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.     

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。     

Interpretation of dynamic retaining wall model tests in light of elastic and plastic solutions

The dynamic response of rigid and flexible walls retaining dry cohesionless soil is examined in light of experimental results and analytical elastodynamic and limit analysis solutions. Following a brief review of the problem, experimental findings from three different testing programs on retaining walls are presented, and compared with theoretical predictions based on the above-mentioned approaches. Reasonable agreement is found depending on the assumptions. It is shown that wall flexibility – which is not taken into account in classical design approaches – should be considered to establish the point of application of seismic thrust on the wall. Detailed calculations and set of graphs and charts are presented, which highlight salient aspects of the problem.     

Experimental developments for studying static and seismic behavior of retaining walls with liquefiable backfills

The effects of earthquakes on cantilever retaining walls with liquefiable backfills were studied. The experimental techniques utilized in this study are discussed here. A series of centrifuge tests was conducted on aluminum, fixed-base, cantilever wall models retaining saturated, cohesionless backfills. Accelerations on the walls and in the backfill, static and excess pore pressures in the soil, and deflections and bending strains in the wall were measured. In addition, direct measurements of static and dynamic lateral earth pressures were made. In some tests, sand backfills were saturated with the substitute pore fluid metolose. Modeling of model type experiments were conducted. The experimental measurements were found internally consistent and repeatable. Both static and dynamic earth pressure measurements were determined to be reliable. It was also observed that for the test configuration adopted, a special boundary treatment such as the use of duxseal is optional. Static and seismic modeling of models were also successful, which indicated that the assumed scaling relations were essentially correct.     

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.     

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.     

Seismic lateral movement prediction for gravity retaining walls on granular soils

At present, methods based on allowable displacements are frequently used in the seismic design of earth retaining structures. However, these procedures ignore both the foundation soil deformability and the seismic amplification of the soil placed behind the retaining wall. Thus, they are not able to predict neither a rotational failure mechanism nor seismic induced lateral displacements with an acceptable degree of accuracy for the most general case. In this paper, a series of 2D finite-element analyses were carried out to study the seismic behavior of gravity retaining walls on normally consolidated granular soils. Chilean strong-motion records were applied at the bedrock level. An advanced non-linear constitutive model was used to represent both the backfill and foundation soil behavior. This elastoplastic model takes into account both the stress dependency of soil stiffness and coupling between shear and volumetric strains. In unloading–reloading cycles, the non-linear shear-modulus reduction with shear strain amplitude is considered. Interface elements were used to model soil–structure interaction. Routine-design charts were derived from the numerical analyses to predict the lateral movements at the base and top of gravity retaining walls located at sites with similar seismic characteristics to the Chilean subduction zone. Thus, wall seismic rotation can also be obtained. The developed charts consider wall dimensions, granular soil properties, bedrock depth, and seismic input motion characteristics. As shown, the proposed charts match well with available experimental data.     

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.     

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.     

岩石场地重力式挡土墙地震土压力振动台实验研究

结合汶川震区调查资料,利用大型振动台模型试验,分析了碎石土填料的岩石场地重力式挡土墙的地震土压力及其分布规律,并以此对我国现行铁路、公路抗震规范做合理性讨论和细化。研究发现,地震作用下,挡土墙的动土压力沿墙高呈单峰曲线状分布,且60%～80%集中作用于挡墙中部;随着地震峰值加速度的增加,地震土压力分布逐渐偏离现行振震设计规范所认为的三角形线性状,而呈现非线性状;合力作用点高于1/3墙高,0.4g地震加速度作用下,接近0.4倍墙高,对岩石场地下粗粒径墙背填料的地震土压力作用点高度,建议取0.35倍墙高。对比计算表明,现行规范能基本满足工程抗震设计需要,但建议对柔性挡土墙的抗震设计作出必要规定。     

Seismic behaviour of flexible retaining systems subjected to short-duration moderately strong excitation

Using finite-element modelling, this paper explores the magnitude and distribution of dynamic earth pressures on several types of flexible retaining systems: L-shaped reinforced-concrete walls, piled walls with horizontal or with strongly inclined anchors, and reinforced-soil walls. The utilized base excitation is typical of earthquake motions of either high or moderately low dominant frequencies having a peak ground acceleration (PGA) of 0.40 g and relatively short duration. Linear as well as non-linear (Mohr–Coulomb) soil behaviour is investigated, under dry conditions. The results show that, as the degree of realism in the analysis increases, we can explain the frequently observed satisfactory performance of such retaining systems during strong seismic shaking.     

Behavior of braced excavation in sand under a seismic condition: experimental and numerical studies

The behavior of braced excavation in dry sand under a seismic condition is investigated in this paper. A series of shake table tests on a reduced scale model of a retaining wall with one level of bracing were conducted to study the effect of different design parameters such as excavation depth, acceleration amplitude and wall stiffness. Numerical analyses using FLAC 2D were also performed considering one level of bracing. The strut forces, lateral displacements and bending moments in the wall at the end of earthquake motion were compared with experimental results. The study showed that in a post-seismic condition, when other factors were constant, lateral displacement, bending moment, strut forces and maximum ground surface displacement increased with excavation depth and the amplitude of base acceleration. The study also showed that as wall stiffness decreased, the lateral displacement of the wall and ground surface displacement increased, but the bending moment of the wall and strut forces decreased. The net earth pressure behind the walls was influenced by excavation depth and the peak acceleration amplitude, but did not change significantly with wall stiffness. Strut force was the least affected parameter when compared with others under a seismic condition.     

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.     

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。     

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。     

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。     

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。     

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.     

Seismic earth pressures on rigid and flexible retaining walls

While limiting-equilibrium Mononobe–Okabe type solutions are still widely used in designing rigid gravity and flexible cantilever retaining walls against earthquakes, elasticity-based solutions have been given a new impetus following the analytical work of Veletsos and Younan [23]. The present paper develops a more general finite-element method of solution, the results of which are shown to be in agreement with the available analytical results for the distribution of dynamic earth pressures on rigid and flexible walls. The method is then employed to further investigate parametrically the effects of flexural wall rigidity and the rocking base compliance. Both homogeneous and inhomogeneous retained soil is considered, while a second soil layer is introduced as the foundation of the retaining system. The results confirm the approximate convergence between Mononobe–Okabe and elasticity-based solutions for structurally or rotationally flexible walls. At the same time they show the beneficial effect of soil inhomogeneity and that wave propagation in the underlying foundation layer may have an effect that cannot be simply accounted for with an appropriate rocking spring at the base.     

Seismic response of retaining walls with cohesive backfill: Centrifuge model studies

Observations from recent earthquakes show that retaining structures with non-liquefiable backfills perform extremely well; in fact, damage or failures related to seismic earth pressures are rare. The seismic response of a 6-m-high braced basement and a 6-m free-standing cantilever wall retaining a compacted low plasticity clay was studied in a series of centrifuge tests. The models were built at a 1/36 scale and instrumented with accelerometers, strain gages and pressure sensors to monitor their response. The experimental data show that the seismic earth pressure on walls increases linearly with the free-field PGA and that the earth pressures increase approximately linearly with depth, where the resultant acts near 0.33 H above the footing as opposed to 0.5–0.6 H, which is suggested by most current design methods. The current data suggest that traditional limit equilibrium methods yield overly conservative earth pressures in areas with ground accelerations up to 0.4g.