Landfilling is the primary method used for municipal solid waste (MSW) disposal. To design, optimize, and manage landfills with a life span of several decades, a deeper understanding of long-term MSW behaviors is necessary and worthwhile. These behaviors should be modeled using approaches that account for coupled processes so as to capture the evolutionary mechanisms that are mainly dominated by biochemical, mechanical, hydraulic, and thermal processes, as well as the complex interactions among them. Many mathematical models have been developed over the past three decades to address this issue. However, most of them only emphasize some of these processes, with only few models accounting for all the processes. In this review, we present a comprehensive overview of the mathematical and numerical formulations of this coupled problem. Each process occurring in landfills is interpreted in detail using different sub-models and the corresponding parameter values. Then, the existing coupled models for MSW are reviewed, and the challenges and perspectives related to the modeling of the long-term behaviors of MSW are highlighted. We conclude that more reliable constitutive formulations based not only on well-designed laboratory tests but also on field tests are necessary to improve the modeling of MSW behaviors in future.

垃圾填埋是处理城市固体废物（MSW）的主要方法。为了设计，优化和管理寿命长达数十年的垃圾填埋场，对长期生活垃圾行为的深入了解是必要且有价值的。这些行为应使用考虑耦合过程的方法进行建模，以捕获主要由生化，机械，水力和热过程以及它们之间复杂的相互作用主导的进化机制。在过去的三十年中，已经开发了许多数学模型来解决这个问题。但是，它们中的大多数只强调其中一些过程，只有很少的模型说明了所有过程。在这篇综述中，我们提出了这个耦合问题的数学和数值公式的全面概述。使用不同的子模型和相应的参数值来详细解释垃圾填埋场中发生的每个过程。然后，回顾了现有的MSW耦合模型，并突出了与MSW长期行为建模相关的挑战和观点。我们得出的结论是，不仅要基于精心设计的实验室测试，而且还要基于现场测试的更可靠的本构公式，对于将来改善MSW行为的建模十分必要。