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Desiccation cracking of soils is of great importance in geotechnical and geoenvironmental engineering. In many circumstances it is the cause of damages in earthen and soil supported structures. Desiccation cracking affects clayey soil barriers for waste storage, causing a dramatic increase of the barrier permeability; late experimental results also reveal that desiccation cracking is a burning issue for underground nuclear waste storage. Yet the mechanisms of drying shrinkage and associated cracking in soils, and the ways to control or avoid such cracking, are still elusive. This study offers a better understanding of such mechanisms, and proposes a modelling of the related processes, in order to predict the occurrence of damage. The thesis includes an experimental and phenomenological study of desiccation, characterizing the drying shrinkage and the cracking of soils (silts and silty clays) and a theoretical and numerical study, including a constitutive approach and some boundary value problem simulations. The experimental study consists in (i) desiccation tests on soil samples with controlled mechanical and drying boundary conditions, and (ii) measurement of tensile strength. Results of the desiccation tests (i) reveal that the stresses that lead to cracking clearly result from the presence of restraining boundary conditions and/or moisture gradient. Desiccation cracking of remoulded and initially saturated soils invariably occurs in a domain of drying for which saturation ratio is almost one and suction is non-zero, close to air entry value. In such a domain, a large part of the deformations are irreversible, while stresses are built up, until a critical point at which tensile strength is reached. The tensile strength clearly depends on suction. The processes related to crack propagation and patterns geometry are also discussed, particularly the effect of energy redistribution through the body, after crack initiation. For the tensile strength experimental determination (ii), two tests method are designed, both performed in the triaxial apparatus, with control of suction. The methods avoid the connexion of the specimen to the traction system during the test, and allow the control of stress field and drainage conditions. The dependence of tensile strength on suction is quantified for a certain suction range. A constitutive approach is subsequently proposed, able to reproduce the essential experimental features. The model ACMEG-DC is developed, on the basis of the reference constitutive model ACMEG, developed by L. Laloui and co-workers. The model is based on the Bishop's generalized effective stress concept, and developed in the frame of isotropic hardening elasto-plasticity. On the basis of test results, a new tensile strength criterion which enables in particular to predict desiccation cracking occurrence is added to this model. The criterion takes into account the evolution of tensile strength arising during desiccation due to suction changes. Such an approach is new indeed; it is original as it unifies the description of drying shrinkage process (viewed as the consequence of change in effective stress, in a consistent elasto-plastic framework) and tensile cracking (predicted through an adapted effective stress criterion). The model is validated on several experimental desiccation studies. Several modelling approaches of desiccation as a boundary value problem are also proposed, based on finite element and discrete element simulations. Such simulations address in particular the modelling of desiccation crack propagation and the related challenges.