高陡横坡段桥梁双桩内力计算有限差分解

Finite Difference Solution of Bridge Double-pile Structure on a Steep Transverse Slope

为了对高陡横坡段桥梁双桩基础进行合理分析,提出一种适用的有限差分法。首先,针对陡坡段桥梁基桩不同特征段的承载特性,将后桩划分为嵌固段及受荷段,同时,将前桩划分为嵌固段、受荷段和自由段。然后,考虑桩土相互作用及桩顶变形协调,并引入边界条件,建立了适用于高陡横坡段桥梁双桩基础内力及位移分析的简化计算模型。在此基础上,综合考虑P(荷载)-Δ(位移)效应及连系梁的影响,分别对各特征段基桩微元进行受力分析,并引入相邻特征段满足的连续条件(即位移连续、转角连续、剪力连续及弯矩连续),推导出各微分段的控制差分方程,以MATLAB为平台编制相应计算程序,迭代求解桩身位移,进而求解其内力。最后,结合室内模型试验与现场试验对理论计算方法进行验证,并以现场试验桩为基础,分析连系梁及P-Δ效应等对高陡横坡段双桩基础内力及位移的影响。研究结果表明:理论计算结果与模型试验及现场试验实测数据均吻合良好,表明该方法可行、合理,可为高陡横坡段桥梁工程设计计算提供参考;有自由段存在的基桩,P-Δ效应明显;连系梁对倾斜荷载下基桩桩身内力具有显著影响,连系梁的存在会对上部荷载进行重新分配,并在一定程度上弱化P-Δ效应,对桩身变形具有一定的约束作用。

To analyze the inner force of a bridge double-pile foundation on a steep transverse slope, a new finite difference method has been presented. First, according to the bearing characteristics in different characteristic segments of piles on a steep slope, the back pile was divided into segments, namely fixed segment and loaded segment, whereas the front pile was divided into fixed segment, loaded segment, and free segment. A simplified calculation model for analyzing the inner force and displacement of piles on a steep transverse slope was proposed. The pile-soil interaction, compatibility of deformation at the piles’ top and boundary conditions were considered in the proposed model. Based on this, the stress of pile elements of different characteristic segments was analyzed considering the effects of a connecting beam and the P-Δ effect. The continuity conditions of displacement, corners, shear forces, and bending moments are conducted to derive the governing differential equations. The finite difference solution of displacement and inner force of piles are obtained through MATLAB. Finally, the suggested method was verified by a model test and field test, and the effects of the connecting beam and the P-Δ effect on the inner force of piles was researched. The predicted results are in good agreement with the experimental data, and the proposed approach is of great significance for the preliminary design of bridge double-pile foundation on a steep transverse slope. The P-Δ effect is obvious in piles with free segment. The connecting beam has considerable influence on the inner force because the upper loads are redistributed. The connecting beam can be frequently used in the practice engineering in term of weakening the P-Δ effect and decreasing the deformation of piles.