Currently, the vertical drain consolidation problem is solved by numerous analytical solutions, such as time-dependent solutions and linear or parabolic radial drainage in the smear zone, and no artificial intelligence (AI) approach has been applied. Thus, in this study, a new hybrid model based on deep neural networks (DNNs), particle swarm optimization (PSO), and genetic algorithms (GAs) is proposed to solve this problem. The DNN can effectively simulate any sophisticated equation, and the PSO and GA can optimize the selected DNN and improve the performance of the prediction model. In the present study, analytical solutions to vertical drains in the literature are incorporated into the DNN—PSO and DNN—GA prediction models with three different radial drainage patterns in the smear zone under time-dependent loading. The verification performed with analytical solutions and measurements from three full-scale embankment tests revealed promising applications of the proposed approach.

目前，垂直排水固结问题通过许多解析解决方案来解决，例如涂片区的时间相关解决方案和线性或抛物线径向排水，尚未应用人工智能（AI）方法。因此，在本研究中，提出了一种基于深度神经网络 (DNN)、粒子群优化 (PSO) 和遗传算法 (GA) 的新混合模型来解决该问题。DNN 可以有效地模拟任何复杂的方程，PSO 和 GA 可以优化所选的 DNN 并提高预测模型的性能。在本研究中，文献中垂直排水的解析解被纳入 DNN-PSO 和 DNN-GA 预测模型中，在时间相关的载荷下，涂抹区具有三种不同的径向排水模式。