Slope slip surface plays a vital role in the prevention and control of landslide hazards. For homogeneous soil slopes, a three-dimensional (3D) limit analysis method was used to analyze the slope critical slip surfaces with a nonlinear strength envelope. The critical slip surfaces can be obtained once the least upper bounds on slope stability were calculated by using a numerical optimization procedure. For various clay slopes, some comparisons of critical slip surfaces associated with linear and nonlinear strength criteria were made to evaluate the effects of soil strength nonlinearity on slip surfaces. For slopes with a nonlinear criterion, the critical slip surface tends to be shallower gradually as the slope inclination increases, which is opposite to that for slopes with a linear strength criterion. Besides, the influences of width constraint on the critical slip surfaces associated with two strength criteria become more significant for steeper slopes. Compared with the solutions for slopes with the linear strength criterion, 3D effects on slope slip surfaces will be more remarkable for slopes considering soil strength nonlinearity.

The direct application of the Hoek–Brown failure criterion to practical slope engineering is still an urgent problem. The slope geometries and earthquake effect need to be considered in the determination of linear Mohr–Coulomb (MC) strength parameters from the Hoek–Brown criteria for slope stability analysis. This study adopted the tangential method to construct a three-dimensional (3D) rotational failure mechanism using the Hoek–Brown failure criterion for homogeneous rock slopes undergoing earthquake. The quasi-static method was employed to treat the seismic action as an external seismic force in the work–energy equation of the limit analysis theory. Based on the numerical optimization, the least upper-bound solutions and equivalent MC strength parameters were derived with respect to different strength parameters and seismic loads. The influences of nonlinear strengths, geometric parameters and earthquake load on the equivalent MC strength parameters were thoroughly investigated. The results suggested that the nonlinear parameters have different influences on the equivalent MC parameters for general steep slopes and vertical slopes. The effects of nonlinear parameters on the equivalent MC parameters become obvious for vertical slopes. The disturbance factor D affects the equivalent MC parameters only for very steep slopes in fractured rock masses. Additionally, the effect of slope inclination on the equivalent MC parameters becomes obvious for slopes in fractured hard rock masses. The 3D effect of the rock slope on the equivalent MC parameters was found to be slight. Moreover, the impact of earthquakes on the approximate MC parameters becomes weaker for steeper rock slopes. The tables of approximate MC strength parameters were given for various slopes with different nonlinear strength parameters. The presented tables can provide certain references for practical slope engineering.

Many experimental data have illustrated that the strength envelops for soils are not linear. Nevertheless, the linear Mohr–Coulomb (MC) strength parameters are widely applied for the conventional method, software codes, and engineering standards in the slope design practice. Hence, this paper developed the 3D limit analysis for the stability of soil slopes with the nonlinear strength criterion. Based on a numerical optimization procedure written in Matlab software codes, the equivalent MC parameters (the equivalent friction angle and the equivalent cohesion) from the nonlinear strength envelopes were derived with respect to the least upper‐bound solutions. Further investigations were made to assess the influences of nonlinear strength parameters and slope geometries on the equivalent MC parameters. The presented results indicate that the equivalent MC parameters are closely related to the nonlinear strength parameters. As the inclination angle increases, the equivalent friction angle becomes bigger, but the equivalent cohesion becomes smaller. Besides, 3D effects on the equivalent MC parameters were found to be slight. The presented approach for the determination of MC strength parameters is analytical and rigorous, and the approximate MC strength parameters in the provided design tables can be alternative references for practical use.

The pore‐water pressure is a vital factor in determining the slope stability. To deal with the stability of slopes undergoing pore‐water pressures, this paper used the pore‐water pressure coefficient to develop the three‐dimensional limit analysis method for slope stability evaluation with a nonlinear strength envelope. For numerical slope examples, the critical heights and corresponding critical slip surfaces associated with linear and nonlinear envelopes were derived by using a numerical optimization procedure. The influences of pore‐water pressures on the slope stability were addressed by comparing the upper‐bound solutions derived by linear and nonlinear strength envelopes (the linear and nonlinear results for short). The obtained two critical inclinations between the linear and nonlinear results both decrease and gradually approach with increasing pore‐water pressure coefficient. For most slopes subjected to pore‐water pressures, using the linear Mohr–Coulomb envelope will obviously overestimate the slope critical height. The overestimation resulted from the linear criterion will become more distinct for slopes with smaller widths. Besides, the presented results showed that the equivalent internal friction angle tends to have a weaker increasing trend for steeper slopes as pore‐water pressure coefficient increases. Hence, when pore‐water pressure coefficient increases, the critical slip surfaces of gentle slopes with nonlinear strength criteria become shallower, but the critical slip surfaces of steep slopes seem to have no consistent change law. These results and analyses can illustrate the significance of the application of nonlinear strength envelopes in slope stability evaluation considering pore‐water pressures and provide certain reference advice in slope engineering design and landslide prevention.

To investigate cyclic deformation behavior of natural soft marine clay-involved principal stress rotation, a series of undrained tests were conducted by using GDS hollow cylinder apparatus. The principal stress rotates 5000 cycles while the deviator stress was kept at a constant level. The tests results show that the deformation behavior of the tested samples are significantly dependent on cyclic stress ratio (CSR). Furthermore, different type of generation of axial strains occur under different CSRs. With the same CSR, the type of axial strain is different between that considering and ignoring principal stress rotation. When CSR is larger than CSR = 0.42 under principal stress rotation, the axial strain grows rapidly after a few cycles. Compared with the results conducted by cyclic triaxial results, the effect of principal stress rotation on the axial strain is significant.

Sea level drawdown may lead to the stability decrease and even the failure of coastal clay slopes. Since few attempts have been made to illustrate the impact of sea level drawdown on coastal slope stability considering three-dimensional (3 D) geometry and nonlinear strength, this paper extended 3 D limit analysis approach with nonlinear criterion for slope stability under different sea level drawdown conditions. The least upper bound on stability number was derived by using an optimization procedure. Stability charts were presented and the influences of sea level drawdown on slope stability were illustrated. The drops of sea levels in three cases were found to have different effects on the decreases in slope stability caused by nonlinear parameters. 3 D slope tends to be unstable in the case of rapid drawdown, but it will become stable when the inside water drops after sea level has rapidly decreased. In the case of sea level slow drawdown, slope stability will reduce to minimum and then increase. Effects of sea level drawdowns on slope stability become less significant for slope soils with obvious nonlinear strengths. Certain reinforcement measures can be taken to improve the stability of coastal slopes undergoing sea level rapid drawdown or slow drawdown.