考虑层间接触状态的路面动力响应解析解及参数反演

为了对现有路面结构FWD检测技术的改进提供相关参考，并进一步完善路面结构质量评价体系，从轴对称动力平衡方程出发，应用Hankel-Laplace积分变换，推导了考虑路面材料横观各向同性特性和路面结构层间接触状态的路面结构力学响应解析解，结合传递矩阵法提出了一种路面结构力学响应快速计算方法，并通过与ABAQUS计算结果的对比验证了所提理论推导的正确性。在此基础上，随机生成6 728组不同竖向模量、模量比、层间滑移系数以及结构层厚度的路面结构，计算其在FWD脉冲荷载作用下的表面位移响应，并应用BP神经网络以及实数编码的多种群遗传算法反演路面结构参数。研究结果表明：对BP神经网络而言，仅土基材料参数以及各结构层竖向模量的预测结果相对较为理想，其相关系数在0.75以上；较BP神经网络的预测结果，实数编码的多种群遗传算法对竖向模量的预测精度有了较大提高，相关系数基本达到0.95以上。但无论采用何种反演方法，对模量比以及层底滑移系数的预测效果均不理想。综上所述，所提出的解析解以及计算方法具有较高的计算精度以及较好的数值稳定性，能够实现路面结构力学响应的快速计算；同时，在进行路面参数反演计算时，应考虑路面结构的层间不完全连续状态以及材料的横观各向同性；而仅依靠路表弯沉数据进行参数反演的结果并不理想，有必要对现有检测技术进行相关改进。

Analytical Solution for the Dynamic Responses and Parameter Inversion of Pavement Structures Considering the Condition of Interlayer Contact

To provide references for the improvement of existing pavement structure falling weight deflectometer (FWD) technology and improve pavement structure quality evaluation systems, this study began with the axisymmetric dynamic equilibrium equation and applied the Hankel-Laplace transform. An analytical solution for the mechanical responses of pavement structures was then derived. This solution considers the transverse isotropic characteristics of pavement materials and interlayer contact states between pavement structures. A fast calculation method for the mechanical responses of pavement structures is proposed in conjunction with the transfer matrix method. The correctness of the theoretical derivation developed in this study was verified through comparisons to the calculation results of ABAQUS. To this end, 6 728 sets of pavement structures with different vertical moduli, modulus ratios, interlayer slip coefficients, and structural layer thicknesses were randomly generated. The surface displacement responses of each group under the action of an FWD pulse load were calculated using a back-propagation neural network (BPNN) and real-coded multi-population genetic algorithm (MPGA) to back-calculate the parameters of the pavement structures. The results demonstrate that for the BPNN, only the prediction results for the soil-based material parameters and vertical modulus of each structural layer are close to ideal with correlation coefficients above 0.75. Compared to the BPNN, the prediction accuracy of the real-coded MPGA for the vertical modulus is significantly improved and the correlation coefficient is greater than 0.95. However, regardless of the method used, the prediction results for the modulus ratio and bottom slip coefficient are not ideal. In summary, the proposed analytical solutions and calculation methods provide enhanced calculation accuracy and numerical stability, allowing them to facilitate the rapid calculation of the mechanical responses of pavement structures. Additionally, in the calculation of pavement parameter inversion, the incomplete continuity of pavement structures and transverse isotropy of materials should be considered. The results of parameter inversion based on road surface deflection data alone are not ideal. Therefore, it is necessary to make relevant improvements to existing detection technologies.