Active faults undergo creep deformation during the interseismic period. Fault creep is a slow but persistent process that lasts for hundreds or thousands of years, accumulating displacements ranging from several meters to tens of meters over hundreds of years. Fault creep can directly induce or exacerbate landslide hazards, particularly when the fault zone traverses a landslide body, as fault activity directly controls slope stability. Such hazards frequently occur in the Sichuan-Yunnan region, where the Xianshuihe fault zone, a typical active fault in the area, exhibits significant creep deformation, with a left-lateral slip rate reaching 9−11 mm/a. Creep-induced landslides in this region are closely correlated with fault activity. Furthermore, the long-term fault creep-induced accumulated displacement poses a significant threat to engineered structures that cross active faults, such as transportation tunnels and water conduits. For example, the Claremont water tunnel crossing the Hayward fault was offset by 0.33 m due to creep. The Berkeley Hills tunnel section of the San Francisco Bay Area Rapid Transit （BART） system, crossing the active Hayward fault, was observed to experience 8 cm of right-lateral offset between 1971 and 1980. Scientifically fault creep deformation prediction is crucial for the seismic resilience of engineering structures and the mitigation of natural disasters.

Numerous researchers have studied fault creep deformation, proposing various computational methods such as the boundary element method （BEM） and three-dimensional boundary integral method. These methods, however, typically model the elastic response of fault slip within a half-space model, neglecting the viscoelastic effects of crustal materials. This omission can lead to significant errors in long-term creep simulations. Employing viscoelastic models is more appropriate for studying postseismic displacement. The semi-analytical three-dimensional elastic model for half-space deformation （hereafter referred to as the Smith3D model） can simulate both stress accumulation on the locked segment of a fault during the interseismic period and the viscoelastic response of the deep crustal medium. Research results indicate that fault stiffness varies during the interseismic period, a phenomenon explainable by the rheological properties of fault-zone materials. While these analytical methods and computational models rely on the assumptions that the fault’s elastic modulus remains constant, they conspicuously fail to capture modulus changes over extremely long timescales.

Uniaxial rock creep experiments reveal a three-stage creep process: decelerating creep （stage I）, steady-state creep （stage Ⅱ）, and accelerating creep （stage Ⅲ）. Throughout these stages, rock stiffness evolves with time. Using uniaxial rock creep experimental data and the Maxwell creep model, we propose a modified Maxwell creep model incorporating variable stiffness. The correlation coefficients between the theoretical model results and the experimental data for mudstone and greenschist creep were 0.974 and 0.983, respectively, validating the model’s effectiveness. Integrating this variable-stiffness model into the Smith3D model, we simulated the long-term creep deformation of the Xianshuihe fault zone from 1990 to 2015. For this simulation, we selected five representative horizontal creep observation sites along the fault zone, ordered from northwest to southeast: namely, Xialatuo, Qiajiao, Goupu, Longdengba, and Laoqianning. The correlation coefficients between the improved model’s simulations and monitoring results were 0.995 6, 0.882 1, 0.954 3, 0.982 9, and 0.931 5, respectively, demonstrating the efficacy of the variable-stiffness Smith3D model for analyzing long-term fault creep deformation.

The influence of three nearby earthquakes, the 2001 Western Kunlun Mountains earthquake （M_S8.1）, the 2008 Wenchuan earthquake （M_S8.0）, and the 2014 Kangding earthquake （M_S6.3） , on the creep displacement of the Xianshuihe fault zone was analyzed. Although the epicenter of the 2001 Western Kunlun Mountains earthquake was distant from the Xianshuihe fault zone, the induced plate motion still caused long-term reversed slip at the Qiajiao site. Coulomb stress changes on the fault zone resulting from the 2008 Wenchuan earthquake led to an increase in creep rate at the Goupu site. The 2014 Kangding earthquake, with its epicenter relatively close to the fault zone, produced co-seismic displacements causing short-term reversed slip at the Laoqianning site. The results from these three earthquakes indicate that fault creep deformation on the Xianshuihe fault zone is associated to both moderate-to-strong earthquakes in the near field and large earthquakes in the far field.