Understanding the impact of degradation of concrete structures
Rene VEERMAN PhD Student Delft, University of Technology Delft, Netherlands r.p.veerman@tudelft.nlRene Veerman received his MSc degree in civil engineering at Delft, University of Technology, Netherlands. Since 2009 he works for ARCADIS Netherlands as structural engineer of concrete bridges and tunnels. In 2011 he started a PhD study within the STW perspective program Integral Solutions for Sustainable Construction (IS2C). Eddie KOENDERS Associate professor Delft University of Technology Visiting professor
COPPE-UFRJ, Rio de Janeiro, Brazil
e.a.b.koenders@tudelft.nl
Eddie Koenders received his MSc and PhD degree from Delft University of Technology. His research area is multi-scale and multi-disciplinary modeling in view of sustainable infrastructure. He is chairman of the STW IS2C
Perspective program and professor at the NUMATS sustainability center at COPPE-UFRJ, Brazil.
Summary
Concrete infrastructures are mostly designed for a service-life of eighty to hundred years. During this service life these structures are loaded by traffic and environmental actions which affect the structural and material induced degradation mechanisms. In the last fifty years, the traffic intensity has increased significantly, i.e. heavier vehicles passing at higher frequencies and at higher velocities, initiating an increased number of local damage types to many infrastructures. In addition, damage caused by material degradation mechanisms such as chloride ingress, ASR and local degradation mechanisms have increased as well. These processes have turned out to reduce the expected service-life of concrete infrastructures to a large extend. In order to assess the effect of structural and material degradation on the performance of infrastructure a simply supported beam has been developed with the aim to include dominant material and structural related degradation phenomena. In this first order approach, the effect of the on-going hydration of compression strength, creep and the effect of stochastic traffic loads on bridge structures have been taken into account while the degradation mechanisms such as ASR and chloride ingress have not been explicitly modelled yet. In this model the influence on the strength capacity and stiffness is calculated and the effect on the bridge performance is evaluated. With the knowledge acquired from this simplified model, in the coming years, a more realistic model will be developed which also accounts for the material degradation mechanisms. The model will be validated with real time data archived from the Hollandse bridge monitoring system.
Keywords: Concrete structures, aging, cracks, degradation, creep, vibrations.
1.
Introduction
In the last decades, assessing the service-life of concrete structures is a theme that has gained an enormous interest. Despite the fact that concrete is a construction material that can last several decades to centuries, it has become clear that external influences may substantially (and often unexpectedly) shorten the service-life of civil infrastructures. More in detail, the factors that affect the service-life of civil infrastructures have various origins, such as traffic, climate conditions and the natural decay of the material phases. The complex interactions between these actions and the response of the infrastructural elements are the main topics to be dealt with, in order to assess the
actual condition of our national stock of infrastructural assets. In this respect, a structural analysis that includes both traffic induced loading and material degradation and the interaction between these is a major issue to be solved. In the National STW perspective program called “Integral Solution for Sustainable Construction” (IS2C), these interactions between materials degradations, monitoring and sensing, and materials and structures are examined. The new knowledge generated by 9 research projects forming together a consistent program will be used to develop a predictive simulation model for service-life assessment of infrastructure. One of the key projects within the IS2C program is the project called ’InfraWatch’. This project is a joint research project between the Leiden University and Delft University of Technology and is scrutinizing the interpretation of real time data. The data used for this project are archived from the monitoring system that is installed at the Hollandse Bridge in The Netherlands. The computational data analysis and data mining is conducted by researchers at Leiden University while the physical interpretation and structural matching with the data is conducted at Delft University of Technology. Within the framework of this project, the initial approach in Delft is to design a numerical simulation model that includes both the structural as well as the material aspects of a bridge. The model can be considered as the theoretical design tool that contains all the knowledge of bridge response representing the current state of the art. Matching the results of this model with the real data achieved from the real time monitored bridge would provide a learning curve about the accuracy of the modelling approach as well as the long term ability to simulate the interacting degrading and structural performance of the bridge. It is of particular interest to include the degradation mechanisms such as ASR and chloride ingress in the numerical model and to account for their effect on the long term performance. In this paper, the first preliminary ideas of a simplified model will be presented that represent a very basic blueprint of the final numerical model. Emphasis will be on the inclusion of the dominant structural and material damage models. However, due to time constrains so far only the compression strength increase due to on-going hydration, long-term creep and stochastic traffic loads have been included in the model. The simplified model is used to calculate these influences of strain, stress, deformation and failure loads. This paper contains the basic structural and material parameters taken into account and explains the results of different aspects.
2.
Simplified model
The simplified model being considered is a simply supported beam on two hinge supports. The cross-section is a rectangular concrete section with a single layer of reinforcement bars. The geometry of the model, the used parameters and the cross-section are shown in fig. 1. For several calculations, a range of different parameters are used. The structural properties are presented in Table 1, the material properties are presented in Table 2 and the load properties are presented in Table 3
Table 1: Structural parameters
Table 2: Material parameters
Table 3: Load parameters
(1)
The traffic load is divided into six vehicles with a different mass, different velocities and different frequencies.
3.
Material properties
3.1 Reinforced concrete
As reinforced concrete is an inherent heterogeneous and brittle material, its mechanical performance shows highly nonlinear and scattered behavior. It contains reinforcement bars and both materials have their own nonlinear stress-strain relation. In the past much research has been done to investigate the stress-strain relation for reinforced concrete and Sima [1] has published a bi-linear formula (1) to calculate the concrete stress-strain relationship.
Parameter Full name Range of used values Common used value L Length 5 m – 25 m 15 m b width 1000 mm - 5000 mm 2000 mm h Height 400 mm – 2400 mm 800 mm s Reinforcement distance 50 mm – 200 mm 100 mm c Concrete cover 30 mm – 100 mm 50 mm
As Steel area 300 mm2 – 5000 mm2 each bar 500 mm2 each bar
Parameter Full name Range of used values Common used value E Modulus of Elasticity 32000 N mm-2 - 38000 N mm-2 34000 N mm-2 fcm Compression strength 28 N mm-2 – 68 N mm-2 43 N mm-2
fctm Tension strength 2,2 N mm-2 – 4,4 N mm-2 3,2 N mm-2
Parameter Full name Range of used values Common used value qper Permanent load 1 kN m
-1
– 125 kN m-1 25 kN m-3 * b * h Np Presterssing load 0 kN – 50000 kN 6 N mm-2 * b * h
Ftraffic Traffic load (1) F1 = 16 kN, v1 = 100 km hr -1, n1 = 40 min-1
F2 = 32 kN, v2 = 100 km hr -1, n2 = 10 min-1
F3 = 60 kN, v3 = 80 km hr -1, n3 = 2 min-1
F4 = 105 kN, v4 = 80 km hr -1, n4 = 2 min-1
F5 = 250 kN, v5 = 80 km hr -1, n5 = 1 min-1
Since all concrete infrastructures built in the Netherlands are designed according to the rules of NEN-EN 1992-1-1 [2] (or earlier codes), this code is also used as a basis for designing the simple model as presented in this paper. Average material properties are used for the calculations and due to its complexity, formula (1) has been linearized by a tetra-linear stress-strain relation. The results are plotted in fig. 2, which represents a concrete stress-strain for a strength class C35/45. The same principle has been employed for the stress-strain relation of the reinforcement steel. Here the tetra-linear relation indicates a starting part, a yielding part and a bitetra-linear hardening part. Beside concrete failure or steel failure, also the bond between these materials can fail. Bond failure is a failure mechanism without deformations or warnings. Since the degradation of the bond [3] has hardly any influence on the failure load of well-designed structures it is not taken into account in the model.
fig. 2: Stress-strain relation of concrete. fig. 3: Influence of creep on the stress-strain relation of concrete.
3.2 Compressive strength hardening
In general, the basis for designing concrete structures is the 28 day strength of the concrete. The corresponding 28 day material properties will, therefore, also be used for structural calculations. However, since after 28 days, the chemical reaction has not completely ceased and continues slowly, characteristics will also further develop with time. Ghali [4] has described the on-going hardening process though a set of formulas. Formulas (2) and (3) have been used to account for the ongoing concrete hardening process.
4.
Permanent load
The girder can be loaded by an axial load and/or a distributed load perpendicular to the girder axis. The permanent axial load could be a prestressing load. The girder weight is part of the permanent distributed load as well as the load of the asphalt layer, installations and the prestressing curvature
E0 if 0 0(1A) A e 0 ' E0 if 0 (1) fcm( ) fcm 28 days( ) e hard 1 28 (2)
Ecm( ) Ecm 28 days( ) e
hard 1 28 (3)
Where ε is the concrete strain, ε0 the
strain at 0,4 fcm, E0 the 28 day modules
of elasticity, ε` the strain at ultimate stress and A is a strain parameter, which contains strain, strength and stiffness of the concrete element.
Where fcm(28) is the 28 day strength of
concrete, Ecm (28) the 28 day stiffness
of concrete, βhard the hardening speed
pressure are examples of permanent loads. In most cases, a curvature pressure of the prestressing load reduces other permanent loads. Quasi-permanent loads, like traffic jams have also a small contribution to the total permanent load. In Table 3 an overview is provided for the load ranges of the permanent load considered in this analysis.
4.1 Creep
Permanent loaded concrete structures will deform in time according to creep. Creep can be seen as a fictitious time dependent reduction of the modulus of elasticity. The external bending moment must be in equilibrium with the internal moment and creep may disturb this balance. A new equilibrium has to be found that complies with the altered stress-strain relation. Due to creep, the concrete strain increases, the concrete stress decreases, the steel stress increases and the internal level arm decreases. With decreasing fictitious the modulus of elasticity, the ultimate strain will be reached at a lower compression stress, see fig. 3. When at the same bending moment, the steel stress increases, the ultimate steel stress will be reached at a lower bending moment. The failure load decreases. In both cases creep has a negative influence on the failure load.
According to Ghali [4], the fictitious reduced modulus of elasticity can be calculated by formula (4) . Many parameters influence creep and, therefore, several structural parameters are hidden in this formula. In fig. 4 a scatterplot of the failure load reduction (the creep failure load divided by the non-creep failure load) is plotted. On the x-axis of fig. 4 the prestressing load (presented in N*mm-2 of concrete cross section) is plotted. In fig. 4 different structural parameters are included. Because of the many parameters, a useful formula to calculate the failure load reduction due to creep has not been found. The calculated reduction can be increased to several per cent of the failure load. A limit of the reduction has not been found.
fig. 4: Scatterplot of creep failure load reduction.
5.
Traffic load
5.1 VibrationsA bridge girder will be mainly loaded by traffic loads. Concentrated loads, representing vehicles, may pass the girder at a different speed and at a different timescale, i.e. different vehicles with different masses, causing so-called traffic induced vibrations to the girder. Galenkamp [5] has derived a formula to calculate the traffic induced vibrations to concrete girders for passing loads. Using this formula it is possible to calculate the bending moment, see (5). The formula contains an infinite number of vibration modes and is less complex when considering only the first mode.
Ecm.crp( ) Ecm ( ) 1 0c( ) Ecm
0 Ecm
1 (4)Where Ecm (τ) is the time-depending modulus of
elasticity, τ0 is 28 days, τ1 is time at first loading, φ0
5.2 Traffic speed
As can be observed from formula (5) many parameters are involved in the calculation of the bending moment due to traffic loads. Important is the fact that the mass of the vehicles (F) is directly proportional to the bending moment, so when the vehicle mass doubles, the bending moment also becomes twice as large. Besides this, traffic speed is also directly proportional to the frequency ratio (in formula (5) called Sn). The frequency ratio is also an important ratio for the
bending moment and showing a nonlinear relation. The frequency ratio also includes the stiffness, the mass and the length of the girder. Increasing the traffic speed does not automatically increase the bending moment. In fig. 5 the influence of traffic speed on the failure load ratio has been plotted. Different structural properties result in different graphs. Changing the traffic speed do influences the bending moment. The amount of influence depends on the section properties.
fig. 5: Influence of traffic speed on traffic bending moment.
6. Mechanical degradation
An infrastructural design has comply with two performance requirements. The first requirement is the ultimate limit state (ULS), which represents the probability of failure. The second requirement is the serviceability limit state (SLS), which evaluates the structural behaviour during service life.
6.1 Ultimate limit state
At ULS, the strength of the structure will be evaluated without considering the crack width and the deformation, which makes the strain an important parameter for the equilibrium stage. In the ULS calculation, the capacity of the cross-section elements can be used while maintaining equilibrium. For a structure loaded in bending, the actual compressive stress level depends on the location considered. The outer “fibre” of the cross-section experiences the highest stress level. When this stress level has reached the ultimate stress, some capacity is left in other fibres and failure has not yet occurred. When the load increases, the stress of the outer fibre decreases somewhat while the
M x t( ) 1 n 2 F L n22 1Sn2 2 4
nSn
2 1Sn
2 sin
n t
2 nSncos
nt
e n nt 2nSn cos
dnt
Sn 1n 2n2 Sn 1 sin
dnt
sin n x L
(5)stresses at the inner fibres increases. Failure occurs if the strain in the outer fibre reaches the ultimate strain. When this happens, concrete compression failure occurs.
Concrete in tension differs from concrete in compression. In the tension stage, concrete will crack when the ultimate stress is reached. The tension force will be fully taken over by reinforcing steel. Since the cross sectional area of concrete is far greater than the cross sectional area of steel, a new equilibrium stage will coincide with large strains.
6.2 Serviceability limit state
A SLS design has three main objectives: 1) controlling the crack width and the crack spacing, 2) controlling the tension stress (in a prestressed concrete structure) and 3) controlling the deflections. The proposed simplified model is mainly based on an ULS design, but is extended with some SLS calculations, i.e. it is also important to know what time dependent degradations do with the structural behaviour during service life. In fig. 6 the bending moment capacity and the steel strain is plotted against the compressive strain of the outer fibre of the girder. The plot clearly shows three typical moments where ‘A’ the structure cracks, ‘B’ the reinforcement starts to yield and ‘C’ steel strength hardening starts. In the steel strain-concrete strain graph, the angle changes as these situations. These situation are measured with A’, B’ and C’.
fig. 6: Bending moment of the girder capacity versus the concrete strain in the outer “fibre” and steel strain versus the concrete strain in the outer “fibre”. A (A’) represents cracking in tension, B
(B’) represents yielding of the reinforcement and C (C’)strain hardening starts.
When the tension stress in a concrete section becomes too large, concrete cracks and the reinforcement bars have to take over the tension strength. The strength transmission takes place over a certain length, so called ‘transmission length’. After this transmission length, the concrete section is fully loaded and can, if the stresses are high enough, crack again [6]. In a bending loaded theoretical structure, the second crack starts directly after the transmission length of the first crack, i.e. the stresses are highest at that location. In the model the location of the cracks is based on a symmetric load. The crack spacing can be calculated by (6), using (7).
Ls.min 12 fctm fbm Ac.eff As tran.rein (6) fbm 12 fctm fcm 1 1 fctm fcm ru2ri2 ru2 ri2 (7)
L crack.width L steel h xcomp d xcomp
(8)
Where fctm is the concrete tension strain,
fbm is the concrete bond stain, Ac.eff is
the effective tension zone, tran.rein is the
steel bar diameter, ru is the distance
between the middle of the bar and the cover, ri is the diameter of the bar,
ΔLsteel is the elongation of the bar, h is
the height, d is the effective height, xcomp is the concrete compression zone.
fig. 7: Crack width for a random traffic load. fig. 8: Deflection at midspan.
The crack width depends on the bending moment and increases when the bending moment increases. The crackwidth is the steel strain multiplied by the tension zone ratio (8). The crackwidth for a random traffic load (parameters depend on load, material and structural properties) is plotted in fig. 7. For the calculation of the deflection, the principle of virtual work has been used. At every (virtual) crack, the angle between the concrete section and the steel tension strain will be determined. Using this angle, the deflection at the crack location can be calculated. This local deflection is converted to the deformation at midspan (fig. 8). Note that fig. 8 looks like fig. 7, but differs at the small loads (simulating the passenger cars).
7. Conclusion
Based on a simple model of a simply supported beam, the influence of strength hardening, creep, and traffic has been analysed. The incomplete hardening process after 28 days, the strength of concrete will continue to increase with time. This hardening process increases the failure capacity with time. Creep disturbs the equilibrium between the internal stresses. This disruption causes a negative influence on the failure capacity. The weight of vehicles is directly proportional to the bending moment. The influence of traffic speed to the failure load depends on the structural properties of the girder. Increasing the speed might have a major influence on the bending moment. The model presented in this paper will be further developed as part of the InfraWatch project. The interaction between the structural and materials degradation will be addressed and the long term performance will be evaluated in terms of service-life reduction. The model will be validated by using real time monitoring data from the Hollandse Bridge monitoring system. The data analysis will be conducted by the LIACS centre in Leiden which is a cooperating partner in this project. The authors like to thank STW and the companies involved in the InfraWatch project for their contribution and financial support.
8. References
[1] SIMA,J. F., ROCA,P., and MOLINS,C. "Cyclic Constitutive Model for Concrete." Engineering Structures 30, no. 3 (2008): 695-706.
[2] STANDARDIZATION,E. C. F. Nen-En 1992-1-1. Eurocode 2: Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings. The Netherlands Standardization Institute, 2005.
[3] VANDEWALLE,L., and MORTELMANS,F. "The Bond Stress between a Reinforcement Bar and Concrete: Is It Theoretically Predictable?". Materials and Structures 21, no. 3 (1988): 179-81.
[4] GHALI,A., FAVRE,R., and ELBADRY,M. Concrete Structures. Stresses and Deformations: Analysis Design for Serviceability. Spon Press, 2012.
[5] GALENKAMP,H. F. "The Influence of Traffic Vibrations on the Hydration Process of Early-Age Concrete." Delft University of Technology, 2009.
