考虑参数空间变异性的边坡稳定可靠性有限元极限分析

当土性参数空间变异性较大时,极限平衡法得到的滑移面不尽合理。阐述了基于广义变分原理的有限元极限分析方法,采用混合有限元方法,构筑了线性应力三角形单元与线性速度三角形单元,结合强度折减法与线性规划算法,建立了边坡稳定安全系数上下限分析方法,分析了土的抗剪强度参数空间变异性对边坡稳定性的影响,并与3种典型极限平衡法进行了对比。结果表明,FELA方法可有效搜索边坡临界滑移面,并给出安全系数的严格上下限。对于简单均质边坡,有限元极限分析与极限平衡法结果接近,极限平衡法结果大多位于极限分析的上下限内;对于空间变异性较大的边坡,有限元极限分析法可以有效搜索可能的多种临界滑移面,而极限平衡法则存在显著偏差,且往往高估滑坡风险。强度参数的空间变异性还导致边坡安全系数分布形式变化显著,仅采用安全系数无法反应这一变化。根据安全系数的分布形式,给出了土性参数设计值建议。     

Finite element limit analysis of load-bearing performance of reinforced slopes using a non-associated flow rule

This paper presents a numerical study on the load-bearing performance of reinforced slopes under footing load using a finite element limit analysis (FELA) method where a non-associated flow rule is assumed in the analysis. The method was validated against results from full-scale model tests and a limit equilibrium (LE) analytical method. A series of parametric analyses was subsequently carried out to examine the influences that the soil dilation angle, footing location, and reinforcement design (i.e. length, tensile strength, and vertical spacing) could have on the load-bearing performance of reinforced slopes. Results indicate that dilation angle has a significant influence on the predicted magnitudes of bearing capacity, slope deformation, and mobilized reinforcement load. The predicted values of bearing capacity using the FELA are smaller than those from the Meyerhof's analytical method for unreinforced semi-infinite foundation, especially for larger friction angle values. Additionally, the ultimate bearing capacity of the slope and its corresponding horizontal deformation increase with the reinforcement tensile strength. Finally, the slip planes under the applied footing load are found to be y-shaped and primarily occur in the upper half of the slope.     

A new design equation for drained stability of conical slopes in cohesive-frictional soils

New plasticity solutions to the drained stability of conical slopes in homogeneous cohesive-frictional soils were investigated by axisymmetric finite element limit analysis. Three parameters were studied, i.e. excavated height ratios, slope inclination angles, and soil friction angles. The influences of these parameters on the stability factor and predicted failure mechanism of conical slopes were discussed. A new design equation developed from a nonlinear regression of the lower bound solution was proposed for drained stability analyses of a conical slope in practice. Numerical examples were given to demonstrate a practical application of the proposed equation to stability evaluations of conical slopes with both associated and non-associated flow rules.     

Stability analysis of leaning historic masonry structures

This paper introduces an automatic, powerful and easy to use procedure for undertaking stability analyses of leaning historic masonry structures, based on an upper bound finite element limit analysis (FELA) approach. The procedure proposed here consists of a comprehensive workflow which involves the automatic point cloud manipulation, the 3D mesh generation of the actual geometry for structural purposes (e.g. FE mesh), and a two-step FELA that reduces drastically optimization variables assuming only active few elements inside a restricted processing zone. To generalize the Heyman's intuition to complex real geometries, the use of a 3D upper bound FELA with a recursive kernel of variables reduction becomes necessary for a precise evaluation of the limit inclination that makes the structure collapse under gravity loads. This outcome permits to estimate the structural health condition of a historic structure by comparing the critical inclination angle against the actual one. To demonstrate the effectiveness of the automated procedure, the southwest leaning tower of the Caerphilly castle (Wales, UK) is investigated and failure mechanisms with collapse inclination angles are evaluated through FELA. The proposed procedure presents a high degree of automation at each operational level and, hence, could be effectively used to assess the stability of historic structures at a national scale and provide useful information to asset owners to classify the structural health condition of leaning historic masonry structures in their care.     

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain:A finite element method based approach

Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams,tunnels,bridges and widening roads.National Highway-58 connects Delhi to Badrinath in India,which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures.In the present investigation,a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas.Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator.Nonlinear generalized Hoek-Brown(GHB) criterion was adopted for stability analyses.Out of 20 slopes,five slopes(S6,S7,S18,S19 and S20) are unstable with factor of safety(FoS) less than or equal to 1,and thus needs immediate attention.The FoS values of four slopes(S2,S9,S13 and S17) lie between 1 and 1.3,i.e.marginally stable,and slopes S1,S3,S4,S5,S8,S10,Sll,S12,S14,S15 and S16 are stable.Mohr-Coulomb(MC) criterion was also adopted to compare the slope stability analysis with GHB criterion.The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values,the difference is marked.For the jointed rock in the Himalayan region,the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions.Accordingly,some suggestions are proposed to strengthen the stability of cut slopes.     

基坑土钉支护安全系数的强度参数折减有限元方法

针对基坑土钉支护讨论其安全系数的强度参数折减有限元计算方法,包括土钉支护体系的三维有限元模型、安全系数的折减强度参数计算、极限状态的确定以及极限状态下的计算方法等。按所建议方法,编制了三维有限元计算程序,并给出算例,展示了所建议计算模型和方法的有效可靠性。此外,还对有限元方法计算的安全系数与现行土钉支护规程建议公式所计算安全系系数的可比性进行了讨论。     

土体结构极限承载力的有限元分析

 在平面应变条件下,采用增量加载有限元方法求解土体结构的极限承载力,以弹塑性有限元计算不收敛作为达到极限破坏状态的判别标准;在得到土体应力场的基础上,用有限元边坡稳定分析中的滑面应力分析法验算土体结构在达到极限破坏状态时安全系数是否趋近于1.0,同时搜索相应的临界滑动面,与增量加载直到土体结构破坏获得的滑动面比较,并分析二者与经典Prandtl解破坏机构的差异。计算结果表明：屈服准则的选取对计算结果的影响很大,对于无自重的边坡和地基,在非关联流动法则下采用 Mohr-Coulomb 匹配圆准则或者在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时,所得到的结果与经典Prandtl解相近;但是在非关联流动法则下采用Mohr-Coulomb匹配圆准则得到的滑动面与经典Prandtl解破坏机构不一致,极限状态下的安全系数也不为1.0;在关联流动法则下采用Mohr-Coulomb 内切圆屈服准则时,其极限状态下的滑动面与有限元稳定分析方法搜索得到的滑动面相近,与经典Prandtl解破坏机构一致,同时在该极限荷载下土体结构沿临界滑动面的安全系数Fs趋近于1.0。对于有自重的边坡,同样在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时,其极限状态下的滑动面与有限元稳定分析方法搜索得到的滑动面一致,在该极限荷载下土体结构沿临界滑动面的安全系数Fs趋近于1.0,说明此屈服准则下求得的极限承载力是土体结构严格意义上的真正的承载力。     

Overall stability of geosynthetic-reinforced embankments on soft soils

Overall stability of geosynthetic-reinforced embankments on soft soils is analysed using two different methodologies: application of a numerical model based on the finite element method; use of a limit equilibrium method. These two methodologies are described and also applied on three geosynthetic-reinforced embankments on soft soils. One of the cases is a case history constructed up to failure. Considering the analysis of the results, some conclusions are formulated on the limit equilibrium method accuracy, namely regarding the critical slip surface, overall safety factor and overturning and resisting moments.     

Stability analysis of slopes using the finite element method and limiting equilibrium approach

The limit equilibrium method is commonly used for slope stability analysis, being relatively simple compared with finite element analysis. Both methods were used to analyse homogeneous and inhomogeneous slopes, taking into account the rapid drawdown condition, the undrained clay soils and the presence of tension cracks. The analyses were carried out using PLAXIS 8.0 (finite element method) and SAS-MCT 4.0 (limit equilibrium approach). The safety factor and location of the critical slip surface obtained from the two methods are compared.      

土体结构极限承载力的有限元分析

在平面应变条件下,采用增量加载有限元方法求解土体结构的极限承载力,以弹塑性有限元计算不收敛作为达到极限破坏状态的判别标准;在得到土体应力场的基础上,用有限元边坡稳定分析中的滑面应力分析法验算土体结构在达到极限破坏状态时安全系数是否趋近于1.0,同时搜索相应的临界滑动面,与增量加载直到土体结构破坏获得的滑动面比较,并分析二者与经典Prandtl解破坏机构的差异。计算结果表明：屈服准则的选取对计算结果的影响很大,对于无自重的边坡和地基,在非关联流动法则下采用Mohr-Coulomb匹配圆准则或者在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时,所得到的结果与经典Prandtl解相近;但是在非关联流动法则下采用Mohr-Coulomb匹配圆准则得到的滑动面与经典Prandtl解破坏机构不一致,极限状态下的安全系数也不为1.0;在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时,其极限状态下的滑动面与有限元稳定分析方法搜索得到的滑动面相近,与经典Prandtl解破坏机构一致,同时在该极限荷载下土体结构沿临界滑动面的安全系数Fs趋近于1.0。对于有自重的边坡,同样在关联流动法则下采用Mohr-Coulomb内切圆屈服准则时,其极限状态下的滑动面与有限元稳定分析方法搜索得到的滑动面一致,在该极限荷载下土体结构沿临界滑动面的安全系数Fs趋近于1.0,说明此屈服准则下求得的极限承载力是土体结构严格意义上的真正的承载力。     

多种材料结构体系塑性极限分析的弹性补偿有限元法

弹性补偿有限元法是一种简单、高效的结构塑性极限分析方法,目前仅用于采用单一材料的结构体系中。在经典弹性补偿有限元法中引入承载比概念,并据此对算法进行了改进,既保留了算法通过结构广义应力场不断平均化获得下限荷载的基本优化思想,又融入了平均化过程按各种材料的广义强度成比例调整的新思想,结构破坏时每种材料同时趋于各自的广义强度,使算法适用于对采用多种材料的结构体系做塑性极限分析。经典算例的对比分析表明,改进算法的分析结果是收敛的、准确的和稳定的。对复杂钢框架结构的极限荷载和破坏模式分析也表明,改进算法可用于采用多种材料的实际工程结构的安全评价中。     

Three-dimensional finite element analysis of geosynthetic-reinforced soil walls with turning corners

The paper presents in-depth three-dimensional finite element analyses investigating geosynthetic-reinforced soil walls with turning corners. Validation of the 3D numerical procedure was first performed via comparisons between the simulated and reported results of a benchmark physical modeling built at the Royal Military College of Canada. GRS walls with corners of 90°, 105°, 120°, 135°, 150°, and 180° were simulated adopting the National Concrete Masonry Association guidelines. The behaviors of the GRS walls with corners, including the lateral facing displacement, maximum reinforcement load, factor of safety, potential failure surface, vertical separation of facing blocks, and types of corners were carefully evaluated. Our comprehensive results show (i) minimum lateral displacement occurs at the corner; (ii) lower strength of reinforcements are required at the corner; (iii) higher corner angles lead to lower stability; (iv) potential failure surface forms earlier at the end walls; (v) deeper potential failure surfaces are found at the corners; (vi) larger numbers of vertical separations are found at walls with smaller corner angles. The paper highlighted the salient influence of the corners on the behaviors of GRS walls and indicated that a 3D analysis could reflect the required reinforcement length and the irregular formation of the potential failure surfaces.     

Numerical study and design of skewed X-type branch plate-to-circular hollow section connections

Structural systems, including space-frames, cable stayed roof systems and bridges, with elements that intersect at non-orthogonal angles necessitating rotated and complex connection geometries, have become commonplace. Non-orthogonal plate-to-circular hollow section (CHS) connections with branch members rotated about their own axis (skewed) have been absent in international literature and design guidelines. A numerical finite element parametric study is presented on the behaviour of skewed X-type plate-to-CHS connections loaded under branch plate tension. A total of 91 connections with wide-ranging values of geometric properties were modelled and analysed using commercially available finite element software. The numerical finite element analysis indicated a smooth sigmoidal (S-shaped) transition between longitudinal and transverse orthogonal extremes. A non-linear interpolation function was developed, for application between longitudinal and transverse design recommendations, that adequately predicts skewed connection behaviour over a wide range of geometric connection configurations. A partial design strength function for skewed X-type plate-to-CHS, which builds on existing design recommendations for non-skewed plate connections, is hence proposed with lower bound reduction (resistance) factors.     

基于强度折减的有限元方法求边坡稳定安全系数

当折减系数达到某一数值时,边坡内的一定幅值的广义剪应变自坡底向坡顶贯通,认为边坡破坏,定义此前的折减系数为安全系数,与极限平衡法相比有限元法具有很多优点。集中讨论屈服准则、内摩擦角和粘聚力、剪胀角、计算范围的选取、坡脚的形状和尺寸、网格疏密程度、不同的破坏标准对全系数的影响以及大变形和小变形有限元对比分析。     

滩海桶形基础破坏机制及极限承载力分析研究

针对饱和软黏土地基上桶形基础结构,基于弹塑性极限分析中的上限法,建立了一种竖向荷载作用下桶形基础的极限分析模型。采用有限元数值分析解验证了所提出极限分析模型的可行性和有效性,进而,据此进行了一系列变动参数比较计算,以此对大量的计算结果进行了系统的分析,所得到的数值计算结果与分析结论为工程设计提供参考依据。     

岩土工程极限分析有限元法及其应用

经典岩土工程极限分析方法一般采用解析方法 ,有些还要对滑动面作假设 ,不适用于非均质材料 ,尤其是强度不均的岩石工程 ,从而使极限分析法的应用受到限制。随着计算机技术的发展 ,极限分析有限元法应运而生 ,它能通过强度降低或者荷载增加直接算得岩土工程的安全系数和滑动面 ,十分贴近工程设计。本文探讨了极限分析有限元法的一些基本原理 ,包括安全系数的定义、岩土体整体失稳的判据、屈服准则的选用等 ,并将该方法应用于边坡、地基、隧道稳定性计算 ,算例表明了此法的可行性 ,拓宽了该方法的应用范围     

轴向压缩下不加劲T型/Y型管节点性能的研究

使用有限元分析软件ABAQUS对轴向压缩载荷下T型和Y型管节点的失效模式﹑极限强度和具体性能进行研究。不加劲管节点的性能可从用于试验的管节点的数据库中提取。在数值分析中,使用修正弧长法可准确地模拟节点的性能,并有助于研究其真正的失效模式。通过数值分析发现,失效模式包括弦构件的局部弯曲、椭圆化变形、弦的塑性破坏。通过数值模拟得出的结果显示:节点表面的临界面积与椭圆化变形﹑变形量和应力有关。此外,对数值分析所预测出的极限强度与已有的试验结果进行了比较和验证。尽管已对管节点进行了大量的研究,但多集中于对极限强度和应力集中系数的估算上而不是对节点性能的具体研究,而此研究是一个全面解释轴向压缩下节点性能的具体研究。在已有的文献资料中很难看到这样深入又详细的节点研究。     

有限元强度折减法中边坡三种失效判据的适用性研究

采用有限元强度折减法进行边坡稳定性分析时,边坡的安全系数在很大程度上依赖选用的失稳判别标准。通常以特征部位位移的突变性、塑性区的贯通性、数值计算的收敛性作为边坡失稳判据。然而,对这三种判据的适用性学术界一直存在不同看法。以一般边坡和陡边坡作为算例模型,对比分析三种常用的判据判定安全系数的大小。结果表明:对一般边坡三种判据有较好的一致性,陡边坡三种判据存在较大的差异。研究发现:以往用于强度折减法的屈服准则没有考虑拉伸截断,即在强度折减过程中过高的估计了材料的抗拉强度是导致三种判据对应的计算结果存在广泛争议的重要原因,并通过计算钟乳石模型的安全系数对这一结论进行验证。因此,有限元强度折减法中应考虑抗拉强度指标与抗剪强度指标同等地减少,才能保证计算结果的正确性及三种判据的一致性。考虑张拉、剪切破坏的强度折减法在边坡稳定性计算中具有普遍的适用性,是对强度折减法的改进和推动。     

An investigation of the block shear strength of coped beams with a welded clip angle connection — Part II: Numerical study

An experimental study of the block shear capacity of ten full-scale coped beams with a welded clip angle connection was presented in Part I. The test results were compared with predictions using block shear design equations in several current design standards. In general, the results showed that the existing design standards did not provide consistent predictions of the block shear capacity of coped beams with welded clip angles. In addition, the equations provided by the standards cannot accurately reflect the failure mode of the specimens observed in the tests. In order to gain a better understanding of the connection behavior, such as the stress distribution in the web near the periphery of the clip angles and the failure mechanism of the connection, an analytical study of the block shear capacity of coped beams with welded clip angles was carried out using the finite element method. Based on the limited test data and the results of the finite element analysis (FEA), a strength model was established and a design equation was proposed to evaluate the block shear strength of coped beams with welded clip angles. It was shown that the proposed design equation gave better predictions of the block shear capacity of the specimens.