COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
Composite Construction in Reinforced Concrete Taking into Consideration the Non-Rigid Bond of Interfaces in Joints
V. Lindig *
Bonhoefferst. 43, 99427 Weimar, Germany
Email: volker.lindig@web.de
Abstract The behavior of the non-reinforced or reinforced concrete-concrete bond interface can have a significant
influence on structural behavior of the composite construction. A three-dimensional, physically non-linear continuum model has been developed on the basis of the finite element method. This enables the multi-parametered influence of the various surface structures and the reinforcement positioning of the concrete-concrete bond interface to
be investigated as a component part of complex constructions. On the basis of the extensive simulation results, it
can be proved, that the relevant European standard EC 2 do not reflect the realistic structural behavior. A novel differentiated design concept for concrete-concrete interface joints has been formulated and recommended therefore
for the first time under consideration of relative displacements of the contact surfaces and with reference to the
bearing structure.
Key words: composite construction, non-linear finite element analysis, constitutive modelling of composite structures in reinforced concrete, concrete bond, composite design
INTRODUCTION
The combination of various building materials is a fundamental component of modern construction. As such, the recording of bond behavior is a crucial factor to be considered in the planning of load-bearing structures in respect of
new building and retrofit. The behavior of the reinforced concrete-concrete bond interface with various rough contact surfaces can have a significant influence on structural behavior.
Therefore, a three-dimensional, physically non-linear continuum model has been developed on the basis of the finite
element method and integrated into FE-Program ANSYS. This enables the multi-parametered influence of the various surface structures and the reinforcement positioning of the concrete-concrete bond interface to be investigated
as a component part of reinforced concrete structures. The realization of this process on the macro-level takes place
by means of a continualization of the interface in the form a so-called bond zone. This explains physical phenomena
on the basis of adaptive, non-linear, constitutive relationships. The model was calibrated according to the past test
results contained in academic publications and was subsequently used to analyze continuous composite systems and
rigid composite frameworks.
ASPECTS OF THE PROBLEM
For the purposes of practical calculations, the general rule is to assume the classical theory of shear friction and a
rigid bond with a general additive approach. A realistic concrete-concrete interface behavior can only be achieved
by incorporating the non-rigid bond of the contact surfaces, which is dependent on the surface structure and reinforcement positioning. In this, the degree to which the cross sections of precast concrete and in-situ concrete function together is decisively influenced by the quantities of kinematic value and force developing between the contact
surfaces connected with non-linear dowel effects. In the most extreme cases, no bond forms, e. g. between the contact surfaces of precast concrete and in-situ concrete, and both structural components function independently of
each other as individual cross sections.
The parameters influencing the bond system of the joint are extraordinarily complex with a partly fractal specification and relatively difficult to quantify. Therefore, the first part in [1] contains a comparison and a critical review of
⎯ 946 ⎯
selected experimental results, applicable international standards, relevant physical theories and approaches, mathematical and mechanical formulations as well as chosen finite elements and favored constitutive models for computational modelling of composite structures.
Consequently, a complex three-dimensional, physically non-linear continuum model has been developed and formulated on the basis of the finite element method and numerically integrated into the multi-purpose finite element
system ANSYS. Fig. 1 shows the principle of the strategy proposed in [1] for the development of a threedimensional finite-element structural model which covers everything from real construction to the continuumtheory-based simulation model, by way of the classical theory of shear friction, itself based on the design concepts
for interface joints which have so far represented the most of international standards. Building on the methods of
continuum mechanics, the macroscopically observed physical characteristics of concrete-concrete contact surfaces
is then phenomenologically described for the simulation model represented in Fig. 1. The essence of the concept
used here is the observation of the fractal contact zones between old and new concrete in the form of a continuum.
α
σn
σn tan α
σn
in-situ concrete
τt
rough interface
(boundary plane)
bond stirrup
vn
precast girder
α
bending tension
reinforcement
τt
wt
σn
a) Typical reinforced concrete-concrete composite
beam as component of modern hybrid construction.
b) Discreet mechanical shear friction
model (shear friction theorie).
concrete elements
adaptive shear softening bond
elements (assb-elements)
y
2
flexural shear elements
bond-link-elements
(combin elements)
y
uniaxial elements
z
concrete elements
bond relation
dowel relation
2
z
1
2
x
coincident nodes
x
c) Principle at the 3-dimensional continuum model in the typical FE-discretisation.
Figure 1: Computational modelling of composite structures in reinforced concrete from the general
model to an exemplary discretized simulation model of a rigid composite framework.
This implies the definition of fictive laws of stress and strain in which the originally isotropic material matrix now
appears orthotropically after the formation of cracks. Discontinuities in the distortions and stresses which appear as
a result of the formation of cracks are progressively incorporated across the element zone, which is part of a specified point of integration, and the material matrix is correspondingly adapted. In practice, this means that relative displacements appear in the elements coupled as a result of the newly-developed bond zone elements. This allows for
the isoparametrically formulated description of geometry and the displacement zone with the same formal functions.
The connection between bond stresses and the attendant relative displacements can thus be described in the usual
way, i.e. by means of the bond rigidity matrix in the form of a fictive material matrix (bond matrix) deduced from
bond relationships.
MODELLING OF CONCRETE-CONCRETE INTERFACE AND FUNDAMENTALLY CONSTITUTIVE RELATIONSHIPS
The structural behavior of composite construction in reinforced concrete is essentially dictated by the behavior of
the concrete-concrete interface. For the purposes of practical design, the rule is generally to assume a rigid bond. A
realistic bond interface behavior can then be achieved by incorporating the displaceability resp. yielding of the bond
interface, which is dependent on the surface structure and reinforcement positioning. In this, the degree to which the
cross sections of precast concrete and in-situ concrete function together is decisively influenced by the quantities of
kinematic energy and force which develop between the contact surfaces. Fig. 2 shows a simplified schematic illustration of position for modelling of composite - interface as bond zone.
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new
h
in-situ concrete
in-situ concrete
new
bd
h
h
=
40...100 mm
bd
h
old
h
bond zone
=
old
40...100 mm
h
bond zone
precast unit
precast unit
(a) bond zone between precast girder
(beam) and cast-in-place slab.
(b) bond zone in area of precast
girder (beam).
Figure 2: Determination of the composite - interface as bond zones for computational modelling and simulation.
In the most extreme cases, no bond forms for example between the precast concrete and in-situ concrete, and both
structural components function independently of each other as individual cross sections. The parameters influencing
the bond system are extraordinarily complex and relatively difficult to quantify. The behavior of the bond interface
can generally be described in terms of three essential influences:
Adhesion as a material component is derived from the chemical and mechanical binding forces which exist between
the individual components of the concrete‘s texture. It is independent of the load placed on it. The load placed on
the bond interface re-creates, by means of pressure, frictional forces which are completely normal. The reinforcement, which is the third component, is usually found perpendicular to the bond interface. It is activated only in the
case of a specified relative displacement of both contact surfaces. This displacement, along with the dowel action
(flexure, shear, kinking) brings about resistance in the surrounding concrete, which appears from out of the elasticplastic bedding of the bond reinforcement bars (stirrups) in the concrete. The effect of the three aforementioned parameters is essentially determined by the relative displacements w and v (horizontal and vertical) of the contact surfaces. Fig. 3 characterizes the classification, independent of w, of the three bond sections with those components
which contribute significantly to the bond strength.
<
<
<
<
<
Figure 3: Quantification of the composite - interface zones and the strength components at
various displacement points and situations, respectively.
However, it is only in ideal cases that the bond components listed above function successively and independently of
each other. More usually, they affect each other interactively. In exceptional cases of interface joints of large area
(i.e. slab systems), reinforced, rigid joints can occur given only very small relative displacements w. The surface
geometry of the bond interface or composite surface exerts, along with the material parameters, the greatest influence on the structural behavior of the bond system..
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σ
τ
τ
σ
yy
τ
zx
τ
yy
wv
v bd
xz
zx
Δγ xyv
bdCo
bd
h
2
bond zone
τ
Cr
bd
v
zx
Δγ
xz
xy
ε
Δγ xzv
bdCr
nnm
bdCr
bd
γ
γ
γ
bd
h
2
τ
adh
s
τ
Co
bd
v
γ
bd
z
x
bdCr
bd
σ
y
Δγ xyv
zx
adh
qs
w
=
τ
=γ
bd
ws
wqs
hbd
xz
γ
Δ
yy
virtual rough concrete interface
---- microcracks ----
bd
Gbd
τ
bdCo
xy
xz
xyv
Δγ xzv
bdCo
y
z
wv
x
Figure 4: assb-element in the zone between
rigid and quasi-rigid bond.
τ
Δγ
zx
v
h
τ
zx
σ
yy
virtual gap
macrocrack
rough bond contact planes
-- differential movement --
Figure 5: assb-element in the zone of
displaceable bond
Additionally, the fractal nature of the bond interface geometry makes generally applicable classification problematic. For this reason, the classification of roughness was established for the design of the interface joints in four areas: smooth, untreated, roughened and zigzag surface (saw tooth). The exemplary structural model shown in Fig. 1
contains the definition of the newly-developed bond-zone element, integrated into the FE-program ANSYS, as an
so-called adaptive-shear-softening-bond-element (or assb-element). The basis for the adaptive control of the assbelement shown in Figs. 4 and 5, for the rigid or quasi-rigid as well as for the displaceable state, lies in a deformation-driven simulation of global and specific degrees of stiffness in correlation with the parameters identified in experiments and taking into account the horizontal and vertical relative displacements of the bond interface.
If relatively little load is placed on the structure, the behavior of the bond interface on the macro-level is more or
less identical to that of uncracked concrete. The sliding angle γ adh
in Fig. 4 results from the constitutive connections
s
of the concrete models used for old and new concrete.
Should distortions of the continued bond interface develop in the course of the incremental analysis, as expressed
through an increase in the sliding angle γbd, the fictive material of the bond zone or bond interface becomes detached, initially on the micro-level, then, in the further course of the load-placement, on the meso-level. This is
physically represented by the appearance of a whole host of micro-cracks.
The adhesive strength from now on decreases in a linear fashion as a function either of the sliding angle γbd or of the
horizontal relative displacements w defined in Fig. 3 until such a point that this strength component completely dissipates at a defined relative displacement of w = 0.05 mm. This diffuse behavior, which is subject to enormously
problematical experimental scattering and which, in addition, is dependent on a large number of influential factors,
is numerically realized by means of a global successive reduction in the fictive material matrix (bond zone matrix
shown in [1]) of the assb-element.
The virtual gap in Fig. 5 is initially equivalent to zero in the rigid and quasi-rigid zone and varies in the displacement zone according to the load-effect in the bond law. Fig. 6 shows to sum up a simplified schematic illustration of
the constitutive relationships for the bond stiffness control in the structural behavior of the continued bond zone
(discretized with assb-elements) within the spectrum from the rigid to the displaceable bond.
It is well known that shear failure (mode II) in the continuum principally develops from a microscopic tension failure or from tensile cracks whose conglomeration under increased load then causes the typical macro-cracks to appear. These successively develop into so-called shear or crack layers (band) within a limited zone. On the basis of
these results, the Mohr-Coulomb hypothesis and the classic crack criterion, tension cut-off, have been implemented
and verified according to Rankine (cracking criteria) in order to initiate the fictive micro-crack (cf. Fig. 5) in the
zone of the displaceable bond. Here, shear and tensile strength harmonize for both criteria, the latter finally proving
to be the most suitable in connection with experiments [1].
The criteria for the opening (cf. Fig. 7: shear reduction), closure (cf. Fig. 8: shear progression) and re-opening (cf.
Figs. 7 and 8: shear reduction) of the virtual contact surfaces and of the residual shear stress components, resulting
from friction and redistributed in dependence on the classified roughness, are defined as terms of the totally stressfree normal local crack strain ε bdcr
nnm . These are explained in Fig. 7 and Fig. 8 and in detail in [1], respectively.
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Figure 6: General scheme for the bond stiffness control of the bond zone element in accordance with the relative
displacement of contact surfaces (non-linear-hyperelastic constitutive model).
(a) bond surface: smooth
(b) bond surface: zigzag (saw tooth)
Figure 7: Constitutive relationships for the shear stiffness control of the bond zone element in dependence on vertical relative displacement of the virtual contact surfaces in state of the opening and the re-opening, respectively, exemplary shown for two various rough contact surfaces.
This fictive normal crack strain of the virtual gap entered in Fig. 5 is calculated from the integral means of all integration points on the assb-element in question, resulting in a special weighting in accordance with the main directions. The adaptive control of the coefficient, i.e. the orthotropic yield matrix which appears in the displaceable
bond zone according to the characteristics of the bond, is produced as a function of a large number of influential parameters (multi-parametrical problem) in correlation with the results of various tests [1]. A complete representation
of the functional contexts in direct correlation with the parameters of the tests and their resulting coefficient can be
deduced from the table for the data input of the assb-elements presented in [1]. This applies to all classes of roughness and all bond zones.
⎯ 950 ⎯
Figure 8: Constitutive relationships for the shear stiffness control of the bond zone element in dependence
on vertical relative displacement of the virtual contact surfaces in state of the closure.
The concept of continuum formulation offers a complex computational simulation model, which, on account of its
numerical robustness, facilitates the three-dimensional structural analysis of all composite constructions in reinforced concrete with reference to the essential physical non-linearity and the displaceable bond. Detailed theoretical
investigations, such as the interaction between dowel action of bond reinforcement and stress-strain intensity of
bending reinforcement also in relation to composite action between rough contact surfaces in course of the loadhistory, can thus be carried out on the complete system.
The computational modelling of the bond reinforcement is carried out discreetly, using special modified elements
which are resistant to bending and shear, respectively. The discreet, explicit treatment of the bond is both tangentially (elastoplastic embedding in the surrounding concrete - dowel action; aggregate interlock type II) and normally
(pullout - aggregate interlock type I resp. surface interlock) related to the bond bar axis in [1], dependent on the material parameters.
These represent analytically formulated bonding laws, which have been implemented in detached, geometrically
dimensionless, non-linear special elements for each of the three global spatial dimensions. These elements facilitate
differential displacements of the two neighbouring coincident joints of concrete element and bond bar. The material
behavior of the steel is approximated by means of a flattened (plain), tri-linear material identification line with kinematic strengthening.
In order to achieve a realistic analysis, a three-dimensional concrete model was numerically integrated in ANSYS as
hyperelastic model. The ´complete steel´ is (except for bending reinforcement) approximated by means of a flattened (plain), tri-linear material identification line and kinematic strengthening according to the effects of the tension stiffening. The treatment of the bond between steel and concrete is indirectly achieved using the material identification line of the steel. The whole model formulations for concrete and steel and here working together are also
contained in [1] .
SOME REPRESENTATIVE RESULTS OF THE SIMULATION AND STRUCTURAL ANALYSIS
The newly-developed bond zone element as a part of the developed complex simulation model was numerically
calibrated and verified according to the experiments [1], e. g. carried out at the Bauhaus University Weimar as well
as the past test results contained in further academic publications and was subsequently used to systematically analyze continuous composite systems and rigid composite frameworks.
The focus of the scientific study was mainly on the influence of the following test criteria, as well as on the structural behavior of the joints and of the overall construction: load setting (shear slenderness – shear span, combined
torsion), load type, bond interface roughness and setting, rate of bond reinforcement and distribution, static system,
prestressing of the construction. Fig. 1 on the right side show exemplary a discretized simulation model of a composite framework. Concerning this Fig. 9 contains typical analysis results.
⎯ 951 ⎯
Applizierte Laststufe Fmax=224 KN
bond zone
uy max= -21.7 mm
crushing
Y
X
Z
a) Hauptdehnungszustand im Riegel- u. Eckbereich.
Applizierte Laststufe Fmax=224 KN
bond zone
E F G H I J K L M N O P Q R S T U
MSz [Nmm]
-11650
-8953
-6257
-3560
-863.576
1833
4530
7226
9923
12619
pq r
AB C D
b) Hauptdehnungen selektierter ASSB-Elemente.
m n o
X
bond zone
Y
MSz [Nmm]
Y
Y
Z
Z
X local-vertikal
local-horizontal
Z
X
global
-16740
-13678
-10616
-7554
-4492
-1430
1632
4695
7757
10819
Y
Z
X global
c) Biegemomente der Verbundbew. i. Riegel- u. Eckbereich sowie i. d. Arbeitsfuge -Ortbetonwand-Platte-.
Applizierte Laststufe Fmax=224 KN
bond zone
E F G H I J K L M N O P Q R S T U
MSy [Nmm]
-7298
-5669
-4039
-2410
-780.808
848.429
2478
4107
5736
7365
pqr
AB C D
m n o
X
bond zone
Y
MSy [Nmm]
Y
Y
Z
X local-vertikal
Z
local-horizontal
Z
X
global
-19290
-14822
-10353
-5885
-1417
3052
7520
11988
16457
20925
Y
Z
X global
d) Biegemomente der Verbundbew. i. Riegel- u. Eckbereich sowie i. d. Arbeitsfuge -Ortbetonwand-Platte-.
Applizierte Laststufe Fmax=224 KN
bond zone
E F G H I J K L M N O P Q R S T U
PSyshear [N]
-485.387
-407.199
-329.01
-250.822
-172.634
-94.446
-16.257
61.931
140.119
218.307
m n o
pq r
AB C D
X
bond zone
Y
Z
X local-vertikal
Z
local-horizontal
σdir [N/mm瞉
Y
Y
Z
X
global
-67.866
-36.581
-5.296
25.99
57.275
88.56
119.846
151.131
182.416
213.702
e) Normalspannungsanteil der Verbundbewehrung.
Y
Z
X global
f) Aktivierte Schubkr鋐te der Verbundbewehrung.
Figure 9: Rigid composite framework ⎯ load setting combined torsion: Representative analysis results of strain
situation and computed appearance of bond bars at computed load-bearing capacity on the left sight as
well as representative crack pattern of significant load situations on the right sight
The concept in [1] offers a complex simulation model which, on account of its numerical robustness, facilitates the
three-dimensional structural analysis of all reinforced concrete bond constructions with reference to the essential
physical non-linearity. Detailed macroscopic tests can thus be carried out on the complete system (cf. Fig. 9). The results of the proposed bond formulations are, however, dependent on a certain unit size, in that this method covers the
influence of the cracked bond interface on the reduction of rigidity or the reduction of residual stresses in the component zones of the unit and, as a result, cannot throw up detailed information on the local stress and strain situation.
Macro-level tests carried out on the structural behavior of bond zone constructions using realistic material models
underline the overwhelming advantages of this concept, and the use of phenomenological bonding laws is thus justified. The correlation between theory and experiment remains of great importance and still represents the basis for
the development of modern numerical simulation models for the analysis of load-bearing structures.
NORMATIVE REDISTRIBUTIONS: A NOVEL DESIGN CONCEPT FOR CONCRETE INTERFACES AND JOINTS, RESPECTIVLY
The relevant standards fail to account for the yielding of old and new concrete joints, with the resulting distribution
potential on assessment and design of the reinforced interface joints. Most of the guidelines to date, for example the
relevant European standard EC 2, have been based on the shear friction theory and the rigid bond, with an added attachment. The new German Standard DIN 1045-1 includes the yielding of interfaces in a roundabout way of course,
but also based on a semi-empirical concept. On the basis of the wide-ranging analytical simulation results [1] , it can
be proved, that especially the relevant European standard EC 2 do not reflect the realistic structural behavior, particularly in the case of narrow joints.
A novel differentiated design concept for concrete-concrete interface joints has been analytical formulated and recommended therefore as a result of the varied research represented in Fig. 10; for the first time under consideration
of relative displacements of the contact surfaces and with specific reference to the type and form of structure and
construction [1]. Finally, an exemplary composite beam with different reinforcement positions and rates, respectively, along the bond interface is presented in Fig. 11 as the result of the complex investigation and extensive research for the practical structural design.
⎯ 952 ⎯
σN
po
Nsdj1
τRdjsm/la
2
1
small:τRdj
sm
large: τ
la
Rdj
τcdj(fri+pre)
τcdjfri
τcdjadh= 0
τcdjadh
adhesion
friction
indirect prestress
τ
crit Sdj
3
pl
Ps,dj
τsdj(da+po)
τsdj
pl
hc,da
1
plastic-ductile zone
2
micro-roughness
3
macro-roughness
po
sdj1
N
bond reinforcement
Figure 10: Postulate at the design concept for concrete-concrete interface joints
minimum bond reinforcement ρj,min
bond stirrup ρj
effective bond stirrup ρj,eff
rough boundary plane
precast girder as component of reinforced
concrete-concrete composite beam
precast girder as component of reinforced
concrete-concrete composite beam
(a) conventional reinforcement along the interface.
(b) effective reinforcement along the interface.
Figure 11: Normative Redistribution at the exemplary composite beam ⎯ comparison of conventional reinforcement
on the basis of traditional design methods and novel differentiated design concept.
REFERENCES
1. Lindig V. Numerical Simulation, Structural Analysis and Design of Composite Constructions in
Reinforced Concrete taking into Consideration the Non-rigid Bond of Interfaces in Joints. Doctoral
Thesis, Bauhaus-University, Shaker Publishing House, Aachen, www.shaker.de, 2005 (print and
online version).
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