# Research Progress in Methods for the Analysis of the Internal Stability of Landslide Dam Soils
## 4 Criteria Considering Stress Conditions
### Triaxial Compression State  
In nature, soils are often subjected to triaxial stress states. To realistically simulate the internal stability of soil under complex stress conditions, researchers use an improved triaxial permeameter to simulate the stability behavior of soil under these conditions.  
The stress ratio, shear stress ratio, and deviatoric stress are used to reflect the relationship between the major and minor principal stresses applied to the sample [67; 68; 69]. These are often correlated with the hydraulic gradient and volumetric deformation to reflect the influence of seepage and stress coupling on the internal erosion of soil. Some researchers [68] have found through experiments that when the shear stress ratio is less than the critical value, the starting hydraulic gradient of the soil increases with the increase in the shear stress ratio, as shown in Figure 3. Similarly, other researchers [69] have found similar situations through experiments, as shown in Figure 4. However, some researchers [70] have found that the relationship between the shear stress ratio and the critical hydraulic gradient is piecewise linear. This is because the porosity reaches a minimum value near the critical shear stress ratio, but suddenly increases after the shear stress ratio slightly exceeds the critical value [70], as shown in Figure 5.  
In Figures 3 and 4, the initial increase in the shear stress ratio or deviatoric stress leads to an increase in the critical hydraulic gradient of the soil. This indicates that when the shear stress ratio or deviatoric stress applied to the sample does not reach the critical value, the soil's density and stability continue to increase. This means that a higher hydraulic gradient is required to induce internal erosion in the soil. Once the shear stress ratio or deviatoric stress exceeds the critical value, the hydraulic gradient in both figures shows a significant decrease. This is because excessive deviatoric stress may lead to the weakening of the soil structure and an increase in porosity, possibly forming shear bands or elongated  
Figure 4: Effect of deviatoric stress on hydraulic gradient that initiates internal erosion [69].  
Figure 3: Effect of shear stress ratios on hydraulic gradient that initiates internal erosion [68].  
pores, which reduce soil stability. Fine particles are more easily carried away by water flow, forming stable seepage channels, thereby reducing the starting hydraulic gradient.  
Additionally, there is a complex interrelationship between the stress ratio, volumetric change (dilatancy or contraction), and particle loss [71; 72; 73]. Under low shear stress ratio conditions, the frictional force between soil particles is relatively small, making particles more prone to relative sliding and dispersion. In this case, as stress increases, the soil sample exhibits dilatant behavior [74]. During dilatancy, the soil becomes loose, internal pores increase, interparticle connections weaken, and particles are more easily carried away by water flow, leading to increased particle loss. Increased particle loss raises the void ratio of the soil, reducing its density, making the soil looser, and increasing the deformation potential. Therefore, after a significant loss of fine particles in the soil sample, the sample transitions from dilatancy to contraction [75; 76; 77; 78], thereby altering the stress distribution in the soil test [78]. However, under high shear stress ratio conditions, the contact force and frictional force between soil particles increase, leading to the tighter packing of particles within the sample, resulting in contraction [79]. In this process, the soil becomes denser, internal pores decrease, particles are locked within the soil, and particle loss is reduced.