中文摘要：

为探讨非均质地基中单桩受扭的非线性特性,假定桩侧地表处地基土剪切模量为非零值（已有方法多假定为零）且随深度呈幂函数分布,引入虚土桩法建立出桩土体系的总能量方程后,基于最小势能原理由变分法分别导得桩身及土体的受扭控制方程,进而采用有限差分法获得桩身扭转角的差分方程式。然后,将桩周土体视为理想弹塑性材料,给出了塑性状态下的单桩受扭分析方法,并基于MATLAB编制了计算程序,再将计算结果与已有方法及实验结果进行了对比验证。最后,通过参数分析获得了桩体参数G_p和r_0以及土体参数α_g和n的取值对桩身扭转响应的影响规律：随桩体剪切模量G_p的增大,桩顶扭转角减小;桩径r_0增大一倍时,相同扭转角下桩顶能承受的扭矩增大5~7倍;α_g≤0.1L时,扭矩传递先慢后快,反之则表现为先快后慢;n≤1时,扭矩传递先快后慢,反之则表现为先慢后快,且桩身扭转响应主要集中于桩身上部。

英文摘要：

To discuss the nonlinear torsional response of a single pile in non-homogeneous subsoil,the modulus profile was taken as a power function varying with depth with a nonzero value on the land surface（ usually treated as zero）. The virtual pile was introduced to establish the total energy function of the pile-soil system,from which the differential government equations for the pile shaft and subsoil were derived by the principle of the minimum potential energy and variational methods,respectively. The finite difference method was adopted to obtain the differential equation of the twist angle along the pile shaft. Regarding the subsoil as elastic-perfectly plastic material,a torsional analysis method of a single pile under the plastic bearing status was given with a program developed with the MATLAB software. The proposed method was verified by comparing the results with those by other available methods and model tests. A parameter analysis was also carried out to find out the influencing rules by the pile shear modulus Gpand pile diameter r_0 as well as the soil parameter α_gand n to the torsional response of pile shaft. The results show that with the increasing Gp,the pile twist angle decreases; if the value of r_0 was doubled,the torque which the pile could withstand increases 5-7times under the same twist angle; If α_g≤0. 1L,the torque transfer efficiency is slow at first and then fast later,while the condition is opposite for α_g 0. 1L. The torque transfer efficiency is fast at first then slow laterfor n≤1 with an opposite result for n 1,and the torsional response is mainly concentrated on the upper part of the pile shaft.