Required unfactored strength of geosynthetics in reinforced 3D slopes

The design of reinforced earth structures uses idealized two-dimensional (2D) geometry – classifying as a plane-strain analysis. This 2D idealization greatly simplifies design by ignoring stabilizing effects posed by three-dimensional (3D) characteristics. While the outcome of this 2D idealization is conservative in terms of required reinforcement strength, ignoring 3D end effects in back-calculations of experimental and field data may overestimate the contribution of the reinforcement to stability thus possibly leading to unconservative learned lessons related to design. The objective of this study is to explore 3D effects on the required strength of reinforcement in geosynthetic-reinforced earth structures (GRESs) using a modified 3D limit equilibrium (LE) slope stability analysis. To determine the stability of GRESs, a rotational, 3D failure mechanism, derived from variational LE analysis, is applied using a log-spiral surface generalized to 3D conditions. In order to determine the long-term strength of geosynthetics required to ensure sufficient internal stability, the moment equilibrium approach is applied and its respective equations solved. In order to conveniently assess the end effects on the required total strength of reinforcement and the volume of failing mass considering the feasible length of potential failure, a series of design charts are presented. These charts can also be useful in forensic studies when back-calculating the in-situ mobilized strength of the geosynthetic for 3D failures. The impact of seismicity and the assumed function of forces distributed amongst the reinforcement layers were investigated to highlight their importance. To keep this study focused on 3D end effects, this study is limited to a simple 3D GRES problem; however, extending the present framework to deal with complex homogenous problems is straightforward.     

Internal stability analysis of reinforced convex highway embankments considering seismic loading

The seismic internal stability of reinforced, convex embankments that are three-dimensional in nature is analyzed. A limit equilibrium based three-dimensional rotational failure mechanism is adopted to calculate the required reinforcement strength to maintain the stability of convex embankments. The results are presented in the form of stability charts and the effects of various parameters on the three-dimensional solution are investigated. The calculation of the required strength and length of reinforcement is demonstrated by two examples using an approach consistent with AASHTO (2012). Comparing the strengths obtained under two and three-dimensional conditions, the results show that the two-dimensional results are more conservative with respect to the strength of reinforcement, but could be unconservative considering the required length of reinforcement, especially for reinforced convex embankments with gentle turning angles. The influence of seismicity causes greater three-dimensional effects when the reinforced convex embankment is vertical, but less so when the slope inclination is gentle.     

Seismic analysis of geosynthetic-reinforced retaining wall in cohesive soils

Although a cohesionless backfill is recommended for geosynthetic reinforced earth retaining walls, cohesive soil have been widely used in many regions across the globe for economic reasons. This type of backfill exposes the soil to the crack formation that leads to reduce the stability of the system. In this paper, to investigate the internal seismic stability of reinforced earth retaining walls with cracks, the discretization method combined with the upper bound theorem of limit analysis are used. The potential failure mechanism is generated using the point-to-point method. Two types of cracks are considered, a pre-existing crack and a crack formation as a part of the failure mechanism. The use of the discretization method allows the consideration of the vertical spatial variability of the soil properties. A pseudo-dynamic approach is implemented which allows the account of the dynamic characteristics of the ground shaking. The presented method is validated using the conventional limit analysis results of an existing study conducted under static conditions. Once the proposed technique to consider the cracks is validated, a parametric study is conducted to highlight the key parameters effects on the lower bound of the required reinforcement strength.     

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.     

Corner reinforced slopes: Required strength and length of reinforcement based on internal stability

This paper develops an analysis procedure for turning corner in Geosynthetic-Reinforced Soil Structures (GRSS's). The procedure includes the calculations of the required strength and length of the reinforcement for internal stability. The calculations are based on the variational limit equilibrium analysis of three-dimensional (3D) stability of slopes. Seismic effects are also considered using the pseudo-static method. Results are presented in a condensed form of design charts, providing a simple tool to determine the required tensile strength and embedment length of the reinforcement. Two examples are given to demonstrate the use of the design charts. Compared with the conventional design based on plane-strain analysis, the presented design procedure yields longer reinforcement for the 3D internal stability of the corners. Generally, 3D design requires longer reinforcement than 2D as the seismic acceleration increases. The trend of obtained result is in good agreement with performance observations related to corners reported in commentary of AASHTO.     

加筋土坡动态稳定性拟静力分析

 加筋土工结构被广泛采用的原因不仅是其具有良好的静力性能,且也在于出色的动力稳定性能,现有研究较少考虑竖向地震效应对加筋土坡动态稳定性的影响。基于塑性极限分析上限理论,假定不同的破坏面,同时考虑水平和竖向地震影响并结合不同加筋模式,采用拟静力分析方法推导一定加筋强度条件下的边坡临界高度和一定边坡高度条件下的临界加筋强度计算公式,并对所导公式采用序列二次规划法进行了优化计算,数值计算与分析表明：简单静态和动态条件下,该结果与现有研究成果有较好的一致性,可以证明该方法的正确性;水平和竖向地震、岩土材料强度特性、边坡倾斜度均对加筋土坡的动态稳定性有重要影响,特别当边坡较陡,岩土填筑材料质量较差和地震影响强度较大时,忽视竖向地震影响将会导致设计偏于不安全;最后针对工程实际,提出相应的工程建议。     

Seismic effects on reinforcement load and lateral deformation of geosynthetic-reinforced soil walls

Current design methods for the internal stability of geosynthetic-reinforced soil (GRS) walls postulate seismic forces as inertial forces, leading to pseudo-static analyses based on active earth pressure theory, which yields unconservative reinforcement loads required for seismic stability. Most seismic analyses are limited to the determination of maximum reinforcement strength. This study aimed to calculate the distribution of the reinforcement load and connection strength required for each layer of the seismic GRS wall. Using the top-down procedure involves all of the possible failure surfaces for the seismic analyses of the GRS wall and then obtains the reinforcement load distribution for the limit state. The distributions are used to determine the required connection strength and to approximately assess the facing lateral deformation. For sufficient pullout resistance to be provided by each reinforcement, the maximum required tensile resistance is identical to the results based on the Mononobe–Okabe method. However, short reinforcement results in greater tensile resistances in the mid and lower layers as evinced by compound failure frequently occurring in GRS walls during an earthquake. Parametric studies involving backfill friction angle, reinforcement length, vertical seismic acceleration, and secondary reinforcement are conducted to investigate seismic impacts on the stability and lateral deformation of GRS walls.     

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.     

Discussion on ‘Required unfactored geosynthetic strength of three-dimensional reinforced soil structures comprised of cohesive backfills’ by Y. Chen et al., (2018) doi.org/10.1016/j.geotexmem.2018.08.004

The authors of the paper “Required unfactored geosynthetic strength of three-dimensional reinforced soil structures comprised of cohesive backfills” (Chen et al., 2018) have presented an interesting study in which limit analysis (LA) upper bound solutions for 3D failure mechanisms in reinforced cohesive backfills are provided for the first time. The discusser would like to comment on four issues related to the paper: (1) no consideration for the onset of cracks in the slopes (2) use of the presented solutions for forensic analyses (3) underestimation of the level of required reinforcement (4) unsuitability of the presented solutions for design purposes.     

Estimation of seismic active earth pressure on reinforced retaining wall using lower bound limit analysis and modified pseudo-dynamic method

Present study estimates seismic active earth pressure on the reinforced retaining wall by combining the lower bound finite element limit analysis and the modified Pseudo-dynamic method. A series of parametric analyses are performed by varying seismic acceleration coefficient, time period of seismic loading, soil friction and dilation angles, reinforcement spacing, length of reinforcement, soil-reinforcement interface, damping ratio of soil, soil-wall interface, wall inclination, and ground inclination. Maximum active earth pressure is exerted when natural time period of reinforced soil matches with the time period of an earthquake. Reinforcement is found to be effective in terms of reducing active earth pressure significantly on the wall subjected to seismic loading. Effectiveness of reinforcement depends upon two factors, namely vertical spacing and soil-reinforcement interface friction angle. For relatively smaller reinforcement spacing, soil-reinforcement behaves like a composite block, which helps to constraint stresses within a small area behind the wall. Maximum tensile resistance is developed when fully rough interface condition is assumed between soil and reinforcement layer. Failure patterns are provided to understand the behaviour of reinforced retaining wall under different time of seismic loading.     

Numerical analysis of the behaviour of mechanically stabilized earth walls reinforced with different types of strips

A mechanically stabilized earth (MSE) wall behaves as a flexible coherent block able to sustain significant loading and deformation due to the interaction between the backfill material and the reinforcement elements. The internal behaviour of a reinforced soil mass depends on a number of factors, including the soil, the reinforcement and the soil/structure interaction and represents a complex interaction sol/structure problem. The use of parameters determined from experimental studies should allow more accurate modelling of the behaviour of the MSE structures.In this article, a reference MSE wall is modelled from two points of view: serviceability limit state “SLS” and ultimate limit state “ULS”. The construction of the wall is simulated in several stages and the soil/interface parameters are back analysed from pullout tests. An extensive parametric study is set up and permits to highlight the influence of the soil, the reinforcement and the soil/structure parameters. The behaviour of MSE walls with several geosynthetic straps is compared with the metallic one. Several constitutive models with an increasing complexity have been used and compared.The results obtained from stress-deformation analyses are presented and compared. The use of geosynthetic straps induces more deformation of the wall but a higher safety factor. To design theses walls the important parameters are: the soil friction, the cohesion, the interface shear stiffness and the strip elastic modulus.It is shown that for wall construction that involves static loading conditions, the modified Duncan-Chang model is a good compromise but induces slightly lower strip tensile forces due to the fact that it do not take into account of dilatancy before failure.     

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...     

Simplified Procedure to Evaluate Earthquake-Induced Residual Displacement of Geosynthetic Reinforced Soil Retaining Walls

Based on a series of shaking table model tests, it was found that the effects of 1) subsoil and backfill deformation, 2) failure plane formation in backfill, and 3) pullout resistance mobilized by the reinforcements on the seismic behaviors of the geosynthetic reinforced soil retaining walls (GRS walls) were significant. These effects cannot be taken into account in the conventional pseudo-static based limit equilibrium analyses or Newmark's rigid sliding block analogy, which are usually adopted as the seismic design procedure. Therefore, this study attempts to develop a simplified procedure to evaluate earthquake-induced residual displacement of GRS walls by reflecting the knowledge on the seismic behaviors of GRS walls obtained from the shaking table model tests. In the proposed method, 1) the deformation characteristics of subsoil and backfill are modeled based on the model test results and 2) the effect of failure plane formation is considered by using residual soil strength after the failure plane formation while the peak soil strength is used before the failure plane formation, and 3) the effect of the pullout resistance mobilized by the reinforcement is also introduced by evaluating the pullout resistance based on the results from the pullout tests of the reinforcements. By using the proposed method, simulations were performed on the shaking table model test results conducted under a wide variety of testing conditions and good agreements between the calculated and measured displacements were observed.     

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.     

Limited reinforced space in segmental retaining walls

Current design of geosynthetic reinforced segmental retaining walls considers an a priori limitless length for reinforcement installation. Such length is typically 0.5–0.7 times the height of the wall. However, often there are constraints on such space; e.g., bedrock formation located at a small distance behind the facing. The objective of this note is to introduce a procedure for assessing the required long-term strength of the reinforcement while considering its limited length. Predictions by a conventional slope stability analysis were first checked against a continuum-mechanics based numerical analysis. Upon obtaining good agreement, a design chart was developed. The chart enables the determination of the reduction in the lateral earth pressure coefficient due to the constrained space. The revised earth pressure coefficient can be used with current analytical methods to account for the limited space. The results appear to be valid for conventional walls retaining a limited volume of soil. Comparison with limited experimental results for unreinforced backfill shows reasonably good agreement.     

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.     

阻滑桩加固土坡稳定性分析与桩基的简化设计

基于极限分析上限定理与土的抗剪强度折减系数概念,建立了土坡稳定的极限平衡状态方程,以此确定土坡稳定的安全系数及相应的潜在破坏模式。通过针对典型算例所进行的对比计算与分析,验证了该方法的可靠性。进而针对潜在失稳土坡,建立了阻滑桩加固土坡的极限平衡状态方程,将桩侧有效土压力作为目标函数,运用数学规划方法确定了极限平衡状态时的临界桩侧有效土压力,以此进行土坡预加固中阻滑桩的简化设计。最后,根据最大、最小值原则,探讨了阻滑桩的最优桩位问题,并通过变动参数比较计算对影响加固力的有关因素进行了分析。     

Analysis of back-to-back mechanically stabilized earth walls

Back-to-back Mechanically Stabilized Earth (MSE) walls are commonly used for embankments approaching bridges. However, available design guidelines for this wall system are limited. The distance between two opposing walls is a key parameter used for determining the analysis methods in FHWA Guidelines. Two extreme cases are identified: (1) reinforcements from both sides meet in the middle or overlap, and (2) the walls are far apart, independent of each other. However, existing design methodologies do not provide a clear and justified answer how the required tensile strength of reinforcement and the external stability change with respect to the distance of the back-to-back walls. The focus of this paper is to investigate the effect of the wall width to height ratio on internal and external stability of MSE walls under static conditions. Finite difference method incorporated in the FLAC software and limit equilibrium method (i.e., the Bishop simplified method) in the ReSSA software were used for this analysis. Parametric studies were carried out by varying two important parameters, i.e., the wall width to height ratio and the quality of backfill material, to investigate their effects on the critical failure surface, the required tensile strength of reinforcement, and the lateral earth pressure behind the reinforced zone. The effect of the connection of reinforcements in the middle, when back-to-back walls are close, was also investigated.     

考虑三维空间效应的砌块土坡侧向土压力分析

在支挡结构稳定性设计中,基于侧向土压力系数的设计方法简单易用,一直被广泛用于实际工程中。已有侧向土压力系数主要在平面应变分析方法下计算获得,忽略了三维空间效应的影响。基于三维边坡稳定分析方法,采用变分法获得安全系数极值下对应的三维破坏机制,建立考虑三维效应的砌块土坡侧向土压力计算方法,从而揭示三维效应对砌块土坡侧向土压力大小的影响规律。提出的方法还考虑了砌块与土摩擦作用力和水平地震力的影响。给定参数值,通过优化计算获得了不同长高比下的三维砌块土坡水平土压力系数,以图的形式给出便于使用。从计算结果可以发现,在地震作用下,三维空间效应对侧向土压力的影响显著,特别是对于垂直的支挡结构。最后结合算例,通过与传统的平面应变下侧向土压力结果进行对比分析,显示了考虑三维效应的土压力系数对支挡结构稳定性设计的重要性。     

Residual Deformation of Geosynthetic-Reinforced Sand in Plane Strain Compression Affected by Viscous Properties of Geosynthetic Reinforcement

A series of plane strain compression (PSC) tests were performed on large sand specimens unreinforced or reinforced with prototype geosynthetic reinforcements, either of two geogrid types and one geocomposite type. Local tensile strains in the reinforcement were measured by using two types of strain gauges. Sustained loading (SL) under fixed boundary stress conditions and cyclic loading (CL) tests were performed during otherwise monotonic loading at a constant strain rate to evaluate the development of creep deformation by SL and residual deformation by CL of geosynthetic-reinforced sand and also residual strains in the reinforcement by these loading histories. It is shown that the creep deformation of geosynthetic-reinforced sand develops due to the viscous properties of both sand and geosynthetic reinforcement, while the residual deformation of geosynthetic-reinforced sand during CL (defined at the peak stress state during CL) consists of two components: i) the one by the viscous properties of sand and reinforcement; and ii) the other by rate-independent cyclic loading effects with sand. The development of residual deformation of geosynthetic-reinforced sand by SL and CL histories had no negative effects on the subsequent stress-strain behaviour and the compressive strength was maintained as the original value or even became larger by such SL and CL histories. The local tensile strains in the geosynthetic reinforcement arranged in the sand specimen subjected to SL decreased noticeably with time, due mainly to lateral compressive creep strains in sand during SL of geosynthetic-reinforced sand. This result indicates that, with geosynthetic-reinforced soil structures designed to have a sufficiently high safety factor under static loading conditions because of seismic design, it is overly conservative to assume that the tensile load in the geosynthetic reinforcement is maintained constant for long life time. Moreover, during CL of geosynthetic-reinforced sand, the residual tensile strains in the geosynthetic reinforcement did not increase like global strains in the geosynthetic-reinforced sand that increased significantly during CL. These different trends of behaviour were also due to the creep compressive strains in the lateral direction of sand that developed during CL of geosynthetic-reinforced sand.