Time dependence of axial pile response

This communication describes an approximate method for generalizing homogeneous, linearly elastic, subgrade type solutions of axial pile response to account for soil creep behaviour. The method is very simple to apply and can be used in conjunction with either analytical or numerical elastic solutions. Exact solutions for limiting cases and finite difference solutions in both space and time are presented to confirm that errors introduced by the approximations are small. Because of the theoretical basis of this approach it is anticipated that method can be used with other pile problems, lateral and axial, for both subgrade adn continuum idealizations. Methods for generalizing the results to more complex conditions such as non-homogeneity or time varying loads are given.     

深部隧道力学分析的离散元与理论解分区耦合方法初探

离散单元法适合室内试验和局部小尺度问题的模拟,但在分析隧道开挖等大尺度问题时计算复杂且耗时.为拓展离散元在大尺度问题分析中的适用性,尝试将离散元与理论解分区耦合.针对深埋圆形隧道围岩开挖过程,采用离散元模拟内部近孔口处围岩,外部采用理论解,耦合边界上使用迭代算法,控制收敛以保证力与位移连续条件,在弹性阶段范围内对两区域进行耦合以分析解法的适用性和误差.针对隧洞有、无内压两类算例,采用该分区耦合方法经15步左右迭代收敛,所得边界位移与理论解分别相差1.86%、3.2%;所得离散元结果与理论解对比良好：位移误差随角度有关、最大处在13.5%以内,应力误差除在少量部位为15%左右外,其余各处在8.6%以内.据此表明,该方法具有相当的精度及可行性.     

基于离心试验与数值模拟的圆砾地层深基坑弹性地基模式研究

本文以南宁轨道交通1号线广西大学站深基坑为工程背景,对圆砾地层深基坑工程进行离心机模型试验,并采用Plaxis数值模拟进行对比分析,分别获取了围护墙体变形、侧向土压力数据。基于以上数据,根据基坑弹性地基反力法基本原理,进一步对圆砾地层深基坑围护结构弹性地基主动区、被动区的计算模式进行了分析研究,结果表明:圆砾地层深基坑墙后土压力大小与墙体位移有关,达到主动土压力状态所需的墙体位移量S/h约为0.1%;主动区土压力分布形态为开挖面以上三角形、开挖面以下矩形,符合弹性地基反力法计算模式;被动区地基水平基床系数K随深度近似呈线性增长关系,即弹性地基模式符合m法的分布形态。     

Evaluation of deformation parameter for deep excavation in sand through case histories

This study back analyzed deformation parameters of in situ sand through two excavation case histories in Kaohsiung, Taiwan. Two main features are highlighted; deformation prediction based on monitoring data at the first excavation stage and in situ Young’s modulus evaluation for sand considering monitoring data at the overall excavation stages. The former tends to establish a reliable method to predict the wall deflection at the critical stage based on the data at the first stage and the latter to enrich the limited database of Young’s modulus correlation for sand, specifically applicable for deep excavations analysis. The two constitutive models, linear elastic perfectly plastic and non-linear stress–strain constitutive models, were selected. The stiffness parameters of the models were discretely distributed along the subdivided soil body mesh to reflect the effect of overburden pressure on the in situ soil. In addition, relationship between Standard Penetration Test value (SPT-N value) and Young’s modulus and relationships for estimating the in situ Young’s modulus of the Kaohsiung sand as a function of depth were evaluated. The results greatly enhanced a framework for estimating the in situ Young’s modulus of sand.     

Semi-Analytical Solution for Stresses and Displacements in a Tunnel Excavated in Transversely Isotropic Formation with Non-Linear Behavior

A semi-analytical solution based on the transfer matrix technique is proposed to analyze the stresses and displacements in a two-dimensional circular opening excavated in transversely isotropic formation with non-linear behavior. A non-isotropic far field can be accounted for and the process of excavation is simulated by progressive reduction of the internal radial stress. A hyperbolic stress–strain law is proposed to take into account the non-linear behavior of the rock. The model contains seven independent parameters corresponding to the five elastic constants of an elastic material with transverse isotropy and to the friction coefficient and cohesion along the parallel joints (weakness planes). This approach is based on the discretization of the space into concentric rings. It requires the establishment of elementary solutions corresponding to the stress and displacement fields inside each ring for given conditions at its boundaries. These solutions, based on complex variable theory, are obtained in the form of infinite series. The appropriate number of terms to be kept for acceptable approximation is discussed. This non-linear model is applied to back analyze the convergence measurements of Saint-Martin-la-Porte access gallery. Short-term and long-term ground parameters are evaluated.     

Inverse Analysis of Deep Excavation Using Differential Evolution Algorithm

This paper presents the applications of the differential evolution (DE) algorithm in back analysis of soil parameters for deep excavation problems. A computer code, named Python‐based DE, is developed and incorporated into the commercial finite element software ABAQUS, with a parallel computing technique to run an FE analysis for all trail vectors of one generation in DE in multiple cores of a cluster, which dramatically reduces the computational time. A synthetic case and a well‐instrumented real case, that is, the Taipei National Enterprise Center (TNEC) project, are used to demonstrate the capability of the proposed back‐analysis procedure. Results show that multiple soil parameters are well identified by back analysis using a DE optimization algorithm for highly nonlinear problems. For the synthetic excavation case, the back‐analyzed parameters are basically identical to the input parameters that are used to generate synthetic response of wall deflection. For the TNEC case with a total of nine parameters to be back analyzed, the relative errors of wall deflection for the last three stages are 2.2, 1.1, and 1.0%, respectively. Robustness of the back‐estimated parameters is further illustrated by a forward prediction. The wall deflection in the subsequent stages can be satisfactorily predicted using the back‐analyzed soil parameters at early stages. Copyright © 2014 John Wiley & Sons, Ltd.     

深基坑支护结构的实用计算方法及其应用

对深基坑支护结构的受力和变形计算提出了一套系统的实用计算方法,较好地解决了基坑支护结构设计、计算的关键问题,并在广州地铁和许多重大基坑工程应用中取得了较好的效果。该方法把支护结构简化为一竖放的弹性地基梁,支撑、锚杆及岩土体用弹簧系统来代替,岩土的弹簧刚度可用岩土的变形模量来计算, 针对基坑工程施工和结构的动态特点,提出了一套系统的计算方法,其中包括考虑施工过程的增量计算法、合理确定支护结构入土深度的计算法、支撑加预应力及支撑拆除的计算方法等,并应用提出的增量法,首次较完整地对国际上著名的支护土压力Terzaghi-Peck表观土压力给出了理论解释,对岩土的变形模量提出采用承载力反算的经验方法,为岩土参数的确定提供了更简便的方法。这一系列的研究成果为深基坑支护结构的设计提供了一套新颖的实用计算方法,较好地解决了基坑支护结构中的一系列设计计算难题,已在工程实践中成功应用。     

Numerical modelling of installation effects for diaphragm walls in sand

The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic.     

NON-LINEAR FAULT BEHAVIOUR NEAR UNDERGROUND EXCAVATIONS — A BOUNDARY ELEMENT APPROACH

A boundary element model for stress/stability analysis of underground excavations in the vicinity of faults is presented. The boundary element formulation adopts the fictitious stress method for the simulation of excavation boundaries and the displacement discontinuity method for the representation of faults. The numerical model employs the Barton–Bandis non-linear joint model for the modelling of the fault behaviour and linear elastic behaviour for the rock. An incremental-iterative in situ stress relaxation algorithm is implemented for the non-linear analysis of the faults. Both deformation and peak strength models of Barton–Bandis are incorporated for modelling the mechanical behaviour of the fault. The non-linear deformation of fault considers the effects of coupling between shear and normal stresses and displacement, joint closure, joint separation, hardening followed by post-peak or residual behaviour. The peak strength model employs a mobilized non-linear shear strength envelope. The differences between linear and non-linear simulation of the fault models are discussed. A comparison of model predictions with the classical Mohr–Coulomb peak strength model with constant joint stiffness is presented. The numerical model is used for a case study of Canadian hard rock underground mine. The shear and normal displacements along the fault during four mining sequences with backfill simulation are presented and discussed.     

Application of nonlinear optimization technique to back analyses of deep excavation

This study presents a nonlinear optimization technique (NOT) for conducting the back analyses of geotechnical engineering problems based on the field observations. Additional auxiliary techniques are incorporated to enhance the convergence and stability of the NOT. The developed NOT and additional auxiliary techniques are incorporated into a finite element code and then applied to the back analysis of excavation-induced wall deflection. A number of hypothetical excavation cases with various scenarios of stratigraphy and two quality excavation case histories are used to validate the developed NOT, in which the dominant soil parameters are treated as target parameters. Results show that the wall deflections of all hypothetical and actual excavation cases at each stage can be accurately and efficiently back-figured. The developed NOT has a potential to be an useful tool for preventing the building damage through accurately and efficiently predicting the excavation-induced deformations at subsequent stages.     

基于能量增减法的深埋绿片岩隧洞稳定性评价方法

基于对现场地质条件和开挖响应的直观认识和对岩石室内试验所得物理力学特性的深刻揭示,建立了深埋条件下软弱围岩大变形挤压程度分级方法及相对应的安全系数计算方法。该方法考虑到隧洞原岩集聚的能量过大是造成开挖后围岩失稳的根本原因,将隧洞原岩能量和围岩的总变形与弹性变形之比相结合,分析了隧洞的围岩稳定性状况,并在此基础上通过增减隧洞原岩能量得到了其安全系数。通过实际工程应用及与传统经验评价方法的对比,验证了该方法的合理性与适用性。该方法考虑了围岩的地质情况、断面形状、尺寸、开挖方式等多种因素,弥补了传统经验评价方法无法适应复杂多变的现场工程施工情况的不足,更加贴近实际。可为大变形隧洞的安全预测、开挖方案、支护设计等提供重要参考依据。     

考虑动态因素的深基坑开挖反演分析及预测

以弹性地基梁法为基础,运用动态施工反演分析的思想,即在常规的反分析过程中引入隧步开挖和隧道支撑的动态施工因素,反算反映基坑土体性态的m值,以求仿真模拟深基坑工程实际施工情况,进而为下一工况的变形预报提供可靠保证。最后通过一个工程实例的计算值与实测值对比分析,验证了该法在基坑支护结构设计和施工过程中是合理可行性的。     

Elastoplastic analysis of jointed rocks using a coupled finite element and boundary element method

This paper presents a coupled, elastoplastic, finite element and boundary element method for the two-dimensional, non-linear analysis of anisotropic jointed rock. The non-linear and anisotropic behaviour of a jointed rock mass is simulated by representing the mass as an equivalent anisotropic, elastoplastic continuum, so that the influence of the jointing system is ‘smeared’ across the continuum, i.e. the individual joints are not modelled as discrete entities. Numerical examples have been solved to verify the capability, accuracy and efficiency of the present technique. The proposed technique has also been applied to the analysis of tunnel excavation problems in plane strain. The effects of anisotropy and non-linearity of the jointed rock mass during excavation have been investigated in some detail.     

Dynamic analysis of an offshore structure on an elastic-plastic foundation-soil system

The effect of foundation stiffness upon the dynamic response of an offshore structure is investigated. The non-linear deformation behaviour of a stratified seabed is included in the finite element simulation. The seabed is represented by a simplified spring model. In the linear elastic analyses the stiffnesses are derived using elastic half-space theory. For the non-linear problems, elastic-plastic finite element analyses are used to generate equivalent properties.An example of the method is given as applied to a three towered concrete gravity platform. Variation of natural frequency is used to indicate the significance of changes in parameters such as soil shear modulus, structural stiffness and deck mass. The forced response behaviour to random wave excitation is also investigated using a linear elastic analysis. The effect of the interaction of the foundation — soil with the structure on the dynamic response is demonstrated by the results.     

节理岩体中应力波传播规律研究的进展

讨论了位移不连续模型与特征值法结合的方法,对垂直于单一线性变形节理、多个平行线性变形节理、单一非线性变形节理,分别采用线性变形不连续模型、双曲线变形不连续模型(BB模型)进行的理论与相应的实验研究。用离散元程序UDEC,对上述问题进行数值模拟;用三维离散元程序3DEC,对节理岩体中三维波的传播进行的数值模拟。并用UDEC与有限差分程序AUTODYN-2D耦合,模拟爆炸过程及爆炸波在节理岩体中的传播。同时提出了几个有待研究的问题。     

线性分布基床系数弹性地基梁有限单元法改进

弹性地基梁法常用于研究土和结构的相互作用,对于均布荷载和边界条件简单的弹地基梁,采用理论解即可方便地进行计算。侧向荷载作用下桩体、嵌入式挡墙一般根据弹性地基梁理论进行分析,并假定基床系数随深度增加。对于基床系数呈线性分布或呈均匀分布但边界条件复杂的弹性地基梁理论求解困难,通常采用有限差分法或有限单元法近似求解。采用有限单元法计算线性分布基床系数弹性地基梁时,若单元划分数量不够,就存在计算精度不足的问题。采用加权余量法推导了更为精确的2节点5次位移函数和相应的单刚矩阵,得出了线性分布荷载作用下挠度的5次多项式近似解,从而实现只需划分很少的单元数,节点位移及单元内位移的分布即可达到较高的计算精度,极大地提高了计算效率,单元内力的分布可直接由位移函数导出,简化了后处理计算程序。     

Ensemble filter methods with perturbed observations applied to nonlinear problems

The ensemble Kalman filter (EnKF) has been shown repeatedly to be an effective method for data assimilation in large-scale problems, including those in petroleum engineering. Data assimilation for multiphase flow in porous media is particularly difficult, however, because the relationships between model variables (e.g., permeability and porosity) and observations (e.g., water cut and gas–oil ratio) are highly nonlinear. Because of the linear approximation in the update step and the use of a limited number of realizations in an ensemble, the EnKF has a tendency to systematically underestimate the variance of the model variables. Various approaches have been suggested to reduce the magnitude of this problem, including the application of ensemble filter methods that do not require perturbations to the observed data. On the other hand, iterative least-squares data assimilation methods with perturbations of the observations have been shown to be fairly robust to nonlinearity in the data relationship. In this paper, we present EnKF with perturbed observations as a square root filter in an enlarged state space. By imposing second-order-exact sampling of the observation errors and independence constraints to eliminate the cross-covariance with predicted observation perturbations, we show that it is possible in linear problems to obtain results from EnKF with observation perturbations that are equivalent to ensemble square-root filter results. Results from a standard EnKF, EnKF with second-order-exact sampling of measurement errors that satisfy independence constraints (EnKF (SIC)), and an ensemble square-root filter (ETKF) are compared on various test problems with varying degrees of nonlinearity and dimensions. The first test problem is a simple one-variable quadratic model in which the nonlinearity of the observation operator is varied over a wide range by adjusting the magnitude of the coefficient of the quadratic term. The second problem has increased observation and model dimensions to test the EnKF (SIC) algorithm. The third test problem is a two-dimensional, two-phase reservoir flow problem in which permeability and porosity of every grid cell (5,000 model parameters) are unknown. The EnKF (SIC) and the mean-preserving ETKF (SRF) give similar results when applied to linear problems, and both are better than the standard EnKF. Although the ensemble methods are expected to handle the forecast step well in nonlinear problems, the estimates of the mean and the variance from the analysis step for all variants of ensemble filters are also surprisingly good, with little difference between ensemble methods when applied to nonlinear problems.     

Simulation of excavation in a poro-elastic material

A method is presented which allows the computation of the displacements and pore pressures which are generated in an elastic soil when excavation is carried out. The formulation is based on Biot's theory and is fully coupled, with consideration also given to the effects of the lowering of the water table which often accompanies the excavation of soil. Example problems are solved to illustrate the theory which has been presented.     

New method for non-linear analysis of laterally loaded flexible piles

The authors' previous application of non-linear analysis of the behavior of rigid piles is extended to the elastic and plastic behavior of flexible piles under lateral load. Using Broyden's approach of solving non-linear simultaneous equations and the conventional p-y concept, a new numerical method of non-linear analysis is developed. Comparisons of the results computed by present method with the results of previous similar methods are presented to show the efficiency and usefulness of the present method. For flexible piles a study of the relationship between effective depth De and relative pile stiffness Kr for both elastic and plastic ranges is carried out. Thus the analytical basis for the method using previous results of the bearing capacity and displacements of laterally loaded rigid piles to predict those of flexible piles is provided.     

隧道开挖引起邻近单桩水平反应分析

隧道开挖会降低邻近桩基承载力,如何更为合理评价桩基水平附加响应是需要解决的问题。基于Pasternak双参数地基模型和三折线弹塑性荷载传递模型,采用两阶段分析法,并考虑侧向土体作用及地基土层的非均质特性,提出了更符合实际的单桩水平反应简化分析方法。通过与Winkler地基梁法及边界元法的对比分析,验证了方法的合理性。结合对单桩水平反应的多种影响因素进行参数分析,通过各因素相应的修正系数来对基准工况中单桩最大水平反应进行修正,得到计算工况中单桩的最大水平位移和最大弯矩。分析结果表明,桩基水平位移计算时可忽略侧向土体作用,而弯矩计算时应予以考虑;桩基计算工况的最大水平位移 最大弯矩 与平均地层损失比 呈现线性关系,而与隧道半径R、隧道轴线深度H、桩距隧道中心线距离x及桩身柔度系数 均呈现非线性关系。