A modification to dense sand dynamic simulation capability of Pastor–Zienkiewicz–Chan model

A modification to the nonlinear Pastor–Zienkiewicz–Chan (PZC) constitutive model without any change in the number of model parameters is introduced in order to simulate stiffness degradation of dense sands at dynamic loading. The PZC model is based on generalized plasticity and was verified by good prediction of liquefaction and undrained behavior of saturated sand. The PZC is a robust model that can predict drained dynamic behavior of sands, especially stiffness increase in loose sand at reloading of dynamic loading. Yet, this model does not show stiffness degradation of dense sand at reloading. The modification is made through modifying the stress memory factor, H _DM, which is multiplied by the plastic modulus, H _L. This modification does not influence reloading behavior of loose sand. The modified PZC model is verified via results of drained cyclic tests. Two cyclic triaxial tests on loose and dense specimens, along with two cyclic plane strain tests on dense sand are utilized for validation. The model simulation shows that the modified PZC model is able to predict the stiffness degradation of dense sand at reloading well.     

A two-surface thermomechanical plasticity model considering thermal cyclic behavior

In thermal-related engineering such as thermal energy structures and nuclear waste disposal, it is essential to well understand volume change and excess pore water pressure buildup of soils under thermal cycles. However, most existing thermo-mechanical models can merely simulate one heating–cooling cycle and fail in capturing accumulation phenomenon due to multiple thermal cycles. In this study, a two-surface elasto-plastic model considering thermal cyclic behavior is proposed. This model is based on the bounding surface plasticity and progressive plasticity by introducing two yield surfaces and two loading yield limits. A dependency law is proposed by linking two loading yield limits with a thermal accumulation parameter n_c, allowing the thermal cyclic behavior to be taken into account. Parameter n_c controls the evolution rate of the inner loading yield limit approaching the loading yield limit following a thermal loading path. By extending the thermo-hydro-mechanical equations into the elastic–plastic state, the excess pore water pressure buildup of soil due to thermal cycles is also accounted. Then, thermal cycle tests on four fine-grained soils (natural Boom clay, Geneva clay, Bonny silt, and reconstituted Pontida clay) under different OCRs and stresses are simulated and compared. The results show that the proposed model can well describe both strain accumulation phenomenon and excess pore water pressure buildup of fine-grained soils under the effect of thermal cycles.

     

循环加载下X形桩竖向承载特性模型试验研究

实际工程中桩基经常受到各种动荷载作用,如高铁路基中的加固桩长期承受列车行车时产生的循环动荷载作用,桩基在循环荷载作用下的承载特性研究对动荷载下的工程设计至关重要。X形桩是一种在传统圆形截面桩基础上发展而来的新型异性桩技术,其承载机制不同于传统圆形截面桩。为了深入研究X形桩在循环荷载作用下的动力特性和荷载与沉降规律,开展了砂土中X形桩竖向循环加载大比尺模型试验。试验结果表明,随着循环加载的进行,X形桩顶产生累计沉降,且循环荷载比越大,加载频率越高,桩顶沉降越快;循环加载初期,X形桩顶动刚度降低,桩身轴力响应增大,桩侧摩阻力发生弱化,之后逐渐趋于稳定,且桩身下半段侧摩阻力较大;在同等加载条件下X形桩与等截面圆形桩相比,承受动荷载能力较强,桩侧摩阻力较大,长期循环加载作用下产生的累计位移较小。研究结果可为X形桩在动荷载作用下的工程设计提供参考依据。     

Cyclic shakedown of piles subjected to two‐dimensional lateral loading

Pile foundations are frequently subjected to cyclic lateral loads. Wave and wind loads on offshore structures will be applied in different directions and times during the design life of a structure. Therefore, the magnitude and direction of these loads in conjunction with the dead loads should be considered. This paper investigates a loading scenario where a monotonic lateral load is applied to a pile, followed by two‐way cycling in a direction perpendicular to the initial loading. This configuration is indicative of the complexity of loading that may be considered and is referred to in the paper as ‘T‐shaped’ loading. The energy‐based numerical model employed considers two‐dimensional lateral loading in an elasto‐plastic soil, with coupled behaviour between the two perpendicular directions by local yield surfaces along the length of the pile. The behaviour of the soil–pile system subjected to different loading combinations has been divided into four categories of shakedown previously proposed for cyclic loading of structures and soils. A design chart has been created to illustrate the type of pile behaviour for a given two‐dimensional loading scenario. Copyright © 2009 John Wiley & Sons, Ltd.     

Pile Head Cyclic Lateral Loading of Single Pile

This paper presents an elastic continuum model using an extended nonlinear Davies and Budhu equations, which enables the nonlinear behavior of the soil around the long elastic pile to be modeled using a simple expression of pile-head stiffness method. The calculated results were validated with the measured full-scale dynamic field tests data conducted in Auckland residual clay. An idealized soil profile and soil stiffness under small strain (i.e. shear modulus, G _s and shear wave velocity, V _s of the soil) determined from in situ testing was used to model the single pile tests results. The predictions of these extended equations are also confirmed by using the three-dimensional finite-element OpenSeesPL (Lu et al. in OpenSeesPL 3D lateral pile-ground interaction: user manual, University of California, San Diego, 2010). A soil stiffness reduction factor, G _s /G _s,max of 0.36 was introduced to the proposed method and model. It was found to give a reasonable prediction for a single pile subjected to dynamic lateral loading. The reduction in soil stiffness found from the experiment arises from the cumulative effects of pile–soil separation as well as a change in the soil properties subjected to cyclic load. In summary, if the proposed method and model are accurately verified and properly used, then they are capable of producing realistic predictions. Both models provide good modelling tools to replicate the full-scale dynamic test results.     

水平循环荷载下桩基变形特性的离心模型试验研究

波浪、船舶等长期水平循环荷载作用下,桩基将不可避免地产生附加应力和变形。针对饱和黏土地层,开展离心模型试验研究了船舶系泊水平荷载作用下单桩和群桩的变形特性。发现水平循环加-卸载诱发了桩周土体的塑性变形,进而导致桩身产生了不可恢复的水平位移和弯曲变形。随着循环荷载的增加,单桩和群桩的桩顶最大水平位移和残余水平位移均同时增加,但残余水平位移明显小于最大水平位移。单桩的桩顶残余水平位移与最大位移比值介于0.17～0.22;群桩的桩顶残余水平位移与最大水平位移比值介于0.30～0.84。水平循环加-卸载作用下,桩身残余弯曲应变明显小于最大弯曲应变。单桩的残余弯曲应变与最大弯曲应变比值介于0.13～0.50;群桩的桩身残余弯曲应变与最大弯曲应变比值介于0.23～0.82。群桩前桩的残余和最大弯曲应变明显大于后桩,前桩与后桩的最大弯曲应变、残余应变比值分别高达3.2和3.1。因此,前桩要采取合理的加固和保护措施,以确保桩基长期服役的安全性。     

A two-surface plasticity model for cyclic behavior of saturated clay

This paper presents a two-surface plasticity model for describing some important features of saturated clay under cyclic loading conditions, such as closed hysteresis loops, cyclic shakedown and degradation, and different stress–strain relations for two-way loading. The model, namely ACC-2-C, is based on the elastoplastic model ACC-2 (an adapted Modified Cam Clay model with two yield surfaces) developed by Hong et al. (Acta Geotech 11(4):871–885, 2015). The small-strain nonlinearity concept is adopted to achieve the nonlinear characteristics of clay during unloading–loading stage. The new hardening law related to accumulated deviatoric plastic strain is proposed for the inner surface to describe the cyclic shakedown and degradation. Following the advantages of the ACC-2 model, the constitutive equations are simply formulated based on the consistency condition for the inner yield surface. The model is conveniently implemented in a finite element code using a stress integration scheme similar to the Modified Cam Clay model. The simulation results are highly consistent with experimental data from drained and undrained isotropic cyclic triaxial tests in normally consolidated saturated clay under both one-way and two-way loadings.

     

Influence of Relative Pile-Soil Stiffness and Load Eccentricity on Single Pile Response in Sand Under Lateral Cyclic Loading

The environment prevalent in ocean necessitates the piles supporting offshore structures to be designed against lateral cyclic loading initiated by wave action, which induces deterioration in the strength and stiffness of the pile-soil system introducing progressive reduction in the bearing capacity associated with increased settlement of the pile foundation. A thorough and detailed review of literature indicates that significant works have already been carried out in the relevant field of investigation. It is a well established phenomenon that the variation of relative pile-soil stiffness (K _rs ) and load eccentricity (e/D) significantly affect the response of piles subjected to lateral static load. However, the influence of lateral cyclic load on axial response of single pile in sand, more specifically the effect of K _rs and e/D on the cyclic behavior, is yet to be investigated. The present work has aimed to bridge up this gap. To carry out numerical analysis (boundary element method), the conventional elastic approach has been used as a guideline with relevant modifications. The model developed has been validated by comparing with available experimental (laboratory model and field tests) results, which indicate the accuracy of the solutions formulated. Thereafter, the methodology is applied successfully to selected parametric studies for understanding the magnitude and pattern of degradation of axial pile capacity induced due to lateral cyclic loading, as well as the influence of K _rs and e/D on such degradation.     

A semi‐empirical method for the liquefaction analysis of offshore foundations

This paper presents a relatively simple method for three‐dimensional liquefaction analysis of granular soil under offshore foundations. In this method, the Mohr–Coulomb model, which defines the elasto–plastic stress–strain relationship under monotonic loading, is modified to accommodate the plastic strains generated by cyclic loading. The effects of cyclic loading, evaluated from the results of laboratory tests on saturated samples of soil, are incorporated into the model. The method is implemented in an efficient finite element program for analyses of three‐dimensional consolidating soil. The practicability of the model is demonstrated by analysis of a typical offshore foundation, and the predictions of the numerical analysis are compared with the observed behaviour of the foundation. Copyright © 2000 John Wiley & Sons, Ltd.     

Combined loading of caisson foundations in cohesive soil: Finite element versus Winkler modeling

The undrained response of massive caisson foundations to combined horizontal, vertical and moment loading is parametrically investigated through a series of 3D finite element analyses. The parameters are: (a) the embedment ratio (D/B), (b) the factor of safety against initial vertical loading (FS_V) and (c) the ratio of the overturning moment to the horizontal force applied at the top of the caisson (M/Q). Emphasis is given on: (i) the identification of all possible failure mechanisms in M–Q–N space, (ii) the developed stress distributions along the caisson walls for various load levels up to complete failure conditions. The results are then used as a feedback for calibrating the parameters of a generalized four-type spring model, originally proposed by Gerolymos and Gazetas (2006), through a genetic algorithm-based optimization procedure. The predictions of the Winkler model compare very well with the FE results, not only at the local response level (in terms of stress distributions along the caisson shafts), but at a global response level (in terms of force–displacement curves and M–Q–N failure envelopes at the top of the caisson) as well. Contrary to established lateral soil resistance theories, it is shown that both the ultimate horizontal soil reaction and resisting moment per unit depth do not solely depend on the strength properties of soil and geometry of the caisson but are also functions of the applied load ratio M/Q and initial soil yielding due to vertical loading. Interesting conclusions are also drawn regarding the transition from the elastic to the ultimate limit state (hardening). Quantifying through analytical expressions the contribution of each of the two basic lateral resisting mechanisms to the response of the caisson, a classification method for embedded foundations is then proposed. The capabilities of the Winkler model are further demonstrated through comparison with FE analysis of the caisson cyclic lateral response.     

Finite deformation analysis of geomaterials

The mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics. We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd.     

黏土中两种不同直径单桩水平循环加载模型试验与分析

为探讨海上风机在风、浪等水平往复循环荷载下大直径单桩基础的循环弱化特性,设计了稳定输出长期循环荷载的机械加载装置,开展了软黏土中长期水平循环荷载下海上风电大直径单桩基础和传统长桩基础的模型试验对比研究。根据API给出的骨干曲线和Masing二倍准则构建循环荷载下的p-y（荷载-位移）曲线,并借鉴前人工作,采用累积塑性应变描述软黏土的不排水抗剪强度弱化,提出了分析大周数水平循环荷载下单桩基础循环弱化的理论方法。该方法将循环荷载次数、幅值等外界条件与桩周土体的循环弱化特性建立联系,以适应海洋环境复杂多变的水平循环荷载形式。通过模型试验和理论研究认为,大直径单桩基础因刚度较大,在同样的水平力循环荷载条件下,其抵抗循环荷载的能力明显优于传统长桩。在海上风机大直径单桩的设计中采用基于黏土残余强度的循环后稳定水平承载力更为合理。     

A two‐surface thermomechanical model for saturated clays

This paper presents an advanced thermomechanical model – TEAM in the framework of two‐surface plasticity for saturated clays, with emphasis put on some important thermomechanical features of natural clays evidenced experimentally such as the limited thermomechanical elastic zone, the smooth transition from elastic to plastic behavior. Two plastic mechanisms are introduced in the model: one is to reproduce the thermoplasticity involving thermal expansion and contraction observed at high over‐consolidation ratios and the second one describes the temperature effect on the yield behavior. The model adopts additional yield surfaces, namely inner yield surfaces that are associated with the two proposed plastic mechanisms to account for the plastic behavior inside the existing conventional thermomechanical yield surface namely yield surfaces. The general expressions of the yield surfaces and plastic potentials in p′–q–T space are introduced. A progressive plastic hardening mechanism associated with the inner yield surface is defined, enabling the plastic modulus to vary smoothly during thermomechanical loadings inside the yield surfaces. Several tests on natural Boom clay along different thermomechanical loading paths have been simulated by TEAM, and results show its relevance in describing the thermomechanical behavior of saturated clays. Copyright © 2015 John Wiley & Sons, Ltd.     

Plastic collapse of long piles under inclined loading

A method is detailed for the plastic collapse analysis of long piles typical of offshore foundations, subjected to inclined loading. The method is based on the upper bound method of plasticity. It easily incorporates both axial and lateral variable soil resistance and variable pile cross section properties. The incorporation of plastic yield interaction between axial load and moment for the pile is a key feature of the method. The solution can itself be cast in the form of a curve representing axial and lateral load interaction and is amenable to incorporation in the analysis of foundation systems such as pile groups.     

Finite element analyses of soil plug response

Open-ended pipe piles are often used in offshore foundations. The response of the soil plug inside a pipe pile is poorly understood, and only limited work has been performed to quantify the response under the different loading conditions relevant to offshore platforms. This paper describes numerical analyses that have been carried out in order to assess the end-bearing capacity of the soil plug under loading conditions which range from undrained to fully drained. The soil plug has been modelled as either elastic, elastic–perfectly-plastic or elastoplastic. The soil–pile interface, an important aspect of the problem, has been examined critically. Comparison with experimental data from model test at laboratory scale indicates that the load–deformation behaviour of the soil plug is modelled well using an elastoplastic model for the soil plug, and an elastic–perfectly-plastic joint element to model the soil–pile interface. The finite element analyses show that, under typical loading conditions, adequate end bearing may be mobilized by the soil plug, largely by high effective stresses in the bottom 3–5 diameters of the soil plug.     

Ultimate lateral bearing capacity of tetrapod jacket foundation in clay

The tetrapod jacket foundations that are always used to support offshore wind turbines have been investigated primarily in laboratory experiments. In this study, the ultimate lateral soil resistance on this type of foundation was investigated using the finite element method and the analytical upper bound plasticity method. The numerical results show good agreement with the theoretical upper bound solutions under the same pile spacings (S) and soil-pile adhesion factors (α). Three distinct failure mechanisms (mechanisms A, B and C) were established in terms of different pile spacings. The ultimate lateral pressure was subsequently determined using numerical analyses with consideration of the loading direction. The most critical loading direction angles (θ) vary with the soil-pile adhesion factors, and are θ = 0 for α = 1 and θ = π/4 for α = 0. Selected empirical equations were proposed to predict the ultimate lateral bearing capacity for engineering practice, considering the pile spacing, soil-pile adhesion and loading direction.     

On the influence of elastic–plastic coupling on sands response

A sand constitutive model accounting for elastic–plastic coupling is presented. To this aim, general constitutive equations describing an elastic–plastic coupling effect are developed first. Afterwards, a modified critical state plasticity model for granular soils is introduced accordingly. Several examples are presented to show the achieved improvements compared to the existing approaches. Comparing directly with experimental data, it is shown that the proposed model provides realistic simulations for pore pressure built-up under undrained cyclic loadings.     

Behavior of monopile foundations under cyclic lateral load

This paper describes the development and application of design charts for monopile foundations of offshore wind turbines in sandy soil under long-term cyclic lateral load. It outlines a numerical model, working with a numerical concept, which makes the calculation of accumulated displacements based on cyclic triaxial test results possible, and it describes important factors affecting the deformation response of a monopile to cyclic lateral loads. The effects of pile length, diameter and loading state on the accumulation rate of lateral deformation are presented and design charts are given, in which a normalized ultimate lateral resistance of a pile is used. For monopiles with very large diameter, the suitability of the “zero-toe-kick” and “vertical tangent” design critera for determining the required embedded length is discussed.     

Scour effects on the response of laterally loaded piles considering stress history of sand

Scour is the removal of soils around pile foundations of bridges or offshore platforms, resulting in reduced capacity of the foundations in either lateral or vertical direction. A common way to analyze the scour-affected pile foundations is to remove the scoured soil layers while keeping the properties of the remaining soil unchanged. However, this approach ignores the fact that the remaining soil experiences different stress histories before and after scour, which can be expected to change the properties of the remaining soil. As a result, the resistance of the remaining soil provided to the pile foundation may be different. The present study focused on the response of laterally loaded pile foundations in sand under scour considering the stress history of the remaining sand. Relative density and coefficient of lateral earth pressure of the sand were evaluated when it changed from a normally consolidated (NC) soil to an over-consolidated (OC) soil due to scour. The relative density was then used to estimate other properties of sand, e.g., unit weight, friction angle, and modulus of subgrade reaction of the sand based on their correlation. The lateral load–deflection (p–y) curve for a pile in sand was modified and input into the computer software, LPILE Plus V 5.0, to account for the effect of the stress history induced by scour. A field test was referenced as an example to compare the calculated results from the modified p–y curves with those from the initially developed p–y curves for the tested sand. The results showed that the change in the over-consolidation ratio (OCR) resulted in the most significant effect on the lateral soil resistance among all the effects due to the changes in the properties of the remaining sand. The sand changing from an NC to OC state increased the lateral soil resistance to the pile foundation. Ignoring the stress history would result in a conservative design of laterally loaded piles under scour.