Probabilistic pseudo-static analysis of pile foundations in liquefiable soils

This paper presents the development, implementation, and application of a probabilistic framework for the pseudo-static analysis of pile foundations in liquefied and lateral spreading soils. The framework allows for rigorous consideration and propagation of the large uncertainties regarding quantification of seismic loads and soil–pile interaction relationships, which exist in the pseudo-static method. Building upon previous relationships proposed by others, the key features of the presented framework are outlined. In particular, the uncertainty estimation of the induced lateral soil displacements; superstructure inertia loads; and stiffness and strength of the liquefied soils are discussed in detail. The results of applying the pseudo-static method to a case study bridge structure are compared to that obtained using a rigorous seismic effective stress analysis within a similar framework. It is illustrated that the consideration of uncertainties in the pseudo-static framework provides enhanced communication of the foundation's seismic performance to end-users, and that the pseudo-static method provides seismic performance prediction consistent with that obtained using advanced seismic effective-stress analyses.     

Experimental investigation of plastic demands in piles embedded in multi-layered liquefiable soils

Multi-layered soil profiles, where one or more layers consist of loose liquefiable material, most commonly require pile foundations extending beyond the liquefiable layer to competent material. Under seismic loads, if the loose layer liquefies, then large localized plastic demands may be generated in the piles. To study this behavior and provide detailed data to validate numerical models, a 1-g shaking table experiment was conducted considering a single reinforced concrete pile embedded in a three-layer soil system. The model pile of 25 cm diameter was tested under increasing amplitude earthquake excitation in a sloped laminar soil box. The test specimen was designed at the lower bound of typical design to promote yielding, per ATC-32 (Applied Technology Council, 1996) [1]. The pile penetrated 7D (D=pile diameter) into a multi-layered soil configuration composed of a stiff uppermost crust overlying a saturated loose sand layer and a lower dense layer of sand. Plastic demands in the pile were characterized using curvature profiles coupled with back-calculation of the plastic hinge length and post-test physical observations. Results from this test quantify the post-yield behavior of the pile and serve as a complement to previously conducted centrifuge tests.     

A simplified method for unified buckling and free vibration analysis of pile-supported structures in seismically liquefiable soils

In seismic-prone zones with liquefiable deposit piles are routinely used to support structures (buildings/bridges). In this paper, a unified buckling and dynamic approach is taken to characterize this vibration. The pile–soil system is modelled as Euler–Bernoulli beam resting against an elastic support with axial load and a pile head mass with rotary inertia. The emphasis here is to obtain a simple expression that can be used by practicing engineers to obtain the fundamental frequency of the structure–pile–soil system. An approximate method based on an equivalent single-degree-of-freedom model has been proposed. Natural frequencies obtained from the exact analytical method are compared with approximate results. Proposed expressions are general as they are functions of non-dimensional parameters. It is shown that this simplified method captures the essential design features such as: (a) the continuous reduction of the first natural frequency of the structure–pile–soil system due to progressive reduction of soil stiffness due to liquefaction; (b) the reduction in the axial load-carrying capacity of the pile due to instability caused by liquefaction. The results derived in this paper have the potential to be directly applied in practice due to their simple yet general nature. An example problem has been taken to demonstrate the application of the method.     

Computation of degradation factors of p-y curves in liquefiable soils for analysis of piles using three-dimensional finite-element model

This paper presents a procedure to compute the values of degradation factors of p-y curves in the pseudo-static analysis of piles in liquefiable soils. Three-dimensional finite-element model was used for the computation of p and y values using OpenSees computer package. The piles were modeled using beam-column elements and elastic section. The soil continuum was modeled using brick elements and a two-surface plasticity model. By comparing the results of models in two cases of liquefiable and non-liquefiable, values of degradation factors were obtained. Validation of the degradation factors computed was conducted through the centrifuge test results. The simulation results showed a similar trend between degradation factor variation in different densities and sands. With increasing depth, the degradation factor increased. By comparing the results of pseudo-static analysis with the centrifuge test results, it was concluded that the use of the p-y curves with computed degradation factors in liquefiable sand gave reasonable results.     

Seismic response comparison and sensitivity analysis of pile foundation in liquefiable and non-liquefiable soils

Case history investigations have shown that pile foundations are more critically damaged in liquefiable soils than non-liquefiable soils. This study examines the differences in seismic response of pile foundations in liquefiable and non-liquefiable soils and their sensitivity to numerical model parameters. A two-dimensional finite element(FE) model is developed to simulate the experiment of a single pile foundation centrifuge in liquefiable soil subjected to earthquake motions and is validated a...     

Dynamic analysis of piles and pile groups embedded in homogeneous soils

A boundary element formulation for the dynamic analysis of axially and laterally loaded single piles and pile groups is presented. The piles are represented by compressible beam-column elements and the soil as a hysteretic elastic half-space. The governing equations of motion for the pile domain have been solved exactly for distributed periodic loading intensities. These solutions are then coupled with a numerical solution for the motion of the soil domain by satisfying equilibrium and compatibility at the pile-soil interface. The results obtained from the analysis compare favourably with those from alternative analyses, e.g. finite element, but at greatly reduced computational costs.     

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.     

Shake-table investigation of scoured RC pile-group-supported bridges in liquefiable and nonliquefiable soils

This paper presents results of one-g shake-table tests on scoured pile-group-supported bridge models in saturated (liquefiable) and dry (nonliquefiable) sands. The primary objective is to reveal the influence of liquefaction on seismic demands and failure mechanism of scoured bridges. To this end, two identical models, each consisting of a 2 × 2 reinforced concrete pile-group with a center-to-center spacing of 3 times pile diameter, a cap and a single pier with a lumped iron block, were constructed and embedded into saturated and dry sands, respectively, with the same scour depth of 4 times pile diameter. Typical test results, including excess pore pressure, acceleration and displacement demands are interpreted first, followed by the focus on curvature demands and associated seismic failure mechanism identification. Finally, inertial and kinematic effects on pile curvature demands are estimated using cross-correlation analyses. Results show that near-pile liquefied soils exhibit more remarkable dilation tendency as compared to far field. For bridges under the given scour depth, soil liquefaction tends to significantly affect the failure modes via transferring damage positions from pier bottom to pile head and meanwhile from underground pile to pile head. In addition, pile group effects appear to be significant in nonliquefiable soils while to be relatively inessential in liquefied soils. Moreover, the inertial effect is more prominent in nonliquefiable soils, while the kinematic effect itself generally appears to be more significant in liquefiable soils. The test results can be used to validate numerical models for future studies.     

地震作用下可液化场地管道上浮动力响应及影响因素分析

地震作用下土体发生液化之后,由于超静孔隙水压力的产生和土体抗剪强度的降低,管道易发生上浮破坏。为研究管道上浮动力反应的影响因素,基于OpenSees有限元软件,通过目标反应谱和谱匹配等方法选取地震波,考虑不同管土特性和地震动特性,对地震作用下管道上浮动力反应进行了二维数值模拟。结果表明:土体相对密度、管径和管道埋深对管道上浮反应的影响较大,分别给出了土体相对密度、管径、管道埋深对管道上浮位移的影响规律及对应拟合公式;长持时地震动作用下,超静孔隙水压力消散较慢,管道上浮位移可达短持时地震动作用下管道上浮位移的2倍左右;近断层脉冲地震动作用下,管道上浮破坏和横向破坏两种破坏模式同时存在,且由于速度脉冲效应,管道横向破坏风险大于上浮破坏风险。     

A critical review of methods for pile design in seismically liquefiable soils

Collapse and/or severe damage to pile-supported structures are still observed in liquefiable soils after most major earthquakes. Poor performance of pile foundations remains a great concern to the earthquake engineering community. This review paper compares and contrasts the two plausible theories on pile failure in liquefiable soils. The well established theory of pile failure is based on a flexural mechanism; where the lateral loads on the pile (due to inertia and/or lateral spreading) induce bending failure. This theory is well researched in the recent past and assumes that piles are laterally loaded beams. A more recent theory based on buckling instability treats the piles as laterally unsupported slender columns in liquefiable soils and investigates the buckling instability (bifurcation). The objective of this paper is to investigate the implications to practical pile foundation design that flow from both these theories. Provisions for design made by major international codes of practice for pile design including the Japanese Highway Code (JRA) will be considered. The necessity for such codes to consider alternative forms of failure mechanisms such as the buckling instability of piles in liquefied ground will be discussed. S. Bhattacharya–Previously Departmental Lecturer in Engineering Science, University of Oxford, UK and Fellow of Somerville College, Oxford. S. P. G. Madabhushi–Fellow of Girton College, Cambridge.     

Evaluation of seismic performance of pile‐supported models in liquefiable soils

The seismic performance of four pile‐supported models is studied for two conditions: (i) transient to full liquefaction condition, i.e. the phase when excess pore pressure gradually increases during the shaking; (ii) full liquefaction condition, i.e. defined as the state where the seismically induced excess pore pressure equalises to the overburden stress. The paper describes two complementary analyses consisting of an experimental investigation, carried out at normal gravity on a shaking table, and a simplified numerical analysis, whereby the soil–structure interaction (SSI) is modelled through non‐linear Winkler springs (commonly known as p–y curves). The effects of liquefaction on the SSI are taken into account by reducing strength and stiffness of the non‐liquefied p–y curves by a factor widely known as p‐multiplier and by using a new set of p–y curves. The seismic performance of each of the four models is evaluated by considering two different criteria: (i) strength criterion expressed in terms of bending moment envelopes along the piles; (ii) damage criterion expressed in terms of maximum global displacement. Comparison between experimental results and numerical predictions shows that the proposed p–y curves have the advantage of better predicting the redistribution of bending moments at deeper elevations as the soil liquefies. Furthermore, the proposed method predicts with reasonable accuracy the displacement demand exhibited by the models at the full liquefaction condition. However, disparities between computed and experimental maximum bending moments (in both transient and full liquefaction conditions) and displacement demands (during transient to liquefaction condition) highlight the need for further studies. Copyright © 2016 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

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.     

二相介质饱和土中群桩动力阻抗分析

用流体饱和多孔介质材料描述土体，由饱和土和群桩及承台系统的位移协调条件和力平衡条件建立饱和土和群桩及承台系统动力相互作用的控制方程，分析饱和土中群桩动力阻抗。结果表明：孔隙流体对饱和土中桩基础动力阻抗有一定的影响；在饱和土具有不同的流体渗透系数时，饱和土中群桩动力阻抗也有一定差别。在地基上与基础结构动力相互作用研究中应该考虑地基土中孔隙流体的影响。     

Seismic analysis of infinite pile groups in liquefiable soil

Numerical analysis of an infinite pile group in a liquefiable soil was considered in order to investigate the influence of pile spacing on excess pore pressure distribution and liquefaction potential. It was found that an optimal pile spacing exists resulting in minimal excess pore pressure. It was also found that certain pile group configurations might reduce liquefaction potential, compared to free field conditions. It was observed that for closely spaced piles and low frequency of loading, pile spacing has little influence on the response of the superstructure.     

Undrained behaviour of two silica sands and practical implications for modelling SSI in liquefiable soils

The aim of the present study is twofold. Firstly, the paper investigates the undrained cyclic and post-cyclic behaviour of two silica sands by means of multi-stage cyclic triaxial tests. Secondly, based on the post-cyclic response observed in the element test, the authors formulate a simplified stress–strain relationship that can be conveniently used for the construction of p–y curves for liquefiable soils. The multi-stage loading condition consists of an initial cyclic loading applied to cause liquefaction, followed by undrained monotonic loading that aimed to investigate the post-cyclic response of the liquefied sample. It was found that due to the tendency of the liquefied soil to dilate upon undrained shearing, the post-liquefaction strain–stress response was characterised by a distinct strain–hardening behaviour. The latter is idealized by means of a bi-linear stress–strain model, which can be conveniently formulated in terms of three parameters, i.e.: (i) take-off shear strain, γ_to, i.e. shear strain required to mobilize 1 kPa of shear strength; (b) initial secant shear modulus, G₁, defined as 1/γ_to; (c) post-liquefied shear modulus at large strain, G₂ (γ⪢γ_to). Based on the experimental results, it is concluded that these parameters are strongly influenced by the initial relative density of the sample, whereby γ_to decreases with increasing relative density. Differently both shear moduli (G₁ and G₂) increases with increasing relative density. Lastly, the construction of new p–y curves for liquefiable soils based on the idealized bi-linear model is described.     

近断层地震下可液化场地土反应的数值模拟

液化条件下场地土大变形是造成工程结构失效的主要原因之一。文中以某高速公路特大桥的可液化岸坡近场场地为研究对象,基于PL-Finn液化本构模型,利用FLAC 3D程序对其在地震作用下的动响应全过程进行了数值模拟分析。结果表明,PL-Finn模型可较好地反映地震过程中孔隙水压、液化区的变化规律,并能较好的预测液化后场地土的变形规律。液化引起的地基土大变形对桥梁桩基的影响需引起重视。     

Modelling non‐linear ground response of non‐liquefiable soils

A non‐linear finite element (FE) model is presented to account for soil column effects on strong ground motion. A three‐dimensional bounding surface plasticity model with a vanishing elastic region, appropriate for non‐liquefiable soils, is formulated to accommodate the effects of plastic deformation right at the onset of loading. The elasto‐plastic constitutive model is cast within the framework of a FE soil column model, and is used to re‐analyse the downhole motion recorded by an array at a Large‐Scale Seismic Test (LSST) site in Lotung, Taiwan, during the earthquake of 20 May 1986; as well as the ground motion recorded at Gilroy 2 reference site during the Loma Prieta earthquake of 17 October 1989. Results of the analysis show maximum permanent shearing strains experienced by the soil column in the order of 0.15 per cent for the Lotung event and 0.8 per cent for the Loma Prieta earthquake, which correspond to modulus reduction factors of about 30 and 10 per cent respectively, implying strong non‐linear response of the soil deposit at the two sites. Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic vulnerability evaluation of axially loaded steel built-up laced members Ⅱ： evaluations

The test results described in Part 1 of this paper （Lee and Bruneau, 2008） on twelve steel built-up laced members （BLMs） subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller kl/r were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger kl/r could meet the ductility demand in most cases. The normalized energy dissipation ratio, EC/ET and the normalized compressive strength degradation, Cr″/Cr of BLMs typically decrease as normalized displacements δ/δb,exp increase, and the ratios for specimens with larger kl/r dropped more rapidly than for specimens with smaller kl/r; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, kl/r, and width-to-thickness ratio, b/t, experienced a larger number of inelastic cycles than those with larger ratios.     

Cyclic behavior of laterally loaded concrete piles embedded into cohesive soil

Modern seismic design codes stipulate that the response analysis should be conducted by considering the complete structural system including superstructure, foundation, and ground. However, for the development of seismic response analysis method for a complete structural system, it is first imperative to clarify the behavior of the soil and piles during earthquakes. In this study, full‐scale monotonic and reversed cyclic lateral loading tests were carried out on concrete piles embedded into the ground. The test piles were hollow, precast, prestressed concrete piles with an outer diameter of 300 mm and a thickness of 60 mm. The test piles were 26 m long. Three‐dimensional (3D) finite element analysis was then performed to study the behavior of the experimental specimens analytically. The study revealed that the lateral load‐carrying capacity of the piles degrades when subjected to cyclic loading compared with monotonic loading. The effect of the use of an interface element between the soil and pile surface in the analysis was also investigated. With proper consideration of the constitutive models of soil and pile, an interface element between the pile surface and the soil, and the degradation of soil stiffness under cyclic loading, a 3D analysis was found to simulate well the actual behavior of pile and soil. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical modelling of the effect of horizontal drains in centrifuge tests on soil-structure interaction in liquefiable soils

Bulletin of Earthquake Engineering - The research presented herein was carried out in the framework of the H2020 LIQUEFACT project ( http://www.LIQUEFACT.eu/ ). This paper presents the results of a...