Sustainable infrastructure with fiber and textile reinforced concrete systems

Sustainable infrastructure with fiber and textile reinforced
concrete systems:
Manufacturing, properties, analysis and design
B. Mobasher
Collaborators:
Y. Yao, J. Bauchmoyer, V. Dey, H. Mehere, N. Neithalath,
A. Arora, K. Aswani, X. Wang
School of Sustainable Engineering and the Built Environment Ira A. Fulton Schools
of Engineering, Arizona State University
Tempe, AZ 85287-5306
June, 2018, Dresden, Germany

Presentation Outline
 Introduction
 Sustainability aspects
 Textile Reinforced Concrete Directions
 Structural Sections using UHPC-FRC-TRC systems
 Experimental Characterization of Distributed Cracking
 Parametric Material Models for TRC, UHPC, and FRC
 Analytical Load-Deflection Solutions for 1-D and 2-D Members
 Experimental Verification
 Conclusions

Length
Scale
Time
Scale
Disciplines
Seconds to
Centuries
(1 to 3x1010
Seconds)
hydration Early age
Long term
Performance
Service life
• Materials Science
• Engineering
• Chemistry
• Mechanics
• Computational Techniques
• Manufacturing products and systems
• Sustainable development
• Technical & non-technical labor poolnanometers to kilometers
(1x10-8 to 1x103 meters)
Construction Products: Temporal, Spatial, and Scientific Span

Sustainable Construction Products
 Societal Challenges, Sustainability
– What are the challenges we face in the next several decades?
– Global warming, societal development, and energy use
– Reuse and recycle, blended cements, low cement concrete
– Design for durability, Quality control, wastefulness
– Structural mechanics, new materials and design systems
 Short and continuous fiber Composite systems
– FRC and TRC
– Ductility based designs utilizing nonlinear material properties
– life cycle energy consumption
– Enabling Technologies for Renewable Energy power generation
– Textile reinforced concrete, FRC, design guide development

The era of unrestricted use of energy &
materials is over
 In 2010, global concrete demand of approx. 21 BT, 2.8 BT
cement, and about 2BT of CO2 was released.
 Portland-cement clinker, will continue to be a major
component of modern hydraulic cements.
 Buildings in the United States consume 39% of energy and
68% of its electricity
 Energy Demand of building is in construction and operation
costs 3%, and 97% respectively.
 The United States spends $20.2 billion annually on air
conditioning for troops stationed in Iraq and Afghanistan —
more than NASA’s entire budget (NPR)
 The same amount of money that keeps soldiers cool is the
amount the G-8 has committed to helping the fledgling
democracies in Tunisia and Egypt.
P.K. Mehta, 2008

Child Labor, outdated construction systems, Slavery,
and the norms of human standards of life
http://www.dailymail.co.uk/news/article-2858775/
Paying-debts-brick-brick-Pakistani-modern-day-slaves-trapped-lifetime-hardship.html

Sustainability of Construction Materials
• At one ton per person per year Concrete is the 2nd consumed material
per capita in the world.
• $1.6 trillion is needed over 5-years to upgrade the US's infrastructure
to a good condition. (ASCE,09)

Globalization- American Model of Economic Development
 China and India have achieved fast economic growth rates by rapid industrialization
 Over 40% of the 1.3 billion Chinese already live in cities with sky-rocketing demand for
energy and energy-intensive materials
 China
– 50% of global cement production, followed by India and US (6% and 3%, resp.)
– 40% of global steel production, followed by Japan and US (9% and 7%, resp.)
– 15% of the global power generation. Projected to triple By 2030
– 80% of electric power generated from coal
– Equivalent of two 500-MW coal power plants built every week for the next 20 years
– China has passed the U.S. as the World’s largest emitter of CO2

Science without borders project , sponsor: Brazil Science Foundation
Objective: develop Alternative Construction Products

Global Warming is Global
Texas, Florida, Caribbean, Bangladesh,..
Hurricane Harvey,
2017
Hurricane Irma,
2017

Motivation: Sustainability in construction
 Challenges for civil infrastructure systems
o Economic growth, Efficient resource utilization
o Global warming, resilient structural systems
 Sustainability – A need of the hour
o Energy efficient, Cost effective structural systems
o Durable and Safe
 Composite Systems – A solution
o Fiber reinforcement and textile composites
o Ductility and Crack control
o Light weight
o Low cement utilization in concrete
Geospatial world, “Sustainable Infrastructure: Geospatial tech in the forefront

Textile Reinforced Concrete (TRC) as Material
Choice for Sustainable design Technologies
 Ductility Based Design
– seismic, impact, earthquake, wind,
– Safety, durability, non corroding, low energy cost
 Reduced Section sizes
– as much as 30% materials savings, reduced dead load
 Durability
– Physical-shrinkage cracking resistance
– Chemical-Decreasing ionic diffusivity, non metal reinforcement
– Serviceability-increased post crack stiffness, deflection criteria
 Economical,
– Reduction of substantial amount of size, rebars & associated costs.
– Fresh Concrete. Forming and placement and detailing
– Opportunity for micro-fabrication grass roots technology development
 High Performance Designs
– high Fatigue cycle applications, thermal barrier, energy production

Textile Reinforced Concrete
Sandwich layers
• Low cost equipment set up
• Uniform production
• high performance fabric-cement composites
• Tension, Compression, beam members
• High pressure pipes

Textile Reinforced Concrete
0 0.01 0.02 0.03 0.04
Strain, mm/mm
0
4
8
12
16
20
Stress,MPa
AR Glass Fabric
GFRC
Vf =5%
PE Fabric
E-Glass
Fabric
Mortar
ECC
500 mm

Homogenization of Crack spacing –Mechanical interlock
0 10 20 30 40
Crack Spacing, mm
0
0.2
0.4
0.6
0.8
1
CumulativeDistributionFunction
Zone 1
= 0.015
Zone 2
.0273
Zone 3
 = 0.0387
AR-Glass Fabric
0 0.02 0.04 0.06
Strain, mm/mm
0
5
10
15
20
25
Stress,MPa
Zone 3
Zone 2
Zone 1
AR-Glass Fabric
AR Glass Bonded
Fabric
Polyethylene (PE)
Woven Fabric
Polypropylene (PP)
Knitted Fabric

Uniaxial Tensile Response large strain capacity and ductility
0 0.02 0.04 0.06
Strain, mm/mm
0
4
8
12
16
20
Stress,MPa
0
20
40
60
CrackSpacing,mm
Stress-Strain
Crack Spacing
Pultrusion
Peled, A. and Mobasher, B., (2005), “Pultruded Fabric-
Cement Composites,” ACI Materials Journal, Vol. 102 ,
No. 1, pp. 15-23.

Development of Polypropylene based Yarn/Fiber and
Textile technology (project sponsored by BASF Corp)
MAC 2200CB MF 40
Loading Rate (mm/min) 0.4 2.5
Gage Length (mm) 25 25
Effective Yarn Dia. (mm) 0.82 0.89
Tensile Strength (MPa) 311 (+/-38) 492 (+/-65)
Elastic Modulus (MPa) 4499 (+/-351) 1601 (+/-117)
Toughness (MPa) 34 (+/-12) MPa 5058 (+/-1748)
2) Microfiber – MF 40
Fibrillated multi filament micro-fiber
500 filaments of 40 microns per yarn
1) Macro-synthetic fiber – MAC 2200CB
Chemically enhanced macro-fiber

Fiber Pullout Test - Experimental setup
Load Cell
Pullout
Specimen

Effect of Fiber Embedded Length Macro PP vs. Steel
Pullout energy as the area
enclosed by load slip response.
maximum for embedded length of
25 mm for all fiber types
Maximum pullout force for MAC is
similar for embedded length 20
and 25 mm. But about 40 % less
at 10 mm.

Development of Woven 2-D PP-Textiles
 The objective is to develop low cost PP based fibers for the development of next
Generation Textile Reinforced Concrete.
 multifilament textiles developed with Partners:
Textile Institute, RWTH Aachen University, Germany
Plain and tricot weave knit patterns with 50% open-closed structure

Development of Pultrusion Process – TRC
 Computer controlled pultrusion process for Textile Reinforced Concrete (TRC)
 Different geometrical cross-sections: rectangular plates, angle, channel sections
 Components: Treatment baths, pressure cylinders, tractor pull clamping, specimen mold, press,
Pneumatic pistons, solenoid valves, Lab view Interface
 Simple set up, with low cost equipment, uniform production

Test setups for plate, angle and channel sections
under compression and tension
Continuous versus 2D
Reinforcement -Tensile

Effect of curing age and dosage, MF series
 MF 40 at dosages of 1.0 and
2.5% tested after 7 and 28
days of moist curing (73 F,
90% RH)
 First crack and ultimate
strength (UTS) increased
marginally with longer
hydration periods
 Toughness increased
considerably due to fiber
content

Effect of Fiber Volume Fraction on Tensile
Response of MAC
 Fiber reinforcement increased the
toughness
 Improvement in strength and toughness
can be seen with increase in volume
fraction.
 First cracking strength increases by
30% and post-crack (tangent) modulus
increases by over 107%.
 The ultimate tensile strength (UTS) and
toughness measured from the area
enclosed within the stress-strain curve
increases by a factor of 2 at 4% dosage
 Strengthening mechanisms - distributed
parallel cracking, crack bridging and
deflection, fiber pullout, fiber failure.

Effect of Fiber Dosage on Tensile Response
 MF 40 vs. MAC – Significantly higher improvement in strength and toughness
with increase in volume fraction from 1.0 – 2.5%
 Possible mechanisms, better bond with the matrix due to matrix penetration
between the filaments.

Continuous Fiber versus 2D Textile
Reinforcement

Micro Toughening Mechanism
1
2
3
Crac k Deflec tion
Debonding
Fric tional Sliding
Fibers and fiber-matrix interface prevents complete
localized failure in the matrix place through a series of
distributed cracks transverse to the direction of the load.
Distributed cracks enable deflection of matrix cracks
through fiber-matrix debonding and frictional
sliding of the fibers under tension

Toughening Mechanisms – MAC
Fiber bridging across loading directionDistributed cracks across loading direction

Automated pultrusion system, full
scale structural shapes composed
of TRC laminates can be
manufactured efficiently and
effectively.
Pultrusion Process Schematic Diagram
Light gage steel sections
Structural Shapes: Development, Analysis, and
Implementation using Design Approach

Pultruded Full Size TRC Structural Shapes
Cross section of pultruded shapes with TRC laminates

TRC Structural Sections
 Full-scale structural sections were manufactured using the pultrusion system and
an ARG textile dosage of 1%
 Angles of 19x75x75 cm2 by 1.22 m were tested in tension with six 8 mm bolts in
three rows of two bolts per leg (UTS of 2.7 MPa)
 Preliminary channels were tested in tension and attached in the web only

Assessment of Structural Shapes
 Angle sections exhibited multiple parallel cracking, a 51% strength reduction from
fixed-fixed testing, and a 40% reduction from fixed-bolt testing

Multiple cracking in tension and flexure
Tensile test
Flexural test
Analytical models
Moment-curvature
Stiffness Characteristics

DIC based analysis of Static and High Speed Testing

Strain Map of Tension Stiffening
Short fiber vs. continuous fiber systems
σ =
0.8 MPa
σ =
2.9 MPa
σ =
4.1 MPa
σ =
4.3 MPa
σ =
2.6 MPa
3.1
MPa
6.1
MPa
16.7 MPa 19.5 MPa 21.6
MPa
Yao, Y., Silva, F. A., Butler, M., Mechtcherine, V., & Mobasher, B. (2015). Tension stiffening in textile-reinforced concrete under
high speed tensile loads. Cement and Concrete Composites, 64, 49-61.

Quantification of DIC strain
 A: Localization Zone – Fiber debonding
 B: Shear Lag Zone – Shear lag bonding stress distribution
 C: Uniform Zone – Fiber and matrix are perfectly bonded
DIC strain versus time histories at different zoneIdentification and label of each zone
Rambo, D. A. S., Yao, Y., et al. (2017). Experimental investigation and modelling of the temperature effects on the tensile
behavior of textile reinforced refractory concretes. Cem. Concr. Compos. 75, 51-61.

Crack Width Measurement
 Non-contact measurement
 Quasi-static to high speed
 Single crack and multiple cracks
Displacement Field
Displacement
Distribution Along
Specimen
Stress-Crack Width
Relationship

Evolution of Crack Spacing in TRC
σ = 3.5 MPa σ = 4.7 MPa σ = 5.5 MPa σ = 11.5 MPa
I II III IV
1.75
2.00
1.50
0.00
yy, %
1.25
1.00
0.75
0.50
0.25
 Multiple cracking in tension
 Tension stiffening
 Development of parallel cracks
 Indication of toughening mechanisms
 Corresponding to the characteristic length
in numerical modelling

New Product Development
 Sandwich composite systems with TRC and light-weight aerated concrete core
 Structural sections with TRC
Aerated concrete
core
Textile reinforced
cement skin layer
Dey, V., Zani, G., Colombo, M., Di Prisco, M., Mobasher, B., “Flexural Impact Response of Textile-Reinforced Aerated
Concrete Sandwich Panels”, Journal of Materials and Design, 2015, doi: 10.1016/j.matdes.2015.07.004

Modelling Approach
 Materials evaluation
– Parametric linearized materials model
– Cross-sectional analysis based on nonlinear stress and strain
– Closed-form solutions of moment and curvature responses
– Back calculation of tensile responses and extraction of tensile properties
 Structural response
– Forward simulation of flexural load-deflection responses
– Parameters for serviceability states: curvature, deflection, post-crack stiffness
– Design parameters: moment capacity, min. reinforcement, serviceability limits
– Characterization of shear stresses and other failure modes.
– Advance to structural analysis using the stiffness matrix, or FEM
 Serviceability Criteria
– Represent the elasticity of variables used in the overall cost, durability, and
structural response in the context of the derivatives of various variables

Classification – Fiber reinforced cement based
composites
 Two categories of tensile response
o Strain hardening
o Strain softening
 Strain softening behavior
o Discrete fiber systems
o SFRC, GFRC, PP-FRC
 Strain hardening behavior
o Discrete & continuous fiber systems
o TRC, SHCC, UHPFRC
GFRC, SHCC
ECC
TRC
ε
Tensile Behavior
σ
Paste
SFRC
Deflection softening
Deflection hardening
UHPFRC

Fracture and plasticity models
43
Geometry

Finite Element Analysis on Shear Behavior
 Limitation of analytical based flexural model
– Cross sectional analysis
– Inclined growth
– Damage
 Finite element analysis in LS-DYNA
– Damage concrete model: MAT159 (*MAT_CSCM)
– Piecewise model for rebar: MAT024
(*MAT_PIECEWISE_LINEAR_PLASTICITY)
– Interface: *Lagrange_IN_SOLID
Minelli, F., Conforti, A., Cuenca, E., & Plizzari, G. (2014). Are steel fibres able to mitigate or eliminate size effect in
shear?. Materials and structures,47(3), 459-473.

Nonlinear hinge
RVE in the context of a nonlinear hinge framework

 Material Properties
– Strain hardening material models
Design Procedure for Modelling SHCC Panels for
Serviceability
 Moment-Load , curvature-displacement relationship
– 1-D: Beam statics
– 2-D: Limit State Analysis (Yield Line Theory)
1
2
3
4
b
Y
X X
Y
45
a
 Curvature-Deflection
– 1-D: Double integration
– 2-D: Kinematically admissible deflections
δmax
θ
 Moment–Curvature Relationship
– Cross-sectional analysis

Material Models for Serviceability Design
Compression Model Tension Model
Soranakom, Chote, and Barzin Mobasher. "Correlation of tensile and flexural responses of strain softening and strain
hardening cement composites."Cement and concrete Composites 30.6 (2008): 465-477.
 Serviceability limits: allowable stress, strain, crack width, curvature, deflection

Derivation of Moment-Curvature Relationship
Strain Stress
Incrementally impose
0 < t < tu
Strain Distribution
Stress Distribution
SF = 0, determine k
Moment: M = SFciyci+ SFtiyti
Curvature: φ=c/kh
Simplified bilinear
moment-curvature
Stage : l>w, b>a

Moment-Curvature Diagram
M
f
f
c
0 < t < tu
k
d
stressstrain Moment curvature
diagram
 Incrementally impose 0 < t < tu
 Strain Distribution
 Stress Distribution
 SF = 0, determine k (Neutral axis)
 M = SCiyci+ STiyti and f=c/kd
 Normalization M’=M/M0 and f’=f/fcr
 1 10
kd
c cF b f y dy 
 1 10
1
kd
c c
c
b
y f y ydy
F
 
C2
T1
T2
T3
C1
FS

1-D Member: Moment-Curvature Distributions
 Use static equilibrium to get
moment distributions
 Moment distributions
3PB 4PB
Bilinear moment-curvature
Curvature distributions

Example – Simply Support Beam
Deflection solutions for four point bending beam
 Region ①: (0 ≤ 𝑥 ≤ 𝜉 ), Pre-cracked region
Stage II: M ’ (x=L/2)> Mcr
Transition point:
From pre-cracked region to post-cracked region: x=ξ
 ' 2 3
crM
M x L L



 ' 2
'
cr
M x L
m
M


3 '
L
m
 
 Region ②
a: (𝜉 ≤ 𝑥 ≤ 𝐿/3), Post-cracked
b: ( 𝐿/3 ≤ 𝑥 ≤ 𝐿/2), Post-cracked, constant moment

Deflection    21 21 40
x
x x dx C  
     22 21 21 22 5( ) 0
x
a x x dx C

       
           22 21 21 22 22 22 63
0 3
x
b a a bL
x L x dx C            
0 x  
3
L
x  
3 2
L L
x 
Solutions
 Region ① :
 Region ②-a:
 Region ②-b:
  2
*
21
3 21
3 ' 2 '
6
x x q L Lq
L
  

   
 
 3 3 2 2* 2 2 2 3
222
1
3 ' 3 3 9 ' 2 ' 9 ' 3 '
6 3
a x q x x L x q xL q xL xLq L q
L L
   

      


2
22 2
* ' ' 1 3 3 '
1 1 '
2 542
b
q x q x q
q
L L LL


   
       
  

 
* 2
 cr L  

Strain and Stress Distributions in ½ 3PB beam

Bilinear Moment-Curvature Model
 
g cr cr
p cr
cr p cr p p
p cr
M( ) EI 0<M M 0<
M M
M( ) M M M M 1
   
    
 
  

      

 
1
1 1
1
p
p
m( ) 0<m 1 0< 1
m
m( ) 1 m 1
  
  

  

    

cr
M( )
m( )
M

 
cr



 u
cr
M
m
M
 p
p
cr




cr
g
EI
EI
 
First cracking moment 21
6
cr crM bd E
First cracking curvature
2 cr
cr
d

 
Normalized moment-curvature

Solutions are available for other loading types
 Different equilibrium equations affecting Moment distribution
 Simply supported beam and cantilever beam.
 8 different loading types

 21 21 10
x
x dx C  
0 x 
2
Lx    22 21 21 20
x
x dx x dx C


     
0 x 
2
Lx    22 21 22 40
   
x
x dx x dx C


  
 21 21 30
x
x dx C  
 Rotation
Region ① :
Region ②:
 Deflection
The constants of integration defined in terms of Ci are
numerical values which are determined based on the
boundary conditions.
Analytical Deflection Solutions
Region ① :
Region ②:

2-D Deflection Contour
Three-point bending
Four-point bending
Loading
type
Span
(L),mm
Width
(b),mm
Height
(d),mm
εcr, µstr E, Mpa η
3PB 300 100 100 244 20400 0.01
4PB 750 100 100 244 20400 0.01
h
Parameters of 2-D deflection distribution

2-D Member: Slab and Panel
Model Approach Type of Members
Round Panel Rectangle Panel Square Panel
Boundary conditions
Simply supported
Clamped
 Stage I: Elastic Solution
 Stage II : Yield Line Approach

Elastic Solution for Panels
Case 1.1 Case 1.2
Case 2.1
Case 2.2
2
3
16 1
PR v
D v
 
 
 
2
16
PR
D
4
0.00406
qa
D  
4
2
3
0.032
1
2
qa
v
Et
 
  
 
4
qa
D
a
 
 
2 4
4 3
0.032 1
1
v qa
Eta
b
  
 
 
Case 3.1 Case 3.2
Clamped support
Simply supported
Free support
Moment Rotation
Round Panel – Point load (P) at center
Rectangular/Square panel— Uniform load (q)
Case 2.2 Westergaard approximate solution. Boresi, Arthur Peter, Richard Joseph Schmidt, and Omar M.
Sidebottom.Advanced mechanics of materials. Vol. 6. New York: Wiley, 1993.

Plastic Solution: Yield Line Moment– Applied Load
ext intW W
( ) ( )N ml   
Assumptions:
 Failure takes place according to the assumed pattern
 Yield lines are straight and end at slab boundary
 Yield lines at vertexes are at 45° to the edges in case of square & rectangular
slabs
 Hogging moment about the yield lines and sagging moment about the
supports are equal
Work done in moving loads = Work done in rotating yield lines
N – Load, δ – Defl., m – moment abt. YL, l – length of YL, θ - Rotation
Kennedy G., Goodchild C., “Practical yield line design”

Yield Line Moment – Applied Load
Case 1.1 Case 1.2
Case 2.1
Case 2.2
Case 3.1 Case 3.2
Clamped support
Simply supported
Free support
Moment Rotation
Round panel – Point load (P) at center
Rectangular/Square panel— Uniform load(q)
2
P
m 
 4
P
m 

 2
3
12(2 2 )
qb b a
m
b a



 2
3
12(4 4 )
qb b a
m
b a



2
24
qa
m 
2
48
qa
m 
Aswani, Karan. Design procedures for Strain Hardening Cement Composites (SHCC) and measurement of their shear
properties by mechanical and 2-D Digital Image Correlation (DIC) method. Diss. Arizona State University, 2014.

Curvature-Deflection Relationship for
Square panels
Square panel
2
( ) 0.5 0a x a z  2 2
( ) 0.5 0a x a z a   
Equation of plane # 1 Equation of plane # 3
Angle between plane # 1 and #3
   
2 2 4 2 2
2 22 2 4 2 2 4
0.25 4
cos2 cos( 2 *)
40.25 0.25
a a a
L
aa a a a
 
   
 
 
  
 
1 cos2 *
2 1 cos2 *
a L
L






Simplifying
1
2
4
3
L* is the hinge length

Curvature-deflection relationship
φL* - Rotation, L* - Hinge length, L – Length, φ – Curvature, δ - Deflection
Rectangular panel
δ
a
Section X-X
δ
b
Section Y-Y
φL* φL*
φL* φL*
Round panel
δmax
2R
δ2θ
φL* φL*
2 2cos( *)
1 2cos( *)
L
R
L






14
14
1 cos2( *)
2 cos2( *)
La
L





1
2
3
4
b
K L
P
Y
MN
O
X X
Y
45
a
b
b a
a

Experimental Verification
Input
Dimension: b, d, L
Material prosperities: E, εcr
Calculate
Mcr=bd2Eεcr /6
φcr=2εcr/d
Select position x
Assume maximum ’ and m
Loop from ’=0 to ’max
If ’ <1
If ’> 1
Stage I
Calculate
M(i), P(i), m’, (i)
Stage II
Calculate
M(i), P(i), δ (i)= δ1
If Region ①
0<x<ξ(i)
δ (i)= δ21
If Region ②
ξ(i)<x<L/2
δ (i)= δ22
Moment-curvature
Load - deflection

Data Set 1 – Textile Reinforced Concrete
 Three-point bending test
 30 (b) × 9(d) × 220 (L) mm
 Textile fabrics:
 Polypropylene
 Aramid
ID εcr,µstr E, Gpa η m q EI, 107
EIcr, 107
100P 130 22 0.01 4.28 298 4.0 0.044
100A 130 22 0.1 17 157 4.0 0.41
25A75P 130 22 0.05 10.48 198 4.0 0.202
100P
Normalized curvature vs. Normalized moment Deflection at mid-span vs. Applied load
Simulated Parameters (Avg.)
Mobasher, Barzin, et al. "Correlation of constitutive response of hybrid textile reinforced concrete from tensile and flexural
tests." Cement and Concrete Composites 53 (2014): 148-161.

100A
25A75P
Data Set 1 – Textile Reinforced Concrete
Mobasher, Barzin, et al. "Correlation of constitutive response of hybrid textile reinforced concrete from tensile and flexural
tests." Cement and Concrete Composites 53 (2014): 148-161.

Data Set 2 – Square Slab
Square slab with point load at center
680 mm x 680 mm, thickness is 80 mm
Steel fiber vf = 1.0% and 1.5%
Khaloo, A.R., Afshari, M.: Flexural behaviour of small steel fibre reinforced concrete slabs. Cem. Concr. Compos. 27, 141–
149 (2005).

Simplified Design Approach
 Step 1: Determine the full range moment-curvature relationship using
the closed-form equations
 Step 2: Obtain simplified relations using polynomial curve fit
For clear span of 680 mm, thickness 80 mm, cracking stress as
1.5 MPa, moment–curvature relationship of Stage 2.1 can be shown as
Similar expression can also be calculated for Stage 3.1:
-4 2 -3
1:
1.882
2.1: 2.805 ( )
(10 ) (10 ) 2.45 ( )
3
7.
.1
9
:
66
Stage m
Stage m ascending
m descending
Stage


 
  
    
    
  2
3949
0.592m

  
2
6
7 2 3
1.882 3.570
2.806 4489.6 ( )
/ (1.5 )
7.111( ) 8497.1
1.5 1 80
610
10 13 0.920 ( ) ( )
M ascending
M desce
N mm
N mm nding

 

 
    
 
 
    
  
     
   
5
2
1.422(10 )
946.72M N mm


 
  



Curve fit of the moment-
curvature relationship

Cont’d
 Step 3: The boundary conditions are simply supported
on all sides. The moment-load relationship for a point
load for square slab is as follows:
 Step 4: The curvature-deflection relationship for a
square slab in cracked stages (2.1 and 3.1) are follows:
 Step 5: Calculate the load-deflection result using the
results from Steps 3 and 4.
08P m
 
2 3
2
0.00406
: ,
12(1
cos * 1 cos *
:
2 co
)
s *
L LL
Cracked
PL Et
stage
L
Elastic stage D
D




 
 
    







Data Set 3 – Round Panel
Round panel with point load at center
Diameter is 750 mm, thickness is 80 mm
Steel fiber vf = 1.0% and 1.25%
Montaignac, R. de, Massicotte, B., Charron, J.-P., Nour, A.: Design of SFRC structural elements: post-cracking tensile
strength measurement. Mater. Struct. 45, 609–622 (2012).

Design Procedures for UHPC
 Introduction
 Microstructure And Rheology Guided Design of Ultra-High Performance
Binders Research Objectives
– Microstructure packing – Selection Criteria and Results
– Rheology of Pastes – Selection Criteria and Results
– Characterization of Selected Binders
 Particle Packing Based Design of Ultra-High Performance Concrete
– Compressible Packing Model
– Concrete Design Considerations
 Mechanical testing Tension, Compression and Flexure
– Test methodologies
– Test results
 Guidelines for Structural Design with UHPC
– Proposed Methodologies
 Summary Results
73

UHPC Pi-girder: FHWA Study
74
Jakway Park Bridge in
Buchanan County, Iowa

UHPC Structural Sections, girders, and decks
Jakway Park Bridge in
Buchanan County, Iowa

Materials for Paste Selection77
Materials selected
 OPC – ASTM C150 cement
 Slag, Silica Fume, Metakaolin
(pozzolanic Silica and Alumina
sources – as well as react with
carbonates present in the system)
 Limestone – 3.0 micron and 1.5
micron. Fine limestone help with
dense packing of microstructure.
 Fly Ash – pozzolanic, spherical
particles aid with workability.

Mix Designs
78
 33 mixes selected
 Cement replacement, up
to 30% by mass
 Water/binder = 0.24
 High-range water reducer
(HRWR), .25% solids
content by mass of binder
Mixture
composition
Replacement material (% by mass of cement)
Fly Ash
(F)/ Slag
(S)
Metakaolin
(K)
Microsilica
(M)
Limestone
(L); d50 of
1.5 or 3
µm#
UHP-control 0 0 0 0
HP-control 0 0 0 0
OPC + F/S 20, 30 0 0 0
OPC + M 0 0 10, 20 0
OPC + K 0 10 0 0
OPC + F/S + M 10, 20 0 10 0
OPC + F/S + K 10, 20 10 0 0
OPC + F/S + L 20 0 0 10a, 10b
OPC + F/S + L 25 0 0 5a, 5b
OPC + F/S + M + L 17.5 0 7.5 5b,5c
OPC + F/S + K + L 17.5 7.5 0 5b,5c

Microstructure Packing
79
 3D volumes are generated using a stochastic particle packing
model assuming spherical particles. OPC is represented in white,
fly ash in blue, metakaolin in red and limestone in green.
 PSDs are discretized to get the number of spheres for each phase.
 These digitized microstructures are used to obtain key parameters
that influence the hydration process.

Microstructural Packing :Results and Selection
Criteria
As the number density increases, the
average particle centroidal distance
decreases while the number of particles
within the radial distance increases.
You want a high Coordination Number,
high Number Density, and low Mean
Centroidal Distance
Model 1 :
𝑀𝐶𝐷𝑖 ≤ 𝑀𝐶𝐷 𝑈𝐻𝑃−𝑐𝑜𝑛𝑡𝑟𝑜𝑙
𝐶𝑁𝑖 ≥ 𝐶𝑁 𝑈𝐻𝑃−𝑐𝑜𝑛𝑡𝑟𝑜𝑙
𝑁𝑑−𝑖 ≥ 𝑁𝑑−𝑈𝐻𝑃−𝑐𝑜𝑛𝑡𝑟𝑜𝑙
Model 2 :
𝑃𝑎𝑐𝑘𝑖𝑛𝑔 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡  =
𝐶𝑁 𝑋 𝑁𝑑
𝑀𝐶𝐷
𝛾𝑖 ≥ 1.0 ∗ 𝛾 𝑈𝐻𝑃−𝑐𝑜𝑛𝑡𝑟𝑜𝑙
80
The actual PSD values used for
various ingredient components.

Rheology of Pastes – Rheometer Studies and Mini
Slump Test
81

Selection based on Overall Analysis
 Out of all the 33 mixes planned, 22 match the theoretical packing
criteria and 23 matched the experimental rheology criteria
 17 mixes matched both rheology and packing criteria
 8 mixtures were further chosen among these candidates for strength
studies
82

Flexural Closed Loop Testing
83
 28 day flexural response was
evaluated on prismatic specimens
(2”x2.5”x15”).
 Initial load-controlled mode was
followed by displacement controlled
mode @ 0.02 in/min until peak load
and @0.004 in/min until failure.
 Midpoint deflection was measured
using LVDT placed in the center of
the bottom face of the beam
 Strain fields were monitored using
digital image correlation (DIC)
technique.

Flexural Test Results
84
The strain distribution in four
quaternary fly ash UHPC
beams at peak load just prior
to failure
Strain fields for fiber reinforced
beam specimens with 1% steel fiber)
at a post peak stress of (a,b) 90%
and (c,d) 50% of the peak stress.

Effect of Binder Composition
0
200
400
600
800
1000
1200
1400
1600
1800
Crackin
Strength,
f1 (psi)
MOR, fP
(psi)
Residual
Strength at
L/600,
fD600 (psi)
Residual
Strength at
L/150,
fD150 (psi)
Strength,[psi]
F17.5M7.5L5
M20L30
• The FML mixture shows enhanced flexural behavior
• The post-peak response of this mixture also shows a
higher residual strength as compared to the ML
mixture
85

Effect of Mixing Method
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Cracking
Strength,
f1 (psi)
MOR, fP
(psi)
Residual
Strength at
L/600,
fD600 (psi)
Residual
Strength at
L/150,
fD150 (psi)
Strength,[psi]
Drill Mixer
Croker Mixer
• The mixtures cast using the high-volume high-shear mixer show a higher flexural
as well as a higher residual strength as compared to those cast using the hand-
drill mixer
• This observation can be attributed to the better mixing, dispersion, and uniform
fiber distribution obtained using the high-shear mixer
86

Effect of Specimen Size
0
500
1000
1500
2000
Cracking
Strength,
f1 (psi)
MOR, fP
(psi)
Residual
Strength at
L/600,
fD600 (psi)
Residual
Strength at
L/150,
fD150 (psi)
Strength,[psi]
Small Beams
Large Beams
• There is no significant difference in the maximum stress, cracking stress
(MOR) and the residual stress, between small and large size specimens
• The large beams and they show more smooth post-peak response
compared to the small beams
• This can be due to the increased depth for the large specimens, which
promote better crack growth, as compared to the smaller beams that are
only 2” deep
87

Effect of Curing Duration
(Small Beams)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Cracking
Strength,
f1 (psi)
MOR, fP
(psi)
Residual
Srength at
L/600,
fD600 (psi)
Residual
Srength at
L/150,
fD150 (psi)
Strength,[psi]
14 Days
28 Dyas
• The strength of 28 days small beams is almost 43% higher than
the beams tested after 14 days of curing
• The residual strength for 28 day beams is as much as 47%
higher than 14 day samples
88

Effect of Curing Duration
(Large Beams)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Cracking
Strength,
f1 (psi)
MOR, fP
(psi)
Residual
Strength at
L/600,
fD600 (psi)
Residual
Strength at
L/150,
fD150 (psi)
Strength,[psi]
14 Days
28 Dyas
• The beams after 28 days of curing show as much as
30% higher strength compared to the 14 days beams
• This increase is more distinguishable at the earlier
stages of the loading process, the first peak strength
and cracking strength (MOR).
89

Characterization of Crack Growth Mechanisms Using Digital Image
Correlation (DIC)
Stage Characteristic
A Initiation of the deformation
B Initiation of the non-linear
response
C Response to the peak load
D beam failure
-3000
[mm/m] - Lagrange
-1562 20000-125 18562171251568714250128121137599378500706256251312 2750 4187
4.7in
2.2in
Stage A
Stage B
Stage C
Stage D
90

Fracture Tests (Cyclic)
Notched
Beam
CMOD
Gage
L=18”
b=4”
d=4”
a=0.25d
S=16”Support
Reaction
Support
Reaction
P
91

Stiffness Degradation Calculation



B A
B A
P P
k
D D
• At the start of the cyclic loading there is a sudden drop in the stiffness
• As the number of the cycles increases, it converges to a stable stiffness value
• The residual stiffness of the UHPC section is about 40% of its initial stiffness
• This shows that the section is still able to keep its stiffness after numerous cycles of
loading and unloading
92

Field-cast UHPC Connections
93
UHPC connection between precast deck panels as
deployed by NYSDOT on I-81 in Syracuse, NY
UHPC connection between precast deck panels as
deployed by NYSDOT on CR47 over Trout Brook.
Deck-level connection between precast deck
panels.
Graybeal, B. (2014). Design and construction of field-cast UHPC Connections (No. FHWA-
HRT-14-084).

Experimental Verification- UHPC beam
 Full size UHPC beam
 2% of smooth/twisted steel fiber
 fc’=201-232 MPa
 Ρ=0.94% or 1.5%
94
Yoo, D. Y., & Yoon, Y. S. (2015). Structural performance of ultra-high-performance concrete beams
with different steel fibers. Engineering Structures, 102, 409-423.

Experimental Verification- RC with Steel
fibers
95
Yoo, D. Y., & Yoon, Y. S. (2015). Structural performance of ultra-high-performance concrete
beams with different steel fibers. Engineering Structures, 102, 409-423.

5 Directions for: Materials Design, Mechanical Properties,
Structural Design
Materials Design:
 TRC materials as new structural components
 Candidate UHPC applications for bridge element connections, accelerated bridge
construction (ABC).
 Develop TRC using economic fibers and UHPC by low cost non-proprietary mixes
Mechanical Properties
 Parametric linearized materials model
 Cross sectional analysis based on stress and strain diagrams
 Closed-form solutions of moment and curvature responses
 Back calculation of tensile responses and extraction of tensile properties
Structural Design
 Serviceability state design: curvature, deflection, post-crack stiffness
 Design recommendations: moment capacity, minimum reinforcement ratio, serviceability
limits

Concluding Remarks
 TRC Composites made with PP fibers can be tailored to meet the
same level of performance as Carbon Fiber systems.
 Parametric material models help in characterization of the compressive
and tensile behavior of SHCC
 Linearized moment-curvature model can be used an extension of
stress-strain models applied to a given crossection.
 Analytical deflection equations of 1-D and 2-D flexural members with
FRC and HRC were derived
 Load-deflection relationships for various types of beams and panel are
derived
 Closed form solutions can be used to obtain gradients of serviceability
functions with respect to input variables.
 Accuracy of analytical deflection equations is identified by comparing
the simulated data with experimental data

Fiber and Textile Reinforced Cement Composites

Rotation
Boundary conditions
 2 0x L      21 22a       22 223 3a b
L L 
Curvature
 1
cr
x x



 0 x  
 
 
2
3 ' '
3
a cr
q x q x L
L
x




  


 2 'b crx q 
3
L
x  
3 2
L L
x 
 21 10
x cr
x xdx C



 
 
 
22 20
3 ' '
3
xcr
a cr
q x q x L
L
x xdx dx C


 

 
  

   
 
 3
22 30 3
3
3
L xcr
b cr crL
x x L
L
x xdx dx dx C


 
  



  

     
0 x  
3
L
x  
3 2
L L
x 
 0 0x      21 22a       22 223 3a b
L L 

Stage I: M ’ (x=L/2)≤ Mcr
 Region ①
 1
3
a x x
L

 
 1b x 
0
3
Lx 
3 2
L Lx 
Rotation:
 1 10
3x
a x xdx C
L

  
  3
1 20
3
3L x
b L
x xdx dx C
L

    
0
3
Lx 
3 2
L Lx 
Boundary Conditions :  1 0
2b
L 
   1 13 3a b
L L 
2C1C
Curvature:
a: (0 ≤ 𝑥 ≤ 𝐿/3), Pre-cracked
b: ( 𝐿/3 ≤ 𝑥 ≤ 𝐿/2), Pre-cracked, constant moment
x

Deflection:
 Region ① -a:
   1 1 30
x
a ax x dx C  
     3 2
1 1 1 40
3
L L
b a bL
x x dx x dx C     
 Region ①-b:
0
3
Lx 
3 2
L Lx 
Boundary Conditions :
 1 0 0a x  
   1 13 3a b
L L 
3C 4C
Solution:
3
*
1 3 32
a
x x
LL
 
 
   
 
2
*
1 2
1
2 542
b
x x
LL
 
 
    
 
* 2
 cr L  *
 deflection coefficient
Maximum Deflection
   
3
1
23
2 1296
b
PLLx
EI
   
'
'
6g g
M PL
EI EI
   

Elastic Solution for Panels
Assumptions
 Material is elastic, homogeneous and isotropic
 Plate is initially flat
 Deflection of the midplane is small compared with thickness of the plate
 Straight lines normal to the mid-surface remain straight and remain normal to the
mid-surface after deformation
 gxz, gyz, ez sz neglected
4 4 4
4 2 2 4
2
w w w p
x x y y D
  
  
  Governing Differential Equation
3
2
12(1 )
Et
D 

w(x,y) – Deflection function, p – Applied load, t– thickness
D – Flexural rigidity, E – Young’s Modulus , v – Poisson’s ratio
Ventsel, Eduard, and Theodor Krauthammer. Thin plates and shells: theory: analysis, and applications. CRC press, 2001

Yield Line Moment – Applied Load
Case study
Square panel with simply supported edges Uniform load: q
2
1
( ) 4
4 3
ext
a
W N q
 
     
 

ext intW W
( ) ( )N m l   
Equivalent point load
δmax is unit
Deflection of the centroid
int
1
( ) 4
0.5
W m l m a
a
 
   
 
 
2
24
qa
m 

θ
2R
δ
Section A-A
dα
R
P
n n( cos( ), sin( ), )OA R Ra a  
uuur
( ,0, )OB R 
uuur
n n( cos( ), sin( ), )OC R Ra a 
uuur
n
2
n

a 
 2
1 n n nsin( ), (1 cos( )), sin( )n OA OB R R R a  a a    
uur uuur uuur
 2
2 n n nsin( ), (1 cos( )), sin( )n OB OC R R R a  a a    
uur uuur uuur
2 2 2
1 11 2 n n
2 2 2
n1 2
cos( ) 2cos( )1 1
cos cos
* * cos( ) 2
n n R R
L L R Rn n
a a 

a 
 
       
    
      
uur uur
g
uur uur
Round panel
Curvature-Deflection Relationship for
Round panels
Yao, Y., Wang, X., Aswani, K., & Mobasher, B. Analytical procedures for design of strain softening and hardening cement
composites. International Journal of Advances in Engineering Sciences and Applied Mathematics 2017.

Analytical Deflection Solutions for Stage I
SS – Simply supported beam, C– Cantilever beam
*S is the distance from start point to loading point

*
 is deflection coefficient
Analytical Deflection Solutions for Stage II

Analytical Deflection Solutions for Stage II
Notations

Sustainable infrastructure with fiber and textile reinforced concrete systems

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Sustainable infrastructure with fiber and textile reinforced concrete systems

Similar to Sustainable infrastructure with fiber and textile reinforced concrete systems (20)

Recently uploaded

Recently uploaded (20)

Sustainable infrastructure with fiber and textile reinforced concrete systems