To explore the creep characteristics of carbonaceous schist under different moisture content conditions, based on the indoor graded loading creep test data, this paper constructed a viscoplastic body capable of describing the nonlinear accelerated creep stage throughout the entire creep process. This is achieved by parallelly connecting a nonlinear viscous element with a plastic element that characterizes yield behavior, based on data from indoor graded loading creep tests. Subsequently, this nonlinear viscoplastic body was integrated in series with the classical Nishihara model. By incorporating the softening patterns of elastic modulus and viscosity coefficient, four damage factors were introduced to establish a damage-based creep constitutive model (i. e., an improved Nishihara model) that describes the entire creep process of carbonaceous slate under different moisture content conditions. Through secondary development of a user-defined material subroutine (UMAT) in ABAQUS finite element software, numerical simulations of triaxial creep tests on carbonaceous slate under varying moisture content conditions were implemented. The applicability of the model was validated by comparing experimental creep data from rock samples with numerical simulation results. The research results show that the constructed improved Nishihara model can significantly improve the simulation accuracy in the accelerated creep stage. The graded loading creep test curves under different moisture content conditions are in good agreement with the numerical simulation curves, and the correlation coefficients are all greater than 0.9. The numerical simulation cloud map accurately reproduced the creep deformation evolution process of rock samples with different water contents, verifying the correctness and effectiveness of the proposed creep constitutive model of carbonaceous shale considering water damage and the development of the UMAT subroutine. This research achievement can provide theoretical support for the long-term stability assessment and disaster early warning of deep-water buried carbonaceous slate tunnel projects.

The consolidation coefficient is a crucial parameter for settlement calculation and stability analysis of soft foundations. Existing in-situ testing methods for the consolidation coefficient have the disadvantages of time-consuming and low accuracy. Based on the penetration mechanism of piezocone penetration test (CPTU) and the dissipation pattern of excess pore water pressure at the cone shoulder, the formation, development, and dissipation processes of excess pore water pressure at the CPTU cone shoulder are described using the theory of circular cavity expansion and the axisymmetric consolidation equation. By incorporating the automatic differentiation capability of neural networks, the axisymmetric consolidation equation is embedded into a deep neural network. The physical information constraints of the neural network are formed through the loss functions of physical equations, boundary conditions, and initial conditions. At the same time, the CPTU pore pressure test data serve as a data-driven term. Consequently, with the minimization of the excess pore water pressure loss function as the optimization goal, a physics-informed neural networks (PINNs) model is established for inversely analyzing the in-situ consolidation coefficient using CPTU pore pressure test data. The effectiveness of the PINNs model in inversely analyzing in-situ consolidation coefficient is verified through example analysis and inversion validation using existing centrifuge test data. The robustness of the PINNs model is also analyzed using CPTU pore pressure test data. The results indicate that the proposed PINNs model can effectively use CPTU pore pressure test data to rapidly and accurately invert the site in-situ consolidation coefficient. Due to the integration of physical mechanism constraints, the model requires only a small amount of training data and exhibits strong robustness and generalization performance against noisy pore pressure test data, providing an effective approach for accurate, rapid, and reliable testing of the in-situ consolidation coefficient.