Functionally graded materials (FGMs) are commonly utilized in construction projects. They enhance the performance of functionally graded beams (FGBs) under various loading conditions. Therefore, the incorporation of variable-section FGBs theory into the analysis of structural and soil interactions is crucial for advancing engineering applications. Employing the variational principle and the transfer-matrix method, and considering the shear stiffness of the axially FGB structure itself, along with the continuity and shear strength of the soil, a semi-analytical solution for displacement and internal force of axially FGBs on Pasternak foundation (termed as P–T model) is derived in this paper. The semi-analytical solution is subsequently compared with finite difference solution results from prior studies, affirming the accuracy and precision of the proposed computational theory. The P–T model degenerates to the Winkler–Timoshenko model (W–T model) when the foundation’s shear layer stiffness is set to zero. Additional analysis is conducted on displacement and internal force variation when the beam stiffness follows different distribution along the axial direction. The results indicate that an asymmetrical distribution of stiffness on either side of the midpoint could increase the displacement at the middle section. Furthermore, when the beam stiffness adheres to a Gaussian distribution along the axial direction of the beam, a significant increase in displacement at the boundary position of the beam is observed. The proposed method is then integrated with the Mindlin stress solution to evaluate construction impact on an existing tunnel within a foundation pit project in Shenzhen. A comparative analysis of theoretical calculations, monitoring data, and numerical simulation results exhibits substantial concurrence across the three methods. The tunnel’s overall deflection adopts an “M” shape, and the computation using the variable-section FGB portrays the existing tunnel’s deformation trend with heightened accuracy, diminishing the calculation error from 35 to 8.3% compared to the conventional normal section beam.

功能梯度材料（FGM）常用于建筑项目。它们增强了功能梯度梁（FGB）在各种负载条件下的性能。因此，将变截面FGBs理论纳入结构与土体相互作用的分析对于推进工程应用至关重要。利用变分原理和传递矩阵法，考虑轴向FGB结构本身的抗剪刚度以及土体的连续性和抗剪强度，提出了帕斯捷尔纳克地基上轴向FGB结构位移和内力的半解析解本文推导了P-T模型（称为P-T模型）。随后将半解析解与先前研究的有限差分解结果进行比较，证实了所提出的计算理论的准确性和精度。当地基剪切层刚度设置为零时，P-T 模型退化为 Winkler-Timoshenko 模型（W-T 模型）。进一步分析了梁刚度沿轴向呈不同分布时的位移和内力变化。结果表明，中点两侧刚度的不对称分布会增加中间部分的位移。此外，当梁刚度沿梁轴向服从高斯分布时，观察到梁边界位置处的位移显着增加。然后将所提出的方法与 Mindlin 应力解决方案集成，以评估施工对深圳基坑项目内现有隧道的影响。理论计算、监测数据和数值模拟结果的比较分析表明，三种方法具有很大的一致性。隧道整体挠度采用“M”形，采用变截面FGB计算更准确地刻画既有隧道变形趋势，计算误差较传统正截面梁减少35%至8.3%。