Dynamic Response And Stability Analysis Of Slope Supported By Frame With Pre-stressed Anchors Under Earthquake In Loess Area

China is the country with the world’s most wide and most thickdistribution of loess. These loess is mostly found in the northwestern regionof loess plateau. There are lots of ravines and slopes in the loess plateau.Since the great development of the west, a lot of highways, railways andurban infrastructure constructions need to be built in the loess area, thus alot of natural slope engineerings will be met. In history, every strongearthquake would cause serious seismic landslides in northwestern loessareas. Therefore, it is very necessary to study the dynamic response andstability analysis of the slope supported by frame with pre-stressed anchorsunder earthquake at the right moment. This paper is based on the NaturalScience Foundation of China: The Seismic Action and Dynamic StabilityAnalysis of Permanent Flexible Slope Supporting Structure. According acertain engineering example, the dynamic response and stability analysis ofthe slope supported by frame with pre-stressed anchors under earthquakehave been studied. The theoretical analysis and the numerical simulationhave been carried out, and the main work and conclusion gained are listedas follows:(1) The calculation model of the frame－pre-stressed anchor－soilsystem under seismic action is established. In this model, the free section ofpre-stressed anchor is regarded as a linear spring, the frame (beams,columns and retaining plates) and the anchorage section of pre-stressedanchor is connected through the spring of the free section, and theinteraction between the anchorage section and the soil is treated as linearspring and damped system related with velocity. In the model, the influenceabout the response of the system with the frame (beams, columns andretaining plates) is also considered, namely, the frame (beams, columns andretaining plates) is also treated as linear spring and damped system relatedwith velocity. Under the seismic action, the frame, the free section, theanchorage section and the soil system are interacting and coordinating. Inthe process of earthquake, the anchor pre-stressing force is changing withthe time. And the change of the pre-stressing force is communicated to the anchorage section through the spring, and then it is transferred to the soilthrough the anchorage section. In the model, the qualities of the frame(beams, columns and retaining plates) and the active area soil were regardedas lumped mass, then connected with the free section end, and thenconnected with the damper through the spring of the free section. Under thecondition of seismic action, the damping differential equation is establishedaccording to this theory. The seismic response of the pre-stressing force andthe anchorage section axial force is solved under harmonic seismic. Finally,through an engineering example, with the previous results of FEA softwareADINA, this calculation model was verified.(2) Based on soil dynamics and structural dynamics theory, a dynamicmodel of slope supported by frame with pre-stressed anchors is proposed.The seismic response of the supporting slope is obtained under thecondition of horizontal earthquake excitation. According to horizontal slicemethod, and the influence of slope height on seismic soil pressuredistribution is considered, the soil pressure dynamic analysis model isestablished. The influence of anchor prestress is considered, a set of lumpedmasses is formed by taking the frame columns as calculating unit based onthe concentrated mass method. Frame structure and soil is connected byanchors with spring supports, pre-stressing force is applied to anchorsthrough the given initial design value, then the corresponding controlequation of motion is established. The axial force response of pre-stressedanchors can be obtained based on dynamic soil pressure, pre-stressing forceand seismic excitation. The soil pressure distribution characteristics, thedisplacement response of the supporting structures and the axial forceresponse characteristics of pre-stressed anchors can be approximatelyreacted by this model. The results of dynamic soil pressure and modelresponse can provide reference for the seismic design of slope supported byframe with pre-stressed anchor. Finally, the applicability of this method isverified by an engineering example.(3) Under the situation of considering the anchor prestress effects onstability of loess slope, according to the failure mode of the soil slidingsurface, stability model of slope supported by frame with pre-stressedanchors under earthquake is established. By the method of lumped-massexplicit finite element, the soil is separated into soil-static-dynamic micro-unit and soil-prestressed micro-unit discretely, and the correspondingdiscrete element dynamic equilibrium equation is established. Thedisplacement response and the stress field in sliding surface of thesupporting slope are analysed. Based on the displacement response and thesoil stress field, a calculation method of stability safety factor for slopesupported by frame with pre-stressed anchors under earthquake is proposed.(4) Based on the practical engineering in the northwest loess area,nonlinear FEM (ADINA) is used to parameter analysis and calculate thedisplacement and anchor axial force response of slope supported by framewith pre-stressed anchors under seismic action. Considering the interactionand collaborative work of frame-anchor-soil,3D nonlinear FEM model ofsystem about slope supported by frame with pre-stressed anchors isestablished. In the model, the soil is simulated by elastic-plastic model, anda bilinear elastic model is used to simulate the anchor, friction-element isused to describe the interaction between soil and frame (beams, columnsand retaining plate), the frame is simulated by a bilinear elastic-plasticmodel. By inputting bidirectional seismic waves, the axial force before andafter the earthquake is compared, and the axial force response is calculated.The dynamic response of the supporting system is compared and analysedunder the different intensity, different conditions and different soilparameters. The influence law of slope seismic response is obtained underdifferent factors.(5) According to the similarity theory, the domestic shaking table testscheme is analysed and researched, Based on an practical engineering, andtake it as the prototype, the prototype is turned into scale model bysimilarity relation, and then the shaking table laboratory scale model wasdesigned. The main contents include similar design of the model, design ofthe model box, boundary treatment of the model box, selection andperformance index test of the material, design of the slope mass,arrangement of the measuring-point, input of the earthquake excitation, andthe load method and the steps of the test are elaborated in the scheme.