Analytical and numerical investigations on the one-dimensional permanent deformations of granular materials under repeated deviatoric loading

Highlights

• This work proposes a theoretical framework for permanent deformation of granular materials.

• The Soil Water Retention Curve (SWRC) is divided into three linear phases." can be eliminated from the highlights.

• The same unique curves of permanent deformations with the normalized suction are developed.

• A good correspondence between the estimated and experimental values is obtained.

• The proposed approach is also injected in a finite difference code.

• The numerical simulations are performed on a full scale test of a typical pavement structure.

Abstract

This work proposes a theoretical framework for the permanent deformation calculation of unsaturated granular materials. The approach is based on the separation of the Soil Water Retention Curve (SWRC) into three linear phases. This representation makes unique the wetting and drying paths with a newly defined normalized suction s/s*. The same unique curves of permanent deformations with the normalized suction value are then developed.

The proposed approach is initially applied to reproduce the experimental permanent deformation of two granular materials with different water contents on the wetting and drying paths. The effect of the deviatoric stress on the permanent deformations is also considered in the multi-stage loading tests. The good correspondence between the predicted and experimental results confirms the good capacity of the proposed approach.

Finally, the proposed approach is injected in a finite difference code to model the tests performed on the two aforementioned granular materials. The numerical simulations show that both modeling concepts with variable and non-variable suction profile predict well the experimental results of the single-stage and multi-stage tests. The maximum deflection of a typical pavement is also estimated at the different hydraulic states, giving more credits to the proposed approach.

Introduction

Generally, the permanent deformation behavior of granular materials depends highly to their applied mechanical stress path, as reported in many researches (Hicks and Monismith, 1971; Uzan, 1985; Dawson, 1990; Lekarp et al., 2000; Ng et al., 2013). As well, the effect of water content on the short and long-term soil mechanical behavior has been investigated (Gidel et al., 2002; Uthus et al., 2006; Duong et al., 2013; Nowamooz et al., 2013; Salour and Erlingsson, 2015; Liu et al., 2019). Recently, the effect of suction (negative pore pressure) on the mechanical behavior of the granular materials has attracted more attentions (Caicedo et al., 2009; Coronado et al., 2011; Nowamooz et al., 2011; Ho et al., 2014; Ho et al., 2015; Duong et al., 2016) since the hydro-mechanical behavior can be explained with one unique parameter which is suction.

Traditional design methods to find the most economical combination of layer thicknesses and material types for the pavement are more or less empirical but there is, worldwide, an increasing desire to develop analytical approaches. A pre-requisite of a successful analytical method is the experimental measurements and the appropriate characterization of the permanent deformation behavior of granular materials (Cao et al., 2018). Jing, et al. (Jing et al., 2018; Jing et al., 2019) reported some experimental results for the permanent axial deformation under a large number of repeated loads for different granular materials with different fine contents, initial water contents and suctions.

The development of a unified analytical approach for the estimation of the permanent deformations of a granular material is also helpful to predict the material behavior under the complex hydro-mechanical solicitations, difficult to be investigated experimentally. In this context, this wok proposes an analytical approach for the permanent deformations of granular materials on their wetting and drying paths. The soil water retention curves (SWRCs) of the two granular materials as well as their permanent deformations are used to calibrate and validate analytically and numerically this new theoretical approach. Some numerical simulations are also performed based on the proposed analytical approach.