Numerical simulation of geosynthetic-reinforced soil walls under seismic shaking

This paper presents the results of numerical simulation of three full-scale geosynthetic-reinforced soil walls that were seismically loaded by a shaking table. Material model parameters were determined from the available laboratory data. In particular, the backfill was simulated with a cap model with parameters dependent of stress level. Hardening parameters of cap model were determined from hyperbolic relation derived from the relevant hydrostatic compression tests. A discussion on the calibration of modeling parameters is presented. Responses compared include (a) maximum wall displacement, (b) maximum backfill settlement, (c) maximum lateral earth pressure, (d) maximum bearing pressure, (e) maximum reinforcement tensile load, (f) absolute maximum acceleration in reinforced soil zone, and (g) absolute maximum acceleration in retained soil zone. Qualities of simulations were evaluated and are discussed. It was found that not all the calculated results agree well with the measured data. However, strong inference or high confidence is anticipated for the closely matched responses such as lateral earth pressure and horizontal displacement utilizing the calibrated model described herein. As indicated by the calculated results, seismic wall displacement decreases with decreasing reinforcement spacing. Factors responsible for comparison discrepancy are discussed. Variability within the measured data is thought to have contributed to some of the comparison discrepancies.     

Upper bound seismic limit analysis of geosynthetic-reinforced unsaturated soil walls

The assessment of the internal stability of geosynthetic-reinforced earth retaining walls has historically been investigated in previous studies assuming dry backfills. However, the majority of the failures of these structures are caused by the water presence. The studies including the water presence in the backfill are scarce and often consider saturated backfills. In reality, most soils are unsaturated in nature and the matric suction plays an important role in the wall's stability. This paper investigates the internal seismic stability of geosynthetic-reinforced unsaturated earth retaining walls. The groundwater level can be located at any reinforced backfill depth. Several nonlinear equations relating the unsaturated soil shear strength to the matric suction and different backfill type of soils are considered in this study. The log-spiral failure mechanism generated by the point-to-point method is considered. The upper-bound theorem of the limit analysis is used to evaluate the strength required to maintain the reinforced soil walls stability and the seismic loading are represented by the pseudo-dynamic approach. A parametric study showed that the required reinforcement strength is influenced by several parameters such as the soil friction angle, the horizontal seismic coefficient, the water table level, the matric suction distribution as well as the soil types and the unsaturated soils shear strength.     

Three-dimensional finite element analysis of geosynthetic-reinforced soil walls with turning corners

The paper presents in-depth three-dimensional finite element analyses investigating geosynthetic-reinforced soil walls with turning corners. Validation of the 3D numerical procedure was first performed via comparisons between the simulated and reported results of a benchmark physical modeling built at the Royal Military College of Canada. GRS walls with corners of 90°, 105°, 120°, 135°, 150°, and 180° were simulated adopting the National Concrete Masonry Association guidelines. The behaviors of the GRS walls with corners, including the lateral facing displacement, maximum reinforcement load, factor of safety, potential failure surface, vertical separation of facing blocks, and types of corners were carefully evaluated. Our comprehensive results show (i) minimum lateral displacement occurs at the corner; (ii) lower strength of reinforcements are required at the corner; (iii) higher corner angles lead to lower stability; (iv) potential failure surface forms earlier at the end walls; (v) deeper potential failure surfaces are found at the corners; (vi) larger numbers of vertical separations are found at walls with smaller corner angles. The paper highlighted the salient influence of the corners on the behaviors of GRS walls and indicated that a 3D analysis could reflect the required reinforcement length and the irregular formation of the potential failure surfaces.     

Study on seismic stability and performance of reinforced soil walls using shaking table tests

The paper reports a 1 g shaking table test that was carried out on a reinforced soil wall with an objective to study the acceleration amplification in the backfill, and phase differences between dynamic responses of the reinforced and retained zones. Results of the study show that including the observed larger acceleration amplification in the upper half of the wall, and the phase difference between maximum lateral earth pressure and inertial load in the backfill in the analysis would lead to more accurate predictions of: (1) the wall response relative to predicted reinforcement load, (2) elevations of line of action for both the inertial and lateral earth forces in the backfill, and (3) wall deformations, as compared to pseudo-static methods of analysis.     

地震作用下模块式面板土工合成材料加筋土挡墙的内部稳定分析

由于造价低廉,性能优良且外表美观,模块式面板土工合成材料加筋土挡墙在我国交通及城建等领域有着广泛的应用前景。大量的工程实践证明,土工合成材料加筋土挡墙的抗震性能良好,但仍有必要进行合理的抗震设计,而内部稳定校核是加筋土挡墙抗震设计的一个重要环节,它一定程度上决定了高烈度地震区加筋土挡墙的配筋方式及配筋密度。应用非线性动力有限元法分析不同加筋长度、加筋间距及不同地震作用下模块式土工合成材料加筋土挡墙在地震作用下的内部稳定,研究了筋材蠕变对加筋土挡墙动力内部稳定的影响,并将有限元分析的结果与国外规范建议的内部稳定校核结果进行比较。研究结果表明,在正常配筋密度条件下,各层筋材最大内力的位置与规范建议的位置有一定的区别,墙体下部更加远离面板;且筋材的最大内力沿高度的分布与该规范计算结果差别较大;而筋材蠕变使筋材的内力出现重分布。     

3D effects of turning corner on stability of geosynthetic-reinforced soil structures

Current design procedures of Geosynthetic-Reinforced Soil Structures (GRSS's) are for walls/slopes with long straight alignments. When two GRSS segments intersect, an abrupt change in the alignment forms a turning corner. Experience indicate potential instability problems occurring at corners. The purpose of this study is to explore the effects of turning corner on the stability of reinforced slopes. Three-dimensional (3D) slope stability analysis, based on limit equilibrium, resulted in the maximum tensile force of reinforcement. Parametric studies required numerous computations considering various geometrical parameters and material properties. The computed results produced efficient practical format of stability charts. For long-term stability of reinforced slopes with turning corner, the influences of pore water pressure and seismic loading are also considered. Turning corner can improve the stability of reinforced slopes by virtue of inclusion of end effects. However, localized increase of pore water pressure or directional seismic amplification may decrease locally thus stability requiring strength of reinforcement larger than in two-dimensional (2D) plane-strain. While using 2D analysis for non-localized conditions may require stronger reinforcement, it also requires shorter reinforcement than in 3D analysis; i.e., 2D analysis may be unconservative in terms of reinforcement length.     

Numerical evaluation of secondary reinforcement effect on geosynthetic-reinforced retaining walls

A finite difference method was employed to evaluate the effect of secondary reinforcement on the performance of Geosynthetic-Reinforced Retaining (GRR) walls. The two-dimensional numerical models used a Cap-Yield soil constitutive model to represent the behavior of backfill. The numerical model was first calibrated and verified by the measured results from a full-scale field test. A parametric study was then performed to investigate the effects of secondary reinforcement length, secondary reinforcement stiffness, secondary reinforcement connection, and secondary reinforcement layout. The numerical results show that an increase in secondary reinforcement length and stiffness can reduce the deflection of the GRR wall and the maximum tensile stress of primary reinforcement. The mechanical connection of secondary reinforcement can also reduce the wall facing deflection and result in relatively small maximum tensile stress and connection stress in the primary reinforcement as compared with no connection to the secondary reinforcement. In addition, a wall with fewer but longer secondary reinforcement layers at certain elevations had relatively smaller wall facing deflections than the baseline case. This comparison demonstrates that more optimal layout of secondary reinforcement exists that could further reduce the maximum wall facing deflections and create a better performing wall while the same or less amount of geosynthetic reinforcement material is used.     

Behavior of cantilever and geosynthetic-reinforced walls on deformable foundations

A series of plane-strain model tests was performed to investigate the behavior of cantilever soil retaining walls (CWs) and geosynthetic-reinforced soil retaining walls with a rigid facing (GRS-RWs) placed on non-deformable and deformable foundations with various subgrade reaction moduli (k_v). The walls were designed to have configurations similar to those used in practice, with similar controlling safety factors against sliding. Screw jacks and springs were used to simulate undeformable and deformable grounds, respectively, with various maximum foundation settlements of S_max ≒ 0, 2.5, 5, and 10% of the backfill height (H). Test results show that the GRS-RW has better settlement-tolerating performances, in terms of the tilting angle (θ), the horizontal displacement (D_h), and the settlement of the crest of the backfill (D_v1), than those of the CW. For both CWs and GRS-BWs, the worst scenario of the wall performance, in terms of D_h, θ and D_v1, occurred at a moderate foundation settlement of S_max/H ≒ 5% (or k_v = 1.8 kPa/mm), rather than at a greater foundation settlement of S_max/H ≒ 10%, which facilitates a tilting-backward displacement mode. Experimental results also indicate that local lateral pressure coefficients against facing (K_f,z) for CWs may reach the at-rest (or K_o) state at the central portion; values of K_f,z may reach the passive (or K_p) state at the lower portion of the wall. In the case of CWs, the measured values of local and global lateral pressure coefficients (K_f,z and K_f) tend to increase with increasing maximum foundation settlement. This is not the case for GRS-RWs, which exhibited a relatively settlement-independent response, in terms of K_f and K_f,z, against facing. To develop relevant limit-equilibrium-based design methods for CWs and GRS-RWs placed on deformable foundations, knowledge of lateral pressure coefficients associated with various displacement and tilting induced by the foundation settlement are required.     

Limit state design framework for geosynthetic-reinforced soil structures

Conventional design of geosynthetic-reinforced soil structures is divided into two categories, walls and slopes, based on the batter of its facing system. Internal stability, characterized as sufficient reinforcement anchoring and strength, is performed using earth pressure-based design criteria for reinforced walls while reinforced slopes are founded on limit equilibrium (LE) slope stability analyses. LE analyses are also used to assess the global or compound stability of both types of structures, accounting for the geometry of the reinforced, retained and foundation soils. The application of LE-based methods typically results in determination of a slip surface corresponding to the lowest attained Safety Factor (SF), known as the Factor of Safety (Fs); however, it yields little information about reinforcement loading or connection load. In this study, use of the analyzed spatial distribution of SF known as a Safety Map, is modified to attain a prescribed constant Fs at any location in the reinforced soil mass. This modified framework, implemented through an iterative, top-down procedure of LE slope stability analyses originating from the crest of a reinforced structure and exiting at progressively lower elevations on the facing, enables the determination of a Tension Map that illustrates the required distribution of reinforcement tension to attain a prescribed limit state of equilibrium. This tension map is directly constrained by a pullout capacity envelope at both the rear and front of each reinforcement layer, providing a unified, LE-based approach towards assessing an optimal selection of mutually dependent strength and layout of the reinforcement. To illustrate the utility of the Limit State framework, a series of instructive examples are presented. The results demonstrate the effects of facing elements, closely-spaced reinforcements, secondary reinforcement layers, and is compared to conventional design approaches.     

Effects of soil non-linearity on the seismic response of restrained retaining walls

Retaining structures characterised by high rigidity and various kinematic constraints, such as bridge abutments and basement walls, do not permit limit-equilibrium conditions to be developed. Therefore, according to contemporary norms and geotechnical design practice worldwide, they are most frequently designed utilising the elasticity-based methods, which usually lead to substantially increased dynamic earth pressures. The present paper aims to examine how and to what extent the potentially developed non-linearity of the retained soil may affect: (a) the dynamic distress of a rigid fixed-base retaining wall, and (b) the seismic response of the retained soil layer. For this purpose, a parametric study is conducted which is based on two-dimensional dynamic finite-element analyses using various idealised or real seismic excitations scaled to several intensity levels. Soil non-linearity is realistically taken into account via the commonly used equivalent-linear approach. The results of the present study demonstrate that potential non-linearity of a soil layer retained by a rigid fixed-base wall alters the soil amplification pattern behind the wall and leads to dynamic earth pressures usually lower than those proposed by seismic norms.     

Overall stability of geosynthetic-reinforced embankments on soft soils

Overall stability of geosynthetic-reinforced embankments on soft soils is analysed using two different methodologies: application of a numerical model based on the finite element method; use of a limit equilibrium method. These two methodologies are described and also applied on three geosynthetic-reinforced embankments on soft soils. One of the cases is a case history constructed up to failure. Considering the analysis of the results, some conclusions are formulated on the limit equilibrium method accuracy, namely regarding the critical slip surface, overall safety factor and overturning and resisting moments.     

横向地震作用下土工合成材料加筋土挡墙筋材拉力分析

土工合成材料加筋土挡墙具备优良的抗震性能,但是,国内外现行的加筋土挡墙筋材动拉力计算方法存在地震动参数选用不尽合理的问题,一方面可能带来结构安全隐患,另一方面也造成了工程界的疑虑.基于此,在前期工作的基础上应用非线性动力有限元法分析了高加筋土挡墙在不同地震激励作用下的地震响应,重点讨论了强震作用下筋材拉力的影响因素.分...     

Performance of geosynthetic-reinforced soil foundations across a normal fault

This paper presents a series of model tests on geosynthetic-reinforced soil (GRS) foundations across a normal fault. The aim was to evaluate the performance of reinforced foundations as a mitigation measure for surface faulting hazards. Experimental tests modeled a 3-m thick foundation in prototype subjected to a fault displacement up to 90 cm. Test variables included the number of reinforcement layers, reinforcement stiffness and location, and foundation height. Digital image analysis techniques were applied to determine the ground settlement profile, angular distortion, shear rupture propagation, and mobilized reinforcement tensile strain at various magnitudes of fault offset. Test results revealed that compared with the unreinforced foundation, reinforcement inclusion could effectively prevent the shear rupture propagating from the bedrock fault to the ground surface. It also spread the differential settlement to a wider influential zone, resulting in an average reduction of 60% in the fault-induced angular distortion at the ground surface. The maximum angular distortion decreased as the foundation height, number of reinforcement layers, and reinforcement stiffness increased. Relationships between the maximum angular distortion and maximum mobilized reinforcement tensile strain with fault displacement were therefore established. Based on the findings from this study, design suggestions and implications are discussed.     

Earth pressure coefficients for design of geosynthetic reinforced soil structures

There are several methods proposed in the last two decades that can be used to design geosynthetic reinforced soil retaining walls and slopes. The majority of them are based on limit equilibrium considerations, assuming bi-linear or logarithmic spiral failure surfaces. Based on these failure mechanisms, design charts have been presented by several authors. However, the use of design charts is less and less frequent. The paper presents results from a computer program, based on limit equilibrium analyses, able to quantify earth pressure coefficients for the internal design of geosynthetic reinforced soil structures under static and seismic loading conditions. Failure mechanisms are briefly presented. Earth pressure coefficients calculated by the developed program are compared with values published in the bibliography. The effect of seismic loading on the reinforcement required force is also presented. To avoid the use of design charts and based on the obtained results, approximate equations for earth pressure coefficients estimation are proposed. The performed analyses show that the failure mechanism and the assumptions made have influence on the reinforcement required strength. The increase of reinforcement required strength induced by the seismic loading, when compared to the required strength in static conditions, grows with the backfill internal friction angle. The effects of the vertical component of seismic loading are not very significant.     

两种加筋土挡墙的动力特性比较及抗震设计建议

为分析比较条带式和包裹式加筋土挡墙的地震动力响应特征,开展了两种加筋土挡墙模型的大型振动台试验.结合震害调查的结果,发现砌块式加筋土挡墙在地震作用下的破坏模式主要表现为局部砌块的松动变形,很少会出现整体垮塌的情况.相比条带式加筋土挡墙,包裹式加筋土挡墙在地震作用下产生的变形量要小.在相同地震量级作用下,包裹式加筋土挡墙相应部位的水平加速度放大系数要小于条带式加筋土挡墙,但峰值动土压力却要比条带式加筋土挡墙大,这是因为包裹式加筋土挡墙面板在地震作用下的变形量小,对土体的约束能力强所致.因此,在抗震设防区,特别是是高地震烈度区进行加筋土挡墙的选型时,包裹式加筋土挡墙应作为一种优选结构.分析认为加筋土挡墙的抗震设计除了要进行整体稳定性的验算外,还应注重墙体变形量的控制,加筋土挡墙在地震作用下的最大变形量应小于允许的变形量.为维持线路的正常使用,加筋土挡墙的变形指数应控制在4%以内.若验算得到的变形量超出允许值,可采取增大墙后填土的压实度和增加拉筋长度,以及加厚墙体和降低墙体坡率等措施.     

Reinforcement load and deformation mode of geosynthetic-reinforced soil walls subject to seismic loading during service life

A Finite Element procedure was used to investigate the reinforcement load and the deformation mode for geosynthetic-reinforced soil (GRS) walls subject to seismic loading during their service life, focusing on those with marginal backfill soils. Marginal backfill soils are hereby defined as filled materials containing cohesive fines with plasticity index (PI) >6, which may exhibit substantial creep under constant static loading before subjected to earthquake. It was found that under strong seismic loading reinforced soil walls with marginal backfills exhibited a distinctive “two-wedge” deformation mode. The surface of maximum reinforcement load was the combined effect of the internal potential failure surface and the outer surface that extended into the retained earth. In the range investigated, which is believed to cover general backfill soils and geosynthetic reinforcements, the creep rates of soils and reinforcements had small influence on the reinforcement load and the “two-wedge” deformation mode, but reinforcement stiffness played a critical role on these two responses of GRS walls. It was also found that the “two-wedge” deformation mode could be restricted if sufficiently long reinforcement was used. The study shows that it is rational to investigate the reinforcement load of reinforced soil walls subject to seismic loading without considering the previous long-term creep.     

重力式加筋土挡墙设计参数的影响分析

重力式加筋土挡墙是将传统重力挡墙和普通加筋土挡墙相结合的一种新型挡墙。采用FLAC程序,模拟先浇筑重力挡墙,后填筑墙后加筋土的施工顺序,在已完成一个典型重力式加筋土挡墙从墙后填土到墙顶和墙顶堆载完成以后两个阶段数值模拟,掌握其工作性状的基础上,进一步对重力挡墙刚度、墙后填土性质、加筋土工格栅性质、加筋长度和间距等主要影响因素进行数值模拟分析,为设计参数的合理选择提供依据。     

对我国钢筋混凝土结构抗震设计的一些理解

本文阐述了抗震设计的基本思路,对我国抗震设计的基点和能力设计法进行了分析,并以框架-剪力墙结构为例说明设计规范的具体做法。     

地震荷载下重力式挡土墙的抗倾覆稳定性分析

基于平面滑裂面假设,采用水平层分析法推导了地震荷载作用下的主动土压力计算公式,并给出了地震土压力沿墙高的分布及土压力合力作用点的位置。在此基础上提出了重力式挡土墙的抗倾覆稳定性验算公式,为实际工程中挡土墙抗震设计提供了理论依据。稳定性分析结果表明,随着水平地震荷载的增大,抗倾覆稳定性显著降低。     

Internal stability analysis of geocell-reinforced slopes subjected to seismic loading based on pseudo-static approach

Seismic stability analysis of geocell-reinforced slopes (GRSs), considering shear and moment strength in addition to tensile resistance for geocells, is a novel topic for which scarce studies are found in the literature. Despite few available studies, an analytical approach is presented in this study to investigate the seismic internal stability of GRSs, employing the pseudo-static method based on a limit state approach. Results are given in terms of conventional design charts representing the required total strength and critical length of geocells. The results show that with increasing the horizontal seismic acceleration (k_h), the internal stability degenerates since the required strength and critical length of geocells increase. For GRSs subjected to greater k_h, the effect of increasing the vertical seismic component (k_v) on increasing the required strength and length of geocells is more considerable than those subjected to lower k_h values. Parametric analyses are conducted, under various seismic conditions, to investigate the effect of increasing the geocell height and raising the number of geocell layers, leading to the reduction in the required strength and length of geocells. Such effects are found to be dependent on the parameters such as the intensity of seismic excitation, material properties and geometry of slope.