# The Effect of Height Scaling on the Flexural Crack Width Controlling Behavior of Hybrid R/SHCC Beams

### A Numerical and Experimental study

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## Abstract

Limiting maximum crack widths is a serviceability limit state, which ensures the durability of reinforced structures. In current practice, maximum crack widths are limited by using additional reinforcement, on top of the amount of reinforcement required for the designed ultimate bearing capacity. Reducing the amount of reinforcing steel used, could make the construction industry more sustainable. Recent studies showed that, hybrid reinforced beams with a 70 mm thick bottom layer of strain hardening cementitious composite (SHCC), so-called hybrid R/SHCC beams, are promising in controlling crack widths under pure bending, without using additional reinforcement (Huang, 2017; Singh, 2019). SHCC

is made from a binder, fine particles and PVA fibers, which leads to ductile material properties and crack bridging. The beams studied in these previous studies were limited to a height of 200 mm. In practice larger heights are demanded. Increasing the height of a hybrid R/SHCC beam, by keeping the

thickness of the SHCC layer constant, reduces the relative contribution of SHCC. In addition, cementitious materials exhibit strong size effects. Therefore, the effect of height scaling on the flexural crack width controlling behavior of hybrid R/SHCC beam is studied in this thesis. In addition, the optimization potential of the crack controlling behavior of the hybrid R/SHCC beams is studied, by the delamination of the SHCC-rebar interface.

The effect of height scaling on the flexural crack width controlling behavior of the hybrid R/SHCC beams is studied both experimentally and numerically, by 200 mm, 300 mm and 400 mm high hybrid R/SHCC beams, with a constant 70 mm thick bottom layer of SHCC. Reinforced concrete beams of the same heights are used as reference. The length of the higher beams are increased, to prevent

direct force transfer. The experimental results of the 200 mm high beams are used from a previous study by (Singh, 2019). To study the effect of delamination of the SHCC-rebar interface, a 300 mm high hybrid R/SHCC beam with smooth and Vaseline treated longitudinal reinforcement bars is used. The beams are tested in a four-point bending configuration, with a 500 mm constant bending moment region. All the beams have the same amount of longitudinal reinforcement. The numerical study is performed with the Delft Lattice Model. As lattice models are only recently used for the modelling of structural behavior, the use of the Delft Lattice model in this study is a contribution to the development

of lattice models. Analytical calculations, with use of the multi-layer model (Yassiri, 2020), are used in the comparison of the numerical and experimental results.

From the performed experiments, it is found that, the load, at which the 0.3 mm crack width limit is reached, decreases from 109% to 97% and 91% of the yielding load, upon increasing the height from 200 mm to 300 mm and 400 mm, respectively. Whereas, the beam with smooth and Vaseline treated longitudinal reinforcement bars, reached the crack width limit already at 59% of the yielding

load. Increasing the height of the reinforced concrete beams does not lead to a reduction in the crack width limit load, relative to the yielding load (76%-78%). From the cracking patterns, it is found that, upon increasing the height, the number of propagated concrete cracks decrease, both in the reinforced

concrete beams and in the hybrid R/SHCC beams, whereas the hybrid beam with smooth and Vaseline treated reinforcement bars showed a single propagated crack in the concrete layer. An effective tensile area is developed for the 300 mm and 400 mm high beams, which was not observed in the 200 mm high beams. Uniform cracking distributions are found in all the SHCC layers of the hybrid beams, except for the hybrid beam with smooth and Vaseline treated

reinforcement bars. The delamination of the concrete-SHCC interface increases, upon increasing the height, whereas the ultimate bearing capacity is similar for the 300 mm and 400 mm high hybrid R/SHCC beams. On the contrary, the hybrid beam with smooth and Vaseline treated reinforcement bars shows very limited delamination. From the out of plane measurements, it is found that, hybrid R/SHCC beams show out of plane displacements, which are highly correlated to the applied vertical forces. This is not observed for the reinforced concrete beams. The numerical models are able to simulate the trends in the cracking patterns, as observed in the experiments. In addition, the numerical models are able to simulate the trends in delamination. Increasing the concrete-SHCC bond strength, in the 400 mm high hybrid R/SHCC numerical model, leads to the formation of an additional propagated crack in the concrete layer. In addition, the deformation capacity and the delamination of the concrete-SHCC layer reduces, for the beam with the stronger concreteSHCC interface bond strength. Using a coarser 25 mm voxel size in the numerical models, instead

of the 10 mm voxel size used in previous studies (Mustafa et al., 2022), leads to similar simulated structural behavior of the beams. The voxel size limits the crack spacing, which is of larger importance for the SHCC, compared to conventional concrete. For the reinforced concrete beams, the numerical

models are able to predict the yielding load, whereas for the hybrid beams, the yielding deformation is underestimated, due to the overestimation of the ductility of the modelled SHCC. The analytical calculations show good comparison with the numerical models, both for the hybrid beams and for the reinforced concrete beams. The hybrid beam with smooth and Vaseline treated reinforcement leads

to an unreinforced hybrid beam, which is different from the experimental results. This difference is attributed to the numerical model simulating a weak bond over the full length of the beam, whereas in the experiments Vaseline is only applied over the 700 mm central span. To conclude, upon increasing the height of the hybrid R/SHCC beams, the effectiveness of the crack controlling behavior decreases. This is both found in the numerical and in the experimental results and holds both for a 0.2 mm and 0.3 mm crack width limit. However, the hybrid beams scaled in height still lead to a significant increase in the crack controlling behavior, compared to reinforced concrete beams of the same heights. Full delamination of the rebar-SHCC interface leads to worse crack controlling

behavior for the hybrid R/SHCC beams. Even more, if the full delamination occurs over the full length of the beam, the beam could be considered unreinforced. The Delft Lattice model shows large potential in the simulation of the structural behavior of both the reinforced concrete beams and the hybrid R/SHCC beams. The coarser 25 mm voxel size is found to be a time efficient and suitable modelling solution to gain insight in trends in the structural behavior of reinforced structures. The numerical model with a stronger concrete-SHCC interface showed potential in improving the crack width controlling behavior of the hybrid R/SHCC beams in height. Therefore, it is recommended

to study the effect of interface roughness for hybrid R/SHCC beams scaled in height. Additionally, determining the material input for SHCC remains a challenge in numerical simulations with the Delft Lattice Model. In order to improve the simulations of the numerical models, it is recommended to

study the material input possibilities for SHCC. Even more, before the beams are applied in practise, it is recommended to gain deeper understanding of the increased out of plane sensitivity of the hybrid R/SHCC beams. Studying the fiber dispersion would be logical start for this.