EASY-TANK: Automated Finite Element Modeling and Optimization of Underground Reinforced Concrete Tanks

Introduction

Underground reinforced concrete tanks are among the most common structures encountered in industrial, infrastructure, water treatment, wastewater treatment, fuel storage, and utility projects. Despite their apparent simplicity, their structural behavior can be surprisingly complex.

A typical underground tank consists of:

- Base slab

- Side walls

- Top slab

- Internal partitions

- Pile-supported foundation system

- Soil and groundwater loading

The interaction between these components often requires finite element analysis (FEM) to obtain realistic internal forces and deformations.

In commercial FEM software, engineers must manually create geometry, define mesh density, insert supports, assign loads, generate combinations, run staged construction analysis, and review results. While this process is manageable for a single project, it becomes repetitive and time-consuming when multiple design iterations are required.

To address this challenge, we developed EASY-TANK, a specialized finite element modeling and optimization tool for rectangular underground tanks.

The philosophy behind EASY-TANK is simple:

> Engineers should focus on engineering decisions, not repetitive model preparation.

Instead of manually constructing FEM models, users only provide a limited set of engineering parameters such as tank dimensions, wall thicknesses, pile locations, material properties, and loading conditions. The software automatically generates the complete finite element model, performs analysis, and can further optimize the structural dimensions.

This significantly reduces modeling effort while maintaining engineering rigor.

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Reissner-Mindlin Shell Formulation

Why Reissner-Mindlin Shell?

Underground tanks typically have relatively thick slabs and walls compared with conventional building floor systems.

For such structures:

- Transverse shear deformation becomes important.

- Classical thin-shell theory may underestimate deflections.

- Thick slab behavior must be captured.

For these reasons, EASY-TANK employs a Reissner-Mindlin (RM) shell formulation.

The element contains:

- Membrane behavior

- Plate bending behavior

- Transverse shear behavior

with nodal degrees of freedom:

- u = translation in X

- v = translation in Y

- w = translation in Z

- θx = rotation about X

- θy = rotation about Y

- θz = drilling rotation

The formulation is particularly suitable for reinforced concrete tank structures where both membrane and bending actions contribute significantly to the overall response.

Drilling Degree of Freedom Stabilization

One challenge in shell finite elements is the presence of the drilling degree of freedom:

θz

This rotational degree of freedom does not possess a natural strain energy term in standard shell formulations.

Without treatment, the element stiffness matrix becomes rank deficient, leading to numerical instability and singular global stiffness matrices.

To overcome this issue, EASY-TANK introduces a stabilization mechanism through a small artificial drilling stiffness.

Conceptually:

Kdrill = α

α = small stabilization coefficient

The stabilization stiffness is intentionally chosen to be several orders of magnitude smaller than the physical bending stiffness.

As a result:

- Numerical stability is achieved.

- Matrix singularities are avoided.

- Structural response remains essentially unaffected.

This technique is widely used in practical shell finite element implementations and provides a robust solution for large-scale shell models.

Automated Stage Construction Analysis

Underground tanks experience different structural conditions during construction and operation.

A single analysis often fails to capture these changing load paths.

EASY-TANK therefore supports staged construction analysis.

## Stage 1 – Empty Tank Construction Condition

The first stage represents the condition immediately after construction.

Typical loads include:

- Self-weight of slabs

- Self-weight of walls

- Backfill soil pressure

- Groundwater pressure

No internal liquid pressure is applied.

This stage is important because:

- Wall bending moments may be governed by external soil pressure.

- Base slab uplift may occur due to groundwater.

- Construction stresses may exceed operational stresses in some regions.

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## Stage 2 – Operational Condition

The second stage represents the tank in service.

Additional loads include:

- Internal liquid pressure

- Stored water or fuel weight

- Hydrostatic loading on walls

- Hydrostatic loading on base slab

The final response is obtained by combining the stress history from Stage 1 and Stage 2.

This approach more accurately represents actual structural behavior than applying all loads simultaneously.

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Adaptive Mesh Generation and Pile Node Insertion

One common difficulty in automated tank modeling is handling pile-supported foundations.

Pile locations are often irregular and do not coincide with the initial shell mesh.

If pile supports are simply connected to the nearest node:

- Support eccentricities occur.

- Load transfer errors increase.

- Local force concentrations become inaccurate.

To solve this problem, EASY-TANK automatically inserts mesh lines passing through pile locations.

The process is:

1. Generate base structured mesh.

2. Extract pile coordinates.

3. Insert additional mesh lines at pile X and Y locations.

4. Rebuild mesh topology.

5. Regenerate shell elements.

As a result:

- Every pile coincides with a shell node.

- Support springs connect directly to structural nodes.

- No interpolation or rigid-link approximation is required.

This technique significantly improves support modeling accuracy while preserving an automated workflow.

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Design Optimization

Beyond finite element analysis, EASY-TANK incorporates numerical optimization.

Traditional design typically follows:

1. Assume dimensions.

2. Analyze.

3. Check stresses.

4. Revise dimensions.

5. Repeat.

This trial-and-error process can require many iterations.

Optimization automates this procedure.

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Design Variables

Typical optimization variables include:

- Base slab thickness

- Wall thickness

- Top slab thickness

- Internal wall thickness

- Concrete strength

- Pile arrangement parameters

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Objective Function

The primary objective is minimizing material volume.

Mathematically:

Minimize

V = Σ(Ai × ti)

where:

- Ai = structural component area

- ti = component thickness

For reinforced concrete tanks, minimizing volume generally correlates well with minimizing cost.

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Constraints

Optimization is performed subject to:

### Strength Constraints

- Flexural capacity

- Shear capacity

- Punching shear

- Bearing pressure

### Serviceability Constraints

- Deflection limits

- Crack control requirements

### Geometric Constraints

- Minimum thickness

- Practical construction limits

Only solutions satisfying all constraints are accepted.

The optimization engine then searches for the most economical design configuration.

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Future Extensions

Although EASY-TANK already automates FEM generation and optimization, several future developments are planned.

## Reinforcement Optimization

Current optimization focuses primarily on geometry.

Future versions may optimize:

- Bar spacing

- Bar diameter

- Layer arrangement

to minimize total reinforcement weight.

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## Soil-Structure Interaction

Future developments may include:

- Winkler soil springs

- Continuum soil models

- Nonlinear soil behavior

for improved foundation modeling.

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## Construction Sequence Simulation

More advanced staging may include:

- Excavation sequence

- Dewatering effects

- Progressive backfilling

- Sequential wall casting

allowing realistic construction simulations.

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## Reliability-Based Design

Future versions may incorporate:

- Probabilistic loading

- Material uncertainty

- Reliability indices

- Risk-based optimization

to provide more rational designs than deterministic approaches.

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## AI-Assisted Design Automation

One long-term vision for EASY-TANK is integration with AI-driven engineering workflows.

Potential capabilities include:

- Automatic design review

- Intelligent mesh control

- Optimization strategy selection

- Automatic report generation

- Design recommendation systems

This transforms the software from a numerical solver into an engineering decision-support platform.

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Conclusion

EASY-TANK demonstrates how specialized finite element automation can significantly improve engineering productivity.

By combining:

- Automated Reissner-Mindlin shell modeling

- Robust drilling DOF stabilization

- Adaptive pile-node meshing

- Staged construction analysis

- Numerical optimization

the software allows engineers to focus on design decisions rather than repetitive FEM model preparation.

As the platform evolves, future integration of advanced optimization, soil-structure interaction, reliability analysis, and AI-assisted decision making will further enhance its capabilities.

The ultimate goal is not merely to analyze underground tanks faster, but to create a practical engineering environment where analysis, design, and optimization operate seamlessly within a single workflow.