تجزیه و تحلیل حساسیت از اثرات سایت بر روی طیف های واکنش از خطوط لوله

In this paper, a numerical sensitivity analysis of the site effect on dynamic response of pipelines embedded in some idealised soil deposits resting on a halfspace covering a wide range of soil profiles encountered in practice and subjected to vertically propagating shear waves, is presented. The power spectrum of the lateral differential displacement between two distant points due to the site effect is formulated analytically by using an analytical amplification function of a viscoelastic inhomogenous soil profile overlying either a compliant halfspace or a bedrock, represented by a more realistic continuous model. Also, Kanai-Tajimi spectrum parameters are estimated and expressed analytically from the soil profile model. Finally, results in the form of stochastic response spectrum of pipelines, for different key soil and pipeline parameters, are given and discussed.

An important aspect of earthquake loads acting on extended structures such as pipelines, is the spatial variability of the seismic motion which can be affected significantly by the unpredictable path of seismic waves generated from an extended source (incoherence effect), the difference in the arrival times of waves at different ground distant points (wave passage) and the spatial variability of the local soil conditions (site response effect). Hence, a rigorous deterministic approach of the spatial character of the seismic input effects on pipelines gives imprecise results. So, a probabilistic method based on the random vibration theory has been developed for seismic analysis of pipelines subjected to incoherent seismic ground motion [1], [2], [3] and [4]. Most of these studies consider only the contributions of the wave passage and the incoherence effects and in consequence neglect the contributions of the site effects on the stochastic response of pipelines. The aim of this paper is to assess the contribution of the site effect on response spectrum of the lateral differential motion at joints (between the pipe segments of pipelines), for different key soil and pipeline parameters, which is of great importance in the earthquake resistant design of pipelines. In this case, one assumes that the spatial variability of the ground motion is the result of the variability of the local soil conditions. The discrete modified model of Nelson and Weidlinger [3] and [5] (in addition to the translational motions of the pipe segments, the rotations are also considered) representing two rigid pipe segments connected by a joint will be used in the present study to evaluate the lateral differential motion between the pipe segments. The soil–pipeline interaction is taken into account by the impedance functions. The power spectrum of the lateral differential displacement between two supports due to the site effect is expressed analytically using an analytical amplification function of a more realistic continuous viscoelastic inhomogenous soil profile overlying either a compliant halfspace or a bedrock. Finally, the response spectrum of pipelines are obtained for different key soil and pipeline parameters.

A numerical sensitivity analysis of the site effects on dynamic response of pipelines, for different key soil and pipeline parameters, is presented. The power spectrum of the lateral differential displacement between two distant points due to the site response effect is formulated analytically by using an analytical amplification function of a viscoelastic inhomogenous soil profile. Also, Kanai-Tajimi spectrum parameters are estimated and expressed analytically from the soil profile model. The results show that the presence of an inhomogeneity in the soil profile introduce more peaks with important amplitudes in the amplification function and an attenuation in the radiation damping. In the same way, the amplification function exhibits an increase in the oscillations with frequency and an increase in amplitude of the peaks that become narrower when the impedance ratio increases. The Kanai-Tajimi ground damping is affected significantly by the variation of the impedance ratio and the inhomogeneity parameter but its ground frequency is not too affected by the impedance ratio at least for q<0.75 and can be considered, at least in approximate way, decreasing linearly with the inhomogeneity parameter varying between 0 and 1. In addition, the response spectra decrease with increasing of both damping and joint stiffness, as expected. In addition, the strongest site effects can be observed when the soft soil is present (firm-soft and medium-soft soil configurations). Finally, the site effect is important and should be taken into account in earthquake resistant design. Indeed, the spatial variability of the mechanical and physical properties of soil produce an important differential displacement depending on the soil configurations and the natural frequency of the rigid body of the soil–pipeline system.