The permanent strain behavior of unbound aggregates under repeated loading has been studied by many researchers over the years. A summarized review of the research into this area is given based on the literature available to date. Different views from various sources are outlined and discussed. A state of the art is presented regarding the factors affecting the permanent strain development in these materials and the modeling techniques available. This paper is the second of two companion papers discussing the current state of knowledge on the structural behavior of unbound aggregates. The resilient properties of these materials are reviewed in detail in the first paper.

State of the art. ii: permanent strain response of unbound aggregates

The shakedown concept has been used to describe the behavior of conventional engineering structures under repeated cyclic loading The possibility has been raised that a critical stress level exists between stable and unstable conditions in pavement According to the "shakedown" concept, this level is termed the "shakedown limit" Several repeated load triaxial tests were performed on crushed rock aggregates at different stress levels The resulting permanent deformation, which accumulated with the repeated loading, was described and compared with the types of responses usually described by the shakedown approach The existing shakedown approach can describe some, but not all, of the observed responses Thus, a modified set of possible responses was defined in shakedown terms The method of description could provide a powerful material assessment and pavement design tool for engineering unbound pavement bases A design chart derived from the data illustrates a possible design approach

Permanent deformation behavior of granular materials and the shakedown concept

Modelling permanent deformation behaviour of unbound granular materials

This paper reports the results of several repeated load triaxial tests performed on a crushed rock aggregate at different stress levels. The development of the resulting permanent deformation that accumulates with the repeated loading is described and compared with the types of responses usually described by the shakedown approach. It is shown that the existing shakedown approach can describe some, but not all, of the observed responses. Thus, a modified set of possible responses is defined in shakedown terms and some explanations of the differences from the conventional approach are given. The elastic shakedown limit can be used to predict whether or not stable behavior occurs in the unbound granular material layer of a pavement construction or whether rutting will occur. With this information a pavement's granular base may be dimensioned. The elastic shakedown limit of a Granodiorite has been used in this manner and the resulting design compared with an empirical German design procedure. The paper concludes with an assessment of the benefits and limitations of the new approach.

Pavement design model for unbound granular materials

Strain and pore pressure development on soft marine clay in triaxial tests with a large number of cycles

The results of a research program aimed at characterizing the permanent deformation behaviors of different types of unbound aggregates under repeated loading are summarized. Tests were performed in a triaxial or hollow-cylinder apparatus, depending on the grading of the materials. The scope of the research was to assess the relationship between total permanent axial strain and both the number of load applications and the stress level. The test results were used to verify a model recently developed in France in which attempts are made to predict the long-term behaviors of granular materials. The French model is examined with particular reference to its validity on the effect of stress level on permanent deformation of unbound granular materials. The results of the study indicate that the French model is generally successful in predicting the permanent strain for a given number of load applications. For one of the materials, however, the model did not seem to fit the data well. The French model also suggests that the variation in total permanent strain with stress level is related to the static failure line and could be determined by comparing the maximum shear stress ratio with the slope of the estimated failure line. This is discussed and shown to be questionable because it results in either unreasonable failure parameters or a very low level of correlation with the observations. An attempt was made to modify the French model, but that also proved to be unsuccessful. The concept of relating the permanent deformation behavior to the static failure condition of the material is therefore questioned.

Influences on Permanent Deformation Behavior of Unbound Granular Materials

The purpose of the study is to increase the understanding of plastic behaviour of unbound granular materials through a literature survey and laboratory testing. Reviews of previous research show that permanent deformation in granular materials is influenced by several factors. Generally, modelling of plastic behaviour is based on the gradual accumulation of permanent strain with number of load cycles and the impact of applied stresses. During the last two decades, attention has been paid to the shakedown theory and its potential for developing true analytical models in road pavement design. The experimental part of the investigation deals with the permanent deformation behaviour of five different aggregates under repetitive loading. Triaxial and hollow cylinder tests are used to assess the relationship between permanent strain and both number of load applications and stress level. The test results are used to verify some of the existing models found in the literature, with greater emphasis on the newly developed Paute model. The general concept suggested by the Paute model regarding the effect of stresses is discussed and shown to be questionable, as it leads to incorrect conclusions about material behaviour. However, the Paute model is found generally suitable for predicting the accumulation of permanent strain with number of load applications. A model is introduced expressing the accumulation of permanent axial strain, at any given number of cycles, as a function of applied stresses, taking into account the maximum shear stress ratio and the length of stress path in p-q space. The results of the analysis indicate similarities between the model and the concept of the shakedown theory. At low levels of shear stress ratio, the growth of permanent strain appears to level off, resulting in an ultimate equilibrium condition characterised by an elastic material behaviour. (A)

Permanent deformation behaviour of unbound granular materials

During recent decades, growing interest in the developmentof so-called analytical or mechanistic road pavement designmethods has resulted in substantial research into themechanical behavior of the ...

Resilient and permanent deformation behavior of unbound aggregates under repeated loading

The present paper attempts to explore the impact of grading scale, or changes in maximum particle size of graded aggregates, on triaxial test results. The study is based on a series of repeated load triaxial tests on three unbound granular materials at different grading scales. The experimental results show clearly that the structural response observed depends on the maximum grain size used in the triaxial specimen. The reduction of grading scale is shown to have a significant impact on both resilient and permanent strain responses of the materials tested. However, the nature and the extent of this impact are complex and inconsistent when different materials are compared, It is therefore recommended that triaxial testing of granular materials be performed at natural gradings.

Fredrick Lekarp

Papers

Modelling permanent deformation behaviour of unbound granular materials

Influences on Permanent Deformation Behavior of Unbound Granular Materials

Permanent deformation behaviour of unbound granular materials

Resilient and permanent deformation behavior of unbound aggregates under repeated loading

The Effects of Grading Scale on Repeated Load Triaxial Test Results