Analyzing the influence of facing batter on reinforcement loads of reinforced soil walls under working stress conditions

The level of reinforcement loads in a reinforced soil retaining wall is important to its satisfactory operation under working stress conditions since it basically determines the wall deformation. Consequently, proper estimation of the reinforcement load is a necessary step in the service limit-state design of this type of earth retaining structures. In this study, a force equilibrium approach is proposed to quantify the influence of facing batter on the reinforcement loads of reinforced soil walls under working stress conditions. The approach is then combined with a nonlinear elastic approach for GRS walls without batter to estimate the reinforcement loads neglecting toe restraint. The approximate average mobilized soil strength in the retaining wall is employed in the force equilibrium analysis. The predictions of reinforcement loads by the proposed method were compared to the experimental results from four large-scale tests. It is shown that the proposed semianalytical approach has the capacity to reproduce the reinforcement loads with acceptable accuracy. Some remaining issues are also pinpointed.     

不同墙趾约束条件下模块式加筋土挡墙离心模型试验

开展了墙趾正常约束、仅对模块–基座界面作光滑处理、仅对基座–地基界面作光滑处理,以及对基座–地基界面作光滑处理且将基座前方土体挖除这4组不同墙趾约束条件的模块式加筋土挡墙离心模型试验,以研究工作应力下墙趾约束条件对挡墙内部稳定性的影响。研究结果表明,墙趾约束条件对模块式加筋土挡墙内部稳定性影响显著;对模块–基座界面作光滑处理的挡墙,其底层模块沿该界面滑移,挡墙中下部的墙面水平位移和筋材应变明显增大,筋材连接力沿墙高呈三角形分布;对基座–地基界面作光滑处理的挡墙,基座前方地基土仍可给基座提供足够的墙趾约束作用,挡墙内部稳定性同墙趾正常约束情况;对于基座–地基界面作光滑处理后又将基座前方土体挖除这种模拟墙趾受到冲刷的挡墙,其基座沿该界面滑移,挡墙中下部的墙面水平位移和筋材应变显著增大,筋材连接力接近极限状态AASHTO法计算的筋材最大拉力,但挡墙仍能保持稳定;在墙趾可能受到冲刷的极端情况下,挡墙在设计上不应考虑墙趾的约束作用,而对于正常服役状态的挡墙,可采用考虑墙趾约束作用的K-刚度法进行挡墙内部稳定性的计算。     

面板倾角对模块式面板加筋土挡墙筋材内力的影响

土工合成材料加筋土挡墙具有良好的力学性能和优越的经济性等优点,在国内外得到了越来越广泛的应用。然而,众多加筋土挡墙的试验数据表明,对加筋土挡墙受力机理的理论研究是滞后于工程建设实践的。针对筋材内力计算这一重要问题,研究了面板倾角对加筋土挡墙筋材内力的影响。首先,以RMC试验挡墙为原型,验证了数值模拟方法的有效性;然后,利用数值模拟方法,分析了不同工况下,加筋土挡墙内竖向土压力和筋材应变随着面板倾角增大的变化趋势。数值模拟结果表明,筋材内力随着加筋土挡墙面板倾角的增大而降低。在数值研究结果的基础上,从潜在滑动面附近土单元应力状态及滑动楔形体的平衡两个方面分析了面板倾角的作用机理,定位了填土竖向土压力以及面板基底水平摩擦阻力两个影响筋材内力的关键因素。     

Influence of toe restraint conditions on performance of geosynthetic-reinforced soil retaining walls using centrifuge model tests

Current design regulations most often require use of limit equilibrium methods for the internal stability analyses of geosynthetic-reinforced soil (GRS) walls. However, the limit-equilibrium based approaches generally over-predict reinforcement loads for GRS walls when comparing with measured data from full-scale instrumented walls under working stress conditions. Wall toe resistance has an important influence on the performance of GRS walls but is ignored in limit equilibrium-based methods of design. This paper reports centrifuge modelling of GRS walls which have different toe restraint conditions but are otherwise identical. The GRS wall models prepared in this study isolate the influence of wall toe resistance on the performance of walls. Based on measured data from four centrifuge wall model tests, a reduction in wall toe resistance (by reducing the interface shear resistance at the base of the wall facing or removing the soil passive resistance in front of the wall toe or both) induces larger maximum facing deformation and reinforcement strain and load. The results also demonstrate that the wall models with typical toe restraint conditions are most likely operated under working stress conditions while those with poor toe restraint conditions may experience (or be close to reach) a state of limit equilibrium.     

Effects of facing,reinforcement stiffness,toe resistance,and height on reinforced walls

This study numerically investigated the combined effect of reinforcement and facing stiffness, wall height, and toe resistance on the behavior of reinforced soil (RS) walls under working stress conditions. For RS walls with vertical segmental block facing, parametric analyses showed that the combined effect of the facing stiffness, wall height, and toe resistance on the distribution of the maximum reinforcement load with depth may be limited to approximately 4 m above the base of the wall. Furthermore, the shape of the distribution of the reinforcement load may be a function of the combined effect of the wall height, reinforcement stiffness, toe resistance, and facing stiffness. For a given facing stiffness and fixed-base conditions, increasing the height of the wall and reinforcement stiffness may change the distribution shape of the reinforcement load from trapezoidal to the triangular. Additionally, the maximum reinforcement loads calculated using finite element analyses were compared to the values predicted by design methods found in the literature. Some limitations of those design procedures are presented and discussed.     

Measured and predicted loads in steel strip reinforced c−ϕ soil walls in Japan

More than 30,000 steel strip reinforced soil walls have been built in Japan since their introduction in the early 1970s. The current Japanese method of computing tensile loads in the reinforcement strips is based on the Coherent Gravity Method first developed in France more than three decades ago. At that time, the method was calibrated against measured loads from seven instrumented structures based on soil friction angles in the range of 35–46°. In Japan, however, there are many reinforced soil walls that have been built successfully using cohesive-frictional soils with fines contents as high as 35% and lower friction angles. The present paper uses the results of load measurements from 18 instrumented wall sections, reported previously in the literature, and nine instrumented Japanese walls to examine the prediction accuracy of the Coherent Gravity Method described in the Public Works Research Center (2003) guidelines. The current design chart for the coefficients of earth pressure, used to compute tensile reinforcement loads, is empirically adjusted for soil backfills falling into three different friction angle ranges. The new design chart is calibrated to satisfy an average load exceedance level that matches the value adopted when the Coherent Gravity Method was first calibrated.     

Deterministic and probabilistic assessment of margins of safety for internal stability of as-built PET strap reinforced soil walls

The paper demonstrates deterministic and reliability-based assessment of strength limit states (tensile resistance and pullout) and the service limit state for soil failure for mechanically stabilized earth (MSE) walls constructed with polyester (PET) strap reinforcement. The general approach considers the accuracy of the load and resistance models that appear in each limit state equation plus uncertainty in the estimate of nominal load and resistance values at time of design. Reliability index is computed using a closed-form solution that is easily implemented in a spreadsheet. Three PET strap MSE wall case studies are used to demonstrate the reliability-based assessment approach and to compare margins of safety using different load and resistance model combinations. In some walls using the Coherent Gravity Method to compute loads, the recommended nominal factors of safety for tensile strength and pullout limit states were not satisfied. However, reliability analyses showed that the walls satisfy recommended minimum target reliability index values for the limit states investigated, usually by large amounts. The most critical limit state is the soil failure limit state which is used in the Simplified Stiffness Method to keep the reinforced soil zone at working stress conditions assumed for geosynthetic MSE walls under operational conditions.     

Numerical modelling of two full-scale reinforced soil wrapped-face walls

The paper reports the details of numerical models used to predict the performance of two 3.6 m-high well-instrumented wrapped-face walls. The walls were nominally identical except that the reinforcement material in one wall was a steel welded wire mesh and in the other a biaxial polypropylene geogrid. The backfill soil was modelled using both linear and nonlinear elastic-plastic constitutive models. A general hyperbolic (nonlinear) axial load-strain-time model was used for the reinforcement. The numerical results show good agreement with measured performance features for the welded wire mesh wrapped-face wall. Agreement between numerical predictions of facing displacements and maximum reinforcement loads was less accurate for the very flexible geogrid wrapped-face wall. The discrepancies are believed to be related to the unusually flexible wrapped face used in the geogrid wall construction. Numerically predicted and measured maximum reinforcement loads are compared to loads using the AASHTO reinforcement strength-based design approach (Simplified Method) and the Simplified Stiffness Method which is an empirical reinforcement stiffness-based method. The paper provides physical test data that can be used to benchmark other numerical models, highlights lessons learned during the development of the models, and identifies reasonable expectations for numerical model accuracy for models of similar complexity used to simulate the performance of mechanically stabilized earth (MSE) wall structures under operational conditions.     

Numerical evaluation of the effect of foundation on the behaviour of reinforced soil walls

This study numerically investigates the influence of foundation conditions, in combination with other factors such as wall height and reinforcement and facing stiffness, on the behaviour of reinforced soil walls (RSWs) under working stress conditions. The foundation was simulated using different stiffnesses and geometries (with and without slope). The results highlight the importance of the combined effect of foundation conditions and the abovementioned factors on the performance of RSWs. The results of these analyses indicate that the shape of the distribution of the maximum reinforcement loads (T_max) with respect to wall height depends on the combined effect of the foundation condition, facing and reinforcement stiffness, and wall height, and varies from trapezoidal to triangular. Additionally, the results indicate that the effect of variations in foundation stiffness on reinforcement tension mobilisation decreases with wall height. Furthermore, the T_max prediction accuracy of three design methods were evaluated and some limitations of each method are presented and discussed.     

采用K–刚度法设计的模块式加筋土挡墙数值模拟

基于一采用K–刚度法设计的模块式加筋土挡墙建立有限差分数值模型,并采用界面双曲线模型真实模拟底层模块–水平基座界面及水平基座–地基界面,研究实际模块式加筋土挡墙在工作应力下的性状,并进一步分析墙趾界面剪切特性。结果表明:数值计算的挡墙筋材应变分布、填土中各层筋材最大拉力、墙面筋材连接力和墙面最大位移值与实测值比较吻合;K–刚度法计算的填土中筋材最大拉力值与数值模拟和实测值吻合较好,但墙面连接处筋材因受地基沉降和填土压实产生的下拉力影响而大于填土中筋材最大拉力,故K–刚度法不能用于墙面筋材连接力的验算;相较于刚性地基,压缩性地基上模块式加筋土挡墙的墙趾正应力系数较大,而墙趾承担荷载比例较小;尽管基座–地基界面剪切刚度较模块–基座界面小很多,由于其承受的剪应力也很小,墙趾并不会沿着基座–地基界面发生滑移破坏,模块–基座界面对挡墙墙趾起到主要的约束作用。     

格栅条带式加筋胎面挡土墙变形性能数值计算

采用土工格栅加筋的方法提高废旧轮胎挡墙的承载性能,促进废旧轮胎挡墙的推广应用,通过数值计算方法分析了不同墙顶荷载下有无土工格栅加筋的废旧轮胎挡墙的水平变形与竖向沉降反应特征,得出铺设土工格栅加筋的方法可显著减小墙体的水平变形和竖向沉降,提高废旧轮胎挡墙结构的承载能力,随着外荷载的增加,墙体变形模式依次呈凹凸微小变化型、“弯弓”型、“似弯弓”型和“鼓腮”型和直线型。考虑土工格栅的加筋长度、竖向加筋间距以及格栅加筋刚度3种因素对废旧轮胎+土工格栅加筋土挡墙的水平变形的影响,得出在废旧轮胎加筋土挡墙设计中,建议土工格栅的加筋长度选取范围为0.5H～0.7H,土工格栅竖向间距的选取范围为0.4 m~0.7 m,格栅刚度不宜大于5 000 kN/m。     

Earth pressure coefficients for reinforcement loads of vertical geosynthetic-reinforced soil retaining walls under working stress conditions

Based on the nonlinear elastic theory and stress-dilatancy theory, two earth pressure coefficients were proposed to analyze the reinforcement loads at the potential failure surface of vertical geosynthetic-reinforced soil retaining walls under working stress conditions. The earth pressure coefficients take into account the force equilibrium and compatible deformations between soil and reinforcement, and can be obtained by solving two implicit functions by an iterative or graphic method. The effects of backfill compaction and facing restriction are taken into account in the earth pressure coefficients by two additional stress factors, which have been derived analytically using straightforward approaches. To validate the effectiveness of the proposed methods, comparisons were made with the results from large scale tests and numerical simulations. It was demonstrated that the reinforcement loads predicted by the proposed methods were in good agreement with the experimental or numerical results.     

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...     

Influence of uncertainty in geosynthetic stiffness on deterministic and probabilistic analyses using analytical solutions for three reinforced soil problems

The paper examines the quantitative influence of uncertainty in the estimate of geosynthetic reinforcement stiffness on numerical outcomes using analytical solutions for a) the maximum outward facing deformation in mechanically stabilized earth (MSE) walls, b) maximum reinforcement tensile loads and strain in MSE walls under operational conditions, and c) the mobilized reinforcement stiffness in a geosynthetic layer used to reinforce a fill over a void. The stiffness of the reinforcement is modelled using an isochronous two-parameter hyperbolic load-strain model. A linear relationship between isochronous stiffness and the ultimate tensile strength of the reinforcement is used to estimate reinforcement stiffness when product-specific creep data are not available at time of design. Solution outcomes are presented deterministically and probabilistically. The quantitative link between nominal factor of safety used in deterministic working stress design practice and reliability index is provided. The latter is preferred in modern performance-based design to quantify margins of safety within a probabilistic framework. Finally, the paper highlights the practical benefit of using product-specific isochronous secant stiffness data when available, rather than estimates of isochronous stiffness values based on reinforcement type or pooled data.     

A laboratory evaluation of reinforcement loads induced by rainfall infiltration in geosynthetic mechanically stabilized earth walls

A laboratory testing that simulates the mechanisms of a geosynthetic-reinforced layer was used to assess the impact of rainwater infiltration on reinforcement loads and strains in mechanically stabilized earth (MSE) walls. The testing device allows measuring loads transferred from a backfill soil subjected simultaneously to surcharge loading and controlled irrigation. Load-strain responses of geosynthetic-reinforced layers constructed with three different geosynthetics under a moderate rainfall are related to suction captured along the depth of reinforced layers. Results show infiltration leading to increases on strains and tensile loads mobilized by reinforcements. Rates of increases of both parameters were found to be dependent of global suction, geosynthetic stiffness and hydraulic properties. In addition, increases in water content at soil-geotextile interfaces due to capillary breaks also had a significant effect on mobilized loads. The loss of interaction due to the interface wetting was observed to affect the stress transference from soil to geosynthetic reinforcement. An approach suggested for calculation of lateral earth pressures in unsaturated GMSE walls under working stress conditions and subjected to rainfall infiltration demonstrated a reasonable agreement with experimental data.     

Long-term behavior of GRS retaining walls with marginal backfill soils

The creep of geosynthetics leads to the increase of Geosynthetic-Reinforced Soil (GRS) wall's deformation. More importantly, the influences of creep of geosynthetics are also affected by the creep properties of soils. In this paper, a Finite Element procedure was validated against a model test on the creep response of a clay–geotextile composite. An extensive parametric study was then carried out to investigate the long-term response of 8-meter-high model GRS walls with marginal backfill soils. The influences of backfill creep, reinforcement creep, reinforcement stiffness, reinforcement length and reinforcement spacing were analyzed. A long-term analysis was conducted for 5 years and the results at the end of construction (EOC) and 5 years afterwards were compared. It is found from the analysis that the relative creep rate between geosynthetic reinforcement and backfill soil influenced not only wall deformation but also reinforcement loads and stress states in the soils. The load distribution in backfill soil and reinforcement is the result of battling between their time-dependent properties. Large reinforcement creep can lead to large post-construction deformation and increase in soil stress; on the other hand, large soil creep can induce a significant increase in reinforcement load. It is hence necessary to take into account the relative creep rate of reinforcement and backfill soil in the design of GRS walls. It may not be adequate to consider only the long-term strength of reinforcement, which is the state-of-the-practice at present.     

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。     

Evaluation of oblique pullout resistance of reinforcements in soil wall subjected to seismic loads

Pullout resistance is one of the most important factors governing seismic stability of reinforced soil walls. The previous studies on the seismic stability of reinforced soil walls have focused on the axial resistance of the reinforcement against the pullout. However, the kinematics of failure causes the reinforcement to be subjected to the oblique pullout force and bending deformation. Considering the kinematics of failure and bending deformation of the reinforcement, this paper presents a pseudo-static seismic analysis for evaluating the pullout resistance of reinforcements in soil wall subjected to oblique pullout forces. A modified horizontal slice method (HSM) and Pasternak model are used to calculate the required force to maintain the stability of the reinforced soil wall and shear resistance mobilized in the reinforcements, respectively. In addition, this paper studies the effect of various parameters on the pullout resistance of the reinforcements in soil wall subjected to seismic loads. Results of this study are compared with the published data and their differences are analyzed in detail.     

Sliding stability and lateral displacement analysis of reinforced soil retaining walls

Field observations have demonstrated that reinforced soil retaining walls generally have superior seismic performance when compared to traditional gravity retaining walls. However, current design guidelines for reinforced soil retaining walls are typically based on pseudo-static methods of analysis, which involve simplifying assumptions. For instance, the reinforced zone is usually assumed as a rigid body in external stability calculations. As a result, the influences of reinforcement arrangement and properties on the sliding stability and displacement of the wall cannot be accounted for in their design. Additionally, the soil shear strength is assumed to be constant in conventional displacement calculations using the Newmark sliding block method. In this paper, an analysis method is proposed to determine the yield acceleration and lateral displacement of reinforced soil walls that includes soil shear strength mobilization and a two-part wedge planar failure mechanism. The proposed method is validated against the results of laboratory model tests, and influences of factors such as ground acceleration coefficients, and reinforcement and backfill properties on the stability of the wall are examined.     

Evaluation of K-Stiffness Method for Vertical Geosynthetic Reinforced Granular Soil Walls in Japan

In this paper the K-stiffness Method as originally proposed by Allen et al. (2003) is re-examined using a total of six new case studies-five from Japan and one from the USA. A common feature of the walls in this new data set is that the walls were all constructed with a vertical face and a granular backfill. However, the walls varied widely with respect to facing type. This new data set together with data for vertical walls previously published by Allen and Bathurst (2002a,b) and Allen et al. (2002) is now used to isolate the effect of the facing stiffness factor on reinforcement loads and to adjust the original equation that was developed to calculate its value. The paper also shows that predicted reinforcement loads using the current AASHTO Simplified Method in the USA and the current PWRC method in Japan give the same reinforcement load predictions, and both grossly over-estimate the values deduced from measured strains. The new data set is used to slightly refine the estimate of the facing stiffness factor used in the original K-stiffness Method. The original and modified K-stiffness Method are demonstrated to quantitatively improve the estimate of the magnitude and distribution of reinforcement loads for internal stability design of vertical-faced geosynthetic reinforced soils walls with granular backfills when compared to the current American and Japanese methods.