1 2 0 0 1 2 t t max , =1 t t (3.4)
where t10and t20are the interface strength for normal and shear directions. Here t and 1 t 2 are the resulting forces due to applied load in the respective directions. When the ratio becomes one, the bond state between the two interfaces breaks down and a gap occurs between them, which can be predicted by FEM. The maximum ratio cannot be greater than one.
3.4 Determining Model Parameters by Laboratory Testing
3.4.1 Determining Rheological Properties of Mastic
Laboratory tests are performed to determine dynamic shear modulus of mastic material and converted to dynamic elastic modulus using following Eq. (3.5). The converted dynamic elastic modulus is used as elastic parameters in ABAQUS for the material property of mastic coating over aggregate.
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* *
E =2.5 G (3.5)
DSR is used to calculate the complex shear modulus (G*) values for mastic. The dynamic shear modulus can be expressed as |G*|. The dynamic modulus presents the magnitude that is the length of complex modulus. A rectangular shape mould is used for preparing the sample. Total 3.6 samples are prepared; 3 samples are tested under dry condition and 3 samples are tested for wet condition. The average theoretical maximum specific (Gmm)
gravity for the sample is 2.319 and the percent air voids of the samples are 11.5±1.0. The wet condition is prepared following AASHTO T-283. The laboratory test is done at 22 °C and 1 Hz frequency. A strain rate of 0.007% is applied on the rectangular shape sample. The modulus values, which are given in Table 3.1. The modulus value is taken as average of three test results under dry and wet conditions. The elastic modulus of aggregate is taken from other studies and described later.
3.4.2 Determining Damage Model Parameters
Laboratory aggregate pull-off tests under both dry and wet conditions are done to measure the stiffness of mastic-aggregate interfaces. Pictures taken in the laboratory are shown in 3.3. For tensile pull-off test, a coated aggregate is cut into half and the flat face is exposed and the other end is embedded into mastic up to the half of the aggregate. The wet and dry mastic samples are compacted to a target void ratio of 4 ±0.5% for both tension and shear tests. The wet condition is prepared following AASHTO T283 method before conducting the pull-off test. The flat end is fixed with the loading frame with glue and the bottom of the mastic material container is also fixed with the base. The sample is
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then load in tension at a rate of 1.27 mm/min (0.05 in/min). Two samples are prepared; one sample kept dry and other is wet conditioned before test.
Aggregate pull-off tests are also performed under direct shear load. The mastic material samples are prepared in similar fashion except the materials are prepared in the shear box of direct shear testing equipment. The hot mastic material are compacted in two lifts into the bottom half of the shear box. Just before the final compaction of the top layer, a coated and fractured face of the hot aggregate is pressed onto the surface of the top lift and the compaction to the required volume is then completed to ensure proper contact between the aggregate and the mastic. One sample is left in a dry condition and the other is conditioned following AASTHTO T283 standard. The top of the shear box is placed on the bottom of the shear box and the apparatus is placed into the direct shear machine. The set screws in the shear box are removed and the height of the top of the shear box is raised so that no mastic material impedes the shearing of the aggregate. The sample is then load in shear at a rate of 1.27 mm/min (0.05 in/min).
The load-displacement graphs due to aggregate pull-off in tension under dry and wet conditions are shown in Figure 3.4. As expected, the tensile strength of aggregate pull-off is higher under dry conditions than under wet conditions. The load-displacement curves due to shear pull-off under dry and wet conditions are shown in Figure 3.5. Under wet conditions, the initial load-displacement curve has lower values and then it increases rapidly. Also the ultimate load under wet condition is higher than the dry condition. Unlike tension pull-off test, the aggregate is not glued to the loading frame for shear pull- off tests. For this reason the load-displacement curve shows wavy and discontinuous phenomena under dry and wet condition. The stiffness of mastic-aggregate interface due
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to tension and shear is determined by measuring the slope of the curve before peak load, also known as secant modulus. The secant modulus is determined by measuring the slope of tangent connecting origin with 50% of maximum strength. The tangent lines for determining secant modulus are shown in Figure 3.4 and 3.5 graphs. The measured sustained loads and stiffness for both tension and shear under both dry and wet conditions are given in Table 3.2. Both tensile and shear interface stiffness under dry conditions are higher than under wet conditions.
3.4.3 Interface Modeling Techniques
Two methods are available in ABAQUS for surface damage simulations, cohesive element approach and cohesive surface approach. For cohesive element approach, the stiffness degradations of materials are considered. On the other hand, for cohesive surface approach, the stiffness degradation of surfaces is considered. For cohesive element approach, the stress-strain distribution and the modulus of material and fracture energy, which is the area under the stress-strain curve, are the essential requirements. For cohesive surface approach, the modulus of materials is necessary, but the strength and stiffness of the interfaces are essential for damage simulations. Also, the separation between the two surfaces is required to simulate the damage evolutions. For example, if two metal plates are lap joined by adhesive materials like glue and the damages of that adhesive material needs to be investigated, the proper way of simulation is to model the adhesive material with cohesive elements. For this particular research there is no additional adhesive material between mastic and aggregate. Mastic works as adhesive material on aggregates and the purpose of simulation is not determining the damages of mastic. The damages at interface are the point of interest. In addition, the laboratory tests
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are conducted to predict the surface damages of mastic and aggregate rather than damages of the mastic itself. For this reason, the surface damage approach is considered for this research.