Determination of passive earth pressure with lower bound finite elements limit analysis and modified pseudo-dynamic method

ABSTRACT

The present study deals with the determination of passive earth pressure under seismic condition by following the lower bound finite elements limit analysis and modified pseudo-dynamic methodology. In accordance with the lower bound finite elements formulation, the stress field was modelled using a three-noded triangular elements, while the passive pressure was determined via linear optimisation. The parametric study was performed, for a vertical rigid retaining wall, by varying the magnitude of seismic acceleration in horizontal direction (k_h) between 0 and 0.3, while the vertical seismic acceleration (k_v) was kept equal to 0 or 0.5 k_h. Furthermore, the damping coefficient for dry cohesionless backfill was kept ξ = 10%. The obtained results in various cases were found to be in good agreement with those found in the literature. It is expected that this method can be further used for solving other important geotechnical stability problems.     

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。     

Sarma法在不同方位地震力下的计算研究

Sarma法是计算边坡和堤坝稳定性分析广泛应用的方法,但在构建平衡方程时假设地震力方向为水平方向,未能考虑不同方位地震力对临界地震系数和边坡稳定系数的影响.为了研究临界地震系数和稳定系数在不同方位地震力下分布规律,本文在原Sarma的基础上,假设地震力非水平方向,在任意角度上尝试给出推导公式,并引入平均值对临界地震系数...     

Vertical acceleration effect on landsides triggered by the Wenchuan earthquake,China

The 2008 Wenchuan earthquake with Ms8.0 triggered extensive throwing-pattern landslides in the area within or near the seismic faults. The resultant landslides from this earthquake brought to the fore the effect of vertical earthquake acceleration on landslide occurrence. The pseudostatic analysis and the dynamic response on landslide stability due to the Wenchuan earthquake are studied with the Chengxi (West Town) catastrophic landslide used as a case study. The results show that the epicenter distance is an important factor which affects the vertical acceleration and thus the stability of landslide. Also, the vertical acceleration was found to have a significant impact on the FOS of landslide if the earthquake magnitude is quite large. Within the seismic fault, the amplitude effect of vertical acceleration is very dominant with the FOS of landslide, for vertical acceleration ranging from positive to negative, having a variation of 25 %. The variation of FOS of landslide for vertical acceleration ranging from positive to negative are 15 and 5 % for landslides near seismic fault and outside seismic fault, respectively. For landslide with a slope angle <45°, the FOS of landslide with both horizontal and vertical accelerations is significantly greater than the one without vertical acceleration. Further, the results computed from both the pseudostatic method and dynamic analysis reveal that the FOS during the earthquake varied significantly whether vertical acceleration is considered or not. The results from this study explain why lots of throwing-pattern catastrophic landslides occurred within 10 km of the seismic fault in the Wenchuan earthquake.     

Observations on the pseudostatic analysis of embankments and slopes with arbitrary seismic force inclination

A simple method for evaluating the seismic stability of embankments and slopes has been developed by modifying the generalized procedure of slices proposed by Janbu. A pseudostatic analysis is carried out. The seismic force is represented through its horizontal and vertical components, acting on the centre of gravity of the soil mass. Defining a nominal state of plastic equilibrium, the safety factor of the slope for a given value of the seismic force is obtained through an iterative procedure that converges very rapidly. Moreover, by assuming a seismic force of intensity varying from zero value (static condition) up to a limit value, depending on the seismicity of the area, one can obtain the “influence lines” of the horizontal and vertical acceleration. Finally, a directional parametric analysis has been carried out considering a seismic force of a given intensity, acting in a direction varying from 0° to 360° with respect to the vertical axis through the gravity centre of the slope. By means of this procedure it is possible to locate a “critical zone” for the slope, i.e., that one within which any seismic force can cause the failure of the slope. Moreover, it appears that it is incorrect to consider only the horizontal acceleration in the stability analyses of slopes under earthquake loading conditions, as the most dangerous direction is usually different from the horizontal one.     

Dynamic Response of Shallow-Buried Small Spacing Tunnel with Asymmetrical Pressure: Shaking Table Testing and Numerical Simulation

A series of shaking table tests were designed and carried out to study the seismic behaviors of a shallow-buried small spacing tunnel with asymmetrical pressure. The key details to shaking table model test, including test equipment, model similarity relation, similarity constant, model box, physical model, layout of transducers, seismic waves, and loading system were presented. The numerical simulation of the shaking table test was also carried out by using a finite element simulation software. The results show that: (1) the Fourier spectrums in the vertical direction and horizontal direction are different at the same measuring point. The structure of tunnel transforms the Fourier spectrum of horizontal direction. (2) The stability of middle rock pillar is poor under seismic wave action. The anchor plays an important role in strengthening the stability of middle rock pillar. The dynamic strain of anchor has accumulative effect. (3) The numerical simulation results are in significant agreement with the shaking table test results. (4) Compared with type of seismic wave, peak seismic wave has a significant effect on acceleration response of tunnel. The peak acceleration response of the tunnel is linear with the peak seismic wave, in the horizontal direction. The peak acceleration response is nonlinear in the vertical direction. (5) The axial force of cross section at arch foot is larger than other position. The shock absorption effect of 10 cm seismic isolation layer is better than 5 and 20 cm.     

拟静力法边坡稳定分析的改进

拟静力法简单适用,在地震边坡稳定分析中发挥了很大作用,积累了较丰富的经验。传统上滑动体都是按竖向条分的。考虑地震惯性力时,竖向条分在计算地震惯性力和抗滑力矩时存在计算上的不合理,从而使地震惯性力与实际值有误差,抗滑力矩偏小。而考虑地基中的地震荷载时,安全系数的计算结果是不确定的,没有一个客观的最小安全系数计算结果。在分析了误差产生的机理后,对拟静力法的计算进行了改进。算例表明,改进后拟静力法计算结果是合理的。     

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。     

Seismic stability analyses for landfill cover systems under different seepage buildup conditions

Drainage of landfill cover systems is often inadequate and buildup of seepage forces can occur over time. However, in most design analyses the seepage buildup is neglected and assumed to have only a minor impact on the seismic performance of landfill cover systems. Actually, simply ignoring the seepage buildup will lead to serious overestimation of the factor of safety. A new two-wedge method was developed to analyze the seismic stability of landfill cover systems under different seepage buildup conditions. The solutions of the factor of safety and the yield acceleration coefficient can be obtained, and the permanent displacement of landfill cover systems can also be calculated using the Newmark method. Based on the developed seismic analysis method, the effects of a parametric variation on the seismic stability and permanent displacement of landfill cover systems are presented.     

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。     

纵横波时差耦合作用下地铁车站地震响应分析

以北京实测地震波作为输入,运用二维显示有限差分程序对北京地区常见的3层3跨矩形断面结构地铁车站进行了动力模拟分析,探讨了纵横波时差耦合作用下车站结构加速度、位移放大效应及动应力变化规律。计算结果表明地震纵横波时差耦合作用导致浅埋地铁车站结构受力变形过程为：首先纵波作用使得结构产生较大的竖向加速度,导致结构产生一定的正应力;继而纵横波时差耦合作用使得结构产生较大的水平加速度,此时结构内力达到最大,容易使得结构产生较大的拉应力;最终随着地震动力作用逐渐减小至消失,结构内力减小,恢复稳定。在地震动力作用下,地铁车站侧墙、中柱等结构的加速度自下而上均发生放大效应,且竖向加速度的放大程度远高于水平加速度。因地震纵波产生较大的竖向加速度,并且具有较强的放大效应,需重视距离震源较近地区的地下结构竖向抗震性能;而纵横波时差耦合作用下,结构的内力往往能达到最大值,是地下结构发生破坏的主控因素。     

弃土堆填对斜坡输电塔桩基地震反应的影响

施工弃土堆填保坎对山区输电线路桩基地震反应会产生何种影响,目前尚不明确。采用FLAC3D数值分析软件建立西南山区典型输电线塔位数值模型,分析桩周有无弃土堆填保坎时桩基础地震动力响应的变化情况,开展定量分析,初步探讨弃土堆填保坎对山区输电线路桩基地震反应的影响。研究表明：桩周弃土堆填保坎后斜坡场地桩基桩身水平峰值加速度、桩身位移、桩身内力、桩周土体位移差的量值均较桩周无弃土堆填保坎时增大。陡坡坡度为35°时,弃土堆填保坎增大了桩基础地震响应,降低了其在陡坡上的抗震性能。     

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。     

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.     

基于拟静力法的不同地震工况斜坡单元危险性评价方法研究

地震造成斜坡失稳是其引起的最为显著的次生灾害,在小震频发,大震多发的现实背景下,开展不同等级地震作用条件下斜坡危险性评价对区域防灾减灾、地质灾害风险管控及国土空间规划的现实意义日渐凸显。基于拟静力法,根据斜坡所处场地类别和不同超越概率水平地震作用,对其地震动峰值加速度进行调整,确定斜坡不同等级地震作用下的综合水平地震系数,计算不同等级地震作用引起的作用于斜坡重心处的水平和竖向惯性力,以极限平衡法为理论基础,计算不同等级地震作用下斜坡稳定性系数,结合危险性指数法,计算不同等级地震作用下斜坡失稳概率和危险性指数,据此对斜坡不同等级地震作用下的危险性进行划分。结果表明斜坡稳定性系数随地震作用的增强逐渐减小,斜坡失稳概率随地震作用的增强逐渐增大,斜坡危险性指数随地震作用的增强逐渐增大,斜坡危险性亦随地震作用的增强逐渐增大。     

充分考虑振动台实验滑移特征的地震滑坡基本单元体永久位移估算方法研究

充分考虑振动台实验揭示出来的基本地震滑坡单元体震动滑移特征,总结得到其永久位移的估算方法:（1）考虑地震动惯性力和重力的联合作用,计算相应向上和向下滑移的屈服加速度,以反应其可能向上和向下滑移的行为;（2）在适度简化斜坡岩土体动力学模型的基础上,考虑斜坡岩土体自振特性和滑体所在高度对地震波的放大效应,得到滑体附近的局部地震加速度;（3）考虑滑体附近局部加速度和滑移屈服加速度的控制作用,计算每一地震波的周期内滑体相对滑床所能达到的最大滑移速度（向上和向下）,进而得到相对动能;（4）考虑到滑体的动能基本耗散在滑带上,基于能量守恒原理,将相对动能除以滑带上的摩擦力,即可估算出每一周期内的永久位移;（5）将每一地震波周期内产生的永久位移相累加,即可得到总体的滑动位移。经与实验结果对比,本估算方法具有较高的精度与可靠性,虽只考虑了水平向地震动作用的影响,但对于存在竖向地震动的情况,其思路同样适用,只是需要计入竖向地震动惯性作用力的影响。     

竖向扩建填埋场变形离心模型试验研究

填埋场扩建是增大库容的重要手段,而其引起的沉降变形对填埋场及内部构筑物的稳定性有重大影响。针对扩建填埋场自重应力作用下的沉降变形问题,采用能够模拟我国固废工程特性的人工固废开展了平原型填埋场竖向扩建的离心模型试验。结果表明,堆体自重应力沉降随固废龄期增大而减小,最大沉降可达到堆体初始高度的20%。新老堆体界面不均匀沉降随老堆体龄期增大而减小,界面水平位移最大值出现在新堆体坡肩附近,且随坡比增加和龄期减小而增大。坡比越小,龄期和垃圾坝的作用越明显。垃圾坝对填埋堆体变形的影响随其相对高度减小而减弱。试验结果略大于常用的填埋场一维沉降计算结果,为填埋场增容及中间衬垫设计和稳定评估等提供了参考。     

反压土对悬臂式支护结构嵌固深度的影响研究

基于Rankine土压力理论、滑移线场理论和Boussinesq解答在均布条形荷载作用下的表达式,建立了考虑反压土自重对坑底土体水平抗力的增强作用和反压土本身的嵌固作用两种机制时悬臂式支护结构嵌固深度的计算方法,并进行了算例分析。研究表明：虽然反压土能提供给支护结构的水平抗力较小,但由于其合力力臂较大,因此对支护结构有明显的嵌固作用;另外,反压土的自重能明显提高坑底土体的水平抗力。综合考虑反压土的以上效应后,支护结构的嵌固深度可以明显减小。基坑内侧预留反压土的施工方法可以省去水平支撑、降低支护结构深度,还可以节约投资和缩短工期,具有良好的经济效益、社会效益和环境效益。因此,在条件许可的情况下,该施工方法应优先选用     

多级支挡结构地震主动土压力的极限分析

多级组合支挡结构形式在高边坡防护工程中得到了广泛采用,但现有研究却较少涉及这种支挡结构形式的地震土压力计算问题。应用拟静力法和塑性极限分析上限定理,并且基于强度折减技术,推导了重力式挡墙与两级锚杆挡墙组合支挡结构形式的地震主动土压力及其系数的上限解。该上限解考虑了水平和竖向地震系数、墙背倾角、坡面形式及多级支护方式、土体黏聚力、土体与墙背的黏附力等诸多因素。二级锚杆挡墙实例分析表明：静力条件下主动土压力计算值与现有相关方法的计算结果一致,土的抗剪强度折减系数、上挡墙锚杆轴力等参数,对下挡墙地震主动土压力影响显著。二级组合支挡结构地震主动土压力影响参数敏感性分析表明：水平地震系数以及重力式挡墙墙高和倾角的敏感性较大,上挡墙锚杆的轴力和倾角等参数的敏感性相对较小     

Lateral force and centroid location caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross‐anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load, and downward nonlinear‐varying strip load. The planes of cross‐anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29 :1341–1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross‐anisotropic backfills generated by the horizontal and vertical uniform, upward linear‐varying and upward nonlinear‐varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross‐anisotropic. Copyright © 2007 John Wiley & Sons, Ltd.