Modeling sand response using two-surface plasticity

This paper presents a two-surface plasticity constitutive model based on critical-state soil mechanics and describes a practical process for the determination of its parameters. Determination of the constitutive model parameters can be done in a hierarchical manner, starting with the model parameters that have the most bearing on sand behavior and that can be determined using routine experimental procedures. Most parameters can be determined through simple curve fitting through experimental data points. The constitutive model is calibrated against experimental data for Toyoura sand, clean Ottawa sand and mixtures of Ottawa sand with non-plastic silt. The model simulates closely the mechanical response of sands under various loading conditions and predicts both drained and undrained behavior of sands at small and large strains using the actual small-strain shear modulus, as measured in resonant column or bender elements tests, along with realistic values of Poisson’s ratio. Performance of the model in simulating sand response is demonstrated for a variety of initial states and loading conditions.     

砂土地层圆形深基坑三维分析与测斜仪测量

介绍了铁皮坑开挖中测斜仪监测和三维有限元反分析的结果。所研究的铁皮坑为深度27 m、总直径26 m的圆形深基坑,最终开挖面以上土层以砂土为主。每个开挖阶段采用腰梁加固的咬合桩作为挡土墙对基坑进行支护。采用硬化土模型作为土体本构模型,反分析结果表明,桩墙位移的趋势与测斜仪测量的结果接近,最大位移为5.1mm。案例中胶结土的有效黏聚力c′取决于胶结砂层的厚度,约为50～200kPa。NSPT为标准贯入试验中分离式取样器打入土体30cm的锤击数。模拟结果表明,砂土模量约为1 400NSPT～2 000NSPT（单位：k Pa）,而对于胶结砂,其模量为7 000NSPT。还研究了腰梁和外部荷载对咬合桩变形和受力的影响。结果表明,外部荷载对桩墙位移具有主导作用;同时,腰梁对减少桩墙位移没有明显作用。     

某砂土液化大变形本构模型参数的敏感性分析

基于Yang和Ahmed[1－5]等提出的砂土液化大变形本构模型,对该模型的硬化规则和弹塑性模量确定方法作了改进,把该本构模型扩展应用到三维液化大变形的数值分析中,实现了基于ABAQUS大型商用软件计算平台上砂土液化大变形的计算子程序开发。基于该计算平台,对该模型的主要参数在描述砂土液化动孔隙水压力增长和动应力-应变关系曲线等方面的可靠性和敏感性进行了研究。给出了模型全过程参数、剪胀过程参数、剪缩与剪胀状态转换点流动变形量控制参数对试样的应力-应变关系曲线的影响程度及其规律,并对模型的主要参数的敏感性进行了分析,所得结论为通过动三轴试验获得相关模型参数提供了有效的指导和帮助,同时也发展了砂土液化大变形新的数值计算方法。     

Deformation effects of porosity variation on soil consolidation caused by groundwater table decline

Soil consolidation has been widely analyzed using the poroelastic theory. As soil consolidation proceeds, porosity variation leads to the changes in hydraulic conductivity, Young’s modulus, and body force. However, the combined deformation effect of porosity variation on soil consolidation is rarely examined. In this study, a poroelastic consolidation model used to simultaneously consider the changes in hydraulic conductivity, Young’s modulus, and body force was developed to investigate the combined deformation effect of porosity variation on soil consolidation caused by groundwater table decline. The results indicate that the deformation effect of porosity variation on soil consolidation is negligible when the body force number is <0.01. For body force numbers >0.01, soil displacement could be overestimated or underestimated if the combined deformation effect of porosity variation is not completely considered. The misestimation of soil displacement increases as the body force number increases. In addition, the combined deformation effect of porosity variation also affects the transmission of pore water pressure. Therefore, it could be concluded that a reliable analysis of soil consolidation must simultaneously account for the variations in hydraulic conductivity, Young’s modulus, and body force.     

考虑土体非线性的CCSG桩复合地基固结解

混凝土芯砂石桩（CCSG）桩复合地基是一种新型多元复合地基。通过引入地基土体的e-lgσ和e-lgk对数模型,考虑地基土体固结过程中压缩模量和渗透系数非线性变化的特征,推导出基于等应变假设的CCSG桩复合地基非线性固结解析解,且现有的考虑土体非线性的砂井固结解和碎石桩复合地基固结解均是文中解的特例。根据该解析解得到桩土模量比、土体压缩指数与渗透指数比、荷载增量等无量纲参数变化时,CCSG桩复合地基的固结度曲线。分析结果表明,按应力和按变形定义的两种固结度不相等,通常按变形定义的固结速度较快;土体压缩模量和渗透系数的非线性变化对固结影响较大。最后通过和由实测数据获得的固结度曲线对比,验证了解析解的正确性。     

A Numerical Comparison of the Behavior of a Braced Excavation Using Two and Three-Dimensional Creep Plastic Analyses

Current study deals with investigating the effects of both time factor and the selection of a constitutive model type on predicting deformations of an excavation braced by nailing using two and three-dimensional finite element analyses. In addition, the effects of stress path and the type of defined initial conditions of the analytical model on deformations of the floor and walls of the excavation are also studied. Time factor, in the form of earth materials’ creep, can largely be entered into calculation of deformations of excavations by conducting viscoelastic and viscoplastic analyses. On the other hand, there hasn’t been done a comprehensive study regarding the creep behavior of excavations through comparing the results of two-dimensional and three-dimensional numerical analyses so far. The results showed that it’s largely possible to approach the actual deformation behavior of an excavation by considering the constitutive model of soft soil creep, SSC model, in the numerical plastic analyses. The effects of stress path on the deformation behavior of the excavation walls and excavation floor are investigated by using OCR stress ratio and POP stress difference; These two factors, both of which are also analogous, represent a boundary value for swelling behavior of the excavation floor and an increasing rate for the deformation behavior of the excavation walls since the increase in OCR or POP is equal to the increase in the soil lateral pressure coefficient at rest.     

Plane Strain Testing with Passive Restraint

A plane strain condition for testing rock is developed through passive restraint in the form of a thick-walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young’s modulus and Poisson’s ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana limestone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young’s modulus and Poisson’s ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.     

K0应力路径试验在上海地区工程勘察中的应用

上海地区在进行软粘性土的变形特性试验时,勘察过程中极少进行对原状土在不同应力路径下的变形及强度试验研究,这使得报告中提供的参数不能很好地和基坑开挖卸荷过程中土体地层的实际相吻合。本文以上海市徐家汇某深大基坑项目为例,在勘察阶段进行K0应力路径三轴试验,试验内容为对选取的代表性土样进行加荷、卸荷及再加荷,并记录各阶段的应力应变及变形模量。对试验结果的分析表明,应力路径对软粘性土的影响较明显,K0应力路径可以较为真实地反映土体在天然状态下进行基坑开挖过程中的变形特性。建议以后在对变形敏感的深大基坑工程中加强推广应用。     

劈裂注浆复合土体三维等效弹性模型理论研究

劈裂注浆可以有效改善土体的变形参数,大大降低土体在受力状态改变时的变形量,对劈裂注浆后复合土体的等效变形参数进行研究十分重要。在综合分析劈裂注浆扩散机制和工程应用实际的基础上,基于均质化理论提出了劈裂注浆后复合土体的三维单元体几何模型,按等效原则给出了浆-土体积及受力分配关系模型图;接着基于横向各向同性本构关系推导了模型的等效弹性模量和等效泊松比的解析解。然后采用有限元方法取得了模型特定条件下的等效弹性模量和等效泊松比,并与解析结果进行对比分析。最后把模型和相应的解析结果引入Flac3D岩土工程专业分析软件,结合一个热力隧道工程实例对隧道劈裂注浆后关键位置的沉降进行预测分析,并与实测值进行了对比。研究表明：对所提出的计算模型,解析计算与有限元方法计算结果吻合度较高,说明了解析结果的正确性;基于该模型及其解析结果得到的隧道开挖后的沉降预测值与实测值具有良好的一致性,说明所提出的模型和相应的解析计算方法具有一定的可靠性和实用性。     

Intelligent model selection with updating parameters during staged excavation using optimization method

Various constitutive models have been proposed, and previous studies focused on identifying parameters of specified models. To develop the smart construction, this paper proposes a novel optimization-based intelligent model selection procedure in which parameter identification is also performed during staged excavation. To conduct the model selection, a database of seven constitutive models accounting for isotropic or anisotropic yield surface, isotropic or anisotropic elasticity, or small strain stiffness for clayey soils is established, with each model numbered and deemed as one additional parameter for optimization. A newly developed real-coded genetic algorithm is adopted to evaluate the performance of simulation against field measurement. As the process of optimization goes on, the soil model exhibiting good performance during simulation survives from the database and model parameters are also optimized. For each excavation stage, with the selected model and optimized parameters, wall deflection and ground surface settlement of the subsequent unexcavated stage are predicted. The proposed procedure is repeated until the entire excavation is finished. This proposed procedure is applied to a real staged excavation with field data, which demonstrates its effectiveness and efficiency in engineering practice with highlighting the importance of anisotropic elasticity and small strain stiffness in simulating excavation. All results demonstrate that the current study has both academic significance and practical significance in providing an efficient and effective approach of adaptive optimization-based model selection with parameters updating in engineering applications.

     

Numerical Analysis of Deformation Control of Deep Foundation Pit in Ulanqab City

The deformation of a deep foundation pit in Ulanqab city was analyzed by in situ monitoring and numerical simulation data. First, a limit equilibrium method was used to evaluate the stability of foundation pit under non-supporting and ribbed plate anchored retaining wall support. The results show that the ribbed plate anchored retaining wall support could control the soil deformation effectively in deep foundation pit. Additionally, a three-dimensional finite difference model of excavation zone and reinforcement structure was established using FLAC3D software to simulate the excavation of deep foundation pit. The simulation results were verified by monitoring field data. The simulation results show that all the bolts are in the tension state, and the maximum axial force is located at the end of the bolt, with a value of 46.4 kN. Foundation pit excavation is a continuous stress release process, making the rock and soil of side wall of foundation pit slide towards the free surface. The largest deformation is 4.0 mm, near the side wall of foundation pit, consistent with the deformation monitoring results.

     

上海地区基坑开挖数值分析中土体 HS-Small模型参数的研究

数值分析方法已成为分析敏感环境下基坑开挖对环境影响的最重要手段,其关键是选择合适的土体本构模型和计算参数。HS-Small模型可以同时考虑土体剪切硬化和压缩硬化,而且还可以考虑土体剪切模量在微小应变范围内随应变衰减的行为,因此,HS-Small模型在基坑开挖数值分析中具有很好的适用性。但HS-Small模型的参数较多,不仅包含了HS模型的参数,还包含了小应变参数,因此,获取完整的HS-Small模型参数存在一定困难。通过上海地区5个基坑开挖数值分析的实例对基于室内试验得出的上海典型土层HS模型参数进行了检验。通过参数的敏感性分析,对HS-Small模型的部分参数的确定方法进行了修正。在此基础上,采用反分析法确定了敏感性最强的小应变参数,从而初步完整地获取了上海典型土层土体HS-Small模型参数。采用文中确定的上海典型土层HS-Small模型参数对该地区若干典型基坑工程实例进行计算,结果表明,计算值与实测值吻合得较好,从而验证了确定的上海典型土层HS-Small模型参数的适用性。     

Progressive degradation of rock properties and time-dependent behavior of deep tunnels

Time-dependent response of deep tunnels is studied considering the progressive degradation of the mechanical properties of the rock mass. The constitutive model is based on a rock-aging law for the uniaxial strength of the rock and for the Young’s modulus. A semi-analytical solution is developed for the stresses and displacements around a deep circular tunnel taking into account the face advance. The evolution of the plastic and damage zones over time is determined. Numerical examples are presented for the case of Saint-Martin-La-Porte access adit in France of the Lyon–Turin Base Tunnel. The computed results which are compared with the field data in terms of the convergence of tunnel wall and of the displacements inside the rock mass monitored by multi-point extensometers show the efficiency of the approach to simulate the time-dependent deformation of a tunnel excavated in squeezing ground. Simple relationships are proposed to evaluate the parameters of the constitutive model directly from those of the empirical convergence law presented in previous work.     

粉质砂土土钉墙水平位移与土钉轴力的FLAC3D研究

以物理模型土钉墙的破坏性试验获得的土体的基本参数和模型的尺寸为基础,应用FLAC3D软件建立土钉墙数值模拟模型。通过数值模型模拟基坑开挖与支护过程,并监测该过程中的土钉墙墙体沿深度方向水平位移情况和各层土钉的轴力变化情况以及它们之间的关系。支护过程结束后,在墙顶分级施加竖向荷载直至墙体产生较大变形,研究了土钉墙在超载状况下的工作状况以及破坏过程,并与物理模型土钉墙的破坏性试验结果进行对比。研究发现,开挖过程中墙体水平位移底部大于顶部,呈“勺形”分布;墙体水平位移最大处附近的土钉轴力也最大;粉质砂土土钉墙变形超过基坑开挖深度的4‰后,墙体的稳定性会极大降低;粉质砂土土钉墙没有下卧软弱层时,在地面超载作用下其破坏形式为体内破坏,表现为部分土体沿滑裂面向下滑动。     

A unified plasticity model for large post-liquefaction shear deformation of sand

Based on previous experimental findings and theoretical developments, this paper presents the formulation and numerical algorithms of a novel constitutive model for sand with special considerations for cyclic behaviour and accumulation of large post-liquefaction shear deformation. Appropriate formulation for three volumetric strain components enables the model to accurately predict loading and load reversal behaviour of sand, fully capturing the features of cyclic mobility. Compliance with the volumetric compatibility condition, along with reversible and irreversible dilatancy, allows for physically based simulation of the generation and accumulation of shear strain at zero effective stress after initial liquefaction. A state parameter was incorporated for compatibility with critical state soil mechanics, enabling the unified simulation of sand at various densities and confining pressures with a same set of parameters. The determination methods for the 14 model parameters are outlined in the paper. The model was implemented into the open source finite-element framework OpenSees using a cutting-plane stress integration scheme with substepping. The potentials of the model and its numerical implementation were explored via simulations of classical drained and undrained triaxial experiments, undrained cyclic torsional experiments, and a dynamic centrifuge experiment on a single pile in liquefiable soil. The results showed the model’s great capabilities in simulating small to large deformation in the pre- to post-liquefaction regime of sand.     

随机分布贯穿裂隙岩体变形特性研究

洞室开挖后,其周边通常会产生许多随机分布的贯穿裂隙,直接影响洞室围岩稳定,研究随机分布贯穿裂隙岩体的变形及变形特性具有重要意义。基于线弹性理论和线性刚度理论计算岩石和裂隙的位移,用概率的方法建立了随机分布贯穿裂隙岩体变形的计算模型,给出了随机分布贯穿裂隙岩体的等效弹性模量和等效泊松比,研究了岩石和裂隙的材料参数和几何参数对岩体等效弹性模量和等效泊松比的影响。可得如下结论：等效弹性模量和等效泊松比随着岩石弹性模量的增大而增大;等效泊松比随着岩石泊松比的增大而增大;等效弹性模量和等效泊松比随着裂隙法向刚度的增大而增大;随着剪切刚度的增大,等效弹性模量逐渐增大,而等效泊松比则逐渐减少;随着裂隙平均间距的增大,等效弹性模量逐渐减小,等效泊松比在平均倾斜角较小时逐渐增大,在平均倾斜角较大时逐渐减小;随着裂隙平均倾斜角的增大,等效弹性模量先减小后增大,而等效泊松比先增大后减小。模型能较全面地考虑构成岩体的岩石和裂隙的材料参数与几何参数对岩体变形的影响,其结果对研究洞室围岩的变形和工程设计有一定的参考价值。     

Response of Euler–Bernoulli beam on spatially random elastic soil

A new method is developed for analysis of flexible foundations (beams) on spatially random elastic soil. The elastic soil underneath the beams is treated as a continuum, characterized by spatially random Young’s modulus and constant Poisson’s ratio. The randomness of the soil Young’s modulus is modeled using a two-dimensional non-Gaussian, homogeneous random field. The beam geometry and Young’s modulus are assumed to be deterministic. The total potential energy of the beam-soil system is minimized, and the governing differential equations and boundary conditions describing the equilibrium configuration of the system are obtained using the variational principles of mechanics. The differential equations are solved using the finite element and finite difference methods to obtain the beam and soil displacements. Four different beam lengths, representing moderately short, moderately long and long beams are analyzed for beam deflection, differential settlement, bending moment and beam shear force. The statistics of the beam responses are investigated using Monte Carlo simulations for different beam-soil modulus ratios and for different variances and scales of fluctuations of the soil Young’s modulus. Suggestions regarding the use of the analysis in design are made. A novelty in the analysis is that the two-dimensional random heterogeneity of soil is taken into account without the use of traditional two-dimensional numerical methods, which makes the new approach computationally efficient.     

季冻区草炭土非线性K-G模型试验研究

季冻区草炭土是沼泽环境中植物残体在氧化分解作用下,堆积形成的含有大量未分解纤维残体的特殊土。草炭土纤维及其含量对其强度和变形特性具有重要影响,目前考虑纤维含量对草炭土强度和变形特性影响的本构关系研究还相对匮乏。K-G本构模型因其模型参数与土的体积模量和剪切模量能建立直接联系,因此在岩土工程非线性理论和数值计算分析方面广泛应用。以不同纤维含量的草炭土为研究对象,进行三轴剪切试验,研究了草炭土的应力应变曲线,得到了草炭土非线性K-G模型参数,分析了各模型参数随纤维含量的变化规律,建立了模型参数与纤维含量之间的线性函数关系。     

Numerical analysis of the installation effects on the behaviour of soft clay improved by stone columns

This paper addresses the installation effects of stone columns in soft soils. Focus is made on the lateral expansion of stone material using the vibro displacement and substitution techniques by means of numerical simulations. The behaviour of reinforced soil after stone column installation is investigated to show how the properties of soft soils can be improved prior to final loading. The effect of such an improvement on the prediction of reinforced soil settlement is evaluated. The axisymmetric unit cell model (UCM) served for the comparison between numerical predictions made by the Mohr-Coulomb and hardening soil constitutive laws adopted for the soft soil. An equivalent group of end bearing columns model was investigated in the axisymmetric condition to predict the settlement of reinforced soil by adopting the Mohr-Coulomb constitutive model for soft clay. The reduction of settlements predicted by the unit cell and group of columns models, due the improvement of the Young’s modulus of soft clay, were compared. It is concluded that a significant reduction of settlement is expected when the group of columns model is considered.     

Back-analysis of soil parameters of the Malutang II concrete face rockfill dam using parallel mutation particle swarm optimization

Deformation control is a central problem in earth-rockfill dam design. The finite element method (FEM) is the primary method used to analyze and predict the deformation of earth-rockfill dams. The parameters of the constitutive model of soil used in earth-rockfill dams determine the FEM analysis results. Using prototype monitoring displacements, the soil parameters of the Malutang II concrete face rockfill dam were back-analyzed using parallel mutation particle swarm optimization. The calculated displacements of the back-analyzed soil parameters are consistent with the prototype monitoring results. The parallel mutation particle swarm optimization has a high optimization rate and can be used in large-scale practical engineering applications. The back-analysis results indicate that the deformation moduli of rockfills in the Malutang II are affected by construction situ.