A MODELLING STUDY OF DRYING SHRINKAGE DAMAGE IN CONCRETE
REPAIR SYSTEMS
Mladena Luković1, Branko Šavija1, Erik Schlangen1, Guang Ye 1,2, Klaas van Breugel1 1-Delft University of Technology
Faculty of Civil Engineering and Geosciences Stevinweg 1, 2628 CN
Delft, The Netherlands
2- Ghent University
Magnel Laboratory for Concrete Research, Technologiepark-Zwijnaarde 904 B-9052,
Ghent (Zwijnaarde), Belgium
KEYWORDS: Concrete repair, shrinkage, strain-hardening cementitious composite (SHCC), lattice model
ABSTRACT
Differential shrinkage between repair material and concrete substrate is considered to be the main cause of premature failure of repair systems (Martinola, Sadouki et al. 2001, Beushausen and Alexander 2007). Magnitude of induced stresses depends on many factors, for example the amount of restraint, moisture gradients caused by different curing and drying conditions, type of repair material, etc. Once stresses exceed the strength, two damage mechanisms may take place: debonding (curling) of the repair material or/and cracking inside the repair material or concrete substrate.
Numerical simulations combined with experimental observations can be of great use when determining the influence of governing parameters and predicting the performance of a repair system. In this work, a lattice type model is used first to simulate moisture distribution inside a repair system in time, and then to model cracking caused by resulting shrinkage. The influence of substrate surface preparation, bond strength between the two materials, thickness of the repair material, and different types of repair materials is investigated. One of the promising materials which was developed recently and showed to have promising properties for application in a concrete repair is a strain hardening cementitious composite - SHCC. Benefits of applying either SHCC or concrete as a repair material over non-reinforced repair mortar are discussed.
INTRODUCTION
Concrete repair implies integration of the new (repair) material with old concrete substrate in order to form a composite system capable of enduring exposure to mechanical loads and varying environmental conditions. What makes this goal difficult is mismatch in age, properties, and performance of two materials which often leads to premature failure of the multi-layered system (Emberson and Mays , Tilly and Jacobs 2007).
After casting, the repair material is exposed to ambient temperature and relative humidity. Due to the environmental drying, ongoing hydration, and moisture absorption by the concrete substrate, repair material loses water and tends to shrink. However, its deformation is restrained by the concrete substrate. As a consequence, stresses build up in the repair system and cracking and/or debonding follows. Cracking or debonding of the overlay reduces the load-carrying capacity of the system and allows water and other hazardous substances to penetrate into concrete and further speed up the deterioration process.
In order to make some practical design recommendations, a number of analytical models for bonded overlays subjected to differential shrinkage have been developed (Birkeland 1960, Silfwerbrand 1997, Denarié, Granju et al. 2004, Beushausen and Alexander 2007, Zhou, Ye et al. 2008, Denarié, Silfwerbrand et al. 2011). Also, a number of two dimensional continuum models were used (Martinola and Wittmann 1995, Asad, Baluch et al. 1997, Granger, Torrenti et al. 1997, Sadouki and Van Mier 1997, Martinola, Sadouki et al. 2001, Habel, Denarié et al. 2006). A way of coupling moisture transport and fracture simulations, while taking into account influence of drying on cracking mechanism is introduced
also through discrete lattice type modelling (Bolander and Berton 2004). Benefits of using lattice models for fracture simulations are that they can mimic physical structure and processes, when realistic crack patterns can be achieved (Schlangen 1993, Landis and Bolander 2009). Besides modelling fracture of brittle materials (i.e. concrete, mortar or cement paste), a ductile behaviour such as that of fibre reinforced composites can be simulated (Li, Perez Lara et al. 2006, Schlangen and Qian 2009). Material micro/mesostructure in these fracture models can be explicitly represented, while randomness of the lattice mesh enables that material aspect are captured in a probabilistic sense. The same concept can be applied for lattice based transport processes modelling. The corresponding transport properties are assigned to the lattice elements which are idealized as conductive “pipes”. Material structure can be captured thorough assigning different diffusivity (conductivity) properties to lattice elements that represent a certain material phase (Sadouki and Van Mier 1997, Šavija, Pacheco et al. 2013).
The aim of this paper is to couple moisture and fracture processes during drying in concrete repair systems. A 3D mesoscale lattice type model is used for simulating moisture distribution and resulting damage development in the repair system. Transport and fracture phenomena are studied based on incorporated mesostructure. The influence of different parameters, for example substrate surface preparation (substrate roughness and moisture preconditioning), bond strength between two materials, thickness of the repair material and different types of repair material on the damage caused by differential shrinkage in concrete repair is investigated. The damage in the repair system can be reduced if repair material is reinforced by fibres, as in case of strain-hardening cementitious composite-SHCC (Li, Horii et al. 2000). Fibres bridge crack faces and prevent that large crack widths are reached. An alternative way of improving performance of concrete repair is through reducing differential shrinkage in the system. This can be achieved by including coarse aggregates in the repair material mixture. Aggregates act as stiff, non-shrinking inclusions in the repair material which restrain shrinkage deformation and enable more stable crack propagation in the repair system. How damage progress changes and subsequent benefits when either fibres or coarse aggregates are included in the repair material mixture are studied.
LATTICE MODEL
Lattice models have been widely used to simulate fracture, moisture transport and chloride diffusion in cement-based materials (Schlangen 1993; Bolander and Berton 2004; Šavija, Pacheco et al. 2012). In the transport lattice approach, concrete is treated as an assembly of one-dimensional “pipes”, through which the flow takes place. In the mechanical lattice approach, concrete is discretized as a set of truss or beam elements which transfer forces. Output from the moisture model is used as an input for simulating fracture. This is a one-way coupling process– moisture transport does effect mechanical fracture, but there is no influence of the (micro)cracking on the moisture transport. This is a reasonable assumption as drying shrinkage microcracks should not have significant effect on drying rate of mortars and concrete (Bisschop and van Mier 2008).
Spatial discretization
The approach proposed here uses the same lattice network for both fracture and moisture simulations. For the spatial discretization of the specimen in three dimensions, the basis is the prismatic domain (Šavija, Pacheco et al. 2013). Discretization of the domain is performed according to the following procedure:
• A cubical grid is chosen (square for 2D lattice) and the domain is divided into a number of cubic cells. In all simulations presented herein, linear dimension of the cubical grid for mesh generation is 1 mm.
• In each cell (square for 2D, cube for 3D lattice), a random location for a lattice node is selected. First the nodes are randomly positioned inside a sub cell of size s in a regular grid with size A (Figure 1a). The ratio s/A is defined as randomness of a lattice and here it is set to be 0.5. This means that some disorder is built into the lattice mesh itself.
• Voronoi tessellation of the prismatic domain with respect to the specified set of nodes is performed. Nodes with adjacent Voronoi cells are connected by lattice elements (Figure 1). Since
Voronoi diagrams are dual with Delaunay tessellation, this approach is equivalent to performing a Delaunay tessellation of the set of nodes (Šavija, Pacheco et al. 2013).
• In order to take material heterogeneity into account, either a computer-generated material structure, or a material structure obtained by micro-CT scanning (Schlangen 2008, Landis and Bolander 2009) can be used. Here, the concrete mesostructure was simulated using the Anm material model originally developed by Garboczi (Garboczi 2002) and implemented in a 3D packing algorithm by Qian (Qian 2012). It is based on placing multiple irregular shape particles separated into several sieve ranges into a predefined empty container. Aggregates smaller than 4 mm are not explicitly modelled and together with matrix are considered as a mortar.
• Material overlay procedure (schematically shown in Figure 1a and 1b) is employed: the beams which belong to each phase are identified by overlapping material mesostructure (i.e. substrate/ repair material mortar and aggregates) on top of the lattice. Interface elements are generated between substrate nodes and repair material nodes (Interface MS/RM, Figure 1a) while aggregate-paste interface (ITZ) elements are generated between mortar nodes and aggregates (Figure 1b). In this manner different transport and mechanical properties are assigned to different phases (Table 1 and Table 2 respectively). Interfaces, as used in the present model, do not exactly coincide with the size of real interfaces. In reality, interface thickness is in a range of tens of micrometres, while interface elements in the present model take up also a piece of aggregate (or repair material) and a piece of mortar (Figure 1). Therefore, the actual size of the interface in the model depends on the characteristic element size and, in presented simulations, is around 1mm.
a) b)
Figure 1: Two-dimensional overlay procedure for generation of the lattice model in interface zone a) between substrate and repair material b) between aggregate and substrate mortar (ITZ) • For the fracture simulations, fibre elements are added in the repair material according to a design
volume content (2%), fibre length (8mm) and diameter (80 microns). The location of the first node of each fibre is chosen randomly in the specified volume and a random direction is defined which determines the position of the second node. If the second node is outside of the mesh boundary, then the fibre is automatically cut off and accounted for in order to ensure preservation of prescribed volume content.
• Extra nodes inside the fibres are generated at each location where the fibre crosses the square (in 3D cubical) grid.
• Fibre/matrix interface elements are generated between fibre nodes and the matrix nodes in the neighbouring cell. Also, the end nodes of the fibres are connected with an interface element to the matrix node in the cell where the fibre end is located (figure 1).
• Both aggregates and fibres are simulated with periodic boundary conditions. This means that one side of the specimen is connected to the other end and that the properties are periodically repeating. The example for the periodic boundary conditions of the fibres is given in Figure 2a and for aggregates in Figure 2b. In following simulations, as the third dimension of the specimen is small (5mm), periodic boundary conditions are simulated only in one direction.
• Fibre elements and fibre/matrix interface elements do not take part in the moisture transport and therefore are not modelled in moisture simulations.
a) b)
Figure 2: Periodic boundary conditions for a) fibres in two directions b) aggregates in three directions (Qian 2012)
LATTICE MOISTURE MODEL
A random lattice (s/A=0.5) is used first to model moisture transport caused by water exchange in repair system. The proposed model treats concrete as an assembly of one-dimensional linear, “pipe” elements, through which moisture transport takes place. A governing partial differential equation for moisture transport is:
(1)
where H is the relative humidity and D(H) is a humidity dependent diffusion coefficient which can be given as:
(2)
Here β and γ are parameters that can be determined by calibration with experimental results (Ayano and Wittmann 2002). In the model presented herein, although transport phenomena is in reality a multi-scale problem, no distinction is made between the different flow mechanisms that take place at the micro-scale (Quenard and Sallee 1992).
If equation (1) is discretized using the standard Galerkin method (Lewis, Nithiarasu et al.), the following set of linear equations arises (in matrix form):
(3)
where M = the element mass matrix; K = the element diffusion matrix and f = forcing vector. Vector H is the vector of unknown quantities (in this case relative humidity) and dot over H indicates the time derivative. M and K, have the following forms:
2 11 2 1 1 1 1 (4)
where lij is the length of the element between nodes i and j, Aij is its cross sectional area, and D(H) its
diffusion coefficient. Cross sectional areas of individual elements are assigned using the so-called Voronoi scaling method (Yip, Mohle et al. 2005). All matrices are equivalent to those of regular one-dimensional linear elements (Lewis, Nithiarasu et al.), except the correction parameter ω in the mass matrix (equation 4). This parameter is used to convert the volume of all lattice elements to the volume of the specimen, due to overlap of volume of adjacent lattice elements (figure 3). Therefore, ω corresponds to the ration between the total area of Voronoi facets through which moisture transport takes place and lattice represented volume, and can be determined as (Nakamura, Srisoros et al. 2006):
∑"#$
% (5)
where m is the total number of elements, Ai and li cross sectional area and length of each lattice element, k
element number, and V the total volume of the specimen.
When flux, qs, occurs between the material boundary and the atmosphere, it is necessary to account for
convective boundary conditions:
Figure 3: Definition of overlap area for determination of parameter ω
Here, Cf is the film coefficient, qs is the moisture flux across the boundary, Hsand Ha are the relative
humidities at the material surface and surrounding atmosphere, respectively. In the lattice model, evaporation rate is implemented through force vector in the element e:
,-.10 01.*,30 + (7)
where Hs,iis the relative humidity of the surface node (node at the surface exposed to drying) and ϑ is the
correction factor which is determined as 4 ∑5#$
- (8)
Here, n is the total number of elements corresponding to the surface nodes, As is the area of Voronoi
facets corresponding to these elements and A is the area of the surface exposed to drying. The concept is similar as for determination of the correction factor ω.
Using the Crank-Nicholson procedure (Lewis, Nithiarasu et al.), the system of linear equations is then discretized in time, and the following equation results:
0.5∆9:;< : 0.5∆9:;< :;< ∆9 (9)
This equation is then solved for each discrete time step (∆t) and moisture contents are obtained. Since parameter D and therefore, K is dependent on relative humidity H, iterative procedure is avoided by calculating relative humidity in each step (n) based on values of hydraulic diffusivity determined from the previous step (n-1). Although this implies a certain amount of error, it significantly shortens the simulation time and, the error is small for small time step ∆t. Benefits of using lattice type moisture model is that transport and fracture simulations can be further coupled while the same material mesostructure and mesh are used.
VERIFICATION OF MOISTURE TRANSPORT MODEL-OVERLAY SYSTEM
For the analysis of the time dependent drying shrinkage, overlay system is simulated. The same problem was studied numerically by Wittmann and Martinola (Martinola and Wittmann 1995), Sadouki and van Mier (Sadouki and Van Mier 1997) and Bolander and Berton (Bolander and Berton 2004). Repair material thickness is 40 mm while substrate thickness is 200 mm. System is exposed to environment with 50% relative humidity (Ha=0.5) and film coefficient of the surface is 0.7mm/day. Concrete substrate was
pre-saturated, which means that top layer of 20 mm has the same initial relative humidity as repair material (H=1). The third dimension of the simulated sample is 5 mm.
To check the accuracy of the lattice model, non-linear solution procedure, and implementation of convective boundary conditions, simulation results are compared with those from commercial finite element model FEMMASSE MLS (Femmasse 1996). The same material parameters and boundary conditions are used for both simulations. In following simulations, the terms in the diffusivity equation (2), β and γ, were set to obtain humidity profiles similar to those proposed by Martinola and Wittmann (Martinola and Wittmann 1995, Martinola, Sadouki et al. 2001). As in the continuum model concrete microstructure is not take into consideration, concrete substrate was first simulated as homogenous material, with the same diffusivity properties of all elements (Mortar substrate from Table 1). Moisture profiles at 1 day, 10 days and 110 days, obtained with FEMMASSE and lattice model are presented in the
Figure 4. Both simulations show the same tendency. Due to the drying, repair system loses water from the top. Also moisture exchange inside the substrate occurs as unsaturated part tends to get water from initially pre-saturated substrate layer.
For different w/c ratio and aggregate content of the materials, diffusion parameters (Table 1) will change. In order to obtain moisture diffusivity, concrete substrate and repair mortar should be exposed to different environmental conditions, and an inverse numerical technique should be applied on processing the experimental data (Martinola and Wittmann 1995). Therefore, for different repair materials and substrates, diffusivity profiles have to be measured and subsequently included as input in simulation.
Table 1: Diffusivity parameters for lattice moisture model and FEMMASSE D [mm2/day] Repair material Interface Mortar Substrate
ITZ Aggregates Evaporation
Cf [mm/day]
β 0.022 0.022 0.022 0.066 0.00022
0.7
γ 7.5 7 4 4 0
Figure 4: Moisture profiles at certain time steps from lattice model and FEMMASSE model
Once the model is verified, concrete substrate mesostructure is included. The volume percentage of the crushed stone in the simulated concrete substrate is 30%. 67% of aggregates are in the sieve range [8,16] mm and 33% are in the sieve [4,8] mm. Aggregates are considered impermeable and are ascribed very low diffusivity properties (Table 1). The surface nodes of the aggregates, which are in contact with surrounding matrix, have the same initial relative humidity as the surrounding matrix. As a zone with higher porosity, ITZ has higher diffusivity properties than bulk matrix. In the simulations, 3 times higher diffusivity compared to the bulk matrix diffusivity is ascribed to ITZ which is in line with ratio obtained by Šavija (Šavija, Pacheco et al. 2013). In their study, effective diffusion rate for chloride penetration in concrete was calculated, and 2.5-7 times higher diffusivity properties for ITZ elements compared to bulk matrix were obtained. Since both diffusivity of chloride penetration and water movement are directly related to the porosity, the same ratio is assumed to be valid in this study.
From the moisture profiles (Figure 5), it can be observed that ITZ and material heterogeneity have significant influence of the drying process and moisture exchange. In the continuum model and homogenous lattice mesh, obtained profiles are uniform (Figure 5a and 7b). However, in the system with explicitly modelled material mesostructure, local conditions around aggregates and higher diffusion rate in the ITZ enables that the moisture profile is not uniform but strongly dependant on aggregate distribution and connectivity of locally more porous ITZ zone. Therefore, although at the location of aggregates no moisture transport occurs, drying around the aggregates is faster compared to drying front in the substrate mortar (Figure 5c). Faster drying in the ITZ zone may cause local stress concentrations
around the aggregates, which can trigger microcracking in this locally weaker zone. Microcracking leads to the reduction of the local constrains in the microstructure and further determines fracture propagation during the ongoing drying. With the included material mesostructure and local moisture gradients, time dependent shrinkage cracking in heterogeneous and multi-layered materials are further studied.
a) b) c)
Figure 5: Moisture distribution at the 110 days when used a) FEMMASSE model b) lattice model without aggregates c) lattice model with material meso-structure included
LATTICE FRACTURE MODEL
In lattice fracture models the material is discretized as a network of truss or beam elements connected at the ends. All the single elements have linear elastic behaviour. In each loading step, an element that exceeds limit stress or strain capacity is removed from the mesh. The analysis procedure is then repeated until a pre-determined failure criterion is achieved. In this way realistic crack patterns can be obtained. Further on, without introducing material softening (elements have locally brittle behaviour) structural softening and ductile global behaviour can be simulated (Schlangen 1993).
For the fracture criterion, only axial forces are taken into account to determine the stress in the beams. An element in lattice fracture model can fail either in tension or in compression, when the stress exceeds its strength.
Coupling lattice moisture model with lattice fracture model
For coupling moisture and fracture analysis, it might be assumed that the moisture distribution produces a shrinkage field according to equation (Martinola, Sadouki et al. 2001):
=*> ?*> ∆ (11)
where εsh is the unrestrained shrinkage strain, ∆H is the moisture gradient and αsh(H) hygral coefficient
of shrinkage which can be measured from drying tests at different relative humidities. Hygral coefficients are taken directly from the experimental measurements of Martinola and Wittmann (Martinola and Wittmann 1995). Therefore, for repair material αsh,RM=0.0048, for interface between repair material and
substrate αsh,INT=0.0028 and for substrate αsh, SUB=0.0013. As well as diffusivity parameters (Table 1), for
different mixtures of repair material and concrete substrate, hygral coefficients will also change and should be measured experimentally.
If material is completely free to deform, shrinkage deformation due to hygral gradients results only in volume change of material and no stress occurs. However, internal restrains in material (i.e. aggregates, stiff inclusions) and external restrains (i.e. bond with substrate) result in eigenstresses and local stress concentrations which might exceed material strength. Once material strength is exceeded, cracking in the material occurs. This behaviour is mimicked by the lattice mesh. Due to hygral gradients, every element
tends to change its length (Figure 6). However, the deformation is restrained by element’s connectivity with other elements in the mesh and this results in generation and building up of tensile stresses. Each of the elements, according to its cross section A, its local E modulus, and the resulting hygral gradient is loaded axially with following force:
@*> =*>A B (12)
Once the element breaks, it is removed from the mesh, stresses in that element are released and other elements connected to the broken element are less restrained. During the further analysis, new restrain levels and moisture gradients in elements lead to stress generation and redistribution among the surviving beams until the strength of the next element is reached. This is analogue to material shrinkage-once the material cracks the magnitude of restraints in the material is reduced and the stresses are partially released. Lower restraint levels lead to higher deformability of the system and therefore lower stresses.
Figure 6: Coupling lattice moisture and lattice fracture model in time (H-relative humidity) Mechanical properties of the elements in the lattice mesh
In fracture simulations, different mechanical properties are ascribed to the elements that characterize certain phase (Table 2). Three different mixtures of repair material are simulated. First, repair material is simulated as a repair mortar, with homogenous local properties and without coarse aggregates. Then, fibres that enable crack bridging properties and strain hardening behaviour are implemented in repair mortar (SHCC). Finally, aggregates acting as a stiff, non-shrinking inclusions are added in the repair material mixture (repair concrete) and simulated in the concrete repair system. Volume fraction of the simulated crushed aggregate in the repair material is 30%. Due to the limitation in thickness and dimensions of patch repairs in practice, all the aggregates in repair material are somewhat smaller than aggregates in substrate and are in the sieve range [4,8] mm.
Values for the mechanical properties of interface elements which connect repair material and mortar substrate are assumed values. As the interface is usually the weakest zone in the system, lower properties are ascribed to elements which characterize this zone. Influence of interface properties of a repair system in a direct tension test and drying shrinkage test is further studied.
Table 2 :Input values for lattice fracture model
Element E [GPa] ft [MPa] fc [MPa]
Matrix (repair mortar-RM) 20 3.5 -10 ft
Fibre [14] 40 7380 - ft
Interface (Matrix/Fibre) 20 90 - 10 ft
Mortar substrate (MS) 20 3.5 -10 ft
Mortar substrate (MS with meso-structure) 25 4 -10 ft 5 Aggregate 70 8 -10 ft ITZ 15 2.5 -10 ft 3.5 Interface (MS/RM) 15 1 3 -10 ft
Bond performance of the repair system in direct tension test
Direct tension test is performed to characterize the influence of interface properties on bond behaviour and mechanical performance of the repair system. Surface roughness is considered to have the greatest influence on the bond strength (Denarié, Silfwerbrand et al. 2011). Sandblasted surface is usually advised
for surface pre-treatment of the substrate (Julio, Branco et al. 2004, Bissonnette, Courard et al. 2011). Surface laitance is removed without providing a high degree of roughness and aggregates are exposed of less than a half of the diameter of the maximum size aggregate (Garbacz, Górka et al.). In following simulations, sandblasted (rough) surface of the concrete substrate is imitated.
Load displacement curves for smooth and rough surface with low interface properties (1 MPa) and smooth surface with high interface properties (3 MPa) are shown in figure 7a. The final fracture patterns are presented in Figure 7b.
a
b 1 2 3
Figure 7: a) Stress-strain diagrams of direct tension test applied to repair system and b) final damage patterns of: 1) rough surface and 2) smooth surface with low interface properties and 3) smooth surface
with high interface properties
In both smooth and rough surface with low properties (1MPa) specimens fail at the interface (Figure 7b-1 and Figure 7b-2). When high strength properties are ascribed to interface elements, specimen fails in the substrate (Figure 7b-3). As the weakest link in the repair system is the original concrete, the bond strength between two materials is higher than the measured strength of the composite system.
For the low interface properties, increased roughness does not affect substantially the bond strength itself, but it enables more stable fracture and more ductile performance under uniaxial tension test. Larger fracture energy is needed for failure, and failure itself is not as brittle as in case of smooth surface. As failure propagates also around the aggregate, there is more interlocking and crack bridging, which enables that more energy is spent during crack formation. This leads to more ductile behaviour of the bond and more stable fracture propagation. These results are in line with previous results about the influence of substrate roughness on different bond strength tests (Lukovic, Schlangen et al. 2013).
DRYING SHRINKAGE DAMAGE IN AN OVERLAY SYSTEM AND DISSCUSION
Performance of the repair system exposed to environmental drying conditions is further simulated. Typical sequence of damage development in a repair system with repair mortar is shown in figure 8. Smooth surface with low interface properties (1MPa) is simulated. Due to the moisture gradient and drying from the top surface, first crack develops at the surface of the repair material (Figure 8a). Soon after forming this initial crack, another crack develops (Figure 8b). Homogeneity and brittleness of a
repair mortar enables that first crack propagate straight and fast until it reaches the interface. Depending on the interface properties, it either continues into substrate and/or kinks in the interface leading to debonding. Since the interface properties are low and smooth surface does not enable crack faces friction or crack interlocking to stop the crack propagation, fast debonding and wide crack opening at the very early stage in the repair system are observed (Figure 8c and 8d).
Figure 8: Damage development in a repair system with low bond strength (interface properties 1 MPa) and 40 mm thickness of repair material after 2, 3, 17 and 110 days (Deformation scaled 300x) In order to improve this performance, influence of different parameters for the time dependent damage development due to drying shrinkage is further studied.
Influence of surface roughness
Moisture profiles at 110 days, for both smooth and rough surface are presented in the Figure 9. Top 20 mm of the concrete substrate was pre-saturated. The same input parameters and initial conditions are used as in model verification (Table 1). Surface roughness does not have significant influence on the resulting moisture profile (Figure 9b). Rough profile has slightly more uneven drying front compared to smooth surface (Figure 9a) which is probably caused by geometry and more exposed aggregates on the surface of the substrate. Locally more porous ITZ and higher conductivity properties in the surrounding of aggregates disturbs the uniform drying front and causes some local moisture gradients.
a b c
Figure 9: Moisture distribution at the 110 days when in the system with a) smooth surface, 40mm repair thickness b) rough surface, 40mm repair thickness c) smooth surface, 20mm repair thickness If final crack pattern is compared for smooth (Figure 10a) and rough (“sandblasted”) surface (Figure 10b) with the same interface properties (1 MPa), there is a substantial difference in the performance of the system. In Figure 10 the final damage pattern and crack widths at the age of 110 days are presented. Cracks wider than 75 microns are represented in red colour. Rough surface enables high mechanical interlocking and therefore more constraint at the contact zone compared to the smooth surface. This results in more cracking in the repair material, smaller length of debonding, but also more microcracking in the concrete substrate as the crack will propagate directly from the repair material. Similar is observed when higher interface properties (3 MPa) are ascribed to the smooth surface (Figure 10c). There is less debonding, but more cracking in the repair material due to higher restrain levels at the interface. Rough
surface with lower bond strength enables similar performance as smooth surface with high bond strength. This explains the significant role of the amount of energy that is lost during crack propagation. Although having lower peak bond strength (Figure 7), rough surface enables high fracture energy and more area which will spend energy during crack formation. Significance of post peak behaviour and achieved ductility, over peak strength, is especially important for imposed deformation type of loading such as in case of restrained shrinkage. Repair systems are not crack free, and therefore, even more important that the peak bond strength itself is the way that fracture propagates and the amount of energy that is lost during its propagation. Therefore, depending on the repair system application, small amount of debonding may be beneficial, as long as there is something that will either stop this crack or deviate it in other direction (inside the repair material or concrete substrate). More heterogeneity in the interface provided by the rough surface enables that the specific surface area of the crack is increased. Consequently, more energy is spent on crack formation and fracture propagation in the system is less brittle.
a b c
Figure 10: Fracture pattern and crack width in a repair system after 110 days, 40 mm thickness of repair material with a) smooth surface (interface properties 1 MPa) b) rough surface (interface properties 1
MPa) and c) smooth surface (interface properties 3 MPa) (Deformation scaled 100x)
Maximum crack width, delamination height (debonding) and crack width in the substrate for different types of surface preparation are presented in Figure 15. Improved bonding properties are beneficial for reducing debonding but lead to higher crack widths inside the concrete substrate. Once the crack reaches the interface, it does not branch on debonding but propagates straight to the concrete substrate. Therefore, care should be taken when original concrete is reinforced as the larger crack widths will enable fast propagation route for chloride penetration and corrosion of the reinforcing steel.
Type of repair material
For repair applications, usually repair mortars (without coarse aggregates) are designed. This is convenient for good workability properties, low viscosity, applications of repair mortars in thin layers or small patch repairs. Fast setting time of the repair material, which is preferred in order to have minimal interruption of operations during repair work, leads to low w/c ratio and application of accelerating admixtures which further increase the brittleness of the system. Without coarse aggregates, the mixture is almost homogenous at the mesoscale, with high amount of cement and high global shrinkage deformations. Without heterogeneities (aggregates or other inclusions), as soon as the crack is initiated, it will tend to propagate extremely fast, in more or less straight manner until is stopped by other pre-existing crack or defect (Colina and Roux 2000). Due to the inherent brittleness of the cement based material and continued drying, this crack will further open and reach large crack widths. Heterogeneities, however, will favour the nucleation of stable microcracks and more “controlled” development of shrinkage cracking (Colina and Roux 2000). Therefore, the influence and benefits of including coarse aggregates in the repair material are also simulated. Volume fraction of the simulated crushed aggregate in the repair material is 30%. All the aggregates are in the sieve range [4,8] mm.
In the repair mortar, once the crack is opened it propagates straight until it reaches the interface (figure 8). No aggregates are present to stop this single crack or to enable branching from the straight path. Due to
the brittleness of homogenous material, as drying continues, this crack widens and becomes susceptible to fast chloride and water penetration. With aggregates, locally porous ITZ zone enables faster moisture loss from the repair material and uneven moisture profile. Further on, crack propagate around the aggregates and enables more tortuous cracks paths for the aggressive substance ingress. As it enables that more cracking occurs in the ITZ zone, locally lower restrain level exist. Also, by including the non-shrinking aggregate, the global shrinkage is reduced and the final crack width is smaller than in case with homogenous repair material (repair mortar). More crack trapping and crack branching, caused by aggregates acting as a stiff inclusions, is observed. This is in agreement with the statement that heterogeneities favour the nucleation of stable micro cracks and give rise to a controlled development of cracking compared to fast growing, straight cracks in brittle homogenous materials (Colina and Roux 2000).
Microcracking in the ITZ zone appears before the main crack initiates (Figure 11a). Cracks that propagate through the matrix bridge several aggregate particles (Figure 11b-d), similar as observed by Wong (Wong, Zobel et al. 2009). With concrete as a repair material, final crack widths are lower compared to crack widths when repair mortar is used (Figure 15). Observations from the simulations and obtained crack patterns are in line with the literature data. Influence of size and amount of aggregates on the shrinkage induced cracking was studied both experimentally (Wong, Zobel et al. 2009) and numerically (Grassl, Wong et al. 2010). It was observed that crack increased with decreasing aggregate volume fraction. Therefore, when less aggregates are present, larger crack widths in the system are measured.
Figure 11: Damage development of a 40 mm thick repair concrete in a repair system with low bond strength (interface properties 1 MPa) after 1, 3, 14 and 110 days (Deformation scaled 300x)
Although more controlled shrinkage cracking with lower crack widths is achieved (Figure 15), aggregates do not prevent the main crack from further widening. Aggregates enable more tortuosity of cracking path, more distributed microcracking and lower global shrinkage. As higher energy is consumed during cracking, some of the cracks are locked by stiff aggregate inclusions. However, concrete is still a quasi-brittle material, which means that once a large crack opens it will grow further until crack faces completely separate. There is nothing except crack faces friction that will transfer stresses and prevent this crack from further widening. Aggregates therefore, enable more stable crack propagation and reduce global shrinkage, but do not limit the final crack widths.
Crack widths in the repair system can be limited and controlled if a repair material is reinforced by discrete fibres, such as in the case of strain-hardening cementitious composite-SHCC (Li, Horii et al. 2000, Li 2009). Fine PVA fibres introduced in this material ensure that once the crack is open, fibres bridging that crack take the stresses and prevent the crack from further widening. As a result, new crack at a different location will open. Consequently, SHCC will result in high ductility which makes it very suitable for application in concrete repairs.
When PVA fibres are added, high shrinkage strains of repair mortar are still measured (Li and Li 2006, Zhou 2010). PVA fibres are not stiff enough nor there are coarse aggregates that will restrain and reduce shrinkage deformation. In addition, once the microcracking starts, it propagates straight through the
material, similar as in non-reinforced repair mortar. However, once the fibres are activated, they arrest this crack and prevent it from further widening.
Figure 12: Damage development of a 40mm thick SHCC in a repair system with low bond strength, rough surface (interface properties 1 MPa) after 1, 10, 37 and 110 days (Deformation scaled 300x) Fracture propagation if fibre reinforced repair material is exposed to drying shrinkage is presented in Figure 12. Instead of one crack with large maximum crack widths (~140 microns) in repair mortar (Figure 13b) or repair concrete (~55 microns, Figure 13a), 4 cracks with small crack widths (~35-40 microns) in SHCC are achieved (Figure 13c). Rough surface in SHCC repair system further enables more cracking with smaller crack widths (5 cracks, max crack width ~30microns) compared to smooth surface (4 cracks, max crack with ~38 microns). As previously addressed, rough surface enables more interlocking and higher constraints level at the interface and therefore higher probability of cracking inside the repair material. Similar was observed in drying shrinkage test in SHCC/concrete and concrete/concrete repair systems (Li and Li 2006). Rougher surface profiles in SHCC/concrete repair system provided more cracking with smaller crack widths and less delamination height between two layers. It was concluded that when material ductility satisfied, free drying shrinkage of repair material becomes less important for performance of the system. Therefore, although SHCC has significantly higher drying shrinkage compared to concrete, measured crack widths in SHCC/concrete repair system were in range of 10-60 microns while in concrete/concrete repair system they were 120-360microns. In addition, provided that roughness profile and bond strength are high enough in SHCC/concrete repair system, delamination length and height are also comparable to concrete/concrete repair system.
a b c
Figure 13: Fracture pattern and crack width in a repair system with smooth surface and 40 mm thickness of repair material, low bond strength and a) with aggregates b) without aggregates-homogenous
mesostructure c) with fibres (SHCC) (deformation scaled 100x)
In structural, three point bending tests and reflective cracking tests, it was shown that smooth surface enables more debonding and lower amount of restraint (Kamada and Li 2000, Lukovic, Schlangen et al. 2013). If SHCC is used as a repair material, this might be beneficial as debonding results in more cracks in the repair material, higher energy dissipation and more ductility of the repair system. However, in these simulations and laboratory experiments, drying shrinkage of repair material was not taken into account. Therefore, care should be taken, as smooth surface might be beneficial only in certain applications when pre-damage through the optimal curing is limited.
Repair material thickness
Another important factor is the thickness of the repair material. It is expected that in the samples with smaller thickness there is a higher probability for cracking compared to the thicker overlays (Zhou, Ye et al. 2008). This is also dependant on the bond strength of the repair material as this determines the amount of constraint at the interface. Therefore, different thickness of the repair material with different bond strengths are simulated. Again, top surface of the substrate (20 mm) was saturated. In Figure 9, drying profiles at the age of 110 days for two samples with repair thickness of 20mm and 40mm are compared. If the thickness of the overlay is reduced, faster drying occurs. In both specimens, concrete substrate with smooth surface is simulated. Again, the benefits of using SHCC as a repair material on fracture propagation in the repair system are investigated.
a b c
d e f
Figure 14: Fracture pattern and crack widths in a smooth surface repair system with interface properties of: a) 1 MPa, 20mm repair mortar b) 3 MPa, 20 mm repair mortar c) 3 MPa and 40 mm repair mortar, d)
1 MPa and 20 mm SHCC, e) 3 MPa and 20 mm SHCC and f) 3MPa and 40 mm SHCC
When high bond strength between the concrete substrate and repair material is simulated, there is higher constrain level at the interface and therefore, more cracks develop (Figure 14b). High constrain levels and moisture gradients results in radial cracks localized between two main cracks. When the interface has lower properties, due to the debonding, main crack opens very wide, and the system completely delaminates (Figure 14a). It is also interesting to notice that for the high bond strength, in a system with 20 mm repair material thickness there are two large cracks (Figure 14b) while in the case of 40 mm repair material (Figure 14c), only one crack is opened. This is in accordance with the results obtained by Colina (Colina and Roux 2000). In their study, in the system consisting of a layer of a paste made of clay, sand and water, deposited on a rigid substrate and exposed to drying, final crack spacing seemed to be simply proportional to the sample thickness. This means that the mean crack spacing is primarily controlled by the thickness of the drying sample. The same was also observed in (Groisman and Kaplan 1994). In both of these experiments bottom friction with the substrate critically influence the final crack pattern. When compared to repair system performance, there is an analogy between friction with the substrate and the bond strength within the repair system.
The importance of good bond when SHCC used as a repair material is also observed from damage patterns in Figure 14d and Figure 14e. With low bond strength, although fibres are used (Figure 14d), system delaminates and only small number of cracks open. These cracks reach higher crack widths (~58microns) and it seems that there are no substantial benefits from fibre reinforcement (Figure 15). However, in specimen with high bond strength, high constraint levels leads to more cracks with limited crack widths (8 cracks, ~28microns, Figure 14d). When 40 mm SHCC thickness simulated, final fracture pattern for smooth surface with high bond strength (Figure 14f) resembles the failure pattern in rough surface with lower bond strength (Figure 12). This is in accordance with results obtained for non-reinforced repair mortar.
Comparison of the maximum crack width in the repair, substrate and maximum debonding for all simulated specimens is shown in the Figure 15 and Figure 16. With increase of the interface properties in smooth surface, debonding is reduced, but the crack width in the substrate is enlarged. Roughness profile, which gives lower peak bond strength but high fracture energy (Figure 7), results in the same damage pattern as the smooth surface with high bond strength. This gives indication that bond strength is not the main parameter when the repair system is exposed to imposed deformations. More meaningful for the damage development and the final crack widths becomes the fracture energy that is lost during crack propagation.
Once the crack is opened, interface properties will determine how wide this crack will further open. If the interface is weak, warping of the overlay results in large surface cracks (Figure 16).
Figure 15: Maximum crack widths in the repair material, interface zone and concrete substrate for 40 mm repair thickness with different types of surface preparation, repair material and bond strength
Figure 16: Maximum crack widths in the repair material, interface zone and concrete substrate for 20 mm repair thickness with different types of repair material and bond strength
With the aggregates in the repair material mixture, global shrinkage is reduced, more stable and tortuous cracking is achieved, and due to the distributed microcracking in the ITZ lower restrain levels exist in the repair mortar. This leads to lower crack widths and more distributed microcracking in the repair system. Although providing lower shrinkage, once the cracks are opened, aggregates do not prevent these cracks from further widening. This can be achieved by implementation of fibres. More cracks with limited crack widths are achieved. However, in order to exhaust full capacity of SHCC, bond strength should be high enough in order to prevent complete interface delamination. If the repair material is delaminated, there is no benefit from the fibres.
CONCLUSIONS
In the present work, a lattice based model is proposed to simulate moisture transport and drying shrinkage induced cracking in the repair systems. Based on above discussion, following conclusions can be drawn:
• In order to enable good prediction of the performance of the repair system, it seems that material mesostructure needs to be included. Existence of aggregates and ITZ as locally more porous and weak area influence both the moisture distribution and the damage development in the system. • For the behaviour of the system under imposed deformation, the way that fracture develops
(whether system exhibits brittle or ductile behaviour) and energy that is lost on crack formation might have as high influence as peak strength values. From the modelling study, higher roughness profiles with even lower bond strength enable more stable crack propagation and less brittle behaviour of the interface.
• When SHCC is used as a repair material, although in flexural and reflective cracking laboratory tests higher fracture energy is measured with smooth surface substrate, in practical applications smooth surface is not advised. Due to the moisture gradients system exhibits pre-damage. Drying shrinkage might cause large and uncontrolled debonding and once the system is debonded, there are no benefits from fibres anymore. Therefore, in order to exhaust full capacity of SHCC under restrained deformation, it seems that adequate bonding should be achieved.
• With adequate bonding, SHCC performed best in the simulated drying shrinkage tests. It shows small crack widths which are beneficial for durability properties of repair systems. Repair material should have strain-hardening behaviour in order to enable multiple crack formation, stable propagation and to prevent wide opening of the crack.
• Depending on the repair application, use of coarse aggregates for the repair material is advised. Aggregates reduce total shrinkage and enable more stable fracture propagation during the drying and less brittle behaviour of the system. From the model, smaller crack widths are obtained compared to the more homogenous materials at the same exposure conditions.
• With the same bond strength and the same drying conditions, more cracks (with lower crack spacing) are observed in thinner overlays. This is in accordance to experimental observations in drying shrinkage tests of different brittle and quasi brittle materials.
Although 3D simulation was done, due to the limited size of specimen thickness (5mm), periodic boundary conditions were applied only in one direction. In real applications, however, material is restrained in two directions and this will probably lead to faster fracture propagation. This will be part of the future study.
In the model, edge boundary conditions were not included. However, it was considered that, once the crack is opened, boundary conditions around this crack represent edge effect in an overlay system.
Model result shows that general performance of the repair system due to drying shrinkage can be well imitated. However, a number of assumptions for the input parameters were made. Diffusivity parameters and hygral coefficients that are used as input are different for every repair material and concrete substrate. Therefore, for every mixture they should be independently measured as they will influence the state of stresses in the repair system. Due to difficulties in experimental quantification of the diffusivity and
fracture properties of interfaces (interface RM/CS, ITZ), values used in the model are also only reasonable assumptions.
The influence of time dependent phenomena, such as development of material properties in repair system is not considered but is important for estimating the performance of the repair system. Due to relaxation properties of repair material, the amount of stresses due to internal and external restrains will be reduced, and therefore, crack initiation will be postponed. As in the case of repair system, relaxation has beneficial influence, neglecting the influence of this parameter is a conservative approach to determining the performance of the repair system. However, in order to enable more thorough estimation and quantification of the performance of the repair system, these aspects should also be considered.
ACKNOWLEDGEMENTS
Financial support by the Dutch Technology Foundation (STW) for the project 10981-“Durable Repair and Radical Protection of Concrete Structures in View of Sustainable Construction” is gratefully acknowledged.
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