Concrete modelled using random elements

Lead Research Organisation: University of Bath
Department Name: Architecture and Civil Engineering


Cement manufacture accounts for about 5% of global carbon dioxide emissions, the single largest contribution of any man-made material. Despite this, research has shown that concrete is generally inefficiently used in the built environment.

This fellowship will look to reduce the global environmental impact of concrete construction through a new method for the analysis of reinforced concrete structures that is well suited to producing the optimised designs that have the potential to significantly reduce material consumption. The new analysis method will be considered alongside practical construction processes, building on previous work by Dr Orr in this field, thus ensuring that the computationally optimised form can actually be built, and the research adopted, in industry.

Most existing computational methods poorly predict the real behaviour of concrete structures, because their underlying mathematics assumes that the structure being analysed remains continuous as it deforms, yet a fundamental property of concrete is that it cracks (i.e. it does not remain continuous as it deforms). In contrast to finite element methods, this fellowship will develop a meshfree analysis process for concrete based on 'peridynamics'. The term 'peridynamic' (from 'near' and 'force') was coined by Dr Silling (see also statements of support) to describe meshfree analysis methods in solids.

This new approach does not presume a continuous displacement field and instead models solid materials as a collection of particles held together by tiny forces, the value of which is a function of each particle's relative position. Displacement of a particle follows Newton's laws of motion, and is well suited to reinforced concrete since: 1) concrete really is a random arrangement of cement and aggregate particles; 2) failure is governed by tensile strain criteria, which is ideal as the only real way that concrete fails is in tension (all other failure modes in everyday design situations are a consequence of tensile failure) and the model can therefore accurately predict behaviour, and 3) since the elements fail progressively in tension, the peridynamic approach automatically models cracking behaviour, which is extremely difficult to model conventionally.

A variety of force-displacement relationships can be defined to model the concrete, the reinforcement, and the reinforcement-concrete bond that together define the overall material response.

The approach models the material as a massively redundant three-dimensional truss in which the randomly arranged particles are interconnected by elements of varying length. Although an optimal 'element density' has not yet been determined (see Section 2.4.1 in the case for support) proof of concept work has used tens of millions of particles and hundreds of millions of elements per cubic metre of concrete. From the simple rules and properties applied to these elements, all the complex behaviour of concrete can be predicted.

Individual element definitions will be determined by laboratory tests and computational analysis, with both historic and new test data utilised. Crucially, the model has been shown in proof-of-concept work to be able to predict the cracking behaviour of concrete, overcoming a key computational challenge.

Optimisation routines, in which material is placed only where it is needed, will then be integrated with the new analysis model to design low-carbon concrete structures. Consideration of the practical construction methods will also be given, building on previous work in this area by Dr Orr. The designs that result from such optimisation processes will have unconventional but completely buildable geometries (as evidenced in Dr Orr's previous work) - making them ideal for analysis using the proposed random elements approach.

Planned Impact

Optimised beams and structures can be built, but their geometries mean that they are not as stiff as prismatic elements. Therefore cracking is a crucially important phenomenon from even moderate loads for geometrically complex structures. Finite element approaches are not appropriate to deal with this behaviour. The impact of this fellowship will be to deliver an entirely new analysis method, providing a much needed step change in the way that concrete is used as a construction material.

The impacts of this fellowship are found in its potential to facilitate the design of truly low-carbon concrete structures, whose form reflects their performance requirements. Such an approach is crucial if we are to meet our carbon reduction targets. The research outcomes will therefore directly impact all users of the built environment.

Within industry, this research has benefits and applications for architects, building contractors and structural engineers. A new understanding of the behaviour of concrete structures of any geometry will be directly relevant to design codes of practice. University of Bath visiting Professor Denton, in his role as chair of the European Committee CEN TC250, will assist in providing the forum needed to make this impact a reality. The new approaches to material analysis achieved through the proposed material model, will ultimately feed into and inform industry standard design tools. This fellowship will facilitate a fundamental change in the structural design of concrete.

In the short term, members of the public will see the construction of new forms of concrete structure that this research enables, with part of the fellowship building specifically on Dr Orr's previous work in the construction of optimised beams.

Savings in energy use that result from the fellowship outputs will positively contribute to tackling climate change and meeting UK government targets for 2025 (33% reduction in initial and whole life cost of assets and a 50% reduction in greenhouse gas emissions in the built environment) and for 2050 (80% reduction in emissions). Both sets of targets are ambitious and will require the realisation of breakthrough technologies to meet them.

Secondary school children will be specifically targeted as part of the impact pathways to meet the EPSRC fellowship goals of inspiring future engineers and looking beyond the pure scientific research of the fellowship to long term engineering leadership from Dr Orr. The public will also engage with the research through the project website and free to attend public events.

Through the support of industry, this fellowship will enhance the knowledge and skills of industrial partners by providing them with new design, analysis and construction methods. The impact pathways include four events specifically designed to help achieve this.

A 'roadshow' to seven international cities, supported by the global network of the Institution of Structural Engineers, will target university and school-age students, as well as interested members of the public in a series of workshops and seminar presentations by Dr Orr. This will allow the fellowship to develop and engage with a new research network.

A key area of impact of this fellowship will be in national, and potentially international, policy making. Simple amendments to design codes can encourage optimisation (for example by specifying minimum AND maximum performance requirements for new structures). The fellowship outputs and test data will provide confidence in these policy decisions which could make a significant difference to the contribution of the built environment to carbon emissions. Dr Orr will work with the University of Bath Institute for Policy Research and the Institution of Structural Engineers on the preparation of short briefing papers for the Department of Energy and Climate Change, the Department of Communities and Local Government and the Department for Business, Innovation and Skills.
Description Methodologies for modelling concrete using peridynamics.
Identification of key technical challenges to overcome.
Use of parallelisation (MPI) to enhance computation time
Importance of cement savings that optimisation may enable
Exploitation Route Use of code developed to date (C++) can be taken on and developed further.
Design of optimised concrete structures.
Design of complex joints and connections in concrete structures
Sectors Construction,Energy,Environment,Transport

Title Data supporting research paper Shear behaviour of fabric formed T beams reinforced using W-FRP 
Type Of Material Database/Collection of data 
Year Produced 2020 
Provided To Others? Yes  
Title Dataset for An Explicit Method for Simulation of Cracking Structures Based on Peridynamic Theory 
Description Conference paper at 12th World Congress on Computational Mechanics 
Type Of Material Database/Collection of data 
Year Produced 2016 
Provided To Others? Yes  
Title Raw numerical output "Predicting shear failure in reinforced concrete members using a three-dimensional peridynamic framework" 
Description Corresponding Journal Paper: Predicting shear failure in reinforced concrete members using a three-dimensional peridynamic framework These files contain the raw numerical output used to create Figures 12 to 18. Load-Deflection Graphs: - each file contains the following data in column format [Load (N), Deflection (mm)] >> Stuttgart_Beam_3_normal_mesh.txt >> Stuttgart_Beam_3_fine_mesh.txt >> Stuttgart_Beam_5_normal_mesh.txt >> Stuttgart_Beam_5_fine_mesh.txt >> Stuttgart_Beam_7_normal_mesh.txt >> Stuttgart_Beam_7_fine_mesh.txt Numerical Fracture Patterns: - each file contains the following data in column format [Node ID, undeformed coordinates (XYZ), deformed coordinates (XYZ), damage] >> Stuttgart_Beam_1_normal_mesh_damage.txt >> Stuttgart_Beam_2_normal_mesh_damage.txt >> Stuttgart_Beam_3_normal_mesh_damage.txt >> Stuttgart_Beam_3_fine_mesh_damage.txt >> Stuttgart_Beam_4_normal_mesh_damage.txt >> Stuttgart_Beam_5_normal_mesh_damage.txt >> Stuttgart_Beam_5_fine_mesh_damage.txt >> Stuttgart_Beam_6_normal_mesh_damage.txt >> Stuttgart_Beam_7_normal_mesh_damage.txt >> Stuttgart_Beam_7_fine_mesh_damage.txt >> Stuttgart_Beam_8_normal_mesh_damage.txt >> Stuttgart_Beam_10_normal_mesh_damage.txt 
Type Of Material Database/Collection of data 
Year Produced 2021 
Provided To Others? Yes  
Description University Visit, MIT 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Undergraduate students
Results and Impact 40 engineering students at MIT attended lecture by Dr Orr and engaged in interesting discussions. Subsequent contact with a number of students regarding research in the UK and specifically Undergraduate dissertation projects.
Year(s) Of Engagement Activity 2015
Description Webinar hosted by Trimble, on the topic of embodied carbon 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Webinar hosted by Trimble "why embodied carbon matters and why structural engineers play a crucial role in achieving reductions". Panel discussion covering many outputs from research grants, and how they relate to professional practice.
Year(s) Of Engagement Activity 2021