Introduction
At the conclusion of the author’s 2008 BEng thesis, the section’ Recommendations for Further Study’ scheduled tasks as follows;
1 Understand derivation of PCA tables
2 Translation of Documents from German Publications
3. Follow up further references
4. Create a design method from scratch using basic shell theory
5. Examination of the effect of deflection in the base slab
6. Investigation into the effects of prestressing on deflection characteristics.
The conclusion of this work is presented here, noting the question set by my professor in now has a different answer. Can cylindrical concrete tank load analysis be carried out without using coefficients? In 2008, the answer was no, but on completing the tasks above, it is now possible to derive from first principle geometric tension analysis.
Project 1 and 2 are substantially complete. Project 3 brings the theory into practice.
Rationale and Background
The design of reinforced concrete cylindrical tanks, silos and containment structures in civil engineering continues to rely heavily on empirical coefficient tables, specifically Domel & Gogate, Circular Concrete Tanks without Prestressing, Portland Cement Association, 1993. These tables, originally issued in 1942, while operationally useful, lack clear and traceable attribution to their original theoretical source — Viktor Lewe’s 1915 thin-shell matrix analysis. The result is a long-standing disconnect between established practice and first-principles geometric understanding of key mechanisms such as ring tension and dilatancy.
This gap has practical consequences. Designs tend to be conservative, leading to higher material consumption and embodied carbon than necessary. More importantly, safety factors are not always fully visible or controllable from fundamental geometry, particularly in critical or ageing infrastructure. The author first identified this referencing problem, and reliance on coefficients in 2008. Subsequent independent work has developed a geometric first-principles extension of Lewe’s approach replacing the tables with an explicit geometric equation, to include the ring tension component. However, this body of knowledge has remained outside mainstream academic and professional discourse.
The civil engineering profession possesses the capability to move beyond purely empirical methods. A transparent geometric mechanics framework offers the potential for more efficient, sustainable and safer design of cylindrical shells, while improving the visibility of safety margins in high-consequence applications, and enhanced understanding of aging viscoelasticity. This portfolio brings together the historical audit, theoretical development and experimental validation needed to establish and test that framework.
Premise
Within civil engineering exists the technological and intellectual capability to design and construct more sustainable, materially efficient and safer thin cylindrical concrete structures through the application of first-principles geometric mechanics — extending and validating Viktor Lewe’s 1915 theory — thereby reducing embodied carbon, enhancing safety factor visibility, and improving performance in both routine and critical applications.
This PhD by portfolio is presented to both correct the scholarly record, ensuring that credit for original work is attributed correctly, and to offer enhancements to design that could lead to significant cost savings, and enhanced visibility of the performance and safety of aging structures, particularly nuclear containment vessels.
Project 1: Historical Provenance & State of Practice Audit
1 Title of the Research Project
Audit of Provenance Gaps in Reinforced Concrete Cylindrical Shell Design Guidance (Lewe 1915 Reference Chain)
2 Introduction
Reinforced concrete cylindrical tanks and containment structures continue to be designed using empirical coefficient tables whose original theoretical foundation is incompletely referenced in modern guidance. Viktor Lewe’s 1915 thin-shell matrix analysis is the primary source of these tables, yet this connection is not acknowledged. The resulting lack of first-principles visibility affects how safety factors are understood and applied, particularly in critical infrastructure.
3 Research Aim and Specific Objectives
Aim: To establish the broken provenance of current design guidance for concrete cylindrical shells and to identify the implications for safety factor transparency and engineering practice.
Objectives
- Document the various historical references and theoretical links from existing engineering practice to Viktor Lewe’s 1915 contribution (specifically the paper in Handbuch fur Eisen und Beton (and its subsequent development in 1923), his first Engineering Dissertation, and also his 1906 Theoretical Physics dissertation) to the 1993 PCA guidance (thesis completed 2008, to be submitted as reference).
Summary to be submitted as introduction to include mapping the restored reference chain across major national and international standards and publications. E.g Batty & Westbrook, Reynolds & Steedman.
- Document and translate key elements of Lewe’s 1915 contribution and trace its relationship to later PCA guidance through 1942=>1965=>1993 (work completed between 2023 and 2025). Original German language Documents with full translations to be submitted as References.
- Identify specific theoretical gaps in mechanistic understanding of geometric effects such as ring tension and dilatancy.
- Using Lewe’s theory produce coefficient tables directly to compare to those in PCA 1993, to demonstrate predicted 18-20% conservatism is already applied in the existing tables.
These objectives are specific, measurable through documented gaps, achievable using existing thesis material supplemented by targeted archival work and relevant to both sustainability and safety.
4 Literature Review
Modern design guidance (PCA documents, Eurocode 2, ACI standards) presents coefficient tables as empirical without clear linkage to Lewe’s original matrix work. Earlier secondary sources (e.g. Carpenter 1927) hint at the connection, but this has not been systematically examined in contemporary literature. The gap lies in the absence of a modern critical audit that connects historical theory to current practice and highlights the consequences for first-principles understanding.
5 Research Methodology
Archival and documentary research, including analysis of primary sources (Lewe 1915, related Handbuch contributions, PCA editions) and verification against ICE library records from 2008. Qualitative gap analysis will be used to assess the impact on engineering understanding and practice.
6 Expected Results
- A clear provenance map demonstrating the reference break.
- Identification of specific gaps in geometric/mechanistic understanding.
- A foundational document that justifies and contextualises the theoretical and experimental work in Projects 2 and 3.
7 Research Plan and Timeline
Substantially complete (2008, 2023–2025). Final analysis, mapping and writing: 3–6 months from registration.
8 Conclusions
This project establishes the historical and professional context for the portfolio. It demonstrates a long-standing gap in foundational mechanics for concrete shells and provides the justification for the geometric extension and experimental validation that follow.
9 References
To be updated but already substantially complete, see link.
Project 2: Geometric First-Principles Extension of Lewe
1 Title of the Research Project
Development of the Lewe Disc Model – Ring-Tension Judder Wave and Augmented Hoop-Stress Equation
2 Introduction
Building directly on the provenance gap identified in Project 1, this project develops a transparent geometric mechanics framework by extending Viktor Lewe’s 1915 matrix approach. Where Lewe treats the tank as ultra-thin wall, the proposed treats the cylinder wall as an infinitely thin 2D ring/disc and reveals ring tension as a circumferential judder wave, introducing geometric restoring forces that are not explicitly captured in conventional empirical methods.
3 Research Aim and Specific Objectives
Aim: To derive and formalise a first-principles geometric mechanics framework for thin cylindrical shells that restores visibility of key mechanisms and quantifies potential benefits for design.
Objectives
- Formulate the Lewe Disc concept and the augmented hoop-stress equation.
- Develop the associated pi-tensor mapping and 3-6-9 harmonic progression.
- Demonstrate the potential for significant material savings while maintaining or improving structural stability and safety factor visibility.
These objectives are specific and measurable through derived equations and quantitative comparisons, achievable with existing notebook derivations and supporting calculations, directly relevant to sustainable design, and time-bound within the early phase of the programme.
4 Literature Review
Lewe’s 1915/1923 matrix work provides the original geometric foundation. Modern approaches rely predominantly on empirical coefficients or finite element analysis, which often obscures explicit geometric contributions such as ring tension and dilatancy. The literature gap lies in the absence of a closed-form, first-principles extension that makes these mechanisms transparent and usable in everyday engineering practice.
5 Research Methodology
Analytical derivation from first principles, supported by force-logic diagrams and geometric (pi-tensor) mappings. Validation is achieved through direct comparison with existing coefficient-based solutions and established structural behaviour.
6 Expected Results
- The augmented hoop-stress equation incorporating ring-tension effects.
- A coherent pi-tensor geometric framework.
- Quantitative evidence of material efficiency gains (approximately 18–20% in relevant cases) alongside improved visibility of safety factors.
7 Research Plan and Timeline
Core derivations and mappings substantially complete (2012–2025). Refinement, documentation and preparation of theoretical outputs: 6–9 months from registration.
8 Conclusions
This project provides the original theoretical core of the portfolio. It fills the mechanistic gap identified in Project 1 and supplies the transparent geometric tools that are tested and applied in Project 3.
9 References
As above, but supplemented by selected recent papers on first-principles shell theory and confinement approaches in structural mechanics as appropriate.
Project 3: Application to Sustainability, Safety & Experimental Validation
1 Title of the Research Project
Application of Lewe Disc Geometry to Sustainable Concrete Design and Critical Infrastructure – Experimental Validation of Geometric Confinement
2 Introduction
This project applies the geometric framework developed in Project 2 to practical questions of sustainability and safety in civil engineering, with particular attention to critical structures such as containment vessels. It addresses the potential incompleteness in current risk assessment arising from limited first-principles visibility and proposes a clear, falsifiable experiment to test the predicted geometric behaviour.
3 Research Aim and Specific Objectives
Aim: To demonstrate the practical benefits of the geometric framework for sustainable design and to provide empirical validation through a targeted, falsifiable experiment.
Objectives
- Quantify potential material and carbon savings and improvements in safety factor visibility for cylindrical structures.
- Develop a risk-assessment perspective relevant to high-consequence applications such as nuclear containment.
- Design and execute a proof-of-concept experiment to test whether the predicted pulsatile/geometric behaviour occurs under external elastic confinement.
These objectives are specific, measurable through calculations and experimental data, achievable in staged laboratory work, relevant to both sustainability and safety priorities, and time-bound within the registration period.
4 Literature Review
Extensive experimental literature exists on external confinement of concrete cylinders (particularly FRP wrapping), demonstrating improvements in strength and ductility. However, there is no published open testing of the specific geometric confinement and pulsatile response predicted by the Lewe Disc extension, nor its application to the risk assessment of existing or new containment assets. This represents a clear gap that the proposed experiment directly addresses.
5 Research Methodology
The methodology combines analytical application of the geometric framework with a staged experimental programme.
Phase 1 (Proof-of-Concept) uses a super-thin steel cylinder (approximately 0.1–0.3 mm wall thickness, set by limits of practicality through testing). The cylinder is initially held in perfect circular form by a rigid internal former. High-strength elastic bands are then applied under controlled tension in a 3-6-9 harmonic pattern. Once tensioning is complete, the former is removed, leaving the shell held in cylindrical geometry purely by external elastic confinement. Instrumentation includes strain gauges, radial displacement sensors and high-speed video. Controlled internal pressure and low-amplitude excitation are used to observe any pulsatile response.
Subsequent phases can progress to scaled concrete specimens as confidence in the geometric principle is established. The approach is justified as a low-risk, low-cost method of isolating and testing the core geometric mechanism before more complex materials are introduced.
6 Expected Results
- Quantified sustainability benefits (material reduction in the order of 18–20% with maintained stability).
- A risk-assessment perspective highlighting the value of geometric first-principles visibility for critical structures.
- A documented experimental protocol, model design, instrumentation plan and initial test data from Phase 1 (whether pulsatile behaviour is observed or the model is refined).
These outputs provide both practical design insight and empirical evidence to support the theoretical framework.
7 Research Plan and Timeline
Analytical application work is substantially complete (2020–2026). Experiment design, model construction and Phase 1 testing: 6–18 months from registration. Analysis and integration into the portfolio: Year 2.
8 Conclusions
This project translates the theoretical contribution of Project 2 into practical sustainability and safety outcomes. The proposed experiment provides a clear, falsifiable route to empirical validation of the geometric principles. Together, the three projects form a coherent portfolio that restores a neglected foundational theory, develops it rigorously, and subjects it to practical testing — delivering an original contribution to geometric mechanics for concrete shells with direct relevance to sustainable and safe civil engineering practice.
9 References
(To be complied. Forensic compilation of relevant confinement/FRP experimental studies, nuclear containment and risk assessment literature, plus core Lewe and geometric mechanics sources.)
ace-consultancy.uk 