近断层强地面运动影响场显式有限元数值模拟的示意性算例

本文通过一个简单的示意性算例，对近断层强地面运动影响场显式有限元数值模拟的主要环节作了概要说明，给出了算例的主要计算结果并对其作了定性和初步的讨论分析。主要观点和结论是：本文的计算结果较好地定性反映和印证了人们对近断层强地面运动特征（如上盘效应、竖向效应、Fling Step效应和速度大脉冲现象）的现有认识水平，验证了采用的计算模型和计算方法的可行性和科学性。本文关于位移峰值场的计算结果对于估算近断层地表破裂带的位置、长度和宽度具有重要参考价值，应进一步深入研究二者之间的相关性。     

某正倾滑断层引起的近断层强地面运动的有限元数值模拟

本文使用与文献[1]相同的数值模拟方法,预测了某城市设定矩震级为MW=6.75的活断层产生的近断层强地面运动。主要定性计算结果是:正倾滑断层(倾角δ=75°)产生的近断层强地面运动也不同程度地存在上盘效应、F ling Step效应、速度大脉冲效应和竖向效应。表明本文采用的震源模型和计算方法可以实际应用于预测城市近断层强地面运动影响场。     

Simulation of near-fault bedrock strong ground-motion field by explicit finite element method

Based on presumed active fault and corresponding model, this paper predicted the near-fault ground motion filed of a scenario earthquake （Mw=6 3/4 ） in an active fault by the explicit finite element method in combination with the source time function with improved transmitting artificial boundary and with high-frequency vibration contained. The results indicate that the improved artificial boundary is stable in numerical computation and the predicted strong ground motion has a consistent characteristic with the observed motion.     

基于GP14.3运动学混合震源模型和SPECFEM 3D谱元法的宽频地震动模拟

基于确定性物理模型的全过程地震动模拟是现代地震工程的重要发展方向.然而受限于合理震源模型和计算资源需求,目前模拟的有效频率还多处于低频范围,难以满足工程结构敏感频带（5~10 Hz或更高）需求.本文即借助运动学混合震源模型能激发宽频地震波和谱元法空间高精度及计算收敛快的优势,首先将确定性的凹凸体震源模型与GP14.3随机震源模型结合得到有限断层运动学混合震源模型,进而将上述混合震源模型开发到SPECFEM 3D谱元法开源代码中,实现了基于谱元法和运动学混合震源模型的全过程宽频带地震动模拟.将方法首先应用于一维波速结构模型0~10 Hz地震动模拟,通过与频率波数域（FK）方法结果进行比较,验证了方法的精度;进而应用于2021年5月21日云南漾濞6.4级地震0.1~5 Hz地震动模拟,通过与4个台站的时程记录和相应反应谱的比较,以及与NGA-West2地震动衰减方程在频率0.1~5 Hz的反应谱的比较,检验了方法的适用性;最后给出了漾濞地区的地震动峰值加速度（PGA）和峰值速度（PGV）云图,分析了漾濞地震下近场强地面运动的空间分布特征.结果显示,震中PGA接近400 cm·s^-2,PGV达到45 cm·s^-1,烈度达到Ⅸ度,且受局部地形起伏影响,大理以及洱海西侧位置出现高烈度异常区.

     

震源参数对强地面震动模拟结果的影响

基于运动学震源模型,进行了不同震源参数情形下强地面震动数值模拟.结果表明,不同的破裂过程会产生差别甚大的强地面运动分布,一次确定性震源参数的模拟结果不能作为活动断层地震危害性评价的指标,只有通过大量三维地震动场模拟计算,给出地面震动评估的统计结果,才是比较合理的发展方向.由于一次三维地震动场计算耗时很大,因此解决问题的关键是如何考虑合理的震源参数.     

Spatial distribution of near-fault ground motion

Introduction In order to explain severe damage of structures and ground surface near earthquake fault, many theoretical and numerical methods have been developed to study strong ground motion near the fault (Somerville, 1998) via the kinematic and dynamic source models. Moreover, a great number of valuable strong ground motion records, especially near the fault, have been acquired in recent years. These valuable records provide useful data for improving simulation approaches. Based on those r…     

Analysis on effect of surface fault to site ground motion using finite element method

Dynamic contact theory is applied to simulate the sliding of surface fault.Finite element method is used to analyze the effect of surface fault to site ground motions.Calculated results indicate that amplification effect is obvious in the area near surface fault,especially on the site that is in the downside fault.The results show that the effect of surface fault should be considered when important structure is constructed in the site with surface fault.     

近断层强地震动场预测

以1997年4月11日新疆伽师地震（Mw6.1）为例,详细介绍了近断层强地震动场的预测方法.首先,用有限断层震源建模方法建立了该次地震的震源模型;然后,基于动力学拐角频率的地震动随机模拟方法,模拟了该次地震仅有主震加速度记录、且位于巨厚土层上的三个台站的加速度时程,并用实际地震记录进行了验证.在此基础上,基于预测的近断层77个节点的加速度时程的峰值绘制了该次地震的加速度场.结果表明,上述方法模拟的加速度时程在0.5 Hz以上的高频段是可行的、实用的;预测的近断层加速度场具有非常明显的上盘效应.地表最大加速度的范围与断层面上最大凹凸体位置相对应,说明与断层面上凹凸体相对应的地面上的建（构）筑物将会遭受到较为严重的震害.     

近断层地震动场预测——以长春市为例

断层带附近地震动场分布的研究,是当前地震工程领域研究的热点问题之一。近断层地震动场的分布对在断层附近进行抗震结构设计时,不仅是提供地震动输入,也是确定建设场地避让范围的重要依据之一。以区域地震构造背景分析、目标断层活动性鉴定、地震危险性评价为基础,结合断层探测结果,利用统计经验关系等最终确定发震断层,并建立相应的震源模型。采用显式有限元和并行计算技术计算目标区域场地的长周期地震动。利用有限断层随机合成的方法,计算高频地震动。将低频和高频地震动合成为目标区域内的宽频带地震动时程。对局部特殊场地条件地区,基于场地调查和勘探的数据,利用等效线性化等方法进行一维土层的非线性反应计算,给出这些特殊场地的宽频带地震动时程。最后,根据地震动时程获得设定地震发生时,目标区域的峰值加速度分布预测图和相应的反应谱。以长春市为例预测了在设定地震发生时,近断层地震动场的分布情况。当长春尖山子—卡伦断层发生6.0级地震时,潜在破坏性地震动的影响范围集中在附近,沿断层走向分布。加速度峰值沿断层垂直变化,主要为90 Gal～140 Gal。只是在长春市南部加速度峰值达到200 Gal。本研究的预测结果具备断层附近地震动的一些最基本的特征,符合当前对断层附近地震动的基本认识。     

In-plane response of two-story structures to near-fault ground motion

Linear and non-linear responses of a two-story structural model excited by near-source fault-normal pulse and fault-parallel displacement are investigated. For the considered linear system, the multi-component differential-motion effects amplify the first-story drifts 3.0–4.0 times relative to the excitation by synchronous horizontal ground motion only. The contribution of horizontal differential ground motion to the total drift is about two thirds, and the contribution of vertical and rocking differential ground motions is about one third. For the considered nonlinear system, the effects of vertical and rocking differential ground motions become more significant for the second-story drifts. The horizontal differential ground motion amplifies the first-story drifts, but the simultaneous action of horizontal, vertical, and rocking differential ground motions can amplify the first- and second-story drifts by more than 2.0 times relative to the drifts computed for uniform horizontal ground motion only.     

1999年台湾集集大地震强地面运动的模拟

利用有限断层模型对1999年台湾集集大地震所产生的近场强地面运动进行了数值模拟,尝试了将具有明确物理意义的震源动力模型的研究结果应用于描述震源过程。计算结果显示,基岩台或接近工程基岩台的计算模拟记录同观测记录符合得很好。进一步研究表明,当综合考虑场地效应对地震动影响时,模拟计算结果得到了明显的改善,同实际观测记录更为相符。本文的研究结果说明,为了科学合理地预测大地震所产生的强地面运动,应综合考虑影响地震所产生的地面运动的"三要素",即:震源过程、传播路径及场地效应。     

波动有限元方程显式逐步积分格式稳定性分析

对常用的波动有限元方程的两种显式格式的稳定性进行了分析,利用单元的最大频率乃是系统的特征频率的上界的概念结合模态分析方法,给出了便于实际应用的稳定性必要条件。同时,利用Von Neumann方法给出了这两种格式稳定性的充分条件,并通过算例对这两种稳定性条件进行验证。     

An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order (M=1) recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.     

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with M being a positive integer for regular grids are discussed and illustrated by constructing the second order (M = 1) and the fourth order (M = 2) recursion formulas.     

Rupture directivity and hanging wall effect in near field strong ground motion simulation

A random synthesis procedure based on finite fault model is adopted for near field strong ground motion simulation in this paper.The fault plane of the source is divided into a number of sub-sources,the whole moment magnitude is also divided into more sub-events.The Fourier spectrum of ground motion caused by a sub-event in given sub-source,then can be derived by means of taking the point source spectrum,attenuation with distance,energy dissipation,and near surface effect,into account.A time history is synthesized from this amplitude spectrum and a random phase spectrum,and being combined with an envelope function.The ground motion is worked out by superposition of all time histories from each sub-event in each sub-source,with time lags determining by the differences between the triggering times of sub-events and ddistances of the sub-sources.From the example of simulations at 21 near field points in a scenario earthquake with 4 dip angles of the fault plane,it is illustrated that the procedure can describe the rupture directivity and hanging wall effect very well.To validate the procedure,the response spectra and time histories recorded at three near fault stations MCN,LV3 and PCD during the Northridge earthquake in 1994,are compared with the simulated ones.     

A simplified method for simulation of strong ground motion using finite rupture model of the earthquake source

We present a simplified method to simulate strong ground motion for a realistic representation of a finite earthquake source burried in a layered earth. This method is based on the stochastic simulation method of Boore (Boore, D. M., 1983, Bull. Seism. Soc. Am. 73, 1865–1894) and the Empirical Greens Function (EFG) method of Irikura (Irikura, K., 1986, Proceedings of the 7th Japan Earthquake symposium, pp. 151–156). The rupture responsible for an earthquake is represented by several subfaults. The geometry of subfaults and their number is decided by the similarity relationships. For simulation of ground motion using the stochastic simulation technique we used the shapping window based on the kinetic source model of the rupture plane. The shaping window deepens on the geometry of the earthquake source and the propagation characteristics of the energy released by various subfaults. The division of large fault into small subfaults and the method for accounting their contribution at the surface is identical to the EGF. The shapping window has been modified to take into account the effect of the transmission of energy released form the finite fault at various boundaries of the layered earth model above the source. In the present method we have applied the correction factor to adjust slip time function of small and large earthquakes. The correction factor is used to simulate strong motion records having basic spectral shape of ² source model in broad frequency range. To test this method we have used the strong motion data of the Geiyo earthquake of 24th March 2001, Japan recorded by KiK network. The source of this earthquake is modelled by a simple rectangular rupture of size 24 × 15 km, burried at a depth of 31 km in a multilayered earth model. This rupture plane is divided into 16 rectangular subfaults of size 6.0 × 3.75 km each. Strong motion records at eight selected near-field stations were simulated and compared with the observed records in terms of the acceleration and velocity records and their response spectrum. The comparison confirms the suitability of proposed rupture model responsible for this earthquake and the efficacy of the approach in predicting the strong motion scenario of earthquakes in the subduction zone. Using the same rupture model of the Geiyo earthquake, we compared the simulated records from our and the EGF techniques at one near-field station. The comparison shows that this technique gives records which matches in a wide frequency range and that too from simple and easily accessible parameters of burried rupture.     

漾濞MS6.4地震长周期强地震动的有限差分初步模拟

根据我国川滇地区的地质地貌特征、前人地质资料和2021年漾濞M_S6.4地震的震源参数初步反演结果,建立三维速度结构模型,采用三维有限差分法对漾濞地震的长周期地震动进行研究.对实际地震烈度和模拟烈度进行对比,同时在区域附近布置了36个观测点,给出其中6个观测点的三分量速度时程,并给出所有观测点阻尼比为5%的速度反应谱,结果表明:(1)模拟的速度峰值已超过25 cm/s,与实际漾濞地区附近的烈度为8度吻合;(2)受断层滑动分布影响,速度水平分量在西北方向分布范围更广,衰减速度明显慢于东南方向,并且在极震区,东北—西南方向的地震动衰减也较慢.方向性效应对峰值大小及其分布范围的影响显著;(3)观测点速度反应谱的特征周期分布在1~3 s范围内,可能会因为共振效应对区域附近的大型建筑物产生较为严重的破坏.需要对漾濞地震进行进一步研究,以期对漾濞地震的长周期地震动有更为细致的认识.     

A varying time-step explicit numerical inte-gration algorithm for solving motion equa-tion

Introduction In linear elastic medium,motion equation for lumped-mass finite element simulation of wave motion is expressed as(LIAO,2002)∑=+lililii ttGtM)()()(FUU&&(1)where Mi is lumped-mass at node i,Gil is stiffness coefficient of node i with respect to node l,üi(t)is acceleration vectors at node i,Ul(t)is displacement vectors at node l,Fi(t)is the external nodal force vectors acting at node i.If acceleration vectorsüi(t),displacement vectors Ul(t)and the external nodal force vectors…     

采用显式有限元方法求解开放系统动力响应的主要环节和问题

分析了采用显式有限元方法求解开放系统动力响应的主要环节中影响精度和稳定性的因素及其相互关系,指出数值解的精度和稳定性是这些因素共同作用的结果。归纳了合理输入数字荷载应满足的条件以及系统离散化准则。基于有限元方法推导了吸收边界的一般表达式,并据此提出吸收边界和透射边界之间存在确定的函数关系,并不是两类独立人工边界的新见解。认为内域的阻尼稳定性和人工边界的近场稳定性是大型复杂开放系统动力响应数值方法研究和应用中的关键科学问题,并从应用的角度提出了解决问题的思路和看法。     

近断层地震动加速度峰值衰减规律的研究

提出了近断层地面运动的衰减模型,对全球范围内6．0≤Mw≤7．6且震源深度均小于20km的636条地震动加速度峰值进行了统计分析,确定了本文研究的近断层区域为断层距25km,利用此范围内的440条记录进行了近断层加速度衰减规律的研究。水平地震记录分为硬土和软土两种场地类型,竖向地震记录只考虑土层场地,利用最小二乘法进行数据拟合分析,得到PGA随断层距和震源深度变化在不同震级处形成的衰减曲面,分析了近断层处水平、竖向的PGA以及竖向与水平PGA之比(V／H)的衰减规律。