基于二阶锥规划有限元增量加载法的条形浅基础极限承载力分析

地基极限承载力分析是土力学研究中的一个经典课题。基于Hellinger-Reissner混合变分原理和有限元方法,将岩土体弹塑性问题构造成基于有限元框架的二阶锥规划（second-order cone programming,SOCP）问题,进而提出一种基于二阶锥规划理论的增量有限元法,即FEM-SOCP法。将岩土体弹塑性问题构造成二阶锥规划的数学优化问题,可以避免采用传统弹塑性计算中复杂的应力点积分等算法和屈服面棱角的平滑处理。此外,对于二阶锥规划问题,可以采用具有原始?对偶内点求解法的标准数学规划求解器MOSEK进行求解。将增量加载FEM-SOCP法应用于经典的基底粗糙的条形浅基础地基极限承载力分析中,分别考虑了关联和非关联塑性条件下的Mohr-Coulomb屈服准则。数值结果表明：所提出的增量加载FEM-SOCP法获得的地基承载力系数及地基承载力与传统FEM计算结果基本一致,而与常规有限元计算结果相比,基于增量加载的FEM-SOCP法所获得的屈服区更加平滑。     

考虑孔隙水压力的土坡稳定性的有限元上限分析

基于塑性极限分析的上限定理,考虑孔隙水压力的影响,以结点速度为未知量,根据塑性流动约束条件、速度间断约束条件、速度边界约束条件以及由外功功率与内功功率相等条件得到的目标函数,建立了求解孔隙水压力条件下土坡稳定性的有限元塑性极限分析线性规划数学模型;可求得边坡安全系数的上限值及相应的机动容许位移场;最后对2个经典算例进行了分析,验证了提出方法和程序是正确可行的。     

桩基水平位移的有限元模拟

有限元数值计算方法在岩土工程中已有较多的应用,但在水平受荷桩分析计算中的应用尚不普遍。有关水平受荷桩土体系水平承载力及变形的数值模拟方法少有文献报道。采用有限元数值模拟方法来研究水平受荷桩土体系的水平位移。首先简要分析了水平受荷桩的主要计算方法及原理。然后,基于ABAQUS软件建立了桩土系统二维及三维的有限单元模型,分别通过按现行规范推荐的m法和按Poulos的弹性理论法计算的两个算例,将数值计算方法与解析方法进行了对比计算分析。有限元数值计算结果与解析解基本吻合,说明了所采用有限元数值模拟方法的可靠性及有效性。     

岩土工程中一类双重非线性问题的处理方法

针对土体和土体与结构接触面上的双重非线性性质,提出了采用理想弹塑性模型来模拟土体和采用非线性弹性-理想塑性模型来模拟土体与结构接触面相结合的方法,详细叙述了该方法的原理和数值实现方法。编制了面向对象的有限元计算程序,通过对地基极限承载力的计算验证了理想塑性模型的正确性,通过对一个受弹性基础梁作用的弹塑性地基分析验证了本文方法的适用性。计算结果表明,该方法简单实用,有一定的推广应用价值。     

基于塑性极限分析上限法理论的土质边坡可靠度分析

将极限分析的上限定理、有限元离散思想、随机规划理论和蒙特卡洛方法这四者结合起来,提出了一种土质边坡可靠度分析的上限数值方法。首先采用三节点有限单元离散土质边坡,然后将土体的抗剪参数设为随机变量,根据上限定理构建同时满足三角形单元的塑性流动约束条件、单元公共边的塑性流动约束条件和单元速度边界条件的机动许可速度场,并根据内功功率等于外功功率条件建立目标函数,构建土质边坡可靠度分析的上限法随机规划模型。采用蒙特卡洛方法求解上限法随机规划模型,同时提出了一种基于上限法速度场的边坡失效风险系数估算方法,该方法特别适用于具有多种失效模式的边坡风险分析。对2个经典算例进行了深入分析,验证了方法的正确性。     

大位移条件下水平受荷单桩的简明弹塑性计算方法

软土地层中当桩顶水平荷载较大时,采用传统m法计算容易低估桩身弯矩与挠曲变形,有必要针对该问题提出相关计算方法。将地基土体简化为理想弹塑性体,假定桩身某一深度处存在土体的弹塑性变形临界点,临界点以上的土体进入塑性变形状态,而临界点以下的土体仍处于弹性变形状态,分段建立桩身挠曲微分控制方程,得到水平受荷单桩简明弹塑性计算方法。现场单桩实测和参数敏感性分析结果表明：采用简明弹塑性计算方法得到的桩身最大弯矩较传统m法计算精度提高38.1%;桩身最大水平位移计算精度提高22.3%;桩顶边界条件对桩身水平位移与弯矩沿桩身的分布规律影响显著;桩身最大弯矩和水平位移对土体的极限抗力系数及其形状参数较敏感,设计中宜按下限值选取。     

关于强度折减有限元方法中边坡失稳判据的讨论

在边坡稳定性分析中采用强度折减弹塑性有限元方法时,所得到的总体安全系数在一定程度上依赖于所采用的失稳评判标准,通常以数值计算的收敛性作为边坡失稳判据。而有限元计算的数值收敛性受多种因素的影响,因而由此所得到的安全系数的合理性及其唯一性受到了质疑。为了考查目前各种失稳判据的合理性及其适用性,分别依据计算的收敛性、特征部位位移的突变性和塑性区的贯通性等3个失稳判据,针对某一典型边坡算例,采用强度折减弹塑性有限元方法进行稳定性分析,并与Spencer极限平衡法所得到的总体安全系数进行了对比。对比分析表明,以有限元数值计算的收敛性作为失稳判据在某些情况下所得到的安全系数可能误差较大,而采用特征部位位移的突变性或塑性区的贯通性作为失稳判据所得到的边坡安全系数与Spencer极限平衡法的计算结果比较接近,考虑到实用性与简便性,建议在边坡稳定性分析的强度折减有限元方法中联合采用特征部位位移的突变性和塑性区的贯通性作为边坡的失稳判据。     

竖向与水平复合加载下桶形基础承载性能的分析

在竖向和水平力共同作用的复合加载条件下地基承载性能及其破坏模式是吸力式桶形基础设计与施工中的关键技术问题。为此,以大型通用有限元分析软件系统ABAQUS为基础建立了桶形基础三维有限元计算模型,运用位移控制法确定了均质软黏土地基极限承载力系数与位移之间的归一化关系;采用Swipe试验加载方法,确定了桶形基础在竖向力与水平力平面上的地基破坏包络图,从极限分析上限方法的角度探讨了由数值计算所揭示的桶形基础破坏机制。     

上限法在加筋土结构物稳定性分析中的应用

将极限分析上限法用于加筋土结构物稳定性分析的关键是滑动面上内力功如何计算的问题。在总结了基于传统塑性理论上限法内力功的计算方法的基础上,将基于广义塑性理论的上限法应用到杨俊杰的内力功计算方法中。对比基于传统和广义塑性理论的上限解及离心试验结果,认为基于传统塑性理论的上限法应用简单,计算结果基本可靠;基于广义塑性理论的上限法虽然理论上比较完善,但当滑动面为曲线时,应用繁琐。     

非轴对称荷载下圆形隧洞围岩弹塑性分析解析解

考虑岩石材料的应变软化及扩容效应,采用岩石材料的弹性-塑性软化-塑性残余三线性应力-应变软化模型和莫尔-库仑屈服准则,推导了非轴对称荷载下圆形隧洞围岩弹性区、塑性软化区和塑性残余区的应力场、应变场、位移场和塑性区半径的近似解析解,适用于围岩塑性区较大且侧压力系数1≤λ<3的情况。该近似解析方法与有限元法的计算结果较为接近,可代替有限元方法进行简单的圆形隧洞围岩弹塑性分析。     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

钙质石灰岩中桩基轴向承载特性的有限元分析

为了研究钙质石灰岩中桩基的合理设计理论及开发相关的变形破坏数值分析方法,利用弹塑性有限元方法对以硫球石灰岩作为持力层的桩基现场轴向载荷试验进行了数值分析。有限元分析中钙质石灰岩被假定为理想弹塑性材料。结果表明,如果能在有限元解析中合理地考虑桩侧摩阻力的低减效果,弹塑性有限元计算可以较好地模拟与分析钙质砂土中桩基的轴向承载力特性。最后还对开口钢管桩基的土塞效应的发生机制进行了分析。     

海上风电桩基水平承载力循环衰减二维简化分析

海上风电的桩基在长期循环荷载作用下会引起承载力的衰减。针对软黏土中水平受荷单桩,通过引入累积塑性应变以考虑土体不排水强度的循环弱化,建立二维有限元数值模拟和简化p-y曲线简化方法,以分析水平循环荷载作用后单桩桩侧侧向抗力的衰减弱化。在小数目循环荷载下简化方法与有限元计算结果比较吻合,在此基础上,采用二维简化分析方法得到长期大数目循环荷载下桩侧水平抗力的衰减规律,发现如荷载幅值与初始极限抗力的比值小于土体灵敏度的倒数,单桩在长期水平循环荷载作用下承载力虽有所衰减,但桩基趋于稳定,不会发生破坏。     

水平荷载短桩桩土共同作用全过程分析

利用三维有限元、无限元和界面单元相耦合的方法对短桩桩土共同作用全过程进行数值模拟,计算了短桩桩土体系中土体对桩身的抗力分布及桩前土体隆起位移和桩后土体与桩分离大小等,较详细地探讨了短桩桩土共同作用机理.     

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.     

Two‐dimensional lower bound analysis of offshore pile foundation systems

The objective of this paper is to present a simplified method to determine the pile foundation system capacity based on the lower bound theorem of plasticity. The motivations for determining the lower bound capacity are the following: (1) to evaluate the accuracy of solutions based on the upper bound method; (2) to provide a conservative and efficient solution to the system capacity; and (3) to provide information about load distribution among individual piles at the verge of failure for the pile system. The failure mechanisms for a single pile and for the pile system are assumed to be two‐dimensional. For a typical long offshore pile, the upper and lower bound analyses produce identical lateral capacities. A simplified failure surface for loads at the single pile head is proposed and verified through analysis of 16 case study piles. With this proposed failure surface for a single pile, the lower bound failure load of the pile foundation system is obtained using the elastic compensation method enhanced with the linear matching method. Comparing with the existing upper bound and finite element solutions, the proposed lower bound method is capable of accurately and efficiently predicting the ultimate capacity of a pile foundation system. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysis of laterally loaded rigid monopiles and poles in multilayered linearly varying soil

A new method for calculation of head displacement and rotation of laterally loaded rigid monopiles and poles in multilayered heterogeneous elastic soil is presented. The analysis considers the soil as a layered elastic continuum in which the modulus vary linearly with depth within each layer. Rational pile and soil displacement fields are assumed, and the interaction between the pile and soil is taken into account by using the principle of virtual work. Two sets of equilibrium equations, one describing the pile displacement and rotation and the other describing the displacements in the soil, are obtained and solved analytically and numerically following an iterative algorithm. The new method produces pile responses as accurate as those obtained from three-dimensional finite element analysis but does not require any elaborate input for geometry and mesh.     

考虑坡度效应的水平受荷桩应变楔计算方法

由于坡度效应的存在,常规方法并不适用于斜坡上水平受荷桩的计算,首先开展了斜坡上基桩的横向加载破坏试验,以确定斜坡上基桩的破坏模式。在此基础上,沿坡体方向对破坏土楔体进行斜向单元划分,提出了考虑坡度效应的土体应变楔模型,对于其中的关键参数应变楔深度与应变楔土体应变采用迭代求解。迭代过程中,建立基桩横向受荷的桩-土相互作用方程并用有限杆单元法求解,当求解得到的桩身地面处位移与应变楔模型中地面处土体位移之差小于某一允许值时,得到的基桩的水平位移及内力即为最终解答。通过与试验测试数据的对比,验证了该方法的合理性。最后,将土体破坏深度与边坡斜率的比值定义为陡坡效应影响范围,并对其影响因素进行了对比分析。结果表明,陡坡效应的影响范围受土体强度参数及基桩尺寸等多因素影响,其随着桩径的增加而减小,且随土体强度的增强而减小。