Ultimate Lateral Capacity of Rigid Pile in c–φ Soil ZHANG Wei-min a, b, c, * a Nanjing Hydraulic Research Institute, Nanjing 210029, China b Key Laboratory of Water Science and Engineering, Ministry of Water Resources, Nanjing 210029, China c National Energy Hydropower Engineering Safety and Environmental Research and Development Center, Nanjing 210029, China Received December 12, 2017; revised December 27, 2017; accepted January 8, 2018 ©2018 Chinese Ocean Engineering Society and Springer-Verlag GmbH Germany, part of Springer Nature Abstract To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c–φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also, the ultimate lateral capacity in the c–φ soil was the combination of the ultimate lateral capacity (f c ) in the clay, and the ultimate lateral capacity (f φ ) in the sand. Therefore, the Broms chart for clay, solution for clay (φ=0) put forward by Poulos and Davis, solution for sand (c=0) obtained by Petrasovits and Awad, and Kondner’s ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values. Key words: pile ultimate lateral capacity, dimensionless analytical solution, c–φ soils, hyperbolic function method Citation: Zhang, W. M., 2018. Ultimate lateral capacity of rigid pile in c–φ soil. China Ocean Eng., 32(1): 41–50, doi: https://doi.org/10.1007/s 13344-018-0005-1 1 Introduction Piles are widely used in bridges, high-rise buildings, wharf infrastructures, power transmission towers, offshore platforms, wind power infrastructures, and other civil engin- eering projects. The ultimate lateral capacities of these piles are important contents of engineering designs and safety as- sessments. To date no analytical solution of the ultimate lat- eral capacity for the general c–φ soil has been obtained, and only under the condition of c = 0 or φ = 0, the analytical solution is available. Although the calculation formula was not obtained, Broms (1964a) put forward the well known calculation charts. Poulos and Davis (1980) further presen- ted the calculation formulas for the ultimate lateral capacity and rotation center in clay under the condition of φ = 0. More relevant research on clay can be found in the study of Reese and Welch (1975) and other researchers. On sand, Petrasovits and Award (1972) put forward a calculation for- mula of the ultimate lateral capacity of sand under the con- dition of p u =kz. However, a calculation method for the rota- tion center was not obtained. For the general c–φ soil, Hansen (1961) proposed an evaluation method that requires repeated iterations, with a more complex process and more time spent on it. In this study, a new dimensionless embedded ratio was proposed. And the strict solutions of the dimensionless ulti- mate lateral capacity and rotation center for three kinds of soils (c=0, φ=0, and c–φ soil) were obtained. The results showed that both the dimensionless ultimate lateral capa- city and the dimensionless rotation center were the univari- ate functions of the new embedded ratio, and that the ulti- mate lateral capacity in c–φ soils is the combination of the ultimate lateral capacity (f c ) in clay, and the ultimate lateral capacity (f φ ) in sand. The ultimate bending moment for c–φ soil was obtained also. In the comparison of the published field and laboratory test results of 93 cases, the average ra- tios of the theoretical values to the experimental values ranged from 0.85 to 1.15. 2 Ultimate lateral resistance of soils For rigid piles the estimation of the ultimate lateral load capacity requires knowledge of the magnitude and distribu- tion of the limit lateral soil resistance for a given soil condi- tion. The ultimate lateral resistance represents the limit load capacity applied by the surrounding soil per unit length. For China Ocean Eng., 2018, Vol. 32, No. 1, P. 41–50 DOI: https://doi.org/10.1007/s13344-018-0005-1, ISSN 0890-5487 http://www.chinaoceanengin.cn/ E-mail: [email protected] Foundation item: This study was financially supported by the National Natural Science Foundation of China (Grant No. 51379132). *Corresponding author. E-mail: [email protected]
Ultimate Lateral Capacity of Rigid Pile in c–φ Soil
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