Evaluation of pseudostatic active earth pressure coefficient of cantilever retaining walls

A stress plasticity solution is proposed for evaluating the gravitational and dynamic active earth pressures on cantilever retaining walls with long heel. The solution takes into account the friction angle of the soil, wall roughness, backfill inclination and horizontal and vertical seismic accelerations. It is validated by means of the comparison with both traditional limit equilibrium methods (e.g. Mononobe–Okabe equations) and static and pseudostatic numerical FLAC analyses. For numerical analyses the soil is modelled as an elasto-plastic non-dilatant medium obeying the Mohr–Coulomb yield criterion, while the wall is elastic. The solutions for the horizontal and vertical seismic coefficients are proposed, which allow one to determine the intensity of the active thrust and its inclination δ with respect to the horizontal. It is demonstrated that the latter also depends on the soil friction angle φ. The inclination in seismic conditions δ_E is greater than the one in static conditions, δ_S, usually adopted in both cases. As a matter of fact, since wall stability conditions improve with the increase of inclination δ, the present method gives solutions that are less onerous than traditional ones, producing less conservative wall designs. Finally pseudostatic results are compared with proper dynamic analyses (by FLAC code) performed utilising four Italian accelerometric time-histories as input ground motion.     

挡土墙地震被动土压力的拟动力分析

对地震土压力的研究是地震区挡土墙安全设计的一项重要课题。地震条件下,目前的研究主要是给出了土压力的近似拟静力解析解。本文采用可考虑动力荷载下的周期和纵波及横波效应的拟动力方法,对挡土墙后的地震被动土压力进行分析。在挡土墙后平面滑裂面假设的基础上,考虑了水平和垂直向地震加速度、纵波速度、横波速度、挡土墙摩擦角、填土内摩擦角、填土坡角对地震被动土压力的影响。与Mononobe-Okabe理论的拟静力法不同的是,用本方法得出了沿墙身地震被动土压力是非线性变化的结果,这更符合地震条件下土压力的变化规律。     

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.     

Pseudo-dynamic active force and pressure behind battered retaining wall supporting inclined backfill

Knowledge of seismic active earth pressure behind rigid retaining wall is very important. Commonly used Mononobe–Okabe method considers pseudo-static approach, which gives the linear distribution of seismic earth force. In this paper, the pseudo-dynamic approach, which considers the effect of primary and shear wave propagations, is adopted to calculate the seismic active force. Considering the planar rupture surface, the effect of wide range of parameters like inclination of retaining wall, inclination of backfill surface, wall friction and soil friction angle, shear wave and primary wave velocity, horizontal and vertical seismic coefficients are taken into account to evaluate the seismic active force. Results are presented in terms of seismic coefficients in tabular form and variation of pressure along the depth.     

Seismic rotational displacement of gravity walls by pseudo-dynamic method: Passive case

Prediction of the seismic rotational displacements of retaining wall under passive condition is an important aspect of design in earthquake prone region. In this paper, the pseudo-dynamic method is used to compute the rotational displacements of rigid retaining wall supporting cohesionless backfill under seismic loading for the passive earth pressure condition. The proposed method considers time, phase difference and effect of amplification in shear and primary waves propagating through both the backfill and the retaining wall. The influence of ground motion characteristics on rotational displacement of the wall is evaluated. Also the effects of variation of parameters like wall friction angle, soil friction angle, amplification factor, shear wave velocity, primary wave velocity, period of lateral shaking, horizontal and vertical seismic accelerations on the rotational displacements are studied. The rotational displacement of the wall increases substantially with increase in amplification of both shear and primary waves, time of input motion, period of lateral shaking and decreases with increase in soil friction angle, wall friction angle. The rotational displacements of the wall also increase when the effect of wall inertia is taken into account. Results are provided in graphical form.     

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.     

Evaluation of active and passive seismic earth pressures considering internal friction and cohesion

The Log-Spiral-Rankine (LSR) model, which is a generalized formulation for assessing the active and passive seismic earth pressures considering the internal friction and cohesion of backfill soil, is reviewed and improved in this study. System inconsistencies in the LSR model are identified, which result from an inaccurate assumption on the vertical normal stress field (σ_z=γz) in a general c–ϕ soil medium, and from omitting the effect of soil cohesion when solving for the stress states along the failure surface. The remedies to the said inconsistencies are presented, and local and global iteration schemes are introduced to solve the resulting highly coupled multivariate nonlinear system of equations. The modified LSR model provides a more complete and accurate solution for earth retaining systems, including the geometry of the mobilized soil body, the stress state along the failure surface, as well as the magnitude and the point of application of the resultant earth thrust.     

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example.     

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.     

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.     

地震作用下非饱和土主动土压力极限分析半解析法

地震是诱发边坡失稳的主要因素之一,重力式挡土墙作为一种广泛采用的岩土支挡结构,有必要对其地震稳定性问题进行深入的研究.为有效评估地震作用下非饱和填土的主动土压力,基于极限分析上限原理和拟动力法,提出一种半解析水平片分法,计算具有非线性分布特征的非饱和土重力和地震惯性力所做外功率,并构建功能平衡方程,得到非饱和填土主动土压力显示半解析解.通过与解析解对比,验证该方法的合理性,并通过算例分析,揭示吸力效应的强化机制和非饱和填土主动土压力的地震响应规律.结果表明:忽略吸力效应会高估填土的主动土压力,吸力的强化作用不仅取决于填土类型,还与地震动特性密切相关;水平和竖向地震动对土压力有较大影响, 土压力系数峰值随土剪切模量的增加略有增加并向负方向移动,随地震周期的增加略有增加并向正方向移动;填土倾角较大时,坡顶附加荷载的影响更加显著;对于倾角大于100°的填土,墙G土界面摩擦角较大时,土压力相对较高.     

Displacement reducer fuses for improving seismic performance of caisson quay walls

This research is to study the efficiency of displacement reducer fuses, installed behind the caisson quay walls for controlling the dynamic backfill thrust and minimizing the displacement, settlement and tilting of the walls. For this purpose, two types of fuses, Displacement Reducer Panels (DRP) and Displacement Reducer Elements (DRE), were constructed and installed behind the wall. The DRPs were constructed by hollow Polypropylene sheets to reproduce elastoplastic and plastic mechanical behaviors. The DREs were cylindrical stainless-steel dampers, working upon friction mechanism that can reproduce perfect plastic behavior. Here, two series of shaking table 1-g tests were performed with DRP and DRE applications. In this regard, different mechanical behaviors and capacities were considered for fuses against demand thrusts of backfill in order to compare the mitigation tests with no-mitigation cases. Harmonic base motions with constant amplitude and constant frequency were used in the model test. The foundation soil and the backfill soil were constructed with the relative densities of 85 and 25%, respectively, to reproduce non-liquefiable base layer and loose backfill situations in the model, respectively. The results showed remarkable reduction in kinetic energy, dynamic backfill thrust and consequently seaward movement, settlement and inclination of the caisson quay wall in case of using fuses with plastic behaviors behind the wall.     

Effect of structural design on fundamental frequency of reinforced-soil retaining walls

The results of a numerical study on the influence of a number of structural design parameters on the fundamental frequency of reinforced-soil retaining wall models are presented and discussed. The design parameters in the study include the wall height, backfill width, reinforcement stiffness, reinforcement length, backfill friction angle and toe restraint condition. The intensity of ground motion, characterized by peak ground acceleration, is also included in the study as an additional parameter. The study shows that the fundamental frequency of reinforced-soil wall models with sufficiently wide backfill subjected to moderately strong vibrations can be estimated with reasonable accuracy from a few available formulae based on linear elastic wave theory using the shear wave speed in the backfill and the wall height. Numerical analyses showed no significant influence of the reinforcement stiffness, reinforcement length or toe restraint condition on the fundamental frequency of wall models. The strength of the granular backfill, characterized by its friction angle, also did not show any observable effect on the fundamental frequency of the reinforced-soil retaining wall. However, the resonance frequencies of wall models were dependent on the ground motion intensity and to a lesser extent, on the width to height ratio of the backfill.     

平面应变条件下基于弹性理论的土压力计算及适用性研究

针对工程中大量存在的平面应变问题,依据平面应变条件和广义胡克定律,基于SMP、Lade-Duncan、AC-SMP和广义Mises强度准则,推导出考虑中主应力及泊松比影响的无黏性土主、被动土压力计算公式,并将其扩展至黏性土,讨论基于各强度准则土压力计算公式的适用范围。结果表明：考虑中主应力对土强度的贡献后,基于各强度准则所计算的主动土压力均小于朗肯主动土压力,被动土压力均大于朗肯被动土压力;主动土压力P_a随着泊松比的增大而减小,被动土压力P_P随着泊松比的增大而增大,且泊松比越大,与实测数据更为接近;基于同一强度准则下得到的主、被动土压力适用的内摩擦角范围随着泊松比的增大而增大;基于各强度准则的土压力计算公式均能较好的描述挡土结构上土压力的大小,其中广义Mises强度准则计算结果与实际工程更为吻合,研究成果可为挡土结构上土压力的计算提供一定理论参考。     

Dynamic passive pressure from c–ϕ soil backfills

This technical note presents an analytical expression for the total passive pressure on a retaining wall from the c–? soil backfill subjected to both horizontal and vertical seismic inertial forces. The developed expression has been analysed for the special cases, and the results have been found identical to those proposed by earlier researchers on the subject. A numerical example, presented to illustrate the steps for the calculation of total dynamic passive pressure using the developed general expression, shows that the design value of total dynamic passive pressure as a resistance to the retaining wall movement should be obtained with upward vertical seismic inertial force in combination with the direction of horizontal seismic force towards the backfill.     

Phasing issues in the seismic response of yielding,gravity-type earth retaining walls – Overview and results from a FEM study

An overview of past and recent developments on the subject of seismic earth pressures on yielding, gravity-type walls, retaining cohesionless backfill, is first presented, focusing on available data on the issue of phase difference that develops between the peak values of wall inertia and seismic earth thrust increment. The results of a FEM parametric study are next presented regarding the dependence on the resulting dynamic earth thrust reduction – acting on the time of peak wall inertia – on backfill rigidity, wall height, and shaking characteristics. The reliability of the numerical analyses was verified by modeling centrifuge tests reported by Nakamura [24] and successfully comparing measured vs. computed behavior. The results of the parametric analyses indicate that the seismic active earth thrust, acting on the wall at the time of maximum wall inertia, is significantly reduced (compared to its peak value) with increasing shaking intensity of backfill, increasing wall displacements, increasing wall height, and decreasing backfill rigidity. No systematic dependence on the ratio of input motion frequency to the natural frequency of the backfill (f/f₁) was observed. The above findings: (1) verify earlier experimental and numerical results, (2) explain the reported lack of damage to retaining walls under strong ground shaking, and (3) indicate the need for revising the pertinent provisions of current seismic codes. Graphs summarizing the results of the numerical analyses are presented which may be used as a guide for selecting the magnitude of seismic active earth thrust that needs to be taken into account in the design of the examined type of earth retaining walls.     

海啸作用下滨水挡土墙抗震转动稳定性上限分析

地震诱发的海啸对沿海围护结构的破坏具有强度大的特点。滨水挡土墙作为重要的围护结构,海啸与地震的联合作用极易造成其发生绕墙踵的被动破坏。采用条分法,将土楔体分割成无数平行于破裂面的刚性土条,并建立绕墙踵转动的挡墙与刚性土条之间的速度容许场。基于极限上限理论,依据外力做功功率等于其内能耗散功率,推导了地震加速度系数的表达式。与经典极限平衡理论相比,该方法考虑了挡墙的位移模式,且无需假设地震土压力的作用位置。分析了浪高与海平面高度之比,内摩擦角φ及墙土摩擦角δ对滨水挡土墙稳定性的影响。     

Extending the application of integral frame abutment bridges in earthquake‐prone areas by using novel isolators of recycled materials

Integral abutment bridges (IABs) are jointless structures without bearings or expansion joints which require minimum or zero maintenance. The barrier to the application of long‐span integral abutment bridges is the interaction of the abutment with the backfill soil during the thermal expansion and contraction of the bridge deck, that is, serviceability, or when the bridge is subjected to dynamic loads, such as earthquakes. The interaction of the bridge with the backfill leads to settlements and ratcheting of the soil behind the abutment and, as a result, the soil pressures acting on the abutment build up in the long term. This paper provides a solution for the aforementioned challenges by introducing a novel isolator that is a compressible inclusion of reused tyre‐derived aggregates placed between the bridge abutment and the backfill. The compressibility of typical tyre‐derived aggregates was measured by laboratory tests, and the compressible inclusion was designed accordingly. The compressible inclusion was then applied to a typical integral frame abutment model, which was subjected to static and dynamic loads representing in‐service and seismic loads correspondingly. The response of both the conventional and the isolated abutment was assessed based on the settlements of the backfill, the soil pressures and the actions of the abutment. The study of the isolated abutment showed that the achieved decoupling of the abutment from the backfill soil results in significant reductions of the settlements of the backfill and of the pressures acting on the abutment. Hence, the proposed research enables extending the length limits of integral frame bridges subjected to earthquake excitations. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic stability of concrete gravity dams strengthened by rockfill buttressing

Rockfill buttressing resting on the downstream face of masonry or concrete gravity dam is often considered as a strengthening method to improve the stability of existing dam for hydrostatic and seismic loads. Simplified methods for seismic stability analysis of composite concrete-rockfill dams are discussed. Numerical analyses are performed using a nonlinear rockfill model and nonlinear dam-rockfill interface behavior to investigate the effects of backfill on dynamic response of composite dams. A typical 35 m concrete gravity dam, strengthened by rockfill buttressing is considered. The results of analyses confirm that backfill can improve the seismic stability of gravity dams by exerting pressure on the dam in opposition to hydrostatic loads. According to numerical analyses results, the backfill pressures vary during earthquake base excitations and the inertia forces of the backfill are the main source for those variations. It is also shown that significant passive (or active) pressure cannot develop in composite dams with a finite backfill width. A simplified model is also proposed for dynamic analysis of composite dam by replacing the backfill with by a series of vertical cantilever shear beams connected to each other and to the dam by flexible links.     

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.