Maintenance Planning Of Reinforced Concrete Structures: Redesign In A Probabilistic Environment Inspection Update And Derived Decision Making

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1 Maintenane Planning Of Reinfored Conrete Strutures: Redesign In A Probabilisti Environment Inspetion Update And Derived Deision Making C Gehlen & C Sodeikat Consulting Bureau Professor Shiessl Germany Summary: In the European Brite-Euram researh projet DURACRETE, a new servie life design onept for reinfored onrete strutures has been established. This new onept enables the durability design of reinfored onrete strutures for a defined lifetime related to limit state formulations. The result of the full probabilisti alulation is a limit state based failure probability of the struture. This new design approah has been used first for a bored tunnel onstrution in The Netherlands (Gehlen and Shiessl 1999). In this paper the appliation of this approah is presented for an existing struture, the Olympi Tower in Munih, Germany, mainly in order to failitate maintenane planning. Taking information from the tender douments into aount, the progress of the arbonation front penetrating into the onrete is predited onsidering environmental load impat and resistane parameters with their variability. This result is ompared with the measured onrete over. Consequently, a time dependent reliability of the struture against arbonation indued reinforement orrosion is alulated. The first alulation is updated with inspetion data whih was measured after 33 years of exposure (arbonation measurements). Based on the updated reliability analysis deisions on future maintenane measures are made. Keywords: Durability design, arbonation, tower, probabilisti approah, reliability. 1 INTRODUCTION A struture under ertain loads may be onsidered reliable if ultimate and servieability limit states - both defined by a predetermined probability - are not exeeded by the end of the defined tehnial lifetime. In the past, strutures were designed with regard to durability following a desriptive approah. Consequently, no information about the performane in terms of limit state based reliability is nowadays available. In the past deade muh effort has been spend to develop performane based probabilisti design tools. These new onepts an also be applied to existing strutures (redesign) in order to reeive information of the time dependent performane of the struture. The television tower in Munih whih was build in 1968 is loated at the Olympi site and therefore also alled Olympi Tower. The overall height of the tower is given as m. For onstrution of the reinfored onrete setions a limbing form has been used. At three levels antenna platforms are loated. Above those antenna platforms a restaurant and an additional platform for visitors are loated, see Figure 1. The outer diameter of the reinfored onrete shaft varies between m at the bottom and 4.5 m at the top. The tower is exposed to the atmosphere, whih is ontaining usual amounts of CO 2 (hlorides are unlikely). The only barrier proteting the reinforement against arbonation indued orrosion is the onrete over. In 1967 the durability design of the reinfored onrete setions was based on a desriptive approah. Consequently, no diret information about the present and future performane of the struture against arbonation indued orrosion of the reinforement was available. Within regular inspetions of the Olympi Tower some very loal areas assoiated with very low onrete overs with arbonation indued rebar orrosion were deteted, mainly at the antilevers of the antenna platforms. Although no visible signs of orrosion were deteted in the strutural important areas at the bottom of the shaft (1 m, 8 m and 28 m above ground), the owner questioned the durability. 9DBMC-2002 Paper 131 Page 1

2 Platform for visitors 192,6 m III Antenna platform 167,7 m II Antenna platform 159,8 m I Antenna platform 151,9 m Ground Figure 1. Olympi Tower, Munih, Germany. For further maintenane planning, the ondition of the bottom of the shaft was investigated intensively. It was agreed upon to perform a durability alulation of the struture dealing with the deterioration mehanism arbonation indued orrosion. The alulation is based on the given environmental ation and the real resistane parameters of the struture. The result of the design gives information about the atual and the time dependent derease of the strutural resistane against arbonation. For further deisions it was from speial importane to get information about the atual arbonation depth, about the expeted progress of arbonation, about the onrete over (non destrutive measurement) and finally, taking these information together, to get time dependent information about the probability, that the arbonation front reahes the rebars and orrosion is likely. Usually, maintenane measures are required if standard requirements in regard to reliability of the struture are not met. Aording to EuroCode 1 (1991), the maximum failure probability with regard to arbonation indued depassivation (servieability limit state, SLS) at the end of the servie life T of the struture has to be lower than p f = p target = 7 %, equation (1). The targeted failure probability orresponds to a reliability index of β = 1.5, (EuroCode ). The so-alled reliability index β is often used for design purposes (EuroCode ). The orrelation between the failure probability and the reliability index is speified in (EuroCode ) and illustrated in Figure 2. However, further demonstration of the durability alulations will primarily refer to the definition of failure probability. 9DBMC-2002 Paper 131 Page 2

3 reliablity index β [-] failure probability p f [%] Figure 2. Interrelation between failure probability p f and reliability index β for a normally distributed reliability funtion. Based on simplified deterioration models, the probability based durability alulation requires an adequate (deterioration) modelling of the prevailing transport and deterioration mehanism, an appropriate identifiation of the environmental loading and the stohasti desription of the material resistane parameters. 2 THE MODELLING, THE DATA The limit state was set to: p{failure} = p f = p {d - x (T) < 0} < p target (1) were the parameters d and x (T) represent subfuntions: d = d,measured d (2) w 1 t ) C T 0 x (T) = 2 k e k (k t R ACC,0 + ε t S (3a) t d, measured : non-destrutively measured onrete over d : x (T): k e : unertainty of the non destrutive onrete over measurement arbonation depth at time T the influene of environment (e.g. realisti moisture at the onrete surfae during use; RH IST ) on the effetive inverted arbonation resistane, f e and g e are regression onstants k : k e g f e e RH IST = f (3b) e RHref parameter taking into aount the influene of uring (uring period, t ) on the effetive arbonation resistane, a and b are regression parameters k b = a t (3) k t : parameter whih onsiders the unertainty of test method [-] R ACC,0-1 inverted effetive arbonation resistane of dry onrete inluding the binding apaity of onrete for CO 2, determined at a time t 0 at speimens with the aelerated arbonation test ACC in [(m 2 /s)/(kgco 2 /m 3 )] 9DBMC-2002 Paper 131 Page 3

4 ε t : C S : additional errorterm whih enables the transfer from laboratory test (ACC) to natural onditions [(m 2 /s)/(kgco 2 /m 3 )] CO 2 -onentration of the ambient air [kgco 2 /m³] t: time in servie [a] W: parameter whih onsiders the influene of meso limati onditions (e.g. orientation and orresponding probability of driving rain (p SR ), time of wetness, ToW), b w is a regression exponent b (p SR ToW) w t 0 2 W = (3d) t ToW = days per year with rain h Nd 2.5 mm/d Statistial information is required to perform a probability-based servie live alulation. The quantified stohasti variables for arbonation indued orrosion are given in Table 1. The listed variables in this table have been taken from the equations (2) and (3). Table 1. List of stohasti variables influening the duration of the initiation period (arbonation indued orrosion) Olympi Tower, Munih/Germany (3e) Parameter No. Param. a. equation (2) and (3) Soure Unit Distribution Mean Value m Standard deviation s 1 d inspetion (mm) normal distribution p. Table 2 2 d testing equipment (mm) retangular a RH IST (k e ) weather station (%) weibull(max) m = 76.9 s = 12.2; ω = 100 3b RH ref (k e ) Gehlen 2000 (%) onstant 65-3 g e (k e ) Gehlen 2000 (-) onstant 2.5-3e f e (k e ) Gehlen 2000 (-) onstant 5.0-4a b (k ) Gehlen 2000 (-) normal distribution b t (k ) tender doument (d) normal distribution 1-5 k t Gehlen 2000 (-) normal distribution R ACC,0-1 tender douments in ombination with Gehlen ε t Gehlen 2000 (m 2 /s/kgco 2 /m 3 ) [(mm 2 /a/kgco 2 /m 3 )] (m 2 /s/kgco 2 /m 3 ) [(mm 2 /a/kgco 2 /m 3 )] normal distribution normal distribution (2145) (315.5) [969] [48] 8 C S Gehlen 2000 (kgco 2 /m 3 ) normal distribution T owner requirement (a) onstant a ToW (W) weather station (-) onstant b b w (W) Gehlen 2000 (-) normal distribution p SR (W) weather station (-) onstant East: North: West: South: d t 0 (W) Gehlen 2000 (a) onstant In the following it will be shown how some of the above given quantities of the stohasti variables were obtained. For the other listed parameters further bakground information an be found in Gehlen (2000). 9DBMC-2002 Paper 131 Page 4

5 2.1 Parameters 1 and 2, onrete over d and measurement error d The onrete over has been measured with non-destrutive testing equipment. The preision of the measurement depends on the testing equipment. Inauraies in measurements are taken into aount by the error term d whih quantifiation depends on the testing equipment. Generally this information is provided by the produer of the equipment. An area of approximately 2 m 2 has been measured with a grid pattern eah 0.25 m in transverse and 0.25 m in lengthwise diretion, eah in the levels 1 m, 8 m and 28 m above ground and eah in the main geographial orientation of the tower, north, east, south and west. The distribution plot of the measured onrete over at level 28 m above ground (east diretion) is given in Figure 3. The data have been statistially quantified by a omputer programme (RCP Consulting 1995). Aording to the statistial quantifiation the over is normally distributed (standard deviation s = 5.7 mm) sattering around the mean value of d,m = 54.9 mm. The following Table 2 shows the results of the statistial evaluation for all sets of onrete over data whih have been determined. Table 2. Conrete over data, Olympi Tower, Munih/Germany Result of the Evaluation Orientation Examination level d,min d,max d,m Standard deviation (mm) (mm) (mm) (mm) East, exposition 1 1 (1 m above ground) entrane - - East, exposition 1 2 (8 m above ground) East, exposition 1 3 (28 m above ground) North, exposition 2 1 (1 m above ground) North, exposition 2 2 (8 m above ground) North, exposition 2 3 (28 m above ground) West, exposition 3 1 (1 m above ground) West, exposition 3 2 (8 m above ground) West, exposition 3 3 (28 m above ground) Normal distribution South, exposition 4 1 (1 m above ground) South, exposition 4 2 (8 m above ground) South, exposition 4 3 (28 m above ground) Parameter 3a, relative humidity, RH IST In order to quantify this parameter the meteorologial offie losest to the Olympi Tower was dediated and data onerning the relative humidity of the last ten years were requested. The nearby meteorologial offie (Munih Town) is in servie sine Thus for the years 1991 till 1996 the weather data of the meteorologial offie Munih-Nymphenburg have been used Parameter 6, inverse arbonation resistane, R ACC,0 The inverse arbonation resistane has been estimated based on Gehlen (2000) taking the few available onrete relevant information into aount: Tower Conrete Mix: Grade C45/55, CEM I, other relevant information, e. g. onerning w/ ratio, ement ontent, strength lass of the ement were not available. In order to bridge that gap of knowledge the following already tested omposition (Gehlen 2000) was used for the alulation: Literature Mix: Grade C35/45, CEM I 42.5 R, = 320 kg/m 3, w/ = 0.50, maximum grain size d = 16 mm, plastiiser FM: 0.5 wt.-%/. The statistial information of the literature mix was taken from Gehlen (2000). 9DBMC-2002 Paper 131 Page 5

6 Cumulative Frequeny [-] Conrete Cover [mm] Figure 3. Statistial evaluation of the onrete over data, Olympi Tower, level 28 m above ground, orientation: east, Munih/Germany. 2.4 Parameter 10, probability of surfaes subjeted to driving rain, p SR The probability of surfaes subjeted to driving rain depends on the orientation of the struture, the geometry and the environmental onditions. This information was also given by the meteorologial offie. 3 THE MEAN VALUE PREDICTION AND THE FIRST FULL PROBABILISTIC CALCULATION Based on mean values of the quantified parameters it is possible to predit the time dependent proess of arbonation (desribed by equation 3) with an ordinary alulator. The result of suh a alulation is given in Figure 4. mean arbonation depth x,m [mm] East North South West inspetion time of exposure [a] Figure 4. Predited mean time dependent progress of arbonation, alulated aording Equation 3 with mean values of Table 1. 9DBMC-2002 Paper 131 Page 6

7 The full probabilisti servie life alulation has been arried out by a omputer programme (RCP Consulting 1995), taking all parameters with their variability into aount. The time dependent inrease of the predited failure probability p f, plotted for an exposure period of 100 years is illustrated in Figure 5. After 100 years of exposure the limit state based failure probability reahes p f = 1.4 %. This failure probability orresponds to a reliability index of β = 2.2 (Gehlen 2000), Figure reliability index β [-] reliability index failure probability failure probability p f [%] time of exposure [a] Figure 5. First probabilisti alulation; time dependent progress of limit state based reliability β and failure probability p f [%], east diretion, level 8 m above ground. 4 COMPARISON OF PREDICTED AND CALCULATED CARBONATION DEPTHS, BASED ON MEAN VALUES During inspetion, the arbonation depth was also measured at all main orientations and all levels (1 m, 8 m and 28 m above ground) of the shaft. In Table 3 the mean values of predited and measured arbonation depths are ompared. Table 3. Comparison of the alulated arbonation depth with the reorded arbonation depth of the four expositions, Olympi Tower, Munih/Germany x,t=33a in (mm) depth of the arbonation front after t = 33a Calulated (p. equation 3) Measured mean value Exposition 1 East Exposition 2 North Exposition 3 West Exposition 4 South One reason for the deviation whih has been determined is partly due to the fat that for a lot of parameters a rough estimation (on the safe side) had to be arried out, ompare variable R ACC,0-1. The other reason an be found in the irular geometry of the shaft. The progress of the arbonation depends on the moisture of the onrete. In the equation 3 the weather funtion W(t) has been introdued, whih ontains the driving rain probability p SR as a parameter. This parameter varies depending to the orientation north, east, south and west, Table 1. The west-east axis represents the main wind diretion. The driving rain probability for the east side is low (p SR = 1.4%) whih leads to a deeper arbonation front. In ontrast the probability of dominant driving rain in the west is larger (p SR = 37.5%), whih represses the progress of arbonation. This is onfirmed by the measurements. For the west and east orientation the results of the alulated arbonation depth orresponds more or less with the reported one. The larger deviations deteted at the north and the south side 9DBMC-2002 Paper 131 Page 7

8 of the tower were supposedly affeted by the irle shaped geometry of the shaft. The expliation an be found in the definition of the parameter p SR. The probability of driving rain represents the average distribution of the wind diretion during rainfall, negleting the effet of wind-flow around a struture whereby rain is arried with. The normally used probability of driving rain is valid for retangular buildings, where at least two sides of the building are in the shadow (lee side) of the wind, that means in the shadow of the driving rain, Figure 6, ). At a tower with a irle shaft, like the Olympi Tower, in priniple only one side is in the shadow of the driving rain, Figure 6, a), the other sides (windward sides) are exposed to the driving rain. That means, that in priniple the Olympi Tower has three west sides (wind respetively driving rain exposed sides) and only one not driving rain exposed side, the east side of the shaft. Under onsideration of the real exposition of the south and north side of the shaft, the alulated arbonation depths orrespond muh better to the reported ones. Figure 6. Wind and driving rain exposed sides of round shafts and retangular buildings. The figure also shows the vortex trails by Karman, aording to Petersen UPDATING OF THE FIRST FULL PROBABILISTIC CALCULATION THROUGH CONSIDERATION OF THE MEASURED CARBONATION DEPTHS Through inorporation of the inspetion data whih have been attained from the struture it is possible to improve the preision of the servie life alulation. The update (Bayesshes Update) an be aomplished by drafting boundary onditions whih take inspetion data into onsideration. The measurements of the arbonation depth after a servie time of t = 33 years represent the inspetion data whih are required for suh an update. The following equation (4) shows the equality onstrain whih is required to realise the update. x 1, insp. = 2 k e k (k t R ACC,0 + ε t ) C S t insp. W ( t insp. ) (4) t insp. : time of inspetion (t = 33 a) x, insp. : arbonation depth at time of inspetion In onsequene of this additional equation the list of stohasti variables (p. Table 1) expands with two supplementary parameters. At this point the parameters x,insp. and t insp. are being introdued whereby x,insp. represents the measured depth of arbonation at the time of inspetion t insp. The following Table 4 (ontinuation of Table 1), represents the statistially evaluated data whih are required for the updated alulation. Table 4. Continuation of Table 1, stohasti variables influening the duration of the initiation period (arbonation indued orrosion), Olympi Tower, Munih/Germany Parameter No. Param. Continuation of Table 1 p. equation (2) Unit Distribution Type Mean Value m Standard Deviation s Orientation 11-e x,inspe (mm) normal distribution East 9DBMC-2002 Paper 131 Page 8

9 11-n x,inspe (mm) normal distribution North 11-w x,inspe (mm) normal distribution West 11-s x,inspe (mm) normal distribution South 12 t inspe (a) onstant Taking the inspetion data into onsideration the update of the durability analysis have been aomplished, p. Figure 6. The progression of the inrease is less distintive as the one being observed for the first design alulation, p. Figure 5. After 100 years of exposure the limit state based failure probability reahes p f = 0.07 % (updated design, taking arbonation measurements after 33 years of exposure into aount). The alulated failure probability of the update orresponds to a reliability index of β = 3.2 (Gehlen 2000), p. Figure 2. reliability index β [-] reliability index, first alulation reliability index, update failure probability, update failure probablility p f [%] inspetion time of exposure [a] Figure 7. Update; time dependent progress of limit state based reliability β and failure probability p f [%,], east diretion, level 8 m above ground. The deviation between both alulations (first alulation and update) is due to the fat, that not only the unertain expeted mean value of the arbonation depth after 33 years of exposure was deteted to be lower but also the variation of the inspetion result was lower than predited one. Both irumstanes had an favourable effet on the strutural reliability. 9DBMC-2002 Paper 131 Page 9

10 6 CONCLUSIONS A full probabilisti alulation for durability for a existing struture was presented. The investigated results of the reliability analysis whih have been introdued an be ompared with the requirements of the EuroCode 1. Table 5. Indiative values for the target reliability indies b (EC 1, part 1, appendix A, table A2, RCP Consulting 1995) Limit states Target reliability index β (at the end of servie life) Ultimate limit state 3.8 Fatigue 1.5 to 3.8 Servieability limit state (irreversible) 1.5 Compared with the requirements of EuroCode 1, p. Table 10 and presupposed, the Olympi Tower is lassified as an engineering struture with a target servie life of 100 years, at least for the investigated surfaes of the shaft an adequate reliability against arbonation indued reinforement orrosion was alulated, Table 6. Calulated reliability indies of investigated expositions of the Olympi Tower in Munih Exposition β target t 100 (-) β t 100 (-) p f t 100 (%) 1 East, level 8 m North, level 8 m West, level 28 m South, level 8 m The outome of the updated alulation is, that no general maintenane (oating or other protetive measures) is neessary. 7 REFERENCES 1. EuroCode 1, DIN V ENV 1991, Grundlagen der Tragwerksplanung und Einwirkung auf Tragwerke, Teil Gehlen, Ch. 2000, Probabilistishe Lebensdauerbemessung von Stahlbetonbauwerken, Zuverlässigkeitsbetrahtungen zur wirksamen Vermeidung von Bewehrungskorrosion, Heft 510 der Shriftenreihe des DAfStb, Beuth Verlag, Berlin. 3. Gehlen, Ch., Shiessl, P. 1999, Probability-Based Durability Design for the Western Sheldt Tunnel, Strutural Conrete Journal of the fib, Vol. P1, No. 2, pp Petersen, Ch. 1988, Stahlbau, Vieweg Verlag Braunshweig, Wiesbaden. 5. RCP Consulting 1995, Strurel, A Strutural Reliability Analysis Program System, RCP Consulting, Münhen. 9DBMC-2002 Paper 131 Page 10