Evaluate the performance of an accelerated initial stiffness method in three dimensional finite element analysis

Newton’s method is a commonly used algorithm for elasto-plastic finite element analysis and has three common variations: the full Newton–Raphson method, the modified Newton–Raphson method and the initial stiffness method. The Newton–Raphson methods can converge to the solution in a small number of iterations when the system is stable; however, the methods can be quite computationally expensive in some types of problems, for example where the tangent stiffness matrix is unsymmetric or the plasticity is highly localized. The initial stiffness method is robust in those cases but requires a larger number of iterations. This prompted the formulation of many acceleration techniques in literature. In this paper, those techniques will be briefly discussed. This will be followed by the development of a modified acceleration technique for the initial stiffness method. The performance of the modified accelerated initial stiffness method will be examined in elasto-plastic analyses, using both direct and iterative matrix solvers. The results will be compared – in terms of the required number of iterations and the computation time – with an existing accelerated initial stiffness method, the non-accelerated initial stiffness method and the Newton–Raphson tangent stiffness method.     

某水电站地下洞室群初始地应力场反演回归分析

采用三维弹塑性有限元法对某水电站地下洞室群三维初始地应力场进行了反演回归分析。计算结果表明,厂区初始地应力场分布规律合理,实测点处地应力计算值与实测值吻合较好,可以作为后续数值分析和地质力学模型试验的依据。     

On a multilaminate model for soil incorporating small strain stiffness

In this paper a constitutive model for soils incorporating small strain stiffness formulated in the multilaminate framework is presented. In the multilaminate framework, the stress–strain behaviour of a material is obtained by integrating the mechanical response of an infinite number of randomly oriented planes passing through a material point. Such a procedure leads to a number of advantages in describing soil behaviour, the most significant being capture of initial and induced anisotropy due to plastic flow in a physically meaningful manner. In the past, many soil models of varying degree of refinement in the multilaminate framework have been presented by various authors. However, the issue of high initial soil stiffness in the range of very small strains and its degradation with straining, commonly referred to as ‘small strain stiffness’, has not been addressed within the multilaminate framework. In this paper, we adopt a micromechanics‐based approach to derive small strain elastic stiffness of the soil mass. Comparison of laboratory test data with results obtained from numerical simulations based on the proposed constitutive model incorporating small strain stiffness is performed to demonstrate its predictive capabilities. The model is implemented in a finite element code and numerical simulations of a deep excavation are presented with and without incorporation of small strain stiffness to demonstrate its importance in predicting profiles of deformation. Copyright © 2008 John Wiley & Sons, Ltd.     

结构性海积软土的弹塑性研究

通过对天津市欠固结海积软土进行的大量试验,研究了土的结构性和弹塑性变形本构关系两个方面的问题。首次引入结构强度系数,建立了微结构定量参数与力学参数之间的关系,并提出一种综合考虑结构性影响的应力应变关系模型,为海积软土的结构性模型研究及实际应用提供了一条新的途径。     

Elastoplastic deformation around underground openings under biaxial initial stress field

Estimation of elastoplastic deformation around an underground opening induced by the excavation of it, especially displacement and strain field in plastic region, is presented in this paper, as well as the formulation for calculating the displacement and strain in the plastic region around the underground opening by the coupled Boundary Element Method - Characteristics Method (BEM-CM). In this method, the non-associated flow rule is adopted to calculate the displacement and strain field in the plastic region, which is determined by the integration of the displacement along characteristics lines under the boundary condition of the elastic displacement on an elastoplastic interface analysed. It is shown that this method is one of the accurate and effective methods for estimating not only the shape and extent of the plastic region but also the state of the displacement and strain in the plastic region around the underground opening, comparing the theoretical solution with numerical results by this method for a circular opening under hydrostatic initial stress condition. Furthermore, this method is applied to rectangular and horse-shoe shaped openings and the characteristics of the strain field in the plastic region are discussed. © 1997 by John Wiley & Sons, Ltd.     

分析初始地应力场的位移函数法

岩体初始地应力的确定是地下洞室、边坡等岩土工程设计和施工的必要条件。笔者从实用的角度出发,提出了一种将位移函数法和有限元法相结合来模拟初始地应力场的分析方法。实例应用的结果表明:该方法能很好地模拟岩体的初始地应力场,并能为后续开挖过程的有限元分析提供一种与初始地应力场等效且方便的加荷途径,具有良好的实用性。     

基于实测动刚度的桥桩承载能力评估研究

提出了适用于批量评估分析的、基于实测动刚度的桥桩承载能力评估方法。结合某公路特大桥大批量桥墩基础评估加固工程,利用瞬态机械阻抗法对680根桥桩进行动测。通过基桩低应变完整性辅助测试及动刚度统计分析,推算了桥桩承载能力并给出加固建议。研究表明,对于桩身完整的桥桩,动刚度与承载能力在统计上具有明显的正相关关系;对于承受相近设计荷载的桥桩,测桩样本较大时动刚度值对桥桩完整性评估具有较好可信度。通过抽样取芯分析,验证了提出的桥桩承载能力评估方法具备较好的可靠性。     

软土初始应力各向异性弹塑性模型

自然土体处于初始应力状态,其强度和应力-应变关系都呈现出各向异性,而以往广泛使用的剑桥模型是建立在重塑土试验结果的基础上的,因此,计算实际问题时有一定缺陷.在总结了一些在修正剑桥模型基础上进行扩展而得到的各向异性模型,尤其是S-CLAY1模型.然后,假定了初始屈服面的倾角为K0线,这样使S-CLAY1的计算更加简单.此外,还编制了相关程序,进行了比较计算.结果表明,该模型简单合理,参数正确,可以在实际工程中应用.     

刚度和阻尼频率相关的等效线性化方法

在实际工程中发现,在强地震动作用下等效线性化方法低估了地表地震动的峰值加速度反应。通过与场地效应竖向台阵观测记录的对比分析证实了这一现象,其主要原因是等效剪应变水平的取值高于高频段实际剪应变水平,从而抑制了土层地震反应中的高频成份。若干分析表明,动力反应过程中土体的剪应变是随频率而变化的,且试验表明土体的刚度和阻尼是与剪应变相关的,据此假设土体刚度和阻尼是与频率相关的。基于这一假设,对传统等效剪应变的选取如何使得土层对基底地震动输入中的高频成分产生滤波效应的原理进行探讨,且通过频率相关的等效线性化方法对该原理进行证明。将该方法应用于Port Island场地效应竖向台阵的分析,并与实际地震动记录进行了对比,结果表明,较之传统等效线性化方法,能更加合理地考虑地震动输入中的高频成分。     

黄土隧道初期支护性能分析

以定西隧道为背景,利用有限元软件进行模拟。通过监控量测获得典型断面围岩的变化规律,并将数值模拟和现场量测结果进行对比分析,得到隧道在开挖扰动后初期支护的受力状态,给出隧道初期支护的优化参数,研究将对该类地区黄土隧道的初期支护提供建议和方法。     

深基坑内撑式支护结构计算的综合刚度和双参数法

将吴恒立提出的用于合理计算桩顶作用水平集中荷载的推力桩的综合刚度原理和双参数法,延伸应用于作用有水平分布荷载（土压力）的深基坑围护结构上,提出其杆系有限元数值解法,对一深基坑内支撑式支护结构实例的开挖和支护过程中的各个工况进行了数值模拟分析,由实测位移试算反分析得到了合理的墙-土的综合刚度和地基土抗力双参数,与现有方法计算结果对比表明,该方法能使所得结果更接近实测值。从而说明,综合刚度原理和双参数法的杆系有限元数值解能更为可靠的计算深基坑内支撑式支护结构,具有参考应用价值。     

考虑饱和黏土初始各向异性的循环边界面塑性模型

天然土体的初始各向异性通常可对其后继循环特性产生显著影响。现有考虑循环载荷作用的土体弹塑性模型,往往采用类似修正剑桥模型的椭圆形屈服面,已有研究表明,该椭圆形屈服面因其拉伸弹性区域偏大,针对天然K0固结状态的土体,其计算精度较差。基于新近提出的广义各向同性硬化准则,在边界面方程中引入初始各向异性张量,并采用空间滑动面破坏准则（SMP）的变换应力法,建立了能考虑饱和黏土初始各向异性的循环边界面塑性模型。分别针对等压和偏压固结的饱和黏土静、动三轴试验进行模拟,结果表明,该模型能合理反映土体的初始各向异性及其后继循环动力特性。     

初始弹性模量的研究

切线模量是增量本构中很重要的一个力学参数,研究其规律性意义很大,本文将从初始弹性模量方面对其进行探讨研究,推导出初始切线模量与围压、超固结比、初始孔隙比之间的关系式,并对杭州某一区域的软土进行了三轴试验进行验证。     

A multilaminate constitutive model accounting for anisotropic small strain stiffness

In this paper an extension of existing multilaminate soil models is presented, which can account for inherent and stress‐induced cross‐anisotropic elasticity in the small strain range and its dependency on the load history. In the multilaminate framework, material behaviour is formulated on a number of local planes in each stress point, and the macroscopic response of the material is obtained by integration of the local contributions. Strain‐induced anisotropy, which adds to the stiffness anisotropy inherently present in the material, is therefore intrinsically taken into account. Micro–macro relations between local parameters on plane level and global parameters on macroscopic level are obtained by the spectral decomposition of the global elastic compliance matrix. The model is implemented into a finite‐element code, and model predictions are compared with experimental data of triaxial tests on different soils involving small and large load cycles. The importance of cross‐anisotropic elasticity within the small strain range for predicting ground deformations in geotechnical boundary value problems is discussed at the example of an excavation problem. Copyright © 2012 John Wiley & Sons, Ltd.     

有限元法中总刚动态存取及其应用

讨论了如何利用FORTRAN 90中指针和派生类型相结合构成的链表结构的方法对总刚实现动态存取、增强总刚的灵活性,从而克服了以往总刚形成和存储的一些缺点。方法不仅能方便地实现总刚矩阵内任意位置上数据的插入和删除而不影响其它数组结构的变化,而且比一般半带宽存储节约更多内存。方法特别适合岩土工程开挖与支护等大型结构的三维有限元分析,能大大提高求解效率。     

地基沉降大变形有限元分析的几何刚度效应

研究了基于完全拉格朗日（Total Lagrangian）描述的大变形有限元法分析地基沉降问题的几何刚度效应。在有限元列式的推导过程中严格考虑了土力学表述习惯的影响。通过算例分析,主要研究了几何刚度效应对荷载-沉降曲线的影响,并对比分析了不同率型大变形分析中的几何刚度效应问题。结果表明,几何刚度效应的存在减小了地基大变形有限元系统的刚度;忽略几何刚度效应将导致沉降计算结果偏小,在地基变形较大的情况下误差更明显,Truesdell率型大变形分析的最终沉降结果与小变形法的结果一致。几何刚度效应在地基大变形有限元分析中具有一定程度的影响,处理不当可能出现结构刚度增大的现象。大变形分析结果的性质偏于刚硬。     

岩体初始应力场的遗传算法与有限元联合反演法

岩土工程问题的有限元分析一般需要考虑初始应力场。实际工程中,岩体往往为非线性。本文采用遗传算法与有限元联合反演法求解非线性岩体初始应力场,通过算例说明文中所提方法是合理的,可在工程应用中推广。     

含初始缺陷地铁隧道的抗震动力学行为研究

针对含初始缺陷的既有地铁隧道受邻近穿越隧道施工影响的首都地铁隧道工程背景,基于有限差分方法,通过对既有地铁车站结构受邻近隧道穿越后的抗震性能研究,揭示其抗震动力响应机理。结果表明,在邻近隧道穿越影响下,含初始缺陷的既有隧道各薄弱控制点在地震作用下位移和应力动力时程的波动趋势具有相似性,说明衬砌结构是整体运动的,其位移、应力较穿越前均有所增加,边墙和仰拱在穿越后抗震性能影响最大,剪切破坏主要以车站结构周边土体为主,新线穿越后其剪切破坏分布范围有所增大,应进行注浆加固处理,与自身结构刚度相匹配,提高抗震能力。     

岩体初始应力场识别的随机方法

利用地下隧道开挖后变形收敛观测数据 ,采用最小二乘法研究了岩体初始应力场识别问题。 考虑了变形观测的随机性 ,建立了岩体初始应力场参数识别的随机方法 ,研究了变形观测的随机特性对识别结果的影响。待识别参数对目标函数的灵敏度越低 ,参数识别结果的标准差就越大 ,其可识别性越差