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 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.     

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.     

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。     

Comparison of Seismic Design Codes between China and the United States for Reinforced Soil Retaining Walls

Because of its excellent seismic performance, reinforced soil retaining walls are increasingly used in civil engineering. Although many countries have published corresponding design codes, the differences between them are still relatively large. Using the FHWA Code and the Code for Seismic Design of Railway Engineering (CSDRE), stability calculations of reinforced soil retaining walls were carried out and the similarities and differences between these two design codes were analyzed. According to the comparative analysis, the following conclusions are drawn: the inertia force, the earth pressure and the tensile force of reinforcements calculated from the CSDRE are less than those from the FHWA Code, and the safety factor calculated from the former is larger. Although the M-O method is recommended to calculate the dynamic earth pressure, the FHWA Code suggests a higher action point as compared to the CSDRE.     

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.     

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.     

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。     

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.     

高烈度区重力式挡墙基于性能的抗震设计方法研究

介绍基于性能抗震设计的核心理念,以支挡结构震害调查分析为背景,阐述开展高烈度区重力式挡墙基于性能抗震设计研究的必要性;构建重力式挡墙基于性能的抗震设计框架,归类分析现行规范与基于性能抗震设计的关键技术问题;依据支挡结构震害调查及大型振动台模型试验,提出位移指数可作为衡量挡墙抗震性能的量化指标,确定重力式挡墙基于性能抗震设计的性能准则及流程;经对比计算基于性能与规范抗震设计的挡墙算例,显示基于性能抗震设计的优越性,为高烈度区重力式挡墙基于性能抗震设计的工程应用提出建议。     

Finite element analysis of structure-borne vibration from high-speed train

Finite element analyses were used to investigate the behavior of the building vibration induced by high-speed trains moving on bridges. The model includes the bridge, nearby building, soil and train. Finite element results indicate that trainload frequencies are more important than the natural frequencies of bridges and trains for building vibrations. If the building natural frequencies approach to the trainload frequencies, which equal an integer times the train speed over the compartment length, the resonance occurs and the building vibration will be large. Moreover, the vibration shape is similar to the mode shape of the resonance building frequency. To isolate the building vibration induced by moving trains, this paper investigates three common types of foundations, which include the extension of retaining walls, pile foundation and soil improvement around the building. Soil improvement around the building is the best way to reduce the building vibration both in horizontal and vertical directions.     

A comparison of two numerical models for the prediction of vibrations from underground railway traffic

Two prediction models for calculating vibration from underground railways are developed: the pipe-in-pipe model and the coupled periodic finite element–boundary element (FE–BE) model.The pipe-in-pipe model is a semi-analytical three-dimensional model that accounts for the dynamic interaction between the track, the tunnel and the soil. The continuum theory of elasticity in cylindrical coordinates is used to model two concentric pipes: an inner pipe to represent the tunnel wall and an outer pipe to represent the surrounding soil. The tunnel and soil are coupled accounting for equilibrium of stresses and compatibility of displacements at the tunnel–soil interface. This method assumes that the tunnel is invariant in the longitudinal direction and the problem is formulated in the frequency–wavenumber domain using a Fourier transformation. A track, formulated as an Euler–Bernoulli beam, is then coupled to this model. Results are transformed to the space domain using the inverse Fourier transform.The coupled periodic FE–BE model is based on a subdomain formulation, where a boundary element method is used for the soil and a finite element method for the tunnel. The Craig–Bampton substructuring technique is used to efficiently incorporate the track in the tunnel. The periodicity of the tunnel is exploited using the Floquet transformation to formulate the track–tunnel–soil interaction problem in the frequency–wavenumber domain and to compute the wave field radiated into the soil.An invariant concrete tunnel, embedded in a homogeneous full space is analyzed using both approaches. The pipe-in-pipe model offers an exact solution to this problem, which is used to validate the coupled periodic FE–BE model. The free field response due to a harmonic load in the tunnel is predicted and results obtained with both models are compared. The advantages and limitations of both models are highlighted. The coupled periodic FE–BE model has a greater potential as it can account for the complex periodic geometry of the tunnel and the layering in a soil medium. The effect of coupling a floating slab to the tunnel–soil system is also studied with both models by calculating the insertion gain.     

Response spectrum predictions for potential near-field and far-field earthquakes affecting Hong Kong: rock sites

To realistically assess the seismic risk relating to built infrastructures in Hong Kong and in the neighbouring coastal cities of southern Guangdong province, it is necessary to predict ground shaking induced by different earthquake scenarios with good accuracy. A companion paper has described the modelling of the spatial and temporal distribution of the diffused seismic activities in the region, based on the newly-developed ‘Expanding Circular Disc’ (ECD) method. Representative Magnitude–Distance (M–R) combinations for both near-field and far-field earthquakes (in relation to Hong Kong) have been derived using the ECD method. The present paper describes the modelling of the response spectrum on rock sites associated with the predicted M–R combinations, using the Component Attenuation Model (CAM) that was also developed recently by the authors, based on stochastic simulations of the seismological model. The significant effects of soil resonance on the response spectrum are described in a separate publication.The accuracy of CAM in modelling ground motion properties on rock sites has been tested here by comparisons with (i) strong motions recorded in Taiwan and South China from the 1999 ‘Chi-Chi’ earthquake in Taiwan (M=7.6), (ii) motions recorded in South China from another earthquake occurring in the southern Taiwan Strait in the same year (M=5.1), and (iii) historical seismic intensity data obtained within South China. The overall capability of CAM in modelling both near-field and far-field attenuation has been shown to be unmatched by existing empirical models. Results of the comparison studies confirm the accuracy of CAM, particularly within an epicentral distance of 300–400 km.This study shows that the developed serviceability response spectra (i.e. at short return periods) are controlled mainly by the earthquake recurrence behaviour of major distant seismic sources. In contrast, the ultimate response spectra (i.e. at long return periods) relate to events with magnitudes close to the maximum credible earthquake (MCE) limit, the effect of which may also be represented by the Characteristic Response Spectrum (CRS). Both types of earthquake scenario can be significantly affected by the regional crustal properties. The proposed response spectrum envelopes have been compared with previously developed recommendations, and a critical review has been conducted. The intrinsic advantages of the ECD–CAM modelling approach have been highlighted, emphasising its directness and transparency when compared with the more complex process required to implement traditional Probabilistic Seismic Hazard Assessment (PSHA).     

Post-earthquake investigation on several geosynthetic-reinforced soil retaining walls and slopes during the Ji-Ji earthquake of Taiwan

This paper gives an overview on the application of geosynthetic-reinforced soil structures in Taiwan. Taiwan has an unique topography and geotechnical conditions that rendered a less conservative and more challenging design compared to that of North America, Europe and Japan. The Ji-Ji (Chi-Chi) earthquake of 1999 gave an opportunity to examine the behavior of reinforced soil structures. The performance of several modular-block reinforced soil retaining walls and reinforced slopes at the vicinity of the fault was evaluated. Reinforced structures performed better than unreinforced soil retaining walls. The failure cases were highlighted and the cause of failure was identified. The lack of seismic design consideration could be a major cause of failure. The compound failure mode, the inertia force of the blocks, and the connection stiffness and strength relative to the large dynamic earth pressure, were among major items that would warrant further design consideration.     

Seismic response of multi-tiered reinforced soil retaining walls

In this study, a validated Finite Element procedure was used to investigate the similarities and differences of seismic performances between single- and multi-tiered reinforced soil walls. Three-tiered walls at a total height of 9 m were analyzed together with vertical walls at the same height. It was found from the Finite Element analyses that the resonant frequency of reinforced soil walls might increase with an increase in the tier-offset. The multi-tiered configuration could considerably reduce the residual lateral facing displacement and the average reinforcement load, and the reinforcement load distribution with height was different from that in vertical walls. With the same reinforcement length and spacing, the multi-tiered walls resulted in smaller reinforcement connection loads with the facing blocks. The study filled the gap of seismic behavior of multi-tiered reinforced soil retaining walls and revealed a few unique dynamic properties of this type of earth structures.     

地震与海啸作用下重力式岸墙旋转位移拟静力分析

被动状态下位移预测是挡墙地震工程设计中的关键,而岸墙后回填土的孔隙水压力对墙体运动具有一定影响。采用拟静力法计算墙后部分浸水土体的被动动土压力,根据静力水压力理论近似计算土颗粒里的动水压力;同时考虑地震荷载和海啸力的作用,根据力矩极限平衡确定旋转门槛加速度系数,采用旋转块体方法计算岸墙被动旋转运动下的地震位移。探讨回填砂土内摩擦角、墙体与土间摩擦角、地震加速度系数、回填土地下水位、海啸波浪高度等参数对旋转位移的影响。     

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.     

三个抗震问题简析及新型挡墙地震反应评述

水平地震作用沿墙高的分布、弱粘性土地震土压力、和挡墙体系考虑水的作用是挡土墙抗震研究中的三个重要问题。首先对其研究进展进行了简要总结。然后针对近年来大量涌现的新型、异型、轻型挡土墙的抗震研究现状进行了评述，包括现场地震调查、振动台及离心机试验、悬臂L型挡土墙、锚杆式及土钉式挡土墙、加筋土挡土墙和地下室挡墙。最后，指出了存在的问题和提出今后的研究方向。     

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.     

Centrifuge modelling of flexible retaining walls subjected to dynamic loading

This paper outlines the results of an experimental program carried out on centrifuge models of cantilevered and propped retaining walls embedded in saturated sand. The main aim of the paper is to investigate the dynamic response of these structures when the foundation soil is saturated by measuring the accelerations and pore pressures in the soil, displacements and bending moment of the walls. A comparison among tests with different geometrical configurations and relative density of the soil is presented. The centrifuge models were subjected to dynamic loading in the form of sinusoidal accelerations applied at the base of the models. This paper also presents data from pressure sensors used to measure total earth pressure on the walls. Furthermore, these results are compared with previous dynamic centrifuge tests on flexible retaining walls in dry sand.