Probabilistic analysis of retaining walls

A methodology for the probabilistic analysis of reinforced concrete cantilever walls is developed and described in this paper. The wall’s external stability under static conditions is addressed and modeled as a series system with correlated failure modes. Computations of reliability are performed using Monte Carlo simulations for assumed probability distributions of the backfill and foundation material engineering properties. A case example is analyzed based on the described methodology. The results indicated that risk, measured by the system probability of failure, is not a linear function of safety ratios. All three safety ratios in question were positively correlated, with bearing capacity being subjected to higher degree of uncertainty. The degree of correlation was found to have an important effect on the system probability of failure. Considering the width of the base as varying design parameter, the study also showed that first-order reliability bounds, which are often applied in practice, may lead to a noteworthy over- or under-estimation of the design.     

Reliability Based Earthquake Resistant Design for Internal Stability of Reinforced Soil Structures

This paper presents a method to evaluate reliability for internal stability of reinforced soil structures using reliability based design optimization. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis is conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. Properties of backfill soil and strength of the geosynthetic reinforcement are considered as random variables. For the seismic conditions, reliability indices of all the geosynthetic layers in relation to tension and pullout failure modes are determined for different magnitudes of seismic accelerations both in the horizontal and vertical directions, surcharge load and design strength of the reinforcement. The efforts have been made to obtain the number of layers, pullout length and total length of the reinforcement at each level for the desired target reliability index values against tension and pullout modes of failure. The influence of horizontal and vertical earthquake acceleration, surcharge load, design strength of the reinforcement, coefficient of variation of soil friction angle and design strength of the reinforcement on number of layers, pullout length and total length of the reinforcement needed for the stability at each level is discussed.     

Stability analysis of an embankment resting upon a column‐reinforced soil

The design against failure of an embankment resting upon a soft soil improved by a group of columns is investigated with the help of the yield design homogenization approach. Assuming that both constituents of the reinforced ground are purely cohesive materials (‘lime column’ technique), an upper bound estimate for the macroscopic strength condition of the reinforced soil as a homogenized medium is first obtained, providing definite evidence of a shear strength anisotropy associated with the reinforcement preferential orientation. The kinematic method of yield design is then performed on the basis of such a criterion, making use of rotational failure mechanisms involving slip circles in the reinforced ground. Upper bound estimates are finally obtained for the embankment stability factor, as functions of the degree of reinforcement and relative thickness of the soil layer. These results are compared with those derived from a simplified analysis, where the reinforced soil is assumed to exhibit an averaged isotropic cohesion. This comparison clearly indicates that the latter simplified analysis may produce quite unsafe estimates for the embankment stability, which can be attributed to the fact that it fails to capture the inherent strength anisotropy of the reinforced soil. Copyright © 2010 John Wiley & Sons, Ltd.     

浅埋圆形隧道开挖面稳定的可靠度分析

开挖面支护压力是影响隧道开挖面稳定的重要施工因素,也是进行隧道开挖稳定性可靠度分析的关键。采用FLAC3D软件计算开挖面的最小极限支护压力,结合响应面法计算浅埋圆形隧道开挖面稳定的可靠度指标卢,将土体粘聚力和内摩擦角作为随机变量,考虑土体粘聚力和内摩擦角之间的相关性。分析结果表明,不考虑参数相关性计算得到的可靠性指标偏于保守。通过计算验算点处的极限支护压力与原支护压力比较,证明响应面法在结合FLAC3D计算开挖面稳定的可靠度方面是足够准确的。     

Seismic stability analysis of soil nail reinforced slope using kinematic approach of limit analysis

Prediction of the critical seismic yield acceleration coefficient and the seismic permanent displacement of soil nail reinforced slope under seismic loading has been playing an important role in helping design in the earthquake-prone areas. In this paper, the seismic stability of soil nail reinforced slope is analyzed using the kinematic theorem of limit analysis. The log-spiral failure mechanism is considered and the corresponding analytical expressions are derived to calculate the critical seismic yield acceleration coefficient and the permanent displacement of slope subjected to earthquake loading. A series of calculations are carried out to illustrate the influence of inertial force on the stability of a nail-reinforced slope. Parametric studies indicate that the strength and geometry of slope as well as characteristic parameters of soil nail have a significant effect on the critical seismic yield acceleration coefficient and the permanent displacement of soil nail reinforced slope.     

Finite element reliability analysis of reinforced retaining walls

This paper presents the reliability analysis of reinforced retaining wall using finite element method. Response surface approach is used to approximate the performance function and a first-order reliability method (FORM) is used to evaluate the reliability index. In the analysis, displacement response of the reinforced retaining wall is considered as performance function and the corresponding reliability index is evaluated with the aid of a spreadsheet. Uncertainties associated with the soil and reinforcement properties are explicitly taken into account in the analysis. A parametric sensitivity analysis has been performed to bring out the effect of important uncertain parameters by evaluating the sensitivity of the reliability index with respect to each of the uncertain parameters. Results of the response surface method coupled with finite element analysis show the ease and successful implementation of the reliability analysis procedure for the reinforced retaining walls.     

浅论深基坑粉喷桩—土层锚杆联合支护技术

粉喷桩与土层锚杆联合支护方式可同时解决支护与止水双重问题,在基坑开挖深度不大,基坑周边环境条件严重受限的情况下,可充分显示出其技术经济方面的优越性,值得应用推广。文中探讨了该联合支护方式的设计方法,建议按喷锚支护模型计算边坡整体稳定性,计算中将粉喷桩等效为一层加固土。通过工程实例,验证了建议的计算模型。并且还对施工中应注意的一些问题进行了阐述。     

A reliability based approach for evaluating the slope stability of embankment dams

Embankment dams are important and costly civil engineering structures that provide an essential infrastructure for the management of water. One of the critical aspects of dam design is the analysis of stability and safety of the earth structure under various operating and environmental conditions. Traditionally, a deterministic approach is used for such analysis. However, the determination of variables such as soil strength parameters, pore pressure and other pertinent properties involves uncertainties, which cannot be handled in the traditional deterministic methods. It is, therefore, highly desirable to develop a reliability based analytical/numerical methodology for stability analysis of dams taking into account these uncertainties. Reliability and probability theories are developed in this paper for assessing the reliability index and the corresponding probability of failure of multi-layered embankment dams and slopes. Two definitions were used to calculate the reliability index (i.e. the normal distribution and the log–normal distribution). The computer program was developed and validated by the Congress Street open cut failure case. The developed approach was used to study the stability of the King Talal embankment dam. The results are discussed and conclusions drawn.     

Bearing capacity of square footings on reinforced layered soil

In the present study, an approximate method has been suggested to calculate the ultimate bearing capacity of a square footing resting on reinforced layered soil. The soil is reinforced with horizontal layers of reinforcement in the top layer of soil only. The pre requisite to the method is the ultimate bearing capacity of unreinforced layered soil, which can be determined from the methods already available in literature. The results have been validated with the model tests conducted on two layered soil compacted at different densities and the top layer reinforced with horizontal layers of geogrid reinforcement.     

刚性桩加固软土路基失稳破坏数值模拟

为控制路堤的整体稳定性,刚性桩现已常用于软土路基的加固。本文引入了桩体的断开机制,采用有限元软件ABAQUS对刚性桩加固软土路基的失稳破坏模式进行分析,相较于传统的数值模拟方法,体现了路堤荷载作用下,刚性桩的渐次失稳破坏过程。在此基础上,考虑桩体可能优先发生的弯曲破坏,提出将临界比例n作为判断桩体优先发生剪切破坏或弯曲破坏的临界值,并将其作为本文桩体断开机制的终止判别条件,合理地规避了数值模拟软件定量计算存在的较大误差。最后,将本文数值模拟与传统的数值模拟、等效砂桩法的数值模拟进行对比,结果反应出本文数值模拟方法的合理性与可靠性,工程上可通过增大前排桩的抗弯强度或限制桩体的水平位移,提高路堤的整体稳定性。     

System reliability-based analysis of cantilever retaining walls embedded in granular soils

Reliability-based analysis of cantilever retaining walls requires consideration of different failure mechanisms. In this paper, the reliability of soil-wall system is assessed considering two failure modes: rotational and structural stability, and the system reliability is assumed as a series system. The methodology is based on Monte Carlo Simulation (MCS), and it deals with the variability of the design parameters in the limit equilibrium analysis of a wall embedded in granular soil. Results of the MCS indicate that the reliability of the failure components increases exponentially by increasing the variability of design parameters. The results of the system reliability indicate how the system reliability is different from the component reliabilities. The strength of the weakest component influences the reliability of the system. The system reliability index increases with the wall section gradually. However it remains constant for the rotational failure mode.     

Analytic hierarchy process for assessing factors influencing the stability of soil slopes reinforced with piles

Changes in the stability of slopes reinforced with piles involve a complex interaction process between piles, soil, hydrogeological conditions and the engineering geological environment. Correlation analysis between each influencing factor will contribute to a better overall understanding of the main influencing factors. This is of great significance for disaster prevention and the optimization of soil slopes reinforced with piles. The 17 factors influencing the stability of soil slopes reinforced with piles were analyzed in this study, and the weighting of each influencing factor was determined using the analytic hierarchy process along with the experiences of various experts and the author’s experience. The results showed that: (1) soil rheological characteristics and physical and mechanical soil properties have the maximum weighting on the stability of soil slopes reinforced with piles; that is, they are the most important factors influencing the stability of soil slopes reinforced with piles; (2) embedded pile depth or pile anchoring depth and the pile position have the second greatest weighting; (3) rainfall, pile sectional dimensions and pile spacing, are also important factors. Each of these factors was not weighted less than 0.059.     

某机场飞行区土工格栅加筋高边坡优化设计

土工格栅加筋土边坡是一种新型的边坡支护结构,对于提高边坡稳定性、节约工程用地、保护生态环境意义重大。为了对机场加筋高填方边坡加固方案进行优化设计,本文以某机场跑道西北角的6#高填方边坡为例,首先基于边坡的地质条件和高填方边坡的实际情况,提出3种不同边坡坡率的加筋土边坡设计方案;其次采用简化Bishop法、Spencer楔形体法以及Morgenstern-Price法分别计算在天然、暴雨以及地震工况下的边坡稳定系数;最后利用有限元法分析3种加固方案下的加筋土边坡在天然工况下的变形特征以及筋材轴力分布规律。结果表明:3种设计方案在天然、暴雨以及地震工况下均能满足边坡稳定性要求,贴坡填筑的多级加筋土边坡的筋材轴力分布规律沿着竖向呈现锯齿状分布,最大筋材轴力在每级边坡的坡脚处突变增大。与加筋土缓坡（坡率1∶1.5）设计方案相比,加筋土挡墙（坡率1∶0.25）在坡高、筋材使用量、护坡面积以及挖填方量等方面均有明显减小。综合考虑稳定性、工程造价以及施工周期,采用加筋土挡墙的设计方案更合理。     

A multiphase approach to the stability analysis of reinforced earth structures accounting for a soil–strip failure condition

A multiphase model, developed in the context of elastoplasticity, is applied to the simulation and design of reinforced earth retaining structures. The main feature of this model is to combine the advantage of a homogenization approach, as regards its computational efficiency, with the ability to account for a specific failure condition at the interface between the soil and the reinforcing strips, which may have a decisive influence on the behavior of the structure. A particular emphasis is put on the stability analysis of this kind of reinforced soil structures, formulated within the framework of the yield design theory. Making use of a generalized rigid block failure mechanism, the stability of a reinforced earth retaining wall is investigated by means of the kinematic approach, leading to upper bound estimates for the stability factor of the structure, which are then favorably compared with the results of an elastoplastic analysis. Special attention is paid to assessing in a quantitative way how a specific soil–strip failure condition affects the stability of the reinforced earth structure as a whole.     

加筋土边坡地震稳定性动点安全系数分析方法

对于地震作用下的土工合成材料加筋土边坡,边坡内部结构的动力响应十分复杂,按照已有的安全系数的方法评价比较困难。结合安全储备系数的原理,并考虑到水平方向和竖直方向地震荷载的共同作用,提出求解加筋土边坡地震稳定性的动点安全系数时程分析方法。在理论分析的基础上,分别定义加筋土边坡土体、土工合成材料和筋-土界面的动点安全系数,并建立数值模型。根据所定义的动点安全系数,在计算过程中使用开发的计算工具对动力响应过程中的动力特性数据进行记录、计算和存储,得到加筋土边坡数值模型在地震荷载作用下的动点安全系数。分析结果表明：动点安全系数时程分析方法具有良好的工程适用性;动点安全系数时程分析方法对复杂的加筋土边坡工程进行的地震稳定性分析考虑了加筋土边坡不同结构的综合稳定性,比现有的分析方法更明确地反应出加筋土边坡工程中相对薄弱的结构,对加筋土边坡工程的抗震设计提供一定参考价值;相比水平方向的地震,竖直方向的地震作用对加筋土边坡中筋材和筋-土界面的稳定性影响较大,但对加筋土边坡土体稳定性影响较小。     

A homogenization approach for evaluating the longitudinal shear stiffness of reinforced soils: column versus cross trench configuration

The macroscopic linear elastic behaviour of inclusion‐reinforced soils, regarded as periodic composite media, is investigated by means of the homogenization theory. Special attention is given here to the determination of their longitudinal shear stiffness properties, which strongly govern the reinforced ground response under lateral loading. Combining the use of analytical, variational and numerical methods, we thoroughly examined three particular engineering‐relevant configurations: single trench, column and cross trench reinforcements. Fairly accurate closed‐form expressions are thus obtained, giving the value of the reinforced soil longitudinal shear stiffness as a function of the individual components shear moduli and reinforcement volume fraction. It is shown in particular that adopting a cross trench reinforcement layout instead of the classical column configuration results in a much higher improvement of the longitudinal shear stiffness. The results are then applied to assessing the reduction of soil liquefaction risk, which can be attributed to the presence of the reinforcing inclusions. Again, they clearly demonstrate the excellent performance of the cross trench configuration as compared with the complete inefficiency of the column reinforcement technique. Copyright © 2013 John Wiley & Sons, Ltd.     

Pseudostatic Seismic Response Analysis of a Pile Group in a Soil Slope

This paper presents a simple approximate pseudostatic method for estimating the maximum internal forces and horizontal displacements of a pile group located in a soil slope. The method is extension of an existing similar method developed by the authors for the case of a horizontal ground surface. The method employed for horizontal ground case involves two main steps: first, the free-field soil movements caused by the earthquake are computed; Then, the response of the pile group is analyzed based on the maximum free-field soil movements as static movements, as well as a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. This newly developed methodology takes into account the effects of group interaction and soil yielding. Simple modifications are applied to take into account the effect of slope on seismic deformations of the pile group, making use of the Newmark sliding block method. The applicability of the approach and the developed program is verified by comparisons made with both experimental shaking table tests and the results of a more refined analysis of a pile-supported wharf. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and horizontal displacement for many practical cases, despite its relative simplicity. The simplifying assumptions and the limitations as well as reliability of the methodology are discussed, and some practical conclusions on the performance of the proposed approach are suggested.     

A FORM-based approach for probabilistic analysis in geotechnics: Application to a reinforced concrete drainage culvert

As numerical models are increasingly used as a design tool in geotechnical engineering, it is highly desirable if geotechnical reliability analysis can be conducted based on numeral models. Currently, the practical use of geotechnical reliability analysis-based numerical models is still quite limited. In this study, an easy to access method is derived to conduct geotechnical reliability analysis based on numerical models. To facilitate its application, a procedure is outlined to implement the suggested method such that geotechnical reliability analysis can be automated using existing geotechnical numerical packages. The procedure is illustrated in detail with an example, and the source codes provided can be easily adapted to analyze other similar problems. The method described in this paper is used to study the reliability of a deteriorating reinforced concrete drainage culvert in Shanghai, China. The suggested method provides a convenient means for reliability analysis of complex geotechnical problems.     

Probabilistic slope stability analysis by a copula-based sampling method

In probabilistic slope stability analysis, the influence of cross correlation of the soil strength parameters, cohesion and internal friction angle, on the reliability index has not been investigated fully. In this paper, an expedient technique is presented for probabilistic slope stability analysis that involves sampling a series of combinations of soil strength parameters through a copula as input to an existing conventional deterministic slope stability program. The approach organises the individual marginal probability density distributions of componential shear strength as a bivariate joint distribution by the copula function to characterise the dependence between shear strengths. The technique can be used to generate an arbitrarily large sample of soil strength parameters. Examples are provided to illustrate the use of the copula-based sampling method to estimate the reliability index of given slopes, and the computed results are compared with the first-order reliability method, considering the correlated random variables. A sensitivity study was conducted to assess the influence of correlational measurements on the reliability index. The approach is simple and can be applied in practice with little effort beyond what is necessary in a conventional analysis.     

基于原位剪切试验的膨胀土边坡稳定性研究

膨胀土边坡稳定性一直是膨胀土研究领域的重要课题,以南阳地区膨胀土为试验对象,根据原位剪切试验给出膨胀土抗剪强度取值方法,在试验的基础上提出了膨胀土抗剪强度的修正计算公式,然后应用到该地区的膨胀土边坡稳定性计算,通过对典型边坡的分析表明,其方法对膨胀土边坡稳定性评价具有重要参考意义。