Study on stress relaxation model of unsaturated reticulated red clay

Tunnel excavation redistributes the in-situ stress field and imposes sustained shear strains on the surrounding unsaturated clay. When these strains are constrained by a stiff lining or grouted annulus, effective stresses decay with time because of stress relaxation. Such decay can unload the support system, trigger delayed over-break, amplify ground settlement and, in extreme cases, precipitate local collapse. Reliable estimates of the magnitude and rate of relaxation are therefore indispensable for selecting lining thickness, bolt pre-tension and construction sequences in shallow tunnels driven through unsaturated soils. To quantify this phenomenon, an unsaturated stress-relaxation model combining the Caputo fractional derivative with a Koeller dashpot is proposed. The Caputo operator captures the history-dependent, long-memory character of the process, while the Koeller element reproduces the energy-dissipative response observed in clays. A suite of triaxial relaxation tests covering a range of net confining pressures and matric suctions was performed on reticulated red clay to calibrate and validate the model. Results demonstrate that the fractional εBurgers formulation accurately reproduces the complete relaxation curves under all test conditions, outperforming classical Burgers, Merchant and Nishihara models (R²>0.98, RMSE<3). The new model offers engineers a practical tool for predicting time-dependent stress decay and deformation in unsaturated tunneling environments, thereby enhancing design accuracy and construction safety. © The Author(s), under exclusive license to Springer-Verlag GmbH Germany, part of Springer Nature 2025.