基于广义位势理论的类剑桥模型

广义位势理论直接从数学原理出发建立本构模型,避开了传统塑性理论中塑性势函数等复杂概念,为研究岩土本构模型提供了新的思路。基于广义位势理论中土的应力空间多重势面模型,对剑桥模型“能量方程假设”的数学原理进行分析,从数学角度上建立了一个改进的剑桥模型（即类剑桥模型）,而修正剑桥模型等可作为其特例。利用不同应力路径下的试验数据对其合理性进行验证,并与剑桥模型进行对比分析。结果表明：类剑桥模型的参数确定方便、自由,计算结果与试验较一致,甚至优于修正剑桥模型;类剑桥模型所采用的数学原理更明确,且避免了确定塑性势函数和能量方程的困难及其所带来的误差,是一个具有较好实用价值的模型。     

基于广义位势理论的接触面本构模型一般表述

基于广义位势理论建立的岩土体材料本构模型以及岩土体材料与结构接触面本构模型原理相通,只是前者是在三轴剪切试验条件下的三维应力空间建模,后者是在单剪试验条件下的二维应力空间建模。单剪试验条件下土与结构的接触面问题可以看作是法向与切向应力空间上的二维问题,其试验结果可以表达成由应力、应变组成的二维矢量。结合接触面力学特性,确定应力空间中的势函数以及塑性状态方程,可以推导出双重势面接触面弹塑性本构方程的一般表达式。进一步取两个势函数分别为法向应力和切向应力,建立简化双重势面接触面弹塑性模型的本构方程,该方程可直接应用于有限元等数值分析。结合试验实例对建模方法的合理性进行验证,模型拟合效果良好。研究结果表明,基于广义塑性位势理论建立接触面本构模型无需推求塑性势函数和屈服函数,可以直接得到弹塑性刚度矩阵,且建模方便。     

基于广义位势理论的弹塑性模型的修正方法

广义位势理论为岩土材料的本构关系研究指出了更开阔的数学背景。基于广义位势理论可以构造出基于应力空间的模型,也可构造出基于应变空间的模型,利用两者之间的对称关系,把常规基于应力空间的模型直接转换到应变空间中,对本构模型自身无需做任何改动。基于广义位势理论也可以对已有的本构模型进行修正,比如,可基于广义位势理论对剑桥模型进行修正,这种修正可使模型利用三轴试验的部分成果,比单纯使用压缩试验的成果要好一些。另外,也初步探讨了模型的三维化问题。     

基于广义位势理论的土的非共轴特性研究

传统的塑性位势理论隐含了应力主方向和塑性应变增量主方向共轴的假定,无法客观地描述主应力轴旋转过程中的非共轴现象。基于广义位势理论提出的拟弹性弹塑性本构模型,把总的塑性应变分解为满足弹性分解准则的拟弹性部分和符合传统塑性理论假设的纯塑性部分,分解后建立的模型更为合理和简便,同时又可以解决土的非共轴问题。通过单剪试验结果的验证表明,基于广义位势理论的拟弹性弹塑性模型的模拟效果较好,传统的弹塑性模型（共轴模型）模拟得到的主应力方向和塑性主应变增量方向保持共轴,而拟弹性弹塑性模型（非共轴模型）的模拟结果则能够合理地描述主应力轴旋转过程中的非共轴特性,结果更符合实际,从而为解决土的非共轴特性问题提供了一种有效的方法。     

等应力增量比路径下接触面应变软化模型

等应力增量比路径单剪试验条件下,部分土体与结构接触面表现出明显的应变软化和剪胀特性。基于广义位势理论,将土与结构的接触面问题看作应力空间上的二维问题,势函数取法向应力和切向应力,用塑性状态方程取代传统的屈服面,建立等应力增量比路径条件下的土与结构接触面应力-应变软化模型。采用指数函数,拟合单向压缩试验中法向应力与法向应变的关系,采用复合指数函数,拟合应力比与切向应变的关系,采用另一复合指数函数,拟合法向剪胀分量与切向应变的关系。通过对拟合函数进行微分,确定模型中待定系数的求解方法。结合试验结果对模型进行验证,模型拟合效果良好,具有一定的合理性。     

岩土塑性理论中功表达的近似性

对广义剪应力、广义剪应变的表达式作了说明,在给出其增量表达的同时,指出了在计算二者增量时可能产生的误解。在此基础上,分析比较由平均主应力、体积应变增量、广义剪应力、广义剪应变增量表述的功的增量以及由三向主应力与三向主应变增量表述的功的增量得出：两种表述在一般情况下并不一致。但在某些特殊情况下,例如等应力Lode角加载并满足应力全量Lode角与应变增量Lode角相等时,二者的表述一致。岩土塑性理论中塑性功增量存在与功的增量相同的问题,然而对于实际岩土材料,应力全量与塑性应变增量等Lode角的假定在一般情况下是不能满足的。因此在岩土塑性理论中,对于一般情况下的等应力Lode加载情况,用平均主应力、塑性体积应变增量、广义剪应力、塑性广义剪应变增量表述的塑性功增量也只是一种近似。     

基于应力空间的多重势面模型及其与邓肯-张模型的比较

多重势面模型直接从数学原理出发建立本构关系,避开了传统塑性理论中屈服面的概念,为研究岩土工程材料本构模型提供了新的思路.本文推导了基于应力空间的多重势面模型本构关系,对同一单元体在不同加载方式下,分别利用多重势面模型和邓肯-张E-μ模型,采用完全相同的模型参数进行了应力、应变计算,并在此基础上对比分析了计算结果.本文的计算分析成果有助于进一步理解和研究多重势面模型.     

基于旁压试验土体弹塑性本构模型初探

在大量旁压试验数据分析的基础上,通过曲线拟合,建立了旁压试验弹塑性阶段曲线的椭圆方程,利用土体SMP屈服准则和Rowe流动法则,推导出土体塑性阶段应力增量与应变增量间关系矩阵。在弹性阶段,假设土体应力-应变服从广义虎克定律,建立了基于旁压试验的土体弹塑性本构模型。编制了相应的计算程序,将文中模型计算结果与实际旁压试验曲线进行对比,初步验证了模型的正确性。将本构模型编译为ABAQUS自定义材料子程序UMAT,通过有限元对比分析,文中模型计算变形较弹性模型小,较摩尔-库仑模型大,与模型建立的假设一致。基于旁压试验的土体弹塑性本构模型参数少,且易于获取,便于在实际工程中应用。     

偏平面上屈服曲线的实验拟合

在土体本构理论中，多重屈服面的引入为合理描述土体剪应变与体应变提供了可能，尽管如此，现有多重本构关系仍不能很好的反映π平面上剪应力增量矢量dq对应应变增量矢量dγ^p的影响。现以广义塑性力学为理论基础，对重庆粘土的真三轴试验资料进行了分析，拟合出了偏转角α与剪应力q的关系式，同时提出了一个新的γq^p，γθ^p屈服面表达式，经过已有试验数据的验证，证明了其合理性。     

基于颗粒物质力学与连续介质热力学的岩土本构模型初探

首先简要介绍颗粒物质力学与模拟岩土材料本构特性的热力学方法,其次对力链及其对应的强弱网络的形成、力学特性与能量耗散特点与机制进行深入地分析,随后在Collins提出的土体热力学模型的基础上,考虑强弱网络结构的应力应变特征,引入合理的假设,探讨建立符合热力学原理的宏细观结合的岩土本构模型的思路与步骤     

基于内变量和张量函数表示定理的本构方程

针对各向同性材料,基于张量函数表示定理,建立了本构关系的张量不变性表示,其中,3个不可约基张量取决于应力的0～2次幂,且相互正交,3个系数由塑性应变增量和应力的不变量表示。基于塑性应变增量的不变量定义内变量,本构关系归结为确定内变量的演化。使用张量函数表示定理,给出了内变量演化方程的一般表达式,它取决于应力不变量的增量,因而与主轴旋转无关。讨论了如何根据试验资料和引入适当的假定,确定具体的演化方程。通过与塑性势理论和多重屈服面理论进行比较,表明所建模型是这些理论的最一般表示,且简捷直观、使用方便。     

Three-dimensional topology optimization for geotechnical foundations in granular soil

This article presents three-dimensional structural optimization in geotechnical engineering for foundations in granular soil. The general design (topology) of a shallow foundation is optimized with respect to its deformational behaviour within the service limit state. The SIMP (solid isotropic material with penalization) method is applied to optimize the distribution of foundation material. The soil is modelled as a hypoplastic material with a constitutive model suitable for optimization using finite element analysis. Two load cases are examined. The optimized topology is validated against two-dimensional optimization and 1g-model test results. The present study proves the applicability and shows the potential of topology optimization in geotechnical engineering.     

Analysis of faulting in porous sandstones

Faults in porous sandstones occur in three forms: deformation bands about 1-mm thick and tens of m long and across which offsets are a few mm; zones of deformation bands constituted of many closely spaced deformation bands across which offsets are a few cm or dm; and slip surfaces, that is, distinct surfaces within zones of deformation bands across which offsets are a few m to a few tens of m. Deformation bands represent highly localized deformation; analogous localization within a field of homogeneous deformation is theoretically possible in inelastic materials with certain ranges of constitutive parameters. Crushing and consolidation of sandstone within a band cause the material there to become stiffer than the surrounding porous sandstone. A zone of deformation bands behaves mesoscopically much as a stiff inclusion in a soft matrix. According to the constitutive model assumed to investigate the formation of deformation bands, an instability can develop, and strain increments within the zone of deformation bands can become boundlessly large when the far-field stresses reach critical values. This instability is here associated with the formation of slip surfaces.     

On integration of a cyclic soil plasticity model

Performance of three classes of explicit and implicit time‐stepping integrators is assessed for a cyclic plasticity constitutive model for sands. The model is representative of an important class of cyclic plasticity models for soils and includes both isotropic and nonlinear kinematic hardening. The implicit algorithm is based on the closest point projection method and the explicit algorithm follows a cutting‐plane integration procedure. A sub‐stepping technique was also implemented. The performance of these algorithms is assessed through a series of numerical simulations ranging from simulations of laboratory tests (such as triaxial and bi‐axial compression, direct shear, and cyclic triaxial tests) to the analysis of a typical boundary value problem of geotechnical earthquake engineering. These simulations show that the closest point projection algorithm remains stable and accurate for relatively large strain increments and for cases where the mean effective stress in a soil element reaches very small values leading to a liquefaction state. It is also shown that while the cutting plane (CP) and sub‐stepping (SS) algorithms provide high efficiency and good accuracy for small to medium size strain increments, their accuracy and efficiency deteriorate faster than the closest point projection method for large strain increments. The CP and SS algorithms also face convergence difficulties in the liquefaction analysis when the soil approaches very small mean effective stresses. Copyright © 2001 John Wiley & Sons, Ltd.     

Simulation-based calibration of geotechnical parameters using parallel hybrid moving boundary particle swarm optimization

Simulation-based optimization methods have been recently proposed for calibrating geotechnical models from laboratory and field tests. In these methods, geotechnical parameters are identified by matching model predictions to experimental data, i.e. by minimizing an objective function that measures the difference between the two. Expensive computational models, such as finite difference or finite element models are often required to simulate laboratory or field geotechnical tests. In such cases, simulation-based optimization might prove demanding since every evaluation of the objective function requires a new model simulation until the optimum set of parameter values is achieved. This paper introduces a novel simulation-based “hybrid moving boundary particle swarm optimization” (hmPSO) algorithm that enables calibration of geotechnical models from laboratory or field data. The hmPSO has proven effective in searching for model parameter values and, unlike other optimization methods, does not require information about the gradient of the objective function. Serial and parallel implementations of hmPSO have been validated in this work against a number of benchmarks, including numerical tests, and a challenging geotechnical problem consisting of the calibration of a water infiltration model for unsaturated soils. The latter application demonstrates the potential of hmPSO for interpreting laboratory and field tests as well as a tool for general back-analysis of geotechnical case studies.     

对岩土工程数值分析的几点思考

首先,介绍了笔者对我国岩土工程数值分析现状的调查结果及分析,然后,分析了采用连续介质力学分析岩土工程问题的关键,并讨论分析了岩土本构理论发展现状,提出对岩土本构理论发展方向的思考,最后对数值分析在岩土工程分析中的地位作了分析。分析表明,岩土工程数值分析结果是岩土工程师在岩土工程分析过程中进行综合判断的重要依据之一;采用连续介质力学模型求解岩土工程问题的关键是如何建立岩土的工程实用本构方程;建立多个工程实用本构方程结合积累大量工程经验才能促使数值方法在岩土工程中由用于定性分析转变到定量分析。     

冻土弹塑性本构模型研究现状

土体的本构模型是分析计算土工结构变形规律的关键。自剑桥模型提出以来,对于土体本构模型的研究,各国学者在不同环境条件下发展研究了适用于相应试验条件下的各类模型。随着寒区经济的发展,关于冻土力学性质的研究日益增多,许多学者借鉴常规融土的研究方法建立了不同条件下的冻土弹塑性本构模型。为了进一步理清冻土变形行为的特征,完善适用于冻土弹塑性行为的本构模拟理论和方法,作者总结和分析了各类冻土弹塑性本构模型的理论基础、建模方法、参数确定方法等内容,对进一步发展可准确描述冻土复杂力学行为的本构模型具有指导意义。