Modeling of Relaxation Parameters and Strength Aging of Silt under the Influence of Initial Strain in Three-Dimensional Stress Conditions

Stress relaxation, as an important time-dependent characteristic of soil, can significantly influence the long-term stability of geotechnical engineering. Existing studies have primarily focused on the stress relaxation behavior of clay and sand under one-dimensional stress conditions, whereas research on silt remains limited. To address this gap, a quantitative relationship among axial strain, cell pressure conditions, relaxation magnitude, residual stress ratio, relaxation rate characteristic parameter, and initial equivalent time has been established through relaxation testing of silt under a three-dimensional stress environment, including axial strain control and cell pressure control loading. The results indicate that the stress relaxation behavior of silt is closely related to the loading path. In the low-strain range (typically below 3%), the material exhibits elastic relaxation, with stress increasing nearly linearly with strain along the isochronous curve. Once the strain exceeds this threshold, the material exhibits viscoelastic relaxation behavior. The normalized relaxation magnitude grows logarithmically with axial strain; however, the growth rate in the elastic–plastic stage drops to about one-fifth of that observed in the purely elastic stage. Concurrently, the residual stress ratio rises markedly and linearly with increasing strain. To better capture the rate of stress decay, the slope of the cut line in the fast relaxation phase is introduced as a new index, providing a more precise representation of the rate increase with cell pressure and strain than existing relaxation rate calculation methods. Moreover, an exponential model describing the stress–time relationship achieves a correlation coefficient above 0.99, providing a reliable and accurate representation of the relaxation process in silt.