Numerical analysis of the behaviour of mechanically stabilized earth walls reinforced with different types of strips

A mechanically stabilized earth (MSE) wall behaves as a flexible coherent block able to sustain significant loading and deformation due to the interaction between the backfill material and the reinforcement elements. The internal behaviour of a reinforced soil mass depends on a number of factors, including the soil, the reinforcement and the soil/structure interaction and represents a complex interaction sol/structure problem. The use of parameters determined from experimental studies should allow more accurate modelling of the behaviour of the MSE structures.In this article, a reference MSE wall is modelled from two points of view: serviceability limit state “SLS” and ultimate limit state “ULS”. The construction of the wall is simulated in several stages and the soil/interface parameters are back analysed from pullout tests. An extensive parametric study is set up and permits to highlight the influence of the soil, the reinforcement and the soil/structure parameters. The behaviour of MSE walls with several geosynthetic straps is compared with the metallic one. Several constitutive models with an increasing complexity have been used and compared.The results obtained from stress-deformation analyses are presented and compared. The use of geosynthetic straps induces more deformation of the wall but a higher safety factor. To design theses walls the important parameters are: the soil friction, the cohesion, the interface shear stiffness and the strip elastic modulus.It is shown that for wall construction that involves static loading conditions, the modified Duncan-Chang model is a good compromise but induces slightly lower strip tensile forces due to the fact that it do not take into account of dilatancy before failure.     

Analysis of installation damage tests for LRFD calibration of reinforced soil structures

North American design codes are now committed to the development of load and resistance factor design (LRFD) for reinforced soil structures including internal stability limit states. Reliability-based analysis is required to carry out these calibrations. A framework for LRFD calibration has been proposed by the writers that requires bias statistics for load and resistance terms for each limit state function. In this paper the formulation of the limit state for reinforcement tensile rupture is developed and the component strength-reduction bias statistics identified. The paper describes how to compute bias statistics from project-specific installation damage trials for use in reliability-based design for the reinforcement rupture limit state or using data from multiple sources for LRFD calibration. A database of results from field installation damage trials on 103 different geosynthetic products was collected from 20 different sources. A total of 799 and 2248 in-air tensile test results were reviewed for undamaged and damaged geosynthetic specimens, respectively. This database is used to compute installation damage bias statistics for six different categories of geosynthetic and four categories of backfill soils classified according to the D₅₀ particle size. A practical outcome is that for analysis purposes, bias statistics can be grouped into two ranges for each geosynthetic type based on D₅₀ of the soil greater than or less than 19 mm. The paper shows how bias statistics together with load and resistance factors for the geosynthetic rupture limit state function recommended by AASHTO (2010) can be used to calculate probability of failure using Monte Carlo simulation and demonstrates the sensitivity of probability of failure to magnitude of installation damage bias statistics. The installation damage data is valuable for future LRFD calibration to select resistance factors for use in design codes for the geosynthetic rupture limit state in reinforced soil structures.     

Limit States Design Calibration for Internal Stability of Multi-Anchor Walls

The paper describes the methodology and results of limit states design calibration for two limit states of Japanese multi-anchor wall (MAW) earth retaining systems: anchor plate pullout and anchor rod rupture due to soil self-weight loading. Bias statistics are computed from measured loads from instrumented MAW structures and in-situ anchor load tests. Two different load models and two different plate load capacity equations are used in the calibrations. A load factor of γ_Q=2.25 is recommended to meet a 3% load exceedance criterion using a new load model by the writers which increases to 3.00 if the current approach recommended by PWRC (2002) is used. A target probability of failure P_f=1% is used in calibrations and is judged to be a reasonable value for the highly load-redundant MAW systems. Resistance factors of 0.80 and 0.95 are recommended for anchor plate and anchor rod rupture limit states using the new load and resistance models proposed by the writers. While the paper is focused on one particular wall system, the reliability-based limit states design calibration approach described in the paper provides an instructive template for limit states calibration of other reinforced soil retaining wall systems in Japan.     

Pullout behavior of a bearing polymeric strap under monotonic and cyclic tensile loads

Soil-reinforcement interaction consists of three factors including frictional resistance, shear strength of the soil and passive resistance. In the ordinary polymeric strap (PS) reinforcement, only frictional resistance contributes to pullout resistance. In this study, in order to develop passive resistance in the soil, a number of angles as transversal elements were attached to PS reinforcement, which is called bearing polymeric strap (BPS). The post-cyclic pullout behaviour of the BPS is evaluated using a large-scale pullout apparatus adopting multistage pullout (MSP) test and one-stage pullout (OSP) test procedures. The results show that a spacing-to-high ratio of angles equal to 3.33 gives the maximum pullout resistance. MSP tests were performed on the BPS with an optimum arrangement to evaluate the influence of various factors including cyclic tensile load amplitude, load frequency and number of load cycles, and also the influence of vertical effective stress on the pullout resistance and the peak apparent coefficient of friction mobilized at the soil-BPS interface. Moreover, for BPS system with a single isolated transverse member, the bearing capacity factor N_q was calculated using equations based on three failure modes and it was found that the N_q calculated in the punching shear failure mode makes the best prediction.     

Seismic effects on reinforcement load and lateral deformation of geosynthetic-reinforced soil walls

Current design methods for the internal stability of geosynthetic-reinforced soil (GRS) walls postulate seismic forces as inertial forces, leading to pseudo-static analyses based on active earth pressure theory, which yields unconservative reinforcement loads required for seismic stability. Most seismic analyses are limited to the determination of maximum reinforcement strength. This study aimed to calculate the distribution of the reinforcement load and connection strength required for each layer of the seismic GRS wall. Using the top-down procedure involves all of the possible failure surfaces for the seismic analyses of the GRS wall and then obtains the reinforcement load distribution for the limit state. The distributions are used to determine the required connection strength and to approximately assess the facing lateral deformation. For sufficient pullout resistance to be provided by each reinforcement, the maximum required tensile resistance is identical to the results based on the Mononobe–Okabe method. However, short reinforcement results in greater tensile resistances in the mid and lower layers as evinced by compound failure frequently occurring in GRS walls during an earthquake. Parametric studies involving backfill friction angle, reinforcement length, vertical seismic acceleration, and secondary reinforcement are conducted to investigate seismic impacts on the stability and lateral deformation of GRS walls.     

Reliability analysis of soil-geogrid pullout models in Japan

The paper examines the accuracy of two geogrid pullout capacity models used in Japan (Public Works Research Center-PWRC, 2000a) by comparing measured capacities from a large database of laboratory pullout tests to predicted capacities. One model is the current default model (Model 1) used when project-specific laboratory pullout testing is not available and the other when this data is available (Model 2). The accuracy of the models is quantified using bias statistics where bias is defined as the ratio of measured pullout capacity to predicted value. Bias statistics are also a necessary precursor for reliability-based load and resistance factor design calibration for the ultimate pullout limit state in the internal stability design of geogrid reinforced soil walls. Bias statistics using Model 2 show that pullout predictions are very accurate with negligible scatter. However, the default model is shown to be very conservative on average with large scatter in bias values which also varies with magnitude of predicted pullout capacity. A modified formulation for Model 1 is proposed that has the same number of empirical coefficients as the current expression (i.e. two). The modified formulation gives improved accuracy based on the computed mean and coefficient of variation of bias values, and eliminates the significant model bias that is present for the current model. A final outcome from analysis of all available pullout data is that a factor of safety F=2 is recommended for allowable stress design (ASD) when using the current PWRC default Model 1, and a value of F=1.25 is recommended when using Model 2 with project-specific pullout testing.     

腐蚀钢绞线预应力混凝土梁受弯承载力评估

考虑腐蚀引起钢筋名义概率强度的降低,采用实用概率极限状态设计表达式中的抗力项进行预应力混凝土梁受弯承载力计算,可以获得基于材料强度平均值、标准值、设计值共3级可靠度水平的受弯承载力评估结果。基于试验结果统计,建立了随腐蚀率变化的腐蚀钢绞线名义抗拉强度与名义条件屈服抗拉强度的平均值、标准值以及设计值计算模型。分析表明：受拉钢绞线的计算极限状态（即条件屈服状态）名义应力低于实际极限状态（即极限受拉状态）名义应力,而其他钢筋的计算极限状态名义应力与实际极限状态名义应力相互吻合。最后结合算例阐述了上述方法的具体应用。图4表4参21     

Pullout behavior of polymeric strip in compacted dry granular soil under cyclic tensile load conditions

Assessment of the reinforcement behavior of soil under cyclic and monotonic loads is of great importance in the safe design of mechanically stabilized earth walls. In this article, the method of conducting a multistage pullout (MSP) test on the polymeric strip (PS) is presented. The post-cyclic behavior of the reinforcement can be evaluated using a large-scale pullout apparatus adopting MSP test and one-stage pullout (OSP) test procedures. This research investigates the effects of various factors including load amplitude, load frequency, number of load cycles and vertical effective stress on the peak apparent coefficient of friction mobilized at the soil-PS interface and the pullout resistance of the PS buried in dry sandy soil. The results illustrate that changing the cyclic tensile load frequency from 0.1 Hz to 0.5 Hz does not affect the pullout resistance. Moreover, the influence of increasing the number of load cycles from 30 to 250 on the peak pullout resistance is negligible. Finally, the effect of increasing the cyclic tensile load amplitude from 20% to 40% on the monotonic pullout resistance can be ignored. The peak apparent coefficient of friction mobilized at the soil-PS interface under monotonic and cyclic load conditions decreases with the increase in vertical effective stress.     

System reliability analysis of soil nail wall using random finite element method

Soil nail wall is a compound system which for safety margin determination, consideration of safety factors of its components and their correlations is required. In this paper, considering a real site using the random finite element method (RFEM), the reliability indices of global stability, lateral displacement stability, tensile strength, and pullout resistance stability as components of the soil nail wall system are obtained. In another section of the paper, using the sequential compounding method (SCM), the importance of the mentioned stability modes and their effects on system reliability and system probability of failure are represented. Results show that the most considerable interdependence is between the global and lateral displacement stabilities. Among the reliability indices of the components, the minimum one is attributed to the pullout resistance. Furthermore, the uppermost row of the nails has the most critical reliability index compared with the others. The locations of the slip surfaces and nail intersections varied from 0.05–0.90 of the nail length, which means that the uncertainty of the soil parameters has the most significant effect on the pullout resistance safety factor of the nails. The performance level of the soil nail wall decreases from below average to poor when the soil nail wall is considered to be a system with series components.

     

Simplified Procedure to Evaluate Earthquake-Induced Residual Displacement of Geosynthetic Reinforced Soil Retaining Walls

Based on a series of shaking table model tests, it was found that the effects of 1) subsoil and backfill deformation, 2) failure plane formation in backfill, and 3) pullout resistance mobilized by the reinforcements on the seismic behaviors of the geosynthetic reinforced soil retaining walls (GRS walls) were significant. These effects cannot be taken into account in the conventional pseudo-static based limit equilibrium analyses or Newmark's rigid sliding block analogy, which are usually adopted as the seismic design procedure. Therefore, this study attempts to develop a simplified procedure to evaluate earthquake-induced residual displacement of GRS walls by reflecting the knowledge on the seismic behaviors of GRS walls obtained from the shaking table model tests. In the proposed method, 1) the deformation characteristics of subsoil and backfill are modeled based on the model test results and 2) the effect of failure plane formation is considered by using residual soil strength after the failure plane formation while the peak soil strength is used before the failure plane formation, and 3) the effect of the pullout resistance mobilized by the reinforcement is also introduced by evaluating the pullout resistance based on the results from the pullout tests of the reinforcements. By using the proposed method, simulations were performed on the shaking table model test results conducted under a wide variety of testing conditions and good agreements between the calculated and measured displacements were observed.     

土体抗剪强度指标变异水平对边坡稳定安全系数取值的影响

针对传统的边坡稳定极限平衡方法不能考虑土体抗剪强度指标变异性影响的问题,基于极限状态的概率分析原理,采用 Monte-Carlo 法对均质路堤边坡的稳定性开展了可靠度计算,讨论了稳定安全系数一定的条件下边坡失效概率随土体抗剪强度指标变异水平的变化规律,分析了安全系数与边坡可靠指标的对应关系及其随土体抗剪强度指标变异水平的变化特征。研究表明：边坡可靠度受土体抗剪强度指标变异性影响显著,呈现出随土体抗剪强度指标变异水平提高而急剧减小的趋势;为保证边坡具有相同的可靠性,安全系数的取值应与土体抗剪强度指标的变异性相适应,据此提出了基于可靠指标和土体抗剪强度指标变异水平的安全系数取值原则及其对应的三参数函数关系式。     

柔性与硬性地工格网在砂土与风化泥岩围压下之力学特性

地工格网（以下称格网）用於加劲土壤时，除考虑无围压下的张力行为之外，围压下之力学性质更是设计考量的重点。实际工程应用而言，基於经济考虑，期以现地土壤作为回填材料。本研究分别以拉出、围压抗张与直剪三种试验来探讨格网放土壤中之力学行为；并利用凝聚性泥岩与非凝聚性细砂作为回填材料，评估两种回填材料对加劲成效之影响。结果显示，柔性格网之肋条在拉出过程中易扭曲，造成主应力面旋转的现象，以致拉出阻抗大放硬性格网；围压下格网抗张的应力-应变行为可分为三阶段，即束制阻抗期、张力发展期与破坏期。束制阻抗期大都於3％应变内即已完成；在低围压情况拉出阻抗达20％～60％之拉出强度（相同应变），在高围压下达150％。由直接剪力试验结果可以预测：（a）格网／泥岩加劲结构-低围压时，剪力破坏面应通过格网／泥岩之界面；而高围压时，剪力破坏面应通过泥岩上体。（b）格网／细砂加劲结构-低围压与高围压下剪力破坏面应通过格网／细砂之界面。     

Influence of uncertainty in geosynthetic stiffness on deterministic and probabilistic analyses using analytical solutions for three reinforced soil problems

The paper examines the quantitative influence of uncertainty in the estimate of geosynthetic reinforcement stiffness on numerical outcomes using analytical solutions for a) the maximum outward facing deformation in mechanically stabilized earth (MSE) walls, b) maximum reinforcement tensile loads and strain in MSE walls under operational conditions, and c) the mobilized reinforcement stiffness in a geosynthetic layer used to reinforce a fill over a void. The stiffness of the reinforcement is modelled using an isochronous two-parameter hyperbolic load-strain model. A linear relationship between isochronous stiffness and the ultimate tensile strength of the reinforcement is used to estimate reinforcement stiffness when product-specific creep data are not available at time of design. Solution outcomes are presented deterministically and probabilistically. The quantitative link between nominal factor of safety used in deterministic working stress design practice and reliability index is provided. The latter is preferred in modern performance-based design to quantify margins of safety within a probabilistic framework. Finally, the paper highlights the practical benefit of using product-specific isochronous secant stiffness data when available, rather than estimates of isochronous stiffness values based on reinforcement type or pooled data.     

Reliability-based design of wind turbine blades

Reliability-based design of wind turbine blades requires identification of the important failure modes/limit states along with stochastic models for the uncertainties and methods for estimating the reliability. In the present paper it is described how reliability-based design can be applied to wind turbine blades.For wind turbine blades, tests with the basic composite materials and a few full-scale blades are normally performed during the design process. By adopting a reliability-based design approach, information from these tests can be taken into account in a rational way during the design process. In the present paper, a probabilistic framework for design of wind turbine blades are presented and it is demonstrated how information from tests can be taken into account using the Maximum-Likelihood method and Bayesian statistics.In a numerical example, the reliability is estimated for a wind turbine blade in both ultimate and fatigue limit states. Information from tests is used to formulate the stochastic models used in the limit state equations. Partial safety factors for use in traditional deterministic design are estimated using the stochastic models.     

Displacement and load transfer mechanisms of geogrids under pullout condition

Reinforcing elements embedded within soil mass improve stabilization through a load transfer mechanism between the soil and the reinforcement. Geogrids are a type of geosynthetic frequently used for soil reinforcement, consisting of equally spaced longitudinal and transverse ribs. Under pullout conditions, the longitudinal ribs are responsible for tensile resistance, while transverse ribs contribute to a passive resistance. This paper describes a new analytical model capable of reproducing both load transfer and displacement mechanisms on the geogrid length, under pullout conditions. The model subdivides the geogrid into rheological units, composed by friction/adhesion and spring elements, mounted in line. Friction/adhesion elements respond to the shear component mobilized at the soil–geogrid interface. Spring elements respond to the geogrid's tensile elongation. Model parameters are obtained through tensile strength tests on geogrids and conventional direct shear tests on soil specimens. The need for instrumented pullout tests becomes therefore eliminated. Results predicted from this new model were compared to instrumented pullout test data from two types of geogrids, under various confining stress levels. The results revealed that the new model is capable of reasonably predicting load and displacement distributions along the geogrid.     

Investigation of bond in concrete member with fibre reinforced polymer (FRP) bars

Bond strength of fibre reinforced polymer (FRP) rebars was experimentally investigated in this study and compared to that of steel rebars. A total of 64 concrete beams reinforced with two types of FRP rebars, respectively, were tested. Four nominal diameters of FRP and steel rebars, namely, 12.7, 15.9, 19.1 and 25.4 mm and three embedment lengths, six, 10 and 16 times the rebar diameter were used. Moreover, three concrete depths of 200, 600 and 1000 mm were investigated in the 18 pullout specimens. Results of the tests indicated that the applied tensile load approached the tensile strength of rebars as the embedment length increased and the GFRP rebars showed lower bond strength values compared to steel rebars. The average maximum bond strength of the FRP rebars varied from 5.1 to 12.3 MPa depending on the diameter and the embedment length. The GFRP rebars showed lower bond strength values compared to steel rebars. A modification factor of 1.30 is recommended for computing the development length, to account for the top bar effect. A new model is proposed for the ascending branch of the bond–slip law.     

Investigation of soil deformation characteristics during pullout of a ribbed reinforcement using X-ray micro CT

Steel-strip reinforced earth walls stabilize through the pullout resistance of the reinforcements. Soil dilation during the pullout of ribbed reinforcements may contribute to the evolution of pullout resistance; however, few studies have clarified this mechanism by investigating how soils behave with increasing pullout displacement. The ribs of the reinforcements enhance the pullout resistance, although the influence of the rib dimensions on the evolution of pullout resistance with increasing pullout displacement has not been sufficiently revealed. In the present study, a triaxial pullout apparatus is developed and pullout tests are conducted using ribbed reinforcements with different rib-inclination angles under isotropic stress. The displacement and strain fields in the soils during the pullout of the reinforcements are investigated by X-ray micro CT and a digital image correlation technique. It is found that larger rib-inclination angles provide higher pullout resistance at an early stage of the pullout because of the higher bearing resistance related to the more significant soil densification above the ribs. With increasing pullout displacement, the reinforcements with different rib-inclination angles come to behave as almost one in the same since a rigid soil wedge related to the passive soil failure is generated above the ribs. This tendency results in similar soil deformation characteristics and pullout resistance levels for every reinforcement beyond the soil failure state, although the rib-inclination angles are different.     

Evaluation of oblique pullout resistance of reinforcements in soil wall subjected to seismic loads

Pullout resistance is one of the most important factors governing seismic stability of reinforced soil walls. The previous studies on the seismic stability of reinforced soil walls have focused on the axial resistance of the reinforcement against the pullout. However, the kinematics of failure causes the reinforcement to be subjected to the oblique pullout force and bending deformation. Considering the kinematics of failure and bending deformation of the reinforcement, this paper presents a pseudo-static seismic analysis for evaluating the pullout resistance of reinforcements in soil wall subjected to oblique pullout forces. A modified horizontal slice method (HSM) and Pasternak model are used to calculate the required force to maintain the stability of the reinforced soil wall and shear resistance mobilized in the reinforcements, respectively. In addition, this paper studies the effect of various parameters on the pullout resistance of the reinforcements in soil wall subjected to seismic loads. Results of this study are compared with the published data and their differences are analyzed in detail.     

What is the role of tensile cracks in cohesive slopes?

The traditional limit equilibrium method (LEM) is often used to search for the failure surface with a minimum safety factor of slope. In this method, the failure surface is considered as a shear surface, irrespective of its form. However, tensile cracks are frequently found at the outcrops of landslides. In this study, three sets of tests on small-scale landslides with different inclination angles were conducted. The test results demonstrated that tensile cracks could arise in the slope sliding process and the failure surface is composed of both a shear and a tensile fracture surface. Based on the test results, we used the improved LEM, and replaced the traditional shear failure surface by a tensile-shear coupling one, thus new tensile failure modes for slope stability analysis can be established. The safety factors of slope in different failure modes were compared, which show that when considering soil tensile failure and tensile strength less than a certain value (e.g. 15 kPa, 44 kPa and 55 kPa for linear, circular and logarithmic spiral failure surfaces, respectively), the safety factors of slope with three different failure surfaces are less than the one that did not consider the tensile failure. The most critical failure surfaces of the slope may be composed of shear and tensile damages because the tensile strength of the soil cannot be generally greater than its cohesion.     

Ultimate strength reliability analysis of corroded steel-box girder bridges

Structural reliability theory is a useful tool for estimating the risks associated with deteriorating structures. The aim of this study is to develop and demonstrate a procedure for the assessment of box girder bridge ultimate strength reliability with the degradation of plate members due to general corrosion taken into account. A probabilistic model for ultimate steel-box girder strength is established on the basis of an analytic formula that considers corrosion-related, time-dependent strength degradation. The study involves the selection of representative structures, formulation of limit state functions, development of resistance models for corroded steel-box girders, development of load models, development of a reliability analysis method, reliability analysis of the selected bridges and development of the time-dependant reliability profiles, including deterioration due to corrosion. The results of this study can be used for the better prediction of the service life of deteriorating steel-box girder bridges and the development of optimal reliability-based maintenance strategies.