Simplified approach for design of raft foundations against fault rupture. Part Ⅰ: free-field

Over the past few decades, earthquake engineering research mainly focused on the effects of strong seismicshaking. After the 1999 earthquakes in Turkey and Taiwan, and thanks to numerous cases where fault rupture causedsubstantial damage to structures, the importance of faulting-induced deformation has re-emerged. This paper, along withits companion (Part Ⅱ), exploits parametric results of finite element analyses and centrifuge model testing in developing afour-step semi-analytical approach for analysis of dip-slip (normal and thrust) fault rupture propagation through sand, itsemergence on the ground surface, and its interaction with raft foundations. The present paper (Part Ⅰ) focuses on the effectsof faulting in the absence of a structure (i.e., in the free-field). The semi-analytical approach comprises two-steps: the firstdeals with the rupture path and the estimation of the location of fault outcropping, and the second with the tectonically-induced displacement profile at the ground surface. In both cases, simple mechanical analogues are used to derive simplifiedsemi-analytical expressions. Centrifuge model test data, in combination with parametric results from nonlinear finite elementanalyses, are utilized for model calibration. The derived semi-analytical expressions are shown to compare reasonably wellwith more rigorous experimental and theoretical data, thus providing a useful tool for a first estimation of near-fault seismichazard.     

Simplified approach for design of raft foundations against fault rupture. Part Ⅱ： soil-structure interaction

This is the second paper of two, which describe the results of an integrated research effort to develop a four-step simplified approach for design of raft foundations against dip-slip （normal and thrust） fault rupture. The first two steps dealing with fault rupture propagation in the free-field were presented in the companion paper. This paper develops an approximate analytical method to analyze soil-foundation-structure interaction （SFSI）, involving two additional phenomena： （i） fault rupture diversion （Step 3）; and （ii） modification of the vertical displacement profile （Step 4）. For the first phenomenon （Step 3）, an approximate energy-based approach is developed to estimate the diversion of a fault rupture due to presence of a raft foundation. The normalized critical load for complete diversion is shown to be a function of soil strength, coefficient of earth pressure at rest, bedrock depth, and the horizontal position of the foundation relative to the outcropping fault rupture. For the second phenomenon （Step 4）, a heuristic approach is proposed, which ＂scans＂ through possible equilibrium positions to detect the one that best satisfies force and moment equilibrium. Thus, we account for the strong geometric nonlinearities that govern this interaction, such as uplifting and second order （P-△） effects. Comparisons with centrifuge-validated finite element analyses demonstrate the efficacy of the method. Its simplicity makes possible its utilization for preliminary design.     

Simplified approach for design of raft foundations against fault rupture. Part Ⅱ: soil-structure interaction

This is the second paper of two, which describe the results of an integrated research effort to develop afour-step simplified approach for design of raft foundations against dip-slip (normal and thrust) fault rupture. The first twosteps dealing with fault rupture propagation in the free-field were presented in the companion paper. This paper develops anapproximate analytical method to analyze soil-foundation-structure interaction (SFSI), involving two additional phenomena:(i) fault rupture diversion (Step 3); and (ii) modification of the vertical displacement profile (Step 4). For the first phenomenon(Step 3), an approximate energy-based approach is developed to estimate the diversion of a fault rupture due to presence ofa raft foundation. The normalized critical load for complete diversion is shown to be a function of soil strength, coefficient ofearth pressure at rest, bedrock depth, and the horizontal position of the foundation relative to the outcropping fault rupture.For the second phenomenon (Step 4), a heuristic approach is proposed, which "scans" through possible equilibrium positionsto detect the one that best satisfies force and moment equilibrium. Thus, we account for the strong geometric nonlinearitiesthat govern this interaction, such as uplifting and second order (P-A) effects. Comparisons with centrifuge-validated finiteelement analyses demonstrate the efficacy of the method. Its simplicity makes possible its utilization for preliminary design.     

Tunnel effect of fractal fault and transient S-wave velocity rupture (TSVR) of in-plane shear fault

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Design of bridges against large tectonic deformation

The engineering community has devoted much effort to understanding the response of soil-structure systems to seismic ground motions, but little attention to the effects of an outcropping fault offset. The 1999 earthquakes of Turkey and Taiwan, offering a variety of case histories of structural damage due to faulting, have （re）fueled the interest on the subject. This paper presents a methodology for design of bridges against tectonic deformation. The problem is decoupled in two analysis steps： the first （at the local level） deals with the response of a single pier and its foundation to fault rupture propagating through the soil, and the superstructure is modeled in a simplified manner; and the second （at the global level） investigates detailed models of the superstructure subjected to the support （differential） displacements of Step 1. A parametric study investigates typical models of viaduct and overpass bridges, founded on piles or caissons. Fixed-head piled foundations are shown to be rather vulnerable to faulting-dnduced deformation. End-bearing piles in particular are unable to survive bedrock offsets exceeding 10 cm. Floating piles perform better, and if combined with hinged pile-to-cap connections, they could survive much larger offsets. Soil resilience is beneficial in reducing pile distress. Caisson foundations are almost invariably successful. Statically-indeterminate superstructures are quite vulnerable, while statically-determinate are insensitive （allowing differential displacements and rotations without suffering any distress）. For large-span cantilever-construction bridges, where a statically determinate system is hardly an option, inserting resilient seismic isolation bearings is advantageous as long as ample seating can prevent the deck from falling off the supports. An actual application of the developed method is presented for a major bridge, demonstrating the feasibility of design against tectonic deformation.     

Dynamic effects of surface fault rupture interaction with structures

Surface fault rupture has caused significant damage to structures in several earthquakes. The propagation of the bedrock fault rupture through the overlying soil deposit has been studied by several researchers; however, the effects of fault rupture dynamics, as opposed to pseudostatic fault movement, have not yet been evaluated. There is the potential for dynamic effects to influence significantly structural damage due to the rapid rate of deformation imposed by surface fault rupture. Numerical simulations are performed to analyze the effects of the rate of fault rupture on dip-slip surface fault rupture for free-field and soil-structure interaction conditions. The numerical results indicate that in some limited scenarios, fault rupture dynamics can influence the amount of structural damage expected for a structure located near a fault. However, in most scenarios, fault rupture dynamics is expected to play a secondary role compared to fault, soil, and structural characteristics in evaluating building performance.     

Estimating kinematic interaction of raft foundations from earthquake records and its effects on structural response

A practical method for estimating kinematic interaction from earthquake records is presented. The kinematic interaction is characterized by a two-parameter model and these parameters can be estimated by using a frequency-domain systems identification method. The simple model can be used to model both wave passage effects and the effects of incoherent wave fields. Numerical simulation tests show that kinematic interaction parameters can be estimated to their best accuracy by using building base responses and the free-field excitation and can also be estimated by using building responses, base responses and the free-field excitation. The method was applied to two buildings with raft foundations and it was found that kinematic interaction was significant during earthquakes. Published theoretical models (wave passage effect) for vertically incident SH waves can be used to estimate the transfer functions up to 4–5 Hz and the models for horizontally propagating waves under-predict the estimated transfer functions by a significant amount at frequencies beyond about 1–2 Hz. Theoretical models for a massless rigid foundation under the excitation of an incoherent wave field predict the general trend of the estimated transfer function reasonably well over a large frequency range. The results of numerical examples show that the recorded response spectral attenuation of basement records at high frequencies with respect to the free-field is mainly caused by kinematic interaction, while the changes in storey shear and overturning moment in a structure due to soil flexibility are mainly the results of inertial interaction.     

覆盖土层场地地震断裂实验

研究了覆盖土层场地在活动断裂位移作用下的实验技术，分别了正断层和走滑断层位移作用下土层模型地震模拟振动台断裂位移反应实验，取得了有意义的结论，为进行进一步的研究奠定了基础。     

2008年汶川大地震单侧破裂过程的动力学机制研究

2008年汶川大地震的破裂过程极其发杂,向东北方向的破裂距离长达300 km,而向西南方向的破裂长度很小,呈现出单侧破裂的主要特征.尽管汶川地震破裂呈单侧传播的现象引起许多地震学家的关注,但其物理机制至今还不是十分清楚.本文利用有限单元计算方法,模拟了汶川地震的破裂过程.模型中根据龙门山断裂带两侧（东南侧为四川盆地,西北侧为川西高原）实际的地震波速度来确定模型的介质物性参数,利用目前观测的应力环境来选定初始应力条件.模拟结果表明：破裂在汶川地震的震中处成核后,先向断层两侧自发传播,但向东北方向的传播距离明显大于向西南方向;断层面上的正应力在东北方向（破裂的正方向）随着传播距离的增大而不断减小,位错速率随着破裂的传播距离而越来越大,其脉冲变得越来越尖锐,即产生了Weertman脉冲.研究结果显示：由于这种脉冲的出现,破裂在正方向上（东北方向）能够自己放大、自己愈合、自行维持,摩擦热极小,所以破裂能够沿着东北方向一直传播,直到应力场方位发生变化,不利于破裂时才最后终止.但在西南方向,破裂过程中断层面上的正应力增大,阻碍破裂继续扩展.最后就出现了汶川地震中破裂朝东北方向单侧优势传播的基本格局.模拟结果还表明：若断层面两侧介质均匀,则破裂向两侧是对称传播,且破裂距离很短,因此这种情况无法产生像汶川大地震那样的特大地震.因此,文中的模拟结果表明龙门山断裂带两侧的物性差异是造成汶川大地震单侧传播的决定性因素.断层两侧物性差异（bimaterial contrast）影响断层破裂过程的研究对于深入认识地震动力学过程、地震灾害预测及评估等有重要的科学意义.     

3D simulation of near-fault strong ground motion： comparison between surface rupture fault and buried fault

In this paper, near-fault strong ground motions caused by a surface rupture fault (SRF) and a buried fault (BF) are numerically simulated and compared by using a time-space-decoupled, explicit finite element method combined with a multi-transmitting formula (MTF) of an artificial boundary. Prior to the comparison, verification of the explicit element method and the MTF is conducted. The comparison results show that the final dislocation of the SRF is larger than the BF for the same stress drop on the fault plane. The maximum final dislocation occurs on the fault upper line for the SRF; however, for the BF, the maximum final dislocation is located on the fault central part. Meanwhile, the PGA, PGV and PGD of long period ground motions (≤1 Hz) generated by the SRF are much higher than those of the BF in the near-fault region. The peak value of the velocity pulse generated by the SRF is also higher than the BF. Furthermore, it is found that in a very narrow region along the fault trace, ground motions caused by the SRF are much higher than by the BF. These results may explain why SRFs almost always cause heavy damage in near-fault regions compared to buried faults. Supported by: National Natural Science Foundation of China Under Grant No. 50408003; National Scientific and Technical Supporting Programs Funded by Ministry of Science & Technology of China Under Grant No. 2006BAC13B01