Pseudo Static Seismic Stability Analysis of Reinforced Soil Structures

The paper pertains to the pseudo-static seismic stability analysis of reinforced soil structures. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis has been conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. The external stability of the reinforced earth wall is also assessed in terms of its sliding, overturning, eccentricity and bearing modes of failure. The influence of the intensity of the surcharge load placed on the backfill is also considered in the analysis. The obtained results are validated by comparing the same with those reported in literature. Studies have also been made regarding the influence of backfill soil friction angle, horizontal and vertical seismic accelerations, surcharge load, the tensile strength of reinforcement, pullout length of the reinforcement and number of reinforcement layers on the seismic stability against various failure modes as mentioned earlier.     

加筋土挡墙地震稳定性的拟动力分析

为研究不同筋材条件下加筋土挡墙地震稳定性,采用两种简化破裂面形式;由于拟静力法的局限和加筋土挡墙的成层特性,对水平和竖向地震力同时作用下的加筋土挡墙,运用拟动力法和水平条分法推导出其筋材拉力总和与临界破裂角的计算公式。算例分析结果表明,筋材拉力总和随着地震加速系数、回填土重度或者滑动体上部超载的增大而增大;随着土体内摩擦角或者填土黏聚力的增大而减小;当条件相同时,可延展性筋材所承受的筋材拉力总和大于不可延展性筋材所承受的。与拟静力法和规范中的方法比较,基于拟动力法的加筋土挡墙的设计也更加经济。     

A procedure for the design and analysis of geosynthetic reinforced soil slopes

Summary A procedure for the stability analysis and design of geosynthetic reinforced soil slopes over a firm foundation is described. Firstly the unreinforced slope is analysed, and for this a circular failure method is used which allows a surcharge load to be taken into account. Any method of slip circle analysis could be used to identify the coordinates of the centre of the slip circle, its radius and the minimum factor of safety. In this study, both internal and external stability analysis of the reinforced slope is presented. Internal stability deals with the resistance to pullout failure within the reinforced soil zone resulting from the soil/reinforcement interaction. The external stability is considered by an extension of the bilinear wedge method which allows a slip plane to propagate horizontally along a reinforcing sheet. The results for total tensile force, internal and external stability are presented in the form of charts.For given properties of soil and slope geometry, the required strength of the geosynthetic and the length of reinforcement at the top and bottom of the slope can be determined using these charts. The results are compared with the published design charts by Schmertmannet al. (1987).     

Pseudo-static Analysis of Reinforced Earth Retaining Wall considering Non-linear Failure Surface

The seismic stability of reinforced earth has been investigated in this paper using pseudo-static method of analysis considering horizontal and vertical seismic acceleration with non-linear failure surface. The sliding wedge is divided into a number of horizontal slices to determine the strength and length of the geo-synthetic reinforcement for seismic internal stability of battered face rigid retaining wall supporting c-Φ backfill. Results are presented in graphical form representing the required length of geo-sythetic reinforcement under seismic condition to maintain the internal stability of reinforced soil. The influences of horizontal and vertical seismic acceleration, soil friction angle, cohesion, adhesion and wall inclination angle on the required length of the geo-sythetic reinforcement have been studied. From the present study it is seen that the required length of geo-synthetic reinforcement increases due to increase in the value of seismic accelerations.     

Load and resistance factor design (LRFD) calibration for steel grid reinforced soil walls

This paper reports the results of load and resistance factor design (LRFD) calibration for pullout and yield limit states for steel grid reinforced soil walls owing to soil self-weight loading plus permanent uniform surcharge. The calibration method uses bias statistics to account for prediction accuracy of the underlying deterministic models for reinforcement load, pullout capacity and yield strength of the steel grids, and random variability in input parameters. A new revised pullout design model is proposed to improve pullout resistance prediction accuracy and to remove hidden dependency with calculated pullout resistance values. Load and resistance factors are proposed that give a uniform probability of failure of 1% for both pullout and yield limit states. The approach adopted in this paper has application to a wide variety of other reinforced soil wall technologies.     

地震效应和坡顶超载对均质土坡稳定性影响的拟静力分析

基于强度折减技术和极限分析上限定理,假定机动容许的速度场破坏面,考虑坡顶超载、水平和竖向地震效应影响推导了边坡稳定性安全系数的计算表达式。采用序列二次规划迭代方法（和内点迭代方法）对边坡安全系数目标函数进行能量耗散最小化意义上的优化计算,与多个算例的对比验证了其方法和程序计算的正确性;对影响土质边坡动态稳定性的一些因素进行了参数分析,分析表明：随着边坡倾角?、坡顶超载q、水平和竖向地震效应影响系数的增大,边坡稳定性安全系数显著下降;随着坡顶超载q、水平地震效应影响系数kh的增大、竖向地震效应影响系数kv的减小,边坡的潜在滑动面越来越深,潜在破坏范围越来越大。竖向地震效应对边坡稳定性也有一定影响,强震条件下的设计计算必须考虑竖向地震效应的影响。     

Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction

Probabilistic stability analyses of constructed wrapped-face reinforced slopes (or embankments) using frictional soils were carried out using the random finite element method (RFEM). Soil properties reported in the literature for unsaturated frictional fills compacted to different densities were used in the simulations. Bar elements were added to the RFEM code to simulate extensible geosynthetic reinforcement layers and the Davis approach was used to improve numerical stability for purely frictional soil slopes at collapse. The influence of isotropic and anisotropic spatially variable soil strength was investigated and shown to have a large influence on the variation of maximum mobilised tensile forces in reinforcement layers for the steep 5 m-high slopes in the study. The influence of fill placed at different layer thickness and compacted to different levels was simulated by adjusting the soil strength and unit weight, and the vertical strength correlation length in the anisotropic spatially variable strength field used in each slope realisation. Numerical results showed that vertical strength correlation lengths approaching the magnitude of fill lift heights can control the probability of failure for reinforced slopes constructed with weak fills placed in lift heights close to but less than the wrapped reinforcement spacing used in the study.     

三维加筋边坡地震稳定性上限分析

基于极限分析上限定理,考虑均匀加筋和三角形加筋两种加筋模式,采用拟静力分析方法推导了一定边坡高度条件下的三维加筋边坡临界加筋强度的计算公式。通过与已有文献结果的对比,验证了所提方法的正确性,并讨论了边坡宽高比、水平和竖向地震力系数对三维边坡稳定性的影响。结果表明:地震力作用下边坡临界加筋强度随边坡宽高比的增大而增加,但其变化速率逐渐减小,当边坡宽高比大于10时,三维边坡加筋强度与二维情况相近;随着水平地震作用的增大,三维边坡临界加筋强度呈非线性增大;随着竖向地震作用的增大,临界加筋强度大致呈线性增加,且随着坡角的增大,竖向地震作用对临界加筋强度的影响更加显著;两种加筋模式下的边坡临界加筋强度值变化规律一致,且三角形加筋模式所需的加筋强度较小,效果较优。最后,针对实际工程提出了一些工程建议。     

有限填土加筋土挡墙的稳定性及破坏模式分析

有限填土加筋土挡墙是短加筋土挡墙的一种特殊情况,其工作性状还没有被清晰地认识。文章在离心模型试验成果的基础上,采用FLAC软件建立有限填土加筋土挡墙的二维数值模型,讨论了加筋间距、加筋长度以及墙面与竖直平面的夹角对挡墙稳定性和破坏模式的影响。结果表明:（1）墙后有限填土情况下主动土压力约为库伦主动土压力的1/2~1/3;（2）在稳定地基工况下,挡墙均为复合破坏模式,滑动面呈折线型,在挡墙中下部,滑动面同时穿过了加筋区和填土区,从墙趾处滑出;在挡墙上部,滑动面基本沿着填土与稳定墙面的接触面向上发展;（3）潜在滑动面是自下向上逐渐形成的,体现为下部剪切、上部拉张的特征;（4）在墙后有限填土情况下,加筋长度减小到0.4H时,挡墙仍能保持稳定,加筋间距在控制挡墙稳定性方面具有重要作用。     

基于强度折减法的三维边坡稳定性与破坏机制

基于强度折减技术的三维弹塑性有限元法是当前较为有效的边坡稳定性评价方法,但很少应用于复杂地质环境及负载条件下的三维边坡稳定性与破坏机制分析。拓展这一方法,利用典型算例,探讨了单元尺寸、边界条件、土体强度、局部超载和地震荷载等因素对三维边坡稳定性及潜在滑动面的影响;在此基础上,着重研究含软弱夹层及地下水的复杂三维边坡在负载条件（坡顶局部超载及地震荷载）下的破坏模式及滑动机制。结果表明：随着黏聚力的增加,潜在滑坡体的剪出位置远离坡脚,滑坡后沿远离坡肩,滑坡深度加深;坡顶超载强度较低时,边坡表现为整体破坏模式,而高超载强度下表现为局部地基破坏;考虑地下水后边坡的稳定性显著下降,且潜在滑动面加深,滑坡体体积有所增大。含软弱夹层的三维边坡,其潜在滑动面呈折线型,当受超载作用时,其破坏模式和滑动机制与地震荷载作用下不同:前者为竖向剪切和水平错动的联合作用,而后者为软弱夹层水平错动起主导作用。     

锚固岩石边坡地震稳定性拟动力分析

地震易发地区的锚固岩石边坡,需要研究其地震稳定性。对于锚固典型岩石边坡,在考虑水平与竖向地震力、张裂缝积水深度、坡顶超载、锚索倾角、锚索位置、锚索拉力及静水与动水压力等的条件下,运用拟静力和拟动力方法分别推导了不同工况条件下其抗滑和抗倾覆地震安全系数。分析表明,竖向向上地震力有利于锚固岩石边坡的抗滑稳定,而竖向下的地震力有利于锚固岩石边坡的抗倾覆稳定;在相同工况条件下,当岩体放大系数等于1.0时,拟动力与拟静力方法所得锚固岩石边坡地震安全系数相差无几,但是,当岩体放大系数逐渐增大时,拟动力方法所得地震安全系数越来越明显地小于拟静力方法所得地震安全系数。因此,在抗震设计当中适当的考虑岩体放大系数,将会有利于锚固岩石边坡的安全设计。     

Design method for local load on a geosynthetic reinforced soil structure

This paper presents a method for the design of geosynthetic reinforced soil structures, adapted for the case of a local surcharge load. The load has an important influence on the mechanical behaviour of the reinforcement. The basic calculation method is described and a design calculation method is proposed for the case of a locally loaded structure. This new approach is validated on the basis of experimental results obtained on several full-scale embankments, locally loaded to failure. These experimental results are compared to the results of calculation with partial safety factors from Eurocode 7.     

地震荷载作用下岩石边坡的抗倾覆稳定性分析及可靠度研究

在地震多发地区,地震荷载对岩石边坡的稳定性影响显著。因此,在边坡抗震设计中,准确有效地评估其稳定性显得非常重要。安全系数法未考虑地震荷载等影响因素的不确定性,因此具有一定的局限性。本文在考虑到破坏面出流缝未堵塞和被堵塞两种情况下,利用拟动力方法计算了岩石边坡抗倾覆稳定性安全系数。在此基础上,考虑到地震荷载、坡顶超载及张裂缝内水位深度的变异性,对岩石边坡的抗倾覆稳定性进行了可靠度分析。研究发现,当破坏面出流缝被堵塞时,岩石边坡的抗倾覆稳定性急剧降低。此外,地震荷载等因素的变异性对岩石边坡的抗倾覆稳定性有着显著的影响。因此,同时利用安全系数及可靠度指标来评估岩石边坡的稳定性,且适当地考虑岩体放大系数,有利于岩石边坡抗震设计的安全性。     

Soil/Geotextile Interface Behaviour in Direct Shear and Pullout Movements

This paper deals with soil/reinforced geotextile interface behaviour in direct shear and pullout movements. A soil/geosynthetic direct shear apparatus, developed in accordance to EN ISO 12957-1 (2004) and ASTM D5321-92 (1992) standards, is presented. Some details of the test (like: specimen fixation, influence of the vertical stress on the registered horizontal force, type of test and measurement of the vertical displacement) are discussed and modifications in the test procedures are adopted. Then, the reinforced geotextile and the residual soil of granite used in the research are described. The behaviour of soil/geosynthetic interface in direct shear is characterized based on modified direct shear tests and maximum interface shear stress is determined at peak and residual for a confining stress of 50 kPa. The modification in the pullout test apparatus described by Lopes and Ladeira (1996a; 1996b) and by Lopes and Lopes (1999) are noticed. The behaviour of soil/geosynthetic interface in pullout is characterized based on pullout tests performed, in accordance EN 13738 (2004), and interface shear stress at maximum pullout force is defined for a confining stress of 50 kPa. Finally, the values of interface coefficient at soil/geosynthetic interface are obtained in direct shear and in pullout and then compared. The main conclusions that can be outlined from the present study are the following: modifications should be made to EN ISO 12957-1 (2004) standard, namely in what concerns the dependence of the measured horizontal force from the vertical stress, the difficulties to perform constant area direct shear test with the lower half box filled with soil and on the measurement of the vertical displacement of the load plate; on the contrary to which is normally accepted the characteristics of the behaviour of soil/geosynthetic interface in pullout, when the geosynthetic has a full plane contact area with the soil, are not able to be obtained based on results of direct shear tests, as in this type of tests the contribution of the geosynthetic deformation on the characteristics of the interface in pullout is not considered.     

Computer aided design of geosynthetic reinforced soil walls

Summary The computer aided design of geosynthetic reinforced soil walls is reported. The magnitude of tensile forces in the geosynthetic reinforcement has also been studied under external vertical and horizontal strip loads.     

Nonlinear analysis of multilayer extensible geosynthetic-reinforced granular bed on soft soil

The paper presents a model for the analysis of granular foundation beds reinforced with several geosynthetic layers. Such reinforced granular beds are often placed on soft soil strata for an efficient and economical transfer of superstructure load. The granular bed is modeled by the Pasternak shear layer and the geosynthetic reinforcement layers by stretched rough elastic membranes. The soft soil is represented by a series of nonlinear springs. The reinforcement has been considered to be extensible and it is assumed that the deformation at the interface of the reinforcements and soil are same. The nonlinear behavior of the granular bed and the soft soil is considered. Plane strain conditions are considered for the loading and reinforced foundation soil system. An iterative finite difference scheme is applied for obtaining the solution and results are presented in nondimensional form. The results from the proposed model are compared to the results obtained for multilayer inextensible geosynthetic reinforcement system. Significant reduction in the settlement has been observed when the number of reinforcement layer is increased. In case of inextensible reinforcements as the number of reinforcement layer is increased the settlement is decreased with a decreasing rate, but in case of extensible reinforcement the reduction rate is almost constant. Nonlinear behavior of the soft soil decreases as number of reinforcement layer is increased. The effect of the stiffness of the geosynthetic layer on the settlement response becomes insignificant for multilayer reinforced system, but the mobilized tension in the reinforcement layers increases as the stiffness of the geosynthetic layers increases.     

水力和超载条件下锚固岩石边坡动态稳定性拟静力分析

基于极限平衡理论,综合考虑水力条件、坡顶超载、地震荷载效应和锚固效应对岩石边坡进行了全面的稳定性分析。计算给出了多影响因素条件下岩石边坡稳定性安全系数的表达式,并重点分析了几种相关参数组合对岩石边坡稳定性的影响。分析表明,坡顶张拉裂缝积水、地下水渗流作用、滑面出流缝被堵塞、地震影响效应不利于岩石边坡抗滑稳定性,而锚索锚固效应则对提高边坡抗滑稳定性有积极作用;坡顶张拉裂缝积水、滑面出流缝被堵塞、水平向地震影响效应都不利于岩石边坡抗倾覆稳定性,但锚索锚固效应、坡顶超载、与竖直方向地震效应则对提高边坡抗倾覆稳定性有益。最后针对工程实际,提出了相应的工程建议。     

Seismic uplift capacity of strip anchors in soil

Uplift capacity of horizontal strip anchors in soil embedded under an inclined ground surface has been obtained under seismic conditions. Limit equilibrium approach with logspiral failure surface together with pseudo-static seismic forces has been adopted. The results have been presented in the form of seismic uplift capacity factors as functions of ground inclination, embedment ratio, angle of internal friction of the soil and seismic acceleration coefficients. The uplift capacity factors have been worked out separately for cohesion, surcharge and density components. Effect of the vertical seismic acceleration coefficient has been found to always reduce the uplift capacity whereas the effect of horizontal seismic acceleration coefficient has been found to reduce the uplift capacity in most of the cases. The obtained results of seismic uplift capacity factors are found to be the minimum when compared with the results available in literature on the basis of planar failure surface. This revised version was published online in July 2006 with corrections to the Cover Date.     

土工格栅加筋土地基平板载荷试验研究

在近年来的岩土工程实践中,土工合成材料加筋土技术得到越来越广泛的应用。采用平板载荷板试验方法,进行了多组加筋砂土地基模型试验,监测和分析了不同加筋材料（双向格栅与四向格栅）和加筋层数对土工格栅加筋土地基承载特性的影响。研究结果表明：土工格栅加筋土地基与无筋地基相比,承载性能得到改善,双层加筋明显优于单层加筋;土工格栅加筋限制了浅层地基的侧向变形,相同荷载下地基沉降减小,可恢复变形增大;模型试验中测得加筋材料应变和拉力很小,与土工格栅强度相比,拉伸模量对加筋土地基承载力的贡献更大。