对数螺旋线破坏下加筋边坡地震稳定分析

以拟静力法的理论框架分析了土工合成材料加筋边坡对数螺旋线破坏模式下的地震稳定性,整个计算过程采用极限分析的动力学理论,推导出的表达式能够容易地计算出地震荷载作用下为阻止边坡破坏所必需的加筋力和屈服加速度系数。     

直线破坏模式下加筋边坡的地震稳定分析

以拟静力法的理论框架分析了土工合成材料加筋边坡直线破坏模式下的地震稳定性,整个计算过程采用极限分析的动力学理论,推导出的表达式能够容易地计算出地震荷载作用下为阻止边坡破坏所必需的加筋力和屈服加速度系数的闭合解。     

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。     

Effect of soil-reinforcement interaction coefficient on reinforcement tension distribution of reinforced slopes

This paper examines the effect of the mobilized reinforcement tension within reinforced soil slope at a different level of soil-geosynthetic interaction. The mobilized reinforcement tension is assumed, in most design methods for the internal stability of reinforced slopes, to be equal to mobilized soil forces computed using a limit equilibrium method. However, comparison with the reinforcement tension force measured in the field has shown that this approach is conservative. This paper examines the effects of the soil-reinforcement interaction coefficient on the tensile redistribution of geosynthetics. The modified process of Bishop Method of slope stability analysis is used to locate the critical slip surface and to calculate the mobilized reinforcement tensile force. The reinforcement forces obtained from field data and on centrifuge model test results for a reinforced slope problem are used to examine the relationship between mobilized reinforcement tensile force and mobilized soil shear strength.     

Force equilibrium-based finite displacement analyses for reinforced slopes: Formulation and verification

Formulation and verification for a force equilibrium-based finite displacement method (FFDM) using test results of reinforced model slopes subjected to increasing pseudo-static seismic forces are reported. The FFDM requires, in addition to force equilibrium for a sliced potential failure mass, a hyperbolic shear stress–displacement constitutive law for the backfill soils, a hyperbolic pull-out force–displacement constitutive law for the reinforcement, and a displacement compatibility requirement for adjacent soil slices. As a result, the mobilized reinforcement force is an analytical output, rather than an empiricism-based input as required in conventional limit equilibrium analyses. Analytical results from the FFDM also indicated that a brittle failure is associated with the lightly reinforced failure surface; a ductile failure is associated with the heavily reinforced failure surface, regardless of the extensibility of reinforcement investigated in the present study. Good agreements between the measured and the computed slope displacements and reinforcement forces in response to increases in pseudo-static seismic forces suggest that the FFDM can be used as an analytical tool for evaluating displacements of reinforced slopes subjected to pseudo-static seismic loads.     

Required strength of geosynthetics in a reinforced slope with tensile strength cut-off subjected to seepage effects

The Mohr-Coulomb (M-C) yield criterion is found to overestimate the tensile strength of cohesive soils. By introducing the concept of tensile strength cut-off, the M-C criterion is modified to reduce or eliminate the tensile strength from the criterion. In this study, a new approach is proposed to investigate the stability of geosynthetic-reinforced slopes in cohesive soils subjected to seepage effects by means of the kinematic approach of limit analysis. The distribution of pore-water pressure is obtained using the numerical modeling software package, FLAC3D. A kinematically admissible failure mechanism is discretized to incorporate the results from the numerical simulation. The strength of geosynthetics required for maintaining the slope stability is evaluated from the work-energy balance equation. An optimization routine is used to seek out the maximum value among all possible results. Design charts providing the normalized required reinforcement under different parameters are plotted for a parametric study and convenient use in engineering. The obtained results show that less reinforcement is required in the presence of soil cohesion, and that the inclusion of the effect of tensile strength cut-off leads to a more conservative solution, which is more obvious in the presence of seepage effects.     

岩质高切坡预应力锚索超前支护研究

采用极限分析上限定理研究遵循Hoek-Brown强度准则岩质高切坡超前支护问题。首先研究无支护岩质高切坡的稳定性,给出无支护岩质高切坡稳定计算方法;其次,分析预应力锚索超前支护岩质高切坡的力学机制,推导相关计算公式和预加固荷载确定方法;最后分析加固岩质高切坡在地震荷载下的临界屈服加速度及其永久位移。揭示了开挖方式、强度参数对预应力锚索加固岩质高切坡的影响。     

Required strength of geosynthetics for reinforced 3D slopes in cohesive backfills with tensile strength cut-off

In extant studies, most of the stability analyses of geosynthetic-reinforced slopes focused on two-dimensional conditions using the Mohr-Coulomb (M-C) failure criterion to describe the strength of backfills. However, in reality, all failures of slopes indicate a somewhat three-dimensional (3D) feature, and the M-C criterion is observed to overestimate the tensile strength of cohesive soils. To partially remedy this shortcoming, the concept of tensile strength cut-off is adopted to include the actual tensile strength of backfills in the yield envelope, and a kinematic approach is presented to evaluate the required strength of geosynthetics for 3D reinforced slopes in cohesive backfills. A 3D rotational mechanism of collapse that is associated with the strength envelope with tension cut-off is developed. The amount of required reinforcement is evaluated and listed as a dimensionless coefficient. The results indicate that the inclusion of the 3D effect and soil cohesion can lead to substantial savings in terms of the reinforcement to be made. In addition, a higher amount of reinforcement is required when the effect of tension cut-off is considered; this effect is more distinct for backfill with a higher amount of cohesion.     

Stability analysis of stone column-supported and geosynthetic-reinforced embankments on soft ground

This study focuses on the stability of stone column-supported and geosynthetic-reinforced embankments on soft soil. An upper-bound limit state plasticity failure discretization scheme (known as discontinuity layout optimization (DLO)), which determines the embankment stability without pre-assuming a slip surface, is used. The relationships between the stability of stone column-supported and geosynthetic-reinforced embankments and various influencing parameters, including the soil strength, geometric configuration, reinforcement strength, and area replacement ratio, are analysed. It is found that geosynthetics provide a significant contribution to embankment stability. Two failure mechanisms of geosynthetics (i.e., rupture failure and bond failure) are revealed and the effect of geosynthetics on embankment stability is governed by the failure mode. The application of stone columns mitigates the risk of geosynthetic failure. To provide an analytical solution for primary design in engineering practice, an approach based on the limit equilibrium method is proposed. Validations are performed with the DLO solution to demonstrate the accuracy and reliability of the developed analytical approach.     

地震作用下锚固土质边坡稳定性解析

极限分析上限方法在边坡地震稳定性评价中受到了广泛关注,但已有研究成果均针对某一类具体边坡,获得的解析解往往不具有普遍适用性。以上限定理为基础,基于组合对数螺线的旋转破坏机制,采用拟静力法,推导了具有任意坡面几何特征、任意土层分布和多排锚加固的复杂边坡外功率与内能耗散率平衡方程。在此基础上,结合强度折减技术和最优化方法,提出了地震作用下多排锚加固复杂边坡的稳定性安全系数和屈服加速度系数解析式,并结合Newmark法求解了边坡的永久位移,发展了锚固土质边坡地震稳定性的通用极限分析上限方法。通过典型算例验证与对比分析,表明本文方法具有较高的精度和广泛的适用性,最后将这一方法应用于实际工程。     

Seismic analysis of 3D geosynthetic-reinforced soil structures in cohesive backfills with cracks

This study proposes a procedure for predicting the required tensile strength of geosynthetics for three-dimensional (3D) geosynthetic-reinforced soil structures (GRSSs) comprised of cohesive backfills subjected to earthquake loadings. This procedure is undertaken using the kinematic approach of limit analysis together with a pseudo-dynamic approach. The influence of cracks is incorporated into the analysis by using a 3D horn-like failure mechanism that includes a vertical crack to characterize the collapse of GRSSs. Two different forms of cracks are considered: cracks forming prior to the collapse of GRSSs (open cracks) and cracks forming simultaneously with the collapse (formation cracks). Based on the work-energy balance equation, the amount of reinforcements needed to maintain the stability of GRSSs is determined. The results of this paper show that the required reinforcements significantly decrease when soil cohesion and 3D effects are considered, whereas accounting for the existence of cracks and seismic forces has an opposite effect.     

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.     

Pseudo-static stability analysis of rock slopes reinforced by passive bolts using the generalized Hoek-Brown criterion

The stability analysis of passive bolt-reinforced rock slopes under seismic loads is investigated within the framework of the kinematic approach of limit analysis theory.A pseudo-static method is adopted to account for the inertial forces induced in the rock mass by seismic events.The strength properties of the rock material are described by a modified Hoek-Brown strength criterion,whereas the passive bolts are modeled as bar-like inclusions that exhibit only resistance to tensile-compressive forces.Taking advantage of the ability to compute closed-form expressions for the support functions associated with the modified Hoek-Brown strength criterion,a rotational failure mechanism is implemented to derive rigorous lower bound estimates for the amount of reinforcement strength to prevent slope failure.The approach is then applied to investigating the effects of relevant geometry,strength and loading parameters in light of a preliminary parametric study.The accuracy of the approach is assessed by comparison of the lower bound estimates with finite element limit analysis solutions,thus emphasizing the ability of the approach to properly predict the stability conditions and to capture the essential features of deformation localization pattern.Finally,the extension of the approach to account for slipping at the interface between reinforcements and surrounding rock mass is outlined.     

高土石坝坝坡地震稳定分析研究

采用有限元动力时程稳定和变形分析方法,对不同高度大坝坝坡稳定进行分析,开展了最危险滑弧确定方法 、地震动持时对稳定和变形的影响、滑弧位置和深度以及坝坡加固范围的研究 。结果表明：拟静力法采用规范建议的加速度分布系数不能反映高土石坝实际地震反应规律,计算得到的最危险滑弧较深且滑动范围偏大,不利于确定坝坡的加固范围;坝坡在地震过程中,最小安全系数与最大滑动量对应的滑弧并不一致且是不断变化的,有限元动力法计算坝坡稳定时,应在每一时刻任意搜索最危险滑弧;地震持时对坝坡安全系数影响不大,但对滑动量有较大影响;不同滑弧深度对坝坡安全系数有较大影响,存在一个临界深度,当滑弧超过临界深度时,坝坡安全系数大于 1.0 ;坝坡稳定安全性评价需要综合考虑安全系数与变形的计算结果。根据计算结果,建议了坝坡加固的范围。     

地震边坡破坏机制及其破裂面的分析探讨

 地震作用下边坡破坏机制是边坡动力稳定性分析的前提,目前主要采用拟静力与动力有限元时程分析的方法进行分析,认为地震边坡破坏机制为剪切破坏,并以极限平衡法计算得到的剪切滑移面作为地震动力作用下的破裂面,而不考虑地震荷载作用下的拉破坏,从而使地震边坡稳定性分析失真。汶川地震边坡调研发现,滑坡上部多数发生拉破坏,甚至有些岩土体被抛出,这是一个很好的启示,为此,采用FLAC动力强度折减法,结合具有拉和剪切破坏分析功能的FLAC3D软件对地震边坡破坏机制进行数值分析。计算表明,地震边坡的破坏由边坡潜在破裂区上部拉破坏与下部剪切破坏共同组成,而不是剪切滑移破坏,通过多种途径给出地震边坡破裂面位置的确定方法,为边坡动力稳定性分析提供更加准确的基础。     

Probabilistic stability analysis of geosynthetic-reinforced slopes under pseudo-static and modified pseudo-dynamic conditions

An efficient and accurate reliability-based design of the geosynthetic-reinforced slopes (GRS) using the pseudo-static and modified pseudo-dynamic framework is proposed in the present study. Deterministic formulation used in the present study is made robust with the help of nonlinear constrained optimization. The collocation based stochastic response surface method (CSRSM) is used to probabilistically analyze the GRS. The critical modes of failure pertaining to the internal and external stability of the GRS are considered in the formation of the performance functions. The horizontal seismic acceleration coefficient (k_h), internal friction angle of soil (φ), soil unit weight (γ), shear wave velocity (V_s), and friction angle at the interface between soil and reinforcement (φ_b) are chosen as the random variables, owing to their high influence on the stability of the GRS. The influence of correlation on the stability of the reinforced slope is illustrated considering the internal and external stability. System reliability analysis considering the internal and external modes of failure is also performed. An illustrative example is presented showing the steps to design a GRS using the proposed formulation. The results confirm the necessity of performing the system reliability analysis to estimate an accurate value of probability of failure of GRS.     

Seismic stability of earth slopes with tension crack

Cracks at the crest of slopes frequently occur during earthquakes. Such cracks result from limited tension strength of the soil. A tension cut-off in Mohr-Coulomb shear strength can represent this limited strength. Presented is an extension of variational analysis of slope stability with a tension crack considering seismicity. Both translational and rotational failure mechanisms are included in a pseudo-static analysis of slope stability. Developed is a closed-form to assess the seismic stability of slopes with zero tensile strength. The results indicate that the presence of the tension crack has significant effects on the seismic stability of slopes, i.e., leading to small value of the yield acceleration. Considering soil tension strength in seismic slope analysis may lead to overestimation on the stability, as much as 50% for vertical slopes. Imposing tension crack results in transit of the critical failure mode to a straight line from a log-spiral, except for flat slopes with small soil cohesion. Under seismic conditions, large cohesion may increase the depth of crack, moving it closer to the slope.     

Centrifuge model study on low permeable slope reinforced by hybrid geosynthetics

The objective of this paper is to study the performance of hybrid geosynthetic reinforced slopes, with permeable geosynthetic as one of its components, for low permeable backfill slopes subjected to seepage. Four centrifuge tests have been performed to study the behavior of hybrid geosynthetic reinforced slopes subjected to seepage, keeping the model slope height and vertical spacing of geosynthetic reinforcement layers constant. Centrifuge model tests were performed on 2V:1H slopes at 30 gravities. One unreinforced, one model geogrid reinforced and two hybrid geosynthetic reinforced slope models with varying number of hybrid geosynthetic layers were tested. The effect of raising ground water table was simulated by using a seepage flow simulator during the flight. Surface movements and pore water pressure profiles for the slope models were monitored using displacement transducers and pore pressure transducers during centrifuge tests. Markers glued on to geosynthetic layers were digitized to arrive at displacement vectors at the onset of raising ground water table. Further, strain distribution along the geosynthetic reinforcement layers and reinforcement peak strain distribution have been determined using digital image analysis technique. The discharge for the performed model tests is determined by performing seepage analysis. It was confirmed by the centrifuge tests that the hybrid geosynthetics increases the stability of low permeable slope subjected to water table rise. The hybrid geosynthetic layers in the bottom half of the slope height play a major role in the dissipation of pore water pressure.     

土工袋加固砂性土质边坡模型试验与上限解

 通过模型试验比较有土工袋加固和无土工袋加固时边坡的破坏形态及承载力,验证土工袋对边坡的加固效果,并基于试验结果建立边坡的许可破坏模式及其速度场,利用极限分析上限法求解了边坡的极限高度上限解,利用模型试验结果对边坡极限高度进行验证。试验及计算结果均表明：边坡越陡,有土工袋加固较无土工袋加固时边坡的极限高度和承载力提高越大,表明土工袋加固效果越好。试验结果与计算结果基本吻合,表明该计算方法的可信性,可为边坡的稳定性设计问题提供理论依据。     

确定岩质边坡地震安全系数的简化方法

 作为岩质边坡地震稳定性评价的规范方法,拟静力法忽略岩体的动力特性和地震动大部分特性的影响,而地震时程分析法考虑的因素较全面,却相对费时费力。目前岩质边坡地震稳定性评价缺乏较好地考虑岩体的动力特性和地震动特性的简化方法。为此,综合利用时程分析法和拟静力法的各自优点,建立地震安全系数与拟静力安全系数间的关系,提出2种岩质边坡地震稳定性评价的简化方法：(1) 对于重要边坡,建立边坡地震安全系数与地震动峰值、边坡拟静力安全系数的统计经验公式;(2) 对于一般边坡,统计边坡地震安全系数与拟静力安全系数的修正系数,建议相应的修正方案。以典型岩质边坡为例,采用显式波动有限元–极限平衡法,阐述所提出的简化方法的详细实施步骤,初步证明所提出方法的可行性和合理性。所建议的简化方法为重要工程岩质边坡震后快速评估和一般工程岩质边坡抗震稳定性评价提供有益的思路和重要参考。