# Structural Safety Analysis for an Oscillating Water Column Wave Power Conversion System Installed in Caisson Structure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Development of an Oscillating Water Column (OWC) Wave Energy Converter

#### 1.2. Objectives of the Study

## 2. Analytical Model and Environmental Forces

#### 2.1. Analytical Model of the Structure

#### 2.2. Environmental Forces

_{b}is the water depth at a distance of five times of significant wave-height away from the caisson structure.

_{3}is presented as

## 3. Mechanic Analysis of Structural Safety

#### 3.1. Global Structural Analysis

^{2}), elastic modulus of concrete: Ec = 30 (kN/mm

^{2}), and the elastic modulus for the steel: Es = 290 (kN/mm

^{2}) according to the ACI code for the structure exposed to an environment with chloride (marine environment) [18].

^{—3}, which is much smaller than the strain allowance for a concrete material 0.003. However, because the location of the largest deformation was at the tip corner of the top, where the chamber of the OWC converter is built-in, a further study of the front wall of the chamber revealed that the strain corresponding to the transverse deformation was close to the allowance of the concrete material. The largest strain that occurred in the front wall was 0.00027 in terms of the thickness 0.60 m of the front wall of the chamber, as shown in the schematic drawing of Figure 2. It is one order smaller than the maximum strain (0.003) allowed for concrete material from the global structural deformation analysis. Therefore, for the global structural analysis of the caisson structure combined with an OWC wave energy converting system, it is quite safe.

#### 3.2. Structural Analysis for the Chamber of OWC Converter

#### 3.2.1. Transverse Deformation for the front Curtain-Wall

#### 3.2.2. Transverse Deformation for the Top Ceiling-Slab

^{—5}m in-plane of the sidewall, and therefore, relative to the height of the sidewall, 11.0 m, the corresponding strain was 0.93 × 10

^{—7}, a value much smaller than 0.003. However, y-direction was in the out-of-plane direction of the ceiling panel and the downward deformation was 0.013488 m. Relative to the thickness of the ceiling slab, 0.5 m, the corresponding strain in the out-of-plane direction was 0.026976, which is a value well over the allowed capacity for the concrete strain.

#### 3.2.3. Transverse Deformation for the Side-Wall

#### 3.2.4. Discussions on the Deformation of Chamber Members

## 4. Evaluation of Air-pressure in the Chamber during the Operation of Wave Energy Conversion

#### 4.1. Theorem of Fluid Mechanics Applied in the Study

_{eff}is the effective viscosity, and p’ is the revised pressure. The effective viscosity and the revised pressure can be presented as

_{t}is the viscosity of the turbulence, which according to the assumption of k-ε model, is related to the dynamic energy and the dissipation of the dynamic energy as presented as

#### 4.2. Analysis of Wave-Induced Air Pressure in the Chamber

^{2}or 31.46 MPa downward (negatively) during the operation of the OWC system. It is small and about 1/10 of the designed allowed pressure that may exert on the ceiling slab. The largest pressure occurred at the corner of the ceiling-slab, where the separation-wall could also provide the tension resistance to the slab. However, even without a wall to brace the ceiling-slab, it could still hold the pressure occurs during a regular operation of OWC system subjected to a wave of 10-year return period. The concern will be more on the issue of fatigue, which was not analyzed in this study since the direction of the pressure on the ceiling slab was applied alternatively and continuously.

## 5. Conclusions

- (1)
- According to the analysis for the structural safety of this study, for the whole structural safety that included both the caisson breakwater and attached OWC system, the deformations induced from the design-wave, which was based on a storm-wave of 50-year return period, was under the capacity of the concrete material.
- (2)
- The second part analysis of the structural safety, particularly focused on the air-chamber of the OWC converter, where the maximum deformation occurred transversely at the ceiling-slab of the air-chamber for the OWC converter, whereas the front curtain wall subjected to wave-impact directly would also deform greatly, but not so significantly. The developed strains for both the ceiling-slab and the front curtain-wall were well over the strain limit for a concrete material and therefore, when the chamber structure was subjected to a wave close to the designed storm-wave as utilized in the analysis, a major damage may occur on both the ceiling-slab and the front curtain-wall.
- (3)
- According to the study of the air-pressure induced by the heave motion of the waves in the chamber, the pressure was small and would not significantly influence the structural safety of the OWC chamber attached to a caisson structure.
- (4)
- It is concluded that when the OWC is attached to a traditional breakwater structure, the location will be an important factor to decide the performance of energy converting efficiency. To design an OWC structure that may sustain a storm wave of 50-year return period could be expensive. In terms of economic consideration, as long as the damage of the associated structure would not affect the structural safety and operation of the main structure, a design-wave based on a storm of shorter return period should be considered.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Side view of a caisson structure with OWC converter (redrawn after Chiu et al. [20]).

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**MDPI and ACS Style**

Lee, H.H.; Wu, T.-Y.; Lin, C.-Y.; Chiu, Y.-F. Structural Safety Analysis for an Oscillating Water Column Wave Power Conversion System Installed in Caisson Structure. *J. Mar. Sci. Eng.* **2020**, *8*, 506.
https://doi.org/10.3390/jmse8070506

**AMA Style**

Lee HH, Wu T-Y, Lin C-Y, Chiu Y-F. Structural Safety Analysis for an Oscillating Water Column Wave Power Conversion System Installed in Caisson Structure. *Journal of Marine Science and Engineering*. 2020; 8(7):506.
https://doi.org/10.3390/jmse8070506

**Chicago/Turabian Style**

Lee, Hsien Hua, Thung-Yeh Wu, Chung-You Lin, and Yung-Fang Chiu. 2020. "Structural Safety Analysis for an Oscillating Water Column Wave Power Conversion System Installed in Caisson Structure" *Journal of Marine Science and Engineering* 8, no. 7: 506.
https://doi.org/10.3390/jmse8070506