Multiobjective optimization-based design of stabilizing piles in earth slopes

Though the technology of using stabilizing piles to prevent landsliding is not new, the design of such piles with a meaningful optimization framework has been rarely reported. In this paper, a multiobjective optimization-based framework for design of stabilizing piles is presented, in which both reinforcement effectiveness and cost efficiency could be explicitly considered. The design parameters considered in the proposed design framework are the pile parameters, including pile diameter, spacing, length, and position, and the design objectives considered are the reinforcement effectiveness and cost efficiency. The design of stabilizing piles is then implemented as a multiobjective optimization problem. In that the desire to maximize the reinforcement effectiveness and that to maximize the cost efficiency are two conflicting objectives, the output of this multiobjective optimization will be a Pareto front that depicts a trade-off between these two design objectives. With the obtained Pareto front, an informed decision regarding the design of stabilizing piles is reached. The effectiveness and significance of the proposed multiobjective optimization-based design framework for stabilizing piles are demonstrated through two illustrative examples: one is the design of stabilizing piles in a one-layer earth slope and the other the design of stabilizing piles in a two-layer earth slope. Further, parametric analyses are conducted to investigate the influences of the pile design parameters on the stability of reinforced slopes.     

A calculation method for the embedded depth of stabilizing piles in reinforced slopes

Embedded stabilizing piles are a significant optimization measure for traditional piles used to reinforce slopes or landslides. The determination of the embedded depth of the pile top is essential for engineering design. On the basis of the potential overtop-sliding failure mechanism for a piled slope, the corresponding overall slip surface is assumed to consist of the upper part from the original slip surface of the landslide, and the lower part occurs in the local slide mass upslope of the piles. The imbalanced thrust force method is used to determine the thrust force of the upper slide mass, and a variational calculus method within the framework of limit equilibrium for the lower slide mass is provided to calculate its limit resistance. According to the equilibrium relationship between the thrust force and the limit resistance under a design factor of safety of the piled slope, a closed-form solution to the piled-slope stability is specifically derived. It can quantitatively exhibit the influences of some important factors, including the embedded depth on the factor of safety and the corresponding slip surface of the slope. The analysis results of some practical examples show that the factor of safety decreases nonlinearly as the embedded depth increases. The proposed method can be applied in practical engineering.     

阻滑桩加固土坡稳定性分析的上限解法

从极限分析机动学方法出发,利用土的抗剪强度折减系数概念,建立了土坡的极限平衡状态方程,由此确定土坡的临界稳定安全系数及其相应的潜在破坏模式.对于典型问题,通过与现有极限平衡解和有限元数值解的对比分析,验证了这种上限解法的合理性.进而对于在给定的荷载条件下不能满足抗滑稳定性要求的土坡,考虑采用阻滑桩加固方式,根据桩侧有效土压力的合理分布模式确定桩体与滑动面相交的截面上等效抗滑力和抗滑力矩,利用极限分析上限定理建立了阻滑桩加固土坡的极限平衡状态方程,将桩侧土压力作为目标函数,运用数学规划方法确定了极限平衡状态时的临界桩侧土压力,以此为土坡加固中阻滑桩设计提供依据.通过数值计算与分析探讨了阻滑桩加固位置的优化布置等问题.     

悬臂式抗滑桩加固黏土边坡地震永久位移算法

为了有效地确定悬臂式抗滑桩加固的黏土边坡地震永久位移,基于极限分析上限定理,针对圆弧滑动式土坡破坏模式,通过对设置抗滑桩条件下土坡进行外力功率和内能耗散率的计算,按严格力学定义推导出坡体在地震作用下的安全系数,进而导出与安全系数相对应的边坡地震屈服加速度计算公式,并结合Newmark滑块位移法对边坡产生的转动加速度进行二次积分,推导出与边坡设计安全系数密切相关的坡体地震永久位移的详细计算公式。以5.12汶川地震卧龙测站东向地震波为例,通过对一算例边坡进行分析,给出了边坡永久位移时程曲线以及不同设计安全系数与永久位移的关系,分析了算法与Ambraseys算法的结果,验证了所提计算方法的有效性,并得到不同设计安全系数时边坡土体黏聚力和内摩擦角对坡体永久位移的影响规律。研究结果表明,坡体永久位移随着设计安全系数的增加逐渐呈指数函数式减小变化,在较低设计安全系数下,坡体永久位移受土体抗剪强度参数影响较为敏感,随着设计安全系数的提高,这种敏感性则逐渐降低。     

Nonlinear analysis of laterally loaded rigid piles in cohesionless soil

In this paper, a method is developed for nonlinear analysis of laterally loaded rigid piles in cohesionless soil. The method assumes that both the ultimate soil resistance and the modulus of horizontal subgrade reaction increase linearly with depth. By considering the force and moment equilibrium, the system equations are derived for a rigid pile under a lateral eccentric load. An iteration scheme containing three main steps is then proposed to solve the system equations to obtain the response of the pile. To determine the ultimate soil resistance and the modulus of horizontal subgrade reaction required in the analysis, related expressions are selected by reviewing and assessing the existing methods. The degradation of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The developed method is validated by comparing its results with those of centrifugal tests and three-dimensional finite element analysis. Applications of the developed method to laboratory model and field test piles also show good agreement between the predictions and the experimental results.     

再论悬臂式抗滑桩合理桩间距的计算方法

为了进一步合理确定悬臂式抗滑桩桩间距,在对以往关于开挖边坡抗滑桩桩间距分析模型缺陷讨论的基础上,提出在抗滑桩桩后局部所形成的拱脚处,两侧土拱在此交汇形成的是倒梯形受压区。在计算确定悬臂式抗滑桩桩间距时,除满足桩间静力平衡条件、土拱跨中及拱脚处的强度条件等基本控制条件外,还需满足桩计算宽度条件、桩土变形协调条件等附加条件,得到了确定桩间净距的方程组,通过迭代试算可以求解。依托一工程实例,定量地说明了在其他因素不变的情况下,桩间净距随桩后土体黏聚力或内摩擦角的增大而非线性增大,且桩间净距受黏聚力的影响更为敏感,同时桩间净距随着桩后坡体推力的增大而呈非线性减小。所提出的方法除可用于黏性土外,还可用于无黏性土。     

考虑桩间土体抗滑作用的单排抗滑桩受力计算方法

为了充分考虑桩间距范围内滑体对抗滑桩受力的影响,从单排抗滑桩加固边坡的整体稳定角度出发,在采用传递系数法分析指定设计安全系数情况下抗滑桩的内力时,提出对一个桩间距范围内的加固坡体进行整体分析,将抗滑桩所在部位单独划分条块,该条块包括桩体受荷段及其两侧桩间距范围内的滑体。推导了与此分析模型相应的桩体受荷段底端内力计算公式,并给出了在滑坡推力线性分布条件下作用于受荷段的净滑坡推力计算表达式。分析结果显示,在不考虑与完全考虑受荷段两侧桩间距范围内滑体抗力作用时,得到是桩体内力及位移的上、下边界值。实例分析进一步表明,理论分析与数值模拟结果具有良好的一致性。所提出的方法比传统方法更有利于抗滑桩设计的经济性。     

边坡土体侧移模式对抗滑桩影响分析

在开挖、降雨或地震等外部因素作用下,边坡土体很容易进入局部或瞬态大变形乃至失稳滑动,使抗滑桩产生附加位移及弯矩。基于两阶段分析方法,采用Winkler模型模拟抗滑单桩与土之间的相互作用,建立单桩水平位移控制方程组,根据内力与位移的连续条件得到考虑不同土体侧移模式下求解桩身响应的矩阵解析表达式,并采用现场监测数据及Poulos弹性理论进行验证,证明该方法是合理可行的,并通过参数分析土体侧移对抗滑桩水平承载性状的影响程度。分析结果表明,土体侧移模式包括最大侧移值、分布形状及重心、侧移势等,对抗滑桩的挠度和弯矩均有显著影响,在工程设计中应予以充分重视。     

施工期间人工挖孔桩桩间土稳定性分析

为预防人工挖孔桩窜孔,探讨了桩间土失稳机制,分析了桩间土失稳时的位移特征,建立了桩间土稳定性分析的力学模型,推导了桩间土稳定系数及安全桩净距的计算公式,提出了窜孔防治措施建议。结果表明,桩间土失稳时,滑动土体位移平行于桩心连线,其宽度等于两桩桩径较小值;桩间土稳定系数与滑动土体宽度及埋深成反比,与桩净距成正比,随滑动层的抗剪强度及残余抗剪强度增大而增大,而滑动层厚度则存在一个最不利值,可通过试算确定;控制桩孔间的混凝土面高差、增大桩孔开挖净距、加强护壁,减少桩间土的扰动等是防治窜孔的有效措施。工程实例表明,桩间土稳定性评价方法合理、实用,可为黏性土场地的人工挖孔桩施工提供参考。     

Three-dimensional finite element analysis for soil slopes stabilisation using piles

This paper presents the analytical methods of slope-stabilising piles using the three-dimensional (3-D) finite element (FE) analysis with the strength reduction method (SRM). This 3-D FE model is employed to overcome the limitations observed in two-dimensional (2-D) FE analysis. The solutions obtained from 3-D FE analyses are verified to be less conservative in this paper. The 3-D analysis is considered to be of particular importance to pile-slope problems. The soil that flows between piles cannot be taken account properly in the 2-D FE analysis. The method adopted in this paper can avoid the assumption of soil movement and the pressure distribution along the piles subjected to soil movement. The numerical analysis employs the Mohr–Coulomb failure criterion with the strength reduction technique for soil and an elastic member for piles. The spacing effect of the pile is considered in the 3-D model, the S/D (S: centre to centre, D: diameter of pile) ratio, equal to 4.0, is found to be equivalent to the single pile stabilisation. The middle portion of the slope is identified as the optimal location to place the piles. The proper length of the pile, which can be used to stabilise the slope, is also examined using 3-D FE analyses. It is concluded that L/H greater or equal 0.70 is recommended (L: pile length, H: slope height). The numerical analyses are conducted based on a coupled analysis, which simultaneously considers both the slope stability and the pile response. The failure mechanisms of the pile-slope system subjected to the pile locations, pile head conditions and pile length are each discussed. The contact pressure, shear force and moment along the piles are presented to illustrate the pile stabilising mechanism herein.     

抗滑桩加固边坡三维数值分析中的几个问题

就当前抗滑桩加固边坡三维数值分析中存在的几个问题,开展了有针对性的研究。利用考虑桩-土-边坡相互作用的强度折减有限元程序,结合典型边坡算例,深入探讨了抗滑桩-边坡体系的计算模型尺度、设桩位置、桩间距（S）与桩径（D）之比（S/D）、桩长与桩底接触模式等因素对边坡稳定安全系数及临界滑动面的影响,以及不同桩头约束下抗滑桩内力分布等。研究表明,单桩取半、单桩、双桩取半、双桩、单桩加双桩取半5种尺度计算模型所得边坡的安全系数并无差异,模型尺度为0.5S时的计算工作量最小;抗滑桩加固于边坡中部可获得最大的安全系数,坡顶或坡脚处安全系数略高于无桩状态,总体上其安全系数与设桩位置的变化曲线近似为一抛物曲线;边坡安全系数随S/D的增加而减小,其最优的比值宜为S/D =2～6,此时桩间存在土拱效应;均质土坡中抗滑桩锚固深度宜为2/5桩长;其结果可为抗滑桩工程设计及规范修订提供参考。     

抗滑桩设计中关于确定桩间距问题的分析

抗滑桩间距的确定是滑坡防治工程中的关键之一。本文基于土拱效应,分析桩间土拱的受力状态,通过土拱能够保持整体稳定性、拱顶和拱脚处截面最不利受力点达到临界应力状态来共同控制桩间距,得到了较为合理的桩间距计算公式,在其它因素不变的情况下,分析了桩间距与桩后滑坡推力、土体粘聚力和内摩擦角之间的关系,并结合工程实例进行了验证。     

基于土拱效应下的地震作用与抗滑桩桩间距关系分析

基于抗滑桩桩间土土拱效应,建立在地震作用下土拱效应的力学分析模型,在Mononobe-Okabe理论的基础上,将土拱作用等效为挡土墙作用,提出在一定地震设防烈度下土拱面上水平地震力的计算方法;在考虑滑坡推力和地震力两种外力作用下,依据桩间土在极限平衡状态下的静力平衡条件和强度条件,得出桩间净距理论计算公式.工程实例和系列试算表明,同等条件下,考虑地震作用比不考虑地震作用桩间净距要减小4％ ～ 23％,由此得出不同抗震设防等级下桩间净距计算的折减系数和桩间净距直接折减计算公式,以指导抗滑桩工程设计.     

Influence of rainfall-induced wetting on the stability of slopes in weathered soils

Shallow failures of slopes in weathered soil are caused by infiltration due to prolonged rainfall. These failures are mainly triggered by the deepening of the wetting band accompanied by a decrease in matric suction induced by the water infiltration. This paper reports trends of rainfall-induced wetting band depth in two types of weathered soils that are commonly found in Korea. Both theoretical and numerical analyses for wetting band depth are presented based on the soil–water characteristic curve obtained using filter paper as well as tensiometer tests. It is found that the magnitude of wetting front suction plays a key role in the stability of slopes in weathered soils. Theoretical analysis based on modified Green and Ampt model tends to underestimate the wetting band depth for typical Korean weathered soils. It was also deduced that for Korean weathered soils, the factor of safety drops rapidly once the wetting band depth of 1.2 m reached.     

被动桩中土拱效应问题的数值分析

被动桩对侧向位移的土层起到遮拦作用的机理主要是土拱效应。采用有限元软件Plaxis 8.1,详细地研究了被动桩中土拱效应的产生机理,分析了导致侧向位移的荷载大小、土体性质、群桩以及桩土接触面性质等影响因素对土拱效应性态和桩土应力分担比的影响,分析表明,桩间距是影响土拱效应的最主要因素。     

柔性群桩承台下变截面角桩与地基相互作用的线性分析

对桩侧土及桩端土均采用线性荷载传递函数,同时考虑桩周土所分担的荷载及桩型对桩基荷载传递规律的影响,利用力学理论及微分方程的近似解法—子域法,推导出了柔性群桩承台下变截面角桩与地基相互作用的近似的解析算式,并通过算例将等截面桩桩侧摩阻力和桩身轴力与变截面桩桩侧摩阻力和桩身轴力作了对比,表明改变桩型能提高桩侧摩阻力。为验证本文方法的可行性,将模型试验结果与本文计算结果进行了比较,表明本文方法有较好的精度。     

Numerical analysis of the geotechnical behaviour of energy piles

Energy geostructures are rapidly gaining acceptance around the world; they represent a renewable and clean source of energy that can be used for the heating and cooling of buildings and for de‐icing of infrastructures. This technology couples the structural role of geostructures with the energy supply, using the principle of shallow geothermal energy. The geothermal energy exploitation represents an additional thermal loading, seasonally cyclic, which is imposed on the soil and the structure itself. Because the primary role of the piles is the stability of the superstructure, this aspect needs to be ensured even in the presence of the additional thermal load. The goal of this paper is to numerically investigate the behaviour of energy pile foundations during heating–cooling cycles. For this purpose, the finite element method is used to simulate both a single and a group of energy piles. The piles are subjected to a constant mechanical load and a seasonally cyclic thermal load over several years, imposed in terms of injected–extracted thermal power. The soil and the pile–soil interface behaviours are reproduced using a thermoelastic‐thermoplastic constitutive model. The thermal‐induced stresses inside the piles and the additional displacements of the foundations are discussed. The group model is used to investigate the interactions between the piles during thermo‐mechanical loading. The presented results are specific to the studied cases but lead to the conclusion that both the thermal‐induced displacements and stresses, despite being acceptable under normal working conditions, deserve to be taken into account in the geotechnical design of energy piles. Copyright © 2014 John Wiley & Sons, Ltd.     

Skin friction features of drilled CIP piles in sand from pile segment analysis

Numerical pile segment analysis is conducted in this study with an advanced soil model to investigate the skin friction behaviour of a drilled Cast‐In‐Place (CIP) pile installed in sand. Although the interface between the sand and pile is considered rough, thin elements adjacent to the pile are used to include effects of localized shear. Unit weights of fluid concrete and accompanied changes in stress are considered as the effects of pile installation. Changes in effective stresses are the most prominent effect due to pile installation with a change in direction of the major principal stress from the vertical to the radial direction. Shear behaviour of the sand at the interface during the early shear stage is related to the contractive tendency of the sand at small strain levels. Changes in the stress field around the pile with little changes in volumetric strain take place during the early shear stage. Stress redistributions during the early shear stage depend on the direction of the major principal stress before shear. Results of the pile segment analyses for drilled CIP piles show good agreement with design methods. Parametric studies are used to characterize the effects of sand density and pile diameter on the skin friction behaviour of drilled CIP piles. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical analysis of soil plug behaviour inside open-ended piles during driving

The plugging mechanism of infinitely-long open-ended piles is examined using numerical simulation of the wave propagation inside the soil plug and pile. It is shown that the key parameters for the plugging mechanism are the pile radius, the shape of the impact load, the shear wave velocity of the soil inside the pile, and the friction at the pile–soil interface. Consequently, the tendency of the pile to plug during driving can be assessed prior to the driving process by consideration of these key parameters. Existing one-dimensional models for the shaft response of open-ended piles are discussed and an improved model is presented. The differences between using one-dimensional models and finite element models to simulate the plugging process are examined. The differences are found to vary with the key parameters. Pile-in-pile and lumped-mass one-dimensional models are found to give satisfactory performance for some parameter combinations, while for others an axisymmetric finite element model must be used. © 1998 John Wiley & Sons, Ltd.     

Nonlinear analysis of laterally loaded rigid piles in cohesive soil

This article presents a method for the nonlinear analysis of laterally loaded rigid piles in cohesive soil. The method considers the force and the moment equilibrium to derive the system equations for a rigid pile under a lateral eccentric load. The system equations are then solved using an iteration scheme to obtain the response of the pile. The method considers the nonlinear variation of the ultimate lateral soil resistance with depth and uses a new closed‐form expression proposed in this article to determine the lateral bearing factor. The method also considers the horizontal shear resistance at the pile base, and a bilinear relationship between the shear resistance and the displacement is used. For simplicity, the modulus of horizontal subgrade reaction is assumed to be constant with depth, which is applicable to piles in overconsolidated clay. The nonlinearity of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The validity of the developed method is demonstrated by comparing its results with those of 3D finite element analysis. The applications of the developed method to analyze five field test piles also show good agreement between the predictions and the experimental results. The developed method offers an alternative approach for simple and effective analysis of laterally loaded rigid piles in cohesive soil. Copyright © 2011 John Wiley & Sons, Ltd.