Analysis of RC slab–beam–column sub‐assemblages subjected to bidirectional lateral cyclic loading using a new 3D macroelement

An existing two‐dimensional macroelement for reinforced concrete beam–column joints is extended to a three‐dimensional macroelement. The three‐dimensional macroelement for beam–column joints consists of six rigid interface plates and uniaxial springs for concrete, steel, and bond–slip, which model the inside of a beam–column joint. The mechanical models for the materials and the stiffness equation for the springs are also presented. To validate the model, we used test results from three slab–beam–column sub‐assemblages subjected to bi‐lateral cyclic load. It is revealed that the new joint model is capable of capturing the strength of beam–column joints and the bidirectional interaction in joint shear response, including the concentration of damage in the beam–column joint, the pinching nature in hysteretic behavior, the stiffness degradation, and strength deterioration resulting from cyclic and bidirectional loading. Copyright © 2017 John Wiley & Sons, Ltd.     

预应力混凝土空间框架节点二维拟静力试验研究

采用拟静力试验方法对预应力混凝土和普通钢筋混凝土空间框架内节点进行了不同轴压比下单、双向循环加载的试验研究,得到不同加载方式下试件的滞回曲线。分析了各个试件的破坏形式、承载力、刚度、延性及耗能能力,通过比较和对滞回曲线的分析得出：双向水平荷载作用对构件耦合作用明显,构件存在扭转效应,构件的强度退化和刚度退化比单向荷载作用严重,节点的耗能能力降低。     

Numerical analyses of pile performance in laterally spreading frozen ground crust overlying liquefiable soils

Lateral spread of frozen ground crust over liquefied soil has caused extensive bridge foundation damage in the past winter earthquakes. A shake table experiment was conducted to investigate the performance of a model pile in this scenario and revealed unique pile failure mechanisms. The modelling results provided valuable data for validating numerical models. This paper presents analyses and results of this experiment using two numerical modeling approaches: solid-fluid coupled finite element (FE) modeling and the beam-on-nonlinear-Winkler-foundation (BNWF) method. A FE model was constructed based on the experiment configuration and subjected to earthquake loading. Soil and pile response results were presented and compared with experimental results to validate this model. The BNWF method was used to predict the pile response and failure mechanism. A p-y curve was presented for modelling the frozen ground crust with the free-field displacement from the experiment as loading. Pile responses were presented and compared with those of the experiment and FE model. It was concluded that the coupled FE model was effective in predicting formation of three plastic hinges at ground surface, ground crust-liquefiable soil interface and within the medium dense sand layer, while the BNWF method was only able to predict the latter two.     

Comparative efficiency analysis of different nonlinear modelling strategies to simulate the biaxial response of RC columns

The performance of different nonlinear modelling strategies to simulate the response of RC columns subjected to axial load combined with cyclic biaxial horizontal loading is compared. The models studied are classified into two categories according to the nonlinearity distribution assumed in the elements: lumped-plasticity and distributed inelasticity. For this study, results of tests on 24 columns subjected to cyclic uniaxial and biaxial lateral displacements were numerically reproduced. The analyses show that the global envelope response is satisfactorily represented with the three modelling strategies, but significant differences were found in the strength degradation for higher drift demands and energy dissipation.     

Fiber-based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

An efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber-based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy-based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub-column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake-induced collapse. The proposed model is implemented in an open-source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four-story steel frame building, which was tested at full-scale through collapse. Limitations as well as suggestions for future work are discussed.     

Investigation of a cyclic laterally loaded model pile group

In certain regions of the world, designing deep foundations to withstand seismic loading is a reality. Seismic loading of structures and foundations reaches its most critical state as a cyclic lateral force. The response of soils and foundations to repetitive lateral forces is highly complex, relegating most design methods to be based upon overly conservative rules-of-thumb. The primary objective of this research was to analyze the mechanics of seismic loading on pile groups in clay soils. To achieve this a model testing facility was constructed to house a fully instrumented 1×5 model pile group that was subjected to cyclic lateral loading. An empirically based method for pile group design is suggested based upon the results generated from model pile group testing.     

Three‐dimensional beam–truss model for reinforced concrete walls and slabs – part 2: modeling approach and validation for slabs and coupled walls

A three‐dimensional beam–truss model (BTM) for reinforced concrete (RC) walls that explicitly models flexure–shear interaction and accurately captures diagonal shear failures was presented in the first part of this two‐paper series. This paper extends the BTM to simulate RC slabs and coupled RC walls through slabs and beams. The inclination angle of the diagonal elements for coupled RC walls is determined, accounting for the geometry of the walls and the level of coupling. Two case studies validate the model: (1) a two‐bay slab–column specimen experimentally tested using cyclic static loading and (2) a five‐story coupled T‐wall–beam–slab specimen subjected to biaxial shake table excitation. The numerically computed lateral force–lateral displacement and strain contours are compared with the experimentally measured response and observed damage. The five‐story specimen is characterized by diagonal shear failure at the bottom story of the walls, which is captured by the BTM. The BTM of the five‐story specimen is used to study the effects of coupling on shear demand for lightly reinforced RC coupled walls. The effect of mesh refinement and bar fracture of non‐ductile transverse reinforcement is studied. Copyright © 2016 John Wiley & Sons, Ltd.     

Damage evolution in reinforced concrete columns subjected to biaxial loading

An analysis of the damage observed in 24 reinforced concrete (RC) columns tested under uniaxial and biaxial horizontal loading is presented. The test results show that for biaxial loading conditions specific damage occurs for lower drift demands when compared with the corresponding uniaxial demand (a reduction of 50–75 % was found). The damage distribution observed in each column is also analysed. No significant differences are found in the plastic hinge length for uniaxial and biaxial loading. The drift demands associated with each damage state are compared with reference values proposed in international guidelines. Finally, and based on the philosophy of the Park and Ang uniaxial damage index, two new expressions are proposed for the evaluation of damage in RC elements under biaxial loading. The results of the application of these expressions to the experimental results are discussed.     

A nonlinear macroelement model for the seismic analysis of masonry buildings

The macroelement technique for modelling the nonlinear response of masonry panels is particularly efficient and suitable for the analysis of the seismic behaviour of complex walls and buildings. The paper presents a macroelement model specifically developed for simulating the cyclic in‐plane response of masonry walls, with possible applications in nonlinear static and dynamic analysis of masonry structures. The model, starting from a previously developed macroelement model, has been refined in the representation of flexural–rocking and shear damage modes, and it is capable of fairly simulating the experimental response of cyclic tests performed on masonry piers. By means of two internal degrees of freedom, the two‐node macroelement permits to represent the coupling of axial and flexural response as well as the interaction of shear and flexural damage. Copyright © 2013 John Wiley & Sons, Ltd.     

液化场地桥梁群桩基抗震分析简化方法

基于已完成的液化场地土—桩—桥梁结构地震相互作用振动台试验,利用两步法、等效单桩法,建立了液化场地群桩基础抗震分析的动力非线性文克尔地基梁模型。该模型考虑了桩—土相互作用的影响。首先,按照等刚度原则将群桩简化为等效单桩;其次,选用弹簧元件和阻尼原件并联的宏单元模拟桩—土动力相互作用;然后,计算地震作用下自由场地的土体位移和孔压比;最后,将地震作用下自由场地土体位移和孔压比作为模型的外部激励,计算桩的动力反应规律。将简化方法计算结果与液化场地桥梁桩基振动台试验结果进行对比发现,两者吻合较好,验证了简化方法的正确性。     

Biaxial testing of unbonded post‐tensioned rocking bridge piers with external replacable dissipaters

The biaxial response of two bridge piers is experimentally investigated. A post‐tensioned precast bridge pier with external replaceable mild‐steel dissipaters is tested under biaxial loading. The performance of the post‐tensioned bridge pier is compared with a conventionally reinforced monolithic bridge pier. The experimental biaxial response is then compared with previous uniaxial experimental testing of identical bridge piers to understand the influence of biaxial loading, specifically concerning post‐tensioned rocking sections. A 3‐dimensional moment–curvature and moment–rotation analysis program is created to generate the monotonic section response of a conventional and post‐tensioned bridge pier. After comparing the accuracy of the section analysis program to the experimental testing of the monolithic pier, the program is validated against the experimental testing of the post‐tensioned bridge pier. This section analysis program is then used in the calibration of a macro‐model to capture the entire cyclic response of the post‐tensioned bridge pier. The macro‐model adopts multiple linear‐elastic compression‐only springs at the rocking interface, combined with non‐linear inelastic springs for each of the mild‐steel dissipaters and returns encouraging results at both local and global levels. The paper concludes with a number of biaxial moment‐interaction design charts for monolithic and post‐tensioned bridge piers as a function of mechanical and geometric section properties. The design charts define the biaxial yield surface at nominal yield and at the design section capacity defined by one of three material limit states. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulations of shake-table experiment for dynamic soil-pile-structure interaction in liquefiable soils

A shake-table experiment on pile foundations in liquefi able soils composed of liquefi able sand and overlying soft clay is studied. A three-dimensional(3D) effective stress fi nite element(FE) analysis is employed to simulate the experiment. A recently developed multi-surface elasto-plastic constitutive model and a fully coupled dynamic inelastic FE formulation(u-p) are used to model the liquefaction behavior of the sand. The soil domains are discretized using a solid-fl uid fully coupled(u-p) 20-8 noded brick element. The pile is simulated using beam-column elements. Upon careful calibration, very good agreement is obtained between the computed and the measured dynamic behavior of the ground and the pile. A parametric analysis is also conducted on the model to investigate the effect of pile-pinning, pile diameter, pile stiffness, ground inclination angle, superstructure mass and pile head restraints on the ground improvement. It is found that the pile foundation has a noticeable pinning effect that reduces the lateral soil displacement. It is observed that a larger pile diameter and fi xed pile head restraints contribute to decreasing the lateral pile deformation; however, a higher ground inclination angle tends to increase the lateral pile head displacements and pile stiffness, and superstructure mass seems to effectively infl uence the lateral pile displacements.     

Generalized cyclic p–y curve modeling for analysis of laterally loaded piles

Owing to their simplicity and reasonable accuracy, Beam on Nonlinear Winkler Foundation (BNWF) models are widely used for the analysis of laterally loaded piles. Their main drawback is idealizing the soil continuum with discrete uncoupled springs representing the soil reactions to pile movement. Static p–y curves, obtained from limited full-scaled field tests, are generally used as a backbone curve of the model. However, these empirically derived p–y curves could not incorporate the effects of various pile properties and soil continuity. The strain wedge method (SWM) has been improved to assess the nonlinear p–y curve response of laterally loaded piles based on a three-dimensional soil–pile interaction through a passive wedge developed in front of the pile. In this paper, the SWM based p–y curve is implemented as the backbone curves of developed BNWF model to study the nonlinear response of single pile under cyclic lateral loading. The developed nonlinear model is capable of accounting for various important soil–pile interaction response features such as soil and pile yielding, cyclic degradation of soil stiffness and strength under generalized loading, soil–pile gap formation with soil cave-in and recompression, and energy dissipation. Some experimental tests are studied to verify the BNWF model and examine the effect of each factor on the response of laterally loaded pile embedded in sand and clay. The experimental data and computed results agree well, confirming the model ability to predict the response of piles under one-way and two-way cyclic loading. The results show that the developed model can satisfactorily simulate the pile stiffness hardening due to soil cave in and sand densification as observed in the experiment. It is also concluded from the results that the gap formation and soil degradation have significant effects on the increase of lateral pile-head deflection and maximum bending moment of the pile in cohesive soils.     

无限层弹性地基中常轴力桩基的地震反应分析

根据Ｗｉｎｋｌｅｒ地基模型，对桩基础通过特性分析建立了合理的力学模型。在动力分析的基础上，给出了桩基础横向自振特性及在常轴力与横向地震载荷作用下的强迫反应解析解。文中的解析公式为桩基础动力分析提供了一种新的解析方法。     

Shaking table tests on the lateral response of a pile buried in liquefied sand

This paper presents an experimental study on the lateral resistance of a pile subjected to liquefaction-induced lateral flow. To observe the soil surrounding the pile during liquefaction, it was modeled as a buried cylinder that corresponded to a sectional model of the prototype pile at a certain depth in the subsoil. In order to create a realistic stress condition in the model ground, the model was prepared in a sealed container and the overburden pressure was applied to the ground surface by a rubber pressure bag. The model pile was actuated back and forth through rods attached on each side by an electro-hydraulic actuator.This paper focuses on observing the deformation of the liquefied soil surrounding the pile when a large relative displacement between the pile and the soil is induced. The loading rate effect on the lateral resistance of the pile in the liquefied sand and the influence of the relative density are also investigated.Test results show that a larger resistance is mobilized as the loading rate becomes higher. When the loading rate is higher, the cylinder displacement required for the lateral resistance becomes smaller. It has been also observed that as the relative density of the soil increases, dilatancy of the soil in front of the pile also increases.     

Nonlinear lateral interaction in pile dynamics

A model for pile lateral response to transient dynamic loading and to harmonic loading is presented allowing for nonlinear soil behaviour, discontinuity conditions at the pile-soil interface and energy dissipation through different types of damping. The approach is used to establish equivalent linear stiffness and damping parameters of single piles as well as dynamic interaction factors for approximate nonlinear analysis of pile groups. The applicability of these parameters to the pile-group analysis was examined, and a reasonable agreement with the direct analysis was found. The superposition technique may be used to analyze the response of small pile groups. Also, the dynamic stiffness of pile groups is greatly affected by both the nonlinear behavior of the soil and the slippage and gapping between the pile and soil. For a basic range of soil and pile parameters, equivalent linear stiffness and damping parameters of single piles and interaction factors for approximate nonlinear analysis are provided.     

平面不对称结构非弹性地震反应分析的平扭耦联Bouc-Wen模型

综合考虑强度退化、刚度退化、捏拢效应等典型滞回特性的影响,建立了双向地震作用下平面不对称结构非弹性地震动力响应分析的平扭耦联Bouc-Wen模型.该模型采用圆形屈服面来描述双向抗侧恢复力之间的耦合效应,而采用锥体或球体屈服面来描述双向抗侧和抗扭恢复力之间的耦合效应,并结合69条强震记录,定量地分析了平扭耦联效应对平面不...     

可液化场地桥梁桩基改进m值法研究

为了合理分析可液化场地桥梁桩基侧向承载力进行了改进m值法的研究。基于振动台试验和m值法,建立了桩-土相互作用体系有限元分析模型;引入反映可液化砂层侧向承载力衰减状态的孔压比指标值Ru;将不同时刻对应墩顶配重惯性力作为体系外部激励施加于墩顶;通过不断试算液化过程中砂土的m值,保证桩的弯矩计算值与试验值吻合较好。建立了考虑孔压比效应的砂土m值衰减因子p与Ru之间关系式。最后,推荐给出可液化场地桥梁桩基侧向承载性能分析的改进m值法。     

Load distribution in large pile groups under static and dynamic loading

Research on the action of pile groups in resisting lateral loading is usually based on analysis, field and centrifuge tests of small pile groups. The interaction between piles in these groups is modelled by modifying the lateral resistance p–y curves developed for a single pile using row dependent reduction factors or a group factor for the entire group to simulate the effect of soil–pile–soil interaction. The modifying factors for the p–y curves and the appropriate group factors for pile groups are based entirely on static tests and there is no direct verification that these factors are appropriate to handle the dynamic loading of earthquake induced ground motions. In this paper we investigate the interaction effects between piles under static and seismic loading using the computer program VERSAT-P3D, which uses an equivalent linear constitutive model for the soil. The analytical procedure is calibrated using data from a static field load test on a single pile. Several pile groups, 2 × 2, 3 × 3, 4 × 4, 5 × 5, 8 × 8, 10 × 10, 10 × 2 and 15 × 2 were analysed for the study. Each group was subjected to static pushover and earthquake loading and the distribution of static and dynamic shear forces at various lateral displacements were evaluated. The study shows that the distribution of load within a pile group under dynamic loading varies significantly from the distribution under static loading and is strongly load intensity dependent. Current practice assumes that the distributions are similar.     

Numerical modeling of centrifuge cyclic lateral pile load experiments

To gain insight into the inelastic behavior of piles, the response of a vertical pile embedded in dry sand and subjected to cyclic lateral loading was studied experimentally in centrifuge tests conducted in Laboratoire Central des Ponts et Chaussées. Three types of cyclic loading were applied, two asymmetric and one symmetric with respect to the unloaded pile. An approximately square-root variation of soil stiffness with depth was obtained from indirect in-flight density measurements, laboratory tests on re...