# Double Strength Reduction Method for Slope Stability Analysis Based on Water Content Variation: A Study and Engineering Application

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## Abstract

**:**

## 1. Introduction

## 2. Fundamental Concepts of SRM

#### 2.1. Description of the Traditional Strength Reduction Coefficient

#### 2.2. Double Strength Reduction Method

_{c}and F

_{φ}for cohesion and friction angle. When it comes to analyzing and evaluating slope stability, it is common to only obtain a single comprehensive safety factor value rather than separate values for cohesion and friction angle. The different approaches currently used to calculate the double-strength reduction factor F are listed in Table 1.

#### 2.3. Performing the FE Strength Reduction Method Based on ABAQUS

#### 2.4. Slope Instability Criteria and Numerical Simulation Constitutive Model

## 3. Example Analysis

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## 4. Engineering Example

#### 4.1. Engineering Geological Characteristics of the Study Area

_{2l}), and the Emeishan Basalt strata (P

_{2β}). Quaternary red soil strata (Q), formed from the weathering of Emeishan basalt strata (P

_{2β}), covers the surface. Pyroclastic rocks, basaltic lava, and tuffs make up the majority of the basalt, which has noticeable columnar joints. A clear division between the basalt and soil layers is visible (Figure 10), with the rock strata trending northeast and a slope inclination of approximately 30°. The soil layer on the slope is inconsistent, being thicker in the valleys and thinner near the crest and waist, where the basalt may be directly exposed.

#### 4.2. Numerical Modeling of Azhuoluo Slope

#### 4.3. Numerical Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Equivalent displacement cloud calculated by the traditional finite element reduction method.

**Figure 5.**Equivalent plastic strain cloud calculated by the traditional finite element reduction method.

**Figure 12.**Friction angles and cohesion vary with water content [28].

Case | Scholar | Equation |
---|---|---|

1 | F. Tang | $F=({F}_{c}+{F}_{\phi})/2$ |

2 | W. Yuan | $F=\sqrt{2}{F}_{c}{F}_{\phi}/\sqrt{{F}_{c}^{2}+{F}_{\phi}^{2}}$ |

3 | X. Q. Xu | $F={F}_{c}{\beta}_{c}+{F}_{\phi}{\beta}_{\phi}$ |

4 | A. Isakov | $F=1/(1-{L}_{\mathrm{min}}),{L}_{\mathrm{min}}=f({F}_{c},{F}_{\phi})$ |

Methods | Safety Factor | |
---|---|---|

Limit equilibrium method | 1.586 | |

Traditional strength reduction method | 1.58 | |

Double strength reduction method | Tang F | 1.502 |

Yuan W | 1.487 | |

Isakov A | 1.503 | |

This paper | 1.532 |

Material | Density ρ (g/cm ^{−3}) | Young’s Modulus E (MPa) | Poisson’s Ratio v | Friction Angle φ (°) | Cohesion c/KPa | Water Content ω (%) |
---|---|---|---|---|---|---|

Weathered-basalt Soil | 1.62 | 100 | 0.35 | 33.6 | 32.3 | 28.8 |

Basalt | 2.74 | 60,000 | 0.17 | 43.7 | 28,000 | - |

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**MDPI and ACS Style**

Liu, X.; Su, M.
Double Strength Reduction Method for Slope Stability Analysis Based on Water Content Variation: A Study and Engineering Application. *Water* **2023**, *15*, 1194.
https://doi.org/10.3390/w15061194

**AMA Style**

Liu X, Su M.
Double Strength Reduction Method for Slope Stability Analysis Based on Water Content Variation: A Study and Engineering Application. *Water*. 2023; 15(6):1194.
https://doi.org/10.3390/w15061194

**Chicago/Turabian Style**

Liu, Xiaoliang, and Mei Su.
2023. "Double Strength Reduction Method for Slope Stability Analysis Based on Water Content Variation: A Study and Engineering Application" *Water* 15, no. 6: 1194.
https://doi.org/10.3390/w15061194