Studies have revealed that rheological characteristics and self‐weight stress are nonnegligible during a consolidation process, especially for land reclamation projects or dredged soils. However, they are rarely considered simultaneously in traditional consolidation theories. This paper presents a general solution to the consolidation system of rheological soils that incorporates a fractional derivative model and self‐weight stress. First, the theory of the fractional derivative is introduced to the Merchant model to describe the consolidation behaviours of rheological soils, and the self‐weight stress of soils is simultaneously considered. Based on this model, the governing equation of a rheological consolidation system that considers self‐weight stress is obtained. Second, the analytical solutions of the effective stress and settlement in the Laplace domain are obtained by applying the Laplace transform to the consolidation governing equation. Further, the actual solutions in the real domain are obtained by a numerical Laplace transform inversion method (Abate's fixed Talbot method). Finally, the reliability and correctness of the consolidation theories and the proposed solutions are verified by comparing the calculated results with the degenerate solutions and experimental results in the existing literature. Furthermore, parametric studies are conducted to investigate the influence of rheological parameters and self‐weight parameters on the consolidation settlement and consolidation rate.

中文翻译：

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考虑自重应力影响的分数阶导数流变固结的半分析

研究表明，在固结过程中，流变特性和自重应力是不可忽略的，尤其是对于土地开垦项目或疏dr的土壤。但是，在传统合并理论中很少同时考虑它们。本文提出了流变土固结系统的一般解决方案，该解决方案包含分数导数模型和自重应力。首先，将分数导数理论引入到Merchant模型中，以描述流变土壤的固结特性，同时考虑土壤的自重应力。基于该模型，获得了考虑自重应力的流变固结系统的控制方程。第二，将拉普拉斯变换应用于固结控制方程，得到拉普拉斯区域有效应力和沉降的解析解。此外，通过数值拉普拉斯变换反演方法（阿贝特固定塔尔伯特方法）获得了实际域中的实际解。最后，通过将计算结果与简并解和现有文献中的实验结果进行比较，验证了固结理论和所提出解决方案的可靠性和正确性。此外，进行了参数研究，以研究流变参数和自重参数对固结沉降和固结速率的影响。实际域中的实际解是通过数值拉普拉斯变换反演方法（阿贝特固定塔尔伯特方法）获得的。最后，通过将计算结果与简并解和现有文献中的实验结果进行比较，验证了固结理论和所提出解决方案的可靠性和正确性。此外，进行了参数研究，以研究流变参数和自重参数对固结沉降和固结速率的影响。实际域中的实际解是通过数值拉普拉斯变换反演方法（阿贝特固定塔尔伯特方法）获得的。最后，通过将计算结果与简并解和现有文献中的实验结果进行比较，验证了固结理论和所提出解决方案的可靠性和正确性。此外，进行了参数研究，以研究流变参数和自重参数对固结沉降和固结速率的影响。通过将计算结果与简并解和现有文献中的实验结果进行比较，验证了固结理论和所提出的解决方案的可靠性和正确性。此外，进行了参数研究，以研究流变参数和自重参数对固结沉降和固结速率的影响。通过将计算结果与简并解和现有文献中的实验结果进行比较，验证了固结理论和所提出的解决方案的可靠性和正确性。此外，进行了参数研究，以研究流变参数和自重参数对固结沉降和固结速率的影响。