By the constant stress tensile creep test method, creep tests were performed on aluminum silicate short fiber-reinforced AZ91D magnesium matrix composite with volume fraction of 30% and its matrix alloy AZ91D under di...By the constant stress tensile creep test method, creep tests were performed on aluminum silicate short fiber-reinforced AZ91D magnesium matrix composite with volume fraction of 30% and its matrix alloy AZ91D under different temperatures and stresses. The results indicate that the composite and the matrix have the same true stress exponent and true activation energy for creep, which are 3 and 144.63 kJ/mol, respectively. The creep of the composite is controlled by the creep of its matrix, which is mainly the controlling of viscous slip of dislocation, and the controlling of grain boundary slippage as a supplement. The creep constitutive model obtained from the experiment data can well describe the creep deformation pattern of the composite.展开更多
The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensi...The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensity, we set the control parameter to be near the critical value, and the external stimulus is introduced to the first cell in coupled system. It is found that, on one hand, when the cells are coupled with some proper topological structures, the external stimulus could transmit through the system, and shows better response ability and higher sensitivity. On the other hand, the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed. Our results display that the topology of coupled system may play an important role in the process of signal propagation, which could help us to understand the coordinated performance of cells in tissue.展开更多
An approach based on equivalent mechanics theory and computational fluid dynamics (CFD) technology is proposed to estimate dynamical influence of propellant sloshing on the spacecraft. A mechanical model is estab- l...An approach based on equivalent mechanics theory and computational fluid dynamics (CFD) technology is proposed to estimate dynamical influence of propellant sloshing on the spacecraft. A mechanical model is estab- lished by using CFD technique and packed as a "sloshing" block used in spacecraft guidance navigation and control (GNC) simulation loop. The block takes motion characteristics of the spacecraft as inputs and outputs of pertur- bative force and torques induced by propellant sloshing, thus it is more convenient for analyzing coupling effect between propellant sloshing dynamic and spacecraft GNC than using CFD packages. An example demonstrates the accuracy and the superiority of the approach. Then, the deducing process is applied to practical cases, and simulation results validate that the proposed approach is efficient for identifying the problems induced by sloshing and evaluating effectiveness of several typical designs of sloshing suppression.展开更多
Effects of four factors on thin sheet metal flow stress were considered, including grain size d, thickness t, grain number across thickness (t/d ratio) and surface property. Surface model was adopted to quantitative...Effects of four factors on thin sheet metal flow stress were considered, including grain size d, thickness t, grain number across thickness (t/d ratio) and surface property. Surface model was adopted to quantitatively describe the effect of t/d ratio on flow stress for pure copper. It is predicted that when t/d ratio is larger than a critical value, effect of t/d ratio on flow stress can be neglected. Existence of critical t/d ratio changes the Hall-Petch relationship and evolution of flow stress with thickness. A criterion was proposed to determine critical t/d ratio. Then a comprehensive constitutive model was developed to consider all the four factors, with parameters determined by fitting experimental data of high purity Ni. The predicted results show the same tendencies with experiment results. Particularly when t/d ratio decreases, Hall-Petch relationship and evolution of true stress show varied slopes with two transition points.展开更多
The nonlinear mixed-effects model with stochastic differential equations (SDEs) is used to model the population pharmacokinetic (PPK) data that are extended from ordinary differential equations (ODEs) by adding ...The nonlinear mixed-effects model with stochastic differential equations (SDEs) is used to model the population pharmacokinetic (PPK) data that are extended from ordinary differential equations (ODEs) by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.展开更多
An analytical model of electron mobility for strained-silicon channel nMOSFETs is proposed in this paper. The model deals directly with the strain tensor,and thus is independent of the manufacturing process. It is sui...An analytical model of electron mobility for strained-silicon channel nMOSFETs is proposed in this paper. The model deals directly with the strain tensor,and thus is independent of the manufacturing process. It is suitable for (100〉/ 〈110) channel nMOSFETs under biaxial or (100〉/〈 110 ) uniaxial stress and can be implemented in conventional device simulation tools .展开更多
In order to eliminate the settlement underestimation in surcharge preload engineering, a study based on Bjerrum's creep diagram and the tangent slope definition of secondary consolidation coefficient was carried o...In order to eliminate the settlement underestimation in surcharge preload engineering, a study based on Bjerrum's creep diagram and the tangent slope definition of secondary consolidation coefficient was carried out to analyze the time effect of secondary consolidation coefficient of over consolidated soil, and a time–growth model for it was formulated. As Bjerrum's creep diagram is an idealized model, oedometer tests were performed to improve the above time–growth model of secondary consolidation coefficient for the purpose of achieving a better agreement with the actual ground situations. It is found that secondary consolidation coefficient of over consolidated soil not only decreases with the ratio of historical maximum to current effective stress of soil(OCR), but also increases with the development time of secondary consolidation. No matter how large OCR is, the long-term time effect of secondary consolidation coefficient of over consolidated soil is all significant. Based on the above results, a model for settlement estimation was formulated and a case study to estimate it indicates that the settlement estimated by our method is 2–5 times larger than that estimated by the previous method. Moreover, the larger the OCR is as well as the longer the service life is, the larger the difference between our method and the previous method is. Thus, the post-construction secondary settlement in surcharge preload engineering will be underestimated when neglecting the time effect of secondary consolidation coefficient in over consolidated state.展开更多
Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced acc...Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.展开更多
A numerical investigation on the co-pyrolysis of 1,3-butadiene and propyne is performed to explore the synergistic effect between fuel components on aromatic hydrocarbon formation. A detailed kinetic model of 1,3-buta...A numerical investigation on the co-pyrolysis of 1,3-butadiene and propyne is performed to explore the synergistic effect between fuel components on aromatic hydrocarbon formation. A detailed kinetic model of 1,3-butadiene/propyne co-pyrolysis with the sub-mechanism of aromatic hydrocarbon formation is developed and validated on previous 1,3-butadiene and propyne pyrolysis experiments. The model is able to reproduce both the single component pyrolysis and the co-pyrolysis experiments, as well as the synergistic effect between 1,3- butadiene and propyne on the formation of a series of aromatic hydrocarbons. Based on the rate of production and sensitivity analyses, key reaction pathways in the fuel decomposition and aromatic hydrocarbon formation processes are revealed and insight into the synergistic effect on aromatic hydrocarbon formation is also achieved. The synergistic effect results from the interaction between 1,3-butadiene and propyne. The easily happened chain initiation in the 1,3-butadiene decomposition provides an abundant radical pool for propyne to undergo the H-atom abstraction and produce propargyl radical which plays key roles in the formation of aromatic hydrocarbons. Besides, the 1,3-butadiene/propyne co-pyrolysis includes high concentration levels of C3 and C4 precursors simultaneously, which stimulates the formation of key aromatic hydrocarbons such as toluene and naphthalene.展开更多
Based on the developed distributed model for calculating astronomical solar radiation (ASR), monthly ASR with a resolution of 1 km×1 km for the rugged terrains of Yellow River Basin was calculated, with DEM data ...Based on the developed distributed model for calculating astronomical solar radiation (ASR), monthly ASR with a resolution of 1 km×1 km for the rugged terrains of Yellow River Basin was calculated, with DEM data as the general characterization of terrain. This model gives an all-sided consideration on factors that influence the ASR. Results suggest that (1) Annual ASR has a progressive decrease trend from south to north; (2) the magnitude order of seasonal ASR is: summer>spring>autumn>winter; (3) topographical factors have robust effect on the spatial distribution of ASR, particularly in winter when a lower sun elevation angle exists; (4) the ASR of slopes with a sunny exposure is generally 2 or 3 times that of slopes with a shading exposure and the extreme difference of ASR for different terrains is over 10 times in January; (5) the spatial differences of ASR are relatively small in summer when a higher sun elevation angle exists and the extreme difference of ASR for different terrains is only 16% in July; and (6) the sequence of topographical influence strength is: winter>autumn>spring>summer.展开更多
Surrounding rocks of weakly consolidated soft rock roadway show obvious strain softening and dilatancy effects after excavation. A damage coefficient concerning modulus attenuation was defined. Response models of stre...Surrounding rocks of weakly consolidated soft rock roadway show obvious strain softening and dilatancy effects after excavation. A damage coefficient concerning modulus attenuation was defined. Response models of stress and displacement of surrounding rock of soft rock roadway and analytical expressions to calculate plastic zones under different interior pressures and non-uniform original rock stresses were derived based on damage theories and a triple linear elastic-plastic strain softening model. Influence laws of dilatancy gradient on damage development, distributions of stresses and displacement in plastic region were analyzed. Interior pressure conditions to develop plastic region under different origin rock stresses were established and their influences on plastic region distribution were also discussed. The results show that the order of maximum principle stress is exchanged between ~0 and trr with the increase of interior pressure P0, which causes distributions of plastic zone and stress shift. Dilatancy effect which has great influences on the damage propagation and displacements in plastic region has little effect on the size of plastic region and stress responses. The conclusions provide a theoretical basis for a reasonable evaluation of stability and effective supporting of weakly consolidated soft rock roadway.展开更多
To predict the failure loads of adhesive joints under different stress states over the service temperature range of automobiles,adhesively bonded carbon fiber reinforced plastic( CFRP)/aluminum alloy joints under shea...To predict the failure loads of adhesive joints under different stress states over the service temperature range of automobiles,adhesively bonded carbon fiber reinforced plastic( CFRP)/aluminum alloy joints under shear stress state( thickadherend shear joints,TSJ),normal stress state( butt joints,BJ) and combined shear and normal stress states( scarf joints with scarf angle 45°,SJ45°) were manufactured and tested at-40,-20,0,20,40,60 and 80 ℃,respectively. The glass transition temperature Tgof the adhesive and CFRP,failure loads and fracture surfaces were used to analyze the failure mechanism of CFRP/aluminum alloy joints at different temperatures. A response surface,describing the variations of quadratic stress criteria with temperature,was established and introduced into the cohesive zone model( CZM) to carry out a simulation analysis. Results show that the failure of CFRP/aluminum alloy joints was determined collectively by the mechanical performances of adhesive and CFRP. Besides,reducing temperature or increasing the proportion of normal stress of adhesive layer was more likely to cause fibre tear or delamination of CFRP,resulting in a more obvious effect of CFRP. The validity of the prediction method was verified by the test of scarf joints with the scarf angle of 30°( SJ30°) and 60°( SJ60°) at-10 and 50 ℃.展开更多
A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil laye...A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil layers under the pile end are assumed to be virtual soil-pile whose cross-section area is the same as that of the pile shaft. Then, by means of Laplace transform and impedance function transfer method to solve the static equilibrium equation of pile, the analytical solution of the displacement impedance fimction at the pile head is derived. Furthermore, the analytical solution of the settlement at the head of single pile is theoretically derived by virtue of convolution theorem. Based on these solutions, the influences of parameters of soil-pile system on the settlement behavior for single pile are analyzed. Also, comparison of the load-settlement response for two well-instrumented field tests in multilayered soils is given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to calculate the settlement of single pile for the preliminary design of pile foundation.展开更多
基金Project(10151170003000002)supported by the National Science Foundation of Guangdong Province,China
文摘By the constant stress tensile creep test method, creep tests were performed on aluminum silicate short fiber-reinforced AZ91D magnesium matrix composite with volume fraction of 30% and its matrix alloy AZ91D under different temperatures and stresses. The results indicate that the composite and the matrix have the same true stress exponent and true activation energy for creep, which are 3 and 144.63 kJ/mol, respectively. The creep of the composite is controlled by the creep of its matrix, which is mainly the controlling of viscous slip of dislocation, and the controlling of grain boundary slippage as a supplement. The creep constitutive model obtained from the experiment data can well describe the creep deformation pattern of the composite.
文摘The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensity, we set the control parameter to be near the critical value, and the external stimulus is introduced to the first cell in coupled system. It is found that, on one hand, when the cells are coupled with some proper topological structures, the external stimulus could transmit through the system, and shows better response ability and higher sensitivity. On the other hand, the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed. Our results display that the topology of coupled system may play an important role in the process of signal propagation, which could help us to understand the coordinated performance of cells in tissue.
基金Innovation Foundation of Aerospace Science and Technology(CASC200902)~~
文摘An approach based on equivalent mechanics theory and computational fluid dynamics (CFD) technology is proposed to estimate dynamical influence of propellant sloshing on the spacecraft. A mechanical model is estab- lished by using CFD technique and packed as a "sloshing" block used in spacecraft guidance navigation and control (GNC) simulation loop. The block takes motion characteristics of the spacecraft as inputs and outputs of pertur- bative force and torques induced by propellant sloshing, thus it is more convenient for analyzing coupling effect between propellant sloshing dynamic and spacecraft GNC than using CFD packages. An example demonstrates the accuracy and the superiority of the approach. Then, the deducing process is applied to practical cases, and simulation results validate that the proposed approach is efficient for identifying the problems induced by sloshing and evaluating effectiveness of several typical designs of sloshing suppression.
基金Projects(50835002,50975174,50821003)supported by the National Natural Science Foundation of ChinaProjects(200802480053,20100073110044)supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Effects of four factors on thin sheet metal flow stress were considered, including grain size d, thickness t, grain number across thickness (t/d ratio) and surface property. Surface model was adopted to quantitatively describe the effect of t/d ratio on flow stress for pure copper. It is predicted that when t/d ratio is larger than a critical value, effect of t/d ratio on flow stress can be neglected. Existence of critical t/d ratio changes the Hall-Petch relationship and evolution of flow stress with thickness. A criterion was proposed to determine critical t/d ratio. Then a comprehensive constitutive model was developed to consider all the four factors, with parameters determined by fitting experimental data of high purity Ni. The predicted results show the same tendencies with experiment results. Particularly when t/d ratio decreases, Hall-Petch relationship and evolution of true stress show varied slopes with two transition points.
基金The National Natural Science Foundation of China(No.11171065,81130068)the Natural Science Foundation of Jiangsu Province(No.BK2011058)the Fundamental Research Funds for the Central Universities(No.JKPZ2013015)
文摘The nonlinear mixed-effects model with stochastic differential equations (SDEs) is used to model the population pharmacokinetic (PPK) data that are extended from ordinary differential equations (ODEs) by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.
文摘An analytical model of electron mobility for strained-silicon channel nMOSFETs is proposed in this paper. The model deals directly with the strain tensor,and thus is independent of the manufacturing process. It is suitable for (100〉/ 〈110) channel nMOSFETs under biaxial or (100〉/〈 110 ) uniaxial stress and can be implemented in conventional device simulation tools .
基金Project(51178419)supported by the National Natural Science Foundation of China
文摘In order to eliminate the settlement underestimation in surcharge preload engineering, a study based on Bjerrum's creep diagram and the tangent slope definition of secondary consolidation coefficient was carried out to analyze the time effect of secondary consolidation coefficient of over consolidated soil, and a time–growth model for it was formulated. As Bjerrum's creep diagram is an idealized model, oedometer tests were performed to improve the above time–growth model of secondary consolidation coefficient for the purpose of achieving a better agreement with the actual ground situations. It is found that secondary consolidation coefficient of over consolidated soil not only decreases with the ratio of historical maximum to current effective stress of soil(OCR), but also increases with the development time of secondary consolidation. No matter how large OCR is, the long-term time effect of secondary consolidation coefficient of over consolidated soil is all significant. Based on the above results, a model for settlement estimation was formulated and a case study to estimate it indicates that the settlement estimated by our method is 2–5 times larger than that estimated by the previous method. Moreover, the larger the OCR is as well as the longer the service life is, the larger the difference between our method and the previous method is. Thus, the post-construction secondary settlement in surcharge preload engineering will be underestimated when neglecting the time effect of secondary consolidation coefficient in over consolidated state.
基金Project(50378036) supported by the National Natural Science Foundation of ChinaProject(200503) supported by Foundation of Communications Department of Hunan Province, China
文摘Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.
基金This work is supported by the National Natural Science Foundation of China (No.51476155, No.51622605, No.91541201), the National Key Sci- entific Instruments and Equipment Development Program of China (No.2012YQ22011305), the National Postdoctoral Program for Innovative Talents (No.BX201600100), and China Postdoctoral Science Foundation (No.2016M600312).
文摘A numerical investigation on the co-pyrolysis of 1,3-butadiene and propyne is performed to explore the synergistic effect between fuel components on aromatic hydrocarbon formation. A detailed kinetic model of 1,3-butadiene/propyne co-pyrolysis with the sub-mechanism of aromatic hydrocarbon formation is developed and validated on previous 1,3-butadiene and propyne pyrolysis experiments. The model is able to reproduce both the single component pyrolysis and the co-pyrolysis experiments, as well as the synergistic effect between 1,3- butadiene and propyne on the formation of a series of aromatic hydrocarbons. Based on the rate of production and sensitivity analyses, key reaction pathways in the fuel decomposition and aromatic hydrocarbon formation processes are revealed and insight into the synergistic effect on aromatic hydrocarbon formation is also achieved. The synergistic effect results from the interaction between 1,3-butadiene and propyne. The easily happened chain initiation in the 1,3-butadiene decomposition provides an abundant radical pool for propyne to undergo the H-atom abstraction and produce propargyl radical which plays key roles in the formation of aromatic hydrocarbons. Besides, the 1,3-butadiene/propyne co-pyrolysis includes high concentration levels of C3 and C4 precursors simultaneously, which stimulates the formation of key aromatic hydrocarbons such as toluene and naphthalene.
基金Major State Basic Research Development Program of ChinaNo.G19990436-01 No.G20000779
文摘Based on the developed distributed model for calculating astronomical solar radiation (ASR), monthly ASR with a resolution of 1 km×1 km for the rugged terrains of Yellow River Basin was calculated, with DEM data as the general characterization of terrain. This model gives an all-sided consideration on factors that influence the ASR. Results suggest that (1) Annual ASR has a progressive decrease trend from south to north; (2) the magnitude order of seasonal ASR is: summer>spring>autumn>winter; (3) topographical factors have robust effect on the spatial distribution of ASR, particularly in winter when a lower sun elevation angle exists; (4) the ASR of slopes with a sunny exposure is generally 2 or 3 times that of slopes with a shading exposure and the extreme difference of ASR for different terrains is over 10 times in January; (5) the spatial differences of ASR are relatively small in summer when a higher sun elevation angle exists and the extreme difference of ASR for different terrains is only 16% in July; and (6) the sequence of topographical influence strength is: winter>autumn>spring>summer.
基金Project(51174128)supported by the National Natural Science Foundation of ChinaProject(20123718110007)supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Surrounding rocks of weakly consolidated soft rock roadway show obvious strain softening and dilatancy effects after excavation. A damage coefficient concerning modulus attenuation was defined. Response models of stress and displacement of surrounding rock of soft rock roadway and analytical expressions to calculate plastic zones under different interior pressures and non-uniform original rock stresses were derived based on damage theories and a triple linear elastic-plastic strain softening model. Influence laws of dilatancy gradient on damage development, distributions of stresses and displacement in plastic region were analyzed. Interior pressure conditions to develop plastic region under different origin rock stresses were established and their influences on plastic region distribution were also discussed. The results show that the order of maximum principle stress is exchanged between ~0 and trr with the increase of interior pressure P0, which causes distributions of plastic zone and stress shift. Dilatancy effect which has great influences on the damage propagation and displacements in plastic region has little effect on the size of plastic region and stress responses. The conclusions provide a theoretical basis for a reasonable evaluation of stability and effective supporting of weakly consolidated soft rock roadway.
基金The National Natural Science Foundation of China(No.51775230)
文摘To predict the failure loads of adhesive joints under different stress states over the service temperature range of automobiles,adhesively bonded carbon fiber reinforced plastic( CFRP)/aluminum alloy joints under shear stress state( thickadherend shear joints,TSJ),normal stress state( butt joints,BJ) and combined shear and normal stress states( scarf joints with scarf angle 45°,SJ45°) were manufactured and tested at-40,-20,0,20,40,60 and 80 ℃,respectively. The glass transition temperature Tgof the adhesive and CFRP,failure loads and fracture surfaces were used to analyze the failure mechanism of CFRP/aluminum alloy joints at different temperatures. A response surface,describing the variations of quadratic stress criteria with temperature,was established and introduced into the cohesive zone model( CZM) to carry out a simulation analysis. Results show that the failure of CFRP/aluminum alloy joints was determined collectively by the mechanical performances of adhesive and CFRP. Besides,reducing temperature or increasing the proportion of normal stress of adhesive layer was more likely to cause fibre tear or delamination of CFRP,resulting in a more obvious effect of CFRP. The validity of the prediction method was verified by the test of scarf joints with the scarf angle of 30°( SJ30°) and 60°( SJ60°) at-10 and 50 ℃.
基金Project(50879077) supported by the National Natural Science Foundation of China
文摘A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil layers under the pile end are assumed to be virtual soil-pile whose cross-section area is the same as that of the pile shaft. Then, by means of Laplace transform and impedance function transfer method to solve the static equilibrium equation of pile, the analytical solution of the displacement impedance fimction at the pile head is derived. Furthermore, the analytical solution of the settlement at the head of single pile is theoretically derived by virtue of convolution theorem. Based on these solutions, the influences of parameters of soil-pile system on the settlement behavior for single pile are analyzed. Also, comparison of the load-settlement response for two well-instrumented field tests in multilayered soils is given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to calculate the settlement of single pile for the preliminary design of pile foundation.