NUMERICAL MODELLING OF REINFORCEMENT OF CONCRETE COLUMNS BY JACKETING

Transcription

1 NUMERICAL MODELLING OF REINFORCEMENT OF CONCRETE COLUMNS BY JACKETING João Duarte Sénica Caeiro Department of Civil Engineering, Architecture and Earth Resources, IST, University of Lisbon 1 INTRODUCTION The need to reuse existing buildings, especially for economic and security reasons, led to the need to seek even more efficient means of rehabilitation, instead of the total demolition of the infrastructure. It is therefore natural that the concept of structural reinforcement keeps appearing, increasingly, in the current language of construction. The reinforcement of columns can be accomplished using different techniques, where one can be more advantageous than other depending on the economical, architectural and technical factors. This study focuses exclusively on strengthening columns by adding an additional layer of reinforced concrete. In the present work, it is presented an alternative of numerical modeling, using the finite element method program ADINA, of a set of laboratory tests previously conducted by Dr. Eduardo Júlio in his Ph.D. Thesis [1], where he studied the influence of the interface on the behavior of reinforced columns with a new jacket of reinforced concrete. For this study it was chosen to model the slow monotonic test related to the non-jacketed column M1G1 and to the monolithically jacketed column. After a large range of attempts on finding a stable model by changing the convergence tolerance, the number of iteration steps, the type of analysis of structures and a lot of more properties found on ADINA [2], two numerical models were created and fully validated with the laboratorial results, one non-jacketed and another one jacketed, After that, it is showed a set of parametric studies, using one of the previous numeric models and changing some properties, where it is analyzed the influence of: 1) Size of the diameters of the steel rebar used in the additional concrete layer by creating two more numerical models and comparing its results; 2) Height of the additional concrete layer by creating two more numerical models and comparing its results; 3) Concrete resistance used in the additional concrete layer by creating two more numerical models and comparing its results; The purpose of this thesis is to increase the knowledge we have concerning reinforcement of old structures, in this case particularly jacketing of columns. Besides that by developing this study, it is given a calibrated numerical model of a jacket column that can be changed to study even more important parameters. 1

2 2 CONCRETE COLUMNS REINFORCED BY JACKETING 2.1 Introduction Column jacketing is a type of structural reinforcement where the initial column s cross section is increased by adding a new concrete layer surrounding it [3]. By doing this the resistance of the column to vertical and horizontal forces is enlarged. This reinforcement can be used when we wish to correct anomalies from the structure s project, construction errors and natural wear or when we want to increase the capacity load of the structure by changing its type of utility. After a long research, we can resume the following parameters as the most important when strengthening a columns by adding a new layer: 1) Roughness of the interface between the initial column and new layer. It depend on the type of treatment used at the surface of the initial column, such as sandblasting, applying epoxy resins or even leaving the surface with no treatment at all; 2) Applying steel connectors between initial column and new layer; 3) Height and thickness of the adding layer; 4) Type of steel rebar used in the jacketing; 5) Capacity load of concrete used in the adding layer. 6) After a long research, we can resume the following parameters as the most important when strengthening a columns by adding a new layer: 2.2 Experimental tests In the experimental tests conducted by Eduardo Júlio [1] there were created 14 specimens to study the jacketing properties, 7 of them were subject to monotonic load and the remaining 7 to cyclic load. All of the models were also subjected to an axial force to simulate the stress that already exists in structures before reinforcing. In this thesis, the cyclic tests will not be talked, leaving it to future studies. We can see description of each conducted model in Table 1. Table 1: Column s specimens conducted in the laboratorial experiment Model Description M1G1 M2G1 M3G1 M4G1 M5G1 M6G1 M1G3 Non-reinforced Model Model with Non-stick Strengthening Monolithic Reinforced Model Model Reinforced with no Interface Treatment Model Reinforced with Sandblasting Interface Treatment Model Reinforced with Sandblasting Interface Treatment and with Steel Connectors Model Reinforced after Application of Axial Force and with Sandblasting Interface Treatment 2

3 Horizontal Load (kn) Horizontal Load (kn) In this experiments, for each specimen, a lot of information was collected such as yield load, maximum load, ultimate load, concrete cracking and concrete crush. However, for the numerical calibration it was only used the horizontal load versus applied displacement curves of models M1G1 (Figure 1) and M3G1 (Figure 2). 1 M1G Displacement (mm) Figure 1: Horizontal load versus applied displacement curves of Model M1G1 1 M3G Displacement (mm) Figure 2: Horizontal load versus applied displacement curves of Model M3G1 The most important conclusions that were taken in these tests were: 1) All reinforced column specimens showed a monolithic behaviour, regardless of which type of interface treatment was used, except for model M2G1; 2) It was not possible to get the pretended non-stick strengthening in model M2G1; 3) The fact of strengthening of the column occurred after or before the application of the axial load is indifferent; 4) The capacity load of the jacketed models is far larger than the non-reinforced model (M1G1); 2.3 Numerical Modelling of Reinforcement Finite Element Method In this study, all the numerical models that were developed are based on the FEM (Finite Element Method). FEM allows us to find an approximate numerical solution of problems involving mechanical structure analysis, heat transfer analysis or even mechanical fluids analysis. 3

4 When using it in structures analysis, FEM is based on the definition of a kinematically admissible approach for the displacement field by using continuous functions that are easy to impose the necessary compatibility conditions. Once we have an approximation of the displacement field, it is easy to get the static field (stresses and strains) by using the constitutive and compatibility relations. In the few cases where the equilibrium conditions are satisfied in all the points of the structure, the approximate solution is the exact solution of the problem. The main steps of FEM to solve physical and geometrically linear problems are as follows [4]: 1) Domain division; 2) Identification of independent displacements and corresponding nodal forces; 3) Approach definition to the displacement field for each element of the mesh; 4) Development of the stiffness matrix and vector of equivalent nodal forces for each element of the mesh; 5) Development of the global equilibrium equation of the structure; 6) Resolution of the system of equations and respective calculation of the independent displacements; 7) Determination of nodal displacements and deformations of the elements; 8) Determination of stresses for each elements, based on the compatibility conditions and constitutive relations; 9) Critical analysis for the obtained solution. The quality of the solution can be obtained by checking the equilibrium conditions. However, when material have a non-linear mechanical behavior, MEF requires the use of incremental and iterative techniques whose presentation is not within the scope of this dissertation. More details can be found in [5] Previous Numerical Studies In [1] and after the laboratorial experiments ended, it was conducted a series of numerical analyses using the commercial program LUSAS [6] to simulate the tests of the models M1G1, M2G1 and M6G1. In these numerical studies, it was conclusive that LUSAS [6] gave satisfactory results when modelling columns subjected to slow monotonic loads. However it was only possible to model columns subjected to a displacement till 2 mm. In the present studies the objective was to go even further using ADINA [2]. 3 NUMERICAL MODELLING AND RESPECTIVE VALIDATION OF RESULTS 3.1 Definition of Numerical Models To develop the two numerical models that represent the slow monotonic tests applied on the nonreinforced column M1G1 and on the reinforced monotonic column M3G1 the following steps were considered: Geometry The following dimensions were assumed: 1) Initial Column,2m x,2m x 1,35m; 4

5 2) Additional Layer Thickness of 3,5mm and height of,9 m; 3) Base Support 1,m x 1,m x,4m 4) Initial Longitudinal Rebar 6ϕ1; 5) Initial Transverse Rebar ϕ6//,15 6) Additional Longitudinal Rebar 6ϕ1; 7) Additional Transverse Rebar ϕ6//,75 The cross section of the column reinforced by jacketing is shown in Figure 3 Figure 3: Cross-section of column reinforced by jacketing Materials The following material s constitutive laws were used in ADINA [2] to simulate concrete and steel: 1) Isotropic Linear Elastic Material To simulate theoretical steel with the same E c that the concrete used in experimental tests; 2) Concrete Material First alternative to simulate concrete used in the experimental tests; 3) DF-Concrete Material Second alternative to simulate concrete used in the experimental tests. This material is simpler that the previous one; 4) Bilinear Elastic-Plastic Material To simulate steel used in rebar Model Mesh Two type of model meshes were created for each numerical column, one more detailed and other one simpler. The purpose of creating the simpler mesh was to give an alternative to the models that revealed computationally heavy. In Table 2, it s illustrated the number of finite elements generated in the non-reinforced model and reinforced model, depending of the mesh assumed. Table 2: Number of finite elements for each type of mesh assumed Detailed Mesh Simpler Mesh Non-Reinforced Model Reinforced Model Boundary Conditions and Applied Loads To simulate to most accurately the laboratorial tests, it was considered that the column was connected with a support base with considerable dimensions that would give a highly rigidity to the bottom of the column. All degrees of freedom were restrain at the bottom surface of the support base. To simulate the slow monotonic test, a constantly growing displacement was applied in the initial column 1 meter from the top surface of the support base. It was also applied a pressure of 425 KPa In the top surface of the column (,2mX,2m) to simulate the axial force of 17 KN. 5

6 3.1.5 Type of analysis ADINA offers a wide range of type of analysis. In this study, two of those options were considered valid: 1) Static Analysis The user controls the value of applied displacement, respective time step and the convergence tolerance. To simulate these models, it was considered a maximum displacement of 2mm and 1 time steps. 2) Collapse Analysis The program controls the value of applied displacement and respective time step so that it can extract the most accurate results with the lowest convergence problems. 3.2 Development and Validation of Non-Reinforced Model with Linear Elastic Material To develop a stable numerical model it is important to go slowly and to calibrate each parameter step by step. In this chapter it is introduced the results of a numerical model that represents an unreinforced column composed with the Isotropic Linear Elastic Material referenced above. The purpose of this model is to calibrate the initial properties of concrete, to check if the model responds to the imposed displacement and axial force, to see if the generated mesh is appropriated and see the convergence properties were ok. By checking Figure 4 we can see that the elastic linear concrete model s curve is tangent to the M1G1 s curve. So we can conclude that the initial properties of concrete are validated. Figure 4: Horizontal Force vs Displacement of M1G1 and non-reinforced linear numerical model In Figure 5 by checking the stress distribution results we can see that traction appears in the same surface as the applied displacement and that compressions appears in the surface in front of the applied load, as it was expected. Figure 5: Stress distribution on concrete of non-reinforced linear numerical model 6

7 Horizontal Load[kN] 3.3 Development and Validation of Non-Reinforced Model We started to get a lot of convergence problems in ADINA when we introduced the non-linear properties in concrete. So it was developed a lot of attempts to find a stable model by changing his type of mesh (Detailed Mesh or Simpler Mesh), concrete constitute law (Concrete or DF-Concrete) and type of analysis (Static of Collapse). It was conclusive that if we create a model with a Simpler Mesh, DF- Concrete Material and Collapse Analysis, the results extracted would be similar to model M1G1. In Figure 6 we can see that the similarity between the numerical model and the experimental model M1G1. So the non-reinforced column was considered validated with the laboratorial results. Numerical Non-Reinforced Model Laboratorial Model M1G , 2, 4, 6, 8, 1, 12, 14, 16, 18, 2, Displacement [mm] Figure 6: Horizontal Force vs Displacement of M3G1 and reinforced numerical model In Figure 7 we can also see that numerical models experienced concrete cracking and concrete crushing in the exact place it was supposed to appear. So even in this aspect, model revealed good results. Figure 7 : Comparison, between M1G1 and non-reinforced numerical model, of concrete cracking propagation (Left) and concrete crushing (Right) 3.4 Development and Validation of Reinforced Monolithic Model To finish all numerical validation, the reinforcement layer was introduced in the previous model. The same steps were taken to find a stable model. It was also conclusive that if we create a model with a Simpler Mesh, DF-Concrete Material and Collapse Analysis, the results extracted would be similar to model M3G1. In Error! Reference source not found. we can see that the similarity between the numerical model and the experimental model M3G1. So the reinforced jacketed column was considered validated with the laboratorial results. 7

8 Horizontal Load [kn] 12 1 Numerical Reinforced Model Laboratorial Model M3G Displacement [mm] Figure 8: Horizontal Force vs Displacement of M3G1 and reinforced numerical model Another important result that ADINA can import from reinforced concrete models is the stress distribution in the steel, as seen in Figure 9. It is also presented in the same Figure the distributed stress in concrete. For both stress distributions, the numerical model gave satisfactory results. Figure 9: Stress distribution on steel rebar (Left) and on concrete (Right) of reinforced jacketed numerical model 4 PARAMETRIC STUDIES As already told, the second goal of this thesis was to change the validated reinforced jacketed numerical model and to conduct a series of parametric studies. So for each parametric studies, two more models were created. 4.1 Influence of the Size of Rebar of the Additional Concrete Layer To study the influence of the size of steel rebar of the additional layer, the new models had larger diameters. 8

9 Horizontal Load [kn] Horizontal Load [kn] In Figure 1 we can clearly see the difference of results for each numerical model when comparing the behaviour of jacketed columns with different sizes of steel rebar s reinforcement. In this matter, it was conclusive that the capacity load of the jacketed columns is strictly dependent on the size of the steel rebar s reinforcement jacket. 12 Model with steel rebar of 1 mm (Longitudinal) and 6 mm (Transverse) Model with steel rebar of 12 mm (Longitudinal) and 1 mm (Transverse) Model with steel rebar of 16 mm (Longitudinal) and 12 mm (Transverse) Displacement [mm] Figure 1: Horizontal load vs displacement of numerical models with different rebar sizes of additional layer 4.2 Influence of the Height of the Additional Concrete Layer To study the influence of the height of the additional layer, the new models had smaller jacketing heights. In Figure 11 we can see a small difference in the behaviour of models with 9cm and 6cm height and a larger discrepancy to the model with 3cm height. In this matter, it was conclusive that the capacity load of the jacketed columns is not directly proportional to the height of the jacketing. However to smaller heights the capacity load of the reinforced column decreases highly when comparing to other larger heights. 12 Model with a reinforcemet layer of 9cm height Model with a reinforcemet layer of 6cm height Displacement [mm] Figure 11: Horizontal load vs displacement of numerical models with different jacketing s height 4.3 Influence of the Resistance of Concrete of the Additional Concrete Layer To study the influence of the height of the resistance concrete of the additional layer, the new models had concrete of the additional layer with higher resistances. 9

10 Horizontal Load [kn] In Figure 12, we can see that there is no significant difference between the behaviour of each column, especially when comparing models with 6MPa and 8MPa of concrete s resistance. If we consider the costs of high-resistance concretes we can assume that if we want to increase the column s capacity load, the reinforcement concrete s resistance isn t the most important parameter to be considered. 12 Model with reinforcement concrete s resistance of 35 MPa Model with reinforcement concrete s resistance of 6 MPa Model with reinforcement concrete s resistance of 8 MPa Figure 12: Horizontal load vs displacement of numerical models with different reinforcement concrete s resistance 5 FINAL CONCLUSIONS Displacement [mm] 5.1 Conclusions With the completion of this work, the most important results, from developing all the numerical models and the from the collected results of the parametric studies, were the following: 1) ADINA can easily simulate reinforced concrete initial s properties. However, if we want to go further and study the non-linear properties of concrete when subjected to high displacement values, ADINA starts to generate non-convergence problems. So we can conclude that ADINA can be a good option to simulate the initial properties of reinforced concrete still need improvements for high values of displacements. 2) ADINA shows a lot of interesting and practical properties of reinforced concrete such as cracking, crush, stress distribution in concrete (both traction and compression) and stress distribution in steel rebar. 3) By increasing the diameter s size of rebar of the additional layer, the capacity load of the monolithic column highly increases. In this case, by changing the diameters from 1 mm (longitudinal rebar) and 6 mm (transverse rebar) to 12 mm and 1 mm, respectively, the capacity load of the column increases by 21%. If we go even further and change to 16mm and 12mm, respectively, the capacity load of the jacketed column increases by 61%. 4) By decreasing the height of the additional layer, the capacity load of the monolithic column slight decreases. In this case, by changing the height of the additional layer from 9 cm to 6 cm, the capacity load decreases by 6%. If we go even further and decrease to 3 cm height, the capacity load of the column decreases by 37%. However, by checking the stress distributed diagram of this numerical model, we can conclude that by lowering the additional layer this leads to a 1

11 concentration of large values of compressions in the the reinforcement layer, which is not recommended. 5) By increasing the resistance of the concrete of the additional layer, the capacity load of the monolithic column slight increases. In this case, by changing the resistance of concrete of the additional layer from 35 MPa to 6 MPa, the capacity load of the column increases by 13%. If we go even further and increase to 8 MPa, the capacity load of the column increases by 27%. However, due to the large prices of the high-resistance concretes, the choice of this type of concrete doesn t pay the increase of strength that the reinforced column gets. 5.2 Further Developments For those who seek to continue the study of numerical modelling of reinforcement of concrete columns by jacketing developed in this dissertation, the following list of studies is presented: 1) Numerical modelling of reinforced of concrete columns by jacketing subjected to high values of slow monotonic loads (larger than 2 mm); 2) Numerical modelling of the interface between different concretes, depending on the type of treatment; 3) Numerical modelling of connectors applied between initial column and additional layer; 4) Numerical modelling of reinforced of concrete columns by jacketing subjected to slow cyclic loads 5) Influence of the thickness of the additional layer on the behavior of the jacketed column; 6) Influence of the surface s treatment of the initial column on the behavior of the jacketed column; 6 REFERENCES [1] Júlio E.S., A influência da interface no comportamento de pilares reforçados por encamisamento de betão armado, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 21. [2] Website of finite method program ADINA: [3] Gomes A., Appleton J., Reforço de estruturas de betão armado por encamisamento das secções, Revista Portuguesa de Engenharia Civil [4] Santos Reis N. F., Análise Estrutural de Pavimentos Rodoviários: Aplicação a um Pavimento Reforçado com Malha de Aço, Instituto Superior Técnico [5] Zienkiewicz O.C., Taylor R.L., ZHU J.Z., Finite Element Method: Its Basis and Fundamentals, Sixth Edition [6] Website of finite method program ADINA LUSAS: 11