Research On The Optimized Shape Of Toppling Fracture Plane In Obsequent Slope And The Deformation Stability Analysis Method

With massive engineering projects carried out in western China,more and more toppling slopes were found and reported,which caused the greater attention of many scholars.The stability evaluation method of slope whose failure mainly controlled by sliding surface is comparatively perfect,but for toppling slope it is far from mature due to the special failure mechanism,and there is also no feasible method to predict whether a toppling slope will continue to deformation or transform into large-scale landslide failure.Therefore,it has great importance to focus on the deformation stability of toppling slope.To estabilish a feasible deformation stability evaluation model for toppling slope,based on the upper bound theorem of limit analysis,the optimized shape of toppling fracture plane in obsequent slope is searched to analyze the breakthough mechanism,and the whole evolution process of toppling slope is researched to put forward the instability criterion and the deflection criterion.Moreover,the deformation stability evaluation model is applied in a practical engineering.Altogether it provides a new way to evaluate the stability and predict the development tend of toppling slope.On these grounds,this paper concludes that the main research results are as follows:(1)The optimized shape of toppling fracture plane is researched by using the upper bound theorem of limit analysis and the minimum principle of optimal control theory.The calculation results show that the critical toppling height of obsequent slope is the minimum only when the fracture plane is perpendicular to the rock layer,which means that the slope requires the minimum external load for toppling deformation.Therefore,the optimized shape of toppling fracture plane is the straight line which always perpendicular to the rock stratum.The rationality of the research result has also been verified by the Phases~2 simulation software.It lays a foundation for studying the deformation-failure process mechanism and the deformation stability issue of toppling slope.(2)The variation of critical toppling height of obsequent slope is analized.The results show that the critical toppling height of the slope decreases monotonically with the increase of slope angle,and increases linearly with the increase of layer thickness.The most unfavorable structure combination of obsequent slope occurring toppling deformation is the double-angle of rock layer plus slope angle equals 180degree(?+2?=180°).Based on these,the“critical toppling circle”concept model of obsequent slope is estabilished to explain and expound the above laws.In the meanwhile,the analysis results show that the critical toppling height of the slope decreases with the decrease of rock mass quality and rock layer characteristic.(3)Combined with the theoretical achievement of the optimized shape of toppling fracture plane and the three-stage mode of high rock slope,the whole evolution process of toppling slope is analyzed.According to this,a process mechanism analysis model for toppling slope deformation and failure is estabilished,and the stability criterion and instability criterion of the toppling slope are put forward.The study result shows that the toppling deformation prerequisite of obsequent slope is gravity load,only when the slope height reaches its critical toppling height,the toppling deformation occurs.While the judgment standard of toppling slope transforming to landslide is that the dip angle of the toppling fracture plane is equal to its equivalence internal friction angle.Moreover,the whole evolution process of toppling slope has been reappeared by the PFC2D simulation software.(4)According to the three-stage mode of toppling slope,a deformation stability evaluation model of toppling slope is estabilished by combining the deflection and rotation angle of cantilever beam under uniform distribution load.It is suggested that the deformation calculated by the evaluation model can be the failure threshold value,so as to evaluate and predict the stability and development trend of the toppling slope.Compared with the traditional limit equilibrium method,the advantage of this model is simple calculation,but the difficulty lies in the reasonable selection of mechanical parameter of the fracture plane.Futhermore,It is considered that the evaluation model is more suitable for the toppling slope composed of hard rock with larger rigidity,and the applicability for flexible soft rock remains to be discussed.In addition,according to the most unfavorable combination relationship of obsequent slope occurring toppling deformation(?+2?=180°),the toppling deformation trends of obsequent slopes with different structures are analyzed.For the slope structure which?+2?>180°,the toppling deformation is not easy to converge,which means the toppling slope will continue to deformation.But for the slope structure which?+2??180°,the toppling deformation is relatively stable.This can be the basis of qualitative judgement on scene.(5)Taking the Xingguangsanzu toppling slope in the reservoir area of the Xiluodu hydropower station as the typical case,the deformation-failure characteristics and development process of the slope are expounded in detail.It is shown that the toppling deformation direction of the slope which is mainly controlled by the underlying rock mass structure is pointing to the upper reaches.And the deformation degree in the plane distribution also presents that the upstream side is larger than the downstream side in general,while that in the vertical distribution presents that the high elevation rock mass of the slope is more intense than the low elevation rock mass.Furthermore,according to the rock mass deformation phenomena revealed by adits,the deformation-failure process of the toppling slope can be divided into 4 stages,which are unloading rebound–layer dislocation,rock mass toppling–layer tension,rock mass bending–interlayer tension,cutting-layer shear–creep(sliding)breakage.(6)Combined with the engineering geology and rock mechanics environment conditions of the slope,the factors influencing the toppling deformation and the deformation mechanism under the action of reservoir water are analyzed.It is considered that the slope has undergone a compression toppling deformation caused by the well free-face condition,thin-layered rock mass structure and soft-hard interbedded rocks during the long process of geological history,and the reservoir storage and fluctuation promote the development.Moreover,the deformation response of the slope under the action of reservoir water and overall deformation trend are systematically analyzed based on deformation monitoring data in 4 aspects that are lateral,longitudinal,settlement and resultant displacement.The analysis shows that the slope deformation rate is decreasing with the fluctuation of reservoir water level,which indicates that the slope deformation is gradually converging and trends to be stable.Meanwhile,the drawn slope displacement vector diagram and nephogram show that the deformation direction and the deformation degree of the slope are consistent with the field survey results,and the deformation regions are accordingly divided.(7)Taking the position of toppling rock mass revealed by adit and the dip angle of rock layer as the main basis,the profile zoning of the Xingguangsanzu toppling slope is divided.The zonation characteristics of the slope show well linear relationships,and the inclination angles of toppling fracture planes are approximately perpendicular to the dip angles of the rock layers,which is consistent with the theoretical result of the toppling fracture plane optimized shape.Meanwhile,the mechanics parameters of the toppling fracture planes are quantitatively estimated by the geological strength index method(GSI)proposed by Hoek-Brown et al..It is concluded that the mechanical properties of the toppling fracture planes are closely related to their development positions,which shows that the weak toppling lower bound is larger than that of upper bound and strong toppling lower bound.(8)The instability threshold of the Xingguangsanzu toppling slope is calculated by using the deformation stability evaluation model,and the stability status and development trend of the slope are evaluated by combining the deformation phenomenon.Analysis shows that the present deformation of the slope has not reached its critical value yet,and the surface cracks are not trap,nor the overall failure signs revealed by adits,and the deformation monitoring data also show the slope in gradual convergence.So the slope is still in the stage of time-dependent deformation,and the possibility of large-scale failure is small.But with the toe rock of the slope continued softening,coupled with the rock mass degradation caused by weathering,unloading,earthquake,rainfall and anyother factors would cause the slope to occur persistent compression toppling deformation.Once the slope deformation value reaches or even exceeds its critical threshold,the toppling slope will transform into sliding failure,thus it enters into progressive failure stage which is uncontrollable.