Limit Equilibrium Theory Of Axisymmetric Based On Rigorous Conditions And Its Application In Calculation Of Earth Pressure

Axisymmetric limit equilibrium theory of axisymmetric is an important branch of rigid-plastic mechanics,which plays an important role in the calculation of earth pressure and foundation bearing capacity of geotechnical engineering.Scholars at home and abroad have studied this issue greatly based on various assumptions of circumferential stress.Based on axisymmetric circumferential geometry condition and axisymmetric compatibility condition,this thesis further studies this problem through conceptual analysis,establishment of equations,mathematical solution,comparison and verification,reveals the physical connotation of axisymmetric limit state,and establishes two forms of characteristic line theories,avoiding the imprecision caused by hypotheses of circumferential stress in existing research.Then the new theories are applied to study the limit earth pressure in single and multilayer soil and non-limit earth pressure under arbitrary lateral displacement mode.The main contents and conclusions of this research include the following aspects:(1)The circumferential force equation of axisymmetric limit state are established and its physical connotations are revealed.Based on the flow equation of rigid-plastic mechanics,the expression equation of ring arch effect stress and circumferential stress are derived according to the axisymmetric circumferential geometry condition,and the compatibility stress equation is derived according to axisymmetric compatibility condition.Based on the expression of ring arch effect stress and the axisymmetric expression of Drucker-Prager yield condition,the mechanism of ring arch effect and the physical connotations of axisymmetric limit state are revealed.Derivation and analysis show that the essence of axisymmetric limit state is that the square combination of the main shear stress and the stress due to ring arch effect reaches the combined strength of medium,and the stress fields of axisymmetric limit state are fixed fields,but dynamic stress fields which vary with the radial velocity field.(2)Limit equilibrium theory of axisymmetric and the general solutions of two boundary conditions are established.Two kinds of governing equations of axisymmetric limit state are established by combining the expression equation of circumferential stress,the compatibility stress equation and the limit stress equations of axisymmetric equilibrium conditions respectively.Binary slip line theory and ternary characteristic line theory for limit equilibrium problem of axisymmetric are established.The general solutions for two types of boundary conditions are derived.The mathematical relations of the two limit equilibrium theories and the general solutions of the two boundary conditions show that that the limit stress fields of axisymmetric are related to the radial velocity of stress boundary,which are actually dynamic stress field.The Mohr-Coulomb criterion is the special case of DruckerPrager criterion in the "static" limit state of axisymmetric and in plane limit state.The calculation results of erth pressure based on the two theories agres well with the experimental data and numerical results,which indicates the rationality of the two theories.(3)The calculation methods of axisymmetric limit earth pressure are established and the distribution laws of it are revealed.Based on the slip line theory,the numerical difference method and analytical calculation method of axisymmetric limit earth pressure under the general case of single-layer soil and under the special case of horizontal surface and smooth vertical retaining wall are established.The analysis shows that the analytical results are greater than the numerical difference results,and the error increases with the depth.The distribution characteristics and laws of earth pressure in single-layer soil for the most general case and in multi-layer soil for four typical strata types are investigated.The results show that the limit earth pressure of axisymmetric present nonlinear distribution,the pressure produced by self-weight increases monotonically with depth,and the pressure produced by surcharge and cohesion tend to be stable with depth.The three kinds of earth pressure in monolayer soil decrease with the increase of friction angle,dilatation angle,interface friction angle and lining inclination angle,the pressure produced by self-weight increases with the increase of the surface inclination angle,while the pressure produced by surcharge and cohesion decrease with the increase of friction angle.The earth pressure in layered soil is distributed continuously within layers and jumps between layers,and the jumping mode is inversely related to the soil strength on both sides of the interface.The earth pressure in the four types of typical strata,such as increasing strength,decreasing strength,soft intercalation and hard intercalation,shows the distribution characteristics of zigzag increase,step increase,concave notch and convex step respectively.(4)The calculation methods of axisymmetric non-limit earth pressure are proposed and the characteristics of it are revealed.Based on the basic concept of soil strength developing gradually with lateral displacement,the relationship between friction angle and lateral displacement in axisymmetric problem is derived from the stress state of element and the hyperbolic stress-strain relationship of soil.According to the equilibrium conditions of element body in the limit state of equivalent medium,using the expression equation of circumferential stress and the compatibility stress equation respectively,the binary potential slip line method and ternary characteristic line method for calculation of non-limit earth pressure are are established.The comparison and analysis between the calculation results of earth pressure based on the preposed methods and measured earth pressure,results of existing method are made.The non-limit earth pressure of the six typical lateral displacement modes is investigated according to ternary characteristic line method.The comparison and investigation show the following conclusions.The methods proposed are applicable to wider range and agrees well with the experimental data.The pressure distribution of the rotation mode around bottom and the upper cantilever mode present the shape of concave curve,and the action point of resultant force moves downwards compared with the initial pressure.The pressure distribution of the rotation mode around top and the underside cantilever mode present the shape of convex curve,and the action point of resultant force moves upwards compared with the initial pressure.The pressure distribution of intermediate flexure mode shows an S shape,and the action point of resultant force is basically stable at 1/3 of the height of the retaining wall.