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.     

刚性挡土墙后轻量土主动土压力特性模型试验研究

为了研究轻量土的主动土压力特性,通过开展大比尺刚性挡土墙模型试验,采用人工控制挡土墙位移的方式,分析轻量土作为墙后填土时的主动土压力分布规律。结果表明：轻量土的侧向土压力随着挡墙位移量的增加先降低后逐渐趋于稳定,侧向土压力在挡墙位移量为3 mm时初步达到稳定状态,对比发现轻量土的主动土压力显著小于重塑黄土,这表明轻量土可以有效降低墙背主动土压力。轻量土的主动土压力系数处于0～0.16之间,沿着挡墙分布较为稳定,而重塑黄土主动土压力系数介于0～0.57之间,显著大于轻量土的主动土压力系数。经朗肯理论值与模型试验值对比分析,发现轻量土的朗肯主动土压力小于试验值,理论值与试验值之间的绝对误差处于0～6.32 kPa之间,其在实际工程中可以忽略不计。鉴于模型试验中墙背与填土之间存在一定的摩擦,朗肯理论在计算轻量土的主动土压力时仍较为准确。通过模型试验研究和传统理论分析,揭示了轻量土的主动土压力特性,对于完善轻量土土压力理论具有重要意义。     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.     

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。     

钢管水泥土围护墙等效弹性模量的有限元计算

分析了水泥土围护墙弹性模量对于控制基坑变形的重要性、根据上海某钢管水泥土墙基坑支护的工程实例建立ABAQUS平面二维有限元模型,计算钢管水泥土围护墙等效弹性模量,量化了内插钢管对提高水泥土重力式围护结构的支护强度所起到的作用,并对钢管长度、外径、间距和插入位置进行了参数分析。     

Dynamic pressures on rigid cantilever walls retaining poroelastic soil media. Part I. First method of solution

The problem of the determination of dynamic pressures and the associated forces on a rigid, vertical cantilever wall retaining a semi-infinite, uniform, fully-saturated poroelastic layer of soil is solved analytically under conditions of plane strain. Hysteretic damping in the soil skeleton may also be present. The rigid wall and the base of the soil layer are both excited by an acceleration harmonically varying with time and spatially invariant. The governing partial differential equations of motion, after separation of variables and the simplifying assumption of zero vertical normal stresses, reduce to a system of two ordinary differential equations for the amplitudes of the horizontal solid skeleton displacement and the pore water pressure, which are easily solved. Soil displacements and stresses, wall pressures and resultant forces as well as the pore water pressure are explicitly expressed. Their variation with frequency, hysteretic damping, porosity and permeability is numerically computed in order to assess the relative importance of the various parameters on the response.     

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.     

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。     

Evaluation of the effect of earthquake frequency content on seismic behavior of cantilever retaining wall including soil–structure interaction

A three-dimensional backfill–structure–soil/foundation interaction phenomenon is simulated using the finite element method in order to analyze the dynamic behavior of cantilever retaining wall subjected to different ground motions. Effects of both earthquake frequency content and soil–structure interaction are evaluated by using five different seismic motions and six different soil types. The study mainly consists of three parts. In the first part, following a brief review of the problem, the finite element model with viscous boundary is proposed under fixed-base condition. In the second part, analytical formulations are presented by using modal analysis technique to provide the finite element model verification, and reasonable agreement is found between numerical and analytical results. Finally, the method is extended to further investigate parametrically the effects of not only earthquake frequency content but also soil/foundation interaction, and nonlinear time history analyzes are carried out. By means of changing the soil properties, some comparisons are made on lateral displacements and stress responses under different ground motions. It is concluded that the dynamic response of the cantilever wall is highly sensitive to frequency characteristics of the earthquake record and soil–structure interaction.     

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.     

Seismic active pressure distribution history behind rigid retaining walls

Evaluating the seismic active earth pressure on retaining walls is currently based on pseudo-static method in practices. In this method, however, it is not simple, choosing an appropriate value for earthquake coefficient, which should fully reflect the dynamic characteristics of both soil and loading is an important problem. On the other hand, by using only two extra dynamic parameters that are shear wave velocity of soil and predominant frequency of probable earthquake, one can benefit from another more accurate tool called pseudo-dynamic method to solve the problem of earth pressure.In this study in the framework of limit equilibrium analysis, pseudo-dynamic method has been applied into horizontal slice method of analysis to account for the effect of earthquake on lateral earth pressure history behind rigid retaining walls. The pressure history resulted from a number of analyses shows that before and after reaching the peak resultant force, different pressure distributions occur behind a wall that put more local pressure than the same at peak. This method would be a tool to control this phenomenon in wall design.     

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.     

景观建筑挡土墙优化设计后抗震性能的实验测试研究

目前的景观建筑设计中往往更注重建筑的景观性,而忽略了建筑的安全稳定性,导致景观建筑的整体抗震效果较差,在景观建筑设计中加入挡土墙设计可以有效提高其抗震性。为此,设计一种具有一定抗震性能的景观建筑挡土墙,利用建筑施工过程中保留的复合纤维材料、建筑垃圾以及纤维绳等作为土墙填充物,并加入具有一定抗拉能力的拉筋材料,以保持土墙内部的稳定性。考虑景观建筑通常注重外观视觉效果,使用"平改坡"设计,在墙体表面种植具有一定视觉冲击的植物,增加土墙自重,促进土墙整体结构的稳定性。分析挡土墙后面无限倾斜填土受力状态,选取菱形微小单元体作为研究对象,计算景观建筑的挡土墙土压力强度。实验证明,优化设计的景观建筑挡土墙结构可以有效增强景观建筑的整体抗震能力。     

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。     

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.     

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。     

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.     

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。