The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequ...The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequently,such models fail to adequately reflect the continuity characteristics of soil deformation.Leveraging the Pasternak foundation-Euler beam model,this study considers the generalized shear force on the beam to account for the influence of soil outside the beam ends on the shear stress.An analytical model for the deformation and internal forces of finite-length beams subjected to arbitrary loads is derived based on the initial parameter method under various conditions.The mechanical model of the elastic foundation beam for advanced umbrella arch under typical tunnel excavation cycles is established,yielding analytical solutions for the longitudinal response of the umbrella arch.The reliability of the analytical model is verified with the existing test data.The improved model addresses anomalies in existing models,such as abnormal upward deformation in the loosened segment and maximum deflection occurring within the soil mass.Additionally,dimensionless characteristic parameters reflecting the relative stiffness between the umbrella arch structure and the foundation soil are proposed.Results indicate that the magnitude of soil characteristic parameters significantly influences the deformation and internal forces of the umbrella arch.Within common ranges of soil values,the maximum deformation and internal forces of the umbrella arch under semi-logarithmic coordinates exhibit nearly linear decay with decreasing soil characteristic parameters.The impact of tunnel excavation height on the stress of unsupported sections of the umbrella arch is minor,but it is more significant for umbrella arch buried within the soil mass.Conversely,the influence of tunnel excavation advance on the umbrella arch is opposite.展开更多
The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic found...The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.展开更多
To obtain the vertical earth pressure on a soft foundation box culvert and investigate the interaction of the soil-culvert-foundation system, both a centrifugal model test and a numerical simulation were conducted and...To obtain the vertical earth pressure on a soft foundation box culvert and investigate the interaction of the soil-culvert-foundation system, both a centrifugal model test and a numerical simulation were conducted and the comparisons with the current methods to determine the load on a culvert were completed. The results of the model test and numerical analysis are in satisfactory agreement, which shows that the direction of the shear stress between the culvert and the adjacent embankment depends on the differential settlement between them. A vertical earth pressure concentration appears on the culvert with a rigid piles foundation because of a downward shear stress. The ratio of the load on a soft foundation culvert and the overburden pressure above the culvert raises first and then decreases as the backfill height increases. In order to reduce the load on a culvert, it is suggested to limit the stiffness difference of the foundations under the culvert and embankment and to use a light backfill over the culvert.展开更多
To reveal the bearing capacity of the X-section concrete piles pile raft foundation in silica sand,a series of vertical load tests are carried out.The X-section concrete piles are compared with circular section pile w...To reveal the bearing capacity of the X-section concrete piles pile raft foundation in silica sand,a series of vertical load tests are carried out.The X-section concrete piles are compared with circular section pile with the same section area.The load−settlement curves,axial force and skin friction,strain on concave and convex edge of the pile,pile-sand stress ratio,distributions of side and tip resistance are presented.The results show that bearing capacity of the X section concrete pile raft foundation is much larger than that of the circular pile raft foundation.Besides,compared with the circular pile,the peak axial force of X-section piles under raft is deeper and smaller while the neutral point of X-section concrete pile is deeper.Moreover,the strain on the concave edge is much larger than that on the convex edge of the pile,and the convex edge has more potential in bearing capacity as the vertical load increases.The X-section pile has higher pile-sand stress ratios and load-sharing between side resistance and tip resistance.Above all,the X-section concrete pile can significantly increase the bearing capacity of pile-raft foundations in silica sand.展开更多
The seepage under a dam foundation is mainly controlled by the performance of the curtain.Its anti-seepage behavior may be weakened by the long term physic-chemical actions from groundwater.According to seepage hydrau...The seepage under a dam foundation is mainly controlled by the performance of the curtain.Its anti-seepage behavior may be weakened by the long term physic-chemical actions from groundwater.According to seepage hydraulics and geochemistry theory,a coupling model for assessing the behavior of the curtain under a dam foundation is set up,which consists of seepage module,solute transport module,geochemistry module and curtain erosion module,solved by FEM.A case study was carried out.The result shows that the curtain efficiency is weakened all the time.Aqueous calcium from the curtain is always in dissolution during the stress period for simulation,which leads to the increasing amount in groundwater reaching 846.35-865.312 g/m3.Within the domain,reaction extent differs in different parts of the curtain.The dissolution of Ca(OH)2 accounts to 877.884 g/m3 near the bottom and is much higher than that of the other parts.The erosion is much more serious near the bottom of the curtain than the other parts,which is the same to the upstream and downstream.Calcium dissolution is mainly controlled by hydraulic condition and dispersion,and it varies in a non-linear way within the domain.展开更多
Based on reasonable assumptions that simplified the calculational model,a simple and practical method was proposed to calculate the post-construction settlement of high-speed railway bridge pile foundation by using th...Based on reasonable assumptions that simplified the calculational model,a simple and practical method was proposed to calculate the post-construction settlement of high-speed railway bridge pile foundation by using the Mesri creep model to describe the soil characteristics and the Mindlin-Geddes method considering pile diameter to calculate the vertical additional stress of pile bottom.A program named CPPS was designed for this method to calculate the post-construction settlement of a high-speed railway bridge pile foundation.The result indicates that the post-construction settlement in 100 years meets the requirements of the engineering specifications,and in the first two decades,the post-construction settlement is about 80% of its total settlement,while the settlement in the rest eighty years tends to be stable.Compared with the measured settlement after laying railway tracks,the calculational result is closed to that of the measured,and the results are conservative with a high computational accuracy.It is noted that the method can be used to calculate the post-construction settlement for the preliminary design of high-speed railway bridge pile foundation.展开更多
At present,shield tunneling often needs to pass through a large number of bridge pile foundations.However,there are few studies on the influence of shield tunneling on adjacent pile foundations by combining with groun...At present,shield tunneling often needs to pass through a large number of bridge pile foundations.However,there are few studies on the influence of shield tunneling on adjacent pile foundations by combining with groundwater seepage.Based on Winkler model,the calculation equations of shield tunneling on vertical and horizontal displacement of adjacent bridge pile are derived.Meanwhile,full and part three-dimensional finite element models are established to analyze the trend of bridge pier settlement,ground surface settlement trough,vertical and horizontal displacement of the pile and pile stress under three calculation conditions,i.e.,not considering groundwater effect,considering stable groundwater effect and fluid-soil interaction.The results show that the calculated value is small when the effect of groundwater is not considered;the seepage velocity of the soil above the excavation face is faster than that of the surrounding soil under fluid-soil interaction,and after the shield passing,the groundwater on both sides shows a flow trend of“U”shape on the ground surface supplying to the upper part of the tunnel;the vertical displacement of the pile body is bounded by the horizontal position of the top of the tunnel,the upper pile body settles,and the lower pile body deforms upward.The horizontal displacement of pile body presents a continuous“S”shape distribution,causing stress concentration near the tunnel.The calculated results of fluid-soil interaction are in good agreement with the field measured data and accord with the actual situation.展开更多
A new analytical solution for ground surface settlement induced by deep excavation is proposed based on the elastic half space Melan’s solution,and the analytical model is related to the physical and mechanical prope...A new analytical solution for ground surface settlement induced by deep excavation is proposed based on the elastic half space Melan’s solution,and the analytical model is related to the physical and mechanical properties of soil with the loading and unloading action during excavation process.The change law of earth pressure of the normal consolidation soil after the foundation pit excavation was analyzed,and elastic displacement calculation methods of analytic solution were further established given the influence of excavation and unloading.According to the change of stress state in the excavation process of foundation pit,the planar mechanical analysis model of the foundation excavation problem was established.By combining this model with the physical equations and geometric equations of plane strain problem with consideration of the loading and unloading modulus of soil,constitutive equation of the plane strain problem was also established.The loading and unloading modulus formula was obtained by using the parameter calculation method in Duncan-Chang curve model.The constitutive equation obtained from the model was used to calculate the soil stress state of each point to determine its loading and unloading modulus.Finally,the foundation pit displacement change after excavation was calculated,and thus the soil pressure distribution after retaining structure deformation.The theoretical results calculated by making corresponding programs were applied to engineering practice.By comparing the conventional calculation results with monitoring results,the practicability and feasibility of the calculation model were verified,which should provide a theoretical basis for similar projects.展开更多
Adjacent high-rise building with CFG pile composite foundation was studied using model test method to investigate stress and displacement of the foundation pile retaining structure, the subsidence and transmogrificati...Adjacent high-rise building with CFG pile composite foundation was studied using model test method to investigate stress and displacement of the foundation pile retaining structure, the subsidence and transmogrification law of the composite foundation. Two different project cases with and without high-rise building adjacent to pile foundation were compared. The relationships of slope pile bending moment, earth pressure, pile top displacement and complex settlement with respect to time were obtained. 1) When there is no adjacent building, the displacement of supporting system caused by excavation is mainly in the horizontal direction; while when the adjacent building exists, the displacement of supporting system will be vertical. 2) When the excavation depth is less than or equal to the adjacent building's composite foundation depth, the force of supporting structure is uniform and has small value, at the same time, the pile strength is in fully use and the foundation is stable; while when the excavation depth is greater than the depth of adjacent building's composite foundation, the results will be opposite. 3) During the excavation process, the adjustment of the composite ground loads on the supporting structure is carried out downward and the force of the supporting structure is reduced through the deformation of the bearing layer.展开更多
A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-indu...A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-induced volume loss effects.The numerical model was verified based on the results of a centrifuge test and a set of parametric studies was implemented based on this model.There is good agreement between the trend of the results of the centrifuge test and the present model.The results of parametric studies show that the tunnelling-induced pile internal force and deformation depend mainly on the pile?tunnel distance,the pile length to tunnel depth ratio and the volume loss.Two different zones are separated by a 45° line projected from the tunnel springline.Within the zone of influence,the pile is subjected to tensile force and large settlement;whereas outside the zone of influence,dragload and small settlement are induced.It is also established that the impact of tunnelling on a pile group is substantially smaller as compared with a single pile in the same location with the rear pile in a group,demonstrating a positive pile group effect.展开更多
The mechanism of long-short composite piled raft foundation was discussed. Assuming the relationship between shear stress and shear strain of the surrounding soil was elasto-plastic, shear displacement method was empl...The mechanism of long-short composite piled raft foundation was discussed. Assuming the relationship between shear stress and shear strain of the surrounding soil was elasto-plastic, shear displacement method was employed to establish the different explicit relational equations between the load and the displacement at the top of pile in either elastic or elasto-plastic period. Then Mylonakis ＆ Gazetas model was introduced to simulate the interaction between two piles or between piles and soil. Considering the effect of cushion, the flexible coefficients of interaction were provided, With the addition of a relevant program, the settlement calculation for long-short composite piled raft foundation was developed which could be used to account for the interaction of piles, soil and cushion. Finally, the calculation method was used to analyze an engineering example. The calculated value of settlement is 10.2 ram, which is close to the observed value 8.8 mm.展开更多
基金Projects(52008403,52378421)supported by the National Natural Science Foundation of ChinaProject(2022-Key-10)supported by the Science and Technology Research and Development Program Project of China Railway Group LimitedProject(202207)supported by the Hunan Provincial Transportation Science and Technology,China。
文摘The existing analytical models for umbrella arch method(UAM)based on elastic foundation beams often overlook the influence of the surrounding soil beyond the beam edges on the shear stresses acting on the beam.Consequently,such models fail to adequately reflect the continuity characteristics of soil deformation.Leveraging the Pasternak foundation-Euler beam model,this study considers the generalized shear force on the beam to account for the influence of soil outside the beam ends on the shear stress.An analytical model for the deformation and internal forces of finite-length beams subjected to arbitrary loads is derived based on the initial parameter method under various conditions.The mechanical model of the elastic foundation beam for advanced umbrella arch under typical tunnel excavation cycles is established,yielding analytical solutions for the longitudinal response of the umbrella arch.The reliability of the analytical model is verified with the existing test data.The improved model addresses anomalies in existing models,such as abnormal upward deformation in the loosened segment and maximum deflection occurring within the soil mass.Additionally,dimensionless characteristic parameters reflecting the relative stiffness between the umbrella arch structure and the foundation soil are proposed.Results indicate that the magnitude of soil characteristic parameters significantly influences the deformation and internal forces of the umbrella arch.Within common ranges of soil values,the maximum deformation and internal forces of the umbrella arch under semi-logarithmic coordinates exhibit nearly linear decay with decreasing soil characteristic parameters.The impact of tunnel excavation height on the stress of unsupported sections of the umbrella arch is minor,but it is more significant for umbrella arch buried within the soil mass.Conversely,the influence of tunnel excavation advance on the umbrella arch is opposite.
文摘The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.
基金Project(2012AA112504) supported by the National High Technology Research and Development Program of ChinaProjects(51108048,51478054) supported by the National Natural Science Foundation of China
文摘To obtain the vertical earth pressure on a soft foundation box culvert and investigate the interaction of the soil-culvert-foundation system, both a centrifugal model test and a numerical simulation were conducted and the comparisons with the current methods to determine the load on a culvert were completed. The results of the model test and numerical analysis are in satisfactory agreement, which shows that the direction of the shear stress between the culvert and the adjacent embankment depends on the differential settlement between them. A vertical earth pressure concentration appears on the culvert with a rigid piles foundation because of a downward shear stress. The ratio of the load on a soft foundation culvert and the overburden pressure above the culvert raises first and then decreases as the backfill height increases. In order to reduce the load on a culvert, it is suggested to limit the stiffness difference of the foundations under the culvert and embankment and to use a light backfill over the culvert.
基金Project(51878103)supported by the National Natural Science Foundation of ChinaProject(2016YFE0200100)supported by the National Key Research and Development Program of China。
文摘To reveal the bearing capacity of the X-section concrete piles pile raft foundation in silica sand,a series of vertical load tests are carried out.The X-section concrete piles are compared with circular section pile with the same section area.The load−settlement curves,axial force and skin friction,strain on concave and convex edge of the pile,pile-sand stress ratio,distributions of side and tip resistance are presented.The results show that bearing capacity of the X section concrete pile raft foundation is much larger than that of the circular pile raft foundation.Besides,compared with the circular pile,the peak axial force of X-section piles under raft is deeper and smaller while the neutral point of X-section concrete pile is deeper.Moreover,the strain on the concave edge is much larger than that on the convex edge of the pile,and the convex edge has more potential in bearing capacity as the vertical load increases.The X-section pile has higher pile-sand stress ratios and load-sharing between side resistance and tip resistance.Above all,the X-section concrete pile can significantly increase the bearing capacity of pile-raft foundations in silica sand.
基金Project(50139030) supported by the National Natural Science Foundation of ChinaProject(501072) supported by the Scientific Research Foundation for the Returned Overseas Scholars of the Ministry of Education of China
文摘The seepage under a dam foundation is mainly controlled by the performance of the curtain.Its anti-seepage behavior may be weakened by the long term physic-chemical actions from groundwater.According to seepage hydraulics and geochemistry theory,a coupling model for assessing the behavior of the curtain under a dam foundation is set up,which consists of seepage module,solute transport module,geochemistry module and curtain erosion module,solved by FEM.A case study was carried out.The result shows that the curtain efficiency is weakened all the time.Aqueous calcium from the curtain is always in dissolution during the stress period for simulation,which leads to the increasing amount in groundwater reaching 846.35-865.312 g/m3.Within the domain,reaction extent differs in different parts of the curtain.The dissolution of Ca(OH)2 accounts to 877.884 g/m3 near the bottom and is much higher than that of the other parts.The erosion is much more serious near the bottom of the curtain than the other parts,which is the same to the upstream and downstream.Calcium dissolution is mainly controlled by hydraulic condition and dispersion,and it varies in a non-linear way within the domain.
基金Projects(2009G008-B,2010G018-E-3) supported by Key Projects of China Railway Ministry Science and Technology Research and Development ProgramProject(CX2013B076) supported by Hunan Provincial Innovation Foundation For Postgraduate,China
文摘Based on reasonable assumptions that simplified the calculational model,a simple and practical method was proposed to calculate the post-construction settlement of high-speed railway bridge pile foundation by using the Mesri creep model to describe the soil characteristics and the Mindlin-Geddes method considering pile diameter to calculate the vertical additional stress of pile bottom.A program named CPPS was designed for this method to calculate the post-construction settlement of a high-speed railway bridge pile foundation.The result indicates that the post-construction settlement in 100 years meets the requirements of the engineering specifications,and in the first two decades,the post-construction settlement is about 80% of its total settlement,while the settlement in the rest eighty years tends to be stable.Compared with the measured settlement after laying railway tracks,the calculational result is closed to that of the measured,and the results are conservative with a high computational accuracy.It is noted that the method can be used to calculate the post-construction settlement for the preliminary design of high-speed railway bridge pile foundation.
基金Project(52078060)supported by the National Natural Science Foundation of ChinaProject(2020JJ4606)supported by the National Science Foundation of Hunan Province,China+1 种基金Project(18A127)supported by the Key Foundation of Education Department of Hunan Province,ChinaProject(2018IC19)supported by the International Cooperation and Development Project of Double-First-Class Scientific Research in Changsha University of Science&Technology,China。
文摘At present,shield tunneling often needs to pass through a large number of bridge pile foundations.However,there are few studies on the influence of shield tunneling on adjacent pile foundations by combining with groundwater seepage.Based on Winkler model,the calculation equations of shield tunneling on vertical and horizontal displacement of adjacent bridge pile are derived.Meanwhile,full and part three-dimensional finite element models are established to analyze the trend of bridge pier settlement,ground surface settlement trough,vertical and horizontal displacement of the pile and pile stress under three calculation conditions,i.e.,not considering groundwater effect,considering stable groundwater effect and fluid-soil interaction.The results show that the calculated value is small when the effect of groundwater is not considered;the seepage velocity of the soil above the excavation face is faster than that of the surrounding soil under fluid-soil interaction,and after the shield passing,the groundwater on both sides shows a flow trend of“U”shape on the ground surface supplying to the upper part of the tunnel;the vertical displacement of the pile body is bounded by the horizontal position of the top of the tunnel,the upper pile body settles,and the lower pile body deforms upward.The horizontal displacement of pile body presents a continuous“S”shape distribution,causing stress concentration near the tunnel.The calculated results of fluid-soil interaction are in good agreement with the field measured data and accord with the actual situation.
基金Project(41672290)supported by the National Natural Science Foundation of ChinaProject(2016J01189)supported by the Natural Science foundation of Fujian Province,China
文摘A new analytical solution for ground surface settlement induced by deep excavation is proposed based on the elastic half space Melan’s solution,and the analytical model is related to the physical and mechanical properties of soil with the loading and unloading action during excavation process.The change law of earth pressure of the normal consolidation soil after the foundation pit excavation was analyzed,and elastic displacement calculation methods of analytic solution were further established given the influence of excavation and unloading.According to the change of stress state in the excavation process of foundation pit,the planar mechanical analysis model of the foundation excavation problem was established.By combining this model with the physical equations and geometric equations of plane strain problem with consideration of the loading and unloading modulus of soil,constitutive equation of the plane strain problem was also established.The loading and unloading modulus formula was obtained by using the parameter calculation method in Duncan-Chang curve model.The constitutive equation obtained from the model was used to calculate the soil stress state of each point to determine its loading and unloading modulus.Finally,the foundation pit displacement change after excavation was calculated,and thus the soil pressure distribution after retaining structure deformation.The theoretical results calculated by making corresponding programs were applied to engineering practice.By comparing the conventional calculation results with monitoring results,the practicability and feasibility of the calculation model were verified,which should provide a theoretical basis for similar projects.
基金Project(41202220) supported by the National Natural Science Foundation of ChinaProject(20120022120003) supported by the Research Fund for the Doctoral Program of Higher Education,ChinaProject(2-9-2012-65) supported by the Fundamental Research Funds for the Central Universities,China
文摘Adjacent high-rise building with CFG pile composite foundation was studied using model test method to investigate stress and displacement of the foundation pile retaining structure, the subsidence and transmogrification law of the composite foundation. Two different project cases with and without high-rise building adjacent to pile foundation were compared. The relationships of slope pile bending moment, earth pressure, pile top displacement and complex settlement with respect to time were obtained. 1) When there is no adjacent building, the displacement of supporting system caused by excavation is mainly in the horizontal direction; while when the adjacent building exists, the displacement of supporting system will be vertical. 2) When the excavation depth is less than or equal to the adjacent building's composite foundation depth, the force of supporting structure is uniform and has small value, at the same time, the pile strength is in fully use and the foundation is stable; while when the excavation depth is greater than the depth of adjacent building's composite foundation, the results will be opposite. 3) During the excavation process, the adjustment of the composite ground loads on the supporting structure is carried out downward and the force of the supporting structure is reduced through the deformation of the bearing layer.
文摘A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-induced volume loss effects.The numerical model was verified based on the results of a centrifuge test and a set of parametric studies was implemented based on this model.There is good agreement between the trend of the results of the centrifuge test and the present model.The results of parametric studies show that the tunnelling-induced pile internal force and deformation depend mainly on the pile?tunnel distance,the pile length to tunnel depth ratio and the volume loss.Two different zones are separated by a 45° line projected from the tunnel springline.Within the zone of influence,the pile is subjected to tensile force and large settlement;whereas outside the zone of influence,dragload and small settlement are induced.It is also established that the impact of tunnelling on a pile group is substantially smaller as compared with a single pile in the same location with the rear pile in a group,demonstrating a positive pile group effect.
基金Project (50378036) supported by the National Natural Science Foundation of China
文摘The mechanism of long-short composite piled raft foundation was discussed. Assuming the relationship between shear stress and shear strain of the surrounding soil was elasto-plastic, shear displacement method was employed to establish the different explicit relational equations between the load and the displacement at the top of pile in either elastic or elasto-plastic period. Then Mylonakis ＆ Gazetas model was introduced to simulate the interaction between two piles or between piles and soil. Considering the effect of cushion, the flexible coefficients of interaction were provided, With the addition of a relevant program, the settlement calculation for long-short composite piled raft foundation was developed which could be used to account for the interaction of piles, soil and cushion. Finally, the calculation method was used to analyze an engineering example. The calculated value of settlement is 10.2 ram, which is close to the observed value 8.8 mm.
