Three-dimensional modeling of anchoring systems in concrete

Fracture Mechanics of Concrete Structures, de Borst et al (eds)© 2001 Swets & Zeitlinger, Usse, ISBN 90 2651 825 0
Three-dimensional modeling of anchoring systems in concrete
J.Nienstedt & R.Mattner
Hilti C01p., C01porate Research, Schaan, Principality ofLiechtenstein
Numerical simulation is a valuable tool for getting inside information on the mechanism occurring in fastening technology. The additional knowledge and understanding of the anchoring behavior, like e.g. the load
transfer and the damaging state in the base material, is the basis for innovative product development. Reliable
simulation results require a sophisticated material modeling, especially for concrete material which is widely
encountered as base material for anchoring systems. Concrete shows completely different behavior underlying different loading conditions, and it often determines the load carrying capacity of the structure and the
corresponding failure mechanism.
The basic knowledge of the working principles of anchors is investigated first and than utilized for a case
study of an undercut anchor. Here the behavior of the anchor in cracked concrete is investigated and compared with the application in undamaged base material.
Numerical simulation, especially the finite element technology is getting more and more into
practice also in the field of fastening systems. Numerical simulation serves for additional knowledge
and general understanding of the occurring mechanism as well as for the speed-up of the development
process for new products.
The development of new, innovative anchors can
only be successful with an in-depth understanding of
the physical phenomena involved in the complete
process of setting and pull-out of the anchor. In order to satisfy these requirements the Hilti AG develop own simulation tools for the specific applications occurring within its product range. Many of
these products are used in combination with concrete
material. Hence a suitable and reliable material
model must be utilized to realistically describe the
concrete behaviour.
In the field of fastening technology the numerical
simulation is a well introduced tool within the development process (Nienstedt & Dietrich (1995),
Nienstedt, Mattner & Wiesbaum (1999)). This was
only possible with the corresponding numerical robustness of the program and especially the material
Fasteners in concrete can generally be divided according to the mechanism of transferring the force
into the base material. These are friction, keying or
bonding (s. Figure 1).
The application of loading force on the anchoring
system is limited by a maximum force which is determined by a failure mechanism, like e.g. concrete
cone break out or steel failure. For the approval pro-
Figure 1. Working principles of anchoring systems, Hilti AG
cess, especially for safety relevant anchors special
application conditions become of increasing interest.
These are for example applications close to the edge
of the base material or fastenings in cracked concrete. These fastenings are illustrated in Figure 2.
Figure 2. Fastening conditions (close to an edge, cracked concrete), Hilti AG (1993)
The numerical simulation presented here first
concentrates on the differences of the working principles mentioned before. The working principles are
investigated with typical representatives for each.
These simulations are performed utilizing axisymmetric simulations.
A more detailed view is taken on the Hilti HDA
undercut anchor. One feature of this anchor is the
applicability in cracked concrete. The undercut
mechanism ensures the load carrying capacity of the
anchor also in case it is set directly in a crack. Applications with these special boundary conditions
lead to the need of 3D-simulations.
4.1 Working principles
The material modelling of the concrete base material uses the well known smeared crack approach
(Hillerborg, Modeer & Petersson (1976)) for concrete under tension loading. The utilization of the
rotating smeared crack approach is integrated in an
uniaxial stress-/strain environment. Figure 3 shows a
schematic sketch of the stress-strain law for uniaxial loading conditions.
The characteristics of the worldng principles will
be illustrated with a typical representative for each.
These are a Hilti HSL heavy duty anchor (friction
principle), a Hilti HVZ adhesive anchor (bonding
principle) and a Hilti HDA undercut anchor (keying
4.1.1 Stress distributions
The main difference of the working principles,
the way of transferring the load into the base material, can be illustrated by displaying the stress distributions. Figures 4 and 5 show the distribution of the
minimum principle stresses in the base material for
the anchor set with the recommended setting conditions. The adhesive anchor shows a large area of
uniformly distributed stresses along the borehole
(see Figure 4). This fact explains the suitability of
these anchors for applications close to an edge.
Figure 3. Constitutive law for uniaxial loading conditions
The complex loading states in the base material,
especially in the area where the load transfer from
the fastening element into the concrete takes place,
require the additional consideration of the multiaxiality of the stress state. This is done by a direct
interaction between the stress state and the stressstrain relationship in the corresponding integration
This constitutive model has been proven for several applications to be very robust and easy to handle
for the development engineer in his daily business.
Comparisons between simulated results and the corresponding experiments show very good agreement
. within the scatter of the experiments.
Figure 4. Distribution of the minimum principle stresses for an
adhesive anchor
The friction principle and the keying principle
show a locally concentrated load transfer in the
depth of the borehole (see Figure 5). Hence, the
magnitude of the stresses is much larger than in the
case of the adhesive anchor.
Figure 7. Distribution of the maximum principle stresses for an
undercut anchor
Figure 5. Distribution of the minimum principle stress for a
friction anchor
4.1.2 Failure mechanisms
Different kinds of failure mechanisms are known
and have to be simulated. The simulation of the frictional anchor show a typical concrete cone failure
(see Figure 8)
Figure 6 illustrates the distribution of the maximum principal stresses for the friction anchor at a
load value above the recommended load during the
pull-out process.
Figure 8. Concrete cone failure
A mixed failure mechanism can be observed in
case of the adhesive anchor (see Figure 9).
Figure 6. Distribution of the maximum principal stresses for a
friction anchor
A comparison with the undercut anchor shows an
advantage of the undercut principle (see Figure 7).
The stress distribution in this figure is plotted for a
comparable loading state.
The level of the stresses above the white zone of
compressive stresses shows much higher stress values for the friction based anchor. The extension of
the zone with comparable high stresses in radial direction is much larger for the friction based anchor.
To achieve a large pull-out force requires a corresponding - due to the frictional principle - radial
Figure 9. Combination of bonding and concrete cone failure
In the lower part of the borehole a bonding failure
occurs combined with a concrete cone failure in the
upper part of the borehole.
For the third principle, the undercut anchor fails
due to steel failure. In this case the steel strength is
reached and a rupture of the anchor rod occurs.
The creation of the undercut is done during the
expansion process of the sleeves, i.e. the tongues of
the sleeve, which is shown in Figure 11.
The geometry of the anchor and the boundary
conditions for the axial pull-out loading also in
cracked concrete allows the limitation of the calculation to one quarter of the complete structure. This
calculation domain is shown in Figure 12.
4.2 Undercut anchor in cracked concrete
The keying principle has its main advantages in
transferring the load into the base material in the
depth of the borehole and its applicability in cracked
4.2.1 Structural modeling
Figure 10 shows the undercut anchor after performing the setting procedure. This procedure includes the drilling of the borehole with a defined
depth. This is followed by the introduction of the
anchor in the borehole. Utilizing a special setting
tool with the rotary hammer the tongues of the
sleeve produce their own undercut.
Figure 12. Calculation domain
In case of concrete base material without crack
the two vertical planes cutting the anchor are symmetry planes. In case of a predefined crack one of
these planes (here the right one) has a small gap to
the plane of symmetry. Hence in this case it exist no
boundary conditions on this plane.
The finite element discretization of the structure
can be seen in Figure 13.
Figure 10. Hilti HDA set in concrete
Figure 11. Expansion process of the sleeves
Figure 13. 3D finite element discretization of the anchor
4.2.2 Simulation results
The general difference of the structural behavior
can be illustrated with the force-/displacement curve
of the anchor for both applications
cracked and
uncracked concrete (see Figure 14). The displacement and the force are measured at the top of the anchor.
The failure criterion for both calculations is steel
failure of the anchor rod. Hence the load carrying
capacity remains the same for both applications. The
level of the maximum load is determined by the steel
strength and is not influenced by the crack.
The compressive domain directly above the undercut is displayed in a white colour. The region of
higher stresses, going up from there, indicates an
area close to the tensile strength of the concrete. The
size of this area is relatively small. Hence the concrete loading shows still some potential for carrying
increasing load.
The only non-symmetry is introduced by the
number of tongues of the sleeve. This has a locally
restricted influence directly in the contact zone between anchor sleeve and concrete.
The distribution of the maximum principal
stresses for the cracked concrete application shows
clearly the disturbed characteristics. The free surface
of the predefined crack has to be stress-free in normal direction. Hence the isolines of the stresses
tends to go towards the anchor approaching the free
surface. This effect can clearly be seen in Figure 16.
- - - - cracked concrete
Displacement [mm]
Fig. 14. Load/displacement curves of the HDA M16
The influence of the crack can be seen by the
slightly decreased stiffness of the fastening system
when set in cracked concrete. The circumferential
load carrying capacity is weakened by introducing
the predefined crack and hence the stiffness decreases. The support in circumferential direction is
missing for the material at the crack surfaces.
The stress distribution in the base material can be
illustrated by displaying the maximum principal
stresses. Figures 15 and 16 show the loading conditions in the base material just before steel failure occurred.
The concrete without a crack shows a clear radial
symmetry with the centre in the axis of the borehole
(see Figure 15).
Figure 16. Stress distribution of maximum principal stresses in
a predefined crack
Fig. 15. Stress distribution of maximum principal stresses in
the uncracked base material
Figure 17. Damage distribution in the contact zone between
sleeve and concrete
The damage occurring directly in the contact area
between the sleeve of the anchor and the concrete
base material is shown in Figure 17. This figure il-
lustrates the initial geometry on the left and the
crack width displayed on the deformed mesh on the
right side.
The direct contact surfaces can be identified by
the white zones on the upper side of the undercut.
The maximum crack width occur around these contact zones.
In case of the structure with the predefined crack
the maximum of the concrete damage can be observed at the free surface of the crack in the direct
neighborhood of the tongue of the sleeve.
The finite element program utilizing the smeared
crack approach has been proven to be a suitable tool
for simulating anchor applications in concrete. Basic
mechanisms can be evaluated, interpreted and the
resulting understanding utilized for further product
development. The finite element program developed
by the Hilti AG is a well introduced tool within the
development process for anchors.
The applicability even to complex 3D-structures
has been shown. Numerical simulation is a successful supplement to experiments. Trends resulting
from changes of e.g. geometrical parameters can be
determined and can be used to steer experiments in
predefined directions.
Hillerborg, A., Modeer, M. & Petersson, P.P. 1976. Analysis of
crack formation and crack growth in concrete by means of
fracture mechanics and finite elements. Cement and Concrete Research 6:773-782.
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