The statistical characteristics and parameters of loads and resistances are systematically studied for the development of probabilistic limit state design method for steel jacket offshore platforms in the China offsho...The statistical characteristics and parameters of loads and resistances are systematically studied for the development of probabilistic limit state design method for steel jacket offshore platforms in the China offshore area. The mean value, standard variance and distribution pattern of resistances and loads in different base perieds are presented. The statistical parameters of structural member resistance, self-weight, deck live load, and environmental loads such as wind, wave, current and ice, which are drawn on a large amount of observatian data of offshore environmental factors, and the design data of platforms in China Bohai Sea form the data set, providing a necessary basis for the calibration of load and resistance factors to realize the reliability-based design of jacket platform structures.展开更多
Adopting the load and resistance factor design format, the design method for steel jaeket platform structures is developed. Firstly, the limit state equations and design format for steel jacket platform structures are...Adopting the load and resistance factor design format, the design method for steel jaeket platform structures is developed. Firstly, the limit state equations and design format for steel jacket platform structures are introduced. Then, the ratio of live load effect to dead load effect is estimated. The target reliabilities for design of offshore structures in China offshore area are calibrated by past practice in API RP2A-WSD code. The load and resistance factors are optimized by minimizing the difference within the target reliability and the resulting reliability over the range of load effect ratios. Considering the concurrence of different loads, load combination factors are obtained through an optimization process, and the relation between the load combination factor and load correlation coefficient is established. Finally, the design formulae for steel jacket structures in China offshore area are recommended.展开更多
In this paper, reliability analysis for the offshore jacket platform with the interaction of structure- pile- soil under extreme environmental loads is carried out. The inherent uncertainties of the environmental load...In this paper, reliability analysis for the offshore jacket platform with the interaction of structure- pile- soil under extreme environmental loads is carried out. The inherent uncertainties of the environmental load, foundation soil, platform itself, and calculating models are evaluated. The action of extreme loads on the offshore platform is modeled as a function of extreme wave height. The system capacity of the whole platform is determined by nonlinear pushover analysis, and the relevant probability property is obtained by the simulation method. The reliability model for the whole jacket platform is described as the relationship between the load and resistance based on the offshore design codes. The reliability of whole platform is calculated by the analytical method and the importance sampling method on the basis of a case study for a tripod jacket platform.展开更多
For the fulfillment of the probability-based structural design for the offshore jacket platforms in the Bohai Bay, the design factors of loads, resistance and load combinations are much necessary to be calibrated acco...For the fulfillment of the probability-based structural design for the offshore jacket platforms in the Bohai Bay, the design factors of loads, resistance and load combinations are much necessary to be calibrated according to the proposed target reliability index. Firstly, the limit states function for the offshore jacket platforms is introduced. Then, four approaches to calibrate the factors of load and resistance are presented and compared. Afterwards, the methods to calibrate the load combination factors are developed. Finally, the factors of load, resistance and load combination for the offshore jacket platforms in the Bohai Bay are calibrated and the corresponding design formulae are recommended. The results are proved to be rational in practice, and also illustrate that the proposed target reliability index for offshore jacket platforms in the Bohai Bay is also appropriate.展开更多
The semi-rigid pile-supported composite foundation is widely used in highway projects due to its effectiveness in increasing the bearing capacity and stability of foundations.It is crucial to understand the stress dis...The semi-rigid pile-supported composite foundation is widely used in highway projects due to its effectiveness in increasing the bearing capacity and stability of foundations.It is crucial to understand the stress distribution across the embankment width and the behaviour of unreinforced foundations.Thus,five centrifuge tests were conducted to examine the bearing and deformation behaviours of NPRS(Non-Connected Piled Raft Systems)and GRPS(GeosyntheticReinforced Pile-Supported systems)with varying substratum stiffness,then a comparative analysis was conducted on embankment settlement,pressures underneath the embankments,and axial forces along the piles.The results indicated that greater substratum stiffness correlates with reduced settlement and deformation at various depths.Deformation occurring 5 meters from the embankment toe includes settlement in NPRS and upward movement in GRPS.The potential sliding surface is primarily located within the embankment in NPRS,whereas it may extend through both the embankment and foundation in GRPS.The pile-soil stress ratio and efficiency in NPRS are higher than in GRPS across the embankment.The axial force borne by end-bearing piles is significantly greater than that by floating piles.As the buried depth increases,the axial force in GRPS initially rises then declines,whereas in NPRS,it remains relatively constant within a certain range before decreasing.This study aids in assessing the applicability of composite foundations in complex railway environments and provides a reference for procedural measures under similar conditions.展开更多
Overall wave loading and local hydrodynamic pressure distributions on a platform mat in regular waves for shallow waters are experimentally investigated in order to examine the severity of the nonlinear effects and sh...Overall wave loading and local hydrodynamic pressure distributions on a platform mat in regular waves for shallow waters are experimentally investigated in order to examine the severity of the nonlinear effects and shallow water effects. Wave focusing phenomenon is observed in the tests. The measured results may also provide a comparison basis for the theoretical development to consider the nonlinear interaction between waves and viscous flow by introducing viscosity into wave theories.展开更多
The working platforms supported with multiple extensible legs must be leveled before they come into operation.Although the supporting stiffness and reliability of the platform are improved with the increasing number o...The working platforms supported with multiple extensible legs must be leveled before they come into operation.Although the supporting stiffness and reliability of the platform are improved with the increasing number of the supporting legs,the increased overdetermination of the multi-leg platform systems leads to leveling coupling problem among legs and virtual leg problem in which some of the supporting legs bear zero or quasi zero loads.These problems make it quite complex and time consuming to level such a multi-leg platform.Based on rigid body kinematics,an approximate equation is formulated to rapidly calculate the leg extension for leveling a rigid platform,then a proportional speed control strategy is proposed to reduce the unexpected platform distortion and leveling coupling between supporting legs.Taking both the load coupling between supporting legs and the elastic flexibility of the working platform into consideration,an optimal balancing legs’ loads(OBLL) model is firstly put forward to deal with the traditional virtual leg problem.By taking advantage of the concept of supporting stiffness matrix,a coupling extension method(CEM) is developed to solve this OBLL problem for multi-leg flexible platform.At the end,with the concept of supporting stiffness matrix and static transmissibility matrix,an optimal load balancing leveling method is proposed to achieve geometric leveling and legs’ loads balancing simultaneously.Three numerical examples are given out to illustrate the performance of proposed methods.This paper proposes a method which can effectively quantify all of the legs’ extension at the same time,achieve geometric leveling and legs’ loads balancing simultaneously.By using the proposed methods,the stability,precision and efficiency of auto-leveling control process can be improved.展开更多
The optimal control is investigated for linear systems affected by external harmonic disturbance and applied to vibration control systems of offshore steel jacket platforms. The wave-induced force is the dominant load...The optimal control is investigated for linear systems affected by external harmonic disturbance and applied to vibration control systems of offshore steel jacket platforms. The wave-induced force is the dominant load that offshore structures are subjected to, and it can be taken as harmonic excitation for the system. The linearized Morison equation is employed to estimate the wave loading. The main result concerns the existence and design of a realizable optimal regulator, which is proposed to damp the forced oscillation in an optimal fashion. For demonstration of the effectiveness of the control scheme, the platform performance is investigated for different wave states. The simulations are based on the tuned mass damper and the active mass damper control devices. It is demonstrated that the control scheme is useful in reducing the displacement response of jacket-type offshore platforms.展开更多
An obvious motivation of this paper is to examine the effectiveness of the lateral vibration control of a jacket type offshore platform with an AMD control device, in conjunction with H-2 control algorithm, which is a...An obvious motivation of this paper is to examine the effectiveness of the lateral vibration control of a jacket type offshore platform with an AMD control device, in conjunction with H-2 control algorithm, which is an optimal frequency domain control method based on minimization of H-2 norm of the system transfer function In this study, the offshore platform is modeled numerically by use of the finite element method, instead of a lumped mass model This structural model is later simplified to be single-degree-of-freedom (SDOF) system by extracting the first vibration mode of the structure. The corresponding 'generalized' wave force is determined based on an analytical approximation of the first mode shape function, the physical wave loading being calculated from the linearized Morison equation. This approach facilitates the filter design for the generalized force. Furthermore, the present paper also intends to make numerical comparison between H-2 active control and the corresponding passive control using a TMD with the same device parameters.展开更多
The failure of one or even more components usually does riot lead to the collapse of the whole structure. Most of the analysis of fatigue is centered on only a single component which the researchers are interested in ...The failure of one or even more components usually does riot lead to the collapse of the whole structure. Most of the analysis of fatigue is centered on only a single component which the researchers are interested in or Much attention should be paid to. However, the collapse of a structure is the result of failure of a series of components in a specific order or path. This paper proposes an integrated approach to fatigue life prediction of whole structural system for offshore platforms, mainly describing the basic principles and prediction method. A method is presented for determining the failure path of the whole structure system and calculating the fatigue life in the determined failure path, The corresponding final collapse criteria for the whole structure system are discussed, A simple method of equivalent fatigue stress range calculation and a mathematical model of structural component fatigue life estimation in consideration of sea wave and sea ice loads are provided. As an application of the proposed approach, a fixed production platform Bohai No. 8 is chosen for the predication of fatigue life of the whole structure system by means of the software OSFAC developed based on the present methods.展开更多
Ice load is the dominative load in the design of offshore platforms in the ice zone, and the extreme ice load is the key factor that affects the safety of platforms. The present paper studies the statistical propertie...Ice load is the dominative load in the design of offshore platforms in the ice zone, and the extreme ice load is the key factor that affects the safety of platforms. The present paper studies the statistical properties of the global resistance and the extreme responses of the jacket platforms in Bahai Bay, considering the randomness of ice load, dead load, steel elastic modulus, yield strength and structural member dimensions. Then, based on the above results, an efficient approximate method of the global reliability analysis for the offshore platforms is proposed, which converts the implicit nonlinear performance function in the conventional reliability analysis to linear explicit one. Finally, numerical examples of JZ20-2 MSW, JZ20-2NW and JZ20-2 MUQ offshore jacket platforms in the Bahai Bay demonstrate the satisfying efficiency, accuracy and applicability of the proposed method.展开更多
On the basis of ice- induced forced vibration model, ice- induced displacement responses of offshore fixed platforms are investigated in both time domain and frequency domain. The relationships of ice-induced displace...On the basis of ice- induced forced vibration model, ice- induced displacement responses of offshore fixed platforms are investigated in both time domain and frequency domain. The relationships of ice-induced displacement responses with ice breaking modes, ice acting directions and platform structures are analyzed and determined. The results lead to an important conclusion obtained for the first time that ice breaking frequency and the natural frequency of the first mode of the platform are the two main factors that dominate the degree of vibration. The present work provides a firm basis for both design and operation of fixed platforms against ice loading.展开更多
As jack-up platforms have recently been used in deeper and harsher waters, there has been an increasing demand to understand their behaviour more accurately to develop more sophisticated analysis techniques. One of th...As jack-up platforms have recently been used in deeper and harsher waters, there has been an increasing demand to understand their behaviour more accurately to develop more sophisticated analysis techniques. One of the areas of significant development has been the modelling of spudean performance, where the load-displacement behaviour of the foundation is required to be included in any numerical model of the structure. In this study, beam on nonlinear winkler foundation （BNWF） modeling--which is based on using nonlinear springs and dampers instead of a continuum soil media--is employed for this purpose. A regular monochrome design wave and an irregular wave representing a design sea state are applied to the platform as lateral loading. By using the BNWF model and assuming a granular soil under spudcans, properties such as soil nonlinear behaviour near the structure, contact phenomena at the interface of soil and spudcan （such as uplifting and rocking）, and geometrical nonlinear behaviour of the structure are studied. Results of this study show that inelastic behaviour of the soil causes an increase in the lateral displacement at the hull elevation and permanent unequal settlement in soil below the spudcans, which are increased by decreasing the friction angle of the sandy soil. In fact, spudeans and the underlying soil cause a relative fixity at the platform support, which changes the dynamic response of the structure compared with the case where the structure is assumed to have a fixed support or pinned support. For simulating this behaviour without explicit modelling of soil-structure interaction （SSI）, moment- rotation curves at the end of platform legs, which are dependent on foundation dimensions and soil characteristics, are obtained. These curves can be used in a simplified model of the platform for considering the relative fixity at the soil- foundation interface.展开更多
Based on investigation and model tests, and in combination with the research work on group effect for pile groups under lateral loads relating to the code of fixed offshore platforms, a series of studies have been per...Based on investigation and model tests, and in combination with the research work on group effect for pile groups under lateral loads relating to the code of fixed offshore platforms, a series of studies have been performed on the behavior and failure mechanism of laterally loaded pile groups, critical pile spacing inducing group effect, lateral bearing capacity of pile groups and its main influence factors, the stress-strain relationship for single piles and pile groups and so on. Some new laws about non-uniformity of load distribution in the longitudinal direction of pile groups and load-deflection (p-y) curves for pile groups have been discovered, and an empirical formula is presented in order to remedy the defect of current calculating methods at home and abroad. These results can be used for reference in the design of pile foundation under lateral loads.展开更多
基金This researchis partiallyfunded bythe National Natural Science Foundation of China (Grant No.59895410)
文摘The statistical characteristics and parameters of loads and resistances are systematically studied for the development of probabilistic limit state design method for steel jacket offshore platforms in the China offshore area. The mean value, standard variance and distribution pattern of resistances and loads in different base perieds are presented. The statistical parameters of structural member resistance, self-weight, deck live load, and environmental loads such as wind, wave, current and ice, which are drawn on a large amount of observatian data of offshore environmental factors, and the design data of platforms in China Bohai Sea form the data set, providing a necessary basis for the calibration of load and resistance factors to realize the reliability-based design of jacket platform structures.
文摘Adopting the load and resistance factor design format, the design method for steel jaeket platform structures is developed. Firstly, the limit state equations and design format for steel jacket platform structures are introduced. Then, the ratio of live load effect to dead load effect is estimated. The target reliabilities for design of offshore structures in China offshore area are calibrated by past practice in API RP2A-WSD code. The load and resistance factors are optimized by minimizing the difference within the target reliability and the resulting reliability over the range of load effect ratios. Considering the concurrence of different loads, load combination factors are obtained through an optimization process, and the relation between the load combination factor and load correlation coefficient is established. Finally, the design formulae for steel jacket structures in China offshore area are recommended.
文摘In this paper, reliability analysis for the offshore jacket platform with the interaction of structure- pile- soil under extreme environmental loads is carried out. The inherent uncertainties of the environmental load, foundation soil, platform itself, and calculating models are evaluated. The action of extreme loads on the offshore platform is modeled as a function of extreme wave height. The system capacity of the whole platform is determined by nonlinear pushover analysis, and the relevant probability property is obtained by the simulation method. The reliability model for the whole jacket platform is described as the relationship between the load and resistance based on the offshore design codes. The reliability of whole platform is calculated by the analytical method and the importance sampling method on the basis of a case study for a tripod jacket platform.
文摘For the fulfillment of the probability-based structural design for the offshore jacket platforms in the Bohai Bay, the design factors of loads, resistance and load combinations are much necessary to be calibrated according to the proposed target reliability index. Firstly, the limit states function for the offshore jacket platforms is introduced. Then, four approaches to calibrate the factors of load and resistance are presented and compared. Afterwards, the methods to calibrate the load combination factors are developed. Finally, the factors of load, resistance and load combination for the offshore jacket platforms in the Bohai Bay are calibrated and the corresponding design formulae are recommended. The results are proved to be rational in practice, and also illustrate that the proposed target reliability index for offshore jacket platforms in the Bohai Bay is also appropriate.
基金financially supported by the National Natural Science Foundation of China(Nos.51878577 and 52378463)the Natural Science Foundation of Shandong Provincial,China(No.ZR2022ME042)the School-Enterprise Cooperation Program of China Railway 14th Bureau Group Co.(QTHT-HGLCHSD-00052)。
文摘The semi-rigid pile-supported composite foundation is widely used in highway projects due to its effectiveness in increasing the bearing capacity and stability of foundations.It is crucial to understand the stress distribution across the embankment width and the behaviour of unreinforced foundations.Thus,five centrifuge tests were conducted to examine the bearing and deformation behaviours of NPRS(Non-Connected Piled Raft Systems)and GRPS(GeosyntheticReinforced Pile-Supported systems)with varying substratum stiffness,then a comparative analysis was conducted on embankment settlement,pressures underneath the embankments,and axial forces along the piles.The results indicated that greater substratum stiffness correlates with reduced settlement and deformation at various depths.Deformation occurring 5 meters from the embankment toe includes settlement in NPRS and upward movement in GRPS.The potential sliding surface is primarily located within the embankment in NPRS,whereas it may extend through both the embankment and foundation in GRPS.The pile-soil stress ratio and efficiency in NPRS are higher than in GRPS across the embankment.The axial force borne by end-bearing piles is significantly greater than that by floating piles.As the buried depth increases,the axial force in GRPS initially rises then declines,whereas in NPRS,it remains relatively constant within a certain range before decreasing.This study aids in assessing the applicability of composite foundations in complex railway environments and provides a reference for procedural measures under similar conditions.
基金The project was financially supported by the Foundation of Doctorate Program of the State Education Commission of China
文摘Overall wave loading and local hydrodynamic pressure distributions on a platform mat in regular waves for shallow waters are experimentally investigated in order to examine the severity of the nonlinear effects and shallow water effects. Wave focusing phenomenon is observed in the tests. The measured results may also provide a comparison basis for the theoretical development to consider the nonlinear interaction between waves and viscous flow by introducing viscosity into wave theories.
基金supported by Shandong Provincial Natural Science Foundation of China(Grant No.ZR2010EL003)
文摘The working platforms supported with multiple extensible legs must be leveled before they come into operation.Although the supporting stiffness and reliability of the platform are improved with the increasing number of the supporting legs,the increased overdetermination of the multi-leg platform systems leads to leveling coupling problem among legs and virtual leg problem in which some of the supporting legs bear zero or quasi zero loads.These problems make it quite complex and time consuming to level such a multi-leg platform.Based on rigid body kinematics,an approximate equation is formulated to rapidly calculate the leg extension for leveling a rigid platform,then a proportional speed control strategy is proposed to reduce the unexpected platform distortion and leveling coupling between supporting legs.Taking both the load coupling between supporting legs and the elastic flexibility of the working platform into consideration,an optimal balancing legs’ loads(OBLL) model is firstly put forward to deal with the traditional virtual leg problem.By taking advantage of the concept of supporting stiffness matrix,a coupling extension method(CEM) is developed to solve this OBLL problem for multi-leg flexible platform.At the end,with the concept of supporting stiffness matrix and static transmissibility matrix,an optimal load balancing leveling method is proposed to achieve geometric leveling and legs’ loads balancing simultaneously.Three numerical examples are given out to illustrate the performance of proposed methods.This paper proposes a method which can effectively quantify all of the legs’ extension at the same time,achieve geometric leveling and legs’ loads balancing simultaneously.By using the proposed methods,the stability,precision and efficiency of auto-leveling control process can be improved.
文摘The optimal control is investigated for linear systems affected by external harmonic disturbance and applied to vibration control systems of offshore steel jacket platforms. The wave-induced force is the dominant load that offshore structures are subjected to, and it can be taken as harmonic excitation for the system. The linearized Morison equation is employed to estimate the wave loading. The main result concerns the existence and design of a realizable optimal regulator, which is proposed to damp the forced oscillation in an optimal fashion. For demonstration of the effectiveness of the control scheme, the platform performance is investigated for different wave states. The simulations are based on the tuned mass damper and the active mass damper control devices. It is demonstrated that the control scheme is useful in reducing the displacement response of jacket-type offshore platforms.
基金This work was partly supported by the Japan Society for the Promotion of Science (JSPS) for RONPAKU program by Foundation for University Key Teacher by the Ministry of Education of China
文摘An obvious motivation of this paper is to examine the effectiveness of the lateral vibration control of a jacket type offshore platform with an AMD control device, in conjunction with H-2 control algorithm, which is an optimal frequency domain control method based on minimization of H-2 norm of the system transfer function In this study, the offshore platform is modeled numerically by use of the finite element method, instead of a lumped mass model This structural model is later simplified to be single-degree-of-freedom (SDOF) system by extracting the first vibration mode of the structure. The corresponding 'generalized' wave force is determined based on an analytical approximation of the first mode shape function, the physical wave loading being calculated from the linearized Morison equation. This approach facilitates the filter design for the generalized force. Furthermore, the present paper also intends to make numerical comparison between H-2 active control and the corresponding passive control using a TMD with the same device parameters.
基金This paper was financially supported by National Natural Science Foundation of China(Grant No.59895410)
文摘The failure of one or even more components usually does riot lead to the collapse of the whole structure. Most of the analysis of fatigue is centered on only a single component which the researchers are interested in or Much attention should be paid to. However, the collapse of a structure is the result of failure of a series of components in a specific order or path. This paper proposes an integrated approach to fatigue life prediction of whole structural system for offshore platforms, mainly describing the basic principles and prediction method. A method is presented for determining the failure path of the whole structure system and calculating the fatigue life in the determined failure path, The corresponding final collapse criteria for the whole structure system are discussed, A simple method of equivalent fatigue stress range calculation and a mathematical model of structural component fatigue life estimation in consideration of sea wave and sea ice loads are provided. As an application of the proposed approach, a fixed production platform Bohai No. 8 is chosen for the predication of fatigue life of the whole structure system by means of the software OSFAC developed based on the present methods.
基金This work was financially supported by the National High Technology Research and Development Programof China(863Program,Grant No.2001AA602015)the National Natural Science Foundation of China(Grant No.50578028and No.10721062)the Programfor NewCentury Excellent Talents in University.
文摘Ice load is the dominative load in the design of offshore platforms in the ice zone, and the extreme ice load is the key factor that affects the safety of platforms. The present paper studies the statistical properties of the global resistance and the extreme responses of the jacket platforms in Bahai Bay, considering the randomness of ice load, dead load, steel elastic modulus, yield strength and structural member dimensions. Then, based on the above results, an efficient approximate method of the global reliability analysis for the offshore platforms is proposed, which converts the implicit nonlinear performance function in the conventional reliability analysis to linear explicit one. Finally, numerical examples of JZ20-2 MSW, JZ20-2NW and JZ20-2 MUQ offshore jacket platforms in the Bahai Bay demonstrate the satisfying efficiency, accuracy and applicability of the proposed method.
基金The project was financially supported by China Postdoctor Science Foundationthe Key Project Foundation of the Chinese Academy of Sciences and China National Offshore Oil Corporation
文摘On the basis of ice- induced forced vibration model, ice- induced displacement responses of offshore fixed platforms are investigated in both time domain and frequency domain. The relationships of ice-induced displacement responses with ice breaking modes, ice acting directions and platform structures are analyzed and determined. The results lead to an important conclusion obtained for the first time that ice breaking frequency and the natural frequency of the first mode of the platform are the two main factors that dominate the degree of vibration. The present work provides a firm basis for both design and operation of fixed platforms against ice loading.
文摘As jack-up platforms have recently been used in deeper and harsher waters, there has been an increasing demand to understand their behaviour more accurately to develop more sophisticated analysis techniques. One of the areas of significant development has been the modelling of spudean performance, where the load-displacement behaviour of the foundation is required to be included in any numerical model of the structure. In this study, beam on nonlinear winkler foundation （BNWF） modeling--which is based on using nonlinear springs and dampers instead of a continuum soil media--is employed for this purpose. A regular monochrome design wave and an irregular wave representing a design sea state are applied to the platform as lateral loading. By using the BNWF model and assuming a granular soil under spudcans, properties such as soil nonlinear behaviour near the structure, contact phenomena at the interface of soil and spudcan （such as uplifting and rocking）, and geometrical nonlinear behaviour of the structure are studied. Results of this study show that inelastic behaviour of the soil causes an increase in the lateral displacement at the hull elevation and permanent unequal settlement in soil below the spudcans, which are increased by decreasing the friction angle of the sandy soil. In fact, spudeans and the underlying soil cause a relative fixity at the platform support, which changes the dynamic response of the structure compared with the case where the structure is assumed to have a fixed support or pinned support. For simulating this behaviour without explicit modelling of soil-structure interaction （SSI）, moment- rotation curves at the end of platform legs, which are dependent on foundation dimensions and soil characteristics, are obtained. These curves can be used in a simplified model of the platform for considering the relative fixity at the soil- foundation interface.
文摘Based on investigation and model tests, and in combination with the research work on group effect for pile groups under lateral loads relating to the code of fixed offshore platforms, a series of studies have been performed on the behavior and failure mechanism of laterally loaded pile groups, critical pile spacing inducing group effect, lateral bearing capacity of pile groups and its main influence factors, the stress-strain relationship for single piles and pile groups and so on. Some new laws about non-uniformity of load distribution in the longitudinal direction of pile groups and load-deflection (p-y) curves for pile groups have been discovered, and an empirical formula is presented in order to remedy the defect of current calculating methods at home and abroad. These results can be used for reference in the design of pile foundation under lateral loads.
