What Is The Optimal Ratio Of Lateral Resistance To Normal Stress For Stabilizing Slope Failures In Weathered Granitic Terrain, Particularly In Regions With High Precipitation Rates And Shallow Groundwater Tables, In Order To Minimize Environmental Disruption And Ensure Sustainable Land Use Planning In Mountainous Watersheds?

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The optimal ratio of lateral resistance to normal stress for stabilizing slope failures in weathered granitic terrain, particularly in regions with high precipitation and shallow groundwater, can be approached by considering the following:

  1. Understanding the Ratio: The ratio is akin to the tangent of the friction angle (tan φ) in the Mohr-Coulomb failure criterion, which relates shear strength to normal stress. In weathered granite, where cohesion is low, this ratio is primarily dependent on the frictional component.

  2. Friction Angle Consideration: For weathered granite, the friction angle φ typically ranges between 30° and 40°. Thus, tan φ ranges approximately from 0.58 to 0.83. This suggests an optimal ratio in the range of 0.6 to 0.83.

  3. Adjustments for Site Conditions: In areas with high precipitation and shallow groundwater, pore pressures increase, reducing effective normal stress. This necessitates a higher factor of safety, potentially increasing the optimal ratio to compensate for reduced shear strength.

  4. Factor of Safety: A common factor of safety (FS) of 1.5 is often applied. This means the ratio of shear strength to applied shear stress should be at least 1.5, which could adjust the optimal ratio to a range of 0.9 to 1.25 when considering safety margins.

  5. Conclusion: While the exact ratio depends on site-specific conditions, a reasonable estimate for the optimal ratio, considering both material properties and environmental factors, is between 0.9 and 1.2. This range balances stability with practical considerations for sustainable land use.

In summary, the optimal ratio is estimated to be between 0.9 and 1.2, reflecting a balance between material frictional properties and necessary safety margins under challenging environmental conditions.