Table 1 The most important nonlinear strength reduction methods used in slope stability analysis.

Equivalent Mohr–Coulomb method

Equivalent strength parameter equation is solved for the equivalent cohesion and internal friction angle, and the safety factor is solved by the Mohr–Coulomb criterion

Basic nonlinear strength reduction method

Hoek and Brown¹⁴

Material parameters reduction method

Hoek–Brown material parameters m_b, s are directly discounted

For Finite Element calculation of slope failure examples

Lin²⁸

Global reduction of GHB envelopes method

Directly shear strength reduction by GHB

Combining GHB with SSR analysis for the Finite Element simulation

Hammah³⁰

Local linearization method

Instantaneous internal friction angle and cohesion are solved by Newton's iterative method based on the relationship between normal stress and shear stress

Computing combined with FLAC^3D

Lin²⁹

Extended HB criterion reduction method

Strength reduction based on the extended HB criterion

For Finite Element calculation of slope failure examples

Benz³¹

Dual factoring strategy strength reduction method

Strength reduction based on uniaxial compressive strength and rock hardness

Numerical tests for a homogeneous, simple slope

Wu³²

Nonlinear shear strength reduction technique

Introduced the Mohr–Coulomb instantaneous friction angle as a variable

A slope example is selected to verify the technique

Fu¹⁵