The earthquake motion at a given point on the surface is commonly represented by elastic response spectra. Seismic codes, however, do not distinguish between ground motion in a county side or within an urban environment. The traditional elastic response spectra are a function of seismological, geological, and geotechnical parameters and they are based on the prediction of the free-field motion at the ground surface, hence, by considering the propagation of the seismic waves in the soil deposit neglecting the presence of nearby buildings. During an earthquake a vibrating structure emanates waves travelling through the ground over large distances that modifies significantly the energy of the free-field seismic waves resulting in decrements of the ground motion energy in some areas and increments in others. In the urban environment, the vibrating buildings generate the occurrence of multiple interactions that are generally referred to as seismic site-city interaction.

This paper presents a first attempt to quantify the impact of the urban environment on the commonly used elastic response spectrum defined at the free-field. A stochastic ground motion analytical model, able to capture the influence of the radiated wave field into the free field ground motion, is developed to determine novel elastic response spectra for urban areas. The proposed approach is verified through a pertinent Monte Carlo study. Moreover, a numerical model of a cluster of buildings is used to analyse the effect of the radiated waves from the ensemble of vibrating structures on the surrounding soil. Comparisons between the proposed and conventional elastic response spectra are carried out at selected locations. Remarkably, this paper shows the limitations of the traditionally used elastic response spectrum that might lead to an underestimation or overestimation of the seismic response of structures in the urban environment. Therefore, the proposed approach presents a promising strategy to predict accurately the seismic response in urban areas offering potential modifications to the current seismic code prescriptions.

表面上给定点的地震运动通常由弹性响应谱表示。但是，地震法规并没有区分县城或城市环境中的地面运动。传统的弹性响应谱是地震学，地质学和岩土学参数的函数，并且它们基于对地面自由场运动的预测，因此，考虑到地震波在土壤沉积物中的传播而忽略了附近建筑物的存在。在地震期间，振动结构会散发出长距离穿越地面的波，从而显着改变自由场地震波的能量，从而导致某些区域的地面运动能量减少，而另一些区域的能量增加。在城市环境中

本文提出了首次尝试，以量化城市环境对自由场定义的常用弹性响应谱的影响。建立了能够捕获辐射波场对自由场地震动影响的随机地震动分析模型，以确定城市地区的新型弹性响应谱。通过相关的蒙特卡洛研究验证了所提出的方法。此外，使用建筑物群的数值模型来分析来自振动结构集合的辐射波对周围土壤的影响。建议的弹性响应谱和常规的弹性响应谱在选定位置进行比较。值得注意的是 本文显示了传统使用的弹性响应谱的局限性，可能会导致低估或高估城市环境中结构的地震响应。因此，所提出的方法提出了一种有希望的策略，可以准确地预测城市地区的地震响应，从而对当前的地震规范进行潜在的修改。