Influence of model type,bias and input parameter variability on reliability analysis for simple limit states in soil–structure interaction problems

ABSTRACT

A general closed-form solution for the true probability of failure of a simple limit state function with one load term and one resistance term is derived. The formulation considers contributions due to model type, uncertainty in method bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety. Example calculations are presented using different load and resistance models for the pullout internal stability limit state of steel strip reinforced soil walls together with matching bias data reported in the literature.     

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.     

Performance-based analysis and design for internal stability of MSE walls

ABSTRACT

Mechanically stabilized earth (MSE) walls must be designed with adequate margins of safety against internal stability failure described by tensile strength and pullout limit states. Probabilities of failure (or reliability index) will vary strongly with the accuracy of the underlying models that appear in limit state performance functions. In this paper, prior work by the authors and co-workers on this topic is reviewed. Relative performance is explored in the context of the reliability (or probability of failure) of steel and polymeric reinforcing elements in MSE walls using limit state performance functions with load and resistance models having different accuracy.     

Analysis of resistance factors for LFRD of soil nail walls against external stability failures

This paper presents reliability analyses of soil nail walls against two external ultimate limit states, global and sliding stabilities, which are related to the external stability failures of soil nail walls. Reliability analyses are conducted using Monte Carlo simulation technique. Soil nailing is a popular retaining system in highway construction and slope stabilization, and its current design practice is still based on the working stress design. There remains a need to establish a more rational design framework—load and resistance factor design—based on the concept of limit state design and reliability analysis for soil nail walls. The development of load and resistance factor design approach must consider multiple ultimate limit states, associated with external, internal, and facing failures. The analyses of resistance factors against two external failures are conducted in this study considering various influencing factors, including statistical parameters of soil friction angle, ultimate bond strength between soil and nails, soil type, wall geometry (wall height, back slope angle, and face batter angle), and nail configurations (nail inclination angle, drillhole diameter, and nail spacing). In the end, a series of resistance factors are proposed for potential application of load and resistance factor design approach against external failures for soil nail walls according to different design codes.     

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.     

粘土与筋带直剪试验与拉拔试验对比分析

在土工合成材料加筋土工程中,土工合成材料与填土的界面作用特性直接决定加筋土工程的内部稳定性,所以土工合成材料与填料的界面作用特性指标是最关键的技术指标。对两种加筋材料与高液限粘土之间分别进行了直剪试验和拉拔试验,通过分析可得筋土之间的剪应力随着垂直压力的增大而增加,但随着垂直压力的增大筋土之间剪应力增长率减小,即随着垂直压力的增加,筋土之间的剪应力收敛于某一上限值;由于加筋材料在试样制作过程中不可避免地在土中发生凹凸变形使土体对筋带产生一定的锚固作用,拉拔试验所测得的似摩擦系数及似粘聚力均大于直剪试验所测得的似摩擦系数及似粘聚力。因此,实际加筋土工程中,拉拔试验更能较好地反映其真实的工作状态。     

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.     

Statistical analysis of the effective stress method and modifications for prediction of ultimate bond strength of soil nails

Uncertainty in the predicted ultimate pullout strength of soil nails can be significant due to the complexity of nail–soil interactions, inherent variability in soil properties and the effects of nail installation. The paper first presents a statistical evaluation of the accuracy of ultimate bond strength of soil nails using the effective stress method (ESM) equation that has been adopted in Hong Kong. A total of 113 ultimate nail capacity data points from field pullout tests were collected from the literature and used to estimate the accuracy of the current ESM. Based on the available data, the current ESM default pullout model is found to be excessively conservative (on average) by at least a factor of three. The spread in prediction accuracy measured by the coefficient of variation (COV) of bias is in the range of 36–43 % after removing anomalous test data. Here, bias is the ratio of measured to predicted pullout load capacity. In addition, the accuracy of the current ESM equation for prediction of nail bond strength is shown to be dependent on the magnitude of predicted ultimate bond strength and magnitude of nominal vertical effective stress which is undesirable. The paper examines four candidate-modified bond strength equations with empirical coefficients that have been back-fitted to measured bond strengths to improve the overall accuracy of the equation and to reduce or remove the undesirable dependencies noted above. One equation with an empirically corrected stress-dependent term is judged to be the best candidate model based on the mean of bias values, spread (COV) of bias values, lack of dependencies and simplicity. Finally, the relative contributions of random variability in soil shear strength to measurement bias in bond strength (prediction accuracy) for each soil type are computed for the best bond strength model. Analysis of the contribution of soil shear strength to prediction accuracy showed that the combination of variability due to factors other than soil shear strength was greater than the variability in soil shear strength alone, where the latter is defined by the soil secant friction coefficient.     

带加强肋土工格栅的极限拉拔阻力分析

在立体加筋体系研究基础上,提出了带加强肋土工格栅加筋,即通过对普通土工格栅的肋进行加强处理,使其肋具有一定的竖向厚度,构成具有立体加筋效果的带加强肋土工格栅。采用染色砂法,通过带加强肋土工格栅的拉拔试验进行了拉拔力机理分析。在拉拔过程中,加强肋前方土体会首先被挤密加强,成为一个刚性的楔体,然后刚性楔与筋材一起运动成为一个土筋共同体。推导了带加强肋土工格栅加筋土的拉拔阻力模型,分析中将加强肋的侧阻力作用简化为侧向土压力的作用,采用极限平衡理论,通过两侧的主动土压力与被动土压力进行计算。根据所建立的拉拔阻力模型计算出带加强肋土工格栅加筋的极限拉拔阻力,并与试验结果进行了对比,两者基本吻合     

细砂中钢带-填土废塑料瓶抗拔性能试验研究

研究利用填土废塑料瓶作为横向构件附在加筋土挡墙（MSEWs）中钢带上可行性。配筋中的横向构件对增加抗拔力有重要影响。该加筋系统是由作为纵向构件的钢带和作为横向构件的填土废塑料瓶组成。为更好地研究以填土废塑料瓶作为横向构件对抗拔性能的影响,对一条独立的钢带和分别带有1～7个瓶子的钢带进行了拉拔试验。在不同的法向应力下进行了超过18次的实验室大型拉拔试验（例如拉拔箱尺寸为长1.2 m、宽0.6 m、高1.0 m）来评估新提出的加固元件的性能。试验结果表明,在扁钢带上建立三维空间对提高抗拔阻力影响很大。提高抗拔阻力最有效的方法是在距离S与直径D之比为3的钢带上加入4个横向构件,其平均抗拔阻力约为单独钢带的5倍。有横向构件和无横向构件钢带的极限抗拔阻力随竖向应力的增大而增大。     

网格状带齿加筋体界面特性的宏细观力学机制研究

网格状带齿加筋是一种新型的土工加筋技术,汲取了传统网格状与条带式带齿加筋的优点,其筋土界面特性是加筋结构设计的基础。利用室内拉拔试验从宏观角度分析筋材与土的界面特性,结合颗粒流程序,筋材用平行黏结模拟,从细观角度分析筋土接触界面的产生和发展演化规律。数值结果表明：齿筋的存在对界面处颗粒的移动及剪切带的宽度影响显著,其破坏模式呈现波浪型,在齿筋附近出现应力集中现象。筋土界面处筋材与土颗粒摩擦、咬合和阻抗作用提供“似黏聚力”是改变网格状带齿加筋体系作用机制的内在原因。研究成果对于明确网格状带齿加筋拉拔的机制及模型的建立都具有意义。     

冻结井钢筋混凝土弧形板井壁力学特性研究

通过实验和有限元计算,对在均匀荷载作用下新型冻结井高强钢筋混凝土弧形板井壁的变形特性、混凝土和钢筋应力的分布规律、极限承载力及其压碎区的位置进行了分析。研究结果表明,弧形构件的径向变形较小,可通过选择合适的可缩接头材料使该井壁结构起到“先柔后刚”的作用;弧形构件的内排钢筋总是比外排钢筋先屈服,并且钢筋发生屈服时对应荷载值一般为该构件极限承载力的60 %左右;构件的极限承载力随混凝土单轴抗压强度的增大而增大,混凝土的强度等级提高10 MPa,其极限承载力提高1.26 MPa;弧形构件的压碎区位于其端部附近,因此,在设计该种井壁结构时弧形构件的两端应该加强,可在弧形构件的两端采用钢纤维混凝土以提高整体结构的承载能力。     

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).     

A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading

The ultimate bearing capacity problem of column‐reinforced foundations under inclined loading is investigated within the framework of static and kinematic approaches of yield design theory. The configuration of a native soft clayey soil reinforced by either a group of purely cohesive columns (lime‐column technique) or a group of purely frictional columns (stone‐column technique) is analyzed under plane strain conditions. First, lower bound estimates are derived for the ultimate bearing capacity by considering statically admissible piecewise linear stress distributions that comply with the local strength conditions of the constitutive materials. The problem is then handled by means of the yield design kinematic approach of limit analysis through the implementation of several failure mechanisms, allowing the formulation of upper bound estimates for the ultimate bearing capacity. A series of finite element limit load solutions obtained from numerical elastoplastic simulations suggests that the predictions derived from the kinematic approach appear to be more accurate than the estimates obtained from the static approach. Comparison with available results obtained in the context of yield design homogenization demonstrates the accuracy of the proposed direct analysis, which may therefore be viewed as complementary approach to homogenization‐based approaches when a small number of columns is involved. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of pressure-grouted soil nails on the stability of weathered soil slopes

Pressure-grouted soil nails have been increasingly used for stabilizing slopes. The pullout resistance of a soil nail is the main factor for reinforcing the slope stability. In this study, a two-dimensional axisymmetric finite element model is developed to simulate the pullout behavior of a pressure-grouted soil nail. This model is verified with field pullout tests result of a pressure-grouted soil nails by comparing with gravity-grouted soil nails. Based on the analysis, a three-dimensional finite element model is proposed for stability analysis of a slope reinforced with pressure-grouted soil nails using the shear strength reduction method. A series of numerical slope stability analyses for a slope composed of weathered soil are performed to investigate the effects of grouting pressure on the slope stability and the behavior of the soil nails. Special attention is given to the installation effect of a pressure-grouted soil nails. It is found from the result of this study that the pressure-grouted soil nails increase the safety factor by fifty percent in a slope by increasing the stiffness of the nailed slope system. Numerical analysis results confirm the fact that the pullout resistance of a soil nail is the main factor for stabilizing slopes rather than the shear resistance of the soil nail.     

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。     

土工格栅与土界面作用特性试验研究

土工格栅与土的界面摩擦特性指标是加筋土工程设计的关键。通过分析土工格栅与土的界面摩擦作用和进行了直剪摩擦试验和拉拔摩擦试验,测试了两种试验条件的界面摩擦特性。在两种试验条件下,土工格栅加筋土复合体的抗剪强度均有界面摩擦角φsq和界面凝聚力csq,且土工格栅与土相对位移量的不同,其复合体的强度机理有区别。在拉拔摩擦试验中,剪应力峰值强度对应的剪切变形值高于直剪摩擦试验中剪应力峰值强度的剪切变形值5～10倍以上。两种试验均有其适用性,而土与土工格栅的相对位移较小时直剪摩擦试验较能反映实际;土与土工格栅相对位移较大时土与格栅双面均发生相对位移,拉拔摩擦试验更为合适。随法向应力的增大,直剪摩擦和拉拔摩擦试验的剪应力峰值以及剪应力峰值对应的位移均提高。直剪摩擦的剪切速度小,剪应力峰值强度高,且达到峰值强度的剪切位移大;增加剪切速度,剪应力峰值强度降低,且对应的位移也减少,其原因是界面上的孔隙水压力消散和筋材的应力松弛。应根据具体工程的需要选择直剪摩擦试验和拉拔摩擦试验确定设计参数。     

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 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.     

锚板抗拉破坏机制试验研究

锚板上拔过程是一个复杂的锚土相互作用过程,锚板周围土体在上拔过程中的变形破坏机制对于锚板抗拔力的可靠预测具有重要意义。为了对锚板破坏机制进行量化分析,基于LabVIEW软件开发环境,开发了力、位移和图像同步采集系统,该系统由力传感器、位移传感器、相机和一台计算机组成,可对锚板上拔过程中的力、位移和图像进行自动同步采集,从而保证了力、位移和图像的一一对应关系。基于PIV（particle image velocimetry）无干扰测量技术对砂土中锚板在上拔过程中的图像进行了测量分析,得到了锚板周围土体的位移场、剪切应变场和体积应变场。变形场试验结果表明：锚板上拔过程中,锚板上部土体中间部分位移大、两边小,最终形成一个倒置的梯形;剪切应变场显示锚板上拔过程经历了局部剪切带形成,扩展并最终在锚板两侧形成一个倾斜向上并贯通到地面的对称剪切带,剪切过程中剪切带内伴随着剪涨。在峰后阶段,剪切带形状由峰值点内倾转为外倾,锚板两侧边缘处出现局部土体流动软化。该试验结果可为锚板上拔预测模型建立以及设计提供参考依据。