Emerging Technology Report (ETR) The Structural Design of

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DRAFT Working Copy – Not for Circulation August 28, 2018

Emerging Technology Report (ETR)

The Structural Design of Ultra-High Performance Concrete

Chair Secretary Benjamin Graybeal* Charles Kennan Crane

Voting Members ACI 239

Theresa M. Ahlborn* Claus Brix

Eckart R. Buhler Dominique Corvez Nicolas Ginouse Brian H. Green

Katrin Habel

James Milligan John J. Myers

Vic Perry* Carin L. Roberts-Wollman

Surendra P. Shah Kay Wille

Sub-Committee ACI 239C Members

Sriram R. Aaleti Mohammed G. Alnaggar Matthew J. Bandelt Jean-Philippe Charron David Conciatori Rafic El-Helou Liberato Ferrara Bradley W. Foust Philipp Hadl Heidi Helmink

Mo Li Luis Felipe Maya Duque Fatmir Menkulasi Barzin Mobasher Cristopher D. Moen Mohamed Moustafa Gregory Nault Ali Semendary Luca Sorelli Paul White

*Members, Subcommittee 239-C SChair, Subcommittee 239-C

Consulting Members

James K. Hicks Antoine E. Naaman

Larry Rowland

This emerging technology report gives an overview on the Structural Design of Ultra-High Performance Concrete. It briefly introduces these concretes, their properties and design principles for their use. It is not intended to provide mandatory design rules, but rather to serve as a starting point for the structural engineer on understanding design methodologies for this class of materials.

Commented [vp1]: Membership will be updated on day of first ballot

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Content 1.0 Introduction and Scope

1.1 Introduction 1.2 Scope 1.3 Global UHPC Codes, Standards and Guides

2.0 Notation and Definitions 2.1 Notation 2.2 Definitions

3.0 Material Properties 3.1 Mechanical Properties

3.1.1 Compressive behavior 3.1.2 Tensile behavior 3.1.3 Flexural behvior 3.1.4 Shear behavior 3.1.5 Bond behavior

3.2 Durability Properties 3.2.1 Absorption 3.2.2 Salt-scaling and Freeze/Thaw 3.2.3 Permeability 3.2.4 Acid and Sulphate Resistance 3.2.5 Delayed Ettringite Formation 3.2.6 Leaching and Efflorescence 3.2.7 Abrasion 3.2.8 Alkali-Silica Reaction

3.3 Time Dependent Properties 3.3.1 Creep Coefficient 3.3.2 Shrinkage 3.3.3 Thermal Coefficient of Expansion

3.4 Fire Properties 3.5 Other Properties

3.5.1 Fibre-Matrix interaction 3.5.2 Cyclic Strength and Stiffness Degradation 3.5.3 Dynamic Strength 3.5.4 Fatigue Behavior 3.5.5 Property Gradients

4.0 Strength Design Considerations

4.1 Compression and Tension 4.1.1 Compression 4.1.2 Tension

4.2 Flexure 4.3 Combined Axial and Bending 4.4 Shear and Torsion

4.4.1 Shear 4.4.2 Torsion

5.0 Serviceability and Durability Design Considerations 5.1 Serviceability 5.2 Durability

5.2.1 Durability requirements for Exposure Classes and crack width limitations in Reinforced Structures

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5.2.2 Crack width control 5.2.3 Durability under Mechanical load 5.2.4 Durability of cracked elements under Chemical load 5.2.5 Durability of cracked elements in a marine environment 5.2.6 Life Cycle Assessment

5.3 Serviceability 5.3.1 Deflection and camber 5.3.2 Crack control 5.3.3 Vibrations 5.3.4 Stress 5.3.5 Fatigue 5.3.6 Time Dependent Effects 5.3.7 Temperature Effects

6.0 Future Research Needs 7.0 References 8.0 Appendices

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ACI 239C – Structural Design of UHPC

1.0 Introduction and Scope – Vic Perry

1.1 Introduction Ultra-high performance concrete (UHPC) was first introduced into the global construction market in the 1990s, and has seen steady growth since. This relatively new family of concretes has improved strength, ductility and durability when compared to normal and high-performance concretes. In 2015, ACI Committee 239 defined UHPC as concrete that has a specified compressive strength of at least 150 MPa (22,000 psi) with specified durability, tensile ductility and toughness requirements; fibers are generally included to achieve specified requirements. Based on an extensive review of the literature on UHPC globally, this document is a synthesis of this information by a group of UHPC experts, as listed on the title page. This document is not a design standard or guide, but does provide a discussion on design methodologies for the designer. The document also does not provide test methods for the characterization of UHPC but it does discuss options for obtaining the mechanical properties based on test methods available. The characterization of the mechanical properties of UHPC is covered in a separate ETR on the Methods and Materials for UHPC. This Emerging Technology Report on the structural design of UHPC is organized as a designer might use it - by first covering material properties and then showing the use of these properties to design for strength (shear, flexure, and compression), and finally to check for durability and serviceability. The structural design of UHPC discusses the structural limit state predictions that apply to members and systems including multiple materials are discussed. The document also identifies research needs for the development of future documents on UHPC.

1.2 Scope This document covers UHPC with discrete fibers and elements with and without primary reinforcing (rebar or prestressing tendons).This document discusses the use of UHPC that is a cementitious material having a minimum specified strength of 120 MPa, containing discrite fibers for tensile post-cracking ductility with a minimum specified direct tensile strength of 4.0 MPa. Material constitutive properties and design stresses are discussed as design inputs in Section 3. The intended outputs are strength and serviceability predictions at structural scale limit states as presented in Sections 4 and 5, respectively. This ETR integrates national and international experiences with UHPC and utilizes recent experimental and computational research to describe a design basis that advances UHPC design and construction. Structural design considerations for cast-in-place concrete and precast construction methods are noted. But the document does not cover or develop new test methods or construction methods. Information on test methods applicable to UHPC has been developed by ASTM and construction methods applicable to UHPC will be developed by new ACI 239D Sub-Committee (Materials and Methods of Construction for UHPC). However, this ETR references these documents and other international standards, guides and research papers. The ETR references and compares the information from current global codes, standards or guides published by the following agencies and jurisdictions: - American Society of Testing and Materials (ASTM, USA)

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- Swiss Institute of Engineers and Architects (SIA, Switzerland) - French Society of Civil Engineers (AFGC, France) - Japanese Society of Civil Engineers (JSCE, Japan) - Standards Australia (SA, Australia) - Canadian Standards Association (CSA, Canada) - German Committee on Structural Concrete (GCSC, Germany) - Spanish Association of Concrete, Scientific-Technical Committee No. 1 (ACHE, Spain) - Federal Highway Administration (FHWA, USA) Section 6 of this ETR provides research needs to advance UHPC to full codes and standards level. Section 7 provides references.

1.3 Global UHPC Codes, Standards and Guides Since the beginning of the year 2000, global standards organizations, code bodies and professional user groups have developed guidelines, standards and codes for the materials, methods of construction and the structural design of UHPC. The following section covers each of these global documents by briefly highlighting the scope of the document.

1.3.1 American Society of Testing and Materials In July of 2017, the American Society of Testing and Materials published it first document specifically for UHPC. The new publication, ASTM C1856/1856M – 17 “Standard Practice for Fabricating and Testing Specimens of Ultra-High Performance Concrete”, provides procedures for fabricating and testing specimens in the laboratory and the field, using a representative sample of UHPC, for the purpose of determining the properties of the material. The standard practice provides procedures for obtaining compressive strength, flexural strength, static modulus of elasticity, Poisson’s ratio, creep in compression, length change, resistance to abrasion, resistance to freezing and thawing and penetration of chloride ions. This standard practice does not provide direct tensile material properties, which are required to use the tensile properties of UHPC in structural design. In order to determine direct tensile properties an inverse analysis would be required to be used in conjunction with the test procedure for flexural strength. Prior to the publication of this new ASTM C1865/C1856M, owners and users of UHPC had no standard method to confirm if the material properties of the supplied material met the specified properties.

1.3.2 French Standards In the late 1990’s, the French Society of Civil Engineers (Association Française de Génie Civil [AFGC]) began the development of a guide on UHPC. The initial guidelines document published in 2003, was revised and re-issued in 2013. Subsequently in 2016 and 2017, the French Standards Institute (Association Française de Normalisation [AFNOR]) published 2 French standards on UHPC, as follows:

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- NF P 18-710: National addition to Eurocode 2 – Design of concrete structures: specific rules for Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC) – April 16, 2016.

- NF P 18-470: Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC): specifications, performance, production and conformity – 2017.

The French standard NF P 18-470 provides the rules for the selection of raw materials, testing methods and QA/QC requirements to determine the fresh and hardened properties of UHPC. It also provides classifications for different categories of UHPC based on the hardened durability and strength (compression and direct tensile) properties. The standard specifies 5 categories for compression ranging from 130 MPa to 250 MPa and 3 categories for direct tension, covering strain hardening through to strain softening. Additionally, it covers the production (batching, transporting, casting, consolidation and curing) and methods to validate in-situ hardened properties. The French standard NF P 18-710 provides the rules for the structural design of buildings and civil engineering structures in unreinforced, reinforced and pre-stressed UHPC containing discrete fibers (UHPFRC). This standard provides the rules and models for compression, tension and shear analysis and design. The standard provides reliability management, limit states design and durability design. Also included are methodologies to determine the direct tensile properties based on flexural prism or plate testing with a detailed inverse analysis. One of the strengths of the French standard is the extensive work that has been completed in the area of understanding of fiber orientation due to the handling and placing of UHPC and its impact on the reliability of the hardened material properties. The standard provides rules for tensile strength reduction factors based on casting methods, element shape and size. Additionally, the two French UHPC standards are written to provide continuity between the constitutive material property behavior and the structural design models.

1.3.3 Swiss Standards In December 2014, the Swiss Society of Engineers and Architects (SIA) published prSIA 2052: “UHPC: Material, Design and Construction (Béton fibré ultra-performant [BFUP]: Matériaux, dimensionnement et exécution)”. The document provides rules for the design of non-reinforced, reinforced and prestressed structures with UHPC. In addition it provides design methodology for composite structures of conventional reinforced concrete with UHPC thin bonded overlays. PrSIA 2015 maybe used for UHPC with a compressive strength of 120 MPa or greater and containing discrete fibers that provide a minimum of 7.0 MPa in direct tension. Three tensile strength categories from strain-softening through strain-hardening are permitted. Tensile material properties are determined using a dog-bone direct tension test or by the use of flexural tests and an inverse analysis. Strength design models and rules are provided for compression, flexure and shear. As well reliability factors are included. A short commentary is provided on fire and fatigue. Also, annexes are provided that cover material property characterization, QA/QC and test methods.

1.3.4 Australian Standards

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In January 2000 the University of New South Wales under contract by VSL (Australia) published “Design Guidelines for RPC Prestressed Concrete Beams”. This document is similar in methodology to guides written in France by the industry and the AFGC in the late 1990’s. The guidance and recommended design principles followed very closely the French Guidelines published in 2003. This guideline also included design examples of UHPC prestressed beams. In 2018, Standards Australia Limited published DR AS 3600 “Concrete Structures” including Section 16 which covers “Steel Fibre Reinforced Concrete”. The standard provides the methodology (test methods and reliability factors) for determining the compressive and tensile properties of FRC, which may be applied to UHPC. Rules are provided to determine the tensile properties from flexural (prisms with inverse analysis) or direct tension tests from dog-bone specimens. The standard covers both strain-hardening and strain-softening FRC with and without reinforcement or prestressing tendons. Design models are provided for compression, flexure and shear (strut & tie).. The standard also provides rules for durability (including fire), serviceability and pre-construction quality testing.

1.3.5 Canadian Standards The Canadian Standards Association, (CSA), similar to the French standards provides two separate standards for UHPC - CSA A23.1 Annex U “Materials and Methods of Construction” and CSA S6 Annex 8 “Structural Design of Bridges with FRC”. Both of the CSA Standards on UHPC have been approved by the technical committees and will be published in 2019, as non-mandatory Annexes but written in mandatory language. The standard CSA A23.1, Annex U “Materials and Methods of Construction” covers UHPC materials as follows: - 2 categories of compressive strength (120 – 150 MPa & >150MPa), - 3 categories of tensile strength (strain hardening, strain softening and non-fibre) - 3 categories for durability The standard provides rules for pre-blended, partial pre-blended and non-preblended supply and batching of UHPC. Also, provided are all of the requirements testing to characterize the material properties, QA/QC, batching, transporting, placing, curing and demoulding. The standard CSA S6, Annex 8 “Structural Design of Bridges with FRC” covers the following: - FRC and UHPC for all categories of compressive strength, - Design models for compression, flexure and shear, - Reliability and strength reduction factors, - Methods to determine the direct tensile properties from prism with inverse analysis or direct

tension tests, - Specific rules for the design of thin bonded bridge deck overlays, waffle deck panels and

UHPC Field Cast Connections.

1.3.6 Japanese Guides In the late 1990’s VSL (Japan), Taisei Construction and Teiheyo Cement Company commenced developing UHPC for the Japanese market. In 2006 the Japanese Society of Civil Engineers (JSCE) published “Recommendations for Design and Construction of Ultra High Strength Fiber Reinforced Concrete Structures (Draft). JSCE Guidelines for Concrete No. 9”. This document is similar in methodology to guides in France by the industry and the AFGC in the late 1990’s. The

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guidance and recommended design principles followed very closely the French Guidelines published in 2003.

1.3.7 German Guides

The German Committee for Structural Concrete, in 2017, has prepared draft guidelines for UHPC which applies to structures exclusively reinforced with steel fibres, both precast and cast-in-place, with passive reinforcing bars or prestressing. This new guidelines in based on European Normes (EN) and the years of UHPC research conducted in Germany under the German Research Foundation priority funding program “Sustainable Building with UHPC” [Schmidt et al, 2014 & 2017]. The guide covers raw materials, mix proportioning, quality control, methods for characterizing the fresh and hardened properties, production, structural design (tensile strength characterization by 3- point bending notched prism) and design examples. The guideline includes 3 categories of compressive strength (C130, C150 and C175) and follows EN requirements for durability. The new German Guidelines for UHPC are expected to be published by the end of 2018.

1.3.8 Spanish Guide

On November 2015, the Spanish Association of Concrete, Scientific-Technical (ACHE) Committee No. 1, created a Task Group to develop the first Spanish Guidelines on UHPFRC [Lopez et al., 2017]. The guideline includes 6 categories of compressive strength (120, 135, 150, 175, 200 and 225 MPa), two categories for tensile strength (strain-hardening and strain-softening, similar to French Guidelines) and follows EN requirements for durability. The guidelines will also cover raw material requirements (including maximum size aggregate and fibre size), workability properties, environmental exposure conditions, placing methods and geometric considerations. It is anticipated that the Spanish Guidelines for UHPC will be published by early 2019.

1.3.9 Federal Highway Administration In 1999, the FHWA became interested in the use of UHPC as a resilient material for building the highway infrastructure. Early research work led to the publication of 2 important US documents -FHWA-HRT-06-103 “Material Property Characterization of Ultra-High Performance Concrete” and FHWA-HRT-06-115: Structural Behavior of Ultra-High Performance Concrete Prestressed I-Girders”. While the FHWA does not publish codes or standards, it does prepare guidelines (known as TechNotes) which the industry does rely on for guidance. Additionally, the FHWA staff experts prepare draft standards of guides for other agencies to adopt. The FHWA publications are based on a UHPC defined as a cementitious composite material composed of an optimized gradation of granular constituents, a water-to-cementitious materials ratio of less than 0.25, and a high percentage of discontinuous internal fiber reinforcement. The mechanical properties of UHPC include 21.7 ksi (150 MPa) and sustained post-cracking tensile strength greater than 0.72 ksi (5 MPa).

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In 2013, the FHWA (under the Highways for Life Program) published FHWA-HRT-13-032 “Design Guide for Precast UHPC Waffle Deck Panel Systems including Connections”. The Guide provides information on general arrangements, Waffle Deck Panel design, UHPC connections between adjacent panels and the panel to beam. In 2014, the FHWA published FHWA-HRT-14-084 “Design and Construction of Field-Cast UHPC Connections”. This 36 page guide provides an overview of UHPC and the utilization of the material for precast connections, examples of projects completed, examples of typical connection details, structural design rules for UHPC connections, construction (batching, casting and curing) methodology suggestions and recommended testing requirements. Currently the FHWA is drafting a UHPC specification for T1 Committee of AASHTO on the Structural design of bridges utilizing UHPC. It is anticipated that this document will be available in 2019. Over the period since 1999, the FHWA has published numerous documents on UHPC, including a State-of-the-Art Report, FHWA-HRT-13-060 in 2013. All of the FHWA documents can downloaded at https://www.fhwa.dot.gov/.

2.0 Notation and Definitions - Vic Perry The following section covers the notations and definitions used in this ETR for the structural design of UHPC.

2.1 Notation

To be completed as sections are finalized. A – Absorption C – Corrosion rate Deff – Diffussion Effective Ec – Young’s Modulus of Elasticity f’c – compressive strength Kair – Permeability in Air KG - a factor calculated by comparing their flexural strength to that of a molded specimen with cast specimen to determine the global impact of random fiber orientation KL – a factor calculated by comparing their flexural strength to that of a molded specimen with cast specimen to determine the local impact of random fiber orientation Kwater – Permeability in Water

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leff – Effective fiber length St -Shrinkage at a given time ν – Poisson’s Ratio vf – Volume fraction of fibers contained in the mixture ε’c – Strain at peak stress σ – Axial stress (MPa) φ – Porosity in water 2.2 Definitions For the purpose of the ETR on the structural design of UHPC the following definitions apply: Batch — a volume of materials placed into a mixer and uniformly blended, then discharged. Characteristic property — the value obtained from tests, which corresponds to a statistical 95% probability of meeting or exceeding. Creep coefficient – the ratio of the load-induced strain per unit of stress at any time difference after the immediate loading compared to the instantaneous load-induced strain. Ductility — the ability to deform without failure after cracking or yielding. Failure — a state in which rupture, severe distortion or displacement, or loss of strength has occurred as a result of load-carrying capacity of a component or connection having been exceeded. Fiber — a discrete, elongated element that imparts tensile and crack resistant properties. Material identity card — a document that provides the details of the components, mixing instructions, curing instructions and properties of a specified UHPC mixture. Matrix — that portion of the UHPC not including fibers or reinforcing elements. Particle packing — the process where the voids between larger sized constituent materials are filled with smaller sized constituent materials to the maximum, providing the minimum void space in the matrix.

Modified particle packing — adjusting the particle packing to improve one or more fresh or hardened properties of the matrix by over filling the voids between the larger sized materials.

Commented [vp2]: ACI Terminology: batch — (1) quantity of material mixed at one time or in one continuous process; (2) to weigh or volumetrically measure and introduce into the mixer the ingredients for a quantity of material.

Commented [vp3]: ACI Terminology: creep — time-dependent deformation due to sustained load.

Commented [vp4]: ACI Terminology: ductility — the ability of a material to undergo large permanent deformation without rupture.

Commented [vp5]: If already in ACI Terminology, then delete

Commented [vp6]: The ACI Terminology definition is “fiber — a slender and elongated solid material, generally with a length at least 100 times its diameter”. This definition doesn’t work for UHPC. For example UHPC typically uses a fiber of 0.2 x 12 mm which has an aspect ratio of 60, which is less than the minimum in the ACI definition.

Commented [vp7]: ACI Terminology: matrix — (1) the cement paste in which the fine aggregate particles in mortar are embedded; (2) the mortar in which the coarse aggregate particles in concrete are embedded; (3) the resin or binders that hold the fibers in fiberreinforced polymer together, transfer load to the fibers, and protect them against environmental attack and damage due to handling

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Post setting – the time following setting when an element has sufficient strength to be self supporting. Pre-blend — a mixed combination of the powder mineral components, to which water, admixtures and fibers are added at the concrete mixer.

Partial pre-blend — a pre-blend where not all of the powder mineral components are pre-blended.

Specified property — the value required in the contract specifications. Strain — deformation. Tension hardening – the ability to carry increasing load beyond the first crack. Tension softening - the ability to carry a reduced load which is less than the first cracking load. Thermal treatment — a process of heating the UHPC to an elevated temperature, above normal heat of hydration, in the presence of high relative humidity, holding the elevated temperature for a period of time to complete the hydration process, and then slowly cooling to ambient temperature. Ultra-high performance concrete (UHPC) — a cementitious composite material, normally containing fibers, with enhanced strength, durability, and ductility compared to high performance concretes. Note: UHPC normally contains fibers for post-cracking ductility, have a specified compressive strength of at least 120 MPa by 28 days, and are formulated with a modified multi-scale particle packing of inorganic materials of normally less than 0.6 mm diameter (larger sizes may be used). Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) – sometimes used to denote UHPC containing fibers. Working Time — the period of time which the mixture maintains a flow within the specified flow limits and without negative impact on the in-situ hardened properties. To be completed as sections are finalized. 3.0 Material Properties The mechanical properties of UHPC are required as inputs for the structural design of elements produced from UHPC. Due to the low permeability and ultra-high performance of UHPC, many of the standard test methods currently used to characterize the mechanical properties of conventional or high performance concrete do not provide accurate results for UHPC, unless there are test modifications. In July 2017, ASTM published a new standard “ASTM C1856/C1856M-2017 Standard Practice for Fabricating and Testing Specimens of UHPC” to address the need for standardized characterization of UHPC. This new standard practice references current ASTM Standard test

Commented [vp8]: ACI Terminology: strain — the change in length per unit of length, in a linear dimension of a body

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methods and states the required exceptions or changes applicable to UHPC so that the results are representative of the mechanical properties of UHPC. A comparison of a range of thetypical values of several mechanical properties of undamaged state (unloaded) UHPC, high performance concrete (HPC) and normal concrete (NC) shown in Table 3.1. Table 3.1: Typical range of property values for undamaged state UHPC, HPC and NC

Property UHPC HPC NC Young’s Modulus, Ecm (GPa) 45 – 65

Characteristic Compressive Strength, fck (MPa) 120 – 200 50 – 100 15 – 50

Mean Compressive Strength, fck (MPa) 130 – 230 60 – 120 20 – 60

Characteristic tensile limit of elasticity, fctk (MPa) 4.0 -10.0 0.5 – 3.0 0 – 1.0

Mean tensile limit of elasticity, fctk (MPa) 5.0 – 12.0 1.0 – 5.0 0.5 – 2.0

Characteristic post-cracking strength, fctfk (MPa) 5.0 – 10.0 0 0

Mean post-cracking strength, fctfk 6.0 – 12.0 MPa 0 0

Linear coefficient of thermal expansion (µm/m/oC) 11 11 11

Poisson’s ratio 0.21 Y Z

Freeze/thaw (ASTM C666) RDM (%) 100 90 70

Permeability (Coulombs Passing) 18-500 500 -1500 1000+

Permeability in air, Kair (m2) < 10-15 10-17 10-15 – 10-16

Permeability in water Kwater (m/s) < 5 x 10-14 10-13 10-11 – 10-12

Diffusion effective Deff (m2/s) 10-14 10-12 - 10-13 10-11 – 10-12

Absorption, A (kg/m2/s1/2) 0.0003 0.003 – 0.01 0.01 – 0.03

Corrosion rate, C (µm/yr) < 0.01 0.25 1.20

Porosity in water, φ (%) 1 - 6 8 - 12 12 - 16

[[Charron & Desmettre] 3.1 Mechanical Properties 3.1.1 Compressive behavior - Rafic

The compression constitutive behavior of UHPC materials vary from conventional and high performance concretes. The material is assumed to have discrete steel fiber reinforcement capable of bridging splitting cracks that develop during compression loading and provide a post-peak ductile behavior. Section 3.1.1.1 describes the typical stress-strain behavior of UHPC and Section 3.1.1.2 covers the existing test methods to obtain different key properties of compression behavior, including strength, f’c, modulus of elasticity, Ec, Poisson’s ratio, ν.

3.1.1.1 Uniaxial Stress-Strain Trends in Compression - Rafic Sample uniaxial compressive stress-strain behavior of thermally-treated UHPC containing 2% fibers by volume (vf = 2%) with typical post-peak crack pattern of the compression cylinder are shown in Figure 3.1.1.1. The average trend is plotted as a thicker solid line and a thin line for the individual results, calculated from ranges of axial stresses at one value of axial strain. Tests performed by El-Helou (2016) on a commercially available UHPC consisted of loading UHPC cylinders, having 3 in (76 mm) diameter and a height of 6 in (152 mm), at a constant circumferential expansion rate. The results show an initial linearly elastic behavior with stiffness equal to modulus of elasticity, Ec. The stiffness begins to degrade as splitting cracks start to form resulting in a non-linear behavior (Note: In a narrow region close to the peak strength) reaching the ultimate compressive strength of the material f’c. As the material

Commented [vp9]: LF: Can we specify if any method was used to reduce friction between specimen and platens?

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is strained beyond the strain at peak stress, ε’c, the fibers provide confinement and improve the ductility of the compression response. For instance, the results of Figure 3.1.1.1 show an average stress equal to 50% of the material ultimate capacity at post-peak axial strain of 0.006 (El-Helou, 2016). The full compressive stress-strain behavior of a commercially available UHPC with 0%, 2%, and 4% can be found El-Helou (2016). The stress-strain trends, obtained for strains up to the strain at peak loading, for 5 commercially available UHPCs are available in Haber et al. (2018).

Figure 3.1.1.1 Sample uniaxial compressive stress-strain response of a commercially available UHPC with 2% fibers (d is the cylinder diameter, h is the height, and θ is the out of plane angle

at cylinder top end) [El-Helou 2016, Ref XX]. Compression tests were conducted using a 220 kip (55 Ton) testing machine operated under closed-loop control. The 2"x 4" cylinders tested were ground to a flatness level of 1/1000” by using grinding equipment. This is an important factor in uniformly distributing the load over the whole specimen. Although the top platen swivels to enable a uniaxial load application, it is preferable to have parallel ends for each specimen to minimize the eccentricity of the applied load. A special fixture was developed to attach the two LVDTs (Linear Variable Differential Transformer) to measure the axial strain in the specimen. A constant gage length of 2.5 inches was used for all specimens. This apparatus is shown in Figure 3.1.1.2. The instrumentation includes a LVDT to measure change in length of the specimen, a radial strain gage to measure radial deformation, and an ultrasonic pulse velocity transducers. The fixture permits the axial and circumferential deformations to be measured as the specimen undergoes the post peak response and cracking results in significant dilatation of the sample. A chain type fixture is used to measure the circumferential strain in the specimen. The test was controlled by LVDTs which measures the axial strain, and the extensometer which measures the circumferential strain.

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Using a combination of these two control parameters in sequence, it was possible to capture the post peak response. By achieving a well-controlled post peak behavior, the specimens do not experience an explosive type of failure mechanism, and the true stress-strain response is measured.

Figure 3.1.1.2 set up of the compression stress strain test to measure axial and circumferential

strain in UHPC specimens Figure 3.1.1.3, compares the compressive response of the control UHPC with a fiber reinforced UHPC mixture. The composition of the UHPC is based on a quaternary OPC-fly ash-micro silica-limestone binder mixture and designated as (F17.5M7.5L5) representing a 30% replacement of Portland cement. The control mixtures reached an axial strain of 0.0032 at an ultimate load of 22.2 ksi, while with the addition of 1% steel fibers, the strain at peak load increased to 0.0041. Fiber addition is best demonstrated in the response under the transverse direction which shows a significantly higher dilatation and a higher strength and ductility as compared to the control samples. [ ADOT Report]

Examination of the strain softening region indicates that the plain UHPC specimens behave in a brittle manner while much ductility is observed in the fiber reinforced samples. This is typical of high strength materials when the strength of the interface increases to the level of aggregates and mortar, therefore the cracks have a lower likelihood of following along the tortuous path of interfaces. This behavior is negated in the presence of fibers which provide a tortuous path for the growth of cracks and increase the toughness by the bridging mechanisms. A larger area under the stress-strain diagram indicates a more ductile failure mode. It has also been observed that stiffness as measured by the slope of the stress strain response in the initial linear range is higher for the fiber reinforced samples. Note, that even when the sample is loaded to strain levels as much as 0.006, the average stress carrying capacity in the post peak region is a minimum of 6 ksi and an average value of 12.5 ksi. This level of ductility must be addressed in design equations as compressive strength is maintained for a large range of applied strain.

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Figure 3.1.1.3 set up of the compression stress strain test to measure axial and circumferential

strain in UHPC specimens Compressive strength gain with age was measured by Ahlborn et. al (2012) for non-thermally treated specimens and specimens thermally-treated at various ages. Thermally-treated specimens gained strength at the same rate as a non-thermally treated until the thermal treatment was applied at which the compressive strength “locked-in” at 30 ksi. Non-thermally treated specimens continued to gain strength beyond 28 days, eventually reaching 25 to 27 ksi. Graybeal (2005) conducted similar tests and found that non-thermally treated specimens approached a strength of 22 ksi. The primary difference was observed to be due to the time at at which specimens were demolded. Graybeal demolded specimens at 24 hours while Ahlborn et. al demolded specimens at 3 days. 3.1.1.2 Tests to Obtain Compression Properties - Vic 3.1.1.2.1 Strength - Vic The common standard test method for the compressive strength of concrete is ASTM C39; however due to the high strength of UHPC this method requires modifications to provide consistent reliable results and facilitate being conducted at most concreting test laboratories [Perry, 2015]. ASTM C39 can be used to determine the compressive strength of UHPC made from 75 mm x 150 mm cylinders with modifications to the end preparation of the specimen and the load rate increased to reduce the required time to complete the test [Graybeal, 2015]. Refer to the ASTM C1856/C1856M-2017, “Standard Practice for Fabricating and Testing Specimens of Ultra-High Performance Concrete” to determine the compressive strength of UHPC. In certain countries such as Denmark and the Czech Republic, cubes have also been used to obtain the compressive strength of UHPC. Research conducted by Ahlborn et. al, (TRB paper), and Graybeal & Davis (Ref 7.3.1.1.3) has shown that cubes or cylinders maybe used as long as

Commented [MOU10]: Dual units will be needed throughout

Commented [vp11]: This will be done once the text is close to final

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the contact surfaces of the test specimen are flat and parallel and the compression machine has sufficient capacity to conduct the test. Other jurisdictions using a standard test method similar to the ASTM C1856/C1856M Standard Practice for Fabricating and Testing Specimens of Ultra-High Performance Concrete are France [AFNOR NF P 18-470], Canada [CSA A23.1 Annex U - UHPC], Switzerland [SIA Design Guideline 2052:2016] and Australia [AS5100.5:2017, Section 16] It is common practice for the characteristic compressive strength property be determined based on a statistically significant number of consecutive strength tests of specimens coming from a minimum number of separate batches of a single mixture design [France AFNOR NF P 18-470 and Canada CSA A23.1 Annex U - UHPC]. The provided values of each parameter should be equal to the average minus X times the standard deviation of the tests, where X is a function of the number of tests The rate of gain in compressive strength vs time is impacted by curing temperatures, similar to normal or high performance concretes; however the rate and magnitude of early strength is significantly higher. Figure 3.1.1.2.1 shows the rate of gain in compressive strength vs time for curing temperatures of 41C(105F), 23C(73F) and 10C(50F). Note, during the first 12 hours of curing at 41C (105F) the hourly increase in compressive strength can be more than 2 MPa/hour(300 psi/hr).

Figure 3.1.1.2.1 Compressive strength gain vs time for various curing temperatures[FHWA HRT-12-064] . 3.1.1.2.2 Modulus of Elasticity and Poisson’s Ratio - Vic

Procedures for direct measurement of Young’s modulus and Poisson’s ratio are presented in The Documet [ADOT Report, Mobasher et al.]. Refer to Table 3.1 for typical values of young’s modulus and Poisson ratio. Also there is a significant post peak ductility in compression due to

Commented [vp12]: Need this reference!!!

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the confining effect of the steel fibers. Post peak strain softening range can have a significant impact in load redistribution and ductile performance of structures utilizing UHPC mixtures. Ahlborn et. al (2011) found that regardless of curing regime or specimen age, UHPC consistently achieved an ultimate modulus of elasticity of approximately 8,000 ksi (55 GPa) and a Poisson’s Ratio of 0.21. Graybeal (FHWA-HRT-06-103) reported modulus of elasticity values between 6200 ksi (42.8 GPa) for untreated specimens and 7650 ksi (52.8 GPa) for steam treated values. Furthermore, the following is recommended by FHWA for determining the modulus of elasticity, Ec, in lieu of test results (FHWA-HRT-14-084).

𝐸𝑐 = 1500 √𝑓𝑐′ for f’c in ksi

In Graybea’sl work, full compression stress-strain response was collected for each set of cylinders under various curing regimes and at various ages (Figure 3.1.1.2.2.1). This data clearly shows the change in the relationship between compressive strength and modulus of elasticity as curing time proceeds.

Figure 3.1.1.2.2.1 Selected stress- strain responses for UHPC cured at various ages [Graybeal 2007] As discussed above empirical relationship exist to relate compressive strength with modulus of elasticity. However, according to Graybeal [2007], these equations are not accurate predictors for modulus of elasticity for compressive strengths of less than 25 MPa (3.6 ksi), due to the non linearity in the gain of the strength vs modulus of elasticity (see Figure 3.1.1.2.2.2).

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Figure 3.1.1.2.2.2 Modulus of Elasticity as a function of compressive strength [Graybeal, 2007] The static modulus of elasticity and Poisson’s ratio can be determined in accordance with ASTM C469/C469M on specimens prepared in accordance with ASTM C1856/C1856M Standard Practice for Fabricating and Testing Specimens of UHPC with a modified Compressometer and Extensometer using displacement transducers for measuring displacement. Also, CSA A23.1 Annex U on UHPC and AFNOR NF P 18-470 provide guidance on obtaining the modulus of elasticity and Poisson’s ratio. 3.1.2 Tensile behavior - Rafic

The tension behavior and constitutive properties are unique features of UHPC. Section 3.1.2.1 describes the typical stress-strain behavior of UHPC in uniaxial tension and Section 3.1.2.2 covers the existing test methods to obtain different key properties of tensile behavior.

3.1.2.1 Uniaxial Stress-Strain Trends in Tension - Rafic Sample tensile uniaxial stress-strain behavior of UHPC in tension for UHPC containing 2% fibers by volume are shown in Figure 3.1.2.1. The average trend is plotted as a thicker solid line and a thin line for the individual results, calculated from ranges of axial stresses at one value of axial strain. These tests were performed at the Federal Highway Administration (FHWA) Turner-Fairbank Highway Research Center (TFHRC) on a commercially available UHPC and results can be found in Haber et al. (2018). The tests consisted of UHPC prisms, having a square cross section of 2 in (51 mm) and a length of 17 in (432 mm), loaded in tension at a constant displacement rate as described in Graybeal and Baby (2013). The results show an initial linearly elastic behavior, with stiffness equal to the modulus of elasticity, Ec. As the tensile

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strain increases, the behavior becomes non-linear until the first discrete crack at which the material enters the multiple cracking phase. Discrete cracks start to consecutively form and the strength is equal to or greater than the first cracking strength. The multi-cracking phase ends with the localization of strains into a single crack at which the material loses strength as strains increase. For information on the idealized behavior of five commercially available UHPCs, refer to Haber et al. (2018).

Figure 3.1.2.1 Sample uniaxial tensile stress-strain response of a commercially available UHPC

with 2% fibers [FHWA, HRT-18-036]. 3.1.2.2 Test methods to obtain Tension Properties- Vic Tensile strain-hardening or strain-softening (Figure 3.1.2.2), or the capacity to retain a non-negligible and reliable tensile strength resistance in the post-cracking regime is a distinct feature of UHPC. Therefore, the experimental identification of post-cracking tensile behavior and defining parameters to suitably characterize the material from a design perspective is of the utmost importance. Many experimental tensile tests, direct or indirect, have been used; however, no widely-acceptable direct tensile test standard has been established to date.

0

2

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10

12

0

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0.4

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0 0.002 0.004 0.006 0.008 0.01

Axia

l S

tres

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Pa)

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l S

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s (k

si)

Average Axial Strain

Average

Individual SpecimensMaterial: U-D

Fiber Volume: 2 %

fc = 18.6 ksi

Age: 7 Days

Samples Included: 4

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Figure 3.1.2.2 Tensile Strain Hardening and Strain Softening Behavior of UHPC. Direct tensile test methods provide the most “direct” way to obtain the tensile properties of UHPC, as shown in Figure 3.1.2.1; however, the end attachments conditions in the testing apparatus can lead to induced bending moments and increased variability of test results; therefore, some jurisdictions specify flexural prism tests in a strain controlled system, then apply an inverse analysis to obtain the tensile properties of the UHPC. The flexural prism test with inverse analysis also has limitations depending on whether the UHPC exhibits tensile strain-hardening or strain-softening properties. In some cases of strain-softening materials, the prism test with inverse analysis can show strain-hardening behavior when it is actually strain-softening. The tensile strength can be determined on prismatic specimens molded or cut from full-sized structures and tested in accordance with ASTM C1856/C1856M Standard Practice for Fabricating and Testing Specimens of UHPC, and calculated in accordance with an inverse analysis of AFNOR NF P 18-470, Appendix D, or SIA Design Guideline 2052:2016 Appendix E. Alternatively, the tensile properties can be determined with direct tensile tests for strain-hardening UHPC only. Direct tensile test methods may be found in the Australian guidelines [AS 5100.5:2017, Section 16], the Swiss Standard [SIA Design Guideline 2052:2016] or from FHWA [Graybeal & Baby ‘Development of Direct Tension Test Method for UHPFRC, ACI Materials Journal March-April 2013]. It is common practice that the characteristic tensile strength property be determined based on a statistically significant number of consecutive strength tests of specimens coming from a minimum number of separate batches of a single mix design (France AFNOR NF P 18-470 and Canada CSA A23.1 Annex U - UHPC). The provided values of each parameter should be equal to the average minus X times the standard deviation of the tests, where X is a function of the number of tests. 3.1.3 Flexural Behavior There are numerous test methods used to determine the flexural strength of concretes based on testing various geometric sized prismatic specimens in 3 or 4 point bending. All of these methods provide different results due to size effects, fiber orientation, casting techniques and other variables. Flexural strength is not a mechanical property commonly used in the design of structures with UHPC. Only the tensile behavior as explained in section 3.1.2 above is applicable. Refer to Section 4.3 for flexural strength design considerations. In the flexural test, due to the disparity between the tensile and compressive response of the UHPC mixtures, the behavior is dominated by the relatively weak tension response. Cracking in tensile zone leads to loss of stiffness, however the fibers that intersect the cracks pullout and stabilize the crack growth. Therefore in a flexural test the contribution of fibers to the resistance to crack propagation is balanced against the superior performance of UHPC in compression. The net effect is that the fibers intersecting the crack growth path provide bridging by forming a closing pressure that resists crack opening and increase the material’s fracture toughness. Correlation between the strengthening of the matrix phase by means of a critical volume fraction of fibers has been studied by many researchers (Yang et al., 2010; Yang and Ye, 2002, Mobasher, Ouyang and

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Shah, 1991). Flexural testing is the key experimental procedure to showcase the interaction between the tensile and compressive behavior. Figure 3.1.3. shows the flexural response of a UHPC plain specimen with a UHPC sample containing 1% steel fibers by volume (Vf = 1% - red line). The unreinforced UHPC beam (Vf = 0% - blue line) behaves as a brittle material and the load-deflection response increases linearly up to a load of about 4 kN (800 lbs), corresponding to an elastic equivalent flexural stress of **** at a mid-span deflection of 0.1 mm (0.004 in). At this point, the failure is imminent as a crack forms in a sample which propagates to the full depth of the specimen. Due to the brittle response, the load carrying capacity is exhausted as a single crack propagates without any resistance from the matrix. The flexural response of the beam containing 1% fiber volume shows the significant ductility obtained with the fibers. This ductility enhancement can be studied at various stages of load-deformation response, as follows:

1) The crack initiation point in the fiber reinforced specimen is identified by the nonlinearity in the ascending response and shown to be at higher loads as compared to the plain unreinforced UHPC. This nonlinearity that takes place prior to reaching the maximum load is quite distinct and corresponds to the stable growth of microcracks, which leads to the accumulation of damage at the peak load.

2) The peak load for the fiber reinforced specimen (red line) is as high as 22% as compared to the unreinforced control specimen (blue line).

3) The post-peak response is dominant in the fiber reinforced specimen and the sample is able to carry a significant portion of the maximum load beyond the ultimate strength point.

Figure 3.1.3 Comparison of the load-deflection response of control sample with a composite containing 1% fiber volume mix series F17.5M7.5L5.

Commented [vp13]: Need the value

Commented [vp14]: This sentence is not clear??? Clarify or delete.

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It is noted that the incorporation of 1% steel fibers has a beneficial effect on the flexural behavior and the post-peak response. While there is no post-peak response for the unreinforced specimen as shown by the brittle behavior (blue line in Figure 3.1.3), the fiber-reinforced specimens demonstrate a considerable non-linear response after the occurrence of the first crack. The flexure testing was terminated at an ultimate mid-span deflection of 4 mm for the fiber reinforced specimens. This value is nearly 40 times greater than the mid-span deflection at the first cracking point in the unreinforced UHPC beams. Additionally, the load carrying capacity at this level is as high as 60% of the peak load. This indicates that after reaching the peak load, the sample is capable to maintain a large percentage of load carrying capacity for a significant range of deformation. The peak load sustained by the UHPC beams containing 1% fiber volume is about 22% , 177 lb. (0.8 kN) higher than the peak load in the unreinforced UHPC beams 799 lb. (3.55 kN). (which corresponds to elastic equivalent flexural stresses of ******) [ADOT report] 3.1.4 Shear Behavior Shear strength is not a mechanical property that can be characterized by a test method. Direct tensile strength across the crack is used in the design model. Refer to section 4.3 on Shear Design Considerations for more information. Explain that the engineering community of shear is not the direct shear but the final failure of when the flexural crack becomes critical. Multiple mechanisms should be looked at like direct shear etc. 3.1.5 Bond Behavior The bond strength of UHPC is considered for three categories; the bond of UHPC to other concretes and surfaces, the bond developed under fiber pullout, and the development length of discrete reinforcement in UHPC. Bond of UHPC to other concrete has been studied by Harris et. al (2011) and Graybeal & Haber (FHWA-HRT-17-097 & HRT-18-036). Harris et al conducted an experimental study to evaluate the bond strength between UHPC overlays and normal strength concrete substrates with variable surface textures. Slant shear and splitting prism tests demonstrated that under compression testing, the bond strength of all roughened surface speimens was greater than the standard smooth finish. Bond strength of indirect tension tests were not as sensitive to surface roughness, but were still within ACI’s Guide for the Selection of Materials for the Repair of Concrete. Graybeal and Haber prepared two different concrete substrates with two different surface preparations (Scarification & hydro demolition) and cast an UHPC overlay. Pull-off testing was conducted in accordance with ASTM C1583. Testing showed that the UHPC bond strength ranged from 0.8 MPa (114 psi) to 4.5 MPa (651 psi). Additionally, Graybeal & Haber conducted ASTM C78 flexural beam tests to determine the bond between normal concrete and UHPC. Results of this testing ranged from 3.0 MPa (430 psi) to 4.3 MPa (620 psi) for UHPC cured for 7 days. The failure of the beam tests was in the constant bending moment region of the beam and predominantly in the normal concrete substrate. Subsequent to those studies , ASTM C1583/C1853M was accepted and can be used to determine the tensile bond strength of UHPC to concrete surfaces. ASTM C1853/C1853M

Commented [vp15]: This sentence does not agree with Figure 3.1.3

Commented [vp16]: Mohammed Comment. Email to Mohammed Aug 24 for info

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Standard Test Method for the Tensile Strength of Concrete Surfaces and the Bond Strength or Tensile Strength of Concrete Repair and Overlay Material by Direct Tension (Pull-off Method)” is a method that can provide bond property values for UHPC. The development length of discrete reinforcement in UHPC was studied by Graybeal [FHWA-HRT-14-084 & HRT-14-090], Emmerson and Hale, [Emerson , 2011], and Fehling,[Fehling, 2014]. In general, the bond strength of discrete reinforcement is higher in UHPC than normal strength concrete or HPC. The higher bond strength will shorten bar development lengths and impact the horizontal shear connections (ie Nelson Stud length, spacing and arrangement) between conventional concrete or HPC and UHPC. FHWA-HRT-14-084 provides guidance for basic development lengths with adjustments for cover and spacing considerations. Due to the very short bond development length of pre-stressing strands or other tension reinforcing, the end anchorage zones should be checked for higher concentrations of tension, particularly in prestressed I-Shaped girders in the region of the web to bulb interface. Test methods for the measurement of bond of steel fibers have been addressed in detail in ACI544-9R-17. The characteristics and behavior of fiber-matrix interface plays an important role in controlling the mechanical performance of UHPC. The bond characteristics of fiber-cementitious matrix is normally measured by means of pullout tests which determine the interfacial fiber-matrix behavior. Parameters that influence the pullout behavior of fibers are affected by fiber and mixture types, embedded fiber lengths, and processing methods. Four main factors influence the bond between fiber and matrix: 1) physical and chemical adhesion; 2) mechanical component of bond, such as deformed, crimped and hooked end fibers; 3) friction and shrinkage clamping effects; and 4) fiber-to-fiber interlock. Fiber pullout has be studied in the context of fiber-matrix interaction and is discussed in more detail in section 3.5.1 Fiber-Matrix Interaction. 3.2 Durability Properties Durability can be addressed in both the uncracked (unloaded( condition and the cracked (loaded) condition. The deterioration mechanisms are different for each condition. This section covers the uncracked condition. The cracked condition is covered in section 5.0. Deterioration of concrete in the uncracked condition is mostly caused by the transport of fluids and gases through the capillary pore structure of the internal matrix. UHPC has a lower porosity than conventional concrete due to its higher packing density which forms a discontinuous pore structure in the matrix. The hydrated matrix of UHPC, therefore, has a low permeability, discontinuous pore structure and the high fiber dosages create a tight cracking pattern resulting in a high durability level; hence more aggressive test methods are required to obtain results that are meaningful and valuable in comparing the relative properties. The durability properties of uncracked UHPC is typically an order of magnitude superior to HPC[FHWA]. Refer to Table 3.1 for typical values. 3.2.1 Absorption The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a low level of absorption. As shown in Table 3.1 from work conducted by Charron et al, the absorption of UHPC is in the range of 0.003 kg/m2/s1/2.

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The absorption of UHPC can be determined on specimens following a 28-day moist curing, in accordance with ASTM C642. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC]. 3.2.2 Salt-scaling and Freeze/Thaw Resistance

The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high level of resistance to salt-scaling and freeze/thaw. Thomas et al. (2012) report on a set of three specimens of UHPC that have been placed at the mid-tide level of the marine exposure site at Treat Island, Maine, over the past 15 years. The exposure conditions at Treat Island were very severe with 6-metre tides and more than 100 freeze-thaw cycles per year. Extensive experimental investigations have been carried out on the specimens, such as measurement of strength and stiffness, electrical properties, chloride profiling, corrosion activity of reinforcing steel and microstructural evaluation. No visible deterioration was evident after exposure periods of 5 to 15 years and there was no evidence of any degradation of mechanical properties after more than 1500 freeze-thaw cycles. Further, no corrosion of rebars has been observed, although the concrete cover was only 25, 19 or 10 mm. The depth of chloride penetration was extremely low, approximately 1/3 of that of typical HPC with 8.5% silica fume and w/c-ratio = 0.33 under same conditions. Consequently, a much longer service life of UHPC structures compared to HPC – elements can be expected.

Ahlborn et. al (2011) reported an increase in RDM (<2%) and mass (<1%), and negligible changes in length (<0.01%), for UHPC specimens after 300 cycles following ASTM C666 (Procedure B), independent of curing regime. Companion wet-dry specimens demonstrated similar increases in RDM and mass, suggesting specimens did not deteriorate but rather continued to hydrate during testing. The resistance of UHPC to freezing and thawing degradation was also quantified by FHWA (2006). In total, 690 cycles according to ASTM C666 (Procedure A) of freezing and thawing were conducted. The results showed only minor changes in mass.

The salt-scaling of UHPC specimens in accordance with ASTM C672 by Graybeal found that independent of curing regime or age, UHPC showed no signs of scaling, spalling, or other deterioration. Extended cyclic testing again showed no deterioration of the UHPC under these conditions. (FHWA-HRT-06-103). Refer to Table 3.1 for typical values.

The freezing and thawing performance of UHPC can be determined on specimens following a 28-day moist curing, in accordance with ASTM C666. The testing should be continued on each specimen until it has been subjected to at least 300 cycles or until its relative dynamic modulus (RDM) of elasticity, as defined in Test Method C666/C666M, reaches 60%, whichever occurs first, unless other limits are specified. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC].

3.2.3 Permeability 3.2.3.1 Chloride ion Penetration

The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high level of resistance to chloride ion penetration [Thomas et al]. Ahlborn et. al (2011) reported chloride ion penetration in the negligible range (<100 Coulombs passing) for thermally-treated and air-cured UHPC specimens. Initially, the creation of an electric short circuit from the steel fiber reinforcement was a concern, but because of the random fiber distribution and short fiber length at a rate of 2% by volume, no such electric short occurred [Thomas et al.,2016]. It should

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be noted that while curing regime does not appear to affect the chloride penetration on the documented scale, air-cured specimens showed higher ranges. Graybeal (FHWA-HRT-06-103) found similar results; thermally treated specimens had negligible penetration and ambient cured specimens bordered on negligible and very low.

The rapid chloride ion penetration of UHPC is often determined on molded or cut specimens in accordance with ASTM C1202/C1202M. The test specimen can be fabricated from the matrix with or without fibers. This test approximates the resistance to chloride ion penetration by measuring an electrical current passing through a sample of UHPC. After 28 to 56 days of moist curing, the penetration potential is typically measured as very low to negligible. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC]. Other test methods that may be used include ASTM C1202, ASTM C666, and AASHTO T259. 3.2.3.2 Carbonation The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high level of resistance to carbonation. Classical test methods to determine the carbonation properties provides extremely low test results, typically within testing error for the test method

[Graybeal]. Carbonation testing is normally not conducted nor a concern with UHPC. If

carbonation test results are required, then tests may be conducted using standard test methods and increasing the CO2 concentration levels and the test duration to provide meaningful results for comparing various UHPC’s for carbonation performance. 3.2.4 Acid and Sulphate Resistance 3.2.4.1 Sulphate Resistance The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high level of resistance to Sulphate attack. Typically UHPC’s perform better than high sulphate resistant concrete performs. Research by Piérard, [Piérard, 2012] showed that UHPC prisms exposed Na2SO4 (at a rate of 16 g of SO4/L) for 500 days did not exhibit any expansion. The sulphate resistance of UHPC can be determined, on specimens without fibers, in accordance with CSA A3004-C8, Procedure A at 23oC for 12 months. [Canadian CSA A23.1, Annex U on UHPC]. The limited studies that are available report little-to-no deterioration of the UHPC when immersed in a sodium sulfate solution for 500 days. There have not been any incidents documented of deterioration of UHPC due to Sulphate attack. 3.2.4.2 Acid Resistance The low permeability of UHPC provides performance under specific acid attack superior to normal or high-performance concretes [Schmidt et al.]. Whereas with conventional concretes acids may permeate throughout the matrix and cause deterioration from within as well as on the exterior, with UHPC the deterioration mechanism is mostly from the surface. The matrix of UHPC has a low permeability, discontinuous pore structure and a tight cracking pattern, resulting in an improved level of resistance to acid attack. Classical test methods to determine the performance of UHPC under specific acid environments

provides low test results [Schmidt et al & Koneig and Dehn]. Testing UHPC’s for acid resistance

can be conducted using standard test methods and increasing the concentration levels and the test duration to provide results for comparing various UHPC’s for acidic performance. Schmidt et al subjected UHPC specimens (heat treated and non heat treated) to sulphuric, lactic and

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ammonium containing waters using a proton consumption method to characterize the UHPC’s performance. Results for the range of tests conducted in accordance with EN standards are presented in their paper. Metallic fibers contained in the UHPC may be subject to corrosion in highly acid environments; however due to UHPC’s low permeability, discontinuous pore structure and tight crack spacing the performance is superior to normal or high performance concrete. 3.2.5 Delayed Ettringite Formation The matrix of UHPC has a low permeability and discontinuous pore structure resulting in a high level of resistance to delayed ettringite formation. According to Canadian CSA A23.1, Annex U, UHPC receiving a thermal treatment with an internal material temperature greater than 70 ºC should contain supplementary cementitious material. There have not been any incidents of delayed ettringite formation problems documented with UHPC. For more information on UHPC subjected to a thermal treatment of more than 70 ºC and measures to control potential for delayed ettringite formation refer to ACI 201.2R-16 and ACI 308R, Clause 3.10. 3.2.6 Leaching and Efflorescence UHPC has a high resistance to through-leaching due to its densely compacted matrix resulting in very low permeability. However, surface efflorescence can appear on new UHPC elements prior to sealing. This type of efflorescence is generally a one-time occurrence and can easily be sand-blasted or pressure washed away for a cleaner finish. UHPC’s resistance to leaching is a factor of crack control which prevents moisture from impregnating the interior of the matrix to draw out the soluble minerals. 3.2.7 Abrasion The abrasion resistance of UHPC is superior to that of high performance concrete. Research by Graybeal [FHWA-HRT-06-103] using a modified (doubling wheel load) ASTM C944 “Test Method for Abrasion Resistance of Concrete or Mortar Surfaces by the Rotating-Cutter Method” showed improved abrasion performance for UHPC. UHPC specimens with various curing regimes gave results of 0.07 to 2.56 grams. The abrasion loss of UHPC can be determined on specimens following a 28 day moist curing, in accordance with ASTM C944/C944M, using a double load of 197 +/- 2 Newtons on the test specimen. [ASTM Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC]. 3.2.8 Alkali-Silica Reaction UHPC has a high resistance to alkali aggregate reactions such as ASR due to its lack of internal free water (low w/c ratio) and its very low permeability which prohibits free water from infiltrating the matrix to initiate the reaction. Additionally, high quality fine aggregates are frequently used in UHPC and are often non-reactive in nature. The use of these material constituents generates a very low permeability and discontinuous pore structure, thereby reducing the possibility of alkali-silica reaction from occurring. Various tests can be used to measure alkali-silica reactivity of UHPC, whereby ASTM C1260 is the most commonly used. The level of expansion measured using this test is typically well below the threshold value considered for innocuous behavior. There have not been any incidents of alkali-silica problems documented with UHPC.

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3.3 Time Dependent Properties Mohammad & Andy- Add Early Age Behavior and effect of age on material properties and curing effect. Young modulus (Rafic will update Mohammad on this based on FHWA work) add this section. 3.3.1 Creep Coefficient UHPC exhibits very low creep coefficients in the range of 0.3 to 0.8 if thermally treated. Fleitstra (2011) studied early age creep and shrinkage behavior under conditions to mimic a prestressing operation. While previous studies considered creep tests on specimens after thermal treatment was applied, Fleitstra studied the creep behavior for specimen thermally treated while under load. Specimens were subjected to creep loads of 20% and 60% of initial strength in an attempt to bound the induced stresses caused during prestressing applications. The average creep coefficient was found to be 0.76 and 1.12 for the 20% and 60% load levels, respectively. These coefficients are much higher than Graybeal at 0.29 (FHWA report) and higher than the conservative values of SETRA (0.20), JSCE (0.40) and UNSW (0.30). However, no other research has incorporated the application of a compressive load (such as prestressing) before,

during and after thermal curing. Mullen (2013) represented Fleitstra’s creep strain data, cr, as a function of time t in days after loading until thermally treated at which point the creep strain is “locked in”.

𝜀𝑐𝑟 =𝑡0.6

4.069 + 𝑡0.6∗ 1713 < 1713

Refer to FHWA HRT-06-103 and HRT-18-036 for more information on creep.

The creep coefficient in compression can be measured on 75 mm x 150 mm cylindrical specimens prepared in accordance with ASTM Standard Practice for Fabricating and Testing Specimens of UHPC and in accordance with ASTM C512/C512M. Creep testing can be conducted at a sustained load of specified strength of the UHPC. Creep testing can be conducted on specimens following a 28 day moist curing. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC, FHWA-].

3.3.2 Shrinkage

Graybeal et al conducted shrinkage tests on UHPC specimens in accordance with ASTM C157 and ASTM C1581 (early age) to characterize the early age and long-term shrinkage of UHPC materials. The results of this testing show that UHPC can have an unrestrained shrinkage comparable to well designed conventional concretes. Graybeal presented the following modified ACI equation for determining the shrinkage as a function of time after casting:

St = S ult x t/(A + t)

Where, A = 35; St is the shrinkage at a given time, t and Sult is the ultimate shrinkage the concrete will undergo.

Graybeal showed the ultimate autogenous (sealed) shrinkage can be as high as 850 microstrain. Drying shrinkage (in air) can be as high as 1400 microstrain.

Commented [MOU17]: Reported test results? Ahlborn ICI 2015, others? Tess can summarize if others provide some more references

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Long-term Shrinkage testing can be conducted on prisms of 75 mm x 75 mm x 280 mm, prepared in accordance with ASTM C1856/C1856M Standard Practice for Fabricating and Testing Specimens of UHPC. The change in length of the UHPC specimens can be measured in accordance with ASTM Test Method C157/C157M or C341/C341M, at 1d, 4d, 7d, 14d, 28d, 56d and 90d. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC]. Early age shrinkage can be determined using ASTM C 1581. Graybeal suggests that this test is difficult to conduct on heavily fibered UHPC and that it may be necessary to run the test without the fiber to obtain results for early autogenous shrinkage [Graybeal, FHWA HRT-18-036, 2018] 3.3.3 Thermal Coefficient of Expansion The coefficient of thermal expansion was measured by Graybeal (FHWA-HRT-06-103) and Ahlborn et. al (2011) for thermally treated and air-cured UHPC specimens using the provisional AASHTO test specification TP60-00. Based on test results, a coefficient of thermal expansion of 8.2 x 10-6/°F was recommended by Ahlborn et. al (2011) for thermally treated specimens independent of age. Ahlborn et. al (2011) also found the coefficient of thermal expansion increased from 7.53 to 7.74 x 10-6/°F as non-thermally treated specimens increased in age from 3 to 28 days. As such, a value of 7.7 x 10-6/°F was recommended for air-cured specimens, a value that lends well to field applications such as concrete bridge deck overlays. These recommendations fell within range of the Japanese recommendations of 7.5 x 10-6/°F for steam-treated UHPC samples and Graybeal’s thermally treated specimens with a coefficient of thermal expansion of 8.3 x 10-6/°F. (FHWA-HRT-06-103). These values are somewhat higher than thermal expansion coefficients of 7.74 x 10-6/°F for normal strength concretes. The thermal expansion coefficient for UHPC has been specified by Ahlborn et al. (2008), JSCE (2010), AFNOR NF P 18-470 (2016), Graybeal (2014), SIA 2052 (2016) and Hussein et al. (2016) as 13.9 x 10-6°C, 13.5 x 10-6°C, 11 x 10-6°C, 14.7 x 10-6°C, 10 x 10-6°C and 16.9 x 10-6°C for temperatures between -60 to 60°C, respectively. Habel (2004) describes that the initial thermal expansion coefficient is between 40 and 60 x 10-6°C and decreases to its final value during the first 36 hours of hydration.

The thermal coefficient of expansion can be measured on 75 mm x 150 mm cylindrical specimens prepared in accordance with ASTM C1856/C1856M Standard Practice for Fabricating and Testing Specimens of UHPC. The Thermal Coefficient of Expansion can be determined in accordance with AASHTO T 336. [ASTM C1856/C1856M Standard Practice on Fabricating and Testing Specimens of UHPC and CSA A23.1 Annex U on UHPC].

3.4 Fire Properties There is limited research material available on the fire performance of UHPC. However, there have been no reported incidents of failure of UHPC structures due to fire [Behloul et al, AFGC/SETRA and Ye et al ]. The following categories can be applied to UHPC: a) FN – Non-fire-exposed UHPC: Conventional UHPC may be used in non-fire exposure

applications without the use of accelerated curing or the inclusion of polypropylene fibers. b) F1 – Fire Exposed UHPC: UHPC that could be exposed to fire shall contain as a minimum

0.2% by volume of polypropylene fibers. c) F2 – Hydrocarbon fire exposure: UHPC that could be exposed to a hydrocarbon fire shall

contain as a minimum 0.3% by volume of polypropylene fibers with an aspect ratio ≥ 65. [Canadian CSA A23.1 Annex U on UHPC].

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Code specified fire resistance ratings are typically assigned to an assembly based on the performance of that assembly in a standard fire test such as the ULC S101 Fire Test and are not assigned on a material basis. UHPC has very low permeability and as a result could be susceptible to explosive spalling when exposed to fire unless mitigating measures are taken. While UHPC has been found to perform better than conventional HPC when exposed to [Behloul et al] fire, the curing status (internal moisture content) and mix design of UHPC can influence the performance of UHPC under fire exposure conditions. The fire resistance of UHPC that has been thermally treated at 90°C for 48 hrs is generally superior to UHPC that has not received accelerated curing. Thermal treatment serves to remove any free water in the concrete matrix, reducing the potential for spalling. The use of at least 0.1% by volume of polypropylene fibers has also been shown to significantly reduce spalling in UHPC by reducing the buildup of hydrostatic pore pressure at elevated temperatures. The use of steel fibres has not been found to reduce spalling but does serve to retain the spalled sections of concrete once the hydrostatic pressure exceeds the tensile strength of the UHPC[Behloul et al and Hosser et al] . Residual strength studies at elevated temperatures have shown that a variety of UHPC mixes will perform similarly to European Code2 Class 1 and Class 2 concrete. Other UHPC mixes however have fallen outside this range and as a result, no prescriptive residual strength values for UHPC are offered at this time. 3.5 Other Properties 3.5.1 Fiber-Matrix Interaction – Luca Sorelli 3.5.1.1 Fiber dispersion, orientation and content The fiber dispersion, orientation and content strongly affect the mechanical response for tensile tests (Bayard 2003) and flexural tests (Bernier et Behloul 1996). The fiber dispersion and orientation depend on the followability of the fresh concrete, the casting procedure, the geometry of the molds and any embedments (Barnett et al. 2010; Ferrara, Ozyurt, et Di Prisco 2011; Folgar et Tucker 1984; Kooiman 2000; Martinie et Roussel 2011). The effective distribution (dispersion and orientation) of fibers can be quite complex due to wall effects and rheology of the mix design. For instance, fibers tend to be locally aligned in the proximity of the molds surface and when flowing around embedded reinforcing. Furthermore, the fiber efficiency (defined as the average fiber length projection along the principal tensile stress direction) increases approximately 25% passing from a tridimensional random distribution to a bidirectional one [Guenet 2012; Kooiman 2000]. The placing method can strongly affect the orientation and dispersion of the fibers (Martinie et Roussel 2011). The orientation normally does not affect the first cracking load but has an effect of up to 50% on the post-cracking ultimate tensile strength in bending [Bernier et Behloul 1996; Maya Duque, De la Varga, et Graybeal 2016] as shown in Figure 3.5.1.1. The highest UHPFC flexural strengths have been achieved when placement is made in the direction of the measured tensile strength. As for thin elements, the fiber orientation is rather bidirectional due to the wall

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effect, which favors the flexural response [Guenet, 2016, 2012]. Theoretically, for a randomly distributed fiber orientation, the fiber orientation coefficient increases from 0.5 to 0.637 (increase of 27%) passing from a three-dimensional configuration to a bi-dimensional one [Kooiman, 2000].

(a)

(b)

Figure 3.5.1.1. Effect of the fiber orientation on the (a) tensile response (Bayard 2003) and on (b) the flexural response (Bernier et Behloul 1996).

3.5.1.2 Fiber pull-out ACI document 544-9R and ACI 544 -10R discuss the history and methodology for fiber pullout testing in detail and the impact of fiber dispersion and orientation.

. Although there are no ASTM or EN standards for testing procedures for fiber pullout in cement matrices to determine bond strength, there is literature that describes the test setup and how loading conditions can strongly affect test results. Single-sided test profiles have been carried out with by Grünewald 2004; Markovic 2006, Naaman and Najm 1991; Groth 2000, Cunha et al. 2007, Silva et al. ,2009. Banthia et al. have extensively studied the effect of fiber geometry and orientation on the pull-out behavior of a single macro-fiber [Banthia 1990]. In UHPC, the fiber-matrix pull-out behavior has been optimized with respect the matrix strength to favor the strain-hardening behavior and dissipation mechanisms (Lee et al. 2010; Wille, Kim, et Naaman 2011; Wille et Naaman 2012). For instance, it was observed that the equivalent bond strength of deformed fibers embedded in UHPC reaches up to 47 MPa (6.8 ksi), which is almost five times the equivalent bond strength of straight fibers (10 MPa [1.4 ksi]) embedded in the same matrix (Wille et Naaman 2012). Furthermore, the equivalent bond strength of straight steel fibers, which are commonly used in UHPC can be doubled to a value exceeding 20 MPa (2.9 ksi) by optimizing the UHPC matrix through composition and particle size distribution, leading to an atypical (preferential fiber orientation) pullout load-slip-hardening behavior.

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3.5.1.3 Fiber dispersion validation There exists practical methods to assess the fiber orientation, which varies from simple fiber counting on cracked surface to image analysis based technique which statistically estimates the average orientation of the fiber from the elliptical shape of the fibers observed on the cut surface (Krenchel 1975; Delsol et Charron 2017). The image analysis can be based from 2D image analysis taken from cut and polished surface or from 3D images reconstructed by X-ray technique (Guenet 2016) as shown in Figure 3.5.1.2. More recently, Magnetic Inductance Methods (MIM) (Ferrara, Faifer, et Toscani 2012) have been applied to reasonable spatial distribution of the fibers (Baril, Sorelli, Réthoré, Baby, et al. 2016). Figure 3.5.1.3 shows the fiber orientation assessed by MIM which well correlate the theoretical prediction of fibers by computational fluid-dynamics and the distribution of micro-cracks detected by stereovision 3D image analysis. (Baril, Sorelli, Guenet, et al. 2016).

(a) (b) (c) (d)

Figure 3.5.1.2. Assessment of steel fiber distribution of a UHPFRC beam by micro-tomography (Guenet 2016) for : (a) 1% of steel fiber; (b) 2% of steel fiber; (c) 1% of steel fiber with a steel

reinforcement; (d) 2% of steel fiber with a steel reinforcement.

(a) (b) (c)

Figure 3.5.1.3 (a) Non-destructive tests (Magnetic Inductance Measurement, MIM) to measure the fiber orientation in thin panels (Ferrara, Faifer, et Toscani 2012); (b) Example of fiber

direction measured in each cell; (c) fiber direction predicted by computational fluid-dynamics (Baril, Sorelli, Guenet, et al. 2016).

3.5.1.4 Fiber factor and impact on tensile properties The fiber orientation may or may not be isotropic depending on the casting techniques, consolidation methodologies, form shape, wall effects and other reasons as has been explained in the sections above. The final orientation of the fibers may or may not be beneficial to the

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tensile properties of the hardened UHPC. It is important for the designer to validate if the in-situ fiber orientation is as assumed in the design In plate elements, fiber orientation can affect the full development of the micro-cracks, which is key to guarantee the structural ductility of a bidirectional UHPCs. For instance, the effect of the fiber orientation on the flexural response of thin UHPCs plates elements has been investigated by considering the presence of a casting flow defect (Baril, Sorelli, Réthoré, Baby, et al. 2016)(see figure 3.5.1.4). The discontinuity in the fiber orientation could reduce the micro-cracking growth with a decrease of the load bearing capacity and the structural ductility.

(a) (b)

Figure 3.5.1.4. (a) Load-deflection curve for a UHPFRCs slab without (a) and with fiber orientation defect (red line in the square on the right high corner of each figure) with view of the

microcracks at different loading stages (b) (Baril, Sorelli, Réthoré, Ferrara, et al. 2016).

More practically, in order to account for the effect of the fiber orientation, French national recommendations (AFGC/SETRA 2013) and national code (AFNOR 2016) proposes a suitability test which consist of extracting UHPC samples according to different directions from the full-scale structure (see example of suitability test for a I-gider beam in Figure 3..5.1.5). Then, the sawn samples are tested in bending and an average K-factor is calculated by comparing their flexural strength to that of a sample molded specimen with random fiber orientation. A local and a global K-factor have been defined to account for local (minimum) and global (average) effects. The K-factor is finally employed to reduce the design tensile law of UHPCs. Based on several experiences the K-factor ranges from 0.6 (favorable) to 2.5 (unfavorable). The French recommendations proposes two coefficients Local and Global, a KL=1.7 and KG=1.3 in the case of lack of a sustainability test. The tensile law employed in design is further reduced by the K-factor to account for the effect of the fiber orientation. The model code 2010 also recognizes the K-factor. The CSA S6, Annex 8, Australian Guidelines, German Guidelines, Swiss Specification and Spanish Guidelines all provide guidance for factors to account for fiber orientation and dispersion.

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Figure 3.5.1.5. Example of sample extraction for the sustainability test as proposed by

AFGC(2013).

. 3.5.2 Cyclic Strength and Stiffness Degradation – Vic Perry The type of cyclic loading (amplitude, frequency, magnitude and duration) in which a structure is subjected is a function of the location and type of application (wind for wind turbine shafts, traffic for bridges or seismic). To date, simulated traffic cyclic loadings have been tested for bridge structures more than either wind or seismic loadings. Research by Graybeal and Hartmann;,Parsekian et al; Scmmidt and others has shown good performance for UHPC under equivalent highway cyclic loadings when the tensile stress level is maintained below 40% of the UHPC’s elastic tensile modulus of rupture, in tests conducted on more than 2 million cycles of loading. Research by Loraux and Sritharan et al provides examples and research on the use of UHPC for tall wind turbine shafts. Constant amplitudes uniaxial compressive fatigue tests were conducted on thin UHPC plates. The fatigue endurance limit of UHPC under compressive stresses at 10 million cycles was determined to be around 65% of the ultimate limit state. UHPC was found to be particularly well suited for offshore turbine support structures [Loraux, 2018]. The seismic performance of UHPC connections for precast bridge super structure elements was undertaken at the SUNY, Buffalo and determined that even in severe earthquakes (mid-spans subjected up to 0.61 g in acceleration) the bridge deck resilience was excellent with no signs of damage [Lee, 2014]. 3.5.3 Dynamic Strength – Tess Ahlborn, Bradley Foust & Barzin Mobasher It is generally accepted that concrete materials experience an increase in compressive strengths under dynamic loading scenarios (Bischoff and Perry 1991). Structural loading can encompass a broad range of strain rates, from creep on the order of 10-8 s-1 to ultra-high dynamic rates at a fraction of a millisecond (Figure 3.5.3.1). A number of experimental techniques exist to investigate high strain rate material properties under uniaxial loads: split Hopkinson pressure bar (SHPB), falling weight devices, flywheel facilities, hydraulic machine, etc. [Meyers, Nicholas & Hoge]. On the other hand, flexural impact behavior of cement composites has also been studied by means of low- and high-velocity impact using Charpy, Izod, drop-weight, and ballistic tests. These tests can be either instrumented or heuristically based and the resistance is measured based on fracture energy, damage accumulation, and measurement of the number of drops to achieve a desired damage or stress level [Bindiganaville et al and Mobasher]. Due to the various test methods, it has been well established that the mechanical response of cement-based materials is affected by the strain rate [Mobasher].

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Creep Quasi-Static Vehicle ImpactHard Impact (Missiles,

Rock Falls)

Earthquake/Induced Shock

Blast Ultra High

Rate

Strain Rate (1/sec) Figure 3.5.3.1 Strain rates vs type of loading Both normal-strength concrete (Bischoff and Perry 1991) and UHPC (Cavill et al. 2006; Rong et al. 2010; Clark 2013) show strength increases at high strain rates. This strength increase is customarily quantified using the dynamic increase factor (DIF), the ratio of dynamic failure strength to quasi-static failure strength. Normal strength concrete, ambient cured UHC, and thermally treated UHPC specimens were tested in compression at 2:1, 1:1, and 0.5:1 aspect ratios using the SHPB method (Clark 2013). Based on results of specimens meeting recommended tolerances, DIFs were found to be between 3.65 and 4 for NSC, 1.73 and 2.95 for ambient cured UHPC, and 1.21 and 2.45 for thermally treated UHPC for strain rates between 102 and 103 s-1. While UHPC experiences a relative increase in dynamic compressive strength, it is less strain rate sensitive than NSC. Dynamic tensile data on fiber reinforced concrete that characterize the full displacement-load history are, however, limited because a standard test methodology does not exist for various strain ranges which can be achieved with different equipment. Characterization of dynamic tensile properties of materials is also challenging as the failure process is affected by the mode and manner of testing. Problems appear at high rate loading due to inertial effect, non-uniform loading, and difficulties in measuring reliable mechanical properties. Lack of general agreement about the standards and methodology used to conduct dynamic tests further complicates the merging of the databases [Xiao]. Xu and Wille investigated the fracture energy of UHPFRC under direct tensile loads with varying strain rate (10-4 s-1 to 10-1 s-1), where the dynamic impact factor (DIF) was as high as 1.53. Meng et al. conducted flexural tests of UHPC beam specimens with displacement ranging from 0.05 to 5.00 mm/min. For the notch-to-depth ratio of 1/6, the flexural strength increased from 23.59 to 38.36 MPa, while pronounced increases in residual strengths were also observed. Rong and Sun conducted spalling tests to determine the dynamic tensile behavior of UHPC using a SHPB test machine. Some important findings were reported including the significant rate sensitivity of spalling strength, crack pattern and successful implementation of numerical modelling using Johnson-Holmquist-Concrete material model. Cadoni and Forni tested notched UHPC specimens using a Split Hopkinson Tensile Bar at stress rates ranging from 400 to 1000 GPa/s. Tran et al. investigated the direct tensile responses of UHPC at quasi-static and dynamic strain rates of 5-24 s-1 using SEFIM and found that the tensile resistance was much higher compared to static loads. Stone and Krauthammer investigated the input energies necessary to fail UHPC and UHPFRC cylinders via a drop hammer. Static and dynamic impact experiments were carried out on 150 mm x 300 mm (6” x 12”) NSC and UHPC (with and without fibers) cylinders using a drop hammer. Mix design for the UHPC (with and without fibers) were the same except for the

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inclusion of 30 mm hooked steel fibers. Test data was analyzed to investigate total input energy and energy distribution at specimen failure. Impact velocities for the UHPC (with and without fibers) specimens were approximately 2.0 and 3.7 m/s, respectively. Static testing indicated similar energy capacities for the UHPC, with and without fiber specimens. Under impact testing, the UHPC specimens with fibers required 477-700% higher input energy to ensure failure compared to the UHPC without fiber specimens. This enhanced energy capacity was primarily attributed to the steel fibers which minimized brittle failure and restricted crack propagation. Larger scale testing of structures is underway. Using a high-capacity shock-tube that can simulate a blast wave generated by the hemispherical free air surface bursts of high explosives, testing was conducted on a series of UHPC columns with variable detailing [Aoude et al.]. Results showed that UHPC in columns significantly improved performance under extreme loading, and seismic detailing further enhance performance. Field tests of columns also showed superior performance to high-strength concrete columns under blast loading conditions [Xu et al.]. Additional research is on-going to study the effect of accumulated damage on the blast response of UHPC columns. Furthermore, the effect of fiber alignment on the dynamic compressive strength and ductility of an ultra-high performance concrete was investigated by Groeneveld, et. al. Flow-induced steel fiber alignment was nondestructively characterized using x-ray computed tomography. While dynamic compression strength was independent of fiber orientation, the ductility, as measured at peak stress, increased with the proportion of fibers oriented perpendicular to the applied load. UHPFRC exhibits excellent performance under high-strain rates and has been successfully employed in military applications and safe barriers. Based on several tests, UHPC demonstrated superior performances under extreme dynamic loading when compared to conventional concrete [(Habel and Gauvreau ; Millard et al. Parant et al.]. UHPC have a high energy-dissipation capacity combined with the transfer of tensile stress after cracking, which could be of interest when intense dynamic loads are involved and the overall strength is an issue. Figure 3.5.3.2 shows the relative tensile strength (normalized to the static tensile strength) of a UHPCs in fiction of the deformation rate [(Millon et al.]. With strain rate greater than 1/s the tensile strength increases up to 16 times. As for applications, the impact strength of UHPCs was also studied in connection with radioactive-waste container applications [(Toutlemonde et al.] and protective structures [(Rebentrost and Wight]. Note that the fiber distribution can lead to considerable anisotropy of both the static and dynamic properties [Adeline]. The effect of possible anisotropy damage due fiber distribution due to blast impact may

require further study for specific marine applications

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Figure 3.5.3.2 Relative tensile strength of UHPCs at different strain rate showing multiplicative factor of 16 at high strain rate [Millon et al.].

Figure 3.5.3.3 shows the effect of the fiber type on UHPC and HSC dynamics behavior. While the steel fibers are the most effective to increase the dynamics tensile strength, the High Density Polyethylene fibers are the most effective to increase the dynamics fracture energy [(Curosu and Mechtcherine].

(a) (b)

Figure 3.5.3.3 (a) Dynamic tensile strength and (b) dynamics fracture energy material properties of ordinary concrete (OC) and UHPC with steel, PVA and HDPE fiber [Curosu and

Mechtcherine 2016].

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While the dynamic strength and ductility of UHPC continues to be investigated, documented design standards are not available for this material under high strain rate loadings. 3.5.4 Fatigue Behavior – Luca Sorelli The main aim of the fatigue tests is to establish relations between the upper stress level S and corresponding number of cycles to failure N, the so-called S-N or Wöhler curves. Figure 3.5.4.1 shows a typical fatigue behavior of UHPC under bending in terms of deflection vs. cycles for a beam tested at a load level of 50% of the static flexural strength [Lappa, Braam, and Walraven]. After the initial stage, where the deformations increase rapidly, the process is stabilized and the deformations increase slowly at a constant rate. These first two stages normally correspond to 80% of the total fatigue life of the test specimen. Before failure at about 30500 cycles, the deformations then again increase rapidly.

Figure 3.5.4.1 Example of deflection increase at increasing number of load cycles during a

fatigue test of a UHPC beam under bending [Lappa, Braam, and Walraven 2004].

The tensile fatigue behavior (Figure 3.5.4.2)of UHPC under constant amplitude fatigue cycles was studied up to a maximum of 10 million cycles with the objective to determine the endurance limit([Makita and Brühwiler]. An endurance limit1 EL was obtained in all three domains of UHPC tensile behavior and at a stress levels of (1) EL = 0.7 in the elastic domain, (2) EL = 0.6 in the strain hardening domain and (3) EL = 0.45 in the strain softening domain. UHPC specimens subjected to a given tensile stress showed rather large differences in local deformations, which confer significant stress and deformation redistribution capacity to the bulk material enhancing thus the fatigue behavior. UHPC fatigue fracture surface showed clear signs of matrix spalling and pulverization, which is the result of snubbing as well as abrasion of fibers.

1 EL is defined as the ratio between the maximum fatigue stress and the elastic limit strength of UHPFRC

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(a) (b) Figure 3.5.4.22 (a) test set-up for tensile fatigue test; (b) Fatigue S-N curve under tension

[Makita and Brühwiler 2014].

For fatigue loading under compression, S-N-curves for UHPCs and NSC are compared in Figure 3.5.4.3 (a), showing a rather good-natured behavior. Fibers are essential to reduce the scatter of those results. The (relative) stress range of UHPFRC for a large number of load reversals (> 2 million) is similar high as for NSC, while the absolute stress level is much higher than for NC. Fatigue testing on UHPCs (Ductal FM ®) was stopped after about 1 million cycles where only little damage was observed on all specimens. After fatigue testing, the specimens were subjected to quasi-static flexural force again and there was no influence of preceding bending fatigue loading on the ultimate resistance of the specimens [(Behloul et al. 2005]. Other researchers found similar results Flexural fatigue test on UHPCs were carried out by [Lappa, René Braam, and Walraven 2006].

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(a) (b)

Figure 3.5.4.3. (a) Comparison of NC and UHPCs in terms of S-N-curves under tension [Fehling et al.2014]; (b) Triaxial and uniaxial S-N curves for UHPCs [Grünberg and Ertel, 2012].

In general, the test results on UHPC fatigue resistance showed a large scatter due to variation in material strength, applied stress level, distribution of fibers, number of fibers at critical cross-sections and test specimen type [Abbas, Nehdi, and Saleem, 2016]. The fatigue behavior of UHPC structures has also been tested. For instance, the thin slab of UHPC waffle deck was tested under cyclical flexural loading according to the Eurocode loading conditions without any sign of damage [Gomes et al., 2011]. When submerged, conventional concrete (not pre-stressed) shows a reduction of fatigue endurance, apparently due to high pore pressures generated within the microcracks. Interestingly, UHPC the addition of microsilica in UHPC did not shown such reduction [Gerwick, 2002]. The effect of the underwater condition on the UHPC may be further experimentally

verified for marine applications due to the limited data in open literature, although the results of Gerwick seems to indicate that this is not critical for UHPC [Gerwick].

3.5.6 Property Gradients Thermal and moisture gradients exist in UHPC structures just as they do in other concrete systems. Thermal gradients can be handled with the same design considerations as normal strength concrete. However, due to the low porosity of UHPC, moisture gradients are more severe compared to conventional concretes or HPC.

4.0 Strength Design Considerations This section on strength design considerations reviews the strength of UHPC members at the ultimate limit state at the cross-sectional level for a variety of structural actions. The failure modes addressed in this chapter are based on material failure. The structural actions considered are flexure, shear, torsion, axial load, and combinations of axial loads and bending moments. Structural limit state predictions are covered so that they apply to members and

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systems including multiple materials or hybrid solutions (for example: UHPC Filled Steel tubes or UHPC Filled FRP Tubes). The required inputs are uniaxial material behavior in compression and tension for UHPC and reinforcing materials. Guidelines for how to obtain these inputs are provided in Chapter 2 – Mechanical Properties. 4.1 Compression and Tension Design Considerations 4.1.1 Compression – Mohamed Moustafa Compression members or struts can be part of different architectural or structural systems such as trusses. However, the most common application is columns under pure axial load, which is the focus of this section. While the ultra-high compressive strength of UHPC makes it an obvious solution for columns and struts, the use of fibers within the matrix provide an additional benefit of being able to reduce the quantity of ties in columns. The tensile capacity of the fiber matrix provides additional resisting to busting forces of column reinforcement in compression. Several studies investigated the behavior of UHPC columns. Kimura et. al. (2007) investigated the effect of (1) volumetric ratio of steel fibers, (2) lateral reinforcement ratio, and (3) axial loading type of reinforced UHPC columns with varying axial load under cyclic loading. They used NSK (Nagashima et al. 1995) model for stress-strain relationship of concrete, developed for HSC, in which the effect of steel fibers is not taken into account. Furthermore, they considered NZS equations for assessment of maximum flexural strength of RC columns, which is suitable for concrete with the maximum strength of 200 MPa and without steel fibers. The results of their tests can be summarized as follows: (1) UHPC columns exhibited very good flexural strength and load carrying capacity up to drift angel of 3% even under varying high axial loading condition; (2) For UHPC with strength of 200 MPa, the maximum flexural strength under varying axial load was about 1.47 times of Ultra High Performance Columns without steel fibers; (3) The NSK and NZS equations are appropriate for calculation of maximum flexural strength of UHPC with maximum strength of 200 MPa, while ACI and AIJ equations overestimate the strength by 4 to 28% (Table 4.1); (4) Addition of steel fibers results in reduction of column damage, crack dispersion, and decreasing crack width. In Table 1, unit 600 is 198 MPa plain concrete without any steel fibers, and unit 601, 602, and 603 are 207 MPa UHPC with 1% steel fibers. Moreover, Illich et. al. (2014) studied the load-carrying behavior of full-scale pre-tensioned columns of UHPC under the same eccentric compression loads at the both ends. They used their special method of loading control to be able to record post-peak behavior of columns.

Table 4.1 Comparison of measured to calculated maximum strength [Kimura et al. 2007].

Hosinieh et al. (2015) examined the influence of UHPC and transverse reinforcement detailing

Commented [vp18]: Define

Commented [vp19]: Define

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on strength, ductility, and failure mechanisms of six large-scale specimens, designed based on Canadian CSA A23.3-14 code, under pure axial load. They observed that for a particular transverse reinforcement configuration, reduction of space of transverse reinforcements results in enhancement of columns post-peak ductility with a moderate increase in the column capacity under axial loads. For a particular spacing of transverse reinforcement, their configurations did not have a significant effect on column strength whereas toughness (area under the load-strain curve) was enhanced. Compared to the same experiments, carried out on HSC columns, UHPC columns have higher load carrying capacity (Fig. 4.1.1a). The influence of UHPC on post-peak ductility was more apparent in low confined and less important in highly confined columns. This means UHPC and transverse reinforcement have hybrid role in enhancement of post peak behavior. The authors also used two literature proposed confinement models for HSC; however, they need to be modified for UHPC. They observed good agreement between the experimental and numerical results from Aoude’s FRP confinement model (2008), and their own proposed model for unconfined UHPC (Fig. 4.1.1b). In Fig. 4.1.1a, CRC stands for Compact Reinforced Composite, a UHPC mixed developed in Denmark. C3-80 column has the reinforcement configuration type of C3 with 80 mm hoop spacing, and CS8 is a HSC column with similar size and configuration to C3-80. In Fig. 1b, HSC1 and HSC2 are confinement models proposed respectively by Razvi and Saatcioglu (1999) and Légeron and Paultre (2003), and FRC1 is fiber-reinforced concrete confinement model proposed by Aoude (2008).

Fig. 4.1.1 Comparison of: (a) normalized load-strain response for UHPC vs. HSC columns; and (b)

experimental and analytical load-strain curves predicted using HSC models (HSC1 and HSC2) and fiber reinforced concrete confinement model (FRC1) after Hosinieh et al. (2015).

Shin et. al. (2017) investigated the axial load response of UHPC columns with compressive strengths of 163 and 181 MPa. They used UHPC of 1.5 % steel fibers. They tested nine UHPC columns with ratios of 0.9-9.9% transverse reinforcement and two different configurations to study the applicability of the existing equations in predicting behavior of UHPC columns.

In addition to studying axial capacity of UHPC columns, few studies considered buckling of UHPC columns associated with the likely UHPC smaller sections compared to conventional concrete. Schmidt and Heimann (2011) and Heiman et. al. (2013) investigated the reliability of slender UHPC structural members to assess the likelihood of their buckling and decrease in safety level, and compared the results of probabilistic analysis of HSC columns of high rise buildings with the conservative design provisions of Eurocode 1 and 2. The study documented a considerable safety deficit in Eurocode 2, Part 1-1 (buildings). The safety elements become ineffective when buckling occurs prior to steel yield or concrete strength. The reliability of UHPC members must be considered and the effects of shrinkage have to be taken into account in a probabilistic model of UHPC.

Commented [vp20]: LF: What does it means “prior to concrete strength”? If it is buckling for sure it will occur before the concrete achieves its strength (and considering compatibility this may also mean before steel yields) Please elaborate better this sentence Also: what do you mean with “safety deficit of EC2?” And “the safety elements become ineffective when …”

Commented [vp21]: LF: The first part of this statement is rather obvious (when we design we consider in some way the “reliability”) … Please explain why shrinkage has to be taken into account (because it induces deformations which in a structural assembly which is redundant may results in stresses e.gf. due to moments and this increases the buckling “proneness?)

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4.1.1.1 Modeling of UHPC Columns Davila (2007) discussed analytical modeling for UHPC and the evolution in design codes and their philosophical bases. Caldwell (2011) used the stress-strain relationship shown Fig. 4.2.1.1 for UHPC modeling to numerically study the incurrence of plastic hinges and inspect the resultant behavior of NSC and UHPC columns under severe and short duration dynamic loads. Using a similar constitutive model (Fig. 4.1.1.1), Astarlioglu and Krauthammer (2014) numerically compared the response of a reinforced UHPC column with the same size and same reinforced NSC column under four levels of idealized loads. They analyzed 16 columns (four axial load cases for each blast load level and four blast load configurations). They observed that the difference of UHPC and NSC in peak displacement, when the load is small enough that does not lead to failure, was relatively small. On average, displacement in UHPC columns was respectively 27% and 30% smaller than NSC columns for simply supported and fixed boundary conditions.

Fig. 4.1.1.1 Stress-strain curve used for UHPC modeling (Caldwell 2011 and Astarlioglu and

Krauthammer 2014).

4.1.1.2 – applicable code discussion? 4.1.2 Tension – Vic Perry There have been very few examples of the use of UHPC for structural elements solely in uniaxial tension. One such example is the canopy shell struts for the Shawnessy LRT Station roof (See Fig 4.1.2) constructed in Calgary, Canada in 2004 [Perry et al, 2005]. The struts designed for axial compression and tension used redundant stainless-steel reinforcing bars in addition to designing the UHPC cross-section to carry the full compression and tension loads. Not only did the redundant reinforcing bars have the capacity to carry the full axial loads in the event of a post-cracking failure, but they also assist in distributing the tensile strains during the strain hardening and strain softening phases.

Commented [vp22]: LF: A plastic hinge is likely to occur when some moment is present So if we are speaking about columns under compression this reference is not appropriate here

Commented [vp23]: LF: Displacements: what do you exactly mean? Axial shortening? Or is the investigation of the column under axial load and lateral deflection?

Commented [vp24]: To be Completed by Mohammed Moustafa

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Fig 4.1.2 UHPC Canopy shells supported on UHPC Struts. Photo Credit: Perry 4.1.2.1 – applicable code discussion?

4.2 Flexure – Fatmir Menkulasi Flexural behavior of reinforced concrete members is understood better than shear behavior, which is typically estimated using semi-empirical approaches. Because of the differences in constitutive relationships between normal strength concrete (NSC) and ultra-high performance concrete (UHPC) the estimation of flexural strength of members constructed with UHPC has resulted in a different yet similar approach to that used for NSC. In essence, the parabolic stress-strain relationship typically used for NSC is replaced with an idealized curve for UHPC. The main difference on the compression side is that often the relationship between stress and strain in UHPC is almost linear with some softening taking place as the peak stress is achieved. Post-peak behavior varies depending on the amount of fibers. Accordingly, the familiar Whitney’s stress block used for traditional reinforced concrete members is typically replaced with either a linear or bilinear curve for UHPC members. On the tension side of the stress-strain curve there is a fundamental difference compared to NSC beam behavior. In NSC members the tensile strength of concrete is typically ignored because tensile strength is typically 1/10 of the compressive strength, tensile failure is brittle and tensile strength cannot be relied upon when ductile member behavior is desired. Depending on the amount of fibers used, UHPC offers a much improved behavior in tension. In several mixes, the peak tensile strength is greater than the first cracking strength exhibiting a strain hardening property. Additionally, tensile strengths in excess of 15 MPa (2 ksi) are possible, which is a significant contribution considering that many concrete structures are built with concrete that has a compressive strength in the range of 20 to 35 MPa (3-5 ksi). The idealization of the tension curve in UHPC members continues to be a subject of research with some researchers proposing a bilinear curve (trapezoid) and others suggesting a rectangular approximation. This section provides a summary of the literature review on the flexural design of UHPC members and it references studies that provide a flexural design approach for the ultimate limit state of reinforced and prestressed concrete sections. All presented approaches are based on the assumption that plane sections before bending remain plane after bending. Studies that deal

Commented [vp25]: To be Completed by VP

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with the subjects of cracking, stiffness, and deflections are discussed under the serviceability section.

One of most comprehensive design guidelines and standards for UHPC to date has been developed by the Association Française de Génie Civil (AFGC), i.e. French Association for Civil Engineering (2016a, 2016b). Flexural design is based on specified stress-strain relationships in compression and tension. For compression, two stress-strain curves are provided depending on whether the goal is to conduct nonlinear analysis or to design for the ultimate limit state (Fig. 4.2.1). A parabolic curve is specified for conducting nonlinear analysis as shown in Fig. 4.2.1a and equations 1 through 7 can be used to develop the curve. In these expressions, fctfm is the mean value of the post-cracking strength (which can be determined based on section 5.5.4 of standard NF P18-470 (2016a)), and Kglobal is the orientation factor associated with global effect.

(a) (b)

Fig. 4.2.1 Stress-strain relation of UHPC in compression for: (a) non-linear structural analysis; (b) design at ULS according to French-Standard (2016a).

𝜎 = 𝑓𝑐𝑚

𝜂.𝜀

𝜀𝑐1,𝑓

𝜂 − 1 + (𝜀

𝜀𝑐1,𝑓)𝜑.𝜂 (1)

𝜀𝑐1,𝑓 = [1 + 4𝑓𝑐𝑡𝑓𝑚

𝐾𝑔𝑙𝑜𝑏𝑎𝑙 . 𝑓𝑐𝑚] [1 + 0.16

𝑘0(𝑓𝑐𝑚

2 + 800)]𝑓𝑐𝑚23⁄

𝑘0 (2)

𝑘0 =𝐸𝑐𝑚

𝑓𝑐𝑚1 3⁄

(3)

𝜂 =𝑘

𝑘 − 1 (4)

𝑘 = 𝐸𝑐𝑚𝜀𝑐1,𝑓

𝑓𝑐𝑚 (5)

𝜑 =

{

1 𝑠𝑖 𝜀 ≤ 𝜀𝑐1,𝑓

𝑙𝑛 (1 − 𝜂 +𝜂0.7

𝜀𝑐𝑢1,𝑓𝜀𝑐1,𝑓

)

𝜂. 𝑙𝑛 (𝜀𝑐𝑢1,𝑓𝜀𝑐1,𝑓

)𝑠𝑖 𝜀 > 𝜀𝑐1,𝑓

(6)

𝜀𝑐𝑢1,𝑓 = [1 + 15𝑓𝑐𝑡𝑓𝑚

𝐾𝑔𝑙𝑜𝑏𝑎𝑙 . 𝑓𝑐𝑚] [1 +

20

𝑓𝑐𝑚] [1 + 0.16

𝑘0(𝑓𝑐𝑚

2 + 800)]𝑓𝑐𝑚23⁄

𝑘0 (7)

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For estimating flexural strength at the ultimate limit state a bilinear compression curve is specified as shown in Fig. 4.2.1b. Equations 8 through 10 can be used to generate the curve where, fctfm is the mean value of the post-cracking strength (which can be determined based on section 5.5.4 of standard NF P18-470) , Kglobal is the orientation factor associated with global effect ( section 4.4.3 of standard NF P18-470), and fcm is the mean value of compressive strength (section 5.5.2 of standard NF P18-470). Physical testing is required to either develop the full stress-strain relationship of UHPC in tension or to obtain key parameters such as those shown in Fig. 4.2.2. For additional information on the French recommendations the reader should refer to references 2016a and 2016b. Once the stress-strain relationship for UHPC in compression and tension is defined, the calculation of nominal moment capacity is based on principles of equilibrium and strain compatibility.

𝑓𝑐𝑑 = 𝛼𝑐𝑐 𝑓𝑐𝑘 𝛾𝑐⁄ (8)

ɛ𝑐0𝑑 = 𝑓𝑐𝑑 𝐸𝑐𝑚⁄ (9)

𝜀𝑐𝑢𝑑 = (1 + 14𝑓𝑐𝑡𝑚

𝐾𝑔𝑙𝑜𝑏𝑎𝑙 . 𝑓𝑐𝑚) . 𝜀𝑐0𝑑 (10)

Fig. 4.2.2 Definition of fctf (a) in case of a local maximum, (b) where there is no local maximum (French-Standard 2016a).

In 2006, the Japan Society of Civil Engineers (JSCE) published Recommendations for Design and Construction of Ultra High Strength Fiber Reinforced Concrete Structures (Draft) that builds on the JSCE Standard Specifications for Concrete Structures. Similar to French Recommendations the use of stress-strain curves rather than an equivalent stress block is recommended for flexural design. No minimum amount of steel reinforcement is required because the bridging action of the steel fibers provides the strength after cracking. Physical testing os required to characterize the stress-strain relationship of concrete in tension. Uchida et. al. (2006) provides a discussion of the JSCE UHPC design and construction recommendations.

Gowripalan and Gilbert (2000) developed design guidelines for Ductal prestressed concrete beams. The idealized stress-strain relationship for uniaxial compression and tension is defined as shown in Figs. 4.2.3 and 4.2.4, respectively, assuming that there is at least 2% steel fibers by volume. Lf indicates the length of fibers and D indicates the depth of the beam. The compressive

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stress-strain relationship features a trilinear curve. The maximum compressive stress is limited to 85% of that obtained from cylinder/cube compressive strength tests and the modulus of elasticity is taken equal to 50,000 MPa. The maximum compressive stress remains constant up to a strain of 0.004 then reduces linearly to zero stress and a maximum compressive strain of 0.007. In tension, the stress-strain relationship also features a trilinear curve with the maximum tensile stress equal to 5.0 MPa. The tensile strain at the end of the yield plateau and the maximum tensile strain are defined in Fig. 4.2.4. However, when estimating the nominal moment capacity of a prestressed concrete beam it is recommended that the strain and stress distributions shown in Fig. 4.2.5a and 4.2.5b be used for cross-section with bonded and no bonded reinforcement, respectively. For cross-sections with bonded reinforcement, the maximum compressive strain is limited to 0.0035. For sections containing no bonded reinforcement the ultimate strength in bending may be assumed to occur when the extreme fiber tensile strain equals εt,p as defined in Fig. 4.2.4. The design flexural strength is obtained by multiplying the theoretical moment by the strength reduction factor ϕ. The strength reduction factor of 0.8 is used for sections containing bonded reinforcement or tendons and 0.7 for sections containing no bonded reinforcement or tendons.

Fig. 4.2.3 Design stress-strain relationship in compression (Gowripalan and Gilbert 2000).

Fig. 4.2.4 Design stress-strain relationship in

tension (Gowripalan and Gilbert 2000).

a) b)

Fig. 4.2.5 Stress and strain distribution at ultimate bending limit state (Gowripalan and Gilbert 2000): a) cross-section with bonded reinforcement, b) cross-section with no bonded reinforcement

Graybeal (2008) states that “until a significant number of full-scale flexure tests are completed, it will not be possible to present a calibrated set of conservative parameters for use in the flexural design of UHPC prestressed girders.” However, in absence of such data Graybeal (2008)

suggests the utilization of the uniaxial stress-strain response depicted in Fig. 4.2.6 and the

following criteria for the flexural design of prestressed UHPC beams maybe used: 1. A maximum compressive strength of 24 ksi (165 MPa) corresponding to 0.85 times the

observed steam-treated compressive strength;

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2. A tensile capacity of 1.5 ksi (10.3 MPa), corresponding to 0.5 times the pre- and postcracking uniaxial tensile capacity;

3. A modulus of elasticity of 7,600 ksi (52.4 GPa), and 4. A limiting tensile strain of 0.007 corresponding to 70% of the tensile strain observed in

the extreme tensile fiber of the girder just prior to gross cracking, strain localization, and girder failure.

A division of the suggested maximum design compressive strength with the modulus of elasticity results in a maximum compressive strain of 0.00316. The design philosophy detailed by Graybeal (2008) is similar to portions of some UHPC structural design procedures detailed elsewhere (Association Française de Génie Civil 2002; Casanova and Rossi 1996; Gowripalan and Gilbert 2000; Uchida et al. 2005).

Fig. 4.2.6. Simplified uniaxial stress-strain behavior for I-girder flexural design (Graybeal 2008)

Almansour and Lounis (2010) used a bilinear curve on the compression side and ignored tensile contribution when estimating the flexural strength of pretensioned UHPC elements. The bilinear approximation of the stress-strain curve was based on the French Code (AFGC 2002), is shown in Fig. 4.2.7, and includes: i) a first line from zero stress and zero strain up to a strength of (fcu) and a strain of (fcu/Euhpc); and ii) a second line that is horizontal up to the ultimate strain of εcu = 0.003, (εcu = 0.0035 in the Japanese recommendations (JSCE 2006)). The ultimate strength (fcu) is given by AFGC (2002) and adapting to CHBDC (CSA 2006) yields:

𝑓𝑐𝑢 =0.85𝜑𝑐𝑓𝑐𝑗

𝜃 (1)

Where fcj is the cylinder compressive strength at age j, which is taken in present study equal to 28 days; θ is a factor related to the probability of the load application period or rate of loading where θ = 1.0 for loads with application period equal to or greater than 24 hours, θ = 0.9 for loads applied over a period between 1 hour and 24 hours, and θ = 0.85 for loads with an application period of less than 1 hour; φc is a coefficient that takes into account the uncertainty and variability of UHPC resistance, as well as localized effects. Fig. 4.2.8 illustrates the distribution of strain and stress in a composite bridge I-beam and deck section.

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Fig. 4.2.7. Mechanical properties of an ultra-high performance concrete (UHPC) and high

performance concrete (HPC) (Almansour and Lounis 2010)

Fig. 4.2.8. Stress and strain distribution at the ultimate limit state for UHPC girders

(Almansour and Lounis 2010)

Aaleti et al. (2013) proposed a linear curve on the compression side and a bilinear one on the tension side for the estimation of flexural strength in UHPC waffle decks (Fig. 4.2.9). This approach is similar to that proposed by Graybeal (2008) for prestressed I-girders and includes the following criteria:

UHPC exhibits tensile capacity well past its initial tensile cracking strength, until fiber pullout occurs at a tensile strain (εtu) of 0.007. This strain value is a conservative estimate for fiber pullout and is recommended for design. The corresponding limiting tensile strength (ftu) of UHPC is taken as 1.2 ksi.

UHPC exhibits a linear compressive stress-strain response up to the compression failure beginning at a compressive strain of 0.0032. Thus, the compressive strain at the ultimate limit state (εcu) is taken as 0.0032 and the corresponding compressive strength (fcu) is taken as 24 ksi.

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Fig.4.2.9. Strain and stress distribution along the cross-section at cracking and ultimate limit

states (Aaleti et al. 2013) The flexural design approaches presented so far include a maximum compressive strain that is either equal to or slightly higher than 0.003. This maximum compressive strain directly limits the amount of longitudinal reinforcement that could be used in flexural members, which in turn limits the flexural capacity of the members (Kaka et al. 2016). Kaka et al. (2016) concluded that the maximum usable compressive strain that could be safely used in the design of UHPC flexural members is εcu = 0.015 (Fig. 4.2.10). This leads to load carrying capacities that were 4.5 to 5 times higher than those of equivalent reinforced concrete beams designed with tension controlled behavior as recommended by ACI 318 (2014) and AASHTO LFRD Specifications (2017). Such a high load carrying capacity was made possible by using five times more flexural reinforcement than what would be allowed based on the current tension controlled limit for reinforced concrete members, which is based on a maximum concrete compressive strain at failure equal to 0.003 and a minimum tensile strain in reinforcement equal to 0.005. In terms of behavior, it was concluded that the UHPFRC beam exhibited very large deflections with a few small flexural cracks. For design purposes it was concluded that the depth of the compression block could be determined using the same β1 parameter that is used for conventional concrete. Finally, it was concluded that the contribution of the tensile stress from UHPFRC to the moment capacity warrants further study.

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Fig. 4.2.10. (a) ACI 318 and AASHTO design criteria; (b) strain profile of RC beam; (c) strain

profile UH-FRC beam (Kaka et al. 2016)

Yao et al. (2016) and Soranakom and Mobasher (2008) used a bilinear stress-strain relationship on the compression side and a trilinear one on the tension side to propose a bilinear moment-curvature relationship for predicting the load deformation response of statically determinate UHPC beams (Fig. 4.2.11). Analytical solutions that characterize the full range distribution of curvature, angle of rotation and deflection at any point along the beam were proposed.

Fig. 4.2.11. Material models for homogenized UHPC: (a) compression model and (b) tension

model Naaman (2018) investigated the influence of various stress-strain relationships on the nominal moment capacity of a fiber reinforced concrete section. Fig. 4.2.12 shows possible distributions at nominal bending resistance and Fig. 4.2.13 shows typical stress block models for simplified analysis. The following observations were made:

1) In all cases the numerical value of nominal bending moment Mn, shows very little sensitivity to the shape of the concrete stress block in compression (rectangular, parabolic, or triangular) and is mainly influenced by the tensile response of the composite.

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2) Changing the shape of the tensile stress block from rectangular with average post-cracking stress �̅�𝑝𝑐 to triangular but with the same �̅�𝑝𝑐 reduces the modulus of rupture

(MOR) by about 28%. Naaman (2018) defines the MOR as the maximum value of equivalent elastic bending stress corresponding to the nominal bending resistance of a beam (that is, moment at maximum load). The MOR can be calculated by dividing the nominal moment capacity, Mn, by the elastic section modulus with respect to the extreme tensile fiber, St.

3) If a stress-elongation response or a stress versus crack opening response is available, estimating the average post-cracking stress �̅�𝑝𝑐 for and estimated crack opening at

nominal bending resistance allows for a rational reasonably accurate prediction of nominal bending moment Mn.

In general, it was determined that the stress-strain relationship for UHPC in tension has a much greater influence on the nominal moment capacity of the section than the stress-strain relationship in compression. This emphasizes the importance of either characterizing the tensile response of UHPC using reliable test methods or developing simplified relationships that are based on reliable test results.

Fig. 4.2.12. Typical examples of strain and stress distributions at nominal bending resistance

(Naaman 2018)

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Fig. 4.2.13 Typical stress block models for simplified analysis: (a) Assumed linear strain diagram, (b) Parabolic compression stress block, uniform tensile stress block, c) ACI rectangular compression stress block, uniform tensile stress block, d) ACI rectangular compression stress block, triangular tensile stress block, e) Triangular compression stress block, uniform tensile stress block (Naaman 2018) This section provided a summary of various flexural design approaches for UHPC members. In general, all approaches were based on the incorporation of the uniaxial stress-strain relationship for UHPC in sectional analysis to estimate the flexural strength at any given section. There is currently no consensus as to: 1) what the maximum usable concrete compressive strain is, 2) what the maximum usable tensile strain is, 3) what is the minimum amount of fibers needed to achieve a certain maximum usable compressive or tensile strain, 4) what are the definitions for tension-controlled, compression-controlled and transition zone behavior, and 5) how to best represent the compressive and tensile behavior of UHPC at a material level when conducting a sectional analysis at the ultimate limit state. Additionally, the type of reinforcement that UHPC interacts with plays an important role in overall member behavior. The use of UHPC in common and repetitive applications will perhaps provide the impetus for arriving at a unified approach for the flexural design of UHPC members. 4.3.x.x – applicable code discussion?

4.3 Combined Axial and Bending – Mohamed Moustafa

In many design cases, columns are designed to carry combined axial loads and bending moments. Only the behavior of UHPC columns under pure axial is briefly discussed in Section 4.2. However, more insight into the general design of UHPC columns under combined axial and bending forces, which can build on flexure design principles, is presented here. The effects of axial loads (mainly compression) can further increase the flexure capacity, which is important to properly quantify when columns are considered as part of lateral load resisting systems, e.g. moment frames in buildings or bridge columns. Limited testing under flexural or axial loads indicates that the flexural and axial strengths of UHPC members can be calculated with reasonable accuracy if the stress-strain relationships of UHPC are included in the analyses. The calculations are more complex than using the simplified approach of a rectangular compressive

Commented [vp26]: To be completed by Fatmir Menkulasi

Commented [vp27]: In the References for this section is listed 53 references but none of them are refered to here in the section. Many of these references are already referred to in other parts of this document, so they are duplicated. My suggestion is delete them all unless any specific ones are relevant to this section.

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stress block and zero tensile strength. Brief survey of how combined axial and flexure UHPC design is tackled in standards and guidelines along with the different experimental and analytical efforts that aimed at response characterization of UHPC is presented here. Moreover, novel UHPC and hybrid column designs, behavior of UHPC columns under different types of hazards, and modeling efforts for UHPC columns are briefly discussed.

4.3.1 UHPC Column Behavior under Lateral Loading and Different Hazards Some studies also considered the behavior of UHPC columns under different types of lateral static or dynamic loads subject to hazards such as earthquakes, fire, or blast and are briefly summarized below.

4.3.1.1 Earthquakes Sugano et al. (2007) studied a series of tests on columns and frames of UHPC buildings under seismic loading to provide guidelines for design and construction. Based on their investigation, UHPC is basically a brittle material which can be confined using high or ultra high strength lateral reinforcements. In this case, the UHPC columns can tolerate very high axial compression forces. The flexural behavior of UHPC columns also can be well assessed when taking the tensile resistance of UFC and confinement by lateral reinforcements into considerations. Steel-fibers in UHPC mixture significantly enhanced the shear resistance of columns and frames. On the other hand, Joe and Moustafa (2016) conducted a preliminary analytical study to investigate the design implications of using UHPC for seismic bridge piers in lieu of conventional concrete. They showed that up to 40% reduction in the columns cross-section can be obtained if UHPC is used to achieve same plastic moment capacity and ductility as conventional concrete piers under seismic loading.

Chao et. al. (2016) studied seismic response of UHPC beams and columns with relatively higher amount of longitudinal reinforcement (> 2.5%) used for moment frame beams compared to what is acceptable for conventional RC beams. Based on their research, UHPC columns have higher strength and drift capacity before significant damages, compared to RC columns. In UHPC columns failure phenomena such as: concrete spalling and crushing, bar buckling and hoop failure are reduced. At moderate drift of 1.0 to 2.0 %, minor damages happens. UHPC column had no strength degradation until 2.5 % drift and could maintain its peak strength at approximately close to a 4 % drift. The researchers also showed that the ACI 318 requirements can be relaxed if UHPC columns and beams are used. Particularly, the confinement requirements and amount of transverse reinforcement can be reduced for high strength concrete (>10 ksi) columns.

Wang et. al. (2016) established a finite element model, using Kent-Park model, to study the seismic performance of a pier of UHPC and high-strength steel. Concrete 02 by OpenSees platform is used as the constitutive model while the modified Kent-Park model is used for the

skeleton curve. Comment: Specify what kind of constitutive relationship is Concrete 02 by open sees (Please avoid software jargon) and also what does minor axial load and medium amount of transverse reinforcement mean Based on their parametric studies, the following

requirements were suggested to be considered for desirable seismic performance of UHPC: (1) Axial load ratio to be less than 0.4; (2) To have a drift ratio less than 1%, for a UHPC pier under minor axial load ratio and medium amount of transverse reinforcement, less than 2% longitudinal reinforcement to be used; (3) For small axial load ratio, the increase of transverse reinforcement can reduce residual drift ratio while it does not have any effect on ductility and energy dissipation of UHPC columns; (4) For short piers with high axial load ratio, the maximum ground acceleration capacity is a little insecure using inelastic response spectra, based on the nonlinear dynamic time history analysis.

Commented [vp28]: LF: It is important to clearly report here if the study of the behavior under seismic loadings was done through (quasi static) cyclic loading tests or through truly dynamic behavior I assume in most cases it is the former

Commented [vp29]: clarify

Commented [vp30]: Define UFC

Commented [vp31]: LF: We should define better what is minor damage, significant damage etc Information on cross sections, height, reinforcement details should be provided both for UHPC specimens and for reference NSC ones

Commented [vp32]: Ratio of what?

Commented [vp33]: This paragraph is not clear

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4.3.1.2 Blast Aoude et. al. (2015) presented the results of a study examining the blast load performance of UHPC columns. Li et. al (2015) carried out field blast tests on the four columns of their own developed UHPC, and compared the results with the numerical model. They noted that UHPC has superior blast resistant features. In the later study, the authors used the material model type 10 in LS-DYNA, which can be defined by user based on the uniaxial compression test on UHPC, to model the UHPC behavior in compression. Similarly, Zhang et. al. (2017) also used LS-DYNA to study the behavior of UHPC filled double skin steel tube columns under blast loading. They derived pressure-impulse diagrams for UHPC filled double skin steel tube columns in terms of residual axial load-carrying capacity after blast load, and examined the effect of axial load ratio, steel tube thickness, column dimension and concrete strength on pressure-impulse diagrams.

Zhang et. al. (2015) evaluated the residual behavior of UHPC infilled double-skin steel tubular columns after close-in blast loading. They carried out eight blast tests on three square and five circular columns with two different axial load levels. Then, they applied static axial compressive loads on the specimens until failure to investigate their residual capacity. Based on their observations, the axial load capacity of both undamaged circular and square columns were the same with negligible difference, which was probably due to better confinement status for circular ones. However, the flexural capacity of square columns was larger than circular ones. The columns with applied axial load of about 25% of their axial capacity, had larger flexural capacity while less ductility, compared to the load free columns. The UHPC infilled double-skin steel tubular columns could retain 60% of their axial load capacity after blast load. Localized buckling of outer steel tubes at mid span/ or column ends were observed. The columns with smaller permanent displacement had larger peak residual axial capacity. Besides, columns with no axial load, were more ductile than those with axial load during blast tests.

Xu et. al. (2016) tested four 0.2m×0.2m×2.5m reinforced UHPC columns under different designed explosions with same standoff distance of 1.5m, and compared their efficiency with four same sized and same reinforced HSC columns. Based on their investigations, use of UHPC rather than HSC can reduce the maximum and residual displacements and enhance the blast resistance of columns. Moreover, the axially loaded specimens have smaller deflections because of the influence of boundary conditions, which outweighs the P-delta effect.

4.3.1.3 Fire Unlike all the outstanding mechanical features of UHPC, its particular material properties and slenderness of structural elements leads to its sensitivity against fire. High packing density causes the high pore pressure, which results in concrete spalling when the remained water is evaporated. Zehfuss and Siemon (2015) showed that it is possible to prevent explosive spalling using polypropylene fibers. They evaluated the load bearing capacity of UHPC columns in expose of fire, and simulated it using finite element method.

4.3.2 Novel Hybrid Beam-Column designs using UHPC The previously mentioned studies considered mainly columns entirely constructed using UHPC. However, numerous other studies considered UHPC as one component of novel and innovative new columns designs (e.g. Xiangguo et al. 2013; Markowski and Lohaus 2017). Two popular hybrid columns are UHPC-filled steel tubes and Fiber Reinforced polymer (FRP) tubes. Other designs include UHPC cores in conventional concrete and segmental UHPC columns.

4.3.2.1 UHPC-filled Steel Tubes Liew and Xiong (2012) tested 18 steel tubes infilled with ultra-high strength concrete, 4 steel tubes infilled with normal strength concrete, and 5 hollow steel tubes. Although tubes filled with

Commented [vp34]: LF: I understand that blast and also fire tests were mdae on columns But there is a conceptual difference between the quasi static cyclic loading tests on columns, which can be interpretated on e.g. M-N diagrams etc and blast and fire tests which resulted in most cases in qualitative comparison observations Also please since there is a section devoted to hybrid design this should also contain the cases of steel columns filled with uhpc Please try to rearrange the section coeherently

Commented [vp35]: Explain what is LS-DYNA

Commented [vp36]: LF: I do not like to include jargon from commercial codes Please say that a finite element modelling was performed (you may cite the code but please detail the model: e.g bilinear compression, trilinear tension etc)

Commented [vp37]: Any conclusions? Relative to HPC or NC?

Commented [vp38]: Same as what? Each other or original columns?

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UHPC had higher load-carrying capacity, they were brittle after the peak load. Their ductility, however, could be improved by applying the load only on the concrete core, adding steel fibers into the concrete core or increasing the steel contribution ratio. Based on their study, on average, Eurocode 4 underestimate the strength of UHPC filled composite stub columns by 14.6%, ignoring confinement effect of fibers, and by 3.5% considering confinement effect of fibers. They recommended use of at least 0.3-1.0% steel fibers. Dexin (2012) examined the structural behavior of Concrete filled steel tubes (CFSTs) with ultra-high strength concrete (UHSC) and high strength steel (HSS) under static loading, to assess the preload effect on the overall buckling resistance of CFST columns under concentric compression, and extend current design codes to UHSC, HSS and preload effect. N.V. Tue et al. (2014) studied load bearing behavior of three different stub columns of confined NSC, HSC, and UHPC in steel tubes. Based on their observations, UHPC, compared to the two other groups of concrete, has higher stiffness, upper level of service load, and a rather intense shrinkage, which leads to closing of the gap between concrete core and steel tube only beyond the service level. Besides, smaller section area can be chosen if UHPC is used as concrete core in the stub columns. Guler et. al. (2013) conducted some experiments on circular UHPC-filled steel tube columns under monotonic axial compression. They investigated the concrete contribution ratio, strength enhancement index and ductility index, in relation to the diameter-to-thickness ratio of the columns. Liew et. al. (2014) investigated the behavior of tubular columns in-filled with UHPC at ambient and elevated temperature. Empelmann et. al. (2016) investigated the behavior of compact thin-walled reinforced UHPC columns with circular hollow sections under centric and eccentric normal force.

Recently, Hoang and Fehling (2017a) presented a review of past experimental studies on UHPC-filled steel tubes under axial loading on entire section and on concrete core. They investigated the behavior of circular UHPC filled steel tube columns under concentric loading on concrete core using a finite element model in ATENA-3D (Hoang and Fehling 2017b). They carried out a parametric study to assess the effect of concrete compressive strength, steel tube thickness, and steel yield strength on compressive behavior. Hoang and Fehling (2017c) also studied the effect of confinement factor and the diameter to thickness ratio on strength and ductility in circular steel tube confined concrete columns infilled with UHPC.

4.3.2.2 FRP-filled Steel Tubes

Commented [vp39]: LF: Is this something comparable to what we are “defining” as UHPC here?

Commented [vp40]: Can we add any conclusions here?

Commented [vp41]: Can we add any conclusion here?

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Zohrevand (2012) developed a hybrid system of UHPC-filled fiber reinforced polymer (FRP) tubes and provided a comprehensive experimental investigation using different fiber types and thickness under uniaxial compression. Zohrevand and Mirmiran (2012, 2013a, 2013b) studied he confinement behavior of UHPC due to FRP tubes and experimentally evaluated its cyclic behavior within twice length of the plastic hinge in columns under a constant axial load and reverse cyclic lateral load. Based on their observations, such a system has significantly higher flexural strength and initial stiffness, lower residual drift, and relatively similar energy dissipation compared to the reinforced concrete. Guler et. al. (2013) and Guler (2014) investigated the behavior of axially loaded UHPC short circular columns wrapped with CFRP, GFRP, and AFRP sheets. They developed a three dimensional finite element model to predict the axial stress-strain relationship and ultimate strength of FRP-wrapped UHPC columns. They evaluated the validity of four confinement models and three codes (ACI-440, CSA-S806-02, and ISIS CANADA) in comparison with the experimental results from six unconfined and 36 different types of the FRP-wrapped UHPC columns under monotonic axial compression. Girgin et. al. (2015) pursued a design oriented combined model to predict the ultimate strength and strain for axially loaded 7 to 190 MPa FRP-confined circular short columns. Ridha (2017) numerically and experimentally investigated the performance of square FRP tubular columns in filled with UHPC under axial-flexural (P-M) loading. They tested eight specimens: four with FRP tubes under initial load eccentricity 0, 10, 85 and 95 mm, three reference columns without FRP tube under initial load eccentricities 0, 10, 85 mm, and one with FRP tube under pure bending. The obtained P-M interaction diagram of UHPC infilled FRP tubular columns are shown in Fig. 5 and compared against theoretical P-M interaction diagrams that are based on ACI principles. 4.3.2.3 Other Hybrid Designs Hudoba and Mikus (2013) compared load carrying capacity of a column of conventional reinforced concrete with four different groups of hybrid columns: solid steel core, smooth 70-mm diameter UHPC core, corrugated 72-mm diameter UHPC core, and 78-mm diameter UHPC core in corrugated steel tube, which all had same steel reinforcement. Zhang et al. (2016) examined behavior of UHPC infilled double-skin tube columns under close-in blast loading. Popa et. al. (2016) investigated the differences in economy and section between design of a 40 story building by two types of columns: simple section (regular columns made of regular concrete class C35/45) and compound section (columns with the core made of UHPC class C130 and an outer shell of RC also class C34/45). They used an equivalent strength and modulus of elasticity to calculate the pre-dimensions for compound sections in Ultimate Limit State (ULS). They analyzed the 40-story building in SAP2000 and processed the data for each column independently. As a conclusion, the reduction of the transversal section was between 32.18% and 62.13% for the columns belonging to the first 30 stories. Ichikawa et al. (2016) tested two different details of UHPC segments, they proposed for plastic hinge region in conventional reinforced concrete columns, under orbital bilateral cyclic loading. They investigated the failure modes, dissipated energy, and equivalent viscous damping.

Using UHPC for column repairs and retrofits can also be considered a hybrid column design. Massicotte et. al. (2013) presented a seismic strengthening technique using UHPC jackets to

Commented [vp42]: Where is this Figure referenced in text?

Commented [vp43]: Can we add that ACI is conservative or more research is required?

Commented [vp44]: LF: Shouldn’t it be 37/45?

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prevent splitting failure mode (lap-splice failure, concrete cover spalling, and longitudinal buckling) in splice regions which does not have adequate reinforcement details. They tested their proposed technique on four large-scale rectangular bridge piers with the 2:1 cross sectional ratio. For unconfined 24db long lap splices, they captured drift ductility ratio up to 8 without any strength reduction for bars up to 45mm in diameter. The longitudinal bar buckling was also eliminated for 300 mm stirrup spacing. Based on their claim, UHPC with 3% fiber content is sufficient for elimination of failure when using reinforcement diameter up to 45 mm. Li et. al. (2017) developed a technique to repair conventional reinforced concrete columns damaged in earthquake, using HPC. They evaluated the efficiency of their proposed technique by comparing load-carrying capacities, displacement ductility, stiffness, and energy dissipation. They recommended 1.5 times of the width or height as the repair height of HPC for damaged columns.

4.4 Shear and Torsion – Ali Semendary

4.4.1 Shear 4.4.1.1 One-way shear – Mohamed UHPC shear behavior is characterized by complex load transfer mechanisms due to the

presence of fibers that gap the cracks and provide additional strength and ductility. Available

literature includes studying of the factors contributing to UHPC shear strength, applicable code

provisions, and modeling. Regular and Prestressed UHPC I beams with and without stirrups

were tested by (Voo et al.(2010), Florent Baby(2013), Zheng et al.(2016), and Randl et

al.(2018)). Tests investigated shear span to depth ratio (a/d), different fiber contents, fiber

orientation, fiber shape, prestressing level and stirrup content. Results generally show higher

shear capacities and much more ductility that are functions of fiber content and distribution.

Researchers also studied shear strength UHPC of beams reinforced with high strength steel

(Xia et al.(2010) and Qi et al.(2016). Their results also have shown ductile failures and multiple

crack bridging by fibers. Additional investigations included UHPC applications to I beams with

web openinings (Zagon et al.(2015)) and shear reinforcement spacing upper limit (Lim et

al.(2016)).

On the modeling side, (Ngo et al.(2016)) proposed a theoritical model for UHPC beams shear

strnegth based on their experiments considering variable a/d ratios. Chen et al.(2011) used a

concrete-damaged plasticity (CDP) model to investigate both shear and bending behavior of

UHPC beams with good agreement with experimental data.

4.4.1.2 Punching Shear Research on the punching shear capacity of UHPC was carried out at Virginia Tech [Harris]. Twelve small slabs 1140 mm x 1140 mm (45 in x 45 in) were tested to failure to characterize the punching shear strength of UHPC. The variables considered were the slab thickness 50, 60, 7 75 mm (2, 2.5, and 3 in) and loading plate dimensions from 25 x 25 mm to 75 x 75 mm (1 in x 1 in to 3 in x 3 in). The results of the testing were compared to several existing models for punching shear. The two equations that predicted strengths most reliably were the current ACI punching shear equation and a modified bolt pullout equation. After evaluation of the test results, the minimum slab thickness required to prevent a punching shear failure in the top flange due to an 200 mm x 500 mm (8 in x 20 in) wheel patch was determined to be 25 mm (1

Commented [vp45]: This solution has been used on a bridge in BC, Canada. Reference Paper Perry & Doiron, CSCE SMSBC, Calgary 2014.

Commented [vp46]: LF: You may also cite works by Beschi et al. (eslevier journals)

Commented [vp47]: Please provide the full reference

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in). Except in the case of very thin slabs (ie waffle deck slabs for highway bridges), punching shear is normally not a critical design factor. Attempts were made to assure fully restrained supports in order to increase the flexural strength thereby increasing the likelihood of a punching shear failure. Both flexural and punching failure modes were observed and it was concluded that the type of failure depends on the area of loading plate and the slab thickness. The two types of failure are shown in Figure 4.541.2.1(a and b).

(a) (b)

Figure 4.4.1.2.1. Typical crack pattern: (a) Punching shear failure;(b) Flexure failure (Harris 2004) The results demonstrated that the punching shear capacity of the slab was significantly improved due to the tensile capacity of UHPC, which caused a 60 mm (2.5 in.) slab thickness to provide sufficient punching shear capacity for bridge applications. The punching shear capacity of UHPC slab could be estimated using the modified ACI equation for concrete breakout strength. This conclusion was conducted based on the failure mode that was observed in the tested specimens. The observed conical failure was similar in appearance to the breakout cone for concrete as shown in ACI 318-02 (ACI 2002) for a surface with an embedded bolt in tension. The size of the bolt head was found to have no impact on the failure cone. However, some modification was made to the equation to be applicable to the commercial UHPC product with tensile strength up to 11 MPa. The tensile load was assumed equivalent to the applied punching load. Similar to the bolt head applying load to the slab through the head (Figure 4.4.1.2.2a), the load applied to the Ductal® slabs results from the loading plate (Figure 4.4.1.2.2b).

(a)

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(b)

Figure 4.4.1.2.2: (a) Concrete breakout failure surface; (b) UHPC (Ductal®) breakout (punching shear) failure surface (Harris 2004) The modified ACI equation for concrete breakout strength was found to provide a best measurement of the punching strength of UHPC slabs.

𝑉𝑐 = 𝑁𝑏 = 𝑘1. 𝑓𝑡.(3. ℎ + 𝑐)2 − 𝑐2

√ℎ (1)

Where:

𝑓𝑡 = split cylinder tensile strength (ksi) 𝐾1 = empirical constant derived using NLREG software = 0.38 ℎ = slab thickness (in.)

𝑐 = loading plate dimension (in.) Joh eta al. (2008) investigated the punching shear capacity of 1600 x 1600 mm (63 in. by 63 in.) unreinforced UHPC slabs. A fixed edge was used to force the punching shear failure. All tested slabs failed in punching shear mode. The results from the test were compared with the values predicted using Harris (2004) and ACI 318-05 (ACI 2005) punching formula. The ACI punching formula gives 73% of actual punching strength, which was considered a good prediction. The modified equation by Harris (2004) gives similar accuracy as the ACI 318-05 (ACI 2005). Zohrevand et al (2015) examined the optimal use of UHPC within the critical punching shear area by conducted an experimental and analytical studies. The tested variables were reinforcement ratios and depth/area of UHPC. For each reinforcement ratio, slabs were made from normal concrete, UHPC or hybrid. The hybrid slabs were made in order to examine different distances from the face of the column using full or partial depth UHPC. The results demonstrated the punching shear capacity of a flat slab, which was made fully from UHPC, is 3 times more than made of NC. Furthermore, the punching shear capacity of the slab enhanced by 70% if a full-depth of UHPC was applied within the area enclosed by a perimeter located at a distance equal to the slab thickness from the column face. However, the punching shear capacity does not significantly improve when the half-depth of UHPC was implemented. The punching shear capacity was examined using ACI 318-11 (ACI 2011) and Harris models. The results showed that both models significantly underestimate the punching shear capacities of flat slabs with partial or full UHPC. Furthermore, the proposed mode by Harris (2004) is not applicable to reinforced UHPC slab. The authors recommend more studies to be done in order to develop analytical models to predict the punching capacity of reinforced UHPC slabs.

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4.4.1.3 Horizontal Shear Also, at Virginia Tech twenty-four push-off tests were performed to determine if the current horizontal shear design equations could accurately predict the horizontal shear strength of composite UHPC (Ductal®) and Lightweight concrete sections. Effects from various surface treatments, reinforcement ratios, and aspect ratios, were determined. The results predicted by the current design equations were compared to the actual results found during testing. The current design equations were all found to be conservative. For its ability to incorporate various cohesion and friction factors, it is recommended that the equation from AASHTO LRFD Specification (2004) be used for design [Banta & Roberts-Wolmann] 4.4.2 Torsion The torsional behavior of members made of UHPC were investigated by many researchers. Fehling and Ismail (2012) conducted an experimental study on twelve UHPC beams with/out steel fibers and with/out traditional reinforcement. The studied parameters were steel fiber type (different bond properties with UHPC), steel fiber volume, longitudinal reinforcement ratio, and web reinforcement ratio. The varied steel fiber volumetric ratios were (0.0, 0.5, and 0.9 %) and varied longitudinal and web reinforcement volumetric ratios were (0.0, 1.4 and 2.48 %) and (0.0, 1.68 and 2.53 %), respectively. The results show that cracking and torsion capacities were enhanced by adding steel fibers to the plain UHPC beams. When the steel fibers volumetric ratio increased, the number of the cracks per meter also increased. When the longitudinal reinforcement was added to the beam along with steel fibers, the ductility of the beam improved but not the ultimate strength. The ultimate torsion capacity and ductility were improved only by adding the web reinforcement along with the longitudinal reinforcement to the UHPC beams with steel fibers. Ismail et al (2016) investigate the capability of three analytical models to predict the ultimate torsional capacity of UHPC beams with/out traditional (longitudinal and transverse) reinforcement. The validated models were based on the well-known thin-walled tube and space truss analogies for reinforced concrete under torsion. The three models also utilize the common additive approach for determining the torsional capacity. The first model was proposed by Empelmann and Oettel (2012) who conducted an experimental study on box girders constructed with UHPC under pure torsional loading and combined loading of torsion moments and normal forces. The experimental study showed that total torsional capacity can be calculated by the sum of the contribution of the traditional (longitudinal or transverse) reinforcement and the steel fiber. The second model was proposed by Joh et al. (2012) who conducted an experimental program to investigate the torsional capacity of UHPC square members having the same cross section but different reinforcement details. The author reported that the models proposed by Empelmann and Oettel (2012) and Joh et al. (2012) consider only the contribution of the steel fibers through tensile force perpendicular to the crack direction. However, the model proposed by the authors was based on experimental observations and literature review considered the contribution of the steel fibers through tensile and shear force along the cracking surface. Furthermore, the authors believe that the model proposed by Empelmann and Oettel (2012) provides no values for the thickness of the thin walled tube for the case of UHPC beams without traditional reinforcement. It instead uses the available wall thickness of the hollow UHPC girder which in some cases may not necessarily be reasonable. The authors reported that the contribution of the steel fibers along the cracking surface was considered not only in normal

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direction to the crack but also in tangential direction. This indicates that the steel fibers contributes to the torsional capacity through both tensile and shear forces. The nominal torsional capacity of fiber-reinforced UHPC member under torsion can be expressed as fellow: .

𝑇𝑛 =𝜎𝑐𝑓0 ×𝐴𝑤

𝑐𝑜𝑠𝜃 × (ℎ − 𝑡𝑒𝑓𝑓)× 2𝐴𝑘 (2)

Where: 𝐴𝐾 = (𝑏 − 𝑡𝑒𝑓𝑓) × (ℎ − 𝑡𝑒𝑓𝑓); 𝐴𝑤 = 𝑡𝑒𝑓𝑓 ×(ℎ−𝑡𝑒𝑓𝑓)

𝑠𝑖𝑛𝜃 ; 𝜎𝑐𝑓0 represents the post cracking

tensile strength of UHPFRC 5.0 Serviceability and Durability Design Considerations Section 3.0 Material Properties covers the mechanical (including durability) properties and characterization of UHPC in the uncracked (unloaded) condition. This section 5.0 Serviceability and Durability covers UHPC in the loaded (elastic or cracked) condition. 5.1 Serviceability – Barzin Mobasher & Yao A sustainability based approach is based on defining the design parameters based on a limit of allowable stress, deflection, crack width, or strain measure. Such an approach cannot be obtained from the limit state, or ultimate strength analysis. Mobasher and co-workers [Soranakom (2009), Mobasher (2011), Mobasher & Yao (2012) & Yao et al (2017)] presented a simplified parametric model based on serviceability limit state (SLS) and ultimate limit state (ULS) criteria for the design of general FRC and hybrid reinforced concrete flexural members. This model can be implemented both for strain softening and strain hardening FRC such as SFRC, TRC and UHPC. A general strain hardening tensile, and an elastic perfectly plastic

compression model as derived by Soranakom and Mobasher [2009] and shown in Fig. 5.1.1 is

used. Tensile response is defined by tensile stiffness, E, first crack tensile strain cr, ultimate

tensile capacity, peak, and post crack modulus Ecr. In order to simplify material characteristics of strain-hardening FRC, and yet obtain closed form design equation generation several assumptions are made. Equations can be simplified to idealized bilinear tension and elastic compression models as shown ignoring the post-peak ranges in both tension and compression.

Fig. 5.1.1 Material models and simplified portions for serviceability limits for strain-hardening

FRC: (a) compression model; and (b) tension model

Moment capacity of a beam section according to the imposed tensile strain at the bottom fiber

(t = cr) can be derived by the following steps: (1) determine linear strain and stress distributions, (2) force components by integration of stresses, (3) solve for the depth of neutral axis location, k, by force equilibrium, and obtain the strain-curvature relationship. The internal

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moment is obtained from the force and strain distribution and expressed as follows:

2 3

2 2

2 1 2( )

1n cr

k k kM C M

k

; where

22

2 1 12 ,6

crcr

bhC C C M

(1)

General derivation of all potential combinations for the interaction of tensile and compressive response are presented in [Soranakom & Mobasher (2008 & 2009)]. The nominal moment capacity of a flexural member Mn must be decreased by a reduction factor to account for variability in materials and workmanships according to ACI-318 Sec. 9.2 [Soranakom &

Mobasher (2009)] where r is the reduction factor for strain-hardening FRC:

r n uM M (2)

Using this approach, one can simulate the flexural response of any member by starting from a known or back-calculated tensile and compressive constitutive response. For example, Meng et al. [Soranakom & Mobasher (2009)] tested UHPC beams with dimension of 400x75x75 mm (16x3x3 inch) in accordance with JCI method. Effect of notch-to-depth ratio were evaluated at three levels of N/D= 1/6 corresponding to notch depth of 12.5 mm (1/2 inch). Using a constant rate of the mid-span deflection as the control parameter, loading rates ranging from 0.05 mm/min (0.002 inch/min) to 5.00 mm/min (0.2 inch/min) were used in accordance with available test methods. Figures 5.1.2(a) and (b) compare the simulated and experimental flexural stress-deflection responses of the UHPC beams with different notch depths and loading rates.

(a)

(b)

Figure. 5.1.2. (a) Tension Models, Comparisons Between Experimental and Simulated Flexural Stress-Deflection Responses for Different N/D of (b) 1/6, (c) 1/3, (d) 1/2.

The tensile material properties illustrated as multi-linear stress-strain diagrams were back-calculated by fitting the experimental flexural responses for N/D of 1/6, as shown in Figure 2(a). The results show that in order to fit the experimental loading rate effect, the tensile and residual strength of have to increase from 9.5 to 15.9 MPa (67%) and 3.1 to 5.2 MPa (67%), respectively. The loading rate effects revealed by the increasing strength in tensile stress-strain

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laws agree with the experimental investigations on tensile properties of UHPC under varying strain rates [Meng et al (2017), Zhang et al (2014) & Pyo et al (2015)]. The percentages of improvement are consistent with those of flexural strength measured from experiment. General procedures for analysis of beams, panels and 2-D slabs have been developed based on this approach in recent publications and calibrated against a wide range of published work [ACI 318]. Appendix I shows a sample set of calculation for a standard UHPC beam. 5.2 Durability – Mo Li The dense microstructure of UHPC provides a low permeability and reduces transport of corrosives to steel reinforcements, leading to improved durability of structures. This concept relies upon the UHPC to remain uncracked within a structure to resist the transport of water, chloride ions, oxygen, etc. In field conditions, cracking can result from various mechanical and environmental factors. For example, the relatively high autogenous shrinkage of UHPC due to a low water-to-cement ratio and lack of coarse aggregates, when restrained, can lead to cracking in UHPC. Cracks provide pathways for the penetration of aggressive ions to cause reinforced concrete deterioration. Designing for more durable reinforced concrete structures with UHPC thus requires the understanding of the crack width control capacity of UHPC under various loading and environmental conditions, and the effects of cracking on the durability and serviceability of UHPC and reinforced UHPC. The following section covers on the design of UHPC for improved durability through crack control, and the characterization of the durability of UHPC that can provide commentary for UHPC structural design with improved durability. 5.2.1 Durability requirements for Exposure Classes and crack width limitations in Reinforced Concrete structures Design standards and codes for concrete structures suggest crack width limitations for different environmental exposure conditions, to ensure structural durability in these environments. Permissible crack widths at the tensile face of reinforced concrete structures for service loads under different environmental conditions, according to ACI 224R-01 and JSCE Standard Specifications for Concrete Structures-2007 are summarized in Table 5.2.1.

Table 5.2.1 Permissble Crack Width vs Exposure Condition

Exposure condition Permissible crack width (mm)

ACI 224R-01

Dry air or protective membrane 0.41

Humidity, moist air, soil 0.30

Deicing chemicals 0.18

Seawater and seawater spray; wetting and drying 0.15

Water retaining structures 0.10

JSCE-07

Deformed bars and plain bars

Prestressing steel

Normal 0.005c 0.004c

Corrosive 0.004c -----

Commented [vp48]: For what service life?

Commented [vp49]: Can we add a column to the table for HPC & NC

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Severely corrosive 0.0035c -----

* c – concrete cover, not exceeding 100 mm

The most stringent crack width limit is placed on water-retaining structures, with maximum allowable crack width of 100 µm (0.004 in.). For exposure conditions of seawater and seawater spray, wetting and drying, the maximum allowable crack width is 150 µm (0.006 in.). For deicing chemical exposure, a maximum crack width of 180 µm (0.007 in.) is specified. Within the current ACI code (ACI 318-14), a maximum crack width is no longer explicitly specified, although previous versions of the design code, such as ACI 318-95, suggested 300 µm (0.012 in.) as an upper limit. The AASHTO (1998) design code relies on the calculation of a “Z” factor, for which maximum crack width limits are set depending on the type of environmental exposure. In JSCE Standard Specifications for Concrete Structures (2007), crack width limit for corrosion of reinforcement is also determined depending on the environmental exposure conditions of the structure, which are classified into “normal environment”, “corrosive environment” and “severely corrosive environment”. Normal environment refers to normal outdoor environment with ordinary conditions without any airborne salt, underground, etc. Corrosive environment refers to environment with more frequent cyclic drying and wetting, and underground environment below the level of underground water containing especially corrosive (or detrimental) substances that may cause harmful corrosion of reinforcement. Normal environment also includes the environment of marine structures submerged in seawater, or structures not exposed to severe marine environment. Severely corrosive environment includes: (a) environment in which reinforcement is subjected to detrimental influences considerably, and (b) environment of marine structures subjected to tides, splash, or exposed to severe ocean winds (JSCE 2007). For the severely corrosive environment, the crack width limit is 0.35% of concrete cover thickness which shall not exceed 100 mm (4 in). 5.2.2 Crack width control – Philipp Hadl Crack width limitation of UHPC with different amounts of steel fibers including or not including conventional steel reinforcement has been investigated by different researchers such as Habel et al. (2007), Leutbecher & Fehling (2008) or Jungwirth (2006). Leutbecher & Fehling (2008) developed an analytical model to predict the crack width and pattern for steel fiber reinforced UHPC combined with conventional steel rebars. Initially the model describes single crack formation of unreinforced UHPC considering shrinkage, followed by crack pattern and spacing at stabilized cracking. The principles of crack formation are similar to normal strength concrete, as can be seen in Figure 5.2.2.2. Subsequently it describes crack width limitation for fiber reinforced UHPC with or without conventional steel rebars including effects of shrinkage. Figure 5.2.2.1 shows the strain distribution at stabilized cracking for fiber reinforced UHPC combined with conventional rebars for the case, that crack spacing is smaller than the load transmission length lef of the fibers (sr,max ≤ 2∙lef). This behavior is usually achieved by high fiber contents (strain-hardening UHPC). Leutbechers & Fehlings (2008) approach can be used for UHPC reinforced with steel rebars (without fibers), fiber reinforced UHPC with tension softening behavior as well as strain hardening behavior. Further, the approach has been verified by experimental investigations with different amounts of steel fibers (0.9, 1.45, 2.0 Vol.-%). The experimental and theoretical studies showed, that the tension stiffening effect increases strongly with increasing fiber content, but crack spacing and crack widths do not decrease in the same manner. The results obtained with different amounts of steel fibers showed that in combination with steel reinforcing bars, the UHPC does not need to show strain hardening behavior to achieve progressive crack formation

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with very small crack spacings and crack widths, which improves the durability of structures. This means, that by combining steel reinforcing bars and fibers, the crack width does not decrease proportionally with increasing fiber content. In addition, the distance of the transverse reinforcing bars strongly affects the crack pattern.

Fig. 5.2.2.1. Strain distribution at stabilized cracking for UHPC without fibers for the case sr,max =

2∙les (left) and with fibers and conventional rebars for crack distance sr,max ≤ 2∙lef (right) In contrast to the described results of Leutbecher & Fehling (2008), Jungwirth (2006) research showed a direct superposition of reinforcing bars and fiber content. Jungwirth used a strain-hardening UHPC and the crack spacing observed in direct tension tests was lower than 15 mm (0.6 in). This research distinguishes between extremely fine so called meso-cracks due to fibers formed before activating the conventional reinforcement and macro-cracks caused due to the bond with conventional reinforcing bars. Habel et al. (2007) investigated numerically and experimentally the behavior of a composite consisting of a normal-strength reinforced concrete beam and an UHPC-topping layer applied in the tensile zone. The fiber-reinforced UHPC showed a fiber content of 6 Vol.-% (fiber length 10 mm [0.4 in]; diameter 0.2 mm [0.008 in]). Additional steel reinforcing bars were used in the UHPC-layer. The maximum crack spacing with combined reinforcement was only 30 mm (1.25 in) and very small crack widths have been observed similar to the results of Jungwirth (2006).

Fig. 5.2.2.2. Crack pattern of UHPC reinforced with steel fibers combined with rebars Habel et

al. (2007) According to the Swiss Recommendations SIA 2052 (2007) Strain-Hardening UHPC is waterproof until a tensile strain of 1‰. For concrete types UA(mild strain-hardening) and UB

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(strain-hardening UHPC) no exact crack-width calculation is required. Further, the French guideline AFNOR NF P 18-470 (2016) requires no crack width limitation for high strain hardening UHPC (strain hardening tensile law also in the ULS), since the crack width is expected to be extremely small. For other types of UHPC (low strain hardening und strain softening UHPC), methods for calculating the exact crack width and spacing are given in AFNOR NF P 18-470 (2016). Further, the Australian guideline provides a simplified calculation method for crack width limitation if the tensile stress exceeds 6.0 MPa (870 psi) in the design. Research by Charron 2008 and Moreira XXXX has shown that small cracks (< 50 µm [ 0.002 in]) that are no longer active and have been subjected to moisture ingress, in the crack open condition, can reseal due to the autogeneous self-healing properties of UHPC. This resealing effect can provide additional protection and improved durability to UHPC structures. More information on the self-healing can be found in section 5.1.3.2, below. 5.2.3 Durability under mechanical load (focusing on crack formation) – Jean-Philippe Charron 5.2.3.1 Crack pattern and crack width Table 5.2.2 summarizes information on crack opening and crack spacing measured in UHPC under various load levels, with or without rebar in addition to the fiber content. For material characterization specimens, crack opening varies between 5 to 11 µm at peak load with a crack spacing ranging between 3 to 6 mm. For structural members without rebar under service load, crack opening varies between 10 to 55 µm with a crack spacing ranging between 20 to 55 mm. Larger values are obtained with a lower fiber content both for crack opening and crack spacing. Under ultimate load, the crack opening increases between 27 to 80 µm, again larger values are related to a lower fiber content. For structural members with rebar under service load, crack opening is approximately 30 mm with a crack spacing around 29 mm. Under ultimate load, crack opening can reach approximately 90 mm. As general trends, crack opening and crack spacing under loads seem smaller in material characterization specimens than in structural members for equivalent fiber content. Structural members with and without rebar present similar crack opening and crack spacing in service condition, however crack opening reaches at ultimate load is higher in presence of rebar since they control partly the failure and increase the maximal load. Besides, all results of Table 5.2.2 were measured in UHPC submitted to a static loading, however Lachance et al. () showed that the application of cyclic loading representing a truck circulation on UHPC bridge slabs increases progressively the crack opening. Research by Graybeal [2010] showed that cyclic loading, in the cracked condtion, of reinforced UHPC beams had an increase in load displacement for the first 2 million cycles then appeared to reach a plateau for the next 3 million cycles, at which time the test was stopped. More information on this research can be found in section 5.1.5.

Table 5.2.2 - Crack opening and crack spacing measured in UHPFRC under load

Reference Application Reinfor- cement

Vf (%) Lf(mm)

s (MPa) or

UHPC (%)

Load condition

w (µm) s (mm)

Wille et al. (2014)

Dog-bone specimens

Without rebar

2 13-30

0.39 - 0.48 %

Peak load (1st crack)

9 - 11

4 - 6

Commented [vp50]: Reference?

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Wille et al. (2014)

Dog-bone specimens

Without rebar

3 13-30

0.41 - 0.45 %

Peak load (1st crack)

5 - 9 3 - 5

Nehdi et al. (2015)

Tunnel segments

Without rebar

1 8-16

- 1st crack 27 - 55 40 - 55

Ultimate load 55 - 80

Nehdi et al. (2015)

Tunnel segments

Without rebar

3 8-16

- 1st crack 10 - 20 20 - 35

Ultimate load 27 - 40

Hubert et al. (2015)

Tie-specimens

With rebar

2 10

250 MPa Service load 29 29

450 MPa Ultimate load 87 12

Lachance et al. (2016)

Bridge slabs

With rebar

4 13

250 MPa Service load 30 -

438 MPa Ultimate load 90 -

Vf and VL: fiber content & Length, s : rebar stress, UHPC : UHPC strain, w : crack opening, s : crack spacing

5.2.3.2 Effect of crack pattern and width on transport properties Water absorption and water permeability were measured on undamaged and damaged UHPC (without rebar) having residual crack opening of about 50 µm (Charron et al., 2008). Sorptivity coefficient measured after 3 days increases from 3.5E-4 to 6.6E-4 L/m2s0.5 in presence of microcracks, while permeability coefficient obtained after 35 days of exposition rises from an undetected value (≤1E−12 m/s) to 2.80E−12 m/s with microcracks. As expected the transport properties increase in presence of microcracks, but they remained lower than those of an undamaged concrete with a water/binder ratio equal to 0.45. Water penetration under load was also evaluated in UHPC with rebar in addition to the fiber content (Hubert et al. 2015). In service condition (rebar stress around 250 MPa), the UHPC showed crack openings of 29 µm with an instantaneous water permeability of 2.8E-8 m/s, while reinforced concrete presented crack widths of 148 µm with an instantaneous water permeability of 3.6E-6 m/s. Very low permeability coefficient of UHPC under load is related to its thin crack openings, but also to their very high surface roughness and multi-branching pattern. Difference between immediate and 35-day measurements of permeability coefficients described above is linked to the strong chemical interactions of water with UHPC, which initiate gradually with time calcium carbonate precipitation in cracks and hydration of residual clinker at crack surface. This provides a high capability of self-healing to the material than can reduce by few orders of magnitude water permeability (Charron et al., 2008). As a matter of fact, Moreira et al () showed recently that crack opening ranging from 42 to 88 µm in UHPC were totally sealed after 3 months of exposition to wet and dry cycles. This explain how UHPC specimens subjected to fatigue tests and then immersed in water with chlorides can exhibit a greater flexural resistance in comparison to control specimens (Parant 2003). The crack openings in UHPC members in service condition are generally inferior to 50 µm (Table 5.2) in comparison to crack width between 200 and 300 µm expected in reinforced concrete. The very thin crack openings, crack roughness and high self-healing capability of UHPC limit significantly transport properties and thus deterioration mechanisms. 5.2.4 Durability of cracked elements under chemical loads – Greg Nault

Commented [vp51]: Reference?

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The durability of UHPC under chemical loads, such as de-icing chemicals, alkali reactivity, and sulphate attack, is largely dependent on the material’s chemical composition, internal pore structure, and susceptibility to penetration. The UHPC’s mix design (which falls outside the scope of this document) determines the compactness and imperviousness of the matrix to chemical ingress. Improvements in durability performance can often be attained by utilizing advanced curing techniques, such as thermal treatment (i.e. accelerated curing), to more thoroughly hydrate the cementitious materials in the UHPC. This, ultimately, decreases the internal porosity of the matrix and reduces the permeability of the material to ingress. With regard to the structural design of UHPC for durability under chemical loads, appropriate concrete cover and crack width control are the key parameters to ensuring the long-term durability and performance of the material. According to the Eurocode 2 specification, minimum cover thickness to reinforcing/prestressing steel should range from 5 mm to 25/30mm depending on the structural class of the element and the exposure class of the UHPC. For highly aggressive environments, such as areas subjected to cyclic wet/dry cycles, frequent freeze/thaw cycles, and salt/salt-water exposure, the cover thickness should be on the higher end of the acceptable range (i.e. 20-30 mm). Likewise, crack widths should be controlled to minimize infiltration by water and other chemical aggressors. Eurocode 2 specifications recommend an allowable crack width of 0.05 mm to 0.3 mm depending on the exposure class, internal reinforcement characteristics, and load combination. In general, an allowable crack width of 0.1 mm is typically sufficient for elements in highly aggressive exposure conditions. For more information on crack width allowances and designing for crack control, refer to sections 5.1.1 and 5.1.2. 5.2.5 Durability of cracked elements in a marine environment – Rafic El-Helou Limited research has been conducted to assess the structural performance of a UHPC section subjected to simultaneous mechanical in an marine environment. Given the exceptional durability characteristics of uncracked UHPC, particularly its low permeability, it is necessary to determine that the cracks in UHPC components (i.e. bridge girder subjected transient loads and deicing chemicals) would not cause significant ingress of liquid into the material resulting in corrosion of steel fiber reinforcement and loss of UHPC’s tensile capacity (Graybeal, 2010). Graybeal (2010) tested a mild steel reinforced UHPC beam having a rectangular cross section, 152 mm wide and 381 mm deep, and a span of 4.88 m. The beam was reinforced with two #4 bars positioned at the bottom of the specimen with 35 mm cover. The beam was subjected to 500,000 loading-unloading cycles over 154 days in a four-point bending configuration during which the tensile face of the beam was continuously wetted using an open-cell sponge soaked in a 15% NaCl solution. The applied load surpassed the first flexural tensile cracking capacity by 14% creating a series of flexural crack near midspan. The simultaneous application of structural and environmental loadings to the cracked UHPC beam during this test did not result in any apparent degradation of the member’s flexural capacity or degradation of the crack bridging fibers. The NaCl was reported to penetrate to a depth of 3 mm on the side faces of the beam and 5 mm on the tensile face. 5.2.6 Life Cycle Assessment – Vic Perry 5.2.6.1 End of Life Treatment

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To date, there are no examples of disposing or decommissioning of a UHPC structure. It is suggested that at the end of the service life, the element should be considered for reuse. Although there are no significant safety or environmental considerations for UHPC that are different from regular concrete, end of life reuse, recycling, or disposal options do have special considerations. Due to the nature of UHPC, it is extremely challenging to demolish UHPC elements as it is designed to be highly resistant to such intentional destructive treatment. Primary consideration should be given to reuse of structural elements if the element meets the required mechanical performance characteristics and this can be achieved with minor physical modifications. If UHPC does need to be disposed of, diamond cutting large elements into smaller, more manageable sizes should be undertaken [7.5.1.7.1]. 5.2.6.2 Service life prediction Currently there is a limited amount of research that has been under taken on developing a life prediction models for UHPC. Research undertaken in France in the late 90’s covered tests methods typically used by the Nuclear Authority of France to predict life performance. This testing indicated that a life rating of 300 years could be achievable. Research was undertaken and sponsored by the US Army Corp of Engineers in the early to mid-90’s by installing test prisms on the long-term exposure site in Treat Island Maine. The test site is a wharf at mean tide, where the test specimens are subjected to wet/dry on each tide cycle and freezing/thawing during winter months ( see section 5.1.5.2 above). Thomas et al has used Fick’s Law to predict it would take 1000 years for a chloride ion to penetrate through 50 mm of UHPC.

6.0 Future Research Needs 6.1 Test methods to characterize the tensile properties of UHPC 6.2 Tension Response Cracking Pattern 6.3 Compressive stress-strain: There is currently no consensus as to: 1) what the maximum usable concrete compressive strain is, 2) what the maximum usable tensile strain is, 3) what is the minimum amount of fibers that need to be included to achieve a certain maximum usable compressive or tensile strain, 4) what are the definitions for tension controlled, compression controlled and members in the transition zone, and 5) how to best represent the compressive and tensile behavior of UHPC at a material level when conducting a sectional analysis at the ultimate limit state. Additionally, the type of reinforcement that UHPC interacts with plays an important role in overall member behavior. The use of UHPC in common and repetitive applications will perhaps provide the impetus for arriving at a unified approach for the flexural design of UHPC members. 6.4 The performance of horizontal Shear-stud interaction confined in UHPC (Deck to beam connections) 6.5 Punching Shear in reinforced UHPC slabs. 6.6 Beam-column Inter-action design methods 6.7 Torsion design equations 6.8

7.0 References

7.1.2 Scope:

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American Society of Testing and Materials (ASTM), Annual Book of Standards, Section 4 Construction, Volume 04.01 Cement and Volume 04.02 Concrete and Aggregates, 2017, USA Swiss Institute of Engineers and Architects (SIA), “Béton fibré ultra-performant (BFUP); Matériaux, dimensionnement et exécution” prSIA 2052- 2014, Switzerland Association Française de Normalisation (AFNOR – French standard institute), “National addition to Eurocode 2 – Design of concrete structures: specific rules for Ultra-High Performance Concrete Fibre-Reinforced Concrete (UHPFRC)”, NF P 18-710 2016, France Japanese Society of Civil Engineers (JSCE) “Recommendations for Design and Construction of Ultra High Strength Fiber Reinforced Concrete Structures” (Draft), 2006, Japan. Standards Australia (SA, Australia) DR AS 3600:2017 Concrete Structures, Section 16 “Steel Fibre Reinforced Concrete”, 2017, Australia. Canadian Standards Association (CSA), CSA A23.1/2 Annex S on Ultra-High Performance Concrete, 2019, Canada Canadian Standards Association (CSA), CSA S6 Annex 8.1 on Fibre Reinforced Concrete, 2019, Canada Federal HighWay Administration (FHWA), “Ultra-High Performance Concrete: A State-of-the-Art Report for the Bridge Community”, Publication No. FHWA-HRT-13-060, 2013, USA Schmidt, M. et al, “Sustainable Building with Ultra-High Performance Concrete”, Press University of Kassel 2014, ISBN: 978-3-86219-480-3, Germany. Schmidt, M., Leutbecher, T., Piotrowski, S. and Weins, U. “The German Guideline For UHPC”, Proceedings of the AFGC-ACI-fib-RILEM Int. Symposium on UHPFRC, October 2017, Montpellier, France, pp 545-554. Lopez, J.A., Serna, P. & Navarro-Gregori, J. “Advances in the Development of the First UHPFRC Recommendations in Spain: Material Classifications, design and Characteristics”, Proceedings of the AFGC-ACI-fib-RILEM Int. Symposium on UHPFRC, October 2017, Montpellier, France, pp 565-574. Material Properties Charron, J.-P., Desmettre, C., (2013) Potential use of fiber reinforced concretes for constructions of durable civil engineering infrastructures, Technical report ST13-01 Polytechnique of Montréal, Canada, 45 pages. In French. 7.3.1 Mechanical Properties 7.3.1.1 Compression

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El-Helou, R. G. (2016). “Multiscale Computational Framework for Analysis and Design of Ultra-High Performance Concrete Structural Components and Systems.” Doctoral Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA. Retrieved from: http://hdl.handle.net/10919/73381.

Haber, Z.B., De La Varga, I., Graybeal, B. A., Nakashoji, B., and El-Helou, R. (2018). “Proporties and behavior of UHPC-class Materials.” FHWA-HRT-18-036. Federal Highway Administration, Washington, DC. Ahlborn, T. M., Harris, D. K., Misson, D. L., Peuse, E. J. (2012) Strength and Durability Characterization of Ultra-High Performance Concrete Under Variable Curing Conditions. Structures 2011 - Transportation Research Record (TRR No. 2251), 68-75. Washington, D.C.: Transportation Research Record (TRR), Journal of the Transportation Research Board. Graybeal. B.A. (2005) “Characterization of the Behavior of Ultra-High Performance Concrete,” PhD Dissertation, University of Maryland, College Park, Maryland. 7.3.1.1.2 Test Methods to Obtain Compressive Properties Perry, V. H., “Ultra-High Performance Concrete Advancements and Industrialization 0 The Need for Standard Testing”, Advances in Civil Engineering Materials, ASTM Volume 4, Issue 2, W. Conshohocken, PA, USA 2015. Graybeal, B. “Compressive Testing of Ultra-High Performance Concrete”, Advances in Civil Engineering Materials, ASTM Volume 4, Issue 2, W. Conshohocken, PA, USA 2015. Graybeal, B. and Davis, M. “Cylinder or Cube: Strength Testing of 80 to 200 MPa (11.6 to 29 KSI) Ultra-High Performance Fiber-Reinforced Concrete", ACI Materials Journal, November-December 2008, pp. 603-9, USA, 2008. FHWA-HRT-06-103 “Material Property Characterization of Ultra-High Performance Concrete”, FHWA, McLean, VA, USA, 2006. FHWA-HRT-12-064 “Compression Response of a Rapid-Strengthening Ultra-High Performance Concrete Formulation”, FHWA, McLean, VA, USA, 2006 Graybeal, B., “Compressive Behavior of Ultra-High Performance Concrete”, ACI Materials Journal, Vol. 104, No. 2, March – April, 2007. 7.3.1.2 Tension Haber, Z.B., De La Varga, I., Graybeal, B. A., Nakashoji, B., and El-Helou, R. (2018). “Proporties and behavior of UHPC-class Materials.” FHWA-HRT-18-036. Federal Highway Administration, Washington, DC. Graybeal, B. A., and baby, F. (2013). “Development of direct tension test method for ultra-high performance fiber-reinforced concrete.” ACI Mater. J., 110(2), 177-186. 7.3.1.3 Flexural

http://hdl.handle.net/10919/73381

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7.3.1.4 Shear 7.3.1.5 Bond Strength 7.3.1.5.1 FHWA-HRT-14-084 “Design and Construction of Field-Cast UHPC Connections. Harris, D. K., Sarkar, J., Ahlborn, T. M. (2011) Interface Bond Characterization of Ultra-High Performance Concrete Overlays. Concrete Materials 2011 - Transportation Research Record(TRR No. 2240), 40-49. Washington, D.C.: Transportation Research Board; Journal of the Transportation Research Board. FHWA-HRT-14-090 - Bond Behavior of Reinforcing Steel in Ultra-High Performance Concrete Graybeal, B. and Haber, Z., “Ultra-High Performance Concrete for Bridge Deck Overlays” FHWA-HRT-17-097, McLean VA, USA, 2017. Emerson E. J., Edmundo D. R., Royce W. F., and Hale, W. M., “Transfer and Development Lengths and Prestress Losses in Ultra-HighPerformance Concrete Beams”, transportationResearch Record: journal of the Transporation Research Board, No. 2251, pp. 76-81, Washington, DC, 2011. Fehling, E. and Lorenz, P., “Anchorage and Overlapping of Non-Prestressed Reinforcement in UHPC”, Sustainable Building with UHPC, University of Kassel Press, Volume No.22, 2014. 7.3.2 Durability Properties FHWA-HRT-06-103 – Material Property Characterization of Ultra-High Performance Concrete 7.3.2.1 Absorption FHWA-HRT-06-103 – Material Property Characterization of Ultra-High Performance Concrete 7.3.2.2 Salt-scaling and Freeze/Thaw FHWA-HRT-06-103 – Material Property Characterization of Ultra-High Performance Concrete 7.3.2.3 Permeability

7.3.2.3.1 Chloride ion Penetration Thomas, M. et al, “Marine performance of UHPC at Treat Island”,3rdInternation Symposiumon UHPC, HiPerMat2016, Kassel, Germany, 2016.

7.3.2.3.2.1 Carbonation Graybeal, B.,–“ Material Property Characterization of Ultra-High Performance Concrete”, FHWA-HRT-06-103, McLean, Va, USA 2006. 7.3.2.4 Acid and sulphate resistance Schmidt, H., Schmidt-Dohl, F., Franke, L. and Deckeimann, G., “Resistance of UHPC to Chemical Attack”, Sustainable Building with UHPC, University of Kassel Press, Volume No.22, 2014. Koenig A., Dehn F. “Acid Resistance of Ultra High-Performance Concrete (UHPC)”, In: Sobolev K., Shah S. (eds) Nanotechnology in Construction. Springer, Cham, 2015.

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Piérard, J., Dooms, B. and Cauberg, N., “Evaluation of Durabillity Properties of UHPC using Accelerated Lab Tests”, Proceedings of UHPC & Nano-Technology in Construction, Kassel, Germany, 2012. 7.3.2.5 Delayed Ettringite Formation 7.3.2.6 Abrasion 7.3.2.7 Alkali-Silica Reaction 7.3.3 Time Dependent Properties 7.3.3.1 Creep coefficient Flietstra, J.C. (2011) Creep and Shrinkage Behavior of Ultra High Performance Concrete under Compressive Loading with Varying Curing Conditions,” MS Thesis, MIchigan Tech University. Mullen, C.H.(2013) Determining the effect of Thermal Treatment Timing on deflections of Ultra-High Performance Concrete Beams”, MS Thesis, MIchigan Tech University. 7.3.3.2 Shrinkage Graybeal, B., Zachary B. Haber, Igor De la Varga, Brian Nakashoji, and Rafic El-Helou, “Properties and Behavior of UHPC- Class Materials” , FHWA-HRT-18-036, McLean, Va., USA, 2018. De la Varga et al., “ Enhancing Shrinkage Properties and Bond Performance of Prefabricated Bridge Deck Coneection Grouts: Material and component Testing”, Journal of Materials in civil Engineering, ASCE, ISSN 0899-1561, USA, 2018 7.3.3.3 Thermal Coefficient of Expansion 7.3.4 Fire Properties

Behloul et al., “Fire Resistance of Ductal -Ultra-High Performance Concrete”, Proceedings of the First fib Congress, Osaka, Japan, 2002, pp. 421–430.

AFGC/SETRA, “Ultra-high performance fibre-reinforced concretes – Recommendations”, Interim Recommendations, AFGC publication, France, 2013. Hosser, D., et al “Theoritical and Experimental Determiniation of the High Temperature Behaviour of UHPC”, Sustainable Building with UHPC, University of Kassel Press, Volume No.22, 2014. Hao-wen Ye, Nai-qian Feng, Yan Ling-hu, Zhi-wei Ran, Li-xun Lin, Shi-kun Qi, and Yi Dong, “Research on Fire Resistance of Ultra-High-Performance Concrete”, Hindawi Publishing Corporation, Advances in Materials Science and Engineering, Volume 2012, Article ID 530948, China, 2012. 7.3.5 Other Properties

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182‑92. Baril, M.A., Luca Sorelli, Thomas Guenet, Florent Baby, Liberato Ferrara, Marco Faifer, et Sébastien Bernardi,. 2016. « Combining Magnetic Method and 3D Digital Image Correlation to Study the Effect of the Fibre Orientation on the Ductility of UHPFRC Slabs ». In First International Symposium on UHPC. Des Moines, Iowa. Baril, M.A., Luca Sorelli, Réthoré, Liberato Ferrara, François Toutlemonde, Florent Baby, Sébastien Bernardi, et Mario Fafard. 2016. « The Effect of Casting Flow Defects on the Crack Propagation of UHPFRC Thin Slabs by Stereovision Digital Image Correlation ». Submitted to Construction Building Materials, juillet. Barnett, Stephanie J., Jean-Francois Lataste, Tony Parry, Steve G. Millard, et Marios N. Soutsos. 2010. « Assessment of fibre orientation in ultra high performance fibre reinforced concrete and its effect on flexural strength ». Materials and Structures 43 (7): 1009‑23. Bayard, Olivier. 2003. « Approche multi-échelles du comportement mécanique des bétons à ultra hautes performances renforcés par des fibres courtes ». Ph.D. Thesis, Cachan, Ecole normale supérieure. Bentur, A., S. T. Wu, N. Banthia, R. Baggott, W. Hansen, A. Katz, C. K. Y. Leung, Victor C. Li, B. Mobasher, et A. E. Naaman. 1996. « Fiber-matrix interfaces ». In RILEM PROCEEDINGS,

149‑92. CHAPMAN & HALL. Bernier, G., et M. Behloul. 1996. « Effet de l’orientation des fibres sur le comportement mécanique des BPR ». In Colloque international francophone sur les bétons renforcés de fibres métalliques, 233‑40.

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Technology 56 (10): 1179‑90. Guenet, Thomas. 2012. « Un modèle numérique pour structures en béton fibré à ultra-hautes performances : prise en compte de l’orientation des fibres par une approche d’endommagement micromécanique ». M.Sc., Faculté Des Sciences Et De Génie Université Laval Québec. http://theses.ulaval.ca/archimede/. ———. 2016. « Modélisation du comportement des Bétons Fibrés à Ultra-hautes Performances par la micromécanique : effet de l’orientation des fibres à l’échelle de la structure ». Paris: Paris Est en cotutelle avec l’Université Laval. http://www.theses.fr/s87756. Kooiman, Alain Geoffré. 2000. Modelling steel fibre reinforced concrete for structural design. TU Delft, Delft University of Technology. Krenchel, H. 1975. « Fibre spacing and specific fibre surface ». Fibre reinforced cement and

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Structures 10 (5): 297‑301. Martinie, L., et N. Roussel. 2011. « Simple tools for fiber orientation prediction in industrial practice ». Cement and Concrete research 41 (10): 993‑1000. Maya Duque, L.F., I. De la Varga, et B. Graybeal. 2016. « Fiber Reinforcement Influence on the Tensile Response of UHPFRC ». In First International Symposium on UHPC. Des Moines, Iowa.

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Journal Proceedings, 68:126‑37. Simon, Alain, Dominique Corvez, and Pierre Marchand. "Feedback of a ten years assessment of fibre distribution using K factor concept." UHPFRC 2013-International Symposium on Ultra-High Performance Fibre-Reinforced Concrete. 2013).

Sorelli, Luca, Nemkumar Banthia, Vivek Bindiganavile, Giovanni Plizzari, Ying-shu Yuan, Surendra P. Shah, et Heng-lin Lü. 2003. « Static and dynamic responses of hybrid fiber reinforced concrete ». In International Conference on Advances in Concrete and Structures, 1023‑30. RILEM Publications SARL. Tucker, C. L., et Suresh G. Advani. 1994. « Processing of short-fiber systems ». Composite Materials Series, 147‑147. Wang, Y., S. Backer, et V. C. Li. 1989. « A statistical tensile model of fibre reinforced cementitious composites ». Composites 20 (3): 265‑74. Wille, Kay, Dong Joo Kim, et Antoine E Naaman. 2011. « Strain-hardening UHP-FRC with low

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Varying Degrees of Fibre and Shear Reinforcement." High Tech Concrete: Where Technology

and Engineering Meet. Springer, Cham, 2018. 500-507.

Voo, Yen Lei, Wai Keat Poon, and Stephen J. Foster. "Shear strength of steel fiber-reinforced

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Zheng, Hui, and Zhi Fang. "Experimental Study on Shear Behavior of Prestressed Ultra-High

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Concr. Inst. JCI-S-001-2003 (2003).

X.X. Zhang, A.M. Abd Elazim, G. Ruiz, R.C. Yu, Fracture behaviour of steel fibre-reinforced concrete at a wide range of loading rates, Int. J. Impact Eng. 71 (2014) 89–96. doi:10.1016/j.ijimpeng.2014.04.009. S. Pyo, K. Wille, S. El-Tawil, A.E. Naaman, Strain rate dependent properties of ultra high performance fiber reinforced concrete (UHP-FRC) under tension, Cem. Concr. Compos. 56 (2015) 15–24. doi:10.1016/j.cemconcomp.2014.10.002. 7.5.2 Durability Durability requirements for Exposure Classes and crack width limitations in Reinforced Concrete Structures 7.5.2.2 Crack width control Leutbecher, T., Fehling, E.: 2008. Crack Width Control for Combined Reinforcement of Rebars and Fibers exemplified by Ultra-High-Performance Concrete. In fib Task Group 8.6 Ultra High Performance Fibre Reinforced Concrete – UHPFRC. Varenna, September 5th 2008.

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E. Parant, Damage mechanisms and mechanical behaviors of a multi-scale under harsh conditions: fatigue, impact, corrosion, Ph.D. thesis of Ecole Nationale des Ponts et Chaussées, France, 2003. Charron, J.-P., Denarié, E., Brühwiler, E., (2008) Transport properties of a UHPFRC in cracking state, Cement and Concrete Research, Vol. 38, pp. 689-698. Lachance F, Charron J-P, Massicotte B. (2016). Development of Precast Bridge Slabs in High and Ultra-High Performance Fiber Reinforced Concretes. ACI Structural Journal, V. 113, No. 5, September-October 2016. Pp. 929-939. Hubert, M., Desmettre, C. Charron, J.-P., (2015) Influence of fiber content and reinforcement ratio on the water permeability of reinforced concrete, Materials and Structures., September 2015, Volume 48, Issue 9, pp 2795-2807. Graybeal, B., “Simultaneous Structural and Environmental Loading of a UHPC Component”, FHWA HER-10-055, McLean, Va., 2010. 7.5.2.4 Durability under Chemical load “Material Property Characterization of Ultra-High Performance Concrete”, FHWA-HRT-06-103, Federal Highway Administration, August 2006. “Ultra-High Performance Concrete: A State-of-the-Art Report for the Bridge Community”, FHWA-HRT-13-060, Federal Highway Administration, June 2013. Acker, P. and Behloul, M., “Ductal® Technology: a Large Spectrum of Properties, a Wide Range of Applications”, Proceedings of the International Symposium on Ultra High Performance Concrete, Kassel, Germany, September 2004. Franke, L et al., “Behaviour of ultra high-performance concrete with respect to chemical attack”, Proceedings of the Second International Symposium on Ultra High Performance Concrete, Kassel, Germany, March 2008. Pierard, J. et al., “Durability Evaluation of Different Types of UHPC”, Proceedings of the RILEM-fib-AFGC International Symposium on Ultra-High Performance Fibre-Reinforced Concrete, Marseille, France, October 2013. Rehacek, S. et al., “UHPC and FRC in Severe Environmental Conditions, Resistance Against Freeze-thaw Cycles, Aggressive Chemical Agents and Dynamic Loading”, Proceedings of the First International Interactive Symposium on UHPC, Des Moines, Iowa, June 2016. 7.5.2.5 Durability Under Temperature Effects Ahlborn, T., Peuse, E., Li Misson, D.: 2008. Ultra-high-Performance-Concrete for Michigan Bridges Material Performance–Phase I. Research Report No. MDOT RC-1525. Behloul, M, Chanvillard, G., Casanova, P., Orange, G.: 2012. Fire Resistance of Ductal Ultra High Performance Concrete. In Proceedings of fib symposium 2012. Osaka, Japan.

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8.0 APPENDICES:

The following Appendices may be included into the ETR, depending on the state of complimentary documents published at the time of balloting this ETR on the Structural Design of UHPC.

Appendix A: Material Characterization Methods

Appendix B: Simulation-Based Design

Appendix C: Examples of UHPC Construction

Appendix D: Research Gaps

Appendix E: Demand Forces and Stresses Appendix F: Design Examples

Solved Example Problems for – Parametric Based Design for UHPC: The sample problem can be constructed under three different cases: Case A - The sizes of the beam and the residual strength of the material are known, the maximum allowable load is required for a given geometry. Case B - Size of the beam and the loading condition (moment demand) are known, the level of residual strength is required. Case C - The residual strength of the material and the loading condition (moment demand) are known, the size of the section is required.

Case A- Calculation of the moment capacity of a given section The aim of this section is to use the simplified ultimate strength approach and compare the parametric design of FRC with the solutions obtained from ACI 544.8R-16 in order to illustrate the process of obtaining moment capacity for a section and compute the allowable service load. Problem Statement- Compute the maximum allowable load on a simply supported beam with a span of

10 ft 3.04 mL and a rectangular Section 6” by 2” (152mm by 305mm) is used. UHPC concrete

has ' 22 ksi (151.6 MPa), 1.2 ksi (8.27 MPa)c tf f . Design for a material with

,3 580 psi 4 MPaeqf . Assume a concrete density as 3 3150 lb/ft (2402.7 kg/m )c and

compute unfactored moment by assuming 1 ( is strength reduction factor which is less than 1 in

accordance to ACI 318-14 Section 10.5.1 (ACI 318-14).

Commented [vp52]: All of these Appendices should be deleted and put into the future Guide.

Commented [MOU53]: I think example problems should be reserved for the guide. This document is intended to review the information that would support development of a guide.

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For illustration of the calculation and comparison, Case A is addressed in this example. Fig. A.1. aFig. A.1. a shows a schematic side view of simply supported beam under a center loading is used.

Fig. A.1. a. Sample problem, simply supported beam with center point loading.

Step 1: Define geometric and material parameters

" " 10 ft (3.3 m), 12 (0.3 m), 6 (0.15 m), 1, ' 22 ksi (151.6 MPa)cL b h f

Assume 1 , thus: cE E ; also ' 6.7 't cf f

657000 ' 8.454(10) psi 58.2 GPacE f

6.7 ' 6.7 =993.77 p22 si000 6.85 MPacr cf

-4993.77

845446 1.17(10

6)cr

crE

tuβ is the normalized ultimate tensile strain in the section and since it is assumed that the section will

maintain its residual tensile strength. This value is expected to be imposed as a large number. In this

example, it is considered to be equal to 50, i.e. / 50tu tu cr . Therefore, maximum tensile strain

allowed is 0.0055tu or 0.55% .

ω is the ratio of compressive strength to tensile strength and obtained as (according to Eq. 5) ' '

'

2200022.24

0.000117 1 8454466

c c

crt

f fω

ε γEf

Step 2: Calculate demand moment

u DL FM M M

Where, 𝑀𝐷𝐿 is moment due to dead weight & MF is the moment due to point load.

72

w 150=75 lb/ft 1.09 kN/m144

2 275 10

937.5 lb-ft 1.27 kN-m8 8

DL

wLM

For a simply supported beam the maximum moment is at the center of the beam:

n

10M 937.5 lb-ft kN-m

4u

FM

Step 3: Calculate Cracking moment Cracking moment is given by:

F

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2 21 1 1(993 psi) 12" (6") 5.95 kips-ft (8.33 kN-m)

6 6 12cr crM bh

Step 4: Determine post crack tensile strength (ACI 544.8R-16) Use the formula for plain FRC, in to consideration (according to Eq. 7)

,3

,3

6 , ξ = 15.8 for inch-lb; ξ = 1.32 for SI

( + 3 )

eq cn cr

eq c

f fM M

f f

6 580 220005.958 2.923 kips-ft (4.2 kN-m)

15.8(580 3 22000)

10937.5 2923.4 lb-ft

4u n

FM M

794.36 (3.53 )F lb kN

In the case of a normal strength beam with same dimensions ( 22000 psi (151.6 Pa)' Mcf ,

6000 psi (41.4 Pa)' Mcf ), the computed allowable load would be 323 (1.4 )F lb kN .

Documents

Emerging Technology Report (ETR) The Structural Design of