Effects of creep on new masonry structures

Transcription

1 CHAPTER 4 Effect of creep on new maonry tructure N.G. Shrive 1 & M.M. Reda Taha 2 1 Department of Civil Engineering, Univerity of Calgary, Calgary, Canada. 2 Department of Civil Engineering, Univerity of New Mexico, Albuquerque, USA. 4.1 Introduction Creep can affect tructure in two way: deformation typically increae and load (tree) can be reditributed among tructural component and, within a member, the contituent material [1]. The effect of creep can be beneficial, neutral, or detrimental for a tructure: beneficial, for example through the relief of tre concentration, detrimental through increaing deformation. The latter can lead to a tructure no longer meeting erviceability criteria. Stre reditribution can caue cracking, epecially in cae where there i deterioration in trength over time due to environmental factor in that element of the tructure which carrie increaing load due to creep effect. Sometime the two effect work together. Creep buckling i one example. An initial lateral imperfection in a column ubject to axial load, or an initial eccentric load, caue an initial lateral diplacement of the column. Conequently, there are higher compreive tree on the inner curvature than on the outer curvature of the column. The ide of the column under the higher tre creep more than the other ide, under the lower tre. The creep train reult in increaing lateral diplacement. In turn, the econdary moment (the axial load time the lateral diplacement) increae, increaing the tre on the inner curvature. Creep increae with the higher tre, o the lateral diplacement increae more and more rapidly with the end reult being a buckling failure of the column. An initial applied load le than the Euler buckling load for the end contraint of the column can thu caue a buckling failure ometime after load application. For ome material, the tre to initiate uch failure can be a low a 60% of the failure tre in a monotonic doi: / /04

2 84 Learning from Failure compreion tet. Binda et al. [2] indicate that for ome type of maonry thi number may be in the order of 45 50%. Crack growth caued by creep in tenion tet ha been recognized a damage in the ame context a that caued by fatigue [3, 4]. Crack alo grow under compreion-induced creep, parallel to the direction of compreion. The caue i imilar to that in creep buckling in that the preence of the crack diturb the local tre field, with a higher than average compreive tre parallel to the edge of the crack. Increaed creep there accentuate the bending component of the tre and deformation beide the crack, increaing the crack width, and thu the tenile tree at the crack tip. The crack extend when the tre and energy condition favor uch growth [5]. Creep crack propagation and it cracking rate dependence on bond breakage at the fracture proce zone were dicued and modeled [6 8]. Binda et al. [9] remark on the exitence of uch crack in the civic tower of Pavia at leat 20 year prior to it collape, and the appearance of uch crack in many hitoric tructure at variou age after contruction [2]. It i now well etablihed that maonry creep. The pioneering work of Lenczner [10, 11] ha led to the realization that creep can be expected with any maonry unit [2, 12 15] perhap with the exception of ome dry tacked tonework. The potential effect of creep therefore need to be conidered in new contruction and in rehabilitation. In rehabilitation intervention in hitoric maonry tructure, eentially a new tructure ha been created, in which one component ha already undergone ome creep and the new component ha yet to creep. Some maonry code of practice now recognize the effect of creep in term of increaed deformation. Such code advie deigner to ue the effective modulu technique to etimate long-term diplacement [16, 17]. Thi technique, however, ignore what may happen in the tructure between the initial and long-term tate. 4.2 The tep-by-tep in time approach to modeling time-dependent effect We demontrate here, uing a imple tep-by-tep in time technique, that element in a tructure may ee increaing, then decreaing, proportion of load over time: that by calculating only the initial and long-term tate, the deigner may mi a peak tre occurring at an intermediate time. We recognize that maonry i complex, multi-component material: an outer kin of brickwork or blockwork may be filled with grout or rubble maonry, and may contain reinforcing bar. Modern technique of rehabilitation may involve ue of fiber reinforced polymer (FRP), ome of which are known to creep [18]. Alternatively, the epoxy binding the FRP to the underlying maonry may relax over time under the hear tree tranferring load between the FRP and the maonry: uch behavior would caue a reditribution of load between thee two component. The tep-by-tep in time method of creep analyi relie on the applicability of the principle of uperpoition. In relation to creep, the principle require that for a material ubjected to tree at different time, the creep train produced at any

3 Effect of Creep on New Maonry Structure 85 time due to a previouly applied tre i independent of the effect of any other tree applied before or after that particular tre. The creep repone to a et of tree applied at different time i thu the ummation of the creep effect of each tre. We demontrate the technique and the conequence for load reditribution and increaing deformation in tructure through the example of an axially loaded maonry column and a beam ubjected to pure bending. We alo demontrate the effect of damage of maonry on tre reditribution. A wall ubjected to both axial and bending load could be analyzed imilarly. The complexity of the analyi can be increaed by including platicity contitutive equation a in [15] or by adopting variable adaptive time-tepping when damage i conidered, a recommended by [19]. At the end of the chapter we introduce the concept of uing Artificial Neural Network (ANN) to predict creep effect, a they can be ubtantially more accurate than explicit equation that bet fit with regreion to experimental data. 4.3 Cae 1: An axially loaded column Creep model Conider a concentric axial load P applied to a ymmetric column made of two material A and B each ymmetrically ditributed about the column axi. Effect due to eccentricity can therefore be neglected. The two material have different time-dependent propertie. The two material have cro-ectional area: A A being that of material A and A B that of material B. Equilibrium require: A A A + A B B = P (4.1) where P i the applied concentric axial load and A and B are the tree in material A and B, repectively. Compatibility require the axial train ε in the column and each repective material i the ame e = e A = e B (4.2) Next we aume that each material creep uch that the creep can be expreed a a compliance function in time, where D A and D B are the compliance of material A and B, repectively. Thi creep function (eqn (4.3)) i hown in Fig t A ea() t = DA() t A = DAf AA 1 e t (4.3) The creep train e A (t) i obtained by imply multiplying the time-dependent creep coefficient, (f A (t)), by the initial train a in eqn (4.3). f A i the creep coefficient for infinite time. The time contant t A denote the time when 63% of the creep ha occurred. Material B i aumed to creep with a mathematical form

4 86 Learning from Failure Aymptotic for t = f A A D A ε A A D A t A Time (t) Figure 4.1: The imple creep function. imilar to material A, but with D B, f B (t) and t B repreenting it compliance, creep coefficient, and the 63% creep time, repectively. Other formulation of the creep function a uggeted by other reearcher [e.g. 11, 12, 20, 21] can be employed in lieu of eqn (4.3) and will have a light effect in the overall concluion. Uing the equilibrium and compatibility conideration above, the initial tree in the two material are: DP B A = AD + AD B A A B DAP B = AD + AD B A A B (4.4) (4.5) Since both material are treed, both will want to creep. We therefore permit a mall increment in time to occur from t = 0 to t = t 1. In thi firt time increment, material A will want to creep an amount of train Δe cra a preented in eqn (4.6). t1 ta Δ ecra (1) = Af ADA 1 e (4.6) Material B will alo have a creep increment of imilar form. However, the increment in creep train will be different. Hence, compatibility will be violated. In order to retore compatibility, the material that want to creep more will have it tre reduced by the one that want to creep le, while the latter will have it train increaed by the former. Compatibility therefore require: Δe cra (1) + Δ A (1)D A = Δe crb (1) + Δ B (1)D B (4.7) where the Δ are the incremental change in tre. Since there i no increae in the overall axial force, equilibrium require: Δ A (1)A A + Δ B (1)A B = 0 (4.8)

5 The incremental tre change are therefore Effect of Creep on New Maonry Structure 87 AB( ΔecrA(1) ΔecrB(1)) Δ A (1) = AD + AD A Δ (1) = B B A A B ( Δe (1) Δe (1)) AD + AD A cra crb B A A B The tre in A (and imilarly in B) at the end of the firt time tep i therefore (4.9) (4.10) A (1) = A + Δ A (1) (4.11) The material, however, want to continue to creep. We therefore invoke uperpoition ince we have made the material linear vicoelatic. The amount of creep train that material A would like to creep in the econd time tep can therefore be expreed a: t1 t2 ta ta Δ ecra (2) = A fa DA e e ( t2 t1) ta +ΔA(1) f ADA 1 e (4.12) The pecific creep (creep train per unit tre) curve for the different tre increment are the ame; they jut tart at each time tep, a hown in Fig Aume c 1 i the pecific creep that material A would like to creep in time tep 1 due to the initial tre. c 1 i alo the pecific creep for the tre increment Δ A (4.1) between time t 1 and t 2, wherea the influence of the initial tre in that time interval will be c 2. When multiplied by their repective tree, the influence are imply added. Equilibrium and compatibility can be enforced again and the third tep conidered. Thi lead to the formula for the (nth) time tep where (n 2). tn 1 ta Δ ecra ( n) = A fa DA e e tn ta n ( tn 1 ti 1) ( tn ti 1) ta ta + ΔA( i 1) f ADA e e (4.13) i = 2 with the tre in material A at the end of the nth time tep being ( n) = + Δ ( i) (4.14) A A A i= 1 With a imilar equation for material B, the total train i e ( n) = e + Δ e () i + D Δ () i n n n A A cran A n (4.15) i= 1 i= 1

6 88 Learning from Failure Figure 4.2: The pecific creep for the different tre increment. Example Conider, for example, a blockwork column (A) filled with grout (B). We conider the following value for the following parameter: A A = 0.6A total, A B = 0.4A total, D A = 1/15 GPa 1, D B = 1/22 GPa 1, f A = 5.0, f B = 2.5, t A = 500 day and t B = 1000 day. The blockwork i modeled to creep more and in a relatively horter time than the grout. The reult in Fig. 4.3 how the tre change in both the blockwork and the grout over time. Baed on their relative tiffnee, the initial tre in the blockwork i 12.6 MPa while that in the grout i 18.5 MPa. A the blockwork want to creep fater than the grout, the blockwork initially offload to the grout. However, a the grout creep more than the blockwork at later age, the blockwork will be re-treed and the grout tre will be reduced during thi phae. The effective modulu method [1, 22] i applied to etimate the final tre in the blockwork uing eqn (4.16): A ( ) = AD DB(1 + fb) (1 + f ) + AD(1 + f ) B A A A B B (4.16) The final tre in the grout can be evaluated imilarly. Final tree of 9.3 and 23.5 N/mm 2 are determined for the blockwork and grout, repectively. Similar tree are attained uing the tep-by-tep analyi (Fig. 4.3). However, a deigner uing the effective modulu method will only detect that creep of the two material will reult in the grout tre riing by 25%, while in reality the grout will be overtreed by 36% from the initial value during an intermediate time period. The model preented here doe not include the poibility that the material in which the tre rie (here the grout) might be damaged (degraded) during the overloading period. Typically, a a quai-brittle material, the grout might be cracked during the overloading, reducing it tiffne. The tre ditribution would therefore be

7 Effect of Creep on New Maonry Structure 89 Figure 4.3: Stre development in blockwork and grout due to creep (Cae 1). changed from what i hown here and the blockwork re-treed to a level higher than hown in Fig The example alo demontrate that the initial and final tre tate are not the extreme. Higher tree occur at intermediate tage Effect of coupling creep and damage in concentrically loaded column Another intereting effect that i difficult to correlate i the coupling of creep and damage. A mentioned, model are being developed for tenile creep and fatigue [3, 4], but there are other mechanim which can induce damage. External deterioration can begin on the urface of maonry from action like freeze-thaw or weathering. Mirza [23] for example, dicued how the reitance of a member in the context of limit tate deign can decline with time after contruction. Valluzzi et al. [24] and Bažant [25] preented method to account for thi coupling effect in finite element modeling of hitorical maonry. Variou damage model are decribed in the literature [26 28]. We have choen a imple model a our objective i to how what can happen, rather than to develop a model for a particular cae or material. We conider the analyi above but we alo introduce a

8 90 Learning from Failure damage model to account for the effect of damage in one material of the column and couple it with creep. Damage i aumed to accumulate in the form n t h t DM( t) = t t (4.17) i= tdtart DM DM t D i the damage time contant which refer to the time where mot damage would occur. The coefficient are taken here a t D = 800, h = 0.3, and n = 10. DM(t) repreent the level of damage accumulated from the time at which damage tart, t Dtart, to the time of evaluation t. In the calculation here, damage i aumed to begin at 400 day. The rate of damage accumulation with thi model i low initially, but accelerate over time, a hown in Fig For the ake of howing the trend and effect, quite coniderable damage i aumed to occur in a relatively hort time in thi example. Following [26] and [29], the modulu of the material change over time with thi model a E A (t) = (1 DM(t))E A (t Dtart ) (4.18) where E A (t Dtart ) i the material tiffne at the time when the damage begin. When DM i zero, there i no damage and when DM equal 1, the material i unable to bear any load. Figure 4.4: The damage model howing the non-linear change of damage ratio with time. Here the blockwork will have a damage factor of about 0.33 after 1000 day with the damage tarting at 400 day. Damage initially accumulate at a very low rate but then increae rapidly.

9 Effect of Creep on New Maonry Structure 91 The effect of combined creep and damage on the Young moduli of both material i hown in Fig. 4.5, while the tree variation with time are hown in Fig Thee tree are different to thoe in Fig. 4.3 in that they begin to change quite rapidly at later age, a the damage accumulate in the outer blockwork, cauing reditribution to the tiffer, undamaged grout. It thu become poible that the grout could now begin to fail, leading to collape of the whole tructure in time. Thi problem ha been analyzed further elewhere [30], with conideration of everal poible combination of creep and damage Examining the effect of rehabilitation Much effort ha been pent on rehabilitating and trengthening tructure, both of hitoric and of imply practical value. Fiber reinforced polymer have been ued on variou occaion a they offer ditinct advantage over teel in term of being light weight and thu adding little ma to a tructure, and highly durable if protected from unlight. Some FRP creep while other do not, unle the tre i a Figure 4.5: The change in effective moduli of the two material with time due to combined creep and damage. Note the change of the lope of tiffne reduction of the blockwork due to the combined effect of creep and damage after 400 day of age while the lope of grout tiffne reduction due to creep only i almot contant after 400 day.

10 92 Learning from Failure Figure 4.6: The change in tre in the two material over time with creep and damage. very high proportion of ultimate [18, 31]. Thu when an FRP i ued to trengthen a tructure, the longer term conequence hould be evaluated. If the tructure i hitoric, creep may well have ubtantially run it coure for the current loading. However, if the FRP i pretreed or change the tree in the tructure in ome other way then creep will tart anew. Eentially a new tructure ha been created and the conequence of time-dependent effect need to be evaluated. One potential effect that need to be conidered i the reduction in load carried by the FRP from flow of the bonding epoxy from the hear that tranfer load between the FRP and the underlying ubtrate. For example, if an FRP trip i applied to a tructure to help carry a dead load, or i applied pretenioned to counteract a dead load, then there i the potential for the bonding epoxy to flow [32]. The FRP trip offload over time. The effect i demontrated with the next problem. Rigid mechanical anchorage of the trip would be required to avoid the conequence hown. 4.4 Cae 2: Compoite tructural element ubject to bending Development of model Conider a reinforced concrete beam where a layer of external reinforcement i bonded to the bottom of the beam a hown in Fig The external reinforcement

11 Effect of Creep on New Maonry Structure 93 Figure 4.7: Schematic repreentation of a reinforced concrete beam cro-ection with one layer of teel reinforcement and externally applied FRP. i added to the model uch that the model i general and the effect of any externally applied trengthening material can be conidered. We conider the cae of pure bending for implicity. Pretreing or axial dead load can be included. Again, for implicity, we have aumed there i no compreion reinforcement. Strain compatibility, with plane ection remaining plane, give e d kd kd = ec e 1 k k = ec h kd ef = ec kd (4.19) (4.20) (4.21) where kd i the depth of the neutral axi. Force equilibrium require Moment equilibrium require Tf + T C = 0 (4.22) 1 Aff + A bkdc = 0 (4.23) 2 kd kd T d + Tf h = M 3 3 kd kd A d = M Aff h 3 3 (4.24) (4.25)

12 94 Learning from Failure Solving the equation provide E 1 k 1 A bkd = A c c f f E c k 2 c = and from the moment equation Thu at t = 0 (no creep) A f 1 E 1 k bkd A 2 E c k 3 k E 1 k kd Ad = M A h 3 3 c f f E c k E h kd = kd f f c Ec f (4.26) (4.27) (4.28) (4.29) f c h kd Af = = kd 1 E 1 kd 2 bkd A E c k leaving the following equation to be olved for k: Ebd c k + dae ( + AE f f) k ( AEh f f + AEd ) = 0 2 Thu the initial tree in the concrete, FRP, and teel are v = Ad k E c k (4.30) (4.31) M ci = (4.32) v 3 k E 1 k kd 1 E 1 k + h bkd A 3 2 E c k E h kd = kd f fi ci Ec Now, for t > 0, the concrete creep and E k = 1 i ci Ec k i Ec() t Ec i (4.33) (4.34) (4.35) e = (4.36) e() t

13 Effect of Creep on New Maonry Structure 95 Further, we need to olve for k a a function of f a f will reduce with time Ad 3 k E 1 k A f f 3 Ec ( t) k 1 E 1 k 2 bkd A E c ( t ) k kd = M Aff h 3 (4.37) kd 1 E 1 k E 1 k Af f h bkd A Ad 3 2 Ec() t k Ec() t k 1 E 1 k = M bkd A 2 E c ( t ) k (4.38) E ( Affdbk ) + 3 bdm ( Affhk ) + 6 A ( M Aff( h d)) k Ec () t E 6 A ( M A ( h d)) = 0 (4.39) f f Ec () t We let the FRP tre decline with time a the epoxy creep (flow) under the hear it i tranmitting. We conider a imple claical formula to repreent FRP tre relaxation due to binding matrix creep [33]. At the end of the firt time tep, the tre in the FRP i a a t1 tr f (1) = fi + (1 )e (4.40) e = (4.41) i Ec(1) Ec i e( t1) Equation (4.39) i olved for k (1) and thi value i ubtituted into eqn (4.27) for c (1) e (1) c c (1) = (4.42) Ec (1) h k (1) d k (1) d Δ ef = ec (1) E h k (1) d Δ (1) = ( (1) ) E (1) k (1) d f f c ci c f f f (4.43) (4.44) (1) = (1) +Δ (1) (4.45)

14 96 Learning from Failure With the increment in concrete tre, force and moment equilibrium are checked. If equilibrium i not obtained, we reiterate the calculation of k. After k ha been computed, c (1) i calculated from eqn (4.27) for the nth tep Δ = (1) i (4.46) Δ = (4.47) c1 c c f1 fi (1) f t n n 1 tn ti t n t f ( n) = f i a+ (1 a)e + Δ f i a+ ( 1 a) e (4.48) i= 1 tn n 1 tn t i t Δ n ci t ec ( n) = e 1+ f 1 e + 1+ f 1 e (4.49) i= 1 Ec ( ti ) e = (4.50) e( n) i Ec( n) Ec i The cracked beam curvature at any ection j along the beam at any time t denoted Ψ 2j (t) can be computed a Ψ Mi 2j () t = E ()I t () t (4.51) where I tj (t) i the tranformed cracked moment of inertia at the jth ection at time t, computed a [ () ] 3 bktd E tj () = + () 3 Ec ( t) E () t + c tj [ () ] f Af h k t d Ec () t [ ] I t A d k t d 2 2 (4.52) The uncracked beam curvature at any ection along the beam at time t denoted Ψ 1j (t) can be computed a Ψ M j 1j () t = E ()I t () t (4.53) Given the effect of tenion-tiffening on beam deflection, an effective curvature can be determined by interpolating between the cracked and uncracked ection curvature uing the moment-curvature approach recommended by the CEB-FIP [34] and Ghali and Favre [1] a ej j2 j1 c gj Ψ () t = xψ () t + (1 x) Ψ () t (4.54) where x i the tenion tiffening coefficient that can be determined uing the CEB- FIP [34] method. Here the tenion tiffening coefficient x wa determined uch

15 Effect of Creep on New Maonry Structure 97 that the error between the experimentally meaured (Section 4.4.2) and model predicted mid-pan deflection i a minimum. The mid-pan deflection of the beam Δ mid (t) can be predicted by integrating the curvature along the pan (S) or etimated approximately by conidering the geometrical relation uing three ection at the end and at mid-pan a 2 S Δ mid () t = ( Ψ left () t + 10 Ψ emid () t +Ψ right ()) t (4.55) 96 where Ψ left and Ψ right can be aumed to be equal to zero a no end curvature due to retrained hrinkage i expected to occur and Ψ emid (t) i the mid-pan curvature computed a in eqn (4.54) Application to a beam The model i now applied to reinforced concrete beam with the dimenion hown in Fig. 4.8 and loaded a hown in Fig The material and load propertie, including the concrete creep are taken a lited in Table 4.1. Two beam were teted. Both beam have imilar propertie (cat from the ame concrete batch, at the ame time and cured in a imilar way) one without FRP trengthening trip and one with FRP trengthening trip. The cro-ection of the FRP trengthened beam i hown in Fig Figure 4.8: Cro-ection dimenion of the concrete beam reinforced with one layer of teel reinforcement and externally applied FRP. Figure 4.9: Schematic repreentation of the beam loading et-up.

16 98 Learning from Failure For the beam without FRP trengthening, the predicted increae in deflection at the center of the beam i compared with experimental data (preented in [35, 36]) in Fig It can be oberved in Fig that the model wa capable of predicting the creep deflection of the beam fairly well at early and late time. It i worth mentioning thi prediction i achieved uing the creep propertie lited in Table 4.1 and by adjuting the tenion tiffening coefficient to reduce the model error. A tenion tiffening coefficient x = 0.9 i needed. Thi high coefficient indicate that the ection will be very cloe to fully cracked in thi cae (x = 1.0 indicate fully cracked ection). In fact, the beam ha numerou flexural crack. Now, if we conider the beam trengthened with the FRP trip to have imilar material propertie, and aume that the only time-dependent effect i the concrete creep, we get the reult Table 4.1: Material propertie of reinforced concrete beam. Concrete compreive trength (MPa) 34.3 Concrete initial modulu of elaticity (GPa) 21.1 Reinforcing teel modulu of elaticity (GPa) 200 CFRP modulu of elaticity (GPa) 165 Concrete creep coefficient f (t, t 0 ) 4.2 Concrete ultimate creep time t c (day) 2000 Figure 4.10: Predicted veru experimentally meaured deflection of reinforced concrete beam including creep effect (Beam 1: no FRP i ued).

17 Effect of Creep on New Maonry Structure 99 Figure 4.11: Predicted veru experimentally meaured deflection of reinforced concrete beam (Beam 2: FRP i ued) including creep effect only. Tenion tiffening coefficient imilar to that of Beam 1 i ued (x = 0.9). hown in Fig It i obviou that the predicted mid-pan deflection doe not meet the meaured mid-pan deflection. The ignificant difference between the meaured and predicted deflection in Fig can be attributed to two factor: the tenion-tiffening effect and the effect of the creep of the epoxy binding matrix. A intalling the FRP trip increaed the cracking capacity of the beam, a lower tenion tiffening coefficient (repreenting a cracked ection) i required compared to that ued in computing the mid-pan deflection of the untrengthened beam. Changing the tenion-tiffening coefficient in the cae with FRP we obtain the curve hown in Fig It can be oberved that predicted deflection in thi curve i cloely related to the experimentally meaured one. The deflection predicted in Fig aume no FRP binder creep ha occurred (a = 1.0). If relaxation of tre in the FRP trip due to the creep in the epoxy binding the FRP trip to the concrete (a = 0.9 and t = 600 day) i included, we get Fig While higher creep coefficient of epoxy at the concrete FRP interface might be aumed, recent experimental invetigation howed that creep of epoxy at the concrete FRP interface would reult in little but fat tre lo in the FRP heet [37]. Therefore the reduction of FRP tre in the analyi preented here due to creep of epoxy wa limited to 90% of the original tre. Figure 4.12 and 4.13 look very imilar, but it i mileading to judge the effect of FRP binder creep from thee time-deflection diagram. Thi i becaue the ection i cloe to uncracked and the influence of FRP tre-relaxation on the

18 100 Learning from Failure Figure 4.12: Predicted veru experimentally meaured deflection of reinforced concrete beam (Beam 2: FRP i ued) including creep effect of concrete and no FRP tre relaxation effect (a = 1.0) and tenion tiffening effect (x = 0.27). Figure 4.13: Predicted veru experimentally meaured deflection of reinforced concrete beam (Beam 2: FRP i ued) including creep of concrete effect, FRP tre relaxation effect (a = 0.9 and t = 600 day) and tenion tiffening effect (x = 0.27). tranformed ection propertie i not reflected in the change in beam deflection. The influence of changing the FRP tre-relaxation coefficient from no relaxation (Cae 1: a = 1.0) to ignificant relaxation (Cae 2: a = 0.9) on the tranformed inertia i hown in Fig

19 Effect of Creep on New Maonry Structure 101 Figure 4.14: Change in tranformed cracked moment of inertia of the FRP trengthened beam with two cae: one with no FRP tre relaxation (Cae 1: a = 1.0) and the other with FRP tre relaxation (Cae 2: a = 0.9). Both cae include tenion tiffening effect (x = 0.27). The reult hown in Fig demontrate the fact that the tranformed cracked ection inertia reduce due to FRP tre relaxation. Thi reduction would reult in a coniderable change in the beam deflection if the beam wa cracked, particularly if the beam were cracked prior to the application of the FRP trengthening trip. Thi change (although happening) did not affect the beam deflection in the cae tudy becaue the beam wa uncracked and thu it deflection i dominated by the uncracked ection inertia. The tep-by-tep in time analyi alo allow the change in the tre in the concrete top fiber, the reinforcing teel bar, and the FRP trip to be followed. Exemplar reult for the change in the concrete tree i hown in Fig The tree hown in the Fig are baed on the FRP tre decreaing due to creep of the epoxy at the FRP concrete interface. With the current model, we force thi reduction in tre through our impoition of relaxation in the FRP. However, uch a reduction i likely not to be correct over the full time domain if the concrete creep extenively, a would occur if the concrete were young. Such creep will increae the curvature of the beam reulting in increaing tre in the FRP after the initial decreae. Thi iue repreent a modeling challenge becaue the concrete and epoxy have different rate of creep. Creep in the epoxy occur in a coniderably horter time compared with that of creep in concrete. Therefore, the analyi above can be ued to model the beam deflection and to give a reaonable etimate of the tree in the concrete but not in the teel or the FRP. The mall

20 102 Learning from Failure Figure 4.15: Change of concrete top fiber tree with time due to combined concrete creep and FRP tre relaxation (a = 0.9 and t = 600 day). Figure 4.16: Change of tree in FRP trip with time due to creep of epoxy at the concrete FRP interface (a = 0.9 and t = 600 day) while creep of concrete i neglected. effect on the accuracy of the concrete tree in thi example i related to the relatively mall change in the FRP tre over the entire analyi time due to tre relaxation (only 3%) given the geometry of the beam analyzed and the relaxation parameter conidered (a = 0.9 and t = 600 day). If the creep of concrete i minimal, a would be the cae in trengthening an old concrete beam under it own weight, then the FRP tre would be accurately etimated from the above analyi a hown in Fig

21 Effect of Creep on New Maonry Structure Maonry wall ubject to axial load and bending Maonry wall are typically ubject to both axial load (example 1) and bending (example 2). Hence to olve for the effect of creep for uch loading, it i neceary to combine the two example above, invoking the need for equilibrium and compatibility in the proce. The equation for thi ituation are being developed. The conequence are well known, in that out-of-plane deformation of the wall will increae, jut a the central deflection of the concrete beam in example 2. The tre on the inide curve of the wall will increae while that on the outide will decreae. Two poible long-term conequence are that failure by cracking or cruhing may develop on the inner curve of the wall, or the wall may buckle. The ituation which hould be carefully analyzed i one where a cracked wall, vault, or beam i trengthened in itu, and the load increaed. The FRP i likely to off-load itelf over time if not anchored mechanically (The FRP trip in the beam a above were anchored with U-haped FRP heet). 4.5 New mathematical approache to modeling creep The above analyi demontrated the importance of conidering time-dependent analyi in evaluating erviceability of maonry tructure. It alo howed the importance of predicting creep with a good accuracy. Here we preent finding of recent reearch effort to enhance the accuracy of predicting creep uing mean of artificial intelligence. The inpiration for ANN came from the deire to produce artificial ytem capable of performing ophiticated (or perhap intelligent) computation that mimic the routine performance of the human brain. Artificial neural network are network of many imple proceor (neuron) operating in parallel, each poibly having a mall amount of local memory. Artificial neural network reemble the brain in two repect: firt, knowledge i acquired by the network through a learning proce and econd, the interneuron connection weight are ued to tore the knowledge [38, 39]. No cloed-form olution for the problem i provided by ANN. However, ANN offer a complex, accurate olution baed on a repreentative et of hitorical example of the relationhip [38]. The unit (neuron) are connected by weighted channel which are adjuted on the bai of learning data. Artificial neural network learn from example (of known input/output equence) and exhibit ome capability for generalization beyond the training data. Artificial neural network normally have great potential for parallelim, ince the computation of the component are largely independent of each other [39, 40]. The creep deformation of maonry prim ubjected to different tre level, repreenting approximately (12, 24, 36, and 48%) of the prim compreive trength, repectively, and expoed to different environmental condition [12] were ued to develop and ae the ANN model. A erie of unloaded prim ubjected to environmental condition imilar to their counterpart loaded prim wa alo meaured at the ame time interval to account for hrinkage and

22 104 Learning from Failure Predicted J(t,t 0) x 10-6 (1/MPa) Predicted J(t,t 0) x 10-6 (1/MPa) (a) Meaured J(t,t 0) x 10-6 (1/MPa) Meaured J(t,t 0) x 10-6 (1/MPa) (b) 15% RTN1 50% GERBER Figure 4.17: Prediction of creep compliance uing (a) an ANN model [41] and (b) a regreion analyi (modified Burger) model [12]. thermal change. Tet reult from fourteen teting group were included in training of the network. A erie of multi-layer ANN for predicting creep performance of maonry tructure wa developed [41, 42]. The creep prediction neural network conit of an input layer, one hidden layer, and an output layer. The network utilize a log-igmoid tranfer function and a linear output function. A backpropagation training algorithm wa ued a the learning rule for the network. A learning matrix including 47 training ample drawn from the 14 teting group wa ued in training the network. The Leveneberg- Marquardt training criterion [42] wa utilized during the learning proce of the network with a training goal of achieving a mean quare error of The network wa then teted againt group of data that had not been ued in training the network. The creep compliance wa computed by the network and the output of the network wa compared to the meaured creep compliance. A comparion between the creep compliance prediction uing ANN and a claical model baed on regreion analyi [12] i hown in Fig While the ANN prediction lie within 15% accuracy, regreion analyi prediction lie within only 50% accuracy. Reearch invetigation howed that ANN accuracy can be further enhanced by optimizing the network architecture [42] and by conidering timedelaying effect in the model [43]. 4.6 Dicuion The tep-by-tep in time technique demontrated here allow tree at intermediate tage to be calculated. However, creep in maonry i a function of the age at loading and the environment [4], o more complex analye will be needed to imulate reality. The tep-by-tep method can be ued with the pecific creep a the input [44] and aging function can be expreed in integral form [1, 21]. Shrinkage and thermal effect can alo be included. However, the number of factor that affect

23 Effect of Creep on New Maonry Structure 105 maonry creep (age of loading, environment, unit type, mortar type, and tre level) ugget that creep for a particular tructure will be very difficult to predict. Few data are available, particularly, long-term data. In thee circumtance, method uing mean of artificial intelligence (e.g. ANN) which can deal with high level of tochatic variation may prove ueful in predicting both the creep and the range of poible outcome from time-dependent effect. It become obviou that uing mean of artificial intelligence in modeling creep have two advantage over claical model, firt: it allow incorporating a large number of interdependent factor that affect creep without adding further complexity. Second, it provide a ytematic approach for model improvement a new data become available. 4.7 Concluion The tep-by-tep in time analyi i a powerful tool to invetigate the change of the tree due to creep over a large time range. Stree in a material can rie and fall due to the effect of creep (or fall then rie). Although the effective modulu method uing the final creep coefficient can accurately etimate the final tree in the component of a compoite material (e.g. maonry) due to creep, the method may not predict intermediate peak tree accurately: one need to know when they will occur. Rehabilitation with FRP may introduce additional creep mechanim with undeirable effect. Particularly, FRP trip may unload a part of any additional dead load applied to a tructure after trengthening. Adequate anchorage mut be deigned. The ue of the tep-by-tep time-dependent analyi in creep tre reditribution can be made more accurate by incorporating ANN where all factor affecting creep deformation can be included in the modeling proce. Reference [1] Ghali, A. & Favre, R., Concrete Structure: Stree and Deformation, 2nd edn, E&FN Spon: London, [2] Binda, L., Gatti, G., Mangano, G., Poggi, C. & Sacchi Landriani, G., The collape of the civic tower of Pavia: a urvey of the material and tructure. Maonry International, 6(1), pp , [3] Shenoi, R.A., Allen, H.G. & Clark, S.D., Cyclic creep and creep-fatigue interaction in andwich beam. Journal of Strain Analyi, 32(1), 1 18, [4] Oh, Y.J., Nam, S.W. & Hong, J.H., A model for creep-fatigue interaction in term of crack-tip tre relaxation. Metallurgical and Material Tranaction A, 31(7), pp , [5] Wang, E.Z. & Shrive, N.G., Brittle fracture in compreion: mechanim, model and criteria. Engineering Fracture Mechanic, 52(6), pp , 1995.

24 106 Learning from Failure [6] De Bort, Feentra, P.H., Pamin, J. & Sluy, L.J., Some current iue in computational mechanic of concrete. Computational Modelling of Concrete Structure, ed H. Mang et al., Pineridge Pre: Sanea, UK, pp , [7] Wu, Z.S. & Bažant, Z.P., Finite element modelling of rate effect in concrete fracture with influence of creep. Creep and Shrinkage of Concrete, ed Z.P. Bažant et al., E. & FN Spon: London, pp , [8] van Zijl, G.P.A.G., de Brot, R. & Rot, J.G., The role of crack rate dependence in the long-term behaviour of cementitiou material. International Journal of Solid and Structure. 38, pp , [9] Binda, L., Saii, A., Meina, S. & Tringali, S., Mechanical damage due to long term behaviour of multiple leaf pillar in Sicilian churche, Proc. Hitorical Contruction, ed Lourenco & Roca, Guimarae, Portugal, pp , [10] Lenczner, D., Creep in model brickwork. Proceeding of Deigning Engineering and Contruction with Maonry Product, ed. F.B. Johnton, Houton, USA, pp , [11] Lenczner, D., Creep in brickwork pier. Structural Engineer, 52(3), pp , [12] Shrive, N.G., Sayed-Ahmed, E.Y. & Tilleman, D., Creep analyi of clay maonry aemblage. Canadian Journal of Civil Engineering, 24(3), pp , [13] Brook, J.J. & Abdullah, C.S., Compoite modelling of the geometry influence on creep and hrinkage of calcium ilicate brickwork, Proc. of the Britih Maonry Society, No. 4, pp , [14] Ameny, P., Jeop, E.L. & Loov, R.E., Strength, elatic and creep propertie of concrete maonry. Int. Journal of Maonry Contruction, 1(1), pp , [15] Van Zijl, G.P.A.G., A Numerical Formulation for Maonry Creep, Shrinkage and Cracking, Serie 11, Engineering Mechanim 01, Delft Univ. Pre: The Netherland, [16] CSA, Maonry Code. Maonry Deign for building (limit tate deign) tructure (deign). CSA-S , Canada, Ontario, [17] SAA, Maonry in Building. Reviion of Autralian Standard-SAA-AS 3700/1988. Standard Aociation of Autralia, Sydney, Autralia, [18] Scott, D.W., Lai, J.S. & Zureick, A.H., Creep behaviour of fibre reinforced polymer compoite: a review of technical literature. Journal of Reinforced Platic Compoite, 1(6), p. 588, [19] Van den Boogaard, A.H., De Bort, R. & Van den Bogert, P.A.J., An adaptive time-tepping algorithm for quaitatic procee. Communication in Numerical Method in Engineering, 10, pp , [20] Harvey, R.J. & Hughe, T.G., On the repreentation of maonry creep by rheological analogy. Proceeding of the ASCE Structural Congre Retructuring: America and Beyond. 1, pp , [21] Neville, A.M., Dilger, W.H. & Brook, J.J., Creep of Plain and Structural Concrete, Contruction Pre: UK, 1983.

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26 108 Learning from Failure [38] Haykin, S., Neural Network: A Comprehenive Foundation, Prentice Hall: New York, [39] Luger, G., Artifi cial Intelligence: Structure and Strategie for Complex Problem Solving, 5th edn, USA: Addion Weley, [40] Toukala, L.H. & Uhrig, R.E.. Fuzzy and Neural Approache in Engineering, Wiley: New York, USA, [41] Reda Taha, M.M., Noureldin, A., El-Sheimy, N. & Shrive, N.G., Artificial neural network to predict creep with an example application to tructural maonry. Canadian Journal of Civil Engineering, 30(3), pp , [42] Reda Taha, M.M., Noureldin, A., El-Sheimy, N. & Shrive, N.G., Feedforward neural network for modelling time-dependent creep deformation in maonry tructure. Proc. of the Intitution of Civil Engineer, Structure in Building, UK, 157(SB4), pp , [43] El-Shafie, A., Noureldin, A. & Reda Taha, M.M., On invetigating recurrent neural network for predicting maonry creep, Proceeding of Third International Conference on Contruction Material: (CONMAT 05), Vancouver, Canada, ed Banthia et al., Augut 2005 [CD-ROM]. [44] Shrive, N.G. & England, G.L., Elatic, creep and hrinkage behaviour of maonry. International Journal of Maonry Contruction, 1(3), pp , 1981.