Chaotic seismic faulting with a mass-spring model and velocity-weakening friction

We present a systematic analysis of the dynamical behavior introduced by fault zone heterogeneities, using a simple mass-spring model with velocity-weakening friction. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by clastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. Symmetry stabilizes the system and generates only cyclic behavior. For an asymmetric system where the frictional forces for the two blocks are not equal, the solutions exhibit chaotic behavior. The transition from stable cyclic behavior to chaos is characterized by the period-doubling route to chaos. Lyapunov exponents are computed to quantify the deterministic chaos and to locate the onset of the chaotic evolution in parameter space. In many examples of deterministic chaos, chaotic behavior of a low-order system implies chaos in similar higher order systems. Thus, our results provide substantial evidence that crustal deformation is an example of deterministic chaos.     

The discrete wave number formulation of boundary integral equations and boundary element methods: A review with applications to the simulation of seismic wave propagation in complex geological structures

We review the application of the discrete wave number method to problems of scattering of seismic waves formulated in terms of boundary integral equation and boundary element methods. The approach is based on the representation of the diffracting surfaces and interfaces of the medium by surface distributions of sources or by boundary source elements, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green's functions are evaluated by the discrete wave number method, and the boundary conditions yield a linear system of equations. The inversion of this system allows the calculation of the full wave field in the medium. We investigate the accuracy of the method and we present applications to the simulation of surface seismic surveys, to the diffraction of elastic waves by fractures, to regional crustal wave propagation and to topographic scattering.     

一种通过共轭地震确定地壳的内摩擦特性的方法

应用国内外24个具有"X"形或"L"形（不完整的"X"形）共轭破裂特征的地震资料,以及云南鲁甸、盈江两次共轭破裂地震的详细重定位数据,运用库仑破坏准则揭示的脆性破裂的共轭破裂角与介质的内摩擦系数之间的关系,测定与计算了地震共轭角与地壳的内摩擦系数,探讨了库仑破坏准则与安德逊破裂理论应用于宏观尺度破裂即天然地震问题.结果表明,在国际、国内不同地区不同年代的多次共轭破裂地震中,共轭角与内摩擦系数的优势分布分别为65°~75°与0.27~0.47.在同一地区或相近地区发生的地震,其共轭角与内摩擦系数在数值上也相近.库仑破坏准则与破裂的安德逊理论,不但适用于实验室的小样本岩石破裂实验结果,而且适用于宏观尺度破裂即天然地震.通过共轭角的测定,可以确定地壳的内摩擦系数,是一种增进对地壳的内摩擦特性的认识的简易、直接的方法.     

摩擦耗能框架体系动力分析

采用粘性屈服模型来模拟摩擦耗能器的力－速度关系。建立了带有摩擦耗能器体系的动力分析8方法，采用增量型Rosenbrock二阶三阶半隐式Runge-Kutta法求解动力方程，得到了带有摩擦耗能器单层框架在正弦波激励下反应的解析解，并据此验证粘性屈服模型及求解动力方程算法的正确性，分析了摩擦耗能器的起滑力和支撑刚度对耗能减振效果的影响。     

APPLICATION OF BOUNDARY ELEMENT ANALYSIS FOR MULTIPLE SEISMIC CRACKING IN CONCRETE GRAVITY DAMS

The previously developed two-dimensional boundary element procedure for analysing the propagation of a single discrete crack is extended to simultaneous multiple cracking in concrete gravity dams. A brief discussion of the generalized methodology is presented and the validity of the extended procedure is verified by performing a fracture analysis of the Fongman dam and comparing the predicted rupture process with the available experimental results. The fracture response of the Koyna dam is then studied extensively under the Koyna earthquake. Both single and multiple cracking models are employed to investigate the fracture process as well as final rupture in the dam. Similar final damage involving complete separation of the crest block of the dam is predicted, irrespective of whether single or multiple crack propagation models are employed. In relation to the phenomenon of hydrodynamic uplift pressure within propagating cracks, openings of the crack on the upstream face of the dam are examined in particular. The results indicate that this phenomenon is not expected to be significant during the crack development phase, and hence unlikely to affect the final rupture characteristics of dams undergoing strong earthquake excitation.     

Reduction of structural response to near fault earthquakes by seismic isolation columns and variable friction dampers

<正>This paper focuses on the investigation of a hybrid seismic isolation system with passive variable friction dampers for protection of structures against near fault earthquakes.The seismic isolation can be implemented by replacing the conventional columns fixed to the foundations by seismic isolating ones.These columns allow horizontal displacement between the superstructure and the foundations and decouple the building from the damaging earthquake motion.As a result, the forces in the structural elements decrease and damage that may be caused to the building by the earthquake significantly decreases.However,this positive effect is achieved on account of displacements occurring in the isolating columns.These displacements become very large when the structure is subjected to a strong earthquake.In this case,impact may occur between the parts of the isolating column yielding their damage or collapse.In order to limit the displacements in the isolating columns,it is proposed to add variable friction dampers.A method for selecting the dampers' properties is proposed.It is carried out using an artificial ground motion record and optimal active control algorithm.Numerical simulation of a seven-story structure shows that the proposed method allows efficient reduction in structural response and limits the displacements at the seismic isolating columns.     

Refraction Effect in Geothermal Heat Flow Due to a 3-D Prism in a Two-Layered Earth

A mathematical model of the disturbance of the stationary geothermal field due to a three-dimensional perturbing body embedded near the surface of a two layered earth. The theoretical analysis is based on the generalized theory of the double-layer potential, similar to the boundary integral method likely to direct current geoelectricity problems. Special attention is paid to cases in which a pan of the body's surface is tangential to the planar boundaries of the substratum or of the surface of the earth The numerical calculations are performed for a three-dimensional prism using methods similar to the boundary element method (BEM). Numerous graphs are shown for the disturbance of the temperature field and of the heat flow on the surface of the earth and along vertical profiles (boreholes).     

A new friction law for sliding rigid blocks under cyclic loading

A rigid block sliding down an inclined plane under the action of gravity was monitored with accelerometers and an LVDT to investigate how the transition from static to kinetic friction develops. Once the transition patterns were identified, experiments were carried out to study the response of a dynamically excited rigid block sliding down the inclined plane of a shaking table. Harmonic time series were used as input motions. The laboratory results allowed the definition of a continuous friction law to model the continuous variation of the friction from its static to kinetic condition. This law was implemented into the commercial 3D distinct element code 3DEC to numerically reproduce the experiments carried out, thus validating the friction law. Afterwards, the friction law was used to evaluate the sliding due to the kinetics of the block. Three cases were analyzed: constant friction coefficient, Coulomb friction law and the proposed friction law. These computations were compared to laboratory measurements. It is found that permanent displacements computed by considering the new law are in better agreement with laboratory measurements.     

断层自发破裂传播的数值模拟:速率状态摩擦定律本构参数的影响

地震往往受控于滑动面的摩擦性质,这种摩擦性质可以由速率状态摩擦定律较好地描述.速率状态摩擦定律中的本构参数a和b与动态摩擦系数相关,从而影响着同震位移与剪切应力的时空演化.本文在前人工作的基础上,采用三维边界积分方程法模拟速率状态摩擦定律控制下均匀全空间中平面断层的自发破裂传播过程,并详细讨论了a和b对滑动速率、剪切应力和破裂传播速度的影响.数值结果表明a和b的不同取值将导致不同的破裂行为,b－a的值越大,断层越不稳定,这种不稳定性有利于裂纹的产生与扩展.但滑动速率的时空分布不只依赖b－a,而且还与a和b的具体取值有关,断层面上滑动速率峰值与剪切破裂强度均随着a的减小而增大,随着b的增大而增大.相关结果有助于加深对断层自发破裂传播的认识.     

Testing the Validity of Simulated Strong Ground Motion from the Dynamic Rupture of a Finite Fault, by Using Empirical Equations

This paper is concerned with testing the validity of the ground motions estimated by combining a boundary integral equation method to simulate dynamic rupture along finite faults with a finite difference method to compute the subsequent wave propagation. The validation exercise is conducted by comparing the calculated ground motions at about 100 hypothetical stations surrounding the pure strike-slip and pure reverse faults with those estimated by recent ground motion estimation equations derived by regression analysis of observed strong-motion data. The validity of the ground motions with respect to their amplitude, frequency content and duration is examined. It is found that the numerical simulation method adopted leads to ground motions that are mainly compatible with the magnitude and distance dependence modelled by empirical equations but that the choice of a low stress drop leads to ground motions that are smaller than generally observed. In addition, the scatter in the simulated ground motions, for which a laterally homogeneous crust and standard rock site were used, is of the same order as the scatter in observed motions therefore, close to the fault, variations in source propagation likely contribute a significant proportion of the scatter in observed motions in comparison with travel-path and site effects.     

Failure of double friction pendulum bearings under pulse‐type motions

Although the behavior of friction sliding bearings is well understood, the failure behavior has not been thoroughly investigated. However, predicting and understanding the failure of bearings is an important key in designing isolated structures to minimize their collapse in extreme events, and thus, this study is critical. Because of its relative simplicity and particular availability in certain markets, the failure of the double friction pendulum (DFP) bearing at its physical displacement limit is investigated. The bearing is modeled with a rigid body model including inertia for each of the bearing components. A nonlinear viscoelastic impact model is included to simulate the impact between bearing components. As isolation systems are particularly vulnerable to long‐period excitations, analytical pulses are used as input excitations to investigate the influences of pulse parameters on the failure of DFP. The influences of DFP design parameters are investigated as well. To confirm that the response to the analytical pulses correctly represents the behavior under long‐period ground motions, wavelet analysis to is performed on 14 pairs of pulse‐type ground motion records to extract their pulses, and the failure prediction made from the extracted analytical pulse is compared with the failure from the real ground motions. It is found that using the extracted pulses provides a good estimation for the failure prediction of the ground motions. Copyright © 2016 John Wiley & Sons, Ltd.     

摩擦摆基础隔震结构双向地震反应分析

采用双向耦合力学模型模拟摩擦摆支座的双向耦合效应,对摩擦摆基础隔震结构进行了单向和双向地震反应对比分忻,分析表明在双向地震作用下结构各层的加速度反应较小,隔震层的层间位移较大,而上部结构的层间位移较小,并且在双向地震作用下,支座的最大位移明显大于单向地震作用时的支座最大位移,因而应考虑双向地震作用对摩擦摆基础隔震结构地震反应和隔震支座性能的影响。     

摩擦摆基础隔震结构多维地震反应分析

对摩擦摆基础隔震结构进行了单向、双向和三向地震反应对比分析,表明考虑双向水平地震动时摩擦摆基础隔震结构的支座位移增大,而结构的加速度和楼层剪力减小,其中对支座位移和结构加速度影响较大;考虑竖向地震动时摩擦摆基础隔震结构的支座位移略有减小,而结构的加速度和楼层剪力增大,其中对结构加速度影响较大.因而,在进行摩擦摆基础隔震结构地震反应分析时,应考虑多维地震动的影响.     

Smart base isolated buildings with variable friction systems: H∞ controller and SAIVF device

A new control algorithm is developed for reducing the response of smart base isolated buildings with variable friction semiactive control systems in near‐fault earthquakes. The central idea of the control algorithm is to design a H_∞ controller for the structural system and use this controller to determine the optimum control force in the semiactive device. The H_∞ controller is designed using appropriate input and output weighting filters that have been developed for optimal performance in reducing near‐fault earthquake responses. A novel semiactive variable friction device is also developed and with the H_∞ controller shown to be effective in achieving response reductions in smart base isolated buildings in near‐fault earthquakes. The new variable friction device developed consists of four friction elements and four restoring spring elements arranged in a rhombus configuration with each arm consisting of a friction–stiffness pair. The level of friction force can be adjusted by varying the angle of the arms of the device leading to smooth variation of friction force in the device. Experimental results are presented to verify the proposed analytical model of the device. The H_∞ algorithm is implemented analytically on a five storey smart base isolated building with linear elastomeric isolation bearings and variable friction system located at the isolation level. The H_∞ controller along with the weighting filters leads to the smooth variation of friction force, thus eliminating the disadvantages associated with rapid switching. Several recent near‐fault earthquakes are considered in this study. The robustness of the H_∞ controller is shown by considering a stiffness uncertainty of ±10%. Copyright © 2006 John Wiley & Sons, Ltd.     

Dynamic rupture process of the 1999 Chi-Chi,Taiwan,earthquake

In this study, we preliminarily investigated the dynamic rupture process of the 1999 Chi-Chi, Taiwan, earthquake by using an extended boundary integral equation method, in which the effect of ground surface can be exactly included. Parameters for numerical modeling were carefully assigned based on previous studies. Numerical results indicated that, although many simplifications are assumed, such as the fault plane is planar and all heterogeneities are neglected, distribution of slip is still consistent roug...     

Dynamic rupture process of the 1999 Chi-Chi,Taiwan, earthquake

In this study, we preliminarily investigated the dynamic rupture process of the 1999 Chi-Chi, Taiwan, earthquake by using an extended boundary integral equation method, in which the effect of ground surface can be exactly included. Parameters for numerical modeling were carefully assigned based on previous studies. Numerical results indicated that, although many simplifications are assumed, such as the fault plane is planar and all heterogeneities are neglected, distribution of slip is still consistent roughly with the results of kinematic inversion, implying that for earthquakes in which ruptures run up directly to the ground surface, the dynamic processes are controlled by geometry of the fault to a great extent. By taking the common feature inferred by various kinematic inversion studies as a restriction, we found that the critical slip-weakening distance &lt;i&lt;D&lt;/i&lt;&lt;sub&lt;c&lt;/sub&lt; should locate in a narrow region 60 cm, 70 cm, and supershear rupture might occur during this earthquake, if the initial shear stress before the mainshock is close to the local shear strength.     

摩擦与粘性流体耗能器串联体系动力分析

采用粘性屈服模型来模拟摩擦耗能器的力－速度关系，建立了摩擦与粘性流体耗能器串联耗能体系的动力分析方法．为考虑框架杆件和支撑材料的几何非线性，采用增量型Ｒｏｓｅｎｂｒｏｃｋ二级三阶半隐式Ｒｕｎｇｅ－Ｋｕｔｔａ法求解动力方程．比较了仅有摩擦耗能器体系与串联组合耗能体系的减振效果，分析了粘性流体耗能器参数对组合耗能体系减振效果的影响。     

移动荷载作用下土体动力反应数值模拟

在研究轨道振动荷载的产生机理基础上,归纳出一个能够涵盖速度、线路不平顺、轮重、轨枕对轮载的分散作用等因素在内的轨道荷载解析表达式,以此作为输入施加到土体模型上,利用ANSYS模拟地基土在轨道移动荷载作用下的三维瞬态弹塑性反应。通过计算得到土体不同位置位移和加速度时程曲线,并得出如下结论:荷载刚施加时地面位移会有一个突变,但是随着荷载的移动会达到一个稳定值,并随着水平面内远离轨道,该值逐渐衰减;荷载刚刚施加时加速度会有一个突变值,随着荷载的移动逐渐趋于零。轨道机车速度对竖向方向的位移和加速度影响不大。     

动载下无筋砌体墙的应力场及裂隙分布

为探索动载下建筑物墙体失稳的力学机制,基于弹性力学理论,分析一端刚性固定无筋砌体墙受垂直地震波扰动时的应力场分布规律,得到墙体的应力解析表达式,结果显示应力特征由墙体质点振速、墙体恒载、墙体密度及其几何尺寸等因素共同决定。结合具体算例发现:墙体水平应力、垂直应力与剪应力具有不同的分布特征。水平应力值分别是剪切和垂直应力值的5倍和25倍,为墙体应力场的主控应力,其应力集中区位于刚性固定侧墙体的顶、底角,应力变化梯度为180MPa/m,且随地震强度增加,其应力场进一步向墙体刚性固定侧集中。在此基础上,基于主应力主导墙体裂隙的原则,预测了墙体张开型裂隙的分布位置、长度及角度,获得了墙体最易出现破坏失稳的部位。通过模型计算可为掌握动载下墙体力学行为提供参考。