覆水和隧道效应的凸形场地 P₁ 波差动模拟及横跨桥梁非线性反应

Simulation of P ₁-waves multi-support seismic motions for seawater convex topography site with buried tunnel and nonlinear response of long-span bridge

摘要

开展了 P₁ 波入射上覆水下埋隧道凸形场地的地震差动模拟，并详细研究其对一横跨桥梁非线性反应的影响。首先，推导得到场地的 P₁ 波理论解并获得自功率谱，引入覆水相干模型并与自功率谱联立获得互功率谱，同时联合传递函数，成功构造出地下功率谱矩阵，进而实现了多点地震动模拟并给予合理性验证。然后，详细讨论了隧道埋深及覆水相干效应分别对地震动的影响。最后，将场地激发的地震动视作“自由场”，把程序计算得到的等效节点力直接输入到“边界-土-刚构桥”有限元体系，进行地震差动激励下结构的非线性响应分析。结果表明：①浅埋隧道情形下的地下多点地震动幅值均大于深埋隧道；②当隧道埋深增加，桥梁位移及内力响应峰值下降；③与传统相干模型相比，覆水相干模型得到的地震动空间变异性明显增强；④采用覆水相干模型生成的多点地震动激励下桥梁反应峰值响应普遍偏高；⑤采用覆水相干模型的超大地震差动激励下桥梁初始破坏时间点明显提前。

Abstract

This study made multi-support seismic simulations for a saturated half-space with buried tunnel and seawater convex topography with P₁-waves incidence. Effect of the resulting seismic motions was thoroughly investigated on the nonlinear response of a long-span bridge crossing the specific terrain. First，the frequency-domain solution for P₁-waves is theoretically derived to obtain the auto-spectrum. Cross-spectrum is obtained by introducing a water-covered coherent model coupled with the transfer function. Construction of underground power spectral matrix is finally performed for the site，which enables the realization of multi-support seismic motion. Rationality of the resulting seismic motions is further validated. Then a detailed discussion is conducted about the effects of tunnel burial depth and coherent functions on seismic characteristics. Finally，the generated seismic motions are regarded as “free field input” and directly applied into the system of “artificial boundary-soil-constitutive finite element model” in the form of equivalent nodal forces. Nonlinear response analysis of the continuous rigid-frame bridge subjected to underground multi-support motions is further made. Results indicate that:①Amplitude of underground multi-support seismic motion for shallow-buried tunnels exceeds that for deep-buried tunnels. ②With the increasing tunnel depth，the peak internal force response of the bridge decreases. ③Spatial variability of seismic motions obtained from the water-covered coherent model is significantly enhanced compared to the traditional one. ④Under seismic excitation generated by the water-covered coherent model，the peak response of the bridge generally surpasses that obtained from the traditional one. ⑤Under the excitation of multi-support rare earthquakes using the water-covered coherent model，the initial failure time of the bridge is significantly advanced.

关键词

桥梁工程 / P₁ 波散射 / 地震差动输入 / 隧道效应 / 非线性响应

Key words

bridge engineering / P₁-waves scattering / input of spatially variable seismic motion / buried tunnel's effect / nonlinear response analysis

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基金资助

国家自然科学基金资助项目(51978461)