| There is the three-dimensional effect in slope stability analysis, containing the shape effect of slip mass and the shape effect of slope topography. Since the3D slope stability analysis methods considering the three-dimensional effect and the algorithm of the3D critical slip surface are still not well developed, the three-dimensional effect can not yet be formed a systematical study and it is not always safe to take the three-dimensional effect out of account for a certain engineering case. Therefore, a comprehensive study on the three-dimensional effect of the slope stability analysis, employing statistical analysis, theoretical calculation, experimental test and engineering application, should be carried out. Several main conclusions can be drawn as following:(1) Based on the statistical analysis of522sets of failure slope data, the shape of slip mass, the aspect ratio of slip mass and the shape of slope topography are analysed emphatically in this study. Preliminary results show that about82.4%of the aspect ratio values are0.5-5.0, the average aspect ratio value is3.08and only3.4%of the aspect ratio values are higher than10. In addition, the shape of slope topography also has a great effect on the slope stability. A statistical analysis of300cases of failure slope shows that the concave slope is the most stable, the horizontal slope is the second and the convex slope is the worst since there are148sets of convex slope (49.3%).112sets of horizontal slope (37.3%) and40sets of concave slope (13.4%).(2) On the analogy of the classical earth pressure theory and Spencer’s assumption about inter-slice forces, the individual inter-slice forces are equivalent to the normal stresses over slip surface. Then, considering the equilibrium conditions of the whole sliding body, a rigorous two-dimensional limit equilibrium method for slope stability analysis is proposed, by which the safety factor can be explicitly solved. Furthermore, the proposed2D method will be developed to a3D non-rigorous limit equilibrium method which satisfies four equilibrium conditions and accommodates to slip surfaces of all shapes.Typical examples show the rationality, reliability and precision of the proposed2D and3D method.(3) Regarding the slip surface of a homogeneous slope as a curved surface yielded from a family of power function rotating on y-axis, slip surfaces of different shapes are obtained by changing the values of the power function’s power. Then, ascertain the simplified3D critical slip surface by optimizing the parameter of power function. Examples show the validity and rationality of the proposed method and the convenience of the procedure. Considering the complexity about the procedure of solving the3D safety factor, a set of calculation curves of the3D safety factor is drawn to obtain the3D safety factor more convenient and faster, which has been verified by other similar results.(4) Based on the3D slope stability analysis method and simplified search algorithm of the3D critical slip surface, the shape effect of the slip mass is studied in detail and several modified curves for shape effect of the slip mass are also drawn, which are verified by experiment and numerical calculation. Several examples show that the two-dimensional slope safety factor modified by considering the shape effect of the slip mass is quite close to those3D analysis methods and the proposed method is more convenient. In addition, independently parameters, containing the shape of slip surface, the length to height, slope gradient, cohesions and the internal friction angles, are analyzed and change rules and influence amplitude on the shape effect of the slip mass are summarized. Furthermore, a limit whether or not to consider the shape effect of the slip mass is suggested. Finally, the formation mechanism on the shape effect of the slip mass is discussed and change relationships between the shape effect of slip mass and parameters are explained.(5) Since the2D back analysis often overestimates the shear strength parameters of slip soil and has some unsafe risks in the slope treatment, a3D back analysis model considering the shape effect of the slip mass is established. The proposed method can take the shape effect of3D landslide mass into account, thus the shear strength parameters calculated is more reasonable. Two case studies show that the shape effect of the slip mass has a significant effect on the back analysis result.(6) The slope topography effect is studied by tilting the model box. The results indicate that the ultimate stable of horizontal slope angle is2°～4°higher than convex slope and3°～5°lower than concave slope under a given gradient. That is to say, the concave slope is the most stable, the horizontal slope is the second and the convex slope is the worst. This phenomenon was explained from mechanical viewpoint. The slope topography has little effect on the shape and location of the main slip surface, which basically shows a circular slip surface. The difference about the three-dimensional configuration is changed obviously with the limitation of the slip mass ends. The runout is big in the middle and small at both ends, of which the maximum value is increased with the gradient.(7) Based on the rigorous limit equilibrium methods, the theoretical solution procedure of the circular convex slope and concave slope is deduced in this study. Furthermore analytical results show that the shape effect of the slope topography(R/H) has a significant influence on the factor of safety and the amplitude is restricted by c/(γHtanφ) and slope gradient β. The amplitude for the convex slope or concave slope is increased with decreasing R/H and the concave slope is more obvious than the convex slope. The larger value of c/(yHtan<p) and slope gradient β are, the more obvious the shape effect of the slope topography under the certain condition of R/H. For engineering application, a set of curves about the safety factor in different cases of convex slope or concave slope is drawn. In addition, a suggestion whether to consider the shape effect of the slope topography on the safety factor is also given as following (only be applicable to the condition of c/(γHtanβ)≤0.6): First, while R/H≥15, the shape effect of the slope topography could be neglected. Second, while15>R/H≥5, the shape effect of the slope topography should be considered.Finally, while R/H<5, the shape effect of the slope topography must be considered.(8) Some project cases are employed to check the engineering practicability of the methods suggested in this thesis. The results indicate that these methods are of value in project cases. |
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