Abstract This paper presents multi-stage cyclic loading tests with three confining pressures and eight dynamic stress amplitudes on frozen subgrade soil at the negative temperature − 2 °C to experimentally study accumulative and resilient deformation properties under different cyclic loadings. The coupled effects of the confining pressure and dynamic stress amplitude on accumulative and resilient deformation properties of frozen sample are analyzed in detail. Accumulative and resilient deformation behaviors of frozen samples at each stage of multi-stage cyclic loading tests exhibit similar patterns as that observed in the single-stage cyclic loading tests. Two-stage evolution feature for resilient modulus of frozen subgrade soil is experimentally determinated. Critical cyclic number is defined as the turning point of two-stage feature for resilient modulus to further distinguish the post-compaction compression stage and secondary cyclic compression stage of frozen subgrade soil. The influence of confining pressure on critical cyclic number is negligible. With the increase of dynamic stress amplitude, critical cyclic number approximately increases. Dynamic stress amplitude, rather than confining pressure, is main influencing factor for critical cyclic number in this investigation range of confining pressure. A new evaluation criterion for three typical deformation areas of granular materials subjected to cyclic loading is proposed based on the shakedown theory. The devlopment features of accumulative permanant strain at the multi-stage cyclic loading tests are studied and judged by two published shakedown criteria and presented new criterion. Two published shakedown criteria's applicability and limitation for frozen subgrade soils are further investigated and discussed. The assessment capacity of this new criterion is validated by all testing results for frozen subgrade soils. The evaluation results based on this new criterion are in approximate agreement to those according to Chen's shakedown criterion ( Chen et al., 2019 ).

中文翻译：

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循环荷载作用下颗粒材料累积塑性变形评价新方法——以冻土路基土为例

摘要 本文提出了在负温度− 2 °C 下冻结路基土的三个围压和八个动应力幅的多阶段循环加载试验，以实验研究不同循环加载下的累积变形和回弹变形特性。详细分析了围压和动应力幅值对冷冻样品累积和回弹变形特性的耦合影响。在多阶段循环加载试验的每个阶段，冷冻样品的累积和弹性变形行为表现出与单阶段循环加载试验中观察到的相似的模式。实验确定了冻结路基土弹性模量的两阶段演化特征。临界循环数定义为回弹模量两阶段特征的转折点，以进一步区分冻结路基土的后压实压缩阶段和二次循环压缩阶段。围压对临界循环数的影响可以忽略不计。随着动应力幅值的增加，临界循环数近似增加。在该围压研究范围内，动态应力幅值是影响临界循环数的主要因素，而不是围压。基于稳定理论，提出了三种典型颗粒材料在循环荷载作用下变形区域的评价新标准。研究和判断了多阶段循环加载试验中累积永久应变的发展特征，并采用了两个已发表的安定标准，并提出了新的标准。进一步研究和讨论了两个已发布的稳定标准对冻结路基土壤的适用性和局限性。冻结路基土壤的所有测试结果验证了这一新标准的评估能力。基于这一新准则的评价结果​​与根据陈氏安定准则（Chen et al., 2019）的评价结果​​基本一致。冻结路基土壤的所有测试结果验证了这一新标准的评估能力。基于这一新准则的评价结果​​与根据陈氏安定准则（Chen et al., 2019）的评价结果​​基本一致。冻结路基土壤的所有测试结果验证了这一新标准的评估能力。基于这一新准则的评价结果​​与根据陈氏安定准则（Chen et al., 2019）的评价结果​​基本一致。