||Internal erosion in soil can be initiated by suffusion, which involves selective erosion of fine particles within the matrix of coarse soil particles under seepage flow. Suffusion in an internally unstable soil will occur when the hydraulic gradient exceeds a certain critical value. Often the critical hydraulic gradients are found using conventional 1-D seepage tests. The core wall and filters in an earth dam are however typically under complex shear stress states. As internal erosion propagates backward in an earth dam, the soil pipe may collapse and the dam failure process may then evolve into an overtopping process. Most landslide dams fail by overtopping directly. The erodibility of soils, therefore, also plays an important role in evaluating the development of breaching of dams. The main objectives of this thesis are to investigate the internal erosion process under complex stress states, characterize the erodibility of soils, and model the dam breaching process. A stress-controlled erosion apparatus was developed to investigate the initiation and development of internal erosion under complex stress states and to study the mechanical response of soil to internal erosion. It allows independent control of hydraulic gradient and stress state. The hydraulic gradient is controlled using a water-head control method. The eroded soil and the outflow rate are measured using a soil collection system and a water collection system, respectively. Extensive internal erosion tests were conducted on a gap-graded soil under complex stress states following three stress paths: isotropic, drained triaxial compression and triaxial extension stress paths. After loss of a significant amount of fine particles in the soil, the original dilative stress-strain behaviour changes to be contractive one and the shear strength decreases. The entire internal erosion process can be divided into four phases: stable, initiation, development, and failure. Accordingly, three critical gradients named initiation, skeleton-deformation, and failure hydraulic gradients can be defined. The initiation hydraulic gradient is mainly controlled by the pore structure of the soil. The initiation hydraulic gradients under compression stress conditions generally increase with the shear stress ratio first and then decrease when the soil approaches shear failure. The skeleton-deformation hydraulic gradient is associated with buckling of the strong force chains within the soil due to the loss of lateral support by the fine particles. It is much larger under isotropic stress conditions than under compression or extension stress conditions. The failure hydraulic gradient depends on the initial stress state and soil shear strength. A theoretical equation is derived to determine the failure hydraulic gradient. The geometric control variables for internal stability of different types of soil were studied based on physical understanding of microstructures of these soils. Modified geometric criteria for these types of soil were developed using such control variables based on information from an internal-stability test dataset. Field jet index tests were conducted at 27 locations on two landslide dams formed during the 2008 Wenchuan earthquake to investigate the erodibility of fresh landslide deposits before the deposits were disturbed. The bulk density increases and the coefficient of erodibility decreases with the depth of deposition. The main factors that control soil erodibility are found to be grain-size distribution, void ratio, fines content, and plasticity index. Particularly, the coefficient of erodibility decreases exponentially with the degree of compaction. Two empirical equations are developed for estimating the coefficient of erodibility and critical erosive shear stress of the fresh landslide deposits based on their basic soil properties. A physically-based breach model considering the variations in soil erodibility along depth is developed to simulate the breaching process of earth dams and landslide dams. The breach evolution, erosion rate, and outflow hydrograph can be predicted. A spreadsheet is developed to numerically implement the model. The erosion processes of Tangjiashan Landslide Dam and Xiaogangjian Landslide Dam induced by the 2008 Wenchuan earthquake are analyzed. The erodibility of the two landslide dams varies significantly along depth. The predicted key breaching parameters considering the variations in the soil erodibility along depth agree well with the observed values.