成层地基中单桩竖向承载力鲁棒性设计

城市建设中桩基应用广泛,单桩竖向承载力的计算方法及可靠性越来越受到设计人员重视。针对桩基设计中岩土参数的不确定性及桩基穿越成层地基对桩身承载力的影响问题,提出基于可靠度理论的鲁棒性设计方法。利用岩土参数变异性的平均值及标准差充分考虑岩土参数的不确定性,并通过扩大考虑地基土的不确定因素将单桩竖向承载力鲁棒性设计由砂土推广到黏土等一般性土壤;提出采用分层计算桩侧摩阻力作为不确定因素考虑地基土成层分布问题,按照承载力极限状态与正常使用极限状态作为目标函数进行桩基竖向承载力设计。单桩承载力鲁棒性设计将鲁棒性作为安全性评价标准,来评估桩基设计方案的可行性,以鲁棒性与经济性为优化目标对桩基设计进行多目标优化,设计方案在满足桩基承载力要求的同时,保证了桩基设计方案的鲁棒性与经济性。     

Uniqueness and localization analysis of elastic–plastic saturated porous media

Conditions for localization of deformation into a planar (shear) band in the incremental response of elastic–plastic saturated porous media are derived in the case of small strains and rotations. The critical modulus for localization of both undrained and drained conditions are given in terms of the discontinuous bifurcation analysis of the problem. Loss of uniqueness of the response of coupled problems is investigated by means of positiveness of the second‐order work density. From the discussion of drained conditions, it is shown that there are two critical hardening moduli, i.e. lower and upper hardening moduli which, respectively, correspond to single phase material (large permeability) and to undrained conditions (small permeability). In analogy to one‐dimensional results, it is shown that there exists a domain of permeability values where we have loss of stability, but the waves can still propagate. In this domain finite element results do not show pathological mesh dependence, and permeability will play the role of an internal length parameter in dynamic models. The length scale prediction is thus given for multi‐dimensional problems. Copyright © 2001 John Wiley & Sons, Ltd.     

水平荷载下导管架平台桩基础的非线性有限元分析

导管架平台桩基础的控制荷载主要为风荷载、波浪荷载、地震荷载等水平荷载,为研究水平荷载下导管架平台桩基础的承载特性,采用非线性有限元分析方法对水平荷载下桩-土之间的相互作用进行研究,提出了有效模拟桩基水平承载特性的有限元模型,分析了模型桩的刚度、直径、土质参数中水平土压力系数、剪胀角对桩基承载特性的影响及水平荷载下群桩承载特性,并将有限元计算结果与API规范及模型试验结果进行对比。研究结果表明,非线性有限元分析方法分析水平荷载下桩-土相互作用是可行的,计算结果可为导管架平台的桩基设计提供参考。     

Analysis of pile‐raft foundations under complex loads in layered soils

Considering there is hardly any concerted effort to analyze the pile‐raft foundations under complex loads (combined with vertical loads, horizontal loads and moments), an analysis method is proposed in this paper to estimate the responses of pile‐raft foundations which are subjected to vertical loads, horizontal loads and moments in layered soils based on solutions for stresses and displacements in layered elastic half space. Pile to pile, pile to soil surface, soil surface to pile and soil surface to soil surface interactions are key ingredients for calculating the responses of pile‐raft foundations accurately. Those interactions are fully taken into account to estimate the responses of pile‐raft foundations subject to vertical loads, horizontal loads and moments in layered soils. The constraints of the raft on vertical movements, horizontal movements and rotations of the piles as well as the constraints of the raft on vertical movements and horizontal movements of the soils are considered to reflect the coupled effect on the raft. The method is verified through comparisons with the published methods and FEM. Then, the method is adopted to investigate the influence of soil stratigraphy on pile responses. The study shows that it is necessary to consider the soil non‐homogeneity when estimating the responses of pile‐raft foundations in layered soils, especially when estimating the horizontal responses of pile‐raft foundations. The horizontal loads and the moments have a significant impact on vertical responses of piles in pile‐raft foundations, while vertical loads have little influence on horizontal responses of piles in pile‐raft foundations in the cases of small deformations. The proposed method can provide a simple and useful tool for engineering design. Copyright © 2013 John Wiley & Sons, Ltd.     

A fully coupled elastic–plastic hydromechanical model for compacted soils accounting for clay activity

A constitutive model, accounting for multiphase and multiscale coupling, is proposed for the water retention domain and the stress–strain response of compacted clayey soils. The model is based on a conceptual interpretation of the microfabric evolution of compacted soils along generalised hydromechanical paths, detected by means of mercury intrusion porosimeter tests. Multiphase coupling is provided by the mutual interaction between the mechanical and the hydraulic states. Multiscale coupling is introduced by a measure of the size of the aggregates, which influences both the retention and the stress–strain response, in the phenomenological constitutive equations. Model capabilities are verified by comparison with relevant experimental data from laboratory tests on compacted Boom clay and other selected experimental data on different compacted clayey soils. Copyright © 2012 John Wiley & Sons, Ltd.     

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Finite element procedures for numerical solution of various engineering problems are often based on variational formulations. In this paper, a parametric variational principle applicable to elastic-plastic coupled field problems in consolidation analysis of saturated porous media is presented. This principle can be used to solve problems where materials are inconsistent with Drucker's postulate of stability, such as in non-associated plasticity flow or softening problems. The finite element formulation was given, and it can be solved by either the conventional method or a parametric quadratic programming method.     

竖向力与水平向力同时作用下管桩的性状研究

用解析方法研究了管桩在轴向力和水平向力（倾斜力）联合作用下的受力及变形性状。在高层建筑、桥梁工程、海洋工程、新型海堤护岸等工程中桩基自由长度上作用土压力、风荷载、波浪荷载等荷载型式,基桩经常在竖向、水平向荷载同时作用下工作。国内外学者通过大量试验和理论研究得出了计算竖向、水平向荷载下基桩内力和挠度的半经验公式以及张氏法公式。为了分析竖向、水平向荷载同时作用下自由荷载的作用,在现行m法假设的基础上,从弹性桩的挠曲微分方程出发,导出了任意自由荷载作用下桩任意截面的水平变位、倾角、弯矩、剪力和地基反力计算表达式。桩的挠曲微分方程是分段函数,包括地上部分和地下部分桩,相应的内力和变位求解也分为两段。最后通过一个算例分析了桩顶竖向荷载、桩顶水平力和自由荷载对桩身的受力性状各参数的影响。计算结果表明, 桩顶水平力对桩身最大弯矩和桩顶水平变位的影响最大,而桩周内外摩阻力及桩身自重对桩身受力性状影响较小。     

Constants for an elastic–plastic cap model for limestone

Triaxial fracture tests with overburden pressures ranging from 0.69 to 136 MPa were performed to determine the material parameters involved in a cap model for limestone. Three material parameters A, B and C, were evaluated through Powell's optimization method and the remaining parameters through simulation-curve fitting procedure. The resulting cap model was tested against separate triaxial fracture and hydrostatic compression tests. Modification of the original hardening function, as proposed by DiMaggio and Sandler, provided an improved fit for the experimental data.     

Dynamic responses of a pile embedded in a layered poroelastic half‐space to harmonic lateral loads

A single pile embedded in a layered poroelastic half‐space subjected to a harmonic lateral load is investigated in this study. Based on Biot's theory, the frequency domain fundamental solution for a horizontal circular patch load applied in the layered poroelastic half‐space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg's method, the second kind of Fredholm integral equation describing the dynamic interaction between the layered half‐space and the pile subjected to a top harmonic lateral load is constructed. The proposed methodology is validated by comparing results of this paper with some existing results. Numerical results show that for a two‐layered half‐space, the thickness of the upper softer layer has pronounced influences on the dynamic response of the pile and the half‐space. For a three‐layered half‐space, the presence of a softer middle layer in the layered half‐space will enhance the compliance for the pile significantly, while a stiffer middle layer will diminish the dynamic compliance of the pile considerably. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical analysis under seismic loads of soils improvement with floating stone columns

Geotechnical Engineering has developed many methods for soil improvement so far. One of these methods is the stone column method. The structure of a stone column generally refers to partial change of suitable subsurface ground through a vertical column, poor stone layers which are completely pressed. In general terms, to improve bearing capacity of problematic soft and loose soil is implemented for the resolution of many problems such as consolidation and grounding problems, to ensure filling and splitting slope stability and liquefaction that results from a dynamic load such as earthquake. In this study, stone columns method is preferred as an improvement method, and especially load transfer mechanisms and bearing capacity of floating stone column are focused. The soil model, 32 m in width and 8 m in depth, used in this study is made through Plaxis 2D finite element program. The clay having 5° internal friction angle with different cohesion coefficients (c 10, c 15, c 20 kN/m²) are used in models. In addition, stone columns used for soil improvement are modeled at different internal friction angles (? 35°, ? 40°, ? 45°) and in different s/D ranges (s/D 2, s/D 3), stone column depths (B, 2B, 3B) and diameters (D 600 mm, D 800 mm, D 1000 mm). In the study, maximum acceleration (a _max = 1.785 m/s²) was used in order to determine the seismic coefficient used. In these soil models, as maximum acceleration, maximum east–west directional acceleration value of Van Muradiye earthquake that took place in October 23, 2011 was used. As a result, it was determined that the stone column increased the bearing capacity of the soil. In addition, it is observed that the bearing capacity of soft clay soil which has been improved through stone column with both static and earthquake load effect increases as a result of increase in the diameter and depth of the stone column and decreases as a result of the increase in the ranges of stone column. In the conducted study, the bearing capacity of the soil models, which were improved with stone column without earthquake force effect, was calculated as 1.01–3.5 times more on the average, compared to the bearing capacity of the soil models without stone column. On the other hand, the bearing capacity of the soil models with stone columns, which are under the effect of earthquake force, was calculated as 1.02–3.7 times more compared to the bearing capacity of the soil models without stone column.     

成层地基中倾斜偏心荷载下单桩计算分析

针对工程中地基土性质变化的具体情况,假定地基系数满足(mz+C)的线性增长规律,考虑P-Δ效应并计入桩身自重和桩侧摩阻力的影响,采用矩阵计算方法,分别得到单层土中倾斜偏心荷载作用、桩段顶端倾斜偏心荷载作用以及桩身水平分布荷载共同作用下的竖向单桩计算分析的幂级数解答。并在此基础上,利用上述两幂级数解答对成层地基中倾斜偏心荷载下单桩的受力进行了分析计算,列出了具体的计算步骤;最后,结合某具体实例,对上述方法进行了验证,结果表明,该解答与实际吻合较好,具有一定的应用价值。     

成层土中考虑桩土相对滑移的单桩沉降分析

基于Mindlin位移解,对成层土中的单桩及桩周土作离散化处理,建立了桩土之间有相对滑移和土体存在极限阻力的单桩分析模型,其中桩体沉降采用有限差分法求解,而桩周成层土体的沉降则利用考虑了各单元土体相互影响的ML法计算。两部分之间通过位移协调建立联系,并采用迭代法求解,建立的模型具有较严密的理论基础,且能反映真实的土体分层特性,算例结果亦表明有较高的计算精度。     

Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model

The theory of consolidation is extended to partly saturated clay soils, and formulated for finite element analyses. This formulation couples the effects of both stress and flow. It takes account of variations of this permeability of the soil and compressibility of the pore fluid with changes in void ratio, and the non-linear stress–strain behaviour of soil. The Cam Clay model is revised to model the stress–strain behaviour of compacted soils. The compressibility of pore fluid is derived using Boyle's Law and Henry's Law, taking into account the effect of surface tension. An empirical equation is developed for permeability of pore fluid. An example of settlement of a footing on partly saturated soil is described and discussed.     

基于能量法的轴横向荷载作用下单桩受力变形分析

轴向和横向荷载作用下单桩的受力变形分析是桩基研究的重点内容之一。单桩在水平荷载作用下会产生一定的水平位移与弯矩,而此时作用轴向荷载会使得桩体出现一定的压曲与附加弯矩,以致轴横向荷载作用下的单桩受力变形与单独作用水平荷载或轴向荷载的单桩存在较大的区别。故本文基于能量法,首先分别建立轴横向荷载作用下单桩的受力变形能量方程以及桩周土体能量方程,然后考虑桩土变形协调与一定的桩土相互作用,基于最小势能原理得到单桩变形控制微分方程,并采用幂级数法进行求解,最终得到轴横向荷载作用下单桩受力变形分析的幂级数解答。通过编程计算,将本文方法计算结果与试验结果、数值分析结果、规范法计算结果进行对比分析,验证了本文方法的合理性和可行性。在此基础上,基于本文解答进行了影响参数分析,结果表明：桩体长径比、桩土弹性模量比、桩周土模量深度变化系数均对轴横向受荷单桩的桩身水平位移与最大弯矩值有一定的影响,其中桩周土模量深度变化系数以不小于0.6为宜。     

Load–Deflection response of transversely isotropic piles under lateral loads

In general, pile materials are assumed to be isotropic during the analysis of the load–deflection response of piles under lateral loads. However, commonly used materials such as reinforced concrete and timber as well as potentially promising new pile materials such as fiber reinforced polymers are typically transversely isotropic materials. Experimental studies have shown that transversely isotropic materials have a high ratio of section longitudinal modulus to the section in‐plane shear modulus (E_zz/G_xz) compared to the value for isotropic materials. The high modulus ratio leads to a more significant shear deformation effect in beam bending. To account for the shear deformation effect, the Timoshenko Beam Theory has been adopted in deriving the solutions for the load–deflection response of transversely isotropic piles under lateral loads instead of the Classical (Euler–Bernoulli) Beam Theory. The load–deflection responses depend on the shear effect coefficient, the lateral soil resistance, the embedment ratio, and the boundary conditions. The deflection of the pile, if the shear deformation effect is considered, is always larger than if it is neglected. Copyright © 2000 John Wiley & Sons, Ltd.     

A self‐consistent approach for micro–macro modeling of elastic–plastic deformation in polycrystalline geomaterials

This paper is devoted to multi‐scale modeling of elastic–plastic deformation of a class of geomaterials with a polycrystalline microstructure. We have extended and improved the simplified polycrystalline model presented in [Zeng T. et al., 2014. Mech. Mater. 69 (1):132–145]. A rigorous and fully consistent self‐consistent (SC) scheme is proposed to describe the interaction among plastic mineral grains. We have also deeply discussed the numerical issues related to the numerical implementation of the proposed micromechanical model. The efficiency of the proposed model and the related numerical procedure is evaluated in several representative cases. We have compared the numerical results respectively obtained from the fully SC model and two simplified ones. It is found that the SC model produces a softer stress–strain response than that of the simplified models. The comparisons between the estimation of overall behavior of a granite in different loading conditions and experimental data are also conducted. Copyright © 2015 John Wiley & Sons, Ltd.     

Template elastic‐plastic computations in geomechanics

In this paper we present a new approach to computations in elasto‐plastic geomechanics. The approach is based on the object oriented design philosophy and observations on similarity of most incremental elastic–plastic material models. This new approach to elastic–plastic computations in geomechanics allows for creation of template material models. The analysis of template material models will in turn allow for an easy implementation of other elastic–plastic material models based on the object oriented design principles. Furthermore we present some illustrative implementation details. Finally we present analysis results that emphasize features of template elastic–plastic computations in geomechanics. Copyright © 2002 John Wiley & Sons, Ltd.     

Response of pile groups subjected to lateral loads

An approach is presented for the prediction of linear and nonlinear load–deformation behaviour of laterally loaded pile groups. The individual pile response is obtained by the conventional p–y curve technique, while group interaction is modelled using the Mindlin's solution. Good agreement is observed when comparing the present method of analysis with the commonly used interaction factor approach for the computation of response of pile groups embedded in a homogenous, isotropic elastic half-space. The predicted pile group behaviour also compares favourably with existing field data on laterally loaded pile groups in soft clay.     

The behaviour of geosynthetic-reinforced pile foundation under long-term dynamic loads: model tests

In order to reduce the effects of the low strength and high compressibility of soft soil, geosynthetic-reinforced pile foundations (GRPF) are widely applied for the construction of high-speed railways. Though its reinforcement effect is proved acceptable in practices so far, it is unclear whether it will keep this performance as the train speed continues increasing. Since it is impossible to study the problem in field tests, only mathematical and physical models can be used. However, the nonlinear behaviour of the soft soil complicates the use of analytical models. Therefore, this paper presents a small-scale model test to study the possible changes in stress distribution and deformation in the GRPF under increasing dynamic loads. One test with a natural foundation, without piles or geosynthetic, shows the difference with a similar construction with GRPF foundation. Furthermore, three GRPF tests show the influence of the embankment thickness. The results show the long-term dynamic loading significantly affects the dynamic stress and displacements of the subsoil between the piles of the GRPF. This effect can be divided into three stages with an increasing level of load amplitude: no impact, advantageous impact, and adverse impact. When the dynamic load reaches the adverse impact stage, the long-term dynamic loads reduce the dynamic pile–soil stress ratio, which means that more soil settlement will develop, because more dynamic stress is applied to the soft soil. The test results show that the reduction in dynamic stress on the subsoil in the GRPF construction is clearly lower than the dynamic stress on the natural foundation, due to the existence of rigid piles. Moreover, a thicker embankment gives significantly lower dynamic stresses on the subsoil between the piles. For the thickest embankment tested, the adverse impact stage was not found at all: the arching kept enhancing under long-term dynamic loading with high load amplitudes.

     

Localized failure of fibre‐reinforced elastic–plastic materials subjected to plane strain loading

We consider discontinuous bifurcations as the indicator of a localized failure for a class of composites that are characterized by elastic fibres reinforcing an elastic–plastic matrix. A macroscopic tangent stiffness tensor for the fibre‐reinforced composite is developed by consistently homogenizing the contribution of fibres in a spherical representative volume element. Analytical solutions are derived for the critical hardening modulus and corresponding bifurcation directions for the case of plane strain loading. Properties of the solutions are further illustrated on the example of the non‐associated Drucker–Prager model at onset of yielding. Results show that presence of fibres decreases the critical hardening modulus, thus inhibiting the onset of strain localization. The rate of decrease in the critical hardening modulus is the highest for pure shear, followed by uniaxial tension, uniaxial compression, biaxial tension and biaxial compression. The main fibre parameters that control the onset of strain localization are their volumetric content and their stiffness modulus whereby very stiff fibres can produce the most significant decrease in the critical hardening modulus, especially for the state of biaxial tension. The critical hardening modulus for the non‐associated Drucker–Prager model exhibits a full range of localization modes including compaction bands, dilation bands, and transition in the form of shear bands regardless of the presence of fibres. Presence of fibres affects bifurcation directions, except in the case when Poisson's ratio of the matrix is equal to 0.25. The results demonstrate stabilizing effects of fibres by which they provide the control against the onset of strain localization. Copyright © 2006 John Wiley & Sons, Ltd.