An elastoplastic model based on the shakedown concept for flexible pavements unbound granular materials

Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by mechanistic empirical formulas. Finite element modelling of realistic boundary value problems with incremental rheological models will lead to unrealistic calculation time for large cycle numbers. The objective of the authors is to present a simplified model which can be used to model the flexible pavements rutting with the finite elements framework. This method is based on the shakedown theory developed by Zarka which is usually associated to materials like steels. It has been adapted for granular materials by introducing a yield surface taking into account the mean stress influence on the mechanical behaviour and a dependency of the hardening modulus with the stress state. The Drucker–Prager yield surface has been used with a non‐associated flow rule. Comparisons with repeated load triaxial tests carried out on a subgrade soil have been done. These comparisons underline the capabilities of the model to take into account the cyclic behaviour of unbound materials for roads. Finally, a discussion, dealing with the use of the simplified method within a finite element modelling of a full‐scale experiment, is presented. Copyright © 2005 John Wiley & Sons, Ltd.     

道路安定理论的进展及其应用

30多年来,国际上的道路设计原理及方法逐渐从传统经验法向运用理论框架方面转变。但这些理论框架主要基于土和粒状材料的弹性假设,从而限制了材料塑性性能的发挥。安定分析基于弹塑性理论,可以确定结构在循环或变值荷载作用下的最大承载力,因此,能够被运用于道路承受交通荷载的问题。阐述了安定理论的概念以及两种经典安定定理,回顾了道路安定分析方法的创始及发展过程,包括与试验结果的比较,讨论了残余应力在道路中的分布、两种求解道路安定荷载极限的方法,以及与塑性极限分析的比较,并把一种下限安定分析方法应用于多层柔性路面的设计,最后展望了道路安定理论未来的发展方向。     

Unsaturated resilient behavior of a natural compacted sand

Granular materials are generally used in unbound layers of road pavement structures. The mechanical behavior of these materials is widely studied with repeated load triaxial tests (RLTT) in which the elastic response is defined as the resilient behavior. Usually observed under total stress conditions, the effect of pore pressure changes during loading are not usually included in design. Further, the unbound layers frequently exist under partially saturated conditions. The influence of the unsaturated state, i.e., the suction, on the mechanical behavior, of unbound granular materials for roads has not been sufficiently studied and is generally not taken into account in models used for these materials.     

基于下限定理的路面结构安定分析

传统的以弹性理论和经验方法为基础的路面结构设计方法,对路面结构的安全性评价存在着不合理性。安定理论可为复杂荷载作用下的路面结构承载力分析提供理论依据,基于该定理发展了一种应用于路面结构的安定分析方法,并应用于2层路面结构的安定分析,计算给出了荷载作用方式、路面结构形式、材料性质变化对路面安定极限影响的定量分析结果,通过对比表明了安定分析应用于路面结构的可行性。安定极限可为路面结构的分析与设计提供一定的参考价值。     

Resilient characterization of pavement materials

The paper presents an approach for characterizing pavement materials using the modified linear elastic behaviour. The secant modulus of elasticity is expressed in terms of the stress invariants and an expression for the secant Poisson's ratio is derived using path independence of the total work along a closed loading cycle. Triaxial test results of granular base–subbase materials which exhibit strong non-linear behaviour and dilatancy are analysed and presented. The constitutive law is included in a finite element program and results of pavement analyses are discussed. It is found that the secant Poisson's ratio of granular base materials reaches values between 0·6 and 0·7, indicating a volume increase under high stress ratios. The pavement response predicted using the above material characterization is compatible with non-destructive test results.     

Limits to the Jaumann stress rate

In this paper it is shown that the Jaumann stress rate is not accurate for moderate deformations with deviatoric strains of more than 10 per cent; in such cases the objective stress rate is better calculated using the material rotation rate as calculated by polar decomposition. For very large deformations of granular materials this approach becomes invalid too because then the fabric tends to rotate together with principal stresses. Apparently in general the fabric rotation of a granular material cannot be described by continuum mechanics alone. For the numerical calculation of the material rotation for moderate deformations a numerical subroutine, based on polar decomposition, has been developed.     

颗粒级配对粗粒土强度与变形特性影响的研究

采用三维颗粒流软件PFC3D的内置FISH语言,进行二次开发,模拟粗粒土级配,建立一个研究高铁填方路基粗粒土变形特性的颗粒流模型。通过粗粒土三轴试验,标定了表征粗粒土细观力学性质的模型参数,并验证了模型的有效性。考虑粗粒土曲率系数和不均匀系数对颗粒级配的影响,模拟并研究了5种不同级配下粗粒土在3种不同围压下的变形特性。试验结果表明,曲率系数对粗颗粒土变形特性影响较大,当其有效粒径与中值粒径及限制粒径的差距过大时,粗粒土中颗粒填充及致密性将变差,变形增大,强度降低。以较大曲率系数与较大不均匀系数组合的粗粒土受力性能较好,但此种级配的粗粒土压缩性大。级配良好且不均匀系数较大,其应力链分布越均匀,颗粒的挤压效果越显著,力的传递和分配也越均匀。     

An analytical solution to the design of precast concrete pavements

Precast concrete pavement units are used in areas with low subgrade CBR values and high static and dynamic loadings. Unlike flexible pavements and rigid pavements, there are no design charts from which pavement engineers can design precast concrete pavements. The author has investigated analytically the relative importance of the factors affecting the ultimate stress and subgrade bearing pressures in precast concrete pavements. Presenting the results in graphical form, the design charts are used toillustrate the new design method.     

A comparison between the stresses computed for finite sized precast concrete pavement units using westergaards equations and a numerical design method

Westergaards equations are widely used in the design of rigid concrete highway and aircraft pavements. The equations assume that the pavements are either infinite or semi-infinite in extent. Recently, a numerical design procedure using finite elements has been introduced for finite sized precast concrete pavement units [raft units]. The present paper compares the computed stress results from the two methods for the interior loading on a two metre square raft unit. The results show that there is no simple “slab-size correction factor” to correlate the stress output from the two design methods as suggested by other authors. Westergaards analysis should not be used to design finite sized raft units; the numerical design procedure is recommended.     

A two‐mechanism elastoplastic model for shakedown of unbound granular materials and DEM simulations

An elastoplastic model has been developed for the finite elements modelling of repeated load triaxial tests. This model is based on the shakedown theory established by Zarka for metallic structures. To the previous works, which were based on the Drucker–Prager yield surface and the plastic potential of Von Mises, a compression cap has been added to each one. The model straightforwardly determines the purely elastic state or the elastic shakedown state or the plastic shakedown state and calculates the deviatoric and the volumetric plastic strains. The calibration of the elastoplastic model has been carried out with DEM simulations and an unbound granular material for roads under repeated load triaxial tests using finite element method. The calculations underline the capabilities of the model to take into account, with a unique formalism, the accumulation of the deviatoric and volumetric plastic strains along the loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

不平整路面上的非稳定车流荷载研究及应用

车辆动荷载是引起路面损坏的最主要原因。目前国内外相关研究多集中于单一车辆对路面结构所产生的动荷载,实际上路面结构所承受的是车流荷载,而且车流在行驶过程中各车辆的车速和车辆之间的距离会产生变化,但关于这方面的研究甚少。针对这一工程实际问题,采用微观交通流模型中的跟车模型来模拟车流行驶过程中各车辆的速度以及它们之间车距的变化,车辆振动模型采用1/4车身结构的两自由度模型,并根据国家标准GB7031-86[1]规定生成路面轮廓的时域信号。最后分析了某水泥混凝土路面在生成的车流荷载作用下的动力响应,为研究车流荷载作用下路面结构动力响应提供了基础性成果。     

Effect of Matric Suction on Resilient Modulus of Compacted Aggregate Base Courses

This research was conducted to investigate the effect of matric suction on resilient modulus of unbound aggregate base courses. The study characterized the water characteristic curves and resilient modulus versus matric suction relationships of aggregate base courses that were compacted at different water contents and between 98 and 103 % of the modified Proctor density. The soil–water characteristic curve (SWCC) and the relationship between resilient modulus (M _r ) and matric suction (ψ) were established for different unbound granular and recycled asphalt pavement materials. This relationship is important for predicting changes in modulus due to changes in moisture of unbound pavement materials. Resilient modulus tests were conducted according to the National Cooperative Highway Research Program (NCHRP) 1-28A procedure at varying water contents, and the measured SWCC was used to determine the corresponding matric suction. Three reference summary resilient moduli (SRM) were considered: at optimum water content, optimum water content +2 % and optimum water content ?2 %. The Bandia and Bargny limestones are characterized by a higher water-holding capacity which explains why the modulus of limestone was more sensitive to water content than for basalt or quartzite. Limestones tend to be more sensitive to changes in water content and thus to matric suction. The shape of the SWCC depends on the particle size distribution and the cementation properties from dehydration of the aggregates. Material properties required as input to the Mechanistic-Empirical Pavement Design Guide (M-EPDG) to predict changes in resilient modulus in response to changes in moisture contents in the field were determined for implementation in the M-EPDG process. Results show that the SRM was more correlated with matric suction than with compaction water content (for resilient modulus testing). The empirical models commonly used to predict the SWCC such as the Perera et al. (Prediction of the SWCC based on grain-size-distribution and index properties. GSP 130 Advances in Pavement Engineering, ASCE, 2005) and the M-EPDG (NCHRP in Guide for mechanistic-empirical design of pavement structures. National cooperative highway research program. ARA, Inc., ERES Consultants Division, Champaign, IL, 2004) models tend to underestimate the SWCC and cannot provide reasonable estimation. SRM normalized with respect to the SRM at the optimum water content varied linearly with the logarithm of matric suction. Empirical relationships between SRM and matric suction on semi-logarithmic scale were established and are reported.     

Shakedown in layered pavements under moving surface loads

Elastic–plastic deformations in pavements consisting of layers of different frictional materials are investigated. The upper bound, kinematic shakedown theorem is used to obtain estimates of the critical shakedown loads. Fully general three-dimensional deformations are considered. The influence of the loading distribution, interactions between loads, and the effect of varying the thickness, stiffness and strength of the layers are explored. Consequences of this investigation for particular existing designs of flexible pavements are investigated. In particular, it is found that the strength of the subgrade has no effect on the magnitude of the critical shakedown load.     

多年冻土区不同路面材料路基热稳定性分析

针对多年冻土区路基路面病害多发的现状,从路面材料入手,对水泥混凝土和沥青两种路面下路基温度场的变化规律进行研究。研究结果表明,在计算高度范围内,对于8.5 m路面宽幅的路基来说,沥青路面下的最大融深大于混凝土路面下的最大融深,尤其在路基高度较低时两种路面下的融深差异更大。最大融化深度和最大融化深度发展速率均与路基高度和路面宽幅有紧密关系,通过研究可以提出有效的措施来保持路基热稳定性,从而减少路基路面病害的发生和公路的运营成本,为今后类似工程提供参考     

The design of precast concrete pavements on low bearing capacity subgrades

By using the finite element method and combining it with Westergaard's analysis for concrete pavements, a new design method using 2 metre by 2 metre precast concrete pavement units is presented for heavy duty pavements on low bearing capacity subgrades. One design example is included.     

Support vector regression to predict the performance of stabilized aggregate bases subject to wet–dry cycles

Durability is a notion that is integrated with the performance of stabilized pavement materials. Also, because it can be quantified and measured, it carries significant influence on the design of pavements. This study focuses on using support vector machine, a machine learning algorithm, in assessing the performance of stabilized aggregate bases subject to wet–dry cycles. Support Vector Regression (SVR) is a statistical learning algorithm that is applied to regression problems and is gaining popularity in pavement and geotechnical engineering. In our study, SVR was shown to be superior to the least‐squares (LS) method. Results of this study show that SVR significantly reduces the mean‐squared error (MSE) and improves the coefficient of determination (R²) compared to the widely used LS method. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization and use of tropical gravels for pavement construction in West Africa

Summary Road transportation is increasingly becoming one of the key factors for promoting economic growth in most developing countries. However, transport and road research in the tropics has received relatively little attention. Experiences in road construction in the tropics within the past 50 years or so have established that local materials specifications and pavement construction technologies have to be developed in relation to the climatic conditions. This would involve knowledge of the processes of formation as well as genetic characteristics of the local gravels. Genetic characteristics exert considerable influence on the geotechnical properties and engineering behaviour of local gravels under pavement. The construction technology of the road pavement should take cognizance of the compositional variabilities of the gravel deposits. Construction studies of pavement sections (as well as assessment of the performance of existing roads) built with different gravels formed over different geological formations in specific climatic, and drainage conditions would provide useful data for evolving local gravel specifications for constructing stable and durable pavements. Stage construction of pavements involving the exposure of the various layers to traffic loading and seasonal climatic influences appears to hold promise for formulating strategies for constructing stable, and long-term durable tropical roads. The problem of achieving reproducible laboratory test data under field conditions is perhaps the most challenging aspect of utilizing local gravels for pavement construction in tropical and sub-tropical conditions. It is noted that the stability of pavements in tropical environments depends not so much on the geotechnical properties of the available gravels as on the appreciation by the designers and construction engineers of the relationship between the genetic and laboratory determined characteristics of the gravels on the one hand and the pavement construction technology and local climatic and drainage conditions on the other. This paper is a contribution to development of highway geotechnics for tropical and sub-tropical conditions.     

Equivalent continuum strain calculations based on 3D particle kinematic measurements of sand

Constitutive modeling of granular materials has been a subject of extensive research for many years. While the calculation of the Cauchy stress tensor using the discrete element method has been well established in the literature, the formulation and interpretation of the strain tensor are not as well documented. According to Bagi, 1 researchers mostly adopt well‐known continuum or discrete microstructural approaches to calculate strains within granular materials. However, neither of the 2 approaches can fully capture the behavior of granular materials. They are considered complementary to each other where each has its own strengths and limitations in solving granular‐mechanics problems. Zhang and Regueiro 2 proposed an equivalent continuum approach to calculating finite strain measures at the local level in granular materials subjected to large deformations. They used three‐dimensional discrete element method results to compare the proposed strains measures. This paper presents an experimental application of the Zhang and Regueiro 2 approach using three‐dimensional synchrotron microcomputed tomography images of a sheared Ottawa sand specimen. Invariant Eulerian finite strain measures were calculated for representative element volumes within the specimen. The spatial maps of Eulerian octahedral shear and volumetric strain were used to identify zones of intense shearing within the specimen and compared well with maps of incremental particle translation and rotation for the same specimen. The local Eulerian volumetric strain was compared to the global volumetric strains, which also can be considered as an averaging of all local Eulerian volumetric strains.     

On accuracy of prediction of pre-failure deformations of granular soils

The problem of accuracy of predictions of pre-failure deformations of granular soils is considered. Firstly, the deterministic incremental equations describing qualitative character of such deformations are presented. These equations are based on extensive experimental data, obtained from the tri-axial compression tests. The parameters appearing in the incremental equations are assumed as random numbers, characterized by their mean values and standard deviations. The normal probability distribution is assumed. Then, such a model is applied to predict strains caused by some simple deterministic stress paths. The incremental equations are integrated for a large number of random coefficients, generated by a computer program. The final results are presented as either paths or points in the strain space, and respective density of probability distribution is calculated. The proposed method and results obtained show, that in mechanics of granular media we cannot expect “a good agreement” between predictions of theoretical models and experimental results, but only a kind of agreement measured by probability. The results presented should be important for both theoretical modellers and experimentalists.