| Inclined eccentrically loaded pile is a pile which bears both horizontal load,vertical load and eccentric moment load.Pile under these loads show much more complicated force deformation characteristics than the pile under single load.And its most obvious characteristic is that vertical load will generate additional bending moment due to pile’s deflection,which forms the so-called P-Δ effect,thereby increasing pile’s flexural deformation.How to consider this effect has become a key problem in the analysis of pile under inclined eccentric load.In order to solve the problem,this paper introduces the additional work of vertical load into the total potential energy equation of pile-soil system to consider the P-Δ effect on the basis of principle of minimum potential energy and variational principle in elastic mechanics and then establishes an energy-based calculation method for the inclined eccentrically loaded pile.Finally,factors affecting pile’s load performance and P-Δ effect are discussed.The specific work is as follows:Firstly,the bearing mechanism of piles under a single vertical load or horizontal load and under the inclined eccentric loads are analyzed,the differences between them are discussed,and the calculation theory of piles under inclined eccentric loads is also analyzed to sum up.Secondly,considering the inclined and eccentrically loaded pile in the elastic homogeneous foundation,the virtual pile is introduced to establish the total potential energy equation of the pile-soil system.Based on the principle of minimum potential energy and variational principle,the governing equation of horizontal displacement of the pile and the horizontal displacement of the soil around the pile are derived.Then,the central finite difference method is adopted to obtain the differential equations of horizontal displacement of the pile and the soil around the pile,and a calculation program is compiled using Matlab software.Finally,the calculation results of this paper are compared with the existing theoretical meth ods and experimental results,to verify the rationality of this method.Thirdly,the energy analysis method in a hom ogeneous foundation is extended to more complex layered soil foundations.Based on the assumption that each layered soil is an elastic body,the energy equation of the pile-soil system in the layered foundation is established,and the horizontal displacement governing equation is derived.The finite difference method is used to obtain the differential equations of horizontal displacement of the pile and the soil around the pile.The difference equations of displacement finally lead to solutions such as the horizontal displacement w(z)of the pile and the bending moment M(z)of the pile.Then the calculation method in this paper is compared with the existing indoor model test and the recommended m method.The results show that the calculation result of the method in this paper is closer to the test result,and the calculation error of the m method is about twice that of the method in this paper.The method is more accurate and reasonable than the m method when considering the vertical load P-Δ effect.Finally,combined with the proposed energy calculation meth od,this paper analyzes some of the main factors that affect the load performance and P-Δ effect of piles under inclined and eccentric loads,such as the vertical and horizontal load rati o,the length of free section at the top of the pile,and the diameter of the pile.The results show that when the ratio of vertical and horizontal loads is less than 2,the P-Δ effect has little effect;when the ratio of vertical and horizontal loads reac hes 5,the P-Δ effect is very significant.In addition,the P-Δ effect increases sharply with the increase of the length of the free section at the top of the pile,and decreases with the increase of the pile diameter and the soil modulus of the shallow fo undation.Moreover,the impact of the P-Δ effect can be greatly weakened by the embedment of the pile top. |
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