An improved pseudo-static method for seismic resistant design of underground structures

This paper describes a commonly used pseudo-static method in seismic resistant design of the cross section of underground structures. Based on dynamic theory and the vibration characteristics of underground structures, the sources of errors when using this method are analyzed. The traditional seismic motion loading approach is replaced by a method in which a one-dimensional soil layer response stress is differentiated and then converted into seismic live loads. To validate the improved method, a comparison of analytical results is conducted for internal forces under earthquake shaking of a typical shallow embedded box-shaped subway station structure using four methods： the response displacement method, finite element response acceleration method, the finite element dynamic analysis method and the improved pseudo-static calculation method. It is shown that the improved finite element pseudo-static method proposed in this paper provides an effective tool for the seismic design of underground structures. The evaluation yields results close to those obtained by the finite element dynamic analysis method, and shows that the improved finite element pseudo-static method provides a higher degree of precision.     

Seismic analysis of deep tunnels in near fault conditions: a case study in Southern Italy

The importance of underground structures in transportation and utility networks makes their vulnerability to earthquakes a sensitive issue. Underground facilities are usually less vulnerable to earthquakes compared to above-ground structures, but the associated risk may be relevant, since even a low level of damage may affect the serviceability of a wide network. Seismic analysis of tunnels close to seismogenic faults is a complex problem, which is often neglected at the design stage for the lack of specific codes or guidelines for the design of underground structures in seismic conditions and also because, as mentioned above, underground structures are considered less vulnerable to earthquake loading. This paper investigates the seismic response of deep tunnels focusing on the required steps for a proper design under both static and dynamic loading. The study aims at contributing to improve the methods currently used for the seismic analysis of underground structures. At this purpose, the seismic response of a deep tunnel in Southern Italy has been investigated along the transversal direction. The infrastructure is part of the railway switch line connecting Caserta to Foggia in the Southern Apennines which is one of the most active seismic regions in Italy. The seismic response in the transversal direction has been analysed by using the pseudo-static approach as well as through advanced numerical modeling using the spectral element method coupled with a kinematic approach for finite fault simulations. The pseudo-static approach has been implemented using a closed-form analytical solution. The results obtained from advanced numerical modeling and the pseudo-static method have been compared to assess their validity and limitations.     

Pseudo-static limit analysis by discontinuity layout optimization: Application to seismic analysis of retaining walls

Discontinuity layout optimization (DLO) is a recent development in the field of computational limit analysis, and to date, the literature has examined the solution of static geotechnical stability problems only by this method. In this paper the DLO method is extended to the solution of seismic problems though the use of the pseudo-static approach. The method is first validated against the solutions of Mononobe–Okabe and Richards and Elms for the seismic stability of retaining walls, and then used to study the effect of a wider range of failure modes. This is shown to significantly affect the predicted stability. A framework for modelling water pressures in the analysis is then proposed. Finally an example application of the method is illustrated through the assessment of two quay walls subjected to the Kobe earthquake.     

随机地震动作用下的结构振动控制试验设计

研究了随机地震动作用下基于MR阻尼器的结构振动控制振动台试验设计的若干问题。首先,由原型结构按动力相似关系进行了模型结构的设计,基于ANSYS模态分析的结果识别出了其结构参数;其次,基于物理随机地震动模型生成了试验地震动样本,根据试验要求调整了各地震动样本的加速度峰值;然后,基于MATLAB对试验模型进行了随机地震动作用下无控与主动控制数值仿真分析;最后,结合ANSYS弹塑性动力时程分析,研究了试验模型的动力稳定性。介绍的振动控制试验设计方法可供进行类似试验设计的研究人员参考。     

基于拟动力法的抗滑桩加固边坡地震稳定性分析

地震力作用下土质边坡动态稳定性研究对实际边坡工程有着重要的意义。采用拟动力法结合简化毕肖普法研究坡顶抗滑桩加固土质边坡在地震力作用下的动态稳定性。尽管拟静力法是目前处理地震力最为广泛的方法之一,但其局限性在于无法考虑地震力随时间变化且忽略了地震波在土体中的传播。而拟动力法采用正弦波模拟地震波在土中传播,并考虑地震波从坡脚传递到坡顶的相位差以及阻尼力对边坡稳定性的影响,通过边坡安全系数的变化揭示土质边坡在地震力作用下的稳定性变化规律。将得到的结果与拟静力法进行对比,突出了拟动力法的优势。最后,考虑水平地震加速度系数、加速度幅值放大系数以及土体内摩擦角对边坡稳定性的影响,以期对实际工程提供理论借鉴。     

Slope seismic stability analysis on kinematical element method and its application

In this paper, kinematical element method (KEM) is extended to the solution of seismic slope stability with the pseudo-static approach. Analytical expressions are derived to calculate the factor of safety of slopes subjected to seismic loading and pore-water pressure. KEM is adopted to assess seismic stability of slope and some examples show that the results obtained from KEM, limit equilibrium method (LEM), variational method and strength reduction method (SRM) are generally in good agreement. And then the seismic slope stability charts are developed on the basis of KEM and pseudo-static approach, providing a rapid and reliable way to calculate the factor of safety and the location of critical slip surface without iteration. Based on the above seismic slope stability charts, a new back analysis method is presented. KEM and pseudo-static approach are applied to study the effect of blasting on the stability of open pit slope, and the approach to determine the relationship between critical explosive weight and distance is presented.     

边坡地震稳定性分析探讨

传统的拟静力法和安全系数时程分析法在评价边坡地震稳定性时存在一定的局限性。在提出准确的评价边坡地震稳定性必需因素的基础上,建议对边坡地震稳定性分析方法重新进行分类。根据动力分析得到的边坡在地震作用下的破坏机制和破裂面的性质和位置,提出基于拉-剪破坏的动力时程分析法和强度折减动力分析法。第一种方法将FLAC计算得到破坏时刻的动应力施加到静力情况下边坡上,采用动力分析得到的拉-剪破裂面,结合极限平衡法求解边坡地震安全系数,是一种改进的动力有限元时程分析法;第二种方法考虑了拉-剪破坏的FLAC强度折减动力分析法,是完全动力的方法。最后通过算例分析验证了新方法的可行性,为边坡地震安全系数计算提供了一种新的思路。     

Multiply supported secondary systems part I: Response spectrum analysis

A response spectrum procedure is developed for seismic analysis of multiply supported secondary systems. The formulation is based on the random vibration analysis of structural systems subjected to correlated inputs applied at several supports. For a proper response spectrum analysis of a multiple support system, the support inputs are required to be defined in terms of the auto and cross pseudo-acceleration and relative velocity floor response spectra. Also information about the floor displacements and velocities as well as their correlations is required. The response of the secondary system is expressed as a combination of the dynamic and pseudo-static response components. The dynamic component is associated with the inertial effects of the support accelerations, whereas the pseudo-static component is due to the displacement of the supports relative to each other. Herein, the correlation between these two parts of the response is included through a term called the cross response component. Each of these components of the response can be calculated by a response spectrum method. The application of the proposed method is demonstrated by numerical examples.     

Mode acceleration-based response spectrum approach for nonclassically damped structures

The paper describes the development of a mode accleration-based response spectrum approach for calculating the seismic design response of the nonclassically damped structures. The response is divided into a pseudo-static part and a dynamic part. The pseudo-static part is calculated by a simple static analysis of the structure for the inertial forces, induced by a unit ground acceleration, applied statically. The dynamic part, of course, pends upon the dynamic characteritics of the structure which are defined in terms of the complex-valued modal characteristics. The correlation between the pseudo-static and dynamic components is properly considered. The design ground input in this approach is defined in terms of the relative acceleration and relative velocity response spectra. The proposed approach has the desired attribute of the mode acceleration approach as the response can be accurately calculated even if only a first few modes are used in the analysis. The approach is computationally more efficient than the convenionally used mode displacement approach. The applicability of the approach is verified by numerical simulation results.     

长应力波对于深部隧道衬砌的作用

应力波与隧道衬砌的相互作用问题为岩石力学的一个十分复杂的问题,到目前为止还没有得到圆满的解决。对于考虑介质与结构弹塑性性质的课题,解析解更难以求得。研究表明长波与深地下硐室的作用问题可以用拟静法解答。本文用拟静法研究了考虑岩体塑性性质时长纵波与地下硐室的相互作用问题。并获得了确定长应力波对于隧道支护作用的解析解。     

桩-液化土相互作用p-y关系分析

基于多工况的桩-液化土体动力相互作用振动台试验,研究地震荷载作用下液化土层中桩土间侧向相互作用力p与桩身和土体间侧向相对位移y之间的关系。将试验得到的实际p-y曲线与采用拟静力法和以API规范为基础的折减系数法计算出的p-y曲线进行对比,结果表明:(1)液化土层中试验得到的桩真实p-y响应及由拟静力法和折减系数法得到的结果都呈非线性变化,三者极限状态有接近一致的趋势,但变化过程差异明显;(2)采用拟静力法和折减系数法都会使液化土层桩基础侧向反力迅速增长,很快达到屈服极限,远远超过实际情况,会导致相当保守的结果;(3)液化进程中控制桩p-y响应的是土体位移而非惯性力,因而拟静力法和折减系数法的原理不适合桩-液化土体动力相互作用分析,不能用于液化土层中桩基础地震响应的计算。     

Critical notch depths for failure of coastal limestone cliffs: case study at Kuro‐shima Island,Okinawa, Japan

Development of a notch at the base of a cliff reduces cliff stability and often induces a collapse. Pleistocene limestone coastal cliffs of elevation 5?m in Kuro‐shima, Ryukyu Islands, have a prominent notch with a depth of 3–4?m at their bases. Around these coastal cliffs, collapses different from previous studies of cliff collapses in the Ryukyu Islands were found; collapses in Kuro‐shima have a horizontal failure surface. The horizontal failure surface, situated at the height of the failure surface corresponding to the retreat point of the notch, is bounded by vertical joints cutting the whole cliff and the reef flat in front of the cliff. Two types of horizontal failure surface were found, triangular and quadrangular; the distinction appears to depend on the angle between the vertical joints and the front face of the cliff. Prior to collapse, these cliffs appear to have been separated from the adjacent cliffs by the development of vertical joints. Consequently, a cliff that will collapse can be identified in advance; cliff instability is strongly dependent on the development of a notch. To study the effect of notch development on cliff collapse, the notch depth at which collapse occurs was calculated using stability analysis. Instability of a cliff increases with notch depth; collapse occurs at the horizontal failure surface when the ratio of the notch depth to the seaward length of the cliff is approximately 0·5–0·7 for a triangular failure surface, and 0·7–0·9 for a quadrangular failure surface. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic behavior of an inverted T-shape flexible retaining wall via dynamic centrifuge tests

In the design procedure for a retaining wall, the pseudo-static method has been widely used and dynamic earth pressure is calculated by the Mononobe–Okabe method, which is an extension of Coulomb’s earth pressure theory computed by force equilibrium. However, there is no clear empirical basis for treating the seismic force as a static force, and recent experimental research has shown that the Mononobe–Okabe method is quite conservative, and there exists a discrepancy between the assumed conditions and real seismic behavior during an earthquake. Two dynamic centrifuge tests were designed and conducted to reexamine the Mononobe–Okabe method and to evaluate the seismic lateral earth pressure on an inverted T-shape flexible retaining wall with a dry medium sand backfill. Results from two sets of dynamic centrifuge experiments show that inertial force has a significant impact on the seismic behavior on the flexible retaining wall. The dynamic earth pressure at the time of maximum moment during the earthquake was not synchronized and almost zero. The relationship between the back-calculated dynamic earth pressure coefficient at the time of maximum dynamic wall moment and the peak ground acceleration obtained from the wall base peak ground acceleration indicates that the seismic earth pressure on flexible cantilever retaining walls can be neglected at accelerations below 0.4 g. These results suggest that a wall designed with a static factor of safety should be able to resist seismic loads up to 0.3–0.4 g.     

Mechanics and performance of a tied-back wall under seismic loads

In this paper the stability of a tied-back wall subjected to seismic loads is analysed for a predetermined mode of failure (rotation about the top of the wall) and the analysis is compared with data from tests on this type of wall using the seismic simulator at the State University of New York at Buffalo. We carried out a pseudo-static analysis of the problem using the Mononobe-Okabe earth pressure coefficients, wherein the dynamic effects due to the seismic loading are converted into equivalent static loads. The acceleration ratio at which the wall fails by rotation about the top was obtained by considering the moments due to the various lateral earth pressure resultants and the inertial forces induced in the soil due to the seismic loading. We found that the presence of wall friction on the passive side significantly enhances the stability of the flexible retaining wall under seismic loads. Thus, flexible retaining walls supporting dry cohesionless soil can be very efficient during earthquakes. Under moderate earthquakes, an increase in the depth of embedment increases the dynamic factor of safety significantly. However, beyond a certain acceleration ratio for a soil with a particular value of ø, any increase in the depth of emdedment has no effect in impeding failure, irrespective of any change in the geometry of the system. Seismic design charts are presented to evaluate the stability of, and to design, flexible retaining walls embedded in dry cohesionless soils under seismic loading.     

Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

Based on the concept of structural passive control, a new type of slit shear wall, with improved seismic performance when compared to an ordinary solid shear wall, was proposed by the authors in 1996. The idea has been verified by a series of pseudo-static and dynamic tests. In this paper a macro numerical model is developed for the wall element and the energy dissipation device. Then, nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table. Furthermore, the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model, and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy. Finally, according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response, the optimal analysis is carried out to select design parameters for the energy dissipation device.     

Development of real-time pseudo dynamic testing

This paper presents a study for the development of a system capable of performing real-time pseudo dynamic testing. The system combines the basics of the pseudo dynamic test with a dynamic actuator, a digital displacement transducer and a digital servo-mechanism. The digital servo-mechanism has been introduced to ensure accurate displacement and velocity control, in which digital feedback control with a time interval of 2 msec has been performed continuously during actuator motion. Using the system, pseudo dynamic tests under sinusoidal and earthquake ground motion are carried out for a structure having a viscous damper, demonstrating that a perfectly real-time pseudo dynamic test can be achieved by incorporating the modified central difference method into an extra buffer operation of the digital servo-mechanism. The responses solved by the pseudo dynamic tests are compared with the responses of the test structure as well as those obtained from post-numerical analysis, and it is found that the real-time pseudo dynamic test conducted in this study is accurate.     

Seismic active pressure distribution history behind rigid retaining walls

Evaluating the seismic active earth pressure on retaining walls is currently based on pseudo-static method in practices. In this method, however, it is not simple, choosing an appropriate value for earthquake coefficient, which should fully reflect the dynamic characteristics of both soil and loading is an important problem. On the other hand, by using only two extra dynamic parameters that are shear wave velocity of soil and predominant frequency of probable earthquake, one can benefit from another more accurate tool called pseudo-dynamic method to solve the problem of earth pressure.In this study in the framework of limit equilibrium analysis, pseudo-dynamic method has been applied into horizontal slice method of analysis to account for the effect of earthquake on lateral earth pressure history behind rigid retaining walls. The pressure history resulted from a number of analyses shows that before and after reaching the peak resultant force, different pressure distributions occur behind a wall that put more local pressure than the same at peak. This method would be a tool to control this phenomenon in wall design.     

Seismic stability analysis of reinforced slopes

In this paper, the seismic stability of slopes reinforced with geosynthetics is analysed within the framework of the pseudo-static approach. Calculations are conducted by applying the kinematic theorem of limit analysis. Different failure modes are considered, and for each analytical expressions are derived that enable one to readily calculate the reinforcement force required to prevent failure and the yield acceleration of slopes subjected to earthquake loading. Several results are presented in order to illustrate the influence of seismic forces on slope stability. Moreover, a suitable procedure based on the assessment of earthquake-induced permanent displacement is proposed for the design of reinforced slopes in seismically active areas.     

敦煌莫高窟崖体锚索加固技术钻孔振动效应测试分析

机械设备施工所产生的振动对文物的影响问题已越来越引起人们的重视。如何科学合理地判定其影响程度并采取必要的防振对策，进行现场实地测试获取数据是非常必要的。针对莫高窟崖体的特点，对拟采用的锚索加固技术所产生的振动情况进行了分析测试，获得了不同距离处崖体不同方向的振动加速度和速度，较好地反映了该施工工艺引起的振动效应的实际情况，并对其安全性进行了评估，为莫高窟崖体的加固提供了重要依据。     

Estimation of additional foundation settlements caused by dynamic loading in urban areas

Response of different soils to dynamic loading is of fundamental interest in many engineering, geophysical and environmental studies. Many methods have been proposed to estimate dynamic stability of soils. One more approach, based on laboratory cyclic testing, is discussed in this paper. In our tests, not only the specific features of examined soils, but also different conditions of static and dynamic loading have been taken into account. An analysis of the obtained experimental data explicitly supports the hypothesis of a logarithmic relationship between the axial deformation of soil in cyclic triaxial compression and the number of loading cycles. Evaluation of soil deformation under vibrodynamic loads can also be based on energy approach. The use of critical amount of energy dissipated by soil per its unit volume has been proved to be reliable even in a low dynamic stress range. Convergence of the proposed solution was proved using field measurements and observations. The proposed approach has been applied to evaluate additional settlements of structures founded on the basis of different soil profiles and under various static and dynamic loading conditions.