Closure to “performance of a transparent Flexible Shear Beam container for geotechnical centrifuge modelling of dynamic problems” by Ghayoomi M., Dashti S., and McCartney J.S.

In response to the discussion, this closure presents a new set of analyses to confirm the satisfactory performance of the recently-developed transparent Flexible Shear Beam (FSB) container and its limitations. The lateral deformations of the box estimated using Finite Element analyses and measured during centrifuge experiments were compared. The maximum deformation to height ratio was sufficiently small to retain at-rest lateral earth pressures for loose to medium-dense cohesionless soils and all cohesive materials. In addition, higher frequency modes of vibration were estimated for the container, and were found to occur where the earthquake energy is less significant. Further, the box is expected to approximately replicate free field conditions under 1-D horizontal shaking for the range of soil properties under investigation. Overall, the deformation and vibration analyses indicate that the selection of appropriate rubber material properties and boundary conditions are critical when analyzing the performance of the container.     

Design and commissioning of a laminar soil container for use on small shaking tables

This paper describes the design, fabrication and commissioning of a single axis laminar shear box for use in seismic soil–structure interaction studies. A laminar shear box is a flexible container that can be placed on a shaking table to simulate vertical shear-wave propagation during earthquakes through a soil layer of finite thickness. The laminar shear box described in this paper was designed to overcome the base shear limitations of a small shaking table at The University of Western Ontario. The design details of the box are provided in addition to results of dynamic tests performed to commission the box. A synthetic clay comprising sodium bentonite mixed with diluted glycerin was used as the model soil and 1-G similitude theory was employed to maintain model to prototype similarity. The model soil was compacted into the container in lifts to achieve soil stiffness that increased with depth. A series of shaking table tests and numerical analyses that were performed to study the performance of the laminar box and non-linear seismic behavior of the model clay are described. The results of this study show that the laminar box does not impose significant boundary effects and is able to maintain 1-D soil column behavior. In addition, the dynamic behavior of the model clay during scaled model tests was found to be consistent with the behavior measured during cyclic laboratory tests.     

土层平均剪切波速确定及其可靠性验证——基于钻井台阵强震动记录

震害资料显示,场地条件对地震动特性以及工程结构破坏程度影响显著。为减少因场地效应而造成的经济损失和社会影响,在进行场地地震反应分析时,需最大限度地减小因场地土层模型参数的不确定性引起的地震动评估偏差,为工程结构地震反应分析选取并生成适当的地震动输入。随着强震动观测技术的逐渐发展,大量可靠的钻井台阵记录为地震过程中场地观测点的动力反应提供了直接数据。以美国加州地区La Cienega钻井台阵强震动观测数据为基础,利用互相关函数,对不同强度地震作用下场地土层的平均剪切波速进行分析,并在此基础上,以Cyclic 1D为模拟平台,建立一维自由场地地震反应有限元分析模型。分析结果表明：通过钻井台阵地震动观测数据识别,得到场地平均剪切波速,能够反映该场地的动力特性,数值模拟计算结果和台阵地震动记录基本吻合,可为数值模型参数选取提供依据。     

Performance of an equivalent shear beam (ESB) model container for dynamic geotechnical centrifuge tests

In dynamic centrifuge tests, appropriate boundary conditions are required in order to simulate the seismic semi-infinite soil layer responses within the confines of a finite size model container. An ESB (equivalent shear beam) model container first designed at the University of Cambridge was built with a stack of light-weight aluminum frames separated by rubber to experimentally achieve this goal. In this paper, a significant number of dynamic centrifuge tests and the corresponding seismic response analyses were performed to evaluate the dynamic performance of a newly constructed ESB model container and to shed light on the range of testable soil conditions. In the set of conducted tests, it appears that the end walls of the ESB model container behave in accordance with the dynamic response of the soil deposit, despite a difference in the natural period depending on the relative density of the sand deposit. This is attributed to the differences in mass and stiffness of the end walls compared to those of the contained soil model. For partially filled model container, significant differences in seismic responses are observed in the end walls and in the soil deposit due to seismic interaction caused by the upper unfilled frames of the container. These findings suggest that dynamic model tests using this ESB model container should be conducted with the container completely filled. In addition, on the basis of a comparison with the seismic soil behavior inside a rigid-walled model container, it is clear that the ESB model container can provide a more representative lateral boundary configuration for dynamic site response studies.     

Response spectral amplification ratios from 1- and 2-dimensional nonlinear soil site models

In order to determine the effect of geometry on the ground response of 2-dimensional (2-D) basins filled with soils that can develop nonlinear response, we use three basin models with width/depth ratios 3, 6 and 10. The three basins are subjected to a suite of rock site records with various magnitudes and source distances. We compute response spectral amplification ratios at four locations on the surface of the 2-D basins, and determine the average variation of the amplification ratios with respect to excitation spectra, for peak ground acceleration (PGA) and 3 spectral periods of 0.2, 0.5, 1 s. Similarly, we compute the average response spectral amplification ratios for two 1-dimensional (1-D) nonlinear models, one having the soil profile at the basin centre and the other having a soil profile at half the depth of the basin. From the relationship between the average amplification ratios and excitation spectra, we determine the cross-over point in terms of excitation spectral values that separate the amplification range from the deamplification range. Our results show that the cross-over point varies significantly from one location to another on the ground surface and from one basin to another, in a range of 0.3–1.1g for PGA. The effects of basin geometry are very strong at weak and moderate excitation, but decrease with increasing excitation spectra in a significant portion around the basin centre. Our results provide some justification for using 1-D models for 2-D basins with a width/depth ratio ?6 if the soil site is subjected to strong ground shaking.     

Boundary effects of a laminar container in centrifuge shaking table tests

Two dynamic centrifuge model tests were performed to simulate dry or saturated sand deposits subjected to 1 Hz base shaking. This experimental study investigated the boundary effects of a laminar container on the seismic response acquired from accelerometers and from pore pressure transducers, both of which were embedded in the sand bed at various depths and distances from the end walls. Under the tested configurations and the employed input motion used in the study, the test results revealed minimal boundary effects on the seismic responses. The measured maximum amplitude, main frequencies, phase lags of acceleration, and the profiles of the calculated RMS acceleration amplification factor were not affected by the boundaries if the instruments were positioned at a distance of more than one-twentieth of the model length from the end walls and were not positioned on the ground surface. No obvious discrepancies were observed in the time histories of excess pore water pressure, measured at a distance of one-fourth of the model length from the end walls. These results infer that variations in the seismic response at the end walls were minimal; hence the laminar container used in the study may be used effectively to simulate 1D shear wave propagation in centrifuge shaking table tests. However, for other testing configurations, a similar study should be undertaken for evaluating the boundary effect of the laminar container on the seismic responses.     

Centrifuge modeling of seismic response of layered soft clay

Centrifuge modeling is a valuable tool used to study the response of geotechnical structures to infrequent or extreme events such as earthquakes. A series of centrifuge model tests was conducted at 80g using an electro-hydraulic earthquake simulator mounted on the C-CORE geotechnical centrifuge to study the dynamic response of soft soils and seismic soil–structure interaction (SSI). The acceleration records at different locations within the soil bed and at its surface along with the settlement records at the surface were used to analyze the soft soil seismic response. In addition, the records of acceleration at the surface of a foundation model partially embedded in the soil were used to investigate the seismic SSI. Centrifuge data was used to evaluate the variation of shear modulus and damping ratio with shear strain amplitude and confining pressure, and to assess their effects on site response. Site response analysis using the measured shear wave velocity, estimated modulus reduction and damping ratio as input parameters produced good agreement with the measured site response. A spectral analysis of the results showed that the stiffness of the soil deposits had a significant effect on the characteristics of the input motions and the overall behavior of the structure. The peak surface acceleration measured in the centrifuge was significantly amplified, especially for low amplitude base acceleration. The amplification of the earthquake shaking as well as the frequency of the response spectra decreased with increasing earthquake intensity. The results clearly demonstrate that the layering system has to be considered, and not just the average shear wave velocity, when evaluating the local site effects.     

1-g Experimental investigation of bi-layer soil response and kinematic pile bending

The effect of soil inhomogeneity and material nonlinearity on kinematic soil–pile interaction and ensuing bending under the passage of vertically propagating seismic shear waves in layered soil, is investigated by means of 1-g shaking table tests and nonlinear numerical simulations. To this end, a suite of scale model tests on a group of five piles embedded in two-layers of sand in a laminar container at the shaking table facility in BLADE Laboratory at University of Bristol, are reported. Results from white noise and sine dwell tests were obtained and interpreted by means of one-dimensional lumped parameter models, suitable for inhomogeneous soil, encompassing material nonlinearity. A frequency range from 0.1 Hz to 100 Hz and 5 Hz to 35 Hz for white noise and sine dwell tests, respectively, and an input acceleration range from 0.015 g to 0.1 g, were employed. The paper elucidates that soil nonlinearity and inhomogeneity strongly affect both site response and kinematic pile bending, so that accurate nonlinear analyses are often necessary to predict the dynamic response of pile foundations.     

Shake table test of soil-pile groups-bridge structure interaction in liquefiable ground

<正>This paper describes a shake table test study on the seismic response of low-cap pile groups and a bridge structure in liquefiable ground.The soil profile,contained in a large-scale laminar shear box,consisted of a horizontally saturated sand layer overlaid with a silty clay layer,with the simulated low-cap pile groups embedded.The container was excited in three E1 Centra earthquake events of different levels.Test results indicate that excessive pore pressure(EPP) during slight shaking only slightly accumulated,and the accumulation mainly occurred during strong shaking.The EPP was gradually enhanced as the amplitude and duration of the input acceleration increased.The acceleration response of the sand was remarkably influenced by soil liquefaction.As soil liquefaction occurred,the peak sand displacement gradually lagged behind the input acceleration;meanwhile,the sand displacement exhibited an increasing effect on the bending moment of the pile,and acceleration responses of the pile and the sand layer gradually changed from decreasing to increasing in the vertical direction from the bottom to the top.A jump variation of the bending moment on the pile was observed near the soil interface in all three input earthquake events.It is thought that the shake table tests could provide the groundwork for further seismic performance studies of low-cap pile groups used in bridges located on liquefiable groun.     

Pile response in submerged lateral spreads: Common pitfalls of numerical and physical modeling techniques

A three dimensional dynamic numerical methodology is developed and used to back-analyze experimental data on the seismic response of single piles in laterally spreading slopes. The aim of the paper is not to seek successful a-priori (Type A) predictions, but to explore the potential of currently available numerical techniques, and also to get feedback on modeling issues and assumptions which are not yet resolved in the international literature. It is illustrated that accurate simulation of the physical pile–soil interaction mechanisms is not a routine task, as it requires the incorporation of advanced numerical features, such as an effective stress constitutive soil model that can capture cyclic response and shear-induced dilation, interface elements to simulate the flow of liquefied ground around the pile and proper calibration of soil permeability to model excess pore pressure dissipation during shaking. In addition, the “conventional tied node” formulation, commonly used to simulate lateral boundary conditions during shaking, has to be modified in order to take into account the effects of the hydrostatic pore pressure surplus that is created at the down slope free field boundary of submerged slopes. A comparative analysis with the two different lateral boundary formulations reveals that “conventional tied nodes”, which also reflect the kinematic conditions imposed by laminar box containers in centrifuge and shaking table experiments, may underestimate seismic demands along the upper part of the pile foundation.     

Seismic response of underground utility tunnels: shaking table testing and FEM analysis

Underground utility tunnels are widely used in urban areas throughout the world for lifeline networks due to their easy maintenance and environmental protection capabilities. However, knowledge about their seismic performance is still quite limited and seismic design procedures are not included in current design codes. This paper describes a series of shaking table tests the authors performed on a scaled utility tunnel model to explore its performance under earthquake excitation. Details of the experimental setup are first presented focusing on aspects such as the design of the soil container, scaled structural model, sensor array arrangement and test procedure. The main observations from the test program, including structural response, soil response, soil-structure interaction and earth pressure, are summarized and discussed. Further, a finite element model (FEM) of the test utility tunnel is established where the nonlinear soil properties are modeled by the Drucker-Prager constitutive model; the master-slave surface mechanism is employed to simulate the soil-structure dynamic interaction; and the confining effect of the laminar shear box to soil is considered by proper boundary modeling. The results from the numerical model are compared with experiment measurements in terms of displacement, acceleration and amplification factor of the structural model and the soil. The comparison shows that the numerical results match the experimental measurements quite well. The validated numerical model can be adopted for further analysis.     

Dynamic response of a geotechnical rigid model container with absorbing boundaries

One of the major challenges encountered in earthquake geotechnical physical modelling is to determine the effects induced by the artificial boundaries of the soil container on the dynamic response of the soil deposit. Over the past years, the use of absorbing material for minimising boundaries effects has become an increasing alternative solution, yet little systematic research has been carried out to quantify the dynamic performance of the absorbing material and the amount of energy dissipated by it. This paper aims to examine the effects induced by the absorbing material on the dynamic response of the soil, and estimate the amount of energy reduced by the absorbing boundaries. The absorbent material consisted of panels made of commercially available foams, which were placed on both inner sides of end-walls of the soil container. These walls are perpendicular to the shaking direction. Three types of foam with different mechanical properties were used in this study. The results were obtained from tests carried out using a shaking table and Redhill 110 sand for the soil deposit. It was found that a considerably amount of energy was dissipated, in particular within the frequency range close to the resonance of the soil deposit. This feature suggests that the presence of foams provides a significant influence to the dynamic response of the soil. The energy absorbed by the boundaries was also quantified from integrals of the Power Spectral Density of the accelerations. It was found that the absorbed energy ranged between a minimum of 41% to a maximum of 92% of the input levels, depending mainly on the foam used in the test. The effects provided by the acceleration levels and depth at which the energy was evaluated were practically negligible. Finally, practical guidelines for the selection of the absorbing material are provided.     

Response of a scale-model pile group for a jacket foundation of an offshore wind turbine in liquefiable ground during shaking table tests

To investigate the seismic response of a pile group during liquefaction, shaking table tests on a 1/25 scale model of a 2 × 2 pile group were conducted, which were pilot tests of a test project of a scale-model offshore wind turbine with jacket foundation. A large laminar shear box was utilized as the soil container to prepare a liquefiable sandy ground specimen. The pile group model comprising four slender aluminum piles with their pile heads connected by a rigid frame was designed with similitude considerations focusing on soil–pile interaction. The input motions were 2-Hz sinusoids with various acceleration amplitudes. The excess pore water pressure generation indicated that the upper half of the ground specimen reached initial liquefaction under the 50-gal-amplitude excitation, whereas in the 75-gal-amplitude test, almost entire ground was liquefied. Accelerations in soil, on the movable frames composing the laminar boundary of the shear box, and along the pile showed limited difference at the same elevation before liquefaction. After liquefaction, the soil and the movable-frame accelerations that represented the ground response considerably reduced, whereas both the movable frames and the piles exhibited high-frequency jitters other than 2-Hz sinusoid, and meantime, remarkable phase difference between the responses of the pile group and the ground was observed, all probably due to the substantial degradation of liquefied soil. Axial strains along the pile implied its double-curvature bending behavior, and the accordingly calculated moment declined significantly after liquefaction. These observations demonstrated the interaction between soil and piles during liquefaction.     

分层土-隧道相互作用体系地震响应分析

为研究地震作用下非均质场地各个土层放大效应以及分层土-隧道的地震响应,以大连某实际工程为背景,基于地震作用下隧道结构动力响应的理论,采用收敛约束法,通过ABAQUS构建分层土-隧道三维有限元模型,并结合振动台试验,验证模拟的准确性;将自由场与有隧道场地进行对比,并结合加速度和傅里叶曲线对模拟数据进行分析。结果表明：(1)土体性质和激励大小对地震波的传递有影响,随着场地由浅到深逐渐增加,峰值加速度逐渐放大,不同分层介质的主要频率和频谱形状发生明显变化;(2)隧道会放大远场的加速度响应,略微降低近场的动力响应;(3)软弱夹层的存在对地震动的放大作用也有明显影响,不同分层介质的不同特性导致土层刚度不同,从而影响地震作用下层状土-隧道的动力相互作用。     

Effects of soil cracking on the seismic response of soil–structure systems

A numerical study on the influence that cracks and discontinuities (closed cracks) can have on the seismic response of a hypothetical soil–structure system is presented and discussed. A 2-D finite-difference model of the soil was developed, considering a bilinear failure surface using a Mohr–Coulomb model. The cracks are simulated with interface elements. The soil stiffness is used to characterize the contact force that is generated when the crack closes. For the cases studied herein, it was considered that the crack does not propagate during the dynamic event. Both cases, open and closed cracks, are considered. The nonlinear behavior was accounted for approximately using equivalent linear properties calibrated against several 1-D wave propagation analyses of selected soil columns with variable depth to account for changes in depth to bed rock. Free field boundaries were used at the edges of the 2-D finite-difference model to allow for energy dissipation of the reflected waves. The effect of cracking on the seismic response was evaluated by comparing the results of site response analysis with and without crack, for several lengths and orientations. The changes in the response obtained for a single crack and a family of cracks were also evaluated. Finally, the impact that a crack may have on the structural response of nearby structures was investigated by solving the seismic-soil–structure interaction of two structures, one flexible and one rigid to bracket the response. From the results of this investigation, insight was gained regarding the effect that discontinuities may have both on the seismic response of soil deposits and on nearby soil–structure systems.     

Nonlinear 3D finite element analysis of soil–pile–structure interaction system subjected to horizontal earthquake excitation

The dynamic response of a seismic soil–pile–structure interaction (SSPSI) system is investigated in this paper by conducting nonlinear 3D finite element numerical simulations. Nonlinear behaviors such as non-reflecting boundary condition and soil–pile–structure interaction modeled by the penalty method have been taken into account. An equivalent linear model developed from the ground response analysis and the modified Drucker–Prager model are separately used for soil ground. A comparison of the two models shows that the equivalent linear soil model results in an underestimated acceleration response of the structure under this ground shaking and the soil behavior should be considered as a fully-nonlinear constitutive model in the design process of the SSPSI system. It was also observed that the dynamic response of the system is greatly affected by the nonlinearity of soil–pile interface and is not sensitive to the dilation angle of the soil. Furthermore, the effect of the presence of pile foundations on SSPSI response is also analyzed and discussed.     

Shaking table test and dynamic response prediction on an earthquake-damaged RC building

This paper presents the results from shaking table tests of a one-tenth-scale reinforced concrete (RC) building model. The test model is a protype of a building that was seriously damaged during the 1985 Mexico earthquake. The input ground excitation used during the test was from the records obtained near the site of the prototype building during the 1985 and 1995 Mexico earthquakes. The tests showed that the damage pattern of the test model agreed well with that of the prototype building. Analytical prediction of earthquake response has been conducted for the prototype building using a sophisticated 3-D frame model. The input motion used for the dynamic analysis was the shaking table test measurements with similarity transformation. The comparison of the analytical results and the shaking table test results indicates that the response of the RC building to minor and the moderate earthquakes can be predicated well. However, there is difference between the predication and the actual response to the major earthquake.     

PART I: Theoretical Site Response Estimation for Microzoning Purposes

— We estimate the theoretical site response along seven cross sections located in the city of Thessaloniki (Greece). For this purpose the 2-D structural models used are based on the known geometry and the dynamic soil properties derived from borehole measurements and other geophysical techniques. Several double-couple sources have been employed to generate the seismic wavefield, and a hybrid method that combines the modal summation with finite differences, has been deployed to produce synthetic accelerograms to a maximum frequency of 6 Hz for all components of motion. The ratios between the response spectra of signals derived for the 2-D local model and the corresponding spectra of signals derived for the 1-D bedrock reference model at the same site, allow us to estimate the site response due to lateral heterogeneities. We interpret the results in terms of both geological and geometrical features of the models and of the characteristics of the wave propagation. The cases discussed confirm that the geometry and depth of the rock basement, along with the impedance contrast, are responsible for ground amplification phenomena such as edge effects and generation and entrapment of local surface waves. Our analysis also confirms that the peak ground acceleration is not well correlated with damage and that a substantially better estimator for possible damage is the spectral amplification.     

An exploration of incorporating site response into PSHA—Part I: Issues related to site response analysis methods

This paper presents a series of analyses for the evaluation of the ground response of two NEHRP class D sites, subjected to shaking by a large number of strong ground-motion records. The two investigated sites have very distinct profiles, but they are characterised by almost identical V_s30 values. The site response analyses are performed using various methods of analysis and input parameters in order to explore the sensitivity of the ground response estimates and to identify the dominating parameters. Equivalent linear analysis is performed using different sets of dynamic soil properties curves, while nonlinear analysis is performed using different target dynamic soil curves, viscous damping formulations and fitting procedures for the constitutive model parameters. Particular focus is given to the sensitivity of the response when soil sites are subjected to high-intensity shaking, a subject of particular interest when the prediction of surface ground motions with low annual probabilities of exceedance is the target of probabilistic seismic hazard analyses (PSHA). The site response analysis results of this paper are incorporated into the probabilistic framework of Bazzurro and Cornell [1] in our companion paper in order to assess their impact on the final soil surface hazard calculation.     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.