In this article, we will see how the DIANA software can be used to perform finite element (FE) modeling of cooling towers, in order to evaluate their structural integrity and design targeted rehabilitation strategies for these structures.
In particular, DIANA allows for non-linear analyses that enable the reproduction of the behavior of the towers and the conditions to which they are subjected with extreme accuracy.
The Structure
The cooling towers in this case study are thin-shell hyperboloid structures made of reinforced concrete. Each tower is 60-70 meters high, with an upper diameter of 25-30 meters and a wall thickness that varies gradually (0.5 meters at the base, thinning to 0.12 meters at the top). The cooling basin at the base consists of a 40-50 meter circular plate and a 0.4-0.5 meter thick retaining wall, which supports a system of inclined circular columns designed to facilitate airflow into the chimney.
Objectives of the analysis
For this case study, as several towers were approaching the end of their service life, a structural assessment was commissioned to determine the safety level and the feasibility of rehabilitation interventions.
The main challenges of the intervention can be summarized in the following points:
- The towers exhibit severe material degradation: cracking, loss of concrete thickness, and reinforcement corrosion.
- Some towers show signs of structural instability caused by ovalization due to wind and thermal stresses (see Figure below).
- Need to extend structural service life without altering mass distribution or imposing excessive new loads on the foundation.
- Minimizing downtime to avoid interruptions to power plant operations.
Traditional assessment methods are unable to fully capture the complexity of these obsolete structures, necessitating the adoption of advanced finite element analysis (FEA).
Structural Analysis
The designers developed non-linear FE models using DIANA software to simulate the cooling towers’ response under operational and extreme loads.
Both geometric and mechanical nonlinearities are taken into account. The towers and basins are modeled with layered shell elements (specifically 8-node elements), while beam elements are used for the columns at the base. Damage, in the form of reduced concrete thickness or cracks, was directly introduced into the model. In particular, cracks were modeled by disconnecting the element surfaces. Reinforcements were explicitly modeled. For the materials, nonlinear constitutive laws were adopted. The mechanical characteristics were calibrated based on experimental tests. Specifically, for concrete, a constitutive law according to the Mohr-Coulomb criterion in compression and Galileo-Rankine in tension was assumed. For steel, an elastic-perfectly plastic law with the Von Mises failure criterion was adopted instead. The structure is considered fixed at the base, as assumed during the design phase, since inspections did not reveal differential settlements. The towers were subjected to a load combination that takes into account self-weight, wind, and thermal gradient, which is increased step-by-step until collapse is reached. The overall model counts approximately 10,000 nodes and 60,000 degrees of freedom. This highly accurate modeling allowed for:
Optimizing rehabilitation strategies, ensuring that selected interventions address the most critical vulnerabilities without significantly increasing the overall mass.
Evaluating structural safety margins, identifying the towers at the highest risk of collapse.
Key Rehabilitation Measures
The rehabilitation interventions hypothesized and accounted for in the FE model are the following:
- Internal Shell Restoration: A 1.5 cm layer of high-strength waterproof mortar was applied to restore the original waterproof layer and the protection of the reinforcement bars.
- External Shell Reinforcement: The upper 15 meters of the towers were stiffened with Carbon Fiber Reinforced Polymer (CFRP) laminates, significantly reducing wind-induced ovalization.
- Chemical Protection: The internal surface was coated with acrylic paint to protect against steam-induced degradation.
Results
I risultati dell’analisi hanno dimostrato la vulnerabilità di tali strutture nei confronti, in particolare, di vento e carico da temperatura.
Specifically, the most severe effect consists of the ovalization of the tower, which produces an adverse flexural state.
The analyses highlighted that the overall behavior of the structure is linear under service conditions, followed by non-linear behavior due to the spreading of cracks in the concrete under tension. Near collapse, ovalization occurs at the top of the tower, with horizontal displacements reaching 1–2 m.
In terms of stress, the most critical conditions are generated by anomalous bending states due to wind and temperature, whereas the structure should ideally exhibit membrane behavior.
For the reinforced towers, the analyses allowed for the determination of the distribution of tangential and vertical stresses along the thickness for 4 levels (base, 1/3 total height, 2/3 total height – throat -, top), under service load conditions.
It is therefore possible to observe how a portion of the mesh reaches tensile strength (estimated at 1.2-1.5 MPa) on the internal face, while the external face is in compression. Furthermore, the discontinuity in the stress distribution highlights the presence of stiffness changes induced by damage/cracking.
The FE model, updated with the reinforcement interventions, allowed for the appreciation of an increase in global stiffness and a reduction in deformations, ensuring long-term stability.
Specifically, the main results obtained are:
- Significantly increased safety margins, with post-rehabilitation collapse loads reaching 1.4-1.5 times the operating loads, compared to 1.1-1.2 times in the most deteriorated towers before the intervention.
- A five-fold reduction in ovalization effects, mitigating one of the primary failure risks.
- A controlled cracking pattern, with rehabilitation measures that prevent further widespread cracking under operational conditions (see Figures 6 and 7).
- Minimal additional mass, ensuring that foundations and existing supporting elements are not affected.
The analyses carried out with DIANA thus allow for the confirmation that the hypothesized rehabilitation plan enables the preservation of the towers’ operational capacities.
Conclusioni
This case study highlights the potential of non-linear finite element modeling in guiding infrastructure rehabilitation choices. With DIANA, engineers were able to extend the useful life of critical structures without excessive reconstruction costs, demonstrating the feasibility of targeted structural rehabilitation and the importance of finite element analysis in managing aging infrastructure.
While industrial plants worldwide face similar challenges with the deterioration of concrete structures, FE-based rehabilitation offers a cost-effective, efficient, and sustainable solution to keep critical infrastructure operational for decades to come.
– Ing. Edoardo Nagliati (e.nagliati@2si.it) –
Taken from FE guided structural rehabilitation of cooling towers (P. Dalmagioni – Former ENEL.HYDRO – B.U. ISMES, Seriate, Italy, now QUALITALIA-CONTROLLO TECNICO, Milan, Italy, and R. Pellegrini – ENEL.HYDRO – B.U. ISMES, Seriate, Italy); the article can be requested here
Conducting Effective Cooling Tower Rehabilitation With DIANA – DIANA FEA