Sana Amir

Conclusions and Future Recommendations

10.1 and conclusions

In this research, an attempt has been made to study the behavior of transversely prestressed concrete decks and investigate the ultimate bearing capacity considering compressive membrane action. A of the research program is given in the following sections along with the main conclusions drawn from the investigation.

10.1.1 The scientific hypothesis

In the beginning of the dissertation, the hypothesis of the research was declared as below:

“The in-plane compressive forces from transverse prestressing in combination with the compressive membrane forces arising from the lateral restraint will enhance the bearing capacity of bridge decks.”

Based on the literature review regarding punching shear in transversely prestressed decks considering compressive membrane action, a strategy consisting of experimental, numerical and theoretical approaches was devised to work on the scientific hypothesis. The research was formulated comprising a 1:2 scale model of the Van Brienenoord bridge in Rotterdam with the objective of magnifying the results of the prototype to the real bridge using laws of similitude and considering size effects. In the following sections, a brief overview of each component of the research strategy is given explaining what steps were taken to prove the scientific hypothesis and general conclusions are made in this regard.

10.1.2 Experimental analysis

The experimental aspect of the research included static tests on a half scale model of a real bridge resulting in punching shear failure of the transversely prestressed deck slabs. In Chapter 3, the design and construction of the model bridge was briefly described and an overview of the experimental program and the test setup was given. Then, in chapter 4, results from 19 tests carried out on the bridge deck were summarized. The ultimate capacity, the failure mode and cracking pattern, the load-deflection behavior, state of stresses and strains at the top and bottom of the loaded area, and the vertical and horizontal displacements of the deck slab were some of the important observations. The main conclusions drawn from the experimental results are the following:

- All the tests showed failure in punching shear. Failure always occurred in the span of the slab regardless of the number and position of the loads. The interface between the girders and the deck slab remained safe.
- Although the governing mode of failure was brittle punching, flexural punching was also observed in some cases when the transverse prestressing level was too low or when the single loads were applied above a duct at midspan. Flexural punching was also observed when double loads were applied at midspan.

The experimental results were further analyzed in the Chapter 5 by carrying out a parametric analysis. The main findings are summarized below:

- The transverse prestressing level enhanced the ultimate bearing capacity and the cracking loads were also higher for higher TPLs.
- For tests failing in brittle punching, a load position close to the interface gave a higher capacity than at the midspan.
- A higher punching shear capacity was observed when the deck slab was loaded directly above a prestressing duct compared to a position in-between the ducts.
- Double loads combined give a higher capacity as compared to single loads regardless of the position of the load; at midspan or close to the interface, or the TPL.
- Generally, the skewness of the interface/joint, loading the exterior or interior panels, or the longitudinal position of the load within a deck slab panel had negligible influence on the punching shear capacity.

10.1.3 Numerical analysis

A 3D, solid, 1:2 scaled model of a real bridge was developed in the finite element software DIANA and nonlinear analyses were performed to simulate the experiments done in the laboratory. Chapter 6 includes a basic analysis comprising eight test cases. The overall load-deflection behavior, ultimate loads and mode of failure, cracking loads and cracking pattern, stress distribution and compressive membrane action were the main results. Following important conclusions can be drawn from the finite element study:

- A nonlinear finite element analysis of a 3D solid bridge model can simulate the punching shear behavior of deck slab with good accuracy.
- The governing failure mode in the finite element analyses was punching shear similar to the experimental observations.
- The higher the transverse prestressing level (TPL), the higher was the initial cracking load.
- Use of composed elements proved to be a beneficial modeling technique. Substantial compressive membrane action was found to occur in the finite element model bridge deck and was established by the in-plane compressive force distribution of the loaded area and its surroundings.
- A default (in-built) compressive membrane action existed even for very low levels of prestressing and was dependent on the level of external restraint arising from the structural and geometrical configuration of the deck slab.
- Increasing the TPL increased the in-plane compressive force and as a result an increase in the ultimate bearing (punching shear) capacity was observed. A linear relationship was found to exist between the in-plane force and the punching shear capacity as well as between the initial transverse prestressing level and the punching shear capacity.

In order to validate the 3D solid finite element model, a detailed parametric study was carried out in Chapter 7. A comparison with the experimental results was also made, where available. The main observations are highlighted below:

- The levels of transverse prestressing were increased from two in the basic analysis to four (0.5, 1.25, 2.5 and 4.5 MPa) in the parametric analysis to confirm the previous experimental and numerical analysis observations. An increase in the TPL linearly increases the punching shear capacity when loads were applied at midspan and at the interface. Cracking loads are also increased with increasing TPLs.
- Generally, a higher bearing capacity was observed when the loads were increased in number (from single to double) or applied close to the interface or above the ducts, as compared to when they were applied at midspan or in-between the ducts. Increasing the loading area by increasing its transverse length also increased the punching shear capacity.
- The load position on the exterior or the interior deck slab panels had negligible influence on the punching shear capacity although a slight increase in stiffness and capacity was observed when interior panels were loaded.
- The larger the size of the ducts, the lower was the punching shear capacity because of the reduction in the cross-sectional area of the slab and in the volume of concrete.
- Increasing the fracture energy increased the deformation capacity of the deck slab as well as the ultimate loads. MC 90 (1993) and MC2010 (fib 2012) show a large difference in the calculation with regard to the fracture energy.
- A higher concrete strength led to an improved behavior of the deck slab. The tensile strength of the concrete had a larger influence on the punching shear capacity than the compressive strength.
- A 3D real bridge model was constructed to investigate the size effect. The fracture energy was increased assuming a larger aggregate size for a larger thickness, but still some size effect was seen when the results of the model bridge were projected using the scale factor. It was also observed that the size factor varied with the level of transverse prestressing. A smaller size effect was observed for higher TPLs or in other words for higher in-plane compressive forces.
- The average ratio of the ultimate loads observed in tests to the ultimate loads observed in the finite element analysis for all the test cases (PT/PFEA) was found to be 1 with a standard deviation of 0.10 and the coefficient of variation of 10%.

10.1.4 Theoretical analysis

A theoretical analysis of the model and the real bridge was made by employing existing codes and methods to calculate the ultimate capacity of the two structures. The critical shear crack theory that grounds the MC2010 shear provisions was also used to carry out the calculations. The following important conclusions are drawn from the analysis.

- Eurocode 2 and ACI 318 gave conservative results since they do not consider compressive membrane action in their provisions. A coefficient of 0.7 instead of the default value (k1 = 0.08 in the background report 25.5-02-37-prENV 1992-1-1 equation 21 and 0.3 in the ACI code equation 22) was found to be sufficient to increase the contribution of the in-plane forces in the punching shear equations and improve the comparison between the experimental results and the code predictions. However, this needs further validation by considering a larger number of experimental cases.
- The elementary level of approximation, LoA (or LoA II from MC2010) using CSCT was devised to calculate the punching shear capacity considering only the prestressing forces.
- The advanced LoA using CSCT was devised to calculate the punching shear capacity considering the compressive membrane action in addition to the prestressing. In this way, the positive influence of compressive membrane action in the load-rotation behavior of a structure was turned into benefit.
- An overall factor of safety of about 3.25 was calculated for the full scale, real bridge against the design wheel load of Eurocode 2. Such a high safety margin was obtained by virtue of the beneficial effects of compressive membrane action and transverse prestressing.

v_Rd,c = C_Rd,c * k * (100 * rho_l * f_ck)^1/3 + k1 * sigma_cp; V_ACI = v_c + v_cp; f_cm; sigma_cp; V_Rd,c; v_ud

10.1.5 Important research findings and conclusions

The following important findings have been obtained after the detailed research carried out on the ultimate bearing capacity of transversely prestressed decks.

- A design and analysis method to incorporate compressive membrane action into the punching shear provisions of the Model Code 2010 based on the critical shear crack theory has been presented in Chapter 9.
- The critical shear crack theory has been found to be versatile in catering to different types of structures and loading conditions as well as incorporating the beneficial effects of the compressive membrane action on the punching shear capacity. Not only it is suitable for research purposes but the proposed Levels-of-Approximation approach makes it helpful for practicing engineers.
- The behavior of a bridge deck with regard to both serviceability and ultimate limit state can be improved if the deck slab is prestressed in the transverse direction and sufficient lateral restraint exists to develop compressive membrane action in the deck slab.
- Most of the experimental and finite element analyses are performed with the load applied in-between the ducts and on exterior panels. The prestressing bars were unbonded in the experiments and the ducts were considered hollow in the finite element model. All these measures along with the ones mentioned in section 3.1.3 lead to conservative ultimate capacities observed in the analyses.
- Using a higher value of the fracture energy for a larger aggregate size (like in some fracture energy based models) is insufficient to properly address the size effect. An overall size effect has to be introduced for thicker structural members.
- A size factor of 1.2 is conservatively obtained after the numerical and the theoretical analyses, where: Model bridge punching capacity × Scale factor = Real bridge punching capacity × Size factor
- For research purposes, sufficient saving in cost can be realized if calibrated numerical models are employed to investigate existing structures rather than doing expensive experimental studies.

The experimental, numerical and theoretical analyses have given sufficient proof for the hypothesis of the research stating that the in-plane compressive forces from the transverse prestressing in combination with the compressive membrane forces arising from the lateral restraint will enhance the bearing capacity of bridge decks. The detailed research results have led to the conclusion that the conventional bridge deck design and analysis methods are quite conservative and existing bridge decks have sufficient residual strength available to satisfy the modern traffic demands.

10.2 Recommendations for future research

The current research deals with static loads applied to bridge decks. It will be interesting to observe the behavior of deck slabs under fatigue or dynamic loading and to see the development of compressive membrane action with the loading history. Research should also be done on skewed bridge decks or composite deck slabs made up of layered reinforced concrete and precast prestressed panels.

The dependency of size effect on the in-plane forces arising from the transverse prestressing level or the restraining action needs further research.

In the experimental research of this study, a single large size specimen with the same concrete strength was cast. Experimentation with varying material properties can also help to study the effect of concrete properties on the punching shear strength. Similarly, higher levels of transverse prestressing can be used in the bridge deck to further verify the linearity of the relationship between the TPL (or the overall in-plane compressive membrane forces) and the punching shear strength found in this study.

For future research work, it is recommended to quantify the compressive membrane action for different types of structures with varying boundary conditions. This will further simplify the proposed approach of using a nonlinear finite element analysis to determine the compressive membrane action.