Keywords: synthesis, spatial variability, earthquake ground motion, spectrum-compatible displacements, site-amplification, baseline correction.

The elegance and economic competitiveness of cable-stayed bridges favours the use of these solutions in a wide variety of situations and spans, ranging from small urban bridges until long span bridges like Normandie Bridge (France, 856m), Tatara Bridge (Japan, 890m), or Stonecutters Bridge (Hong-Kong). The latter, presently under design stage and to be concluded up to 2007, will become the largest cable-stayed bridge in the world, with a central span of 1018m. However, most bridges of this type have central spans within the range 300-500m.

The remarkable world-spreading in the construction of these structures is a consequence of the continuous scientific and technologic research regarding new materials, erection systems and analysis procedures.

One major concern in the analysis and design of these structures is its behaviour under earthquake loads, in cause of its increasing slenderness and flexibility. The fundamental vibration modes have close low frequencies and, as a consequence, these bridges are not as vulnerable to imposed accelerations, resulting from an earthquake, as they are to the maximum displacement that is originated by the ground motion.

In this context, it's necessary to know how to handle the spatial variability of earthquake ground motion (SVEGM). This problem is a sum of a number of effects: (i) the wave-passage effect, that arises from a finite velocity of seismic waves propagation; (ii) the site-response effect, that is determined by properties of the soil layer; (iii) the incoherence effect, resulting from scattering and differential superposition of waves in heterogeneous medium of the ground. Given the assumption of the same acceleration's auto power spectral density function (APSDF) in all supports, this effect was not considered in this paper. It was also assumed that no significant change in frequency contents of APSDF occurs within the distance between the piers. The first component depends directly on the distance and inversely on propagation's velocity. In fact, each wave component, Primary, Secondary, Rayleigh and Love has its own velocity, but for far-field analysis an apparent constant velocity it usually assumed. The site amplification is modeled by a vertical propagation of seismic waves through the soil. The necessary parameters to characterize the amplification are: height of layer, damping coefficient, shear wave velocity; impedance constant. The Figure 1 illustrates the basic approach for handling with SVEGM.

In order to perform a dynamic analysis in the time domain, the seismic load with spatial variability must be defined by a series of displacements records. Such functions must be artificially synthesized, because a large database of actual accelerograms for the local of structure's implementation is not usually available. The information concerning the synthesis of strong ground motion is, most commonly, described by means of accelerations. The case under study, however, requires the evaluation of displacements. One problem arising in that transformation is the baseline correction. Two methods proposed in bibliography are reviewed in this paper. Another question is how to generate correlated displacements that simulate SVEGM. Those functions must be consistent with respect to the response spectrum, which is the usual way to define the seismic load.

In this paper, the following approach for this problem is proposed: (i) estimate the auto power spectral density function of acceleration by using the standard response spectrum which defines the seismic action; (ii) generate one record of stationary stochastic process that was defined by APSDF; (iii) modulate that realization with a intensity function that simulates the non-uniformity in time of ground motion; (iv) perform a baseline correction; (v) integrate the accelerogram to obtain displacements. The correlated movements are realized with records of stationary process. The vertical shear waves propagation is similar to shear building and is modeled in frequency domain.

A numeric example is used to illustrate this method. A cable-stayed bridge with a longitudinal unrestrained deck is analyzed under the affect of an earthquake. For such design, the first vibration mode has the higher contribution. Therefore, a simple structure with a single degree of freedom may adequately represent the longitudinal displacement of the bridge. This assumption is confirmed by the results of a global model of the bridge. With this simplification it is possible to illustrate the influence of some parameters in the proposed method.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)