基于位移的模块式加筋土挡墙抗震设计方法研究

性态设计是支挡结构工程抗震设计的前沿科学问题。以模块式加筋土挡墙为试验对象,通过振动台试验,探究模块式加筋土挡墙的变形模式;收集归纳挡土墙位移计算方法,分析不同破坏模式下屈服加速度系数分布规律;对比不同计算方法计算值与实测值的一致性。研究结果表明：挡墙的位移模式为平移与转动耦合,且以转动为主;不同破坏模式下安全系数法求解的屈服加速度系数均随输入加速度幅值增大而减小,简便方法和能量法所得屈服加速度系数为常数;将屈服加速度系数代入不同位移计算方法对比,提出在不同峰值加速度时,可分别采用Richards and Elms上限法(0.4g以下)、Cai and Bathurst平均上限法(0.4g～0.6g)、Newmark上限法(0.6g～0.8g)、Whitman and Liao平均拟合法(0.8g～1.0g)进行位移计算。最后,对模块式加筋土挡墙的抗震设计流程进行归纳。     

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.     

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.     

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.     

重力式挡土墙地基抗震承载力探讨

高烈度地震区重力式挡土墙由于地基承载力不足导致墙身失稳是一种较常见震害类型。基于拟静力法原理,利用极限分析上限定理对地震作用下挡土墙地基极限承载力进行求解,通过典型算例分析了极限承载力随地震动峰值加速度的变化关系与机理,讨论了地基土强度参数对其变化趋势的影响,提出了同时考虑设防烈度和地基土性的挡土墙地基抗震容许承载力修正方法及相应修正系数取值建议。结果表明:设防烈度在9度及以内时,随着地震动峰值加速度增加,挡土墙地基极限承载力近似呈线性下降,下降速率与地基土黏聚力呈负相关性,而受内摩擦角的影响不显著;地震作用加剧挡土墙基底荷载倾斜与偏心导致地基破坏区缩减是造成极限承载力下降的主要原因;设防烈度大于7度时,挡土墙地基抗震容许承载力较天然工况下有所降低,8度和9度设防烈度对应的修正系数约为0.9和0.7。     

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。     

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.     

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。     

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.     

Seismic behavior of an inverted T-shape flexible retaining wall via dynamic centrifuge tests

In the design procedure for a retaining wall, the pseudo-static method has been widely used and dynamic earth pressure is calculated by the Mononobe–Okabe method, which is an extension of Coulomb’s earth pressure theory computed by force equilibrium. However, there is no clear empirical basis for treating the seismic force as a static force, and recent experimental research has shown that the Mononobe–Okabe method is quite conservative, and there exists a discrepancy between the assumed conditions and real seismic behavior during an earthquake. Two dynamic centrifuge tests were designed and conducted to reexamine the Mononobe–Okabe method and to evaluate the seismic lateral earth pressure on an inverted T-shape flexible retaining wall with a dry medium sand backfill. Results from two sets of dynamic centrifuge experiments show that inertial force has a significant impact on the seismic behavior on the flexible retaining wall. The dynamic earth pressure at the time of maximum moment during the earthquake was not synchronized and almost zero. The relationship between the back-calculated dynamic earth pressure coefficient at the time of maximum dynamic wall moment and the peak ground acceleration obtained from the wall base peak ground acceleration indicates that the seismic earth pressure on flexible cantilever retaining walls can be neglected at accelerations below 0.4 g. These results suggest that a wall designed with a static factor of safety should be able to resist seismic loads up to 0.3–0.4 g.     

A new limit equilibrium method for the pseudostatic design of embedded cantilevered retaining walls

This paper describes a new pseudostatic limit equilibrium method for the design of cantilevered retaining walls under seismic actions. The method has been applied in a parametric study of the effects of the geometry of the wall, considering different excavated and embedded depths, of the strength of the soil, and of the contact between the soil and the wall. The pseudostatic predictions are in very good agreement, both in terms of horizontal contact stress and bending moment distributions, with the results of truly dynamic 2-D finite difference analyses and published experimental data. It is found that for increasing strengths of the soil–wall system both the critical acceleration and the maximum bending moment on the wall increase. In other words, a stronger soil–wall system will experience smaller displacements during the earthquake, but this is paid for by increasing internal forces in the wall.     

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.     

直立式加筋土挡墙基于极限分析的抗震性能研究

研究直立式加筋土挡墙抗震性能时,采用的NCMA方法未全面运算其墙外功率,抗震性能分析结果存在较高偏差。采用极限分析的方法对直立式加筋土挡墙破坏模式展开极限分析,得到该挡墙运动极限表达式。根据运动极限表达式,对一实例墙体计算出此挡墙外功率(包括土重所做的外功率和地震作用所做的外功率),分析其抗震性能。实验结果表明,计算得到直立式加筋土挡墙各层筋材最大外功率分别为18.5 kN·m和20 kN·m,与实际最大外功率18 kN·m差距不大,说明该方法的抗震性能分析与实际情况相符,具有应用性。     

Computation of sliding displacements of bridge abutments by pseudo-dynamic method

The paper focuses on seismic sliding displacement calculations of gravity wall bridge abutments when subjected to passive condition during earthquakes. Pseudo-dynamic approach has been used for the calculation of the passive seismic earth pressure. A novel element of the present investigation is the computation of seismic passive earth pressure coefficients by considering the composite curved rupture surface behind the abutment wall in the framework of limit equilibrium method. Sliding failure along the wall base is considered in the new pseudo-dynamic method. The critical seismic acceleration coefficient for sliding and sliding component of the displacement, resulting from horizontal and vertical sinusoidal ground accelerations, are computed by using Newmark's sliding block method. The effect of sliding on the response of earth structures is evaluated and comparisons are made between sliding displacements calculated using planar and composite failure mechanisms. Results of the comparative study showed that the assumption of planar failure mechanism for rough soil–wall interfaces significantly overestimates the critical seismic accelerations for sliding and underestimates the sliding displacements.     

地基条件对仰斜式挡墙地震响应影响及墙高限值研究

地基条件和墙高是影响挡土墙地震响应特征的重要因素。建立不同地基条件的仰斜式挡土墙有限元时程分析模型,以墙身外倾最大危险状态为最不利时刻,研究地基条件和墙高对挡墙动力响应及墙-土相互作用的影响特征,并以满足力学检算和墙身位移限值为出发点,提出同时考虑地基条件和地震峰值加速度PGA的仰斜式挡墙墙高控制建议。结果表明：岩质地基挡墙墙背动土压力沿墙高呈中部大、上下小的凸形分布,大震下土压力较中震时有小幅减小;基底反力呈墙踵为0、墙趾集中的三角形图式,且随PGA和墙高的增加踵部脱空趋势更为明显;土质地基挡墙因墙底地基土变形对墙后填土的牵连作用,填土跟随墙身运动的趋势加剧,墙背动土压力与PGA呈正相关并沿墙高近似呈线性分布,于墙底处最大;墙身往复摆动使踵趾端地基土体塑性变形较基底中部明显,基底反力峰值向中部转移;根据最不利时刻稳定性、承载力检算,考虑对墙身位移合理限制,提出地震区仰斜式挡墙的允许墙高在设防PGA不超过0.2g时为8 m, 0.4g大震下硬质岩地基挡墙可达8 m,软质岩地基挡墙不宜超过6 m,碎石土、砂质黏土地基挡墙不宜超过4 m。     

挡土墙地震反应非线性波动模拟

本文运用解耦近场非线性波动数值模拟方法研究挡土墙地震反应，为反映墙土体系在地震作用下的位移机制，引入了Desai薄层单元模拟墙土间接触面，并采用双线型本构关系作为接触面单元和土体的非线性模型，在此基础上给出了解决P—SV问题的非线性显式有限元时域递推公式，为进一步发展非线性波动数值模拟技术提供了有益经验。为验证本文方法及适用性，将数值模拟结果与Zeng，X．和Madabhushi，X．P．G．等的离心机试验和弹塑性数值模拟结果进行对比。结果表明：墙土体系加速度、挡土墙顶底相对滑移、沉降和墙体倾角等同离心机试验模拟结果基本吻合，与弹塑性数值模拟结果相似。     

地震作用下重力式挡土墙土压力特性数值模拟研究

重力式挡土墙在地震作用下的土压力特性一直是挡土墙设计的重要内容。本文通过数值模拟,在挡土墙墙背轴线上设置一系列监测点,得到地震过程中监测点的加速度、土压力强度时程曲线;然后根据时程曲线分析墙后土压力强度分布特征、根据土压力强度分布求出总土压力、根据总土压力求出其对墙趾的力矩;最后分别将土压力强度分布、总土压力、总土压力对墙趾的力矩与现有的研究方法及规范对比。结果表明:地震作用下墙背各点加速度峰值在同时刻发生,但土压力峰值不在同时刻发生;现有的一些研究方法未考虑土压力强度峰值时程变化,其结果比实际偏大;在低地震烈度条件下,规范计算的总土压力及倾覆力矩偏于保守,而在高烈度条件下则偏于危险。     

Seismic Displacement of Gravity Walls by a Two-body Model

Gravity walls retaining dry soil are modeled as a system of two bodies: (a) the gravity wall that slides along the wall-foundation soil boundary and (b) the critical soil wedge in the soil behind the wall. The strength of the system is defined by both the frictional and the cohesional components of resistance. The angle of the prism of the critical soil wedge behind the wall is obtained using the limit equilibrium method. The model accounts for changes in the geometry of the backfill soil behind the wall by considering the displacements at the end of each time step under limit equilibrium. The model shows that the standard (single) block model is over-conservative for the extreme case of critical-to-applied-seismic acceleration ratios less than about 0.30, but works well for cases where this ratio ranges between 0.5 and 0.8. The model is applied to predict the seismic displacement of gravity walls (a) tested in the shaking-table and (b) studied numerically by elaborate elasto–plastic analyses.     

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.     

加筋格宾新型组合支挡结构设计研究

依托湖南省湘潭至衡阳西线高速公路K 124＋300～K 124＋895段国内首座加筋格宾组合式挡土墙工程,介绍了以双绞合六边形金属网为筋材的2种新型加筋支挡结构：加筋格宾结构与绿色加筋格宾结构;以极限平衡理论为基础,吸收国外先进加筋土技术,提出了该组合结构的稳定性验算方法与公式;编制相关程序,深入研究了填料粘聚力、内摩擦角、网面拉力、地震力、填土重度、车辆荷载以及加筋间距等重要参数对安全系数的影响。研究表明,各设计参数对安全系数的影响程度不同。同时,也验证了该加筋格宾组合式挡土墙设计的科学性和合理性。研究成果可应用于具体支挡结构设计。