| Q3-loess is commonly distributed in the upper-layer of loess stratum,and is one kind of disaster-induced loess for construction engineering.For Q3-loess,seismic subsidence of loess site is one kind of concernful disaster.At present,most of the theoretical researches on seismic subsidence of loess are generally based on the research ideas and conclusions of sand dynamics,while have not totally taken consideration of the stress condition and mechanical property of loess under earthquake loads.This paper mainly pays close attention to the dynamic mechanical problems of undisturbed Q3-loess during the deformation under large strain and conducts several key issues on loess dynamic as follows.Firstly,based on a series of cyclic simple shear tests on loess under different conditions,the figures of hysteresis loop,backbone curve and seismic subsidence curve under different test conditions and their change laws influenced with water content,consolidation pressure,amplitude of shear strain and cyclic loading number are analyzed,and the expression formulas of backbone curve and increment of seismic subsidence coefficient are presented.Secondly,the cyclic shearing contraction equation of loess is presented by analyzing the relationship between stress ratio(shear stress amplitude/consolidation pressure)and strain ratio(volume strain/shear strain amplitude)for loess under cyclic simpe shearing condition,mainwhile,a modified Iwan model considering the cyclic hardening behavior of loess is proposed by analyzing the law of cyclic hardening as the volume strain is hardening parameter.Combined with both of the cyclic shearing contraction equation and modified Iwan model,the modified Iwan model is improved to be a modified Iwan-shearing-contraction constitutive model which could reflect the cyclic hardening behavior and volume strain of loess.Furthermore,a one-dimensional loess site seismic response model is proposed for the deformation under large strain via the modified Iwan-shearing-contraction constitutive model,and the corresponding solution procedure is given with central difference method.Thirdly,a series of dynamic triaxial tests conducted on loess under random earthquake wave and harmonic wave with the same amplitude are analyzed,thereby the algorithm of equivalent earthquake load based on energy dissipation theory is verified to be suitable for loess;moreover,a method to determin the equivalent earthquake load for loess is recommended by integrating the cyclic simple shear tests on loess under different amplitudes of shear strain,and the correspondence between earthquake magnitude and equivalent cyclic number for loess is proposed.Fourthly,the relationship between stress reduction factor and depth for loess is brought up according to the results of site seismic response analysis on loess,thereafter the evaluation formula of equivalent shear strains at any depth is gotten combined with the backbone curve formula;furthermore,a simplified calculation model of seismic site subsidence is constructed combined with the increment formula of seismic subsidence coeffient and the correspondence between earthquake magnitude and equivalent cyclic number.Finally,this work have fully taken account of the dynamic property and deformation of loess,and proposed a refined calculation model as well as a simplified calculation model for seismic loess site subsidence from different points of view.The achievements under the above-mentioned research works are summarized as follows.(1)Based on documentations and literatures regarding the historical earthquake disaster in loess area,some disasters of seismic site subsidence induced by several strong and moderately strong earthquakes in loess area are verified;damage forms,developing features and formation conditions of disasters of seismic site subsidence are analyzed;and the physical conditions and its regional change law for generating seismic subsidence of loess are compared and analyzed.(2)A new cyclic simple shear apparatus with hinged structures for a cubical specimen is developed and produced.The apparatus successfully settles such technical problems as non-uniform shear stress and strain,un-determined boundary condition,potential shear plane,and size effect of specimen existing in current cyclic simple shear devices.(3)A series of cyclic loading tests were conducted on un-disturbed Q3-loess under different water contents,consolidation pressures and shear strain via the new cyclic simple shear apparatus.The influence of water content,consolidation pressure and shear strain on hysteresis loops,backbone curves and seismic subsidence curves are studied.The backbone curve formula is expressed in terms of consolidation and water content,and the increment seismic subsidence coefficient versus cyclic loading number in terms of water content,consolidation pressure and the amplitude of shear strain is proposed.(4)The cyclic shearing contraction equation of loess in terms of consolidation pressure,amplitude of shear stress,amplitude of shear strain,and volume strain is proposed by analyzing the relations between stress ratio(shear stress amplitude/consolidation pressure)and strain ratio(volume strain/shear strain amplitude)for loess under different cyclic simple shear tests.Moreover,the physical implication of the cyclic shearing contraction equation of loess is analyzed.(5)According to the cyclic hardening rule of undisturbed Q3-loess under cyclic simple shearing,a cyclic hardening function by introducing the volume strain as hardening parameter is presented.Combining with the simplified parallel Iwan model,a modified Iwan model considering the cyclic hardening property of loess is brought up.Furthermore,a modified Iwan-shearing-contraction constitutive model that could take both the properties of cyclic hardening and shearing contraction is constructed,by tandeming a cyclic shearing contraction element with the modified Iwan model.(6)By dynamic triaxial tests on undisturbed loess under random earthquake wave loads as well as harmonic wave loads,the chang law of energy dissipation for loess under different test conditions is analyzed,and the algorithm of equivalent earthquake load based on the energy dissipation theory is verified to be suitable for loess.Furthermore,the algorithm of equivalent cyclic number of earthquake load for loess is presented on the basis of cyclic simple shear tests under different amplitude of shear strain,and the correspondence between earthquake magnitude and equivalent cyclic number suitable for loess is given on the basis of many earthquake calculation examples.(7)A one-dimensional site seismic response analysis medol,which could take the cyclic hardening behavior as well as the cyclic shearing contraction into account,is constructed according to the modified Iwan-shearing-contraction constitutive model.Moreover,the solving process for the model is given by central difference method.(8)The expression of stress reduction ratio in terms of depth for loess have been proposed via the results of a great number of earthquake site response analysis,meanwhile the transfer coefficient of dynamic shear modulus from low frequency to high frequency is give based on the dynamic triaxial tests under different loading frequencies.Furthermore,the formula of equivalent shear strain for loess site is derived from the equation of backbone curves.Then,the simplied calculation model for the seismic subsidence of loess site is put forward based on the backbone curve formula,increment equation of seismic subsidence coefficient and the correspondence between earthquake magnitude and equivalent cyclic number. |
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