In this paper some problems about the analytic estimations for movements of a pile foundation are discussed, and a new analytical procedure is presented. A model law for the relation between interaction shear stress and displacementat as the pile circumference is introduced, which shapes a parabola. Another model law at the pile tip is that axial stress and settlement are to develope in a constant ratio called tip-displacement factor. Suitable steps for analysis are presented with the series of equations, in which a pile is divided into several segments to simplify the calculations. The shear strength between pile and soil, tip-displacement factor, and a special tip-displacement value, at which shear stress reaches its strength at full length of the pile, must be determined to be used in the procedure of analysis. A numerical example is given, in which steps of calculation are presented in Table 1 and 2, and the results are shown. Although this analytical procedure will be useful in engineering practice to predict the movements of pile foundations, the constants and initial values for the equations must be determined considerately before performing calculations, because it must be noted that the informations obtained by only analytical methodes without any loading test will not always agree with that of actual foundations in natural soil.
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