Mechanistic-empirical permanent deformation models: Laboratory testing, modelling and ranking

Abstract

Geomaterials exhibit elastoplastic behaviour during dynamic and repeated loading conditions. These loads are induced by the passage of a train or vehicle which then generates recoverable (resilient) deformation and/or permanent (plastic) deformation. Modelling this behaviour is still a challenge for geotechnical engineers as it implies the understanding of the complex deformation mechanism and application of advanced constitutive models. This paper reviews on the major causes of permanent deformation and the factors that influence the long-term performance of materials. It will also present the fundamental concepts of permanent deformation as well as the models and approaches used to characterise this behaviour, including: elastoplastic models, shakedown theory and mechanistic-empirical permanent deformation models. This paper will focus on the mechanistic-empirical approach and highlight the evolution of the models, and the main similarities and differences between them. A comparison between several empirical models as well as the materials used to develop the models is also discussed. These materials are compared by considering the reference conditions on the type of material and its physical state. This approach allows for an understanding of which properties can influence the performance of railway subgrade and pavement structures, as well as the main variables used to characterise this particular behaviour. An innovative ranking of geomaterials that relate to the expected permanent deformation and classification (UIC and ASTM) of soil is also discussed because it can be used as an important tool for the design process.

Introduction

Pavements and railway structures are designed for a certain lifespan and they usually require reconstruction and/or major maintenance work because the materials may experience fatigue, cracking or be under an excessive amount of cumulative permanent deformation (or rutting in the case of pavements) due to the passage of traffic. Plastic or permanent deformation usually occurs in the geomaterials (base, sub-base or subgrade soils) which are responsible for the surface rutting and that can lead to significant passenger discomfort [60]. This is why knowing and understanding the deformation and failure mechanisms of geomaterials under dynamic and cyclic loading is so important when designing and planning the maintenance of pavements and railway structures [49]. Indeed, an accurate estimation or prediction of the amount of cumulative settlement will help pavements and /or railway structures avoid a mediocre performance [6], [54], [59]. This is why the permanent deformation of geomaterials should be included in the design since otherwise, it can lead to higher annual rehabilitation costs [59].

Over the past decades, researchers have been so concerned about permanent deformation and they continually search for the most accurate methods and models that will measure and predict these values [54], [48], [72], [30], among others. To achieve these objectives, laboratory investigations using cyclic triaxial tests, simple and cyclic shear tests, resonant column and hollow cylinder tests, among others have been carried out. These tests were often used to determine shear stress–strain behaviour, resilient modulus (M_r) of subgrade geomaterials considering reversible and irreversible deformation under cyclic loads [32], [24]. The reversible (elastic) is usually described by non-linear elastic models, but since permanent deformation is more complex, it depends on the accumulation of N loading cycles.

One of the main objectives of this paper is to review on the main causes of permanent deformation on pavements and railway structures and the factors that can increase this phenomenon. It is noted that while the materials should be able to resist permanent deformation, this resistance will depend on the number of load cycles and stress levels [46], the thickness of the layer, and the granulometry of the material. This also includes other external factors such as the physical state of the soil, which is often difficult to control because it depends on other environmental aspects such as the moisture content, and degree of saturation, etc.

The behaviour of geomaterials under cyclic loads can be characterised by either using complex elastoplastic models (recoverable and permanent deformation are both considered) or by shakedown theory and mechanistic-empirical models [37]). The elastoplastic models, however, despite their ability to accurately predict permanent deformation (the loading history is considered because the equation is solved based on incremental steps), they are difficult to implement, time consuming, and complex [50]. Most of these models only consider a low number of load cycles, which is not in accordance with the in situ conditions where the number of loads is up to million cycles. Indeed, these models are very demanding computationally because they require the simulation of repeated load applications in pavements/railway structures. The development of formulations based on cyclic constitutive laws may be expressed through conventional concepts such as the yield condition, hardening and flow rules. The main problem with the numerical implementation is that the increment of permanent deformation per cycle becomes very small quickly, and this leads to problems with the computational accuracy of the results [1]. The focus of this work will be on mechanistic-empirical models. These models are based on extensive laboratory testing results, so they can correctly simulate the response of materials; they are easy to implement, and they depend on fewer parameters than conventional elastoplastic models.

In order to select the best testing approach and the most suitable model, it is important to understand the conditions needed for its development such as the properties of the materials tested, degree of compaction, moisture content, etc., as well as the main variables/factors that can influence the response of the material. This paper reviews on the existing methods used to estimate the irreversible deformation of geomaterials, followed by a parametric study that includes comparisons among some selected models on different materials with different classifications (UIC and ASTM), properties, granulometry, and physical states. This comparison allows to estimate the permanent deformation and to rank materials according to the predicted deformation data and soil classification, which is a helpful tool in the design of the pavement and railway structures. It is also noted that this ranking should be interpreted as a reference value because it depends on several properties and soil conditions.