B. Moller, W. Graf, A. Hoffmann & F. Steinigen · 2014-05-15 · B. Moller, W. Graf, A. Hoffmann &...

Long-term damage processes in RC-folded plate

structures with textile reinforcement

B. Moller, W. Graf, A. Hoffmann & F. SteinigenDresden University of Technology, Department of Civil EngineeringD-01062 Dresden, Mommsenstr. 13, Germany

Abstract

Temporal and spatial progressive damage processes in reinforced concrete foldedplate structures with additional textile reinforcement are described by means of amulti-reference-plane model (MRM). The global damage state is described using adynamic damage indicator. By considering the example of a spatial reinforcedconcrete floor construction with textile post-reinforcement, the change in thedamage indicator during its service life is demonstrated.

Introduction

The aim of structural planning is to realize economic, safe and durableconstructions. In the standard procedure for analyzing reinforced concreteconstructions - semi-probabilistic safety concept (e.g. Eurocode 2) - only the initialstate of the supporting structure is considered. Using constant partial safety factorsfor external loads and resistances, safety is ensured with regard to limit states.

Initial damage and progressive damage during the life cycle are to a largeextent unaccounted for. Existing uncertainties in the data and model are often notdeterminate to a sufficient degree of accuracy.

Alternatively, nonlinear computational methods for describing the systemload-bearing behavior at the ultimate limit state and at the serviceability limit stateare permitted in Eurocode 2. Although the degree to which nonlinear FEcomputations reproduce actual conditions is decisively influenced by the qualityand complexity of the computational models and methods adopted, this alsodepends on reliable input data. Realistic safety concepts including stochastic or

Damage & Fracture Mechanics VI, C.A. Brebbia, A.P.S. Selvadurai, (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-812-0

120 Damage and Fracture Mechanics VI

non-stochastic data uncertainties are not available (to a sufficient extent),particularly in the case of existing structures. The latter presuppose accuratedeterministic fundamental solutions [1], [2].

In the following, improved algorithms are presented to account for theload-bearing reserves of reinforced concrete constructions with superficial textilereinforcement under arbitrary loading processes. This includes a consideration oftime-varying damage processes.

The starting point for the present investigation is the FE formulationdeveloped at the Institute for Structural Analysis at the Dresden University ofTechnology, which leads to hybrid finite elements with assumed stress distribution[3], and is applied for the numerical simulation of reinforced concrete folded platestructures [4]-[10]. The incremental form of the hybrid energy functional is basedon member force form functions within the elements and displacement formfunctions along the element boundaries. The transition to the 2D continuum leadsto folded plate elements. Mixed hybrid finite elements with assumed stressdistribution are based on additional displacement form functions within theelements (( -compatibility with the boundary displacement form functions). Thehybrid and mixed hybrid finite elements possess 6 local displacement degrees offreedom per node. The displacement compatibility along the edges of the foldedplates is thus ensured; transformation problems do not arise. In plane shear lockingat the element corners is prevented by means of additional nodal shear straindegrees of freedom. Stresses are determined directly from the member force formfunction and not from the derivatives of a displacement form function. For thesame element size they are thus more accurate than in the case of displacementelements (advantageous for a physical nonlinear reinforced concrete simulation).

Modeling of textile reinforcement

An up to date appraisal of the application of textiles in reinforced concreteconstructions is given in [11]. The further development and manufacture of newsuperficial textile wefts, including investigations of material behavior and thecorresponding derived constitutive laws, tests on structural components as well asthe numerical simulation of load-bearing behavior, and a safety assessment takinginto account the uncertainties in structural parameters constitute the research workpresented in [12].

The textile surface structure (comprised of knotted filament yarns with avariable opening angle between the normal and diagonal webs) is very thin, may beembedded in single or multi layers in a fine concrete matrix, and actsanisotropically under uniaxial and biaxial loads.

For the nonlinear FE simulation of the load-bearing behavior ofreinforced concrete constructions with textile reinforcement the layered model, assuccessfully applied over many years with only one reference plane [3], isextended in such a way that several discrete coupled parallel reference planes [9]may be introduced (multi-reference-plane model (MRM), Fig. 1). FE nodes withindependent nodal degrees of freedom are present in each reference plane. An


Damage and Fracture Mechanics VI 121

arbitrary number of individual layers are assigned to the individual referenceplanes. In each case the KIRCHHOFF hypothesis (Fig. 2) applies in the thicknessdirection. Shear deformations and thickness changes of the individual layers areexcluded. The flexible coupling in the thickness direction is achieved by means ofkinematic coupling conditions in interface layers (Fig. 2). A consideration of thegoverning nonlinear effects of the composite construction in the chosenmulti-reference-plane model is far less complex than in a 3D formulation.

reference-plane 1interface 1

reference-plane 0 reference-plane 22' 2 2" interface 2 10" 10

77*textile reinforcement

3' 3 3"reinforced concrete

12" 12textile reinforcement

FE-node with independent nodal degrees of freedom

Figure 1: Multi-reference-plane model

x-z-plane

textilereinforcement

interface

reinforcedconcrete"

interfacetextile

reinforcement

independent nodal degrees of freedom0 0 0 1 1 1 2 2 2U, V, W U, V, W U, V, W

or relative displacementdegrees of freedom

000 0-1 0-1 0 1e.g. u, v, w Au Aip* = q>, - cp*

0-2 0-7. 0 2Au A^ = (p, - IP*

Figure 2: Kinematics of the multi-reference-plane model

The relative displacements A = {Au Av Aw} of the layers immediately in contactwith the interface, e.g.



o-lr i Ho

(1)

where E ... Eccentricity of the boundary layer relative to the correspondingreference plane

I/... Element displacement form function [4] within the reference planeq*... Element nodal displacements in the reference plane

result in the following stresses o = {o^ a^ a^} along the interface

where V... Composite matrix dependent on o and the degree of damage d.

The nonlinear composite matrix V describes the local tensile stresses as a functionof the degree of damage d up to the point of attainment of the sustainablecomposite stresses and also takes account of delamination. In the case ofcompressive stresses the inter-penetration of elements (contact problem) must beruled out. The "weak" formulation of the equilibrium conditions

(3)

where F ... equivalent nodal forces along the interface£... virtual displacements in the directions of FA... virtual relative displacements

yields the stiffness K^ of the interface

Fj_,= /G? V(o,d) G dA qj_, = K' qj_, (4)

A

Nonlinear material behavior

In order to describe the composite construction comprised of reinforced concreteand textile reinforcement, nonlinear material laws (for concrete, steel and textile)are assigned to the individual layers of the multi-reference-plane model.

In the case of monotonic loading processes the nonlinear elastic materiallaw after KUPFER/LINK (with stress-dependent anisotropy) may be adopted forconcrete layers whereas the linear elastic ideal plastic material law may be appliedfor uniaxial and biaxial reinforcement layers (including single-bar reinforcement)[3]. For the textile surface structure, either a smeared biaxial anisotropic materiallaw (nonlinear-elastic brittle) may be adopted, or, if the position and direction ofthe bundled filament yarns are described as realistically as possible, acomponent-oriented uniaxial material law (linear-elastic brittle) may be applied.



For general loading and constraint processes, including prestressing,endochronic material laws (for concrete and steel) are adopted [5], [6]. By meansof intrinsic time scales material damage, including strain softening, areaccumulated.

The concept of smeared, fixed cracks for concrete leads to an anisotropiccontinuum with stress restrictions. Depending on the principal stresses, up to 2non-orthogonal cracks may form on a layer-to-layer basis at a material point.

The composite behavior between concrete and steel (tension stiffening) issolely attributable to the reinforcement steel. Alternatively, the composite behaviorsubsequent to crack formation is modeled in the endochronic concrete material lawby a linearly decreasing branch of the tensile stress curve. The composite actionbetween the reinforced concrete and the textile reinforcement (delamination andthe composite stress/slip law) is assigned to the interface. The delamination zoneis large compared with the thickness of the textile reinforcement layer and thebasic construction. Although the delamination front is not linked to element nodes,it may run through the finite elements.

Creep and shrinkage effects are integrated into the numerical simulationaccording to CEB Model Code 90.

Time-dependent loading processes and system modification

The superposition law does not apply in the case of nonlinear computations. Theparameters of influence for critical loading situations can thus no longer bedetermined by the extremization of individual loading cases.

All loads of practical relevance acting on the structure must be processedin their actual chronological sequence. Arbitrary loading processes includemonotonically increasing loads, cyclical loading processes including initialloading, unloading and repeated loading, transient (quasi-static or dynamic) loadsand/or long-term load applications [7].

In accordance with the FE procedure the load history is processed on anincremental-iterative basis. For this purpose a modified NEWTON-RAPHSONmethod (load-controlled up to the attainment of the ultimate load) or an arc lengthmethod after RAMM (displacement-controlled, also for post-ultimate loading) isadopted.

The subsequent reinforcement of existing constructions represents asystem modification and leads to time-varying systems under arbitrary loadingprocesses. Arbitrary system modifications (in this case, particularly theintroduction of additional cross-sectional members as well as changes of geometry,bearing conditions etc.) are taken into account during the service life.

Safety with regard to system failure may be demonstrated when special(critical) load components are increased at selected times during the simulation ofthe load history to the point of attainment of the ultimate load, while the remainingload components remain constant. Tracking of the resulting stress redistributionsthereby indicates the existing load-bearing reserves of the system, as the failure ofindividual cross-sections is no longer the governing factor.



Global dynamic damage indicator

Generally speaking, complex nonlinear models are necessary in order to computedamage accumulation. A structure may remain in its undamaged initial state forsome time. If initial local damage zones develop, these usually have little influenceon the global load-bearing behavior. If, however, damage zones increaseover-proportionally in both time and space, a progressive nonlinear damageprocess occurs up to the point of system failure. Each structure is susceptible tospecific types of damage. Especially in the case of alternating or cyclic externalloads it is only possible to forecast damage processes by means of suitable realisticnumerical simulations.

Damage to a supporting structure during its service life due to thenonlinear material damage of concrete, steel and textile, crack formation and crackpropagation as well as composite and long-term behavior leads to significantchanges in stiffnesses.

In the nonlinear FE simulation of a structure up to system failure theseforms of damage are computed on an element-to-element basis and accumulatedlocally in the first instance. The effects of progressive local damage on the globalload-bearing behavior are accounted for in the solution algorithm.

The dynamic response of the structure is conformal with the progressivedamage process. The natural frequencies of the system and changes in the latterthus provide a suitable means of estimating the global load-bearing behavior. Thequantification is achieved with the aid of an indicator D, which sharply demarcatesthe undamaged structure in its initial state (D=0) from partial damage or limitingdamage state (D=l) at arbitrary times in the load history [13].

X. (V,d)D =1 - —' , 1 < i <; m (5)

X, (V,d=0)'

Depending on the number m of the computed natural frequencies \ (V describesthe nodal displacement degrees of freedom of the system; d=0, the undamagedstate and d#0, the partially damaged state) a set of scalar damage indicators D* isobtained.

The load-bearing behavior of the global system, of course, cannot beassessed exclusively using these scalar indicators. Owing to the elementalcomputational capability and high sensitivity they are nevertheless suitable as ameans of interactively controlling the FE simulation and estimating the residualload-bearing capacity of the system. Critical loading situations or critical localdamage states affecting the load-bearing behavior of the global system aresensitively indicated [8].

Example

The reinforced concrete floor with joists [9], [10] (Fig. 3), is provided withunidirectional textile reinforcement at different points in time.



oo

rigidly fixed — jointed

node 249 \ node 89j eccentric beam (EB),

joist,

point support

textile reinforcement

loading

DW: dead wightSL: superfical load 1.0 kN/m*

(all fields)BL: boundary load LOkN/m

(along the joists)C/S: creep and shrinkage

field

= 0.40 m

materials

concrete: R = 26.EO= 30000 N/mm*v =0.2

reinforcement steel:Rg = 420 N/mm*EQ =210000N/mm^

yarn 620 tex: R = 1088 N/mm*EO = 20900 N/mm^

reinforcement(layer thickness [mm])

fieldlayer no.

6,97,8

steel0.5590.2519.8200.900

joistlayer no.

14151618

textile reinforcement10 0.200 17

Figure 3: Geometry, loading, materials, layering



The following times at which reinforcement was applied wereinvestigated (Table 1): variant I-IV ... after 1100, 365, 30 and 0 days; variant 0 ...unchanged system. The basic loading cases; dead weight (DW), constantsuperficial load (SL) acting on the entire system as well as creep/shrinkage (C/S)constitute a loading process. The action of dead weight and creep/shrinkagecommences after 14 days; a superficial load of 2.0 kN/nf is applied at a concreteage of 30 days. The boundary load (BL) along the joists is increased at differenttimes up to system failure (variants A, B and C, Table 1). The corresponding loadincrease factors n^L are listed in Table 1. Attention is drawn to the increase of theultimate load due to a (thin) textile reinforcement layer, which was applied after365 days.

Table 1: Load increase factors n^ for the boundary load

variant

load increase[day]

A [30]

B [365]

C [1100]

0 I II III IV

system change after ... days

none

8.75

3.75

3.5

1100

(8,75)

(3.75)

3.62

365

(8,75)

425

3.75

30

9.00

4.75

4.25

0

10.00

5.25

4.5

Fig. 4 shows the behavior of the natural frequencies during the load history forvariant C-IV. Only slight changes occur under service loads. In the case of thissupporting structure concrete shrinkage leads to a rise in the natural frequencies.Creep effects predominate during the investigated time period and the naturalfrequencies become smaller. Stiffness losses due to progressive crack formationfor a short-term load increase result in a sharp drop in the natural frequencies. Thequantitative effects of damage on the natural frequencies vary from case to case.The assigned damage indicators were plotted against the loading factor (Fig. 5).

A comparison of the 1st natural frequency in each case for thecomputation variants C-O, C-II and C-IV, (Fig. 6), clearly illustrates an increasein the load-bearing capacity due to post-reinforcement. Initially, the naturalfrequencies only differ slightly; the stiffness increase due to the textilereinforcement is small. As soon as the first signs of damage occur during theloading process the stiffness loss in the reinforced system is smaller due to thealtered crack formation [10], the reduction in the natural frequencies is delayed andthe load-bearing capacity of the system increases.

The nonlinear simulation in the present investigation was carried out(still) using the layered model. Other types of damage, such as e.g. delamination,may be accounted for by implementing the multi-reference-plane model and/or byadopting endochronic material laws [8].



naturali

AC (\45.U

35.0-

25.0

i< n

i-equencies [I/sec]I variant C-IV

mode 3

— — — mode 2

mode 1

/ rvQ / r*VQ/, V//IJ | /| L//o

FALT-FEMnonlinear

"H

\,BL

- — *—

0 45 90 135 increment

Figure 4: Natural frequency curves; variant C-IV

damage indicators

0.5

FALT-FEMvariant C-IV nonlinear

0.0 2.5 5.0

Figure 5: Damage indicators; variant C-IV

loading7.5 factor

Istnatu

33.0

27.0

21.0

ral frequency [I/sec]L

variant C-IVc-nC-0

DW^ SL

FALT-FEMnonlinear

— ^n

iC/S ,BL

, . ^b.

0 45 90 135 incrementFigure 6: Comparison of the 1st natural frequencies; variants C-O, C-II

and C-IV



References

[1] Moller, B. Fuzzy-Modelle in der Baustatik, Bauingenieur, 72(2), pp. 75-84, 1997[2] Moller, B., Beer, M., Graf, W. & Hoffmann, A. Possibility theory based safety

assessment, Special Issue on Fuzzy Modeling in Civil Engineering, Computer-Aided Civil and Infrastructure Engineering, Blackwell Publ.: Maiden, Oxford, 14,pp. 81-91, 1999

[3] Muller, H. & Moller, B. Lineare und physikalisch nichtlineare Statik vonFaltwerken Bausteine 1 und 2 des Programmsystems FALT-FEM Grundlagen undBeispiele, Bauforschung - Baupraxis, Heft 155, Bauinformation: Berlin, 1985,Nachdruck TU Dresden: Lehrstuhl ftir Statik, 1995

[4] Muller, H. & Hoffmann, A. Zur mechanischen Analyse von Faltwerken mitFALT-FEM, Technische Mechanik, 11(4), pp. 60-75, 1990

[5] Muller, H., Moller, B, Graf, W. & Kluger, J. Numerical ananlysis of RC-foldedplate structures for general technologies of prestressing and variable loadingprocesses, eds. Meskouris, K. & Wittek, U. Festschrift Prof. Kratzig 65 Jahre, A.A. BalkemaPubL: Rotterdam, pp. 215-229, 1997

[6] Moller, B., Graf, W. & Kluger, J. Endochronic material modelling in nonlinearFE-analysis of folded plates, eds. Anagnostopoulos, P., Carlomagno, G.M. &Brebbia, C.A. Computational Methods and Experimental Measurements VIII,Rhodos, Computational Mechanics Publ.: Southampton, pp. 97-106, 1997

[7] Moller, B., Hoffmann, A. & Kluger, J. Assessment of critical load situationsduring the life cycle of concrete structures, eds. Matikainen, Y. & Sarja, A.Computers in the Practice of Building and Civil Engineering, Worldwide ECEE-Symposium, Lahti, pp. 189-193, 1997

[8] Moller, B., Graf, W., Hoffmann, A. & Kluger, J. Judgment of damage in RC-folded plate structures using a global dynamic damage indicator, eds. Fryba, L. &Naprstek, J. Proceedings of the fourth European conference on StructuralDynamics, EURODYN 99 Prag, A. A. Balkema Publ.: Rotterdam, pp. 599-604,1999

[9] Moller, B., Graf, W., Hoffmann, A. & Beer, M. Ultimate limit loads of RC-foldedplate structures with textile reinforcement, eds. Carlomagno, G.M. & Brebbia,C.A. Computational Methods and Experimental Measurements IX, Sorrento,WITpress: Southampton, pp. 453-462, 1999

[10] Moller, B., Beer, M., Graf, W., & Hoffmann, A. FE-Modellierung vonComposite-Konstruktionen aus Stahlbeton und textilen Verstarkungen, FiniteElemente in der Baupraxis, Darmstadt, W. Ernst u. Sohn: Berlin, pp. 151-160,1998

[11] Curbach, M. et.al. Sachstandsbericht zum Einsatz von Textilien im Massivbau,Deutscher Betonverein DBV, Heft 203, 1998

[12] Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 528, TextileBewehrungen zur bautechnischen Verstarkung und Instandsetzung, TU Dresden,1999, http://www.tu-dresden.de/biwitb/sfb528

[13] Kratzig, W. B. & Noh S. Y. Computersimulation progressiverSchadigungsprozesse von Stahlbetonkonstruktionen, Finite Elemente in derBaupraxis, Darmstadt, W. Ernst u. Sohn: Berlin, pp. 123-132, 1998


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