# Research Progress in Methods for the Analysis of the Internal Stability of Landslide Dam Soils
## 2 Qualitative Identification of Internal Stability Based on Physical Properties of Soils
### Identification Methods Based on Fine Content and Porosity
#### 2.2.3 Empirical Formula  
[PERSON], building on the research of [PERSON] and [PERSON] and [PERSON], classified soils into two categories: well graded and gap graded. Based on different fine particle contents, he further subdivided each soil type and developed geometric identification methods for internal stability that are suitable for different soil types [31]. This identification method targets broadly graded non-cohesive soils, which aligns well with the characteristics of dam soils. Therefore, this method is recommended for assessing the internal stability of dam soils.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Researcher** & **Applicable Soils** & **Identification Method** & **Stability** \\ \hline \multirow{3}{*}{[PERSON] [29]} & \multirow{3}{*}{Non-cohesive soils} & \(P_{f}\leq 0.9P_{op}\) & Stable \\  & & \(0.9P_{op}<P_{f}<1.1P_{op}\) & Moderate stable \\  & & \(P_{f}>1.1P_{op}\) & Unstable \\ \hline [PERSON] [24] & Non-cohesive soils & \(4P_{f}(1-n)\geq 1\) & Stable \\ \hline \multirow{6}{*}{[PERSON] [25]} & \multirow{3}{*}{Non-cohesive soils} & well-graded soil \\ \cline{3-4}  & & \((d_{90}/d_{60})/(d_{20}/d_{10})>1.05\) & Stable \\ \cline{3-4}  & & \(0.52<\frac{d_{90}/d_{60}}{d_{30}/d_{10}}<1.05\) & Moderate stable \\ \cline{3-4}  & & \(\frac{d_{90}/d_{60}}{d_{30}/d_{60}}<0.52\) & Unstable \\ \cline{3-4}  & & \(10\%<P_{f}<20\%\) & \((H/F)_{\min}>-0.04P_{f}+0.8\) & Stable \\ \cline{3-4}  & & \(P_{f}>20\%\) & Stable \\ \cline{3-4}  & & gap-graded soil \\ \cline{3-4}  & & \(P_{f}<10\%\) and \(G_{r}<3.0\) & Stable \\ \cline{3-4}  & & \(10\%<P_{f}<35\%\) and \(G_{r}<3P_{f}\) & Stable \\ \cline{3-4}  & & \(P_{f}>35\%\) & Stable \\ \hline \hline \end{tabular} Note: \(P_{op}\) refers to the optimal fine content within the soil pores, as specified in the equation; \(d_{90}/d_{60}\) indicates the degree of non-uniformity among the coarse particles in the soil; \(d_{20}/d_{10}\) measures the non-uniformity among the fine particles; \(P_{f}\) is the mass percentage of fines that fill the voids in the coarse particles; \(n\) denotes the porosity of the soil; \(H\) is the mass percentage corresponding to any given particle size \(d\) in the soil; \(F\) represents the mass percentage for particles between any given particle size \(d\) and \(4d\); \(G_{r}\), the discontinuity ratio, is given by \(G_{r}=d_{max}/d_{min}\), where \(d_{max}\) and \(d_{min}\) are the maximum and minimum particle sizes (in mm), respectively, within the discontinuity interval.  
\end{table}
Table 2: Identification methods considering the fine particle content.  
In summary, both the characteristic particle size method and the fine content method are gradation-based methods for assessing the internal stability of soils. The characteristic particle size method focuses on assessing certain key particle sizes within the soil, while the fine content method focuses on the proportion of fine particles within the soil. These two types of identification methods provide some references for further research on geometric identification methods for the stability of dam soils. However, not all the above methods are suitable for identifying the internal stability of dam soils, and further validation is required.