Predicting The Maximum Ocean Depths For Submerged Concrete Structures
Authors: Highberg Roy Scott , Haynes Harvey H. 
Published: December 2007

Abstract
This paper presents equations to predict implosion (collapse) of thick-walled concrete spherical and cylindrical structures subjected to hydrostatic pressure loading. For the spherical structures, plain concrete and steel reinforced concrete spheres are considered. The reinforcement consists of steel liners located on the inside, outside and both inside and outside of the concrete wall. For cylindrical structures, only plain concrete is considered. Figures are plain concrete is considered. Figures are presented that can be used as design charts. Example presented that can be used as design charts. Example structures, with wall thickness to outside diameter ratios defined by neutral buoyancy, are analyzed to give their maximum operating depth in the ocean.

Introduction
Commercial enterprise is looking at large undersea structures to service the offshore oil industry as it moves into deeper water depths. Quite appropriately, concrete structures are being considered for such applications as production structures, manifold structures, manned production structures, manifold structures, manned habitats, and oil storage containers. At the deep depths, hydrostatic pressure is the princip load to be resisted by the structure. Thick-walled concrete structures are required to meet the loading condition. The use of thick-walled structures has both desirable and undesirable aspects. For thick-walled concrete structures, material failure defines the implosion pressure (collapse pressure), thus full utilization of the strength of the construction material is achieved. In contrast, thin-walled structures have instability (buckling) dominated failure; here, the material is not stressed to its ultimate capacity. The undesirable aspect is that thick-walled structures are heavy. Using today's construction technology, when a structure becomes too heavy to float, the resulting wall-thickness-to-diameter ratio defines the maximum collapse depth.
The state of the art approach for the construction of massive offshore concrete structures is to build the structure in protected waters and then float it to the offshore location. In the future, methods may be developed to build massive structures on the seafloor. At that time, it may be desirable to build structures which are designed for negative buoyancy. Deeper depths for concrete structures will be an outcome. The purpose of the paper is to present a simplified design purpose of the paper is to present a simplified design approach to predict the implosion strength of thick-walled concrete spheres and cylinders. The end objective is to summarize information on the maximum depth in the ocean that pressure-resistant concrete structures are likely to be used.

THICK-WALLED SPHERES
Thick-walled spheres are defined as those spheres having a geometry in which material failure controls the implosion pressure. For concrete spheres this geometry occurs at a t/Do of about 0.02.
The design approach for predicting implosion of thick-walled spheres is based on the average wall stress at implosion. From implosion test results it was apparent that spheres withstood wall stresses at implosion, sigma im, greater than the uniaxial compressive strength, f'c, of the concrete. The average wall stress was used because observed crack development in the wall prior to implosion resulted in redistribution of stresses across the thickness. The average wall stress at implosion is expressed as:
(1)
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