Simulation of Cracking and Failure of Concrete Structures

V. Cervenka*, R. Eligehausen**

"Building Research Institute, Czech Technical University, Solinova 7, CS· I 6608 PIaha 6, CSRR

""Institut filr WerkslOffe im Bauwesen, Universitllt Stuugart Pfaffenwaldring 4, 0·7000 Stuttgart 80, Germany

ABSTRACT

The computer simulation of the cracking process in concrete structures is performed by means oC t.he program system SBETA. The program is based on a. nonlinear bypo-clastic const.it.utive model, which covers all important. experimentally derived material propert.ies, namely, cracking, nonlinear sLress·strain law in compression, softcnning in compression and t.ension. biaxial failure funelion, etc. The nonlinear fracture mechanics is included by means of t.he fict.itious crack model and smeared crack approach. Two examples of computer simulation of concrete fracture are shown. In the first. example t.he failure mode of a pun-out test is presented. In the second example, the process of the crack development and shear failure of a reinforced concrete beam is simulated.

KEYWORDS; finite element analysis, simulation, fracture, concrete, cracking, computer graphics

INTRODUCTION

The program system SRETA was recently developed in cooperation between Stuttgart University and the Technical University in Prague. It was designed for analysis of rein-forced concrete structures in plane stress state wah emphasis on capability to simulate the processes of crack growth and material failure. New numerical and graphical tools have been designed for presentation of strain localization in the smeared material envi-ronment. It is the purpose of this paper to illustrate the potentials of a numerical model which is based on standard FEM for the simulation of the cracking process. The paper is focused on the description of the material model and on the demonstration of results. The program system SBETA is documented in the report Pl. The techniques used for graphical postprocessing arc treated in another paper of this proceedings [2J. Further applications arc presented in Ref. [3],[4).

NUMERICAL MODEL

The numerical solut.ion of t.he strudural failure is based on a number of assumptions which approximate the rcit) behavior. The approximat.ions arc required due to practical limits ami sought cfTccli\"lIt'Ss of a solution. They arc also inevitable because of our limited knowledge of the reality. Having Lliis in mind tlte numerical model ill the program Snt~TA Wi\!> couslructNl wilh balanced .l[lproximations on all levels: structure, fiuile l'iCIII<.'lIt, materi",1 model (S('(' Fig.I). IkLails are tre;i\t<.-d ill tile report [I) and IU're W('

324 FEMCAD. STRUCENG & OPTIMIZATION-90

shall mention only the concept of the lHaterial model.

All important effeds of the behavior of concrete arc included. The constitutive relation is bas<.'ti on the hypo-clastic modd. Its hasic lools arc lIolllionc SLrt~ss-slraili law "nd biaxial failure function, Fig.2,3. Defore cracking the material is isotropic and after cracking it is considered orthotropic. The cracks arc lherdorc modelled by a smeared orihotropic mao teriaL Both, fixed and roLated cracks arc implemented. The nonlinear fracture mechanics of the crack growth is implemented. by means of the crack banc.lthoory, Bazanl and Ott (71 · In this model the softening modulus Et of the descending branch of the smeared material is derived Crom the fracture energy G, (material property of the crack), rigA.

PULkOUT TEST An example taken out of the parameter study (4) is shown next. An a~choring clement is cmbeded in a. concrete block and is loaded by a. tensile force. The goal of the study was to investigate the elTed of the geometry (size and shape) on failure load, ductility and failure mode. The embedment length of the an.chor is 50 mm, the span of the support is 200 mm and the thickness of the 11late is 10 mm. The specimen is latera.lly constra.ined. The analysis was done with the rotated crack model. The final crack pattern after failure is shown in Fi,;:.5. left. It corresponds to the stage of the last point on the descending branch of the load-displacement diagram, Fig.5, right. Note that the arch length method, which was employed a.s the nonlinear solution strate~. enabled to obtain a complete descending branch of the load-displacement diagram down to zero resistance.

The failure crack pattern can be observed from the strain localization in a narrow crack band. It is a matter of further investigation to compare this computer simulation with experimental results.

SHEARIEST

This exampLe shows the simulation of a shear failure of the reinforced concrete beam, which was tested experimentally by Leonhardt. Re£.l5J . The purpose of this simulation was to im'estigate the applicability of the program SBETA, which is based on the smeared crack approach, to the modelling of the shear failure mode. The post-processing provides variety of graphical representations including deformed shapes, principal stresses and principal strains (in three types of representation: vectors, isolincs, isoareas), and crack patterns. Here we show mainly the last one, which is also most interesting for the fracturing process. (The other types of graphics are treated in the accompanying paper (2).)

The dimensions of the analyzed beam arc as follows: cross section is 0.32xO.19m, spacing of supports is 1.95m. Two loading forces are applied near the cenLre of the span. The finite clement mesh with boundary conditions and reinforcement. scheme are shown in Fig.G. The beam has only horizontal bending reinforcement and no web reinforcement ill the span. Some vertical reinforcement is provided in the parts exceeding the supports, which has no cITed on the shear failure med1anism.

The development of the failure process is shown in Fig.7. Tlte s(.'quenccs of the crack patterns show the process of the crack (ormation and localization of the main shear failure crack. The 10ad-deOcction diagram and the experimcntal crac:k I)(Lttcrn at (ajlun: . arc shown in the bottom right or Fig.7_ The cracking proc:(..'Ss ill the lIulllcric.'\1 Ill(xld starts hy (ormation of the crack process zone. In the pro('{~s.<; ZOllt' the tensile strcngth is rcachetl and matcrial c:-xhibils strain soflening. By incn'a..'.:ing 11.(> In;uling till: str'lill

SIMULATION OF CRACKING AND FAll.URE OF CONCRETE STIWCfURES 325

localizes only in some clements, Fig.S, left, in which full tension stress-free cracks arc formed. while most of the other clements unload without cfc-.aLing macro-cracks, Fig.S, right. Following this observation only the open cracks arc plotted in the filial stages of failure. The method of graphical representation of this process by means of "crack filter" is described in paper (2).

CONCLIlSION

The numerical studies performed with the program SllETA, which were partially de-scribed in this paper, indicated that the smeared crack approach can be succcsfully used to simulate the fracture of concrete strudures. In this approach the discrcle cracks are approximated by crack bands in which strains arc localized. The identification of the fail-ure mode was madc possible by specially developed post· processing procedure for crack localization.

ACKNOWLEpGEMENT

This invcstigation was carried out within the research cooperation agrccment betwccJl the Institut fUr WerkstolTe im Dauwesen of the Stuttgart University and tllC Building Research Institute of the Czech Technical University. The sponsorship of both institutions is greatly appreciated.

References

(I) CERVENKA, V., ELIGEIIAUSEN, R., PUKL, R. - SBETA Compuler Program For Nonlinear Finite Element Analysis of Concrete Structures, Part 1, Program Dcscrip· tion, Part 2, User's Manual, Part 3, Examples of Applications, Institut fUr \Verkstoffe im Bauwesen, Unh'ersitat Stuttgart, 1989.

(2) CERVENKA, V., ELIGEIIAUSEN, R., PUKL, R. - Posl-Processing Tools For Non-linear FEM Analysis Of Concrete FracLure, STRUCENG & FEMCAD, Grenoble, 17-1S.0ctober, 1990.

(31 CERVENKA, V., PUKL, R., ELIGEHAUSEN, R. - Compuler Simulalion Of An-choring Technique In Reinforced Concrete Beams, Proc. Sec. Int. Conf. Computer Aided Analysis And Design Of Concrete StrucLurcs, Zell am See, Austria.., 4th-6th April 1990, Ed. N.Bicanic,H.Mang, Pincridge Press,

(41 CERVENKA, V., PUKL, R., ELIGEIIAUSEN, R. - rEM Simulalion Of Concrele Fracture, Conference 8 ECF Fracture BehM'ior And Design Of Materials And Struc-tures, I-3.0ctober 1990, Torino, Italy.

(5) LEONHARDT, r., WALTHER, R. - Schub,·ersuche an cinfcldrigen Stahlbelonbalkcn mit und ohne Schubbcwchrung, Deutscher Ausschuss fucr Stahl beton, Heft 151, Berlin 1962.

(61 IIII.Lt:;RBORG, A., ~10J)t:;t:;R. M., PETERSSON, P.E.· Analysis of crack formalion and crack growth ill concrete by means of fracture mechanics and finite clements. Cement And Concrete Res., 6,1976, pp. 773-782.

[ij BAZANT, h.P., 011. 11.11. - Crack Iland Theory ror FracLure or Concrete, lo.fat('r. SLTlIf"L. RILE~I. Paris. Fmlln.-, 16, pp. 15fi-I77.

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