In the solution of the semi-
infinite
elastic medium for a point load excitation of the soil surface, an
infinite
integral appears. In order to evaluate the resoonse, the value of this
infinite
integral must be obtained. The method to transform this
infinite
integral to a finite integral has been already reported in the case of no internal damping of the soil. In this paper, a same kind of method is introduced to transform the
infinite
integral to finite integral considering internal damping of the soil. In this method, an adequate complex function corresponding to the integrand is adopted and an identical equation which involves the
infinite
integral is obtained based on Cauchy's theorem. Using this identical equation, the
infinite
integral in the original solution can be teplaced by the finite integral. This method is very useful by the following reasons. 1) If the numerical integral procedure is applied directly to the
infinite
integral, it is impossible to execute it to
infinite
range. It must be stopped at a suitable range. In this case, a cut off error is produced. But when the numerical integral procedure is applied after transforming the
infinite
integral to finite integral, this cut off error is not produces. 2) There is the Rayleigh oole near or on the contour of the
infinite
integral. Near the pole, the integrand falls into ill condition for a numerical integration and special procedure is required especially in the case of small or zero internal damping of soil. But this pole does not exist near the contour of the transformed finite integral and there is no difficulty in the numerical integral process. 3)The range of numerical integral is very short. It is only from 0 to 1.
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