Study On Failure Mode And Stability Of The Slope With Bedrock Based On Upper Bound Method Of Limit Analysis

Slope is a common landform in southwest China,and it is easy to cause landslide disaster due to the influence of external factors.The slope with bedrock whose lower part is hard bedrock and the upper part is loose accumulation body has unique dual structure.Under the action of earthquake and other external disturbances,this kind of slope is more prone to instability,not only easy to form secondary disasters such as dammed lakes,but also bring very adverse effects to the rescue work.Therefore,the possible failure mode and load stability analysis of the slope with bedrock under various conditions is of great engineering practical significance,which is helpful to accurately evaluate its stability in advance and implement better landslide disaster prevention and control measures.On the basis of previous studies,this paper first develops and extends the stability charts provided by MICHALOWSKI based on the upper bound method of limit analysis and quasi-static method.Then four kinds of global failure modes that may occur in the slope with bedrock under various complex conditions and two kinds of local failure modes under reinforcement conditions are discussed.After that,the accuracy of the previous theoretical analysis was further verified by the indoor model loading tests.Finally,the stability equilibrium state equation of anchoring the slope with bedrock under seismic loads is derived by combining the upper bound method of limit analysis with pseudo-dynamic method.The main conclusions of this paper include:（1）When the physical and mechanical parameters of the slope are given,the safety factor can be quickly obtained through the stability charts,so as to realize the preliminary evaluation of the stability of the actual slope engineering.The parameter analysis shows that when k_h is less than 0.4,with the increase of slope inclination β,the slip surface parameter L?H increases,but it is always less than 1.0,that is,the crack length at the top of the slope is smaller than the height of the slope,while when k_h is more than 0.4,the parameter L?H decreases gradually with the increase of β,but it is always greater than 1.0,that is,the crack length at the top of the slope will be larger than the height of the slope.And this phenomenon becomes more significant with the increase of k_h .（2）The main factors affecting the failure mode of the slope with bedrock are the shear strength of the interface between bedrock and overburden layer and its upper and lower inclination angles.When the shear strength of the interface is not less than the corresponding strength of overburden layer soil（that is,the soil strength near the interface is very high）,the critical failure mode of the slope is mode 1.When the shear strength of the interface is less than the corresponding strength of overburden layer soil（that is,the soil near the interface tends to be transformed into a weak interlayer）,the change of the upper and lower inclination angles of the interface will lead to the transformation of the critical failure mode of the slope between the four modes.When the shear strength of the interface is much smaller than the corresponding strength of overburden layer soil（that is,the soil near the interface has actually become a weak interlayer）,even if the upper and lower inclination angles of the interface are both of slow,the critical failure mode of the slope is still mode 2.（3）Considering the horizontal seismic load and anchoring effect,when k_h <0.3,the arrangement of anchor cables near the toe of the slope with bedrock is the most dangerous for the slope,and the upper part of the slope is prone to local instability;when k_h ≥0.3,the most unfavorable anchorage position of anchor cables is near the top of the slope,which is prone to global instability.When the seismic fortification requirement of the slope is very high,multiple rows of anchor cables should be used to ensure that the slope has sufficient safety reserves.（4）The critical failure mode of the slope with bedrock is mainly controlled by geometric and mechanical parameters such as the inclination angles of the interface between bedrock and overburden layer,slope inclination angle and the roughness of the interface,but has nothing to do with the type of external loads on the slope,and it will only affect the development range of slip surface and safety factor.The theoretical solution of the slope case in which the seismic waveform is a sine wave is in good agreement with the results of the model test,which is due to the fact that the waveform of sine wave is more stable and uniform.（5）The results obtained by the pseudo-dynamic method are closer to the model test values,because the pseudo-dynamic method takes into account the amplification effect and time-history characteristics of earthquake action and has higher accuracy and is a better upper bound solution.The parameter analysis shows that the effect of seismic acceleration amplification factor f_a on the safety factor is more obvious when k_h >0.1,and the effect of f_a on the interface inclination angle θ₄ is also more obvious when k_h >0.2.With the increase of the interface inclination angle θ₄,the slope stability decreases at first and then increases,and the larger f_a is,the smaller the optimal interface inclination angle θ₄ is,but it is always larger than the corresponding angle of the vertical interface.This shows that the safety factor obtained by using the idea of vertical partition is not the most dangerous value in the past,and the actual safety factor of the slope should be smaller,and the smaller the value of f_a is,the more obvious the gap between them is.