Static and seismic limit equilibrium analysis of sliding retaining walls under different surcharge conditions

The static and seismic sliding limit equilibrium condition of retaining walls is investigated, and analytical solutions for the angle of the active slip surface, the critical acceleration coefficient and the coefficient of active earth pressure are provided for different surcharge conditions. In particular, walls retaining a horizontal backfill without surcharge, walls supporting an extended uniform surcharge applied at different distances from the wall and walls supporting a limited uniform surcharge or linear uniform surcharge parallel to the wall are considered in the analysis.The solutions have been derived in the framework of the limit equilibrium approach, considering the effect of the wall through its weight, and accounting for the shear resistance at the base of the wall and the inertia force arising in the wall under seismic conditions.For the wall without surcharge the effect of the vertical component of the seismic acceleration as well as the effects of the inclination of the wall internal face and of the soil–wall friction were also investigated.The angle of the slip plane, the critical seismic acceleration coefficient and the coefficient of active earth pressure are given as functions of dimensionless parameters and the boundary conditions for the applicability of each solution are specified. The influence of soil weight, surcharge conditions and inertia forces on the active earth pressure coefficient is analysed.     

Reliability assessment of internal stability of reinforced soil structures: A pseudo-dynamic approach

A methodology for reliability based optimum design of reinforced soil structures subjected to horizontal and vertical sinusoidal excitation based on pseudo-dynamic approach is presented. The tensile strength of reinforcement required to maintain the stability is computed using logarithmic spiral failure mechanism. The backfill soil properties, geometric and strength properties of reinforcement are treated as random variables. Effects of parameters like soil friction angle, horizontal and vertical seismic accelerations, shear and primary wave velocities, amplification factors for seismic acceleration on the component and system probability of failures in relation to tension and pullout capacities of reinforcement have been discussed. In order to evaluate the validity of the present formulation, static and seismic reinforcement force coefficients computed by the present method are compared with those given by other authors. The importance of the shear wave velocity in the estimation of the reliability of the structure is highlighted. The Ditlevsen's bounds of system probability of failure are also computed by taking into account the correlations between three failure modes, which is evaluated using the direction cosines of the tangent planes at the most probable points of failure.     

Seismic passive earth resistance using modified pseudo-dynamic method

In earthquake prone areas, understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures. In this study, the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill. A composite failure surface is considered in the present analysis. Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking. The present method satisfies the boundary conditions. The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion. The acceleration distribution along the depth of the backfill is found to be nonlinear in nature. The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient. The effect of different parameters on the seismic passive earth pressure is studied in detail. A comparison of the present method with other theories is also presented, which shows the merits of the present study.     

Predicting seismic permanent displacement of soil walls under surcharge based on limit analysis approach

Seismic permanent displacement of the soil walls plays an important role in design of these structures. Due to the increase in growth of urban areas and the limitations in use of flat grounds, many structures are built near slopes and retaining walls. During earthquakes, these structures can apply an additional surcharge on the wall. The intensity and location of the surcharge is of considerable importance on the seismic displacements of the soil wall. In this study, by using the limit analysis and upper bound theorem, seismic permanent displacement of the soil wall under surcharge has been analyzed. Thus, a formulation is presented for calculating the yield acceleration and seismic displacement for different surcharge conditions. The effect of seismic acceleration, surcharge intensity, its location and soil properties is investigated. A parameter called the “displacement coefficient” is proposed, and is a potential modification for Newmark’s sliding-block method.     

Numerical analysis of reinforced soil walls with granular and cohesive backfills under cyclic loads

Novel approaches to the dynamic analysis of the reinforced soil walls have been reported in the literature. Use of marginal soils reduces the cost of geosynthetic reinforced soil walls if proper drainage measures are taken. Therefore the affect of using cohesive marginal soils as backfill in geosynthetic reinforced retaining structures were investigated in this research. The dynamic response of reinforced soil walls was investigated in a similar focus, using finite element analysis. The results obtained from walls with cohesive backfill were compared to the results obtained from walls with granular backfill. The height of the wall was chosen as 6 m in the two-dimensional plane strain finite element model and the base acceleration was chosen to be a harmonic motion. The effects of various parameters like the backfill type, facing type, reinforcement stiffness, and peak ground acceleration on the cyclic response of reinforced soil retaining walls were investigated. After analyzing the wall response for end of construction and dynamic excitation phases, it was determined that the deformations and reinforcement tensile loads increased during the cyclic load application and that the amount of additional deformation that occurred during cyclic load application was strongly related to backfill soil type, facing type, reinforcement type and peak ground acceleration. It was determined that a cohesive backfill and geotextile reinforcement was a good combination to reduce the deformations of geosynthetic reinforced walls during cyclic loading for medium height walls.     

地震荷载作用下加筋土挡墙动力特性分析

利用有限元软件对加筋土挡墙在地震荷载作用下的动力特性进行模拟分析,重点分析其在不同加筋长度、加筋间距以及峰值加速度条件下的动力响应特性。通过有限元分析一个高6m、底部为基础土的加筋土挡墙在地震荷载作用下的行为,针对理想化墙体研究加筋土挡墙的某些动力特性。模拟计算结果表明加筋土挡墙的加筋长度、加筋间距以及峰值加速度的变化对其水平位移、沉降及受力有较大影响。采用长度大的加筋材料可以有效减小加筋土挡墙的水平位移,但这样将导致加筋拉伸荷载的增大,同时也将导致加筋土挡墙的隆起增大。峰值加速度的大小对加筋土挡墙的水平位移有很大影响,当峰值加速度增大时水平位移也随之增大,但并不呈线性增长关系。减小加筋间距会有效地限制加筋土挡墙面板整体的水平位移,但在一定范围内减小加筋间距也会使加筋区域内土体底部挡墙的水平位移出现相对增大的现象,因此通过减小加筋间距来限制加筋土挡墙的位移在一定程度上具有局限性。     

Seismic active earth pressure of cohesive-frictional soil on retaining wall based on a slice analysis method

The M–O (Mononobe–Okabe) theory is used as a standard method to determine the seismic earth pressure. However, the M–O theory does not consider the influence of soil cohesion, and it cannot determine the nonlinear distribution of the seismic earth pressure. This paper presents a general solution for the nonlinear distribution of the seismic active earth pressure of cohesive-frictional soil using the slice analysis method. A new method is proposed to determine the critical failure angle of the backfill wedge under complex conditions, and an iterative calculation method is presented to determine the tension crack depth of the seismic active earth pressure. The considered parameters in the proposed method include the horizontal and vertical seismic coefficients, wall inclination angle, backfill inclination angle, soil friction angle, wall friction angle, soil cohesion, wall adhesion and uniform surcharge. The classical methods of the M–O and Rankine theories can be regarded as special cases of the proposed method. Furthermore, the proposed method is compared with the test results and previously existing solutions to validate the correctness of the results. Additionally, the parameters׳ effect on the critical failure angle, the resultant force, the application-point position, the tension crack depth and the nonlinear distribution of seismic active earth pressure are studied in graphical form.     

地震中整体面板式土工格栅加筋土挡墙动土压力研究

土工格栅加筋挡土墙是一种柔性挡土结构,目前尚未建立较严密的设计方法,作用在土工格栅加筋墙壁上的地震动土压力研究是抗震设计的重要内容之一。应用基于拉格朗日法的完全非线性动有限差分法研究整体面板式土工格栅加筋土挡壁在地震作用下各设计参数对挡壁动土压力的影响。采用弹塑性模型模拟填土,采用耦合弹性参数描述格栅与土接触界面特性,参数包括加筋间距、长度、刚度、地震强度和填土性质等,分析墙壁的动土压力沿墙身的分布特征,得出了影响地震动土压力的显著参数,证明了土工格栅加筋墙体的优异吸震能力,研究结果为整体面板式土工格栅加筋土挡墙抗震设计中的动土压力研究提供参考。     

Uniform reliability safety format for seismic design of reinforced concrete structures

A safety format is proposed for the flexural design of reinforced concrete members for the combination of seismic and gravity loads, with load and resistance factors which depend on member type, on the value of the target theoretical probability of failure and on the ratio of the load effect due to gravity loads to that due to the nominal value of the seismic action, both obtained by elastic analysis. Safety factors are computed through an advanced Level II reliability procedure, using a limit state inequality between the member rotation ductility supply under monotonic loading and the peak rotation ductility and cyclic energy dissipation demands. Uncertainties considered are: for resistance, the uncertainty of failure under imposed cyclic deformations, and for action, the maximum peak ductility and energy dissipation demands in the structure's lifetime, as obtained through a series of non-linear dynamic analyses of multistorey buildings in 3D. using as input ensembles of bidirectional acceleration time-histories which describe probabilistically the extreme bidirectional seismic action in the structure's lifetime. Computed load and resistance factors are practically independent of the load-effects ratio. The load factor on the seismic action is found to be independent of member type and to increase with the theoretical probability of failure much faster than the elastic spectral value at the structure's fundamental period with probability of exceedance in the structure's lifetime. Simple rules for the dependence of the resistance modification factors on the theoretical failure probability are also derived. As for the computed values of the load factors the moment due to gravity loads is negligible in comparison to the factored seismic moment, a simplified safety checking inequality between the design flexural capacity and a reduced seismic moment is proposed, in which the ratio of the resistance to the load factor plays the role of a force reduction or effective behaviour factor for the member.     

Seismic passive resistance with vertical seepage and surcharge

Present paper focuses on the computation of the seismic passive earth pressure acting on a vertical rigid retaining wall by a soil mass subjected to vertical steady-state seepage and a uniform surcharge load. Based on the basic assumptions of Coulomb's theory and a pseudo-static method of analysis, a general solution for the passive earth pressure containing two coefficients is presented. In the solution, many parameters, such as unit weight of saturated soil, soil effective internal friction angle, soil/wall friction angle, water/soil unit weight ratio, surcharge intensity coefficient, horizontal and vertical seismic acceleration coefficients, Poisson's ratio of soil mass, hydraulic gradient, and coefficients of pore water pressure, are considered. The effects of hydraulic gradient and seismic forces on passive earth pressure coefficient and passive earth pressure distribution are investigated. The results indicate that passive earth pressure increases with increasing hydraulic gradient for downward water flow case, but decreases for upward water flow case, and that the presence of seismic forces induces a reduction in passive earth pressure.     

Earthquake-induced displacements of gravity retaining walls and anchor-reinforced slopes

This paper examines in terms of seismic performance, the effectiveness of anchor reinforcement against gravity retaining walls used to stabilize a dry homogenous fill slope in earthquake-prone environment. Both analyzed stabilizing measures have the same design yield acceleration estimated from a limit equilibrium approach. The earthquake-induced displacements are calculated using a sliding block formulation of the equation of motion. Sliding failure along the base of the gravity retaining wall and rotational failure of the soil active wedge behind the wall, as well as rotational failure of the slide mass of the anchor-reinforced slope were considered in the present formulation. For the specific characteristics of the analyzed fill slope and input horizontal ground motion, the slope reinforced with anchors appears to experience vertical and horizontal seismic displacements at slope crest smaller by 12% and respectively, 32% than the vertical and horizontal earthquake-induced deformations estimated at the top of the active wedge behind the gravity retaining wall.     

An alternative to the Mononobe–Okabe equations for seismic earth pressures

A closed-form stress plasticity solution is presented for gravitational and earthquake-induced earth pressures on retaining walls. The proposed solution is essentially an approximate yield-line approach, based on the theory of discontinuous stress fields, and takes into account the following parameters: (1) weight and friction angle of the soil material, (2) wall inclination, (3) backfill inclination, (4) wall roughness, (5) surcharge at soil surface, and (6) horizontal and vertical seismic acceleration. Both active and passive conditions are considered by means of different inclinations of the stress characteristics in the backfill. Results are presented in the form of dimensionless graphs and charts that elucidate the salient features of the problem. Comparisons with established numerical solutions, such as those of Chen and Sokolovskii, show satisfactory agreement (maximum error for active pressures about 10%). It is shown that the solution does not perfectly satisfy equilibrium at certain points in the medium, and hence cannot be classified in the context of limit analysis theorems. Nevertheless, extensive comparisons with rigorous numerical results indicate that the solution consistently overestimates active pressures and under-predicts the passive. Accordingly, it can be viewed as an approximate lower-bound solution, than a mere predictor of soil thrust. Compared to the Coulomb and Mononobe–Okabe equations, the proposed solution is simpler, more accurate (especially for passive pressures) and safe, as it overestimates active pressures and underestimates the passive. Contrary to the aforementioned solutions, the proposed solution is symmetric, as it can be expressed by a single equation—describing both active and passive pressures—using appropriate signs for friction angle and wall roughness.     

水泥砂浆面层加固砌体墙抗震可靠指标研究

采用水泥砂浆面层加固方法加固砌体房屋是一种简单有效的方法。对比分析了《砌体结构加固设计规范》(GB 50702-2011)^[3]和《建筑抗震加固技术规程》(JGJ 116-2009)^[4]中钢筋网水泥砂浆面层加固砌体墙的可靠性;对10片未加固低强度砖墙和20片单面钢筋网水泥砂浆面层加固低强度砖墙进行拟静力试验,分析了未加固和加固墙体的破坏模式和机理,并提出了适用于钢筋网水泥砂浆面层加固砌体墙的抗震验算公式。研究表明：两标准的可靠水平差别较大,实际应用时,易产生矛盾;未加固墙主要发生沿阶梯形斜裂缝受剪破坏,加固墙主要发生沿通缝受剪破坏和沿阶梯形斜裂缝受剪破坏;建议公式的计算值与试验值吻合良好,未加固墙抗震可靠指标为2.2,加固墙抗震可靠指标为2.5～3.1;砂浆面层加固砌体结构可以显著提高结构的抗震性能。     

Towards multiple hazard resilient bridges: a methodology for modeling frequent and infrequent time-varying loads Part I, Comprehensive reliability and partial failure probabilities

The current AASHTO load and resistance factor design (LRFD) guidelines are formulated based on bridge reliability,which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability.This is a major advancement in bridge design specifications.However,LRFD is only calibrated for dead and live loads.In cases when extreme loads are significant,they need to be individually assessed.Combining regular loads with extreme loads has been a major challenge,mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure.To overcome these difficulties,this paper suggests a methodology of comprehensive reliability,by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant.Based on these conditions,the extreme loads (also referred to as multiple hazard or MH loads) can be broken down into single effects.In Part Ⅱ of this paper,a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example.There are three major steps in establishing load factors from MH load distributions:(1) formulate the failure probabilities;(2) normalize various load distributions;and (3) establish design limit state equations.This paper describes the formulation of the failure probabilities of single and combined loads.     

甘肃典型夯土民房承重墙体加固试验研究

武都是甘肃省典型夯土民房使用地区,研究其夯土民房的抗震性能对于防灾减灾具有重要意义。在试验中,使用武都当地常用土料,完全按照其施工工艺夯筑4片夯土墙体试件,利用伪静力方法研究了素土墙体与使用铁丝网加固墙体的抗剪强度。结果显示：①在竖向荷载10 kN条件下,加固墙体试件较素土墙体试件的水平开裂荷载和极限荷载分别增长了73%和38%,在竖向荷载18 kN条件下,加固墙体试件素土墙体试件的水平开裂荷载和极限荷载分别增长了76%和5%;②随着竖向荷载从10 kN增加到18 kN,素土墙体试件的水平开裂荷载与极限荷载分别增长了217%和359%,加固墙体试件的水平开裂荷载与极限荷载则增长了223%和249%;③在水平往复荷载的作用下,夯土墙体始终沿着夯土层间的水平和垂直接触裂缝产生破坏,最终碎裂成块体。     

Seismic stability analysis of gravity retaining walls

A new approach based on the category of upper bound theorem of limit analysis is presented in this study to consider the seismic stability of gravity retaining walls. The retaining wall and the backfill soil were taken as a whole system. For a translational failure mechanism assumed, formulas are provided to calculate directly the yield acceleration and the inclination of the failure surface. An example is shown to illustrate the method. Comparisons are made with limit equilibrium method, and the results are found consistent. Based on a limited parametric study, it is shown that the wall roughness has remarkable influence on the yield acceleration.     

Dynamic active thrust from c–ϕ soil backfills

This technical note presents an analytical derivation of the expression for the total dynamic active thrust on a retaining wall from the c–? soil backfill considering both horizontal and vertical seismic coefficients. The derivation is based on the Coulomb sliding wedge concept, and it considers tension cracks, wall adhesion, and surcharge in order to make the expression useful for practical applications. It is found that the special cases of the general expression result in the expressions for total static and dynamic active thrusts presented by earlier researchers for different field conditions of soil backfills with and without seismic loadings.     

Towards multiple hazard resilient bridges: a methodology for modeling frequent and infrequent time-varying loads Part II, Examples for live and earthquake load effects

The current AASHTO load and resistance factor design (LRFD) guidelines are formulated based on bridge reliability,which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability.This is a major advancement in bridge design specifications.However,LRFD is only calibrated for dead and live loads.In cases when extreme loads are significant,they need to be individually assessed.Combining regular loads with extreme loads has been a major challenge,mainly because the extreme loads are time variable and cannot be directly combined with time invariant loads to formulate the probability of structural failure.To overcome these difficulties,this paper suggests a methodology of comprehensive reliability,by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant.Based on these conditions,the extreme loads (also referred to as multiple hazard or MH loads) can be broken down into single effects.In this paper,a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example.     

Seismic stability of retaining walls with surcharge

The use of pseudo-static methods for the computation of soil thrust acting on retaining walls under seismic condition is well established in the design of such structures. Although different methods, based on the limited displacement concept, have been developed in the last 20 years, the most common design method is still the method derived from the theory developed by Mononobe and Okabe. However, the Mononobe–Okabe method presents a basic shortcoming: the solution is based on the limit equilibrium of the soil wedge without taking into account the presence of the wall. In the paper a new solution based on the pseudo-static equilibrium of the soil–wall system is presented. The developed solution takes into account the effect of the presence of the wall and it is applied to soil–wall systems with surcharged backfills. Formulas are provided to calculate directly the yield acceleration and the inclination of the failure surface. The effect of the intensity of the surcharge and of its distance from the wall is investigated and the results are compared to those obtained in the case of soil–wall systems without surcharge.     

Mechanics and performance of a tied-back wall under seismic loads

In this paper the stability of a tied-back wall subjected to seismic loads is analysed for a predetermined mode of failure (rotation about the top of the wall) and the analysis is compared with data from tests on this type of wall using the seismic simulator at the State University of New York at Buffalo. We carried out a pseudo-static analysis of the problem using the Mononobe-Okabe earth pressure coefficients, wherein the dynamic effects due to the seismic loading are converted into equivalent static loads. The acceleration ratio at which the wall fails by rotation about the top was obtained by considering the moments due to the various lateral earth pressure resultants and the inertial forces induced in the soil due to the seismic loading. We found that the presence of wall friction on the passive side significantly enhances the stability of the flexible retaining wall under seismic loads. Thus, flexible retaining walls supporting dry cohesionless soil can be very efficient during earthquakes. Under moderate earthquakes, an increase in the depth of embedment increases the dynamic factor of safety significantly. However, beyond a certain acceleration ratio for a soil with a particular value of ø, any increase in the depth of emdedment has no effect in impeding failure, irrespective of any change in the geometry of the system. Seismic design charts are presented to evaluate the stability of, and to design, flexible retaining walls embedded in dry cohesionless soils under seismic loading.