Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.

Approximation approach to the SRM based on root decomposition in the simulation of spatially varying ground motions

The spectral representation method （SRM） is widely used to simulate spatially varying ground motions. This study focuses on the approximation approach to the SRM based on root decomposition, which can improve the efficiency of the simulation. The accuracy of the approximation approach may be affected by three factors： matrix for decomposition, distribution of frequency interpolation nodes and elements for interpolation. The influence of these factors on the accuracy of this approach is examined and the following conclusions are drawn. The SRM based on the root decomposition of the lagged coherency matrix exhibits greater accuracy than the SRM based on the root decomposition of the cross spectral matrix. The equal energy distribution of frequency interpolation nodes proposed in this study is more effective than the counter pith with an equal spacing. Elements for interpolation do not have much of an effect on the accuracy, so interpolation of the elements of the decomposed matrix is recommended because it is less complicated from a computational efficiency perspective.

Running safety assessment of a train traversing a three-tower cable-stayed bridge under spatially varying ground motion

To explore the influence of spatially varying ground motion on the dynamic behavior of a train passing through a three-tower cable-stayed bridge,a 3D train–track–bridge coupled model is established for accurately simulating the train–bridge interaction under earthquake excitation,which is made up of a vehicle model built by multi-body dynamics,a track–bridge finite element model,and a 3D rolling wheel–rail contact model.A conditional simulation method,which takes into consideration the wave passage effect,incoherence effect,and site-response effect,is adopted to simulate the spatially varying ground motion under different soil conditions.The multi-time-step method previously proposed by the authors is also adopted to improve computational efficiency.The dynamic responses of the train running on a three-tower cablestayed bridge are calculated with differing earthquake excitations and train speeds.The results indicate that(1)the earthquake excitation significantly increases the responses of the train–bridge system,but at a design speed,all the running safety indices meet the code requirements;(2)the incoherence and site-response effects should also be considered in the seismic analysis for long-span bridges though there is no fixed pattern for determining their influences;(3)different train speeds that vary the vibration characteristics of the train–bridge system affect the vibration frequencies of the car body and bridge.

The limit properties of spatial coherence of seismic ground motion

The limit properties of spatial coherence of seismic ground motion are studied based on the differential relation between rotation and translation in elastic theory, the results show that the empirical mathematical model of spatial coherence must satisfy some functional characteristics. It is also indicated that the key problem to estimate rotational power spectrum densities is to obtain precisely the two order derivative of spatial coherence.

Simulation of multi-support depth-varying earthquake ground motions within heterogeneous onshore and offshore sites

This paper presents a novel approach to model and simulate the multi-support depth-varying seismic motions（MDSMs） within heterogeneous offshore and onshore sites.Based on 1 D wave propagation theory,the three-dimensional ground motion transfer functions on the surface or within an offshore or onshore site are derived by considering the effects of seawater and porous soils on the propagation of seismic P waves.Moreover,the depth-varying and spatial variation properties of seismic ground motions are considered in the ground motion simulation.Using the obtained transfer functions at any locations within a site,the offshore or onshore depth-varying seismic motions are stochastically simulated based on the spectral representation method（SRM）.The traditional approaches for simulating spatially varying ground motions are improved and extended to generate MDSMs within multiple offshore and onshore sites.The simulation results show that the PSD functions and coherency losses of the generated MDSMs are compatible with respective target values,which fully validates the effectiveness of the proposed simulation method.The synthesized MDSMs can provide strong support for the precise seismic response prediction and performance-based design of both offshore and onshore large-span engineering structures.

A coherency function model of ground motion at base rock corresponding to strike-slip fault

At present, the method to study spatial variation of ground motions is statistic analysis based on dense array re-cords such as SMART-1 array, etc. For lacking of information of ground motions, there is no coherency function model of base rock and different style site. Spatial variation of ground motions in elastic media is analyzed by deterministic method in this paper. Taking elastic half-space model with dislocation source of fault, near-field ground motions are simulated. This model takes strike-slip fault and earth media into account. A coherency func-tion is proposed for base rock site.

A modified method for simulating non-stationary multi-point earthquake ground motion

A spectral-representation-based algorithm is proposed to simulate non-stationary and stochastic processes with evolutionary power,according to a prescribed non-stationary cross-spectral density matrix. Non-stationary multi-point seismic ground motions at different locations on the ground surface are generated for use in engineering applications. First,a modified iterative procedure is used to generate uniformly modulated non-stationary ground motion time histories which are compatible with the prescribed power spectrum. Then,ground motion time histories are modeled as a non-stationary stochastic process with amplitude and frequency modulation. The characteristic frequency and damping ratio of the Clough-Penzien acceleration spectrum are considered as a function of time in order to study the frequency time variation. Finally,two numerical examples are presented to validate the efficiency of the proposed method,and the results show that this method can be effectively applied to the dynamic seismic analysis of long and large scale structures.

Effects of near-fault ground motions on the nonlinear behaviour of reinforced concrete framed buildings

The design provisions of current seismic codes are generally not very accurate for assessing effects of near-fault ground motions on reinforced concrete （r.c.） spatial frames, because only far-fault ground motions are considered in the seismic codes. Strong near-fault earth- quakes are characterized by long-duration （horizontal） pulses and high values of the ratio ~PGA of the peak value of the vertical acceleration, PGAv, to the analogous value of the horizontal acceleration, PGAH, which can become critical for girders and columns. In this work, six- and twelve-storey r.c. spatial frames are designed according to the provisions of the Italian seismic code, considering the horizontal seismic loads acting （besides the gravity loads） alone or in combination with the vertical ones. The non- linear seismic analysis of the test structures is performed using a step-by-step procedure based on a two-parameter implicit integration scheme and an initial stress-like itera- tive procedure. A lumped plasticity model based on the Haar-K^n~m principle is adopted to model the inelastic behaviour of the frame members. For the numerical investigation, five near-fault ground motions with high values of the acceleration ratio C^p6A are considered. Moreover, following recent seismological studies, which allow the extraction of the largest （horizontal） pulse from a near-fault ground motion, five pulse-type （horizontal） ground motions are selected by comparing the original ground motion with the residual motion after the pulse has been extracted. The results of the nonlinear dynamic analysis carried out on the test structures highlighted thathorizontal and vertical components of near-fault ground motions may require additional consideration in the seis- mic codes.

跨断层工程输入地震动模拟及地震响应

为解决跨断层结构输入地震动的问题,揭示其地震响应规律,基于断层物理模型并引入等效脉冲函数,构建考虑地震动空间变化特征的转换矩阵,提出一种高、低频叠加的混合模拟方法,实现断层两侧输入地震动的模拟。首先,依据建立的桥址场地断层模型,采用随机有限断层方法生成目标点位的高频地震动;再由走滑断层两侧地震动的脉冲效应和永久位移的特征,采用不同的等效脉冲模型分别模拟断层平行向和法向的低频脉冲分量,两者在截止频率处采用Butterworth滤波器进行高通和低通滤波,依据场地模型以及走滑断层两侧地震动的空间相干性,建立转换矩阵以模拟其空间变异性,最终将匹配滤波后的高、低频分量在时域叠加得到断层两侧的输入地震动。从时程、频谱以及结构响应三方面验证了模拟结果的合理性。以实际的跨断层悬索桥为研究对象,基于OpenSees建立全桥的三维有限元模型,采用模拟的断层两侧地震动进行动力时程分析。研究结果表明:桥梁跨断层的角度和位置,以及永久位移幅值对跨断层桥梁地震响应有显著影响,较大的残余内力和残余位移是造成跨断层桥梁破坏的重要原因。

融合时频空间特征的土石坝地震易损性分析改进MLP模型研究

针对现有地震易损性分析中采用的峰值加速度、峰值速度等地震动指标未能充分反映地震动复杂的时频空间特征,且现有基于对数空间线性函数关系假设的地震需求模型难以揭示地震动指标与地震响应间复杂非线性关系的问题,提出一种融合时频空间特征的土石坝地震易损性改进多层感知机(Multi Layer Perceptron,MLP)模型。该模型利用胶囊网络(Capsule Network,CapsNet)能够充分捕捉和表征目标特征空间位置分布的优势,从地震动小波时频图中提取反映地震动时频空间分布的深层特征,并以特征拼接的方式与既有特征进行融合,构建地震动融合指标;进一步地,采用树形Parzen优化算法(Tree structured Parzen Estimator,TPE)对MLP的神经元数量、学习率等超参数进行优化,提出基于TPE-MLP的土石坝地震需求模型,以反映地震动融合指标与地震响应间的复杂非线性关系,进而实现土石坝地震易损性的可靠分析。案例分析表明,相比于既有地震动指标,基于地震动时频空间特征融合指标的土石坝地震需求模型的MAE降低了40.5%,表明了所提模型的可靠性和优越性。

空间效应下超长型钢混凝土结构地震响应研究

超长结构空间效应下的地震响应分析是当前抗震研究的热点之一,空间效应对尺寸较小的建筑影响不大,但对平面投影尺度很大的结构地震响应的影响不可忽略。在传统三角级数法合成人工一维地震的基础上采用了三维相干函数矩阵,通过选取合适的模型及相应参数合成考虑空间效应的人工三向地震动。采用了4条自然波及2条人工波对超长型钢混凝土结构进行抗震计算。结果表明:超长结构不适宜仅采用振型分解反应谱法进行地震计算,还需采用地震时程分析法补充计算;与一致激励相比,行波效应会促使构件内力响应两极分化,既能减小整体内力响应,又能增大部分峰值内力,其效果不仅与视波速有关还与激励方向有关,低视波速和长边激励时行波效应加强;与单向激励相比,双向激励下的行波效应影响更复杂,既能改变构件内力响应和主、次动力响应的变化趋势,也能改变不利构件的分布位置;相干效应与行波效应叠加时,会进一步改变构件动力和内力响应。高视波速下相干效应为主导,底层构件内力响应增大。低视波速下行波效应为主导,地震响应呈现两极分化;不利构件的分布不仅与建筑的开洞、设缝及楼层刚度变化等因素有关,还与地震激励方向有关,不利构件沿激励方向有规律地延伸分布。

基于谱元法的近场地震动空间相干性分析

由于专门用于地震动空间相关性研究的台阵强震记录偏少,基于强震记录统计回归的经验模型发展受限,采用谱元程序SPECFEM2D合成了不同震源机制引起的近场强地震动。通过对地震动场模拟结果进行地震动空间相关性分析,着重比较了不同的震中距对地震动空间相关性的影响,给出了不同震中距对应的相干函数,并得到如下结论:基岩地震动的相干性随震中距的增加而降低;震中距小于或等于15 km时的相干系数大于倾滑断层结果,震中距大于15 km时的相干系数小于倾滑断层结果,但均大于走滑断层结果;基于地震动模拟结果得到的相干性高于基于实测记录的统计结果。

On time-step in structural seismic response analysis under ground displacement/acceleration

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

考虑沉积河谷非线性放大效应的空间相关多点地震动模拟

提出了一种考虑土体非线性特性的沉积河谷空间相关多点地震动模拟方法,该方法结合了合理的谱密度函数、相干函数以及考虑土体非线性和场地散射效应的位移幅值比。其中,场地非线性位移幅值比由有限元——间接边界元耦合的等效线性化法计算,并以V形半满河谷模型为例验证了该方法的合理性与可行性。计算结果表明:同线性模型结果相比,考虑土体非线性后,地面运动加速度时程峰值减小,反应谱卓越周期有所延长,且变化幅度与覆盖层厚度有关。覆盖层越厚,变化幅度越大,非线性效果越显著。该文研究可为河谷场地大跨度工程结构抗震设防提供重要方法和科技支撑。

不同地震作用输入模式的跨断层桥梁地震反应分析

大地震在近断层场地产生强烈地震动的同时,还会由于断层错动直接导致基岩甚至上覆土层破裂,在断层两侧产生显著差异性永久位移,造成位于断层附近或跨越断层的工程结构破坏。因此,跨断层桥梁面对的地震作用是断层两侧桥墩处场地的不同地震动,包括存在永久性位移的地震动。本文以垂直跨越走滑断层的多跨简支梁桥为例,基于OpenSees有限元模拟平台建立了桥梁结构的三维计算模型,计算分析了不同地震作用输入模式下桥梁结构的地震反应及其差异。考虑的地震作用模式包括:(1)断层两侧场地的地震作用视为相同的无永久位移的地震动,即无永久位移的一致地震动作用模式;(2)断层主动盘一侧场地的地震作用具有永久位移地震动,被动盘一侧采用无永久位移地震动,即具有永久位移的非一致地震动作用模式;(3)在断层主动盘一侧场地以静力方式施加断层错动位移,而被动盘一侧场地固定不动,即断层错动位移静力作用模式。计算结果分析表明,不考虑永久位移的一致地震动作用模式的地震动输入会导致严重低估桥梁反应计算结果,这也说明地震动的断层两侧永久性位移差异会显著增大桥梁结构反应;而一致地震动作用叠加断层错动永久位移静力作用的结果与非一致地震动作用模式的结果非常接近。为此,在某种程度上说,跨断层桥梁结构地震反应可采用一致地震动作用叠加断层错动位移静力作用的桥梁结构反应来近似模拟。

2022年9月5日四川泸定M_(S)6.8地震近断层地震动特征

2022年9月5日12时52分四川甘孜州泸定县发生M_(S)6.8地震,造成重大人员伤亡和财产损失。本文利用此次地震中距离发震断层80 km以内获得的92个三分量加速度记录,研究此次地震近断层地震动峰值加速度(PGA)、峰值速度(PGV)和不同周期加速度反应谱(Sa)的空间分布与衰减特征,探讨了近断层地震动的脉冲特征及其对地震动反应谱的影响。研究结果表明:(1)此次地震近断层地震动表现出随观测方向变化的较强极性特征,其中51LDJ记录的南北分量约达到东西分量的3倍,这主要受地震的走滑破裂特征影响。(2)近场地震动强度的空间分布主要受此次地震发震断层的走向控制,峰值加速度、速度和加速度反应谱值的分布与断层走向特点一致。较强的观测值多位于烈度VII度以上的区域,与震害分布相符,地震动强度分布从一定程度决定了震害分布。(3)从实际观测结果与地震动经验模型的对比来看,经验模型对本次地震PGA和0.2 s的短周期地震动有较好的预测;对于PGV和周期0.5 s以上的地震动反应谱,本文考察的6个经验模型均有不同程度的高估。(4)本次泸定地震有2条典型脉冲记录,均位于距离发震断层15 km以内,脉冲记录波形具有明显的双向脉冲特征,记录的PGV分别达到56.0 cm/s和37.0 cm/s。速度脉冲在其脉冲特征周期附近,对加速度反应谱有显著放大作用。受此影响,距离断层最近的T2471台站记录的东西向和南北向反应谱在周期0.6~1.5 s范围均显著高于VIII度罕遇地震设计谱。此外,局部地形对地震动短周期成分有重要影响,T2471记录东西向反应谱在0.1~0.2 s,也远远超过了VIII度罕遇地震设计谱。

汶川地震动摇摆分量参数的衰减特征分析

受接收设备和记录数量的限制,对摇摆分量内在属性及参数的统计分析了解甚少。为揭示摇摆分量的工程特性,便于结构抗震分析合理选取地震动参数,基于“5·12”汶川8.0级地震的348条数据记录,对比分析平动分量和摇摆分量的幅值以及频谱和持时的空间分布特征和随断层距的衰减规律。研究表明:摇摆分量与平动分量相比,在数量上峰值小很多,能量持时稍小且特征周期偏大。摇摆分量参数的空间分布特征为峰值具有沿断层破裂传播方向的方向性效应,峰值比、特征周期、能量持时的方向性效应不明显;除特征周期外,峰值、峰值比和能量持时均存在上下盘效应,上盘大于下盘。随断层距的变化特征为摇摆分量参数与平动分量参数的规律性一致,均表现为随断层距的增大,峰值减小,峰值比、特征周期和能量持时增加。

An extended multiple-support response spectrum method incorporating fluid-structure interaction for seismic analysis of deep-water bridges

The effects of ground motion spatial variability(GMSV)or fluid-structure interaction(FSI)on the seismic responses of deep-water bridges have been extensively examined.However,there are few studies on the seismic performance of bridges considering GMSV and FSI effects simultaneously.In this study,the original multiple-support response spectrum(MSRS)method is extended to consider FSI effect for seismic analysis of deep-water bridges.The solution of hydrodynamic pressure on a pier is obtained using the radiation wave theory,and the FSI-MSRS formulation is derived according to the random vibration theory.The influence of FSI effect on the related coefficients is analyzed.A five-span steel-concrete continuous beam bridge is adopted to conduct the numerical simulations.Different load conditions are designed to investigate the variation of the bridge responses when considering the GMSV and FSI effects.The results indicate that the incoherence effect and wave passage effect decrease the bridge responses with a maximum percentage of 86%,while the FSI effect increases the responses with a maximum percentage of 26%.The GMSV and FSI effects should be included in the seismic design of deep-water bridges.

Generation of endurance time excitation functions using spectral representation method

In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.

空间多点地震激励下简支梁桥碰撞响应数值模拟

为研究桥梁结构在空间多点地震激励下的碰撞响应,采用LS-DYNA建立了两跨简支梁桥三维精细化有限元模型,考虑了相邻桥跨之间面-面碰撞及偏心碰撞效应,计入了板式橡胶支座系统的非线性、钢筋混凝土在碰撞荷载作用下的材料非线性和应变率效应,详细分析了空间多点地震下桥梁上部结构的碰撞响应,研究了双向多点地震激励及局部场地效应对碰撞响应的影响。研究结果表明,碰撞会导致伸缩缝处桥梁上部结构的局部破坏;双向多点地震激励引起的桥梁偏心碰撞响应导致碰撞次数增加,但减小了碰撞力;局部场地效应对桥梁上部结构碰撞响应影响较大,基础场地条件越差,上部结构碰撞响应越大,碰撞引起的梁端局部破坏越严重。