Study On Stress And Deformation And Design Method Of Frozen Wall In Inclined Shaft

In this paper,the stress and deformation and design method of frozen wall in inclined shaft are studied by means of theoretical analysis,numerical simulation and physical test,refers to the non-uniform stresses and irregular shape of the frozen wall in the western inclined shaft.Based on the theoretical analysis method,the unloading mechanic model of circular frozen wall considering the interaction with surrounding rock under non-uniform stresses is established,and the elastic analytical solution of stress and displacement field in circular frozen wall and surrounding rock is deduced.Through numerical simulation,the accuracy of analytical solution is verified by establishing the same numerical model.The results of influence factors show that the increase of the Young's modulus of frozen soil to unfrozen soil can significantly reduce the radial deformation of frozen wall,but at the same time increase the hoop stress of inner frozen wall.The increase of outer radius of frozen wall can significantly reduce the stress and displacement of frozen wall,however the effect is mainly reflected in ?<2.2;the unloading rate reflects the size of unloading value during excavation,so the greater the unloading rate,the greater the stress and displacement of frozen wall.The lateral pressure coefficient reflects the uneven load on the frozen wall,in the range of 0.4<?<1,the frozen wall is in the compression state,and when ?<0.4,the tensile stress occurs at 90° position of the shaft.Based on the obtained elastic analytic solution for circular frozen wall,the elastic design of frozen wall thickness under Tresca,Mises and Mohr-Coulomb yield criteria are deduced,respectively.The results show that the elastic design thickness of circular frozen wall deduced by Mises yield criterion is smaller than the value deduced by MohrCoulomb yield criterion which is smaller than the valued deduced by Tresca yield criterion.The elastic design thickness of frozen wall under these three yield criteria increases with the growth of depth.The diminution of cohesion and internal friction angle of frozen soil will increase the elastic design thickness of frozen wall,and the smaller the cohesion of frozen wall,the greater the influence range of internal friction angle.On account of the composite optimization method,the mapping formula of the semicircular arch frozen wall with straight wall to concentric ring is calculated,which has great accuracy.The unloading mechanics model of semi-circular arched frozen wall with straight wall subjected to non-uniform stresses is established with complex variable method.Based on the conformal mapping formula,the elastic analytical solutions of the stress and displacement field of frozen wall and surrounding rock are deduced.Through numerical simulation,the accuracy of the analytical solution is verified.The results of influence factors show that considering the interaction between the surrounding rock and frozen wall,the stress and deformation of frozen wall can be diminished,and the influence becomes more obvious with the decline of frozen wall thickness.The stress and displacement of frozen wall are linearly related to the overburden pressure.The lateral pressure coefficient affects the deformation characteristics of the frozen wall,the frozen roof and floor appear to have the effect of tensile stress and deformation outside of side wall when the lateral pressure coefficient is less than 0.4).The increase in the thickness of frozen wall can significantly reduce the internal stress and displacement of frozen wall,but the displacement effect is mainly concentrated in the thickness ratio of less than 1.2.The effect of Young's modulus on the deformation of frozen wall at each side is consistent.With the increase of Young's modulus,the deformation of frozen wall decreases,but the effect is obviously weakened when ?>9.The effect of Young's modulus on the stress of frozen wall is complicated.The hoop stress in frozen roof and floor drops and increases in inner side wall with the increase of Young's modulus ratio.The growth of side wall height of frozen wall and the drops of frozen floor radius are equivalent to increasing the horizontal load on frozen wall,which leads to the gradual increase of the horizontal force and the increase of the hoop compressive stress of roof and floor.The increase of sidewall height significantly reduces the hoop compressive stress of the sidewall,however it increases the deflection of sidewall.The curvature radius of floor is reduced to avoid tensile stress.According to the approximate elastic solution of frozen wall,an orthogonal combining experiment is organized with six factors,such as the outer diameter of frozen wall,the overburden pressure,the Young's modulus ratio of frozen wall to ground,the side wall height,the floor radius and the side pressure coefficient,and four values for each factor.By using the multivariate statistical method,a relationship among the frozen floor radius,the side wall height and the side pressure coefficient is worked out for protecting the frozen wall from tensile stress.Then,the elastic design formula of frozen wall thickness under Tresca,Mises and Mohr-Coulomb yield conditions is analyzed,respectively,and the variance analysis method is used to verify the regression formula.The results show that the regression equations of frozen wall are significant and can be used to predict and judge the thickness of the frozen wall.Similar to the circular frozen wall,the elastic design of frozen wall thickness under the Mises yield criterion is smaller than the Mohr-Coulomb criterion which is smaller than Tresca criterion.The influence of internal friction angle is mainly concentrated on ? <10°,and the smaller the cohesion is,the larger the influence range is.Based on Mohr-Coulomb criterion,the elastic-plastic analysis of circular and semicircular arch and straight wall shaped frozen wall subjected to non-uniform stresses is carried out by numerical simulation.The ratio of outer radius of frozen wall to inner radius(?= r1/r0),overburden pressure p,cohesion force c and internal friction angle ? of frozen wall,lateral pressure coefficient ? and Young's modulus ratio E1/E2 are studied on the distribution of plastic zone in frozen wall.When the lateral pressure coefficient ?<1,the plastic zone of the circular frozen wall occurs mainly in the side region,and it lies in the side straight wall in irregular frozen wall,which starts from the corner of side wall and invert floor to inside wall along the angles 45°~50°.When the lateral pressure coefficient ?>1,the plastic zone in the sidewall gradually diminishes,and the plastic zone in the floor and roof increases gradually with the increase of the lateral pressure coefficient.The results show that the thickness of plastic zone in frozen wall is approximately linearly proportional to the overburden pressure.The increase of wall thickness,the cohesion and internal friction angle of frozen soil can reduce the size of plastic zone in frozen wall,and the effect is gradually weakened with the increase of the factor values.The increase of the Young's modulus of the frozen soil can promote the growth of plastic zone in frozen wall.When the lateral pressure coefficient ?<1,the radius of frozen floor has little effect on the plastic zone,and the plastic zone increases first and then decreases with the growth of sidewall height because of the reduction of wall rigidity.Based on the above six factors,the 6-factor and 4-level orthogonal combination test is carried out on the circular and irregular frozen wall.The results show that the effect of overburden pressure,Young's modulus ratio,cohesion and internal friction angle of frozen wall is significant.According to the multivariate statistical analysis method,the orthogonal test results of the circular and semi-circular arch with straight wall shaped frozen wall are analyzed by regression analysis,and the regression formula between the wall thickness of frozen wall and the influencing factors is obtained.Based on the existing three dimensional test equipment,a three-dimensional model test system is established for simulating the whole process of loading,freezing,excavation and thawing in inclined shaft.In the case of geometric similarity ratio CL=16,the freezing excavation tests are carried out in two kinds of freeze forms,axial freezing and vertical freezing five rows of pipes.The model size is 2m × 2m × 1.2m(width × height × depth)refers to the test equipment scale,the maximum vertical pressure in the test reaches 2.13 MPa,and the freezing pipes remain unbroken.The freezing wall thickness and the average temperature obtained by these two kinds of freezing tests meet the design requirements.In the sand layer,the main influence range of deformation of frozen wall due to the excavation is about 0.15 m ~ 0.2m before and after the monitoring section.During the excavation process,the circumferential stress near the roof and the floor gradually decreases with the excavation,which leads to reverse variation on frozen side wall.The radial stress in the frozen wall gradually decreases with the excavation proceeding.The stress change law at different region performs similar with the theoretical result.In the vertical freezing test,because the middle three-row pipes which lie in the range of shaft,are cut off during the excavation process,and only the outermost freezing pipes keep working,so the temperature and thickness of the frozen side wall can be maintained.The results show that the average temperature of side wall is about-5? and the thawing thickness of the frozen side wall is maintained at 0.06 m,the average temperature of frozen roof and floor ranges between-2?~-3 after the excavation,and then the wall thickness ?keep decreasing,especially in frozen floor.In the axial freezing test,the freezing pipes is not affected by excavation,and the solution keep circulating while excavation,which can effectively maintain the temperature and thickness of the frozen wall.The results show that the thawing thickness of frozen wall is maintained at 0.07 m during the excavation,and the average temperature of frozen wall can be maintained at about-6 with salt ?solution temperature waving between-8?~-10?.Through these two kinds of tests,it can be found that the temperature and thawing thickness of frozen roof and floor are greater than side wall in the vertical freezing test.While in the axial freezing test,the variation of temperature and thawing thickness at different region is relatively uniform.Besides the average temperature of frozen wall in axial freezing test is lower than that in vertical freezing test.The frozen side wall thickness is reduced by 27.4% in vertical freezing test,and which decreases by 14.7% in axial freezing test during the negative freezing period.On the perspective of excavation deformation,the wall deformation in the vertical freezing test is greater than that in the axial freezing test.It can be concluded that the axial freezing scheme is better than the vertical freezing scheme in the construction of inclined shaft.Finally,the design issue of the frozen wall in inclined shaft is discussed from the aspects of freezing scheme and reasonable section size of frozen wall.After then the elastic and elastoplastic design values of the frozen wall are given refers to a specific example.The results show that in the given example,the designed thickness of semicircular frozen wall with straight side wall is greater than that of circular frozen wall,and the designed thickness of semi-circular frozen wall with straight side wall regarding freezing soil as elastoplastic materials is approximately 1/15~1/20 of the elastic design thickness,therefore the irregular shape should be concerned in inclined shaft and the use of elastoplastic design method is needed with regard to deep burial problem.