Numerical Analysis of a Cooling Tower Foundation Using FEM

This case study presents the application of the Finite Element Method (FEM) to design a ring foundation for a 185-meter-tall cooling tower located in Opole, Poland. The project faced notable geotechnical challenges due to highly heterogeneous subsoil conditions. These included a sharp transition from soft rock (marl and weathered marl) to low-stiffness tertiary deposits along the foundation perimeter, raising significant concerns about differential settlement and serviceability.

The numerical analysis was performed using ZSoil software and featured a comprehensive 3D model with dimensions of 200 m × 200 m × 36 m. The model included over 67,800 Enhanced Assumed Strain (EAS) solid elements, 2,368 shell elements representing the reinforced concrete shell of varying thickness, and 216 beam elements modeling 36 meridional precast columns. Structural elements such as precast beams were accounted for indirectly through adjusted shell thickness parameters.

The subsoil stratigraphy was interpolated using kriging techniques, based on data from 39 soil profiles and CPTU testing. Thirteen distinct materials were defined to represent the geological layers, with nonlinear Hardening Soil models with small strain stiffness (HSs) used for critical strata. Parameter selection was grounded in in-situ and laboratory testing, including triaxial, CSWS/SASW, DMT, and CPTU, interpreted via empirical correlations.

The construction sequence was staged, but consolidation was neglected due to the short-term focus and presence of shallow groundwater. Boundary conditions allowed vertical movement at the sides and were fixed at the base. The ring foundation, modeled with linear-elastic properties (E = 30 GPa), interacted with the subsoil through standard contact elements.

Key results included:

• Identification of localized zones prone to excessive deformation due to weaker soils.
• Application of differentially derived subgrade reaction moduli for structural input.
• Recommendation for soil replacement and a 0.5 m sand drainage layer under the foundation.

Settlement predictions were validated with real-time monitoring from leveling pins installed on all columns. The final vertical displacement measurements fell within acceptable Eurocode 7 serviceability limits (~50 mm), with observed discrepancies explained by organic soils and construction-induced ground disturbance.

This example highlights the successful integration of geotechnical modeling with structural design. By leveraging 3D FEM, realistic shell behavior, and advanced constitutive models, the team was able to propose a shallow foundation solution in a geologically complex setting, achieving both reliability and cost-effectiveness. The collaboration between structural and geotechnical teams, and the validation of simulation outputs with field data, underscores best practices in soil-structure interaction modeling.

References

Cardoso, A. S., Borges, J. L., Costa, P. A., Gomes, A. T., Marques, J. C., & Vieira, C. S. (Eds.). (2014). Numerical Methods in Geotechnical Engineering – NUMGE 2014: Volume 2. CRC Press/Balkema.

Bogusz, W., & Kociniak, M. (2018). Numerical analysis of a foundation of a cooling tower in difficult geotechnical conditions. In Cardoso et al. (Eds.), Numerical Methods in Geotechnical Engineering