摘要
大跨度桥梁作为重要的公共设施,其安全性格外重要。如何在设计和建造阶段就使它们具有足够的抗震能力以及合理的安全度,一直是国内外学术界和工程界关注的重要课题。几十年来,桥梁的抗震研究取得了很大成果,但由于抗震问题的多样性和复杂性,尚有许多问题需要进一步研究。其中,结构动力学的随机理论在桥梁抗震中的应用就是近年来桥梁工程中研究的热点问题。论文就这一问题进行了研究,主要内容有:
(1)修正了《与规范反应谱相对应的金井清谱的谱参数》一文中求解绝对加速度反应方差积分的解析表达式中公式(13)的缺点,推导了地震激励为白噪声时,绝对加速度反应标准差σ_0(ω_c,ξ)的解析表达式。
(2)在桥梁抗震分析中,运用质量弹簧阻尼模型来模拟桩-土-结构的动力相互作用,分析了考虑桩-土作用与否对桥梁地震响应的影响。
(3)基于随机振动理论及反应谱方法,研究了大跨度桥梁的行波效应、相干效应及局部场地效应影响,并与规范反应谱方法计算结果进行了分析比较。结果表明:不计地震动空间变化时,随机振动分析与反应谱方法本质上是一致的;行波效应和相干损失对连续刚构内力有一定影响,多数情况下,随机振动计算结果要大于反应谱分析结果;局部场地效应对结构响应的影响相当大,对于基础地质条件差异较大的桥梁,分析时应当考虑局部场地效应。
(4)结构参数和地震激励的随机性是桥梁抗震分析中较为重要的问题。在随机有限元中引入虚拟激励法,推导了有随机参数的结构在平稳随机地面加速度作用下的随机有限元递推方程。按局部平均理论和空间杆系分离随机场模型来离散、建立有限元模型,并利用矩阵正交化技术,减少计算量。然后求解随机有限元零阶、一阶和二阶递推方程组,即可求出具有二阶精度的均值和具有一阶精度的方差的结构响应。运用程序开发工具C++Builder编制了相应的计算程序,并用Monte Carlo检验了程序的有效性和正确性,最后,计算了具有随机参数的高墩大跨连续刚构桥梁和新式钢箱提篮拱桥在随机地震激励下的动力响应。
(5)根据交变荷载作用下弹塑性有限元的基本理论,运用增量初应力方法,采用Jhansale模型描述材料的瞬态应力应变关系,推导了随机交变荷载作用下的弹塑性有限元迭代列式。依据随机疲劳寿命分析的基本原理,运用局部应力-应变法和疲劳累积损伤的Palmgren-Miner理论,结合随机加载下的弹塑性有限元方法,提出了一种估算桥梁构件在交变的地震荷载作用下随机疲劳寿命的估算方法,研究了大跨度钢拱桥有孔洞或截面受削弱的构件在地震激励下的低周疲劳寿命。
(6)考虑结构参数随机性的动力可靠度是桥梁抗震研究中的重要问题。基于随机分析的响应面理论和规范反应谱方法,提出了一种分析具有随机结构参数桥梁抗震可靠度的方法。通过拟合的多项式函数来近似替代表示结构随机输入与输出变量之间作用关系的功能函数,按照结构的破坏准则及其极限状态方程,进行可靠度分析。运用该方法研究了高墩大跨连续刚构桥在地震激励下设计基准期内的动力可靠度,分析时考虑了结构参数和场地土的随机性,分别计算了连续刚构在多遇地震、设防地震和罕遇地震作用下的失效概率,得到了结构在设计基准期内,“三水准设防标准”条件下的地震可靠度。结果表明,该桥设计满足抗震规范要求。
As the important communal constructions, security of the long-span bridges is very crucial to their builders. How to make them have the enough aseismatic ability and the reasonable traffic safety during their constructional period is the important problems paid a lot of attention to by the domestic and the oversea scholars and engineers all the while. In the few past decades, researches for bridges' seismic responses have obtained a large number of achievements. But because of the variety and the complexity of the bridges' seismic problems, there are a lot of problems need farther investigations yet. In all the problems, the stochastic theory of dynamics of structural applications to bridge earthquake engineering is the hotspot recently in bridge's constructions. Therefore, the problem is studied in this doctoral dissertation and the main research works are as follows:
(1) The equation 13 used to solve the integral of absolute values of the response variance of accelerations in spectral parameters of Kanai-Yajimi spectrum in accordance with response spectral method of code written by Sun Jing-jiang and Jiang Jin-ren is corrected. The analytical expression of the response standard deviation of acceleration was developed on condition that the seismic excitation was the white sound.
(2) Using mass-spring-damp model to simulate the dynamic interactions of the pile-base-structure in seismic analysis of bridge, the impacts on seismic response of bridge, whether or not take the pile-base co-action into account, were studied.
(3) Based on theory of random vibration and response spectral method, the wave propagation effect, the coherence loss, and the site conditions of the bases of the long-span bridges are investigated. The conclusions show that: analysis of random vibration is in accord with the response spectrum method excluding the spatial variation effect of the seismic action; second, the wave propagation effect and the coherence loss would surely change the internal forces of the continuous rigid frame-beam bridges and the computed conclusions by random vibration are greater than by response spectrum in most circumstance; third, the large differences of the site conditions of the bases significantly change the response of the continuous rigid frame-beam bridges, which should be included in the seismic design of the bridges.
(4) Random of the structural parameters and seismic excitation is very important to the seismic design of the bridge. The perturbation equations were developed by combining the SFEM with the pseudo-excitation method. Based on theory of local average random fields and spatial structure member model, the FEM model of the long-span bridge with random parameters and subjected to random seismic excitation was meshed. In order to improve the computed speed, the matrices orthogonal transform technique was applied. The means with second-order precision and the variances with first-order precision of the structural responses could be obtained by solving the zeroth-order, first-order and second-order perturbation equations. A computer program is developed by C++builder, and its correctness and validity is verified by Monte Carlo method. As a sample, the dynamic response of a high-piers and long-span rigid frame bridge and a new type basket-handle arch with random parameters and subjected to random seismic excitation is computed.
(5) Employing basic theory of elastic-plastic FEM under cyclic loading and incremental prestressed method, the iterative formulas of elastoplastic FEM under random loading method were deduced. According to theory of random fatigue life, local stress-strain method, Palmgren-Miner's rule for fatigue damage accumulation and the elastoplastic FEM under random loading, an algorithm for bridge component's stochastic fatigue life was proposed. The low-cycle fatigue life of the component of the long-span steel bridge which has hole or across section is weakened under seismic excitation was studied.
(6) Dynamic reliability of the structures with random parameters is very important to the anti-seismic design of the bridge. Based on theory of the response surface of random vibration and response spectral method, an algorithm for the seismic reliability analysis of the structure with random parameters is proposed in this paper. The response surfaces generally take a approximate polynomial form to replace the function which denotes the relationships of the input random parameters and the output parameters. The reliabilities are studied according to structural failure criterions and the equations under their limit states. The anti-seismic reliabilities of the high-piers and long-span rigid frame subjected to seismic excitation in its design basic period are studied by this method. The random of the structure parameters and the site condition of this bridge are taken into account when it's failure seismic reliabilities are computed respectively at the low-level earthquake, design earthquake and high-level earthquake. According to the "three-level seismic fortification criterion" in the code for seismic design of bridge, the seismic reliabilities of the bridge are calculated in their design basic period. The conclusion shows that the design of this bridge meets the demands of the seismic code.
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