# A Comprehensive Review of Open Caisson Modeling Technology: Current Practices and Future Prospects
## 4 Advances in Computational Modeling Method
### Sph  
In view of significant soil deformation, mesh distortion, and computation errors, conventional techniques such as FEM have limited application when dealing with numerical simulations of sinking caissons. The Lagrangian-based smoothed-particle hydrodynamics (SPH) approach, on the other hand, is a possible substitute since it manages interface migration and large deformations effectively. [PERSON] et al. [107] used a single-phase soil particle and the SPH method to model the sinking process of open caissons. However, the method's inability to precisely reproduce the conditions of wading engineering construction limited its usefulness. Even though the modeling accounted for the significant soil deformation, the intricate soil-water relation was, however, neglected, making it impossible to determine the fluctuation rule of pore water pressure (PWP). In order to examine the changing failure of caisson foundations in sand, [PERSON] et al. [108] used a combined Lagrangian-SPH technique, examining different loading combinations and caisson dimensions. Using SPH, [PERSON] et al. [109] modeled floating bodies in the surf zone, showing good agreement with experimental data for caisson breakwater displacement and realistic behavior for a floating box. These investigations demonstrate SPH's adaptability and efficiency in simulating intricate caisson-related events. To overcome this limitation and to simulate the whole sinking and excavation process of open caisson, [PERSON] [110] presented a coupled soil-water-caisson interaction algorithm. The \(\delta\)-SPH approach was used to address support domain truncation close to the blade, which ensured precise pore water pressure distribution and reduced pressure fluctuations from density oscillations. Furthermore, realistic underwater soil excavation was made possible by the dynamic particle birth and death technique, which successfully captured the intricate interactions that take place during the caisson sinking process. A small time step determines the algorithm's stability, which raises the computational cost and necessitates a certain particle resolution. Performance can be increased by particle refining and GPU parallel processing. In geotechnical engineering, numerical simulations rely on soil constitutive models that differ in complexity, parameter requirements, and computational demands. Mohr-Coulomb models use fundamental parameters like cohesion and friction angle, are computationally effective, and are employed for broad applications [111], but may not perform well under complicated stress [112]. According to [113], comparative study revealed that despite increased parameter requirements and calibration difficulties, modified Mohr-Coulomb models yielded more reliable forecasts in pipeline-soil interactions than the Drucker-Prager model. This model considered a linear stress-strain relationship until failure, followed by plastic deformation without hardening [114]. Inaccurate predictions of soil deformation may result from the model's assumption of a linear elastic response and failure to take into consideration non-linear stress-strain behavior or small-strain stiffness, particularly in stiff or soft soils [115; 116]. Also, this model did not take into account the anisotropic behavior of soils, which can be crucial for clays and other deposited soils [117]. The elastoplastic Hardening Soil (HS) model took stress-dependent stiffness and non-linear stress-strain behavior into consideration. It was frequently used for deep excavation analyses and was especially appropriate for soils that showed strain hardening, including sands and clays [118]. In order to simulate deep excavations in Warsaw's pre-consolidated clays, [119] the Hypoplastic Clay model and Hardening Soil models were employed. He concluded that the Hypoplastic Clay model was most effective in properly predicting wall behavior and ground displacements, even if basal heave was slightly underestimated. Hardening Soil models, on the other hand, greatly overestimated wall deformations and displacements.