A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading

The ultimate bearing capacity problem of column‐reinforced foundations under inclined loading is investigated within the framework of static and kinematic approaches of yield design theory. The configuration of a native soft clayey soil reinforced by either a group of purely cohesive columns (lime‐column technique) or a group of purely frictional columns (stone‐column technique) is analyzed under plane strain conditions. First, lower bound estimates are derived for the ultimate bearing capacity by considering statically admissible piecewise linear stress distributions that comply with the local strength conditions of the constitutive materials. The problem is then handled by means of the yield design kinematic approach of limit analysis through the implementation of several failure mechanisms, allowing the formulation of upper bound estimates for the ultimate bearing capacity. A series of finite element limit load solutions obtained from numerical elastoplastic simulations suggests that the predictions derived from the kinematic approach appear to be more accurate than the estimates obtained from the static approach. Comparison with available results obtained in the context of yield design homogenization demonstrates the accuracy of the proposed direct analysis, which may therefore be viewed as complementary approach to homogenization‐based approaches when a small number of columns is involved. Copyright © 2016 John Wiley & Sons, Ltd.     

Ultimate bearing capacity of a foundation reinforced by columns or cross trenches under inclined loads: a homogenization approach

This paper addresses the geotechnical engineering problem of evaluating the ultimate bearing capacity of a strip foundation resting upon a reinforced soil, by means of the yield design homogenization approach. The analysis is notably focused on the determination of the macroscopic strength criterion of such reinforced soils, where both constituents are purely cohesive, which can be conveniently expressed through the notion of anisotropic cohesion. A comprehensive comparison is made between the classical configuration of reinforcing columns and the more original one of orthogonal reinforcing trenches. Among the most outstanding results of the analysis is the conclusion that the cross trench configuration is notably more efficient in terms of load bearing capacity than the reinforcement by columns, notably when significantly inclined loading is concerned. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability analysis of an embankment resting upon a column‐reinforced soil

The design against failure of an embankment resting upon a soft soil improved by a group of columns is investigated with the help of the yield design homogenization approach. Assuming that both constituents of the reinforced ground are purely cohesive materials (‘lime column’ technique), an upper bound estimate for the macroscopic strength condition of the reinforced soil as a homogenized medium is first obtained, providing definite evidence of a shear strength anisotropy associated with the reinforcement preferential orientation. The kinematic method of yield design is then performed on the basis of such a criterion, making use of rotational failure mechanisms involving slip circles in the reinforced ground. Upper bound estimates are finally obtained for the embankment stability factor, as functions of the degree of reinforcement and relative thickness of the soil layer. These results are compared with those derived from a simplified analysis, where the reinforced soil is assumed to exhibit an averaged isotropic cohesion. This comparison clearly indicates that the latter simplified analysis may produce quite unsafe estimates for the embankment stability, which can be attributed to the fact that it fails to capture the inherent strength anisotropy of the reinforced soil. Copyright © 2010 John Wiley & Sons, Ltd.     

水平加筋地基极限承载力的极限上限分析法

水平加筋是广泛应用的软土地基处理方法之一,而水平加筋地基极限承载力的确定是其地基处理设计的重要依据。因此,首先结合条形基础下水平加筋地基的工程特点,在探讨其承载机制和破坏特点的基础上,考虑破坏间断面上筋材与地基土体的变形协调,构建出反映加筋参数变化影响的可变破坏模式及机动允许速度场;然后,在此基础上,通过重点研究筋材的能量耗散分析方法,并引入上限极限分析理论,建立出条形基础下水平加筋地基极限承载力分析模型,再引入序列二次规划优化分析理论,建立出条形基础下水平加筋地基极限承载力确定方法,它能充分反映加筋设计参数对地基破坏模式及承载力的影响;最后,通过试验结果与该方法及现有同类分析模型结果的比较分析,表明了该模型与方法的合理性与可行性。     

基于极限分析的圆形浅基础地基承载力上限解

地基承载力问题是岩土工程领域最重要的研究课题之一。针对圆形浅基础地基,从空间问题着手,根据极限分析上限分析理论,选择合适的地基破坏模式及机动位移速度场,首次考虑了单元土体所受的侧向土压力对地基极限承载力的影响,同时考虑到土体自重及地面超载等因素的作用,推导出理论上更为合理的三维圆形浅基础地基极限承载力上限解。结合工程实例,用相应Matlab计算程序计算出上限解,并与实测值进行了对比,证明了其方法的合理性与实用性。     

Calculation of the critical height of a homogenized reinforced soil wall: A numerical approach

This paper is devoted to the stability analysis of a vertical embankment in reinforced soil, assuming that a very large number of reinforcements are periodically distributed throughout the soil mass. The reinforced soil is modelled as a homogeneous medium that obeys a macroscopic yield condition. Two numerical formulations of the homogenized problem, derived from the lower and upper bound theorems of limit analysis, respectively, with a finite element discretization technique, are described. They both lead to a linear programming problem, which is carried out by means of XPRESS industrial LP code. The practical implementation of both the static and kinematic finite element programs on the case of a vertical reinforced earth wall results in close estimates of its failure height, which are in good agreement with available experimental data. This points to the ability of such programs to provide a rigorous evaluation of the limit loads of structures through the determination of lower bound and upper bound estimates sufficiently close to each other.     

加筋带布置对地基承载力的影响

现场原位载荷试验表明：素碎石薄垫层(Z/B=0.2)地基经土工带加筋后，能提高地基承载力。通过承载力比BCR分析加筋层数Ⅳ、加筋首层间距U、加筋带间距H、加筋线密度LDR对地基承载力的影响，并对极限稳定时筋带的设计拉力进行了讨论，提出用筋带的设计强度预估加筋地基极限承载力。     

复合加载情况下非均质地基上条形基础的极限承载力研究

复合加载情况下精确求解非均质地基上条形基础的极限承载力以及评价影响极限承载力的相关因素,具有很强的工程实用与理论参考价值。基于极限平衡原理,在Mohr-Coulomb破坏准则的基础上,将非均质地基上条形基础极限承载力问题等价为一个边界待定的泛函极值问题。利用变分原理得到与平衡方程相等价的积分约束条件以及相应的欧拉方程与横截条件。引入问题边界条件,利用VC++6.0编制了数值计算程序,求得了复合加载情况下非均质地基破坏时的滑裂面函数与破坏包络曲线。从理论上研究了土体内摩擦角、土体黏聚力、土层强度比与地下水位变化等因素对地基破坏包络曲线的影响。研究结果表明,其解答是地基极限承载力真实解的某一最小上限。     

无厚度界面单元边坡浅基础极限承载力上限值的数值分析

采用研发的有限单元分析程序,并同时考虑以库仑摩擦界面为组成模式的多段式无厚度界面单元,藉以探讨边坡坡角与坡缘距离对边坡坡顶浅基础极限承载力的影响,并应用于不同几何破坏机制条件,计算边坡基础在凝聚性土体的最小荷载上限值,模拟土体间的滑动破坏趋势与渐进式破坏行为。研究分析内容包含：（1）浅基础位于半无限空间;（2）在不同边坡坡角条件下,浅基础位于坡顶边缘处;（3）在不同边坡坡角条件下,浅基础位于不同坡缘距离等。经由数值计算分析结果显示,坡缘距离值愈小或边坡坡角愈陡峭时,边坡浅基础极限承载力值则愈小。换言之,当浅基础位于坡顶边缘处且坡角为垂直开挖情况时,则导致浅基础极限承载力降低约50 %。     

Seismic stability analysis of piled embankments: A multiphase approach

The seismic stability analysis of an embankment lying over a soft foundation soil reinforced by a group of vertical piles is performed within the framework of the upper bound kinematic approach of yield design. The analysis is based on a previously developed ‘multiphase’ model of the reinforced ground, which explicitly accounts for the shear and bending resistances of the piles. Making use of appropriate failure mechanisms involving shear zones across which the reinforcements are continuously deforming, along with ‘plastic hinge’ surfaces, upper bound estimates to the critical seismic coefficient of the structure are derived. The results, which are confirmed by the simulations obtained from a finite element elastoplastic code, give clear evidence of the key role played by the bending strength capacities of the piles in ensuring the stability of the pile reinforced embankment. Copyright © 2009 John Wiley & Sons, Ltd.     

Calculation of seismic bearing capacity of shallow strip foundations using the cell-based smoothed finite element method

This paper adopts an upper bound procedure using the cell-based smoothed finite element method (CS-FEM) to estimate the seismic bearing capacity of shallow strip footings, focussing on seismic soil-structure interactions. In simulations, soil behaviour is assumed as the Mohr–Coulomb material, and increment of plasticity deformation obeys the associated flow rule. The first step of the numerical procedure involves approximating the kinematically admissible displacement fields using the cell-based smoothed finite element method, while the second relates to the establishments of the optimization problem as the conic programming. The inclusion of seismic conditions in the simulations was made using the pseudo-static approach. Initially, three seismic bearing capacity factors were resolved for both smooth and rough foundations by including horizontal and vertical inertia forces caused by the soil weight, the superstructure and the surcharge in the analyses. All seismic bearing capacity components obtained are in excellent agreement with those obtained using the method of characteristics and other finite element analyses. Subsequently, the reduction coefficients that correlate static and seismic bearing capacity factors were computed to facilitate the seismic design of the foundation.

     

波浪荷载作用下斜向抗拔桩的承载特性分析

针对浮式海洋结构采用的桩基础,考虑土的循环软化效应,将软土的循环强度与Mohr-Coulomb屈服准则相结合,基于拟静力弹塑性分析建立了循环波浪载荷作用下斜向抗拔桩循环承载性能的计算模型,确定了斜向上载荷作用下抗拔桩的循环承载力,并与单调加载作用下的斜向抗拔桩的极限承载力进行了对比,进一步探讨了桩长、桩径、桩体模量及载荷循环次数等因素对斜向抗拔桩循环承载力的影响。研究结果表明：循环波浪荷载的作用导致了斜向抗拔桩土体循环强度的分布不均匀,从而降低了地基的循环承载力。斜向抗拔桩的动态极限承载力随循环次数的增加而降低,随桩长、桩径及桩体模量的增大而增大。     

Stability analysis of membrane‐reinforced curved earth retaining walls,using a multiphase approach

The stability analysis of curved earth retaining walls, stabilized by reinforcing membranes, is investigated by means of a multiphase model developed in the framework of the yield design approach. This model is an extension of that previously developed for soils reinforced by linear inclusions. It combines the advantage of a homogenization approach in terms of improved computational efficiency, with its capability to account for a specific soil–reinforcement failure condition, in a rational and systematic way. Application of this model is performed on the illustrative example of a cylindrical‐reinforced retaining wall by means of the kinematic approach of yield design, which provides upper bound estimates for the retaining wall stability factor. Nondimensional charts are finally presented assessing the influence of relevant parameters such as the curvature of the wall, the length of the reinforcing membranes or the reinforcement pull‐out resistance. Copyright © 2009 John Wiley & Sons, Ltd.     

条形基础加筋砂土地基极限承载力计算

基于传统的极限平衡条分法,利用临界滑动场法计算了条形基础的加筋地基极限承载力。假定土体处于极限平衡状态时,土体与筋材间存在均匀的摩擦力,通过建立土体条块极限平衡方程,推导了地基承载力的递推关系式。首先,设定计算土体范围,并划分条块和离散状态点;其次,根据递推公式计算各个状态点的参数,并搜索临界滑面;最后,根据搜索出的滑面计算地基承载力。通过实例比较进一步验证了计算结果的可靠性,并分析了首层筋带埋深、铺设层数和长度对地基承载力和滑面位置的影响。研究结果表明：地基承载力随着筋带埋深的增加先增大后减小;随着层数和长度的增加先逐渐增大,最后趋于稳定;滑面位置的变化规律主要是垂直影响深度和水平影响范围增大或减小。该方法原理简单、易于编程,为条形基础加筋地基承载力的计算提供了一种新思路,是临界滑动场法在地基承载力计算中的推广应用。     

吸力式沉箱基础极限拉拔承载力的数值分析

作为新型的深水海洋基础型式,吸力式沉箱基础被广泛地用于系泊深水海洋设施中,从而承受巨大的倾斜上拔荷载。在上拔荷载水平分量与竖向分量的共同作用下,吸力式沉箱的承载特性及其工作性能评价是海洋工程设计与建设中的关键技术问题之一。然而现有的理论分析与试验研究并不能满足工程实践的需要,因此,对吸力式沉箱基础的极限承载力分析建立了有限元数值计算方法。当沉箱基础在快速拔出过程中,正常固结黏土处于完全不排水状态,沉箱基础发生整体破坏时表现出反向地基承载力失稳模式,此时沉箱基础所发挥的极限承载能力往往最大。为此,在数值计算中直接假定沉箱基础及其周围土体处于完全不排水状态,针对不同的沉箱长径比,分别确定了在竖向上拔荷载和水平拉拔的单独作用下沉箱基础极限承载力。对比发现：竖向上拔极限承载力有限元解能够较好地与理论计算结果相符合,而水平极限承载力解与理论计算结果存在一定的差异。     

Seismic Bearing Capacity of Strip Footings Located Close to the Crest of Geosynthetic Reinforced Soil Structures

This paper investigates the performance of geo-reinforced soil structures subjected to loading applied to strip footings positioned close to a slope crest. The kinematic theorem of limit analysis, which is based on the upper bound theory of plasticity, is applied for evaluating the ultimate bearing capacity within the framework of pseudo-static approach to account for earthquake effects. The mechanism considered in this analysis is a logarithmic spiral failure surface, which is assumed to start at the edge of the loaded area far from the slope, consistent with the observed failure mechanisms shown in the experimental tests reported in the literature. A parametric study is then carried out to investigate the influence of various parameters including the geosynthetic configuration, backfill soil friction angle, footing distances from the crest of the slope, slope angles and horizontal seismic coefficients. Attention is paid to the failure mechanism because its maximum depth is the depth at least to which the reinforcements must be placed. Results of the analyses are presented in the form of non-dimensional design charts for practical use. Finally, a simple procedure based on the assessment of earthquake-induced permanent displacements is shown for the design of footing resting on reinforced slopes subjected to earthquake.     

Bearing capacity tests of strip footings on reinforced layered soil

The ultimate bearing capacity of strip footings resting on subsoil consisting of a strong sand layer (reinforced/unreinforced) overlying a low bearing capacity sand deposit has been investigated. Three principal problems were analysed based on results obtained from the model tests as follows: (1) the effect of stratified subsoil on the foundations bearing capacity; (2) the effect of reinforcing the top layer with horizontal layers of geogrid reinforcement on the bearing capacity; (3) effect of reinforcing stratified subsoil (reinforced and unreinforced) on the settlement of the foundation. It has been observed that reinforcing the subsoil after replacing the top layer of soil with a well-graded soil is beneficial as the mobilization of soil-reinforcement frictional resistance will increase.     

基础宽度对地基承载力影响的数值分析

利用数值方法对传统的地基极限承载力的计算公式进行了验证,结果表明传统的理论公式中基础宽度对极限承载力的贡献是正确的。通过数值计算结果,针对目前地基规范中地基承载力特征值限定基础宽度的贡献,研究了地基承载力的合理确定方法,认为地基的承载力应根据实际基础的沉降和地基承载力的安全系数来确定更科学合理。基础宽度对地基承载力的影响已在沉降和承载力安全系数上得到反映,从而计算时不必限定基础宽度,由此可以获得更合理的地基承载力值。     

空洞上方浅基础地基破坏模式与极限承载力分析

利用极限分析上限法求解地基极限承载力问题的关键在于构造合适的破坏模式。当地基下方存在空洞时,地基的破坏模式变得相当复杂。通过分析空洞存在时地基的受力特点及破坏形态,将地基破坏范围划分成为不同的刚性区和过渡区,构造了空洞上方条形基础地基的破坏模式。利用上限法,建立与破坏模式对应的速度场,推导了破坏模式不同区域内的耗散功率和外力功率,得到地基极限承载力的目标函数,并采用数学优化方法进行求解,获得了极限承载力的上限解。通过算例分析,讨论了空洞顶板厚度、空洞大小与地基极限承载力的关系,并与无空洞条件下地基极限承载力进行对比分析。结果表明,随着空洞顶板厚度增加,地基极限承载力增加,破坏模式也由地基与空洞之间扩散到地基两侧;空洞顶板厚度存在临界值,当超过此临界值时,空洞对地基极限承载力的影响可忽略。     

软岩地基中大直径布袋桩抗拔试验研究

西北地区深大基础工程日益增多,兼顾基础抗浮和耐久性问题的研究空白,借助西宁火车站综合改造工程,引入大直径布袋桩技术,有效解决了基础抗浮和耐久性问题;选择6根试桩进行了现场单桩抗拔载荷试验,最大加载量为9 060 kN;运用MATLAB软件分别拟合出3种抗拔极限承载力预测函数模型的曲线,同时运用PLAXIS软件对不同等级荷载桩-土位移进行模拟,并与实测的荷载-位移曲线对比分析。研究发现：双曲线和幂函数模型较适合此类抗拔桩极限承载力预测;本地区类似地基预测大直径缓变形抗拔桩极限荷载所需的极限位移标准应由0.030D减小为0.025D;仅根据土层的物理力学特征确定抗拔桩桩周土的极限摩阻力不够完善,至少还要考虑埋深不同对具有相似物理力学特征土层性质的影响。