.

2.1 The Probability of Loads During the Earthquake of a Given Intensity

The probability PI (a,T) of no excess exposure "a", for a fixed period of time T, during the implementation of earthquakes with intensity I, is calculated by the total probability formula [83]:

(2.1)

Here, P0(a|N) is the conditional probability of the exceeding level of exposure to "a" with N earthquakes with a given intensity, I. PN(T) is the probability of N earthquakes during the time, T. If, the probability to take effect in various earthquakes in the same area are statistically independent, then the conditional probability, P0(a|N), can be expressed through the probability distribution function F(z) defined parameters influence "z":

(2.2)

From the system of equations (2.1) and (2.2) for a given value of the probability, PI, (for example, fifty or ninety-five percent) and period, T, (for example, one hundred or one thousand years) with a known PN(T) and F(z) is estimated security impact

p(a) = 1 - F(a)

in the ensemble effects of given intensity and it is estimated exposure level, "a", is at a fixed intensity of earthquakes.

The probability, PN(T), is a characteristic of the seismic regime of a particular region and specified seismological research. In the absence of specific data for PN(T), use the Poisson law:

(2.3)

where T0 is the average interval between earthquakes and considered intensity from equations (2.1) through (2.3) is obtained

(2.4)

(2.5)

Knowing the value of p at a known distribution function, F(z)=1 - p(z), we find the estimated level of exposure to a:

(2.6)

Here, F-1 is the inverse function to the function F(z), different for different exposure parameters.

The function of a probability distribution, F(z), is based on ensembles of data related to the earthquake of the same intensity for a specific region specifically for the impact parameter, which is to be used in the calculation of seismic stability. Of the probability distribution function of the amplitude characteristics of the impact, maximum acceleration, am, spectral acceleration, ac, module or "image" acceleration, Fourier a* at the intensity of earthquakes is not to exceed eight points should logarithmically follow normal law (Figure 2.1) [83].

Figure 2.1 Function of the probability distribution of acceleration of seismic vibrations. 1 - maximum values of acceleration in a seven-point earthquakes [2], 2, 3, 4 spectral accelerations on the period of one second, with a relative damping of five percent in cases of earthquakes with an intensity of Isix, seven, or eight points MSK [115], 5 - the module of the Fourier spectrum for the period of one second with seven-point earthquakes [84, 116]. n is the number of data processed in the ensemble. Line - lognormal law.

For very strong earthquakes (I > 8), the probability distribution function, F(z), is close to the normal law of Gauss.

Figure 2.2 shows a graph of the solution of equation 2.6, which has the same fork (line 1) for the normal and lognormal distributions using different scales (I and II, respectively) [83].

Figure 2.2 The estimated level of impact depending on the average number of earthquakes in the period under review and the probability of absence of...