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 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.     

Recent applications of sliding block theory to geotechnical design

The sliding block theory was proposed by Newmark for determining the permanent displacement of embankments and dams under earthquake loading. This paper highlights recent applications of sliding block theory to different geotechnical structures. The equations to determine seismic factor of safety, yield acceleration and permanent displacement are given for rock block, soil slope, landfill cover, geosynthetic-reinforced soil retaining wall, and composite breakwater. The presented equations for seismic stability degenerate to that of static stability in the absence of earthquake. The permanent displacement for various structures can be obtained from that of a horizontal sliding block through a correction factor. A simplified procedure is included for the permanent displacement under vertical acceleration. The sliding block approach is rational for design under high seismic load.     

地震区跨活动断层桥梁桩基动力时程响应分析

为了研究强震区桥梁跨活动断层时,桩基在地震中的动力响应,以海文大桥为工程背景,利用Midas GTS有限元软件建立其强震区桩-海床岩土体-断层耦合作用的数值模型,研究不同强度(0.20g～0.60g)的50年超越概率为10%的地震波(后文简称5010地震波)作用下,桥梁桩基加速度、位移、弯矩及剪力的动力时程响应特性。结果表明：上部大厚度松散土体对桩身加速度有放大及滤波作用,而基岩对桩身加速度几乎不产生作用;断层上、下盘桩基础的桩顶水平位移随输入地震动强度的增大而增大,但达到振幅的时刻一致;上、下盘桩基础桩顶竖向位移时程响应都在50 s以后产生永久沉降;桩身最大弯矩截面处时程响应均在40 s以后产生永久弯矩;应重点考虑上部覆盖层软硬土体界面和基岩界面的抗弯承载力设计,及桩顶和基岩面附近的抗剪承载力设计;上盘桩基础按桩身加速度、弯矩、桩顶水平位移等动参数控制设计,下盘桩基础按动剪应力控制设计。     

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.     

Deterministic sliding block methods for estimating seismic displacements of earth structures

A review and quantitative comparison of existing deterministic sliding block methods for predicting permanent displacements of earth structures subjected to seismic loading is presented. The reviewed sliding block methods are divided into two main groups based on the characteristic earthquake parameters referenced in each method. One group uses the maximum horizontal ground acceleration and velocity, and the other uses the maximum horizontal ground acceleration and the predominant period of the acceleration spectrum. Displacement functions published by previous authors are reformulated to give common non-dimensionalized displacement functions of the critical acceleration ratio which are then used to compare the different methods for the estimate of permanent seismic displacement of soil structures. The results show that despite the fact that the different methods were formulated using a wide range of earthquake records and different characteristic seismic parameters, permanent displacement values predicted using these methods fall within a reasonably narrow band. Selected acceleration data from three recent earthquakes that occurred in California are used to evaluate and compare the accuracy of the reviewed displacement methods for practical applications.     

强震作用下桩-土-断层非线性动力相互作用特性

为研究强震区跨断层桥梁桩基非线性动力相互作用特性,依托海文大桥实体工程,利用MIDAS/GTS有限元软件,建立了桩-土-断层相互作用模型,分析0.20~0.60g地震动强度下断层上下盘桩基加速度响应、桩顶水平位移、桩身弯矩以及桩身剪力响应情况。结果表明:覆盖层土体对桩身加速度放大作用明显,且随着输入地震动强度的增大,放大作用逐渐减弱;覆盖层对地震波的滤波作用显著,随着输入地震动强度的增大,滤波作用逐渐减弱;上盘桩基达到桩顶峰值加速度的时刻滞后于下盘;随着输入地震动强度的增大,上、下盘桩的桩顶产生的永久位移和水平位移峰值逐渐变大,上盘桩顶产生的永久位移和桩顶峰值位移均大于下盘,产生显著的"上盘效应";不同强度地震动作用下,断层上、下盘桩基弯矩均在上部土层界面处达到峰值,剪力均在基岩面处达到峰值,下盘桩基弯矩和剪力峰值大于上盘桩基,呈现出显著的"下盘效应"。在桥梁桩基抗震设计时,应着重考虑断层上、下盘桩基的差异和不同强度地震作用对桩基承载特性的影响。     

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.     

地铁车站与隧道连接处地震响应分析

结构截面刚度突变处是地下结构抗震的薄弱部位,为研究地铁车站与隧道连接处的地震响应,本文建立有限差分数值模型,分析地震作用下车站与隧道连接处的薄弱部位、连接处附近的侧墙变形分布特征以及地表沉降分布特征,重点探究埋深、地震动特征以及周围土体刚度对连接处隧道应力的影响。结果表明:连接处端墙底部跨中、端墙洞口的顶部和底部是抗震的薄弱部位;连接处端墙存在对侧墙变形分布、地表沉降分布有一定影响;结构埋深,地震动频谱、幅值对连接处隧道应力响应有较大影响,结构周围土体的刚度在一定范围内对连接处隧道应力有较大影响。     

近岸水平场地液化侧向大变形影响因素分析

利用改进的软化模量分析方法,对近岸水平场地液化侧向大变形进行数值计算,以研究地震波波形和幅值大小、液化、竖向地震动对侧向大变形的影响。结果表明:不同的地震波作用下,即使峰值加速度相同,液化程度与侧移距离也可能有较大不同,表现了土体变形的强非线性性质,但大地震下液化导致的侧移几乎都在米的量级上;计算区域中无液化区时,岸壁侧向永久位移很小,在几公分左右,随水平峰值加速度及不同地震动输入改变不大;计算区域中有液化区时,岸壁侧向永久位移显著增大,且随输入水平峰值加速度的增大而明显增大,其机理是强地震动使液化范围加大;水平竖向两向地震动输入与单独水平地震动输入相比,前者场地液化范围增大,平均增大42%,侧移量增加,平均增加37%。     

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。     

考虑动态临界加速度的地震边坡永久位移预测模型研究

在区域边坡地震危险性评价中主要采用永久位移预测模型进行地震边坡永久位移计算。永久位移预测模型以Newmark滑块理论为基础,通过大量实测地震时程记录统计拟合得出。针对Newmark理论中滑动面抗剪强度参数保持不变和已有位移预测模型的计算位移小于实测位移的问题,利用动态临界加速度理论,分别构建含有峰值加速度和阿里亚斯强度的两种位移预测模型。对该模型计算出的永久位移合理性进行讨论,发现永久位移计算结果符合滑坡实测位移的数量级。采用本文模型计算的永久位移更加接近地震滑坡位移实际大小,可以解决一直存在的预测位移小于实测位移的问题。在更进一步讨论发展的基础上,本文模型可满足更多的理论应用和工程实际,为区域边坡地震危险性评价提供思路。     

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。     

地震动永久位移对结构地震反应影响

本文推导了基于位移激励计算单自由度体系拟速度谱公式,通过构造的脉冲位移时程对公式精度进行了验证;之后利用小波变换去除强震记录噪声而保留地震动永久位移,再基于去趋势项方法和滤波方法去除永久位移后,计算拟速度谱。算例结果表明:短周期段内,不保留永久位移的位移激励拟速度谱值与保留永久位移的位移激励拟速度谱值相差很小;中长周期段内,不保留永久位移的位移激励拟速度谱值总体上小于保留永久位移的位移激励拟速度谱值,且不保留永久位移时,滤波方法引起的拟速度谱降幅大于去趋势项方法所引起的拟速度谱降幅。因此,基于位移激励计算中长周期结构的地震反应时,应保留地震动永久位移,或基于去趋势项方法去除永久位移。      

小高层住宅结构方案--大开洞剪力墙与异型柱框剪结构对比分析

通过对某小区小高层住宅2种结构方案的综合讨论,分析了小高层住宅的合理结构型式,提出了设计建议可供工程设计参考。异型柱框架-剪力墙结构框架柱布置灵活、隐蔽性好,但其柱截面不规则、计算理论不成熟、抗震能力较差、构造措施不理想、而且建筑自振周期长,侧向位移大,难以用于较高的高层住宅和抗震烈度较高的地区;大开洞剪力墙结构受力明确、计算理论成熟,又有较为精确的计算程序,而且墙厚可以在规范允许的范围内减薄,从而进一步降低了工程造价。通过2种方案比较,认为大开洞剪力墙体系与异型柱框剪结构相比,配筋总量基本接近,但其侧移较小,具有较好的延性,可应用于小高层住宅和地震烈度较高地区并可取得显著经济效益。     

Soil slopes under combined horizontal and vertical seismic accelerations

Conventional methods of designing earth structures are based on pseudo-static stability analysis employing a horizontal seismic coefficient. This paper discusses the stability and permanent displacement of a slope subject to combined horizontal and vertical accelerations. A log-spiral failure mechanism is used. It is shown that seismic force has a significant effect on stability and permanent displacement of slopes. The parametric study reveals that vertical acceleration may play an important role on stability and permanent displacement if the corresponding horizontal acceleration is large. © 1997 John Wiley & Sons Ltd.     

地震作用下夯土城墙动力响应分析——以山丹明长城为例

2022年1月8日门源M6.9地震造成山丹明长城局部破坏。为研究此次地震作用下夯土城墙的动力响应与破坏特征,基于地震现场考察结果,采用振幅等效处理后的记录地震波为输入地震动,开展双向地震荷载作用下夯土城墙的动力响应数值分析,研究不同位置测点的最大位移、峰值加速度与墙体应力分布特征,探讨地震导致夯土城墙破坏的主要内因。研究结果表明：双向地震荷载作用下,墙体位移和峰值加速度(PGA)随着高度的增加逐渐增加,但距墙体底部0.5 m高度范围内PGA放大效应不明显,最大位移、加速度均出现在墙体顶部裂缝位置处;水平地震荷载作用下墙体的地震动响应更为显著;墙体的最大主应力、最大剪应力均出现在有裂缝处的底端掏蚀悬空部位,墙体裂缝、夯筑搭接、掏蚀悬空处应力集中明显;裂缝对夯土城墙的地震动放大效应在一定高度范围内表现为弱化作用,但随高度增加逐渐过渡为强化作用;裂缝可显著增强墙体顶部地震动响应,可能是本次地震诱发城墙破坏的主要内因。研究成果可为古城墙遗址的加固修缮提供科学指导。     

Shake-table testing of a self-centering precast reinforced concrete frame with shear walls

The seismic performance of a self-centering precast reinforced concrete (RC) frame with shear walls was investigated in this paper. The lateral force resistance was provided by self-centering precast RC shear walls (SPCW), which utilize a combination of unbonded prestressed post-tensioned (PT) tendons and mild steel reinforcing bars for flexural resistance across base joints. The structures concentrated deformations at the bottom joints and the unbonded PT tendons provided the self-centering restoring force. A 1/3-scale model of a five-story self-centering RC frame with shear walls was designed and tested on a shake-table under a series of bi-directional earthquake excitations with increasing intensity. The acceleration response, roof displacement, inter-story drifts, residual drifts, shear force ratios, hysteresis curves, and local behaviour of the test specimen were analysed and evaluated. The results demonstrated that seismic performance of the test specimen was satisfactory in the plane of the shear wall; however, the structure sustained inter-story drift levels up to 2.45%. Negligible residual drifts were recorded after all applied earthquake excitations. Based on the shake-table test results, it is feasible to apply and popularize a self-centering precast RC frame with shear walls as a structural system in seismic regions.     

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.     

轨道交通地下结构抗震设计相关反应加速度法分析

通过梳理轨道交通地下结构抗震设计流程,明确抗震设计方法选择的原则和依据。在阐明反应加速度法基本原理基础上,引出土层地震反应分析的一维等效线性化法,并对影响土层地震反应计算结果关键参数进行讨论。针对一维土层地震反应得到的加速度时程提出合理拟合抛物线型二阶基线方程,可以消除加速度时程长周期随机分量引起的漂移问题,经自然积分可以得到消除基线漂移的位移时程;同时阐明数值分析软件Origin Pro有效解决积分得到位移时程的基线漂移问题并得到合理位移分布的途径和方法。以北京地铁3号线体育中心站为例,详细说明反应加速度法相关各个技术环节实现的方法和结果,并指出反应加速度法或位移法所依据的土层地震反应分析和位移时程的确定具有较强专业性,应做专项咨询分析工作;只有一维土层地震反应分析获得的加速度反应谱及时程客观合理,有限元计算所需相应地震动水平的等效剪切模量才可信;积分得到的位移时程需要有效消除基线漂移影响。只有上述相关结果真实客观可信,有限元计算结果才能模拟真实的土层-地下结构地震反应。