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Applying the Verified Equivalent Cooling Surface Method in DIANA: Full-Scale Simulation of an Arch Dam Monolith

Recapping the Verification

In Part 1, the newly developed Equivalent Cooling Surface (ECS) method was verified against the conventional Discrete Cooling Coil (DCC) modeling approach using DIANA. The comparative block-scale analysis demonstrated that ECS achieved near-identical temperature predictions with a computational efficiency improvement of more than 11 times, confirming its physical accuracy under adiabatic conditions.

Building on that verified foundation, the research team applied ECS to a real dam construction scenario — the central monolith of a 111 m-high Portuguese arch dam — representing one of the most demanding post-cooling simulations ever performed using DIANA.

Modeling the Arch-Dam Monolith in DIANA

The simulated structure represented the central monolith of the dam, which was cast over a period of 672 days in 60 lifts, each approximately 2 m thick. Every lift incorporated horizontal cooling coils spaced 1.8–2.0 m apart. Cooling operations occurred in three distinct phases — initial, intermediate, and final — using either river or chilled water to maintain the concrete below design temperature thresholds prior to joint grouting.

Two distinct simulation frameworks were developed for comparison in DIANA:

  • DCC model: Over 54 000 8-noded hexahedral elements, with each cooling coil discretized as coupled 1D pipe elements; shown in figure 1.
  • ECS model: Approximately 7 000 solid elements, where each coil plane was represented by equivalent convective surfaces embedded in the solid domain; shown in figure 2.
Figure 1. Finite element mesh of the DCC model: (a) concrete monolith and foundation; (b) discrete cooling coils integrated into the solid mesh.
Figure 2. Finite element mesh of the ECS model: (a) concrete monolith and foundation; (b) internal convective surfaces representing equivalent cooling planes.

The mesh refinement comparison for Lift 5 is presented in Figure 3, highlighting the difference in element density between the ECS and DCC approaches.

Figure 3. Local mesh detail for Lift 5 comparing (a) ECS and (b) DCC discretizations. The ECS model achieves similar resolution with fewer elements by replacing coils with equivalent surfaces

Monitoring and Field Data

To validate the numerical results, temperature data were recorded from ten thermocouples (S1–S10) embedded in the dam during construction. Their positions are shown in Figure 4, distributed vertically from the foundation to the upper lifts to capture both local and global temperature evolution.

Figure 4. Cross-section of the dam monolith indicating thermocouple locations (S1–S10) used for temperature monitoring.

Thermal Loading and Material Properties

Thermal parameters for both the dam concrete and foundation rock were obtained from laboratory testing and literature data. For the concrete, the measured thermal conductivity was 2.6 W m⁻¹ K⁻¹, the specific heat 2087 kJ m⁻³ K⁻¹, and the density 2400 kg m⁻³.

Hydration heat generation was modeled in DIANA using experimentally calibrated activation energies and equivalent age factors, enabling the solver to capture temperature-dependent hydration kinetics during staged construction.

Thermal loading reflected real construction and environmental conditions. Boundary definitions incorporated:

  • Convective–radiative exchange with air, governed by wind-dependent coefficients;
  • Zero-flux interfaces at dam–rock contacts and monolith joints; and
  • Layered resistances for formwork and insulation materials.

Time-varying air temperatures and cooling-water inlet temperatures from site records were applied throughout the simulation. DIANA’s phased-analysis framework synchronized lift casting, formwork removal, and cooling activation with the construction schedule, ensuring thermal history was captured continuously across all stages.

Boundary Conditions and Environmental Inputs

The DIANA models accounted for all relevant environmental and construction factors through four primary boundary types:

  1. Convective–radiative exchange with air, characterized by combined heat transfer coefficients that vary with time and weather.
  2. Adiabatic interfaces representing thermal contact with adjacent monoliths.
  3. Thermal resistance layers modeling formwork and geotextile insulation.
  4. Contact with the rock foundation, represented as a semi-adiabatic interface.

Time-varying environmental inputs — including convection coefficients, wind speed, and air temperature — were applied throughout construction, as shown in Figure 5.

Figure 5. Time evolution of thermal boundary inputs: (a) combined convection–radiation coefficient hcr; (b) daily wind speed vwind; (c) formwork convection coefficient hwf; (d) ambient air temperature Tair.

A representative mapping of these boundaries for construction phase 146 is presented in Figure 6, illustrating DIANA’s ability to manage evolving surface conditions across hundreds of simulation phases.

Figure 6. Thermal boundary assignments for construction phase 146: (a) upstream view of air-exposed boundaries; (b) foundation and insulation layers.

Results and Discussion

Temperature evolutions from all ten sensors (S1–S10) were compared with DIANA’s simulated results for both ECS and DCC models. The ECS model reproduced measured data with high precision, as shown in Figure 7.

Across all sensors, the ECS and DCC curves overlapped closely, with maximum deviations below 3.5 °C. Both models accurately captured hydration-induced temperature rise, the cooling phase, and gradual stabilization once post-cooling ceased.

Figure 7. Comparison between monitored (MON), ECS, and DCC temperatures at sensors S1–S10, with ambient daily temperature (ADT) included for reference.

Spatial temperature distributions further confirmed the ECS model’s accuracy. Figure 8shows temperature contour maps at key construction stages—before, during, and after the cooling phases—comparing ECS and DCC predictions. Both displayed nearly identical thermal gradients and maximum–minimum temperature ranges across the monolith core.

Figure 8. Temperature contour maps at representative stages of cooling: (a) DCC model; (b) ECS model. Both show similar temperature fields and extrema.

The ECS approach required only one-tenth the computational time of DCC, reducing solver runtime while maintaining stable convergence and accurate results—demonstrating that DIANA’s implementation of ECS achieves an optimal balance between computational efficiency and modeling fidelity.

Conclusion

The full-scale application confirms that the Equivalent Cooling Surface (ECS) method, implemented in DIANA, can reliably simulate temperature evolution in massive concrete structures with remarkable efficiency.

By transforming discrete cooling networks into internal convective boundaries, DIANA enables engineers to perform high-resolution, multi-phase thermal simulations that align closely with field measurements while remaining computationally feasible.

This study bridges the gap between research verification and real-world engineering practice — showing how DIANA allows the same physically grounded formulation to scale seamlessly from laboratory blocks to entire dam monoliths.

Together, the verification and application studies establish ECS as a dependable tool for modern dam design, supporting more efficient construction workflows and improved control of thermal cracking risks.

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