Reliability Based Earthquake Resistant Design for Internal Stability of Reinforced Soil Structures

This paper presents a method to evaluate reliability for internal stability of reinforced soil structures using reliability based design optimization. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis is conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. Properties of backfill soil and strength of the geosynthetic reinforcement are considered as random variables. For the seismic conditions, reliability indices of all the geosynthetic layers in relation to tension and pullout failure modes are determined for different magnitudes of seismic accelerations both in the horizontal and vertical directions, surcharge load and design strength of the reinforcement. The efforts have been made to obtain the number of layers, pullout length and total length of the reinforcement at each level for the desired target reliability index values against tension and pullout modes of failure. The influence of horizontal and vertical earthquake acceleration, surcharge load, design strength of the reinforcement, coefficient of variation of soil friction angle and design strength of the reinforcement on number of layers, pullout length and total length of the reinforcement needed for the stability at each level is discussed.     

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).     

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.     

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.     

Analysis and Design of Retaining Wall having Reinforced Cohesive Frictional Backfill

The case of a rigid wall with inclined back face retaining reinforced cohesive-frictional backfill subjected to uniformly distributed surcharge load has been analyzed using limit equilibrium approach. The analysis considers the stability of an element of the failure wedge, which is assumed to develop in the reinforced earth mass adjoining the back face of wall. The non-dimensional charts have been developed for computing the lateral earth pressure on wall and the height of its point of application above the base of wall. The theoretical findings have been verified by model tests on a rigid wall retaining a dry cohesive-frictional soil reinforced by geogrid strips. Experimental results are in good agreement with the theoretical predictions. A design example has been included to illustrate the design procedure.     

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。     

布筋尾砂胶结充填体顶板力学性状试验研究

胶结充填体顶板的稳定性是决定下向分层胶结充填回采断面尺寸的主要因素,结合武山铜矿工程实际,采用相似模拟与现场监测手段,研究了下向分层胶结充填法充填体顶板的破坏模式、变形特征、充填体内钢筋受力特征等。相似模拟试验结果表明,钢筋布置方式不影响顶板的最终破坏形式,竖直布置钢筋与水平布置钢筋相比,更有利于提高顶板整体稳定性。应变监测结果表明,充填体顶板应变状态十分复杂,与通常将下向胶结充填体顶板简化为梁的计算结果有较大不同,垂直方向上应变表现为拉伸应变,而沿分条和垂直分条方向应变均呈现拉、压交错变化。在竖直布置的8根钢筋上布置了24个钢筋测力计,得到了钢筋受力与开采时间的关系曲线,据此将钢筋受力划分为4个阶段,即起始受拉阶段、相对稳定阶段、拉压变化阶段、承载阶段,其中承载阶段钢筋首先承受最大压力,充填体暴露为顶板后,钢筋由受压状态变为受拉状态,并急剧上升到最大拉力,即表现出悬吊作用,并且,进路与分条连接处钢筋承受拉力最大。     

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。     

加筋砂土作用在挡土墙上的土压力研究

以土的塑性极限分析理论和拱体理论为基础，结合挡土墙的长高比，提出了墙后砂土的两种三维破坏模式，并把两种模式与加筋相结合，求出了在加筋水平间距Sx和竖向间距Sx下作用在墙上主动土压力的上限解和设计的加筋长度。最后通过实例验证了本文的理论。     

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。     

土工织物与吹填土界面作用特性试验研究

筋-土界面强度参数是加筋结构设计和稳定分析的关键技术指标。拉拔试验能较好模拟现场加筋行为而得到广泛的应用。基于拉拔和直剪试验研究了拉拔（剪切）速率对筋-土界面特性和吹填砂强度特性的影响规律及机制,同时探讨了不同填料界面、筋材类型的加筋效果。结果表明：随着拉拔（剪切）速率的增大,吹填砂-筋材-吹填砂界面的抗剪强度下降明显,而软土-筋材-吹填砂界面以及砂本身强度则变化不大。从强度指标来看,拉拔速率增大,筋-砂界面强度的降低主要表现为似黏聚力的降低,筋-软土界面抗剪强度的增加表现为内摩擦角增大,剪切速率对吹填砂则基本无影响。筋-土界面特性受拉拔速率和正应力的共同影响,与筋材类型和填料特性有关。筋-土界面内摩擦角小于填料摩擦角,但在一定正应力下低速剪切时（如<0.53 mm/min）可获得高于填料的抗剪强度。宜根据似黏聚力大小合理选择摩擦参数进行加筋结构的设计与评价。     

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.     

Performance of Counterfort Walls with Reinforced Granular and Fly Ash Backfills: Experimental Investigation

Experimental investigations on model counterfort retaining walls have been carried out to study the lateral movement of the walls and the nature of the failure modes. Mild steel plates of size 1,000 × 900 × 8 mm were used as model retaining walls and were placed in a tank of size 900 × 900 × 670 mm. Ennore sand, obtained from Madras India, and Fly ash, obtained from Panki Thermal Power Plant, India were used as backfill material. Tests were carried out both with and without reinforced backfill. Two types of loading conditions were applied: (i) line load and (ii) uniform surcharge. The shape and size of the failure wedge was studied by observing displacement of bands of colored through a Perspex plate fixed on one side of the tank. Plots of overturning moment against the rotation of a wall top show that with the increase in rotation of wall, the overturning moment decreases. The minimum value of overturning moment is taken as the limiting value. The failure surfaces obtained in different cases are linear and parabolic in shape.     

基于二楔块法的加筋土挡墙屈服加速度及破坏模式极限分析

加筋土挡墙具有优越的抗震性能,并在土建工程中被广泛应用,因此,加筋土挡墙抗震设计方法的研究尤为重要。为了能够分析加筋体内部筋材布置方式、筋材抗拉强度等对屈服加速度的影响,假定破坏模式为双楔块模式,根据极限分析理论推导了加筋土挡墙屈服加速度系数表达式。与规范计算值相比,计算结果更接近模型测试值与数值模拟结果,同时计算方法可以反映模型的真实破坏模式。参数分析表明：屈服加速度随着筋材抗拉强度的增大而增大,特别是筋材长度较长时;随着筋材竖向间距的增大,屈服加速度逐渐减小;面板的宽度对屈服加速度几乎不产生影响;与面板宽度相比,筋材抗拉强度与竖向间距对加筋土挡墙破裂面形状的影响更大。     

Seismic response analysis of geosynthetic reinforced soil segmental retaining walls by finite element method

The paper presents the results of a finite element analysis of the dynamic response of a geosynthetic reinforced soil retaining wall that is constructed with dry-stacked modular concrete blocks as the facia system. In the finite element model, the cyclic shear behavior of the backfill soil is described by a hyperbolic stress-strain relationship with Masing hysteretic unload-reload behavior. The reinforcement material is modelled using a similar hysteretic model which takes into account the measured response of cyclic load-extension tests performed on unconfined geogrid specimens in the laboratory. Interface shear between wall components is simulated using slip elements. The results of finite element analyses giving the seismic response of a typical geogrid reinforced segmental retaining wall subjected to prescribed acceleration records are presented. The results of analyses highlight the influence of dynamic loading on: (1) wall displacement; (2) cumulative interface shear force and displacement between facing units; (3) tensile forces developed in the reinforcement and; (4) acceleration response over the height of the wall. A number of implications to the design of these structures are identified based on the results of these simulations.     

External seismic stability of vertical geosynthetic-reinforced soil walls using pseudo-static method

Analysis of external stability of vertical geosynthetic-reinforced soil (GRS) walls is very important in the seismic prone zone. The scope of this paper is to obtain required minimum reinforcement length, L _min, for external seismic stability of vertical GRS walls by pseudo-static limit equilibrium method. Then, L _min can be calculated to resist sliding, eccentricity, and bearing capacity failure modes. The parameters considered include both horizontal and vertical seismic coefficients (k _h and k _v ), surcharge load (q), wall height (H) and the properties of retained backfill, GRS, and foundation soil. Results show that L _min against sliding failure mode, L _min,S , increases more quickly than that against the other two failure modes with the increase in k _h , q, or unit weight of retained backfill, γ _b , while L _min,S decreases more quickly than that against the other two failure modes with increase in friction angle of retained backfill, ? _b , or unit weight of GRS, γ _r . For the different failure modes, the effect of k _v on L _min is not identical with the change of k _h , and in addition, L _min/H will tend to remain unchanged with the increase in H. In general, L _min against bearing capacity failure mode, L _min,BC, is larger than L _min against the other two failure modes. However, L _min,BC will be less than L _min against eccentricity failure mode, L _min,E , for k _h exceeding 0.35, or friction angle of foundation soil, ? _f , exceeding 37°, and L _min,BC will also be less than L _min,S for friction angle of GRS, ? _r , being no more than 26°.     

Inextensible reinforcement on non‐linear elasto‐plastic subgrade under oblique pull

In this paper, a rational analysis of pullout resistance of inextensible sheet reinforcement subjected to oblique end force has been presented considering a non‐linear (hyperbolic), elasto‐plastic, normal stress–displacement relationship of the subgrade. Under an oblique pull, high normal stresses develop on stronger subgrades, thus mobilizing high shearing resistance at the reinforcement–soil interface. The higher the bearing resistance of the subgrade, the higher the horizontal component of pullout force and the lower the end displacement of the reinforcement. On the other hand, the end displacement at pullout can become very high for weaker subgrades especially at high values of the angle of obliquity. Also, the pullout capacity under oblique loading for weaker subgrades may approach or even fall below the axial pullout capacity at high values of the angle of obliquity. These adverse pullout responses owing to a low value of bearing resistance of subgrade are magnified when the subgrade stiffness is also small. On weaker subgrades, improvement in angle of interface shear is not advisable as this leads to further reduction in the pullout force and increase in the end displacement. Results are compared with back analysis of published test data on model reinforced soil walls. The comparison suggests that the present model leads to a more rational and better prediction of the pullout failure. Copyright © 2008 John Wiley & Sons, Ltd.     

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 stability analysis of soil nail reinforced slope using kinematic approach of limit analysis

Prediction of the critical seismic yield acceleration coefficient and the seismic permanent displacement of soil nail reinforced slope under seismic loading has been playing an important role in helping design in the earthquake-prone areas. In this paper, the seismic stability of soil nail reinforced slope is analyzed using the kinematic theorem of limit analysis. The log-spiral failure mechanism is considered and the corresponding analytical expressions are derived to calculate the critical seismic yield acceleration coefficient and the permanent displacement of slope subjected to earthquake loading. A series of calculations are carried out to illustrate the influence of inertial force on the stability of a nail-reinforced slope. Parametric studies indicate that the strength and geometry of slope as well as characteristic parameters of soil nail have a significant effect on the critical seismic yield acceleration coefficient and the permanent displacement of soil nail reinforced slope.