As noted earlier, most studies rely on the classical integer order viscoelastic model, which frequently overlooks the higher-order differential term or imposes limitations on its applicability. This conventional model, constructed on the basis of the time's integral derivative, establishes a non-power law constitutive relationship between stress, strain, and time. However, many common engineering materials, such as metals, plastic, concrete, glass, ceramics, and geological substances like soil, asphalt, and rock, exhibit the rheological behavior of power-law phenomena. To address this issue, Bagely et al. established a relationship between the dynamic behavior of viscoelastic media and the fractional differential theory, proposing that the fractional derivative constitutive relation can be used to describe the stress-relaxation and creep of some viscous materials via experiments. The fractional viscoelastic model, requiring fewer parameters and exhibiting superior memory performance, can provide more precise descriptions of material properties. Therefore, researchers have increasingly applied the fractional viscoelastic theory to various materials, including asphalt, concrete, rock, minerals, and soil. As a result, some researchers have begun to employ the fractional viscoelastic model to investigate the dynamic response of foundation beams.


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