To) Determination of the area of seismic influence that affects to the emplazamiento in which goes to evaluate the dangerousness.
b) Move to the point, by means of the corresponding laws of mitigation of any one of the parameters of the movement of the soil, the effects on the terrain, of all the earthquakes occurred in the area of influence during the period of time considered.
c) Once determined the random variable Andthat defines us the movement of the soil, apply to this the corresponding function of distribution of extreme values that it was more representative of the sample, which will mean us the probability that the movement of the soil in the emplazamiento do not exceed a determinate level fixed ' and ' whose functional expression is:
Where fx(x) is the function of density of the probability. If we wished to determine the seismic dangerousness in an interval of time T, the previous expression has to be used jointly to a stochastic model of occurrence of earthquakes in the time, whose functional expression is:
Where PS, seismic dangerousness in the emplazamiento, represents the probability of superación of the level fixed 'and' in an interval of clear-cut time T.
MODEL PROBABILISTICO ZONIFICADO
It is the most generalised procedure for the calculation of the seismic dangerousness, consider that the seismic region that surrounds the place of interest is integrated by n potential seismic sources. With νi denotes the half proportion of occurrences of earthquakes of the source i, with equal or upper magnitudes tom 0, in where m0 represents the minimum threshold of magnitude of earthquakes of interest for the calculation of the seismic dangerousness. The half proportion of total occurrence ν on the place is:
By what, for an earthquake given, the probability And to exceed the level of intensity and, in the place considered, comes given by the expression:
Where fx(x) is the conjoint function of density of probability of X and the integration effect on all the values X=x. For the case, in that And only depend of the distance to the focus and of the size of the earthquake, the equation purchases a remarkable simplification and can express eat:
For the calculation of this expression, have proposed diverse methods. Formal solutions adjusted, can obtain when we assumed simplifications in the formula, as for example, in the method of Cornell (1986), in which because of the modelling of the source of earthquakes, as a point, the distance R is independent of the size M, and of here that the equation remain reduced to his version simplified, given by the following equation:
This equation resolve to obtain directly the function acumulativa of density of And, and thus the calculation of probability of excedencia is analytical.
To calculate the seismic dangerousness during a specific interval of time T, the before distinguished probability has to use beside a stochastic model of occurrence of earthquakes in the time. For example, if it applies the model of Poisson, the more frequently used by his simplicity and adaptability to the data, obtain the following expression:
In which the approximation is valid only for small values of vTP(And>and).
The period of return associated to the level of intensity and is:
Maps of results
Of the practical application of both models obtains the following maps: