Concrete Damage under Fatigue Loading in Uniaxial Compression

Size: px

Start display at page:

Download "Concrete Damage under Fatigue Loading in Uniaxial Compression"

Simon Bridges
5 years ago
Views:

1 ACI MATERIALS JOURNAL TECHNICAL PAPER Title No. 114-M21 Conrete Damage under Fatigue Loading in Uniaxial Compression by Benard Isojeh, Maria El-Zeghayar, and Frank J. Vehio Despite rigorous efforts in the derivation of various fatigue damage still limited to loading onditions similar to those of the experiments used for developing the models. Most models are void of salient fators affeting the fatigue behavior of onrete suh as further investigation is required. onrete strength and fatigue seant modulus using experimental into the damage funtion result in robust models that aount for variations in loading parameters. Keywords: ompressive strength; damage; fatigue; fatigue seant modulus; residual onrete strength; strain evolution; variable loading. INTRODUCTION During fatigue loading, the properties of onrete undergo alterations that result in damage. The progressive damage of a onrete element an be observed from the evolution of various deformation parameters, suh as total strain, residual strain, stiffness degradation, strength degradation, heat dissipation due to mirorak, rak growth, and speed of sound in onrete. 1,2 Based on previous investigations on the fatigue behavior of onrete, the damage evolution for eah parameter is nonlinear. 3-7 fators, unlike the fatigue behavior of steel reinforing bars. 8 Murdok and Kesler, 9 Hilsdoft and Kesler, and Oh 12 have shown that the inrease in maximum fatigue stress a higher minimum stress level orresponds to an inrease Hulsbos 13 of loading inreases. of the fatigue life will our if a fatigue model developed - Brenner, 14 Spark and Menzies, Holmen, 17 Naik et al., 18 and Zhang et al. 19 all indiate that the ACI Materials Journal/Marh-April 2017 of loading dereases. This behavior has been observed to be more pronouned as the maximum fatigue stress level inreases. For higher fatigue stress levels, the behavior of to a redution in the fatigue life. 10 et al., 20 minute for stress levels of 0.8 and 0.9 (frations of average It has also been reported in the literature that the shape of stress levels equal to or greater than 0.8, or at maximum with a sinusoidal waveform will be about half of the number waveform under the same stress level. 2,21 The impat of stress reversal under fatigue loading was 19 on 171 beams with seven stress ratios, inluding negative stress ratios. The ratios were the onrete speimens as the stress ratio redued. The effets of other fators suh as the shape of the speimen, the water-ement ratio ( / tion, onrete strength, uring onditions, age at loading, and moisture onditions that affet onrete an be removed of onrete under stati load. 16,22-25 This onept redues prediting the behavior of onrete elements under fatigue load to the loading parameters alone. 2 The pereption of damage evolution of a material provides - ACI Materials Journal 225

2 mation an be orrelated. Obtaining the damage evolution for parameters suh as residual strength and seant stiffness imens To obtain the disrete test points, speimens are Due to the stohasti nature of onrete, the atual even under the same magnitude of fatigue load. Hene, the is inappropriate, and the orresponding models developed do not 15 Cornelissen and Reinhardt, 28 5 a orrelation exists rate an be obtained for eah speimen tested, the failure seant modulus at failure has been reported to onverge at 2,17 In a similar manner to the fatigue seant modulus, the strength of omposite materials also deteriorates under fatigue loading. Hene, it has been reported that the same damage evolution model an be used for residual strength and stiffness. 34 However, the initial stage of fatigue loading of onrete is 5,27,33,37 This phenomenon is attributed to the onsolidation or the losing up of mirovoids in onrete at the initial stage of fatigue loading. 29 the stohasti nature of onrete One strength damage initiates, an inrease in damage will lower ompressive strength. In this paper, the stress ratios for the experiments onduted are either equal to or greater than zero; hene, no fatigue stress reversal is onsidered. In addition, a sinusoidal waveform is used for all fatigue tests onduted. 37 model 19,38 are developed for onrete strength and residual fatigue seant modulus using data from tested speimens. Fig. 1 Fatigue loading setup. Table 1 Average ompressive strength and orresponding strain Bath (No. of ompressive orresponding strain Mixture ratio / :2:2 * :2:2 * :2:3 * :2:4 * 0.6 * Cement:sand:oarse aggregate. RESEARCH SIGNIFICANCE strain rate for obtaining fatigue life in the formulation of improved damage models for onrete in ompression. fatigue loading onditions for onrete strutures. The models proposed an be implemented into general onrete onstitutive models for prediting strength and stiffness deterioration EXPERIMENTAL INVESTIGATION quent residual strengths and fatigue seant moduli as the and fatigue modulus, eah speimen was tested to a different 10 3 generate a pulsating load of a ontinuous sinusoidal waveform throughout the test duration. Eah speimen was mounted with attahed linear variable displaement trans- Fig. 1. The LVDTs were used to measure average strains in the speimens throughout the duration of the fatigue tests. strength, as shown in Table 1. The stress levels (maximum perentages of the average ompressive strength. 226 ACI Materials Journal/Marh-April 2017

3 Table 2 Speimen fatigue parameters and test failure data Speimen Compressive strength f f N f logn f E , E , E E E E , E , H H I I I I I Table 3 Strength and seant modulus degradation test data Speimen Initial ompressive strength f loading Residual strength after stati (psi 10 3 E E9 430 E E E E E E H H H H H H H H H H * Failed before reahing maximum fatigue load applied. The maximum stress level, the onrete strength, and the tigation. Maximum stress levels of 0.69 to 0.80, as frations of the average ompressive strength, were used as the fatigue loads. Sixteen speimens were loaded to failure to observe the evolution of the maximum strain as indiated in Table 2, while 22 speimens, as indiated in Table 3, were loaded to ACI Materials Journal/Marh-April

Fig. 2 Conrete speimen in undamaged and damaged states. The 22 speimens tested were used to observe the evolution of strength and fatigue seant modulus of onrete. - the fourth bath.

4 Fig. 2 Conrete speimen in undamaged and damaged states. The 22 speimens tested were used to observe the evolution of strength and fatigue seant modulus of onrete. - the fourth bath. For all fatigue tests onduted, a onstant Test speimens The onrete speimens were made from portland ement - in Table 1, were ast using a mixture proportion of 1:2:2 ( /tions of 1:2:3 with a / of 0.5 and 1:2:4 with a / of 0.6 used was estimated to be 2.6. The slumps observed from the fresh onrete from all bathes were 100 to 150 mm (4 number added to eah alphabet in the table indiates the number assigned to the speimen before testing. Results at a dereasing rate was observed due to the losing up of onrete pores and miroraks between aggregates and was onstant while miroraks within the ement mortar inreased. Within the last stage of fatigue damage evolution, the miroraks merged to form maroraks. Similar to Fig. 3 Maximum strain evolution. parallel to the diretion of loading. Further, the ends of these maroraks merged and developed a failure plane that resembled a fault ( to failure were reorded for the 16 speimens tested and are given in Table 2. The standard deviations (in terms of the N f mean values are 3.86, 3.51, 4.36, and However, the standard deviation of the error (logn f - 19 is 0.26 and the Maximum strain evolution The strain evolutions for the 16 speimens tested to failure under fatigue loading were plotted against the normalized of the strain evolutions were similar, irrespetive of the onrete strength and stress level. The three stages of the strain evolution shown in Fig. 3 for the stress levels used are 2-7 to failure, indiates a nonlinear deformation of onrete at a dereasing rate. The seond stage is haraterized with a with an inreasing rate of damage leading to failure. This MODEL FORMULATION and fatigue modulus models involves the estimation of the expeted fatigue life for eah speimen, beause the applied is often not appropriate. This is due to the fat that the atual 228 ACI Materials Journal/Marh-April 2017

be higher or lower than the value estimated using an S-N Relationship between seondary strain rate and number of yles to failure se were all estimated, as illustrated in Fig. 4.

The oef- different loading parameters from different researhers were obtained and inluded in the plot, as shown in Fig. 6. 5,15,39 In are also required for orroboration. N f se 0.

5 be higher or lower than the value estimated using an S-N Relationship between seondary strain rate and number of yles to failure se were all estimated, as illustrated in Fig. 4. The logarithms of fatigue life (N f se ison of the model with other models in the literature. The oef- different loading parameters from different researhers were obtained and inluded in the plot, as shown in Fig. 6. 5,15,39 In are also required for orroboration. N f se ACI Materials Journal/Marh-April 2017 Fig. 7 Normalized residual strength against normalized for the 22 speimens to obtain a plot of the residual onrete strength against the orresponding normalized number of Fig. 7 and 8 well represented using the proposed model. f/f R N f R is the ratio of the minimum stress level to the maximum stress level. f to f of the onrete onsidered. On the other hand, the residual strength of onrete orresponds to the atual stress at whih a fatigue-damaged speimen will fail when loaded mono- of onrete due to fatigue loading, the residual strength 229

6 Fig. 8 Normalized residual strength against normalized strength in its undamaged state. Strength and stiffness degradation under fatigue loading During the initial stage of the fatigue loading, the residual strengths of the onrete speimens were observed to inrease. This observation has also been reported in the literature on fatigue tests of onrete speimens in ompression. imental data points, obvious strength degradation began estimating the stati and fatigue seant moduli of onrete (E and E se The fatigue seant modulus degradation began within the the residual strength degradation. The degradation of the normalized fatigue seant moduli is also shown in Fig. 10. Toward failure, an abrupt drop was observed in the residual fatigue moduli data points. σ E = E se max σ = σ Δε max v min σ ε Damage evolution model for onrete strength and fatigue seant modulus From the fundamentals of damage mehanis, the rate of 37 the min δd (,, ) exp δn FN fd k sδf K = Δ = 1 N f Fig. 10 Degradation of residual fatigue seant modulus. N, D = k D = D r. D r 1 = k 1 K + 1 sδf N exp f ( K + 1) K + 1 sδf ( N f ) exp f ( K + 1) Δf Dr K K N f f = 1 ( + 1) + 1 ln ln s k s 1-8,38 affeting the fatigue behavior of onrete, was implemented. 230 ACI Materials Journal/Marh-April 2017

7 where Δf Cf R N f N ft f = [ 1 β ( 1 ) log 2 γ2 log( ζ )] 2 = R 2 = ,38 C f aounts for the 2 is a onstant that aounts for high stress level. Δf Cf N ft Cf R N f f = [ 1 γ log( )] ( ( 1 2 ζ β2 )) ln where logn f = 0.434lnN f. Fig. 11 Estimation of damage parameter s. ( K + 1) = Cf ( β2( 1 R)) s K + 1 = 0.434sC f 2 (1 R C f 1 Dr ( K + 1) ( 1 γ2 log( ζn ft)) = ln s k k1 Dr exp( scf ( 1 γ2 log( ζn f T)) = K then Δf v D = Dr exp s u N f u = C f 2 N f v = 0.434sC f 2 (1 R From Zhang et al. 19 C f = ab logf + ACI Materials Journal/Marh-April 2017 where a, b, and and f The residual strength of onrete and modulus damage at a given stress level an be obtained using the damage model. of the onstants K and k 1. - From alibration using the tests data, the values of the parameter s Fig. 12 Normalized onrete strength degradation model. and modulus damage an be obtained from Fig. 11. From the experiments onduted, the degraded fatigue modulus tends 2,17 ritial damage value D r for the onrete fatigue seant data in Fig. 12, the residual strength of onrete at failure tends toward 0.65; hene, the damage value for the residual strength of onrete is taken as modulus alongside other residual onrete strength models in the literature 29,33,34,40 were plotted. The residual strength models are shown in Fig. 12. The proposed damage evolution model plot mathes well with the Shaff et al. 33 residual strength damage plot. However, toward failure, there is is assumed in Shaff et al. 33 that failure will our at the point where the onrete strength degrades to the maximum fatigue stress applied. On the other hand, the proposed model assumes that failure will our at a ritial damage value based on the experimental observations. Figure

8 Fig. 13 Normalized fatigue seant modulus degradation model. ompressive strength. Fig. 14 Effet of stress level on fatigue damage of onrete ompressive strength. also shows the fatigue modulus damage evolution superimposed on the experimental data. Influene of loading parameters on fatigue damage of onrete damage evolution of onrete strength using the proposed damage model. The fatigue life that orresponds to the rit- Figures 15 and trend as in the residual strength an also be observed. Fig. 16 Effet of stress ratio on fatigue damage of onrete ompressive strength. VARIABLE-AMPLITUDE FATIGUE LOADING variable in nature. Hene, it is imperative that the proposed loading in a simple and expliit manner. 41,42 fatigue damage aumulation when onsidering variable fatigue loading. The damage per stress level is estimated as life. The summation of all estimated damage values gives should be equal to 1 or a given ritial value. in the literature show that fatigue behavior of onrete is Miner Rule does not aount for loading sequene; hene, ACI Materials Journal/Marh-April 2017

Davidson 33 is desribed as follows and is illustrated in Fig. 17 and 18. However, experiments on variable fatigue the proposed strain-rate approah or stress life, 38 an approah 43 an also be used.

9 Davidson 33 is desribed as follows and is illustrated in Fig. 17 and 18. However, experiments on variable fatigue the proposed strain-rate approah or stress life, 38 an approah 43 an also be used. Irrespetive of the magnitude of a urrent stress level i, indue damage equal to a previous damage value an be 18, the stresses 1, 2, and 3 are applied for N 1, N 2, and N 3 of 3 for N 3 Step 1 D 1 level ( 1 N 1 Step 2: N D 1 and the seond stress level ( 2 of N N eqv2 for the seond load stage. This step onverts the previous damage Step 3: To alulate the damage (D 2 level ( 2 N 2 seond stress level is added to N eqv2 N 2 + N eqv2 model and using the seond stress level D 2 for the residual strength is estimated. Step 4: The third stress level ( 3 N eqv3. Subse- N the summation of N eqv3 and N 3, as desribed for D 2 in Step 3. Step 5 N 3 + N eqv3 and the third stress level ( 3 D 3 an be estimated. Based on this onept, the value of the estimated damage takes into aount the previous damage. For more variable fatigue loading, this proedure ontinues until the last variable load is reahed. The proedure desribed for onrete strength under variable fatigue loading an also be used for the residual fatigue seant modulus; hene, similar to residual strength of onrete, the degradation of onrete Fig. 18 Damage evolution for variable loading. under different loading onditions. CONCLUSIONS work onduted, the following onlusions were derived: 1. The behavior of onrete elements under fatigue loading ingful preditions and results. 2. In the development of the damage models, the use of is a reasonable alternative to the use of S-N models. 3. The residual strength and fatigue seant modulus of hene, the use of ritial damage values is appropriate as observed from experimental results. 4. The evolution of the maximum strain is phased into are observed from all tested speimens, although the gradi- - ACI Materials Journal/Marh-April

10 5. The proposed damage models for onrete residual strength and fatigue modulus give reasonable orrelations to the observed experimental data and represent an improve- effet of loading has been proposed for variable fatigue tion using variable fatigue loading tests of onrete. AUTHOR BIOS Benard Isojeh - Maria El-Zeghayar - Canada, in Frank J. Vehio ACKNOWLEDGMENTS aknowledge the assistane reeived from the Niger Delta Development of this researh. NOTATION a = material parameter b = material parameter C f = material onstant D = damage D r = ritial damage E = fatigue seant modulus E se = stati seant modulus f f K k 1 N N eqv N f max = maximum stress level s = onstant parameter R = stress ratio u = damage parameter v = damage parameter 2 = material onstants 2 = material onstants f = maximum stress level v max max stress-strain urve se max = min = maximum stress level minimum stress level REFERENCES Reinfored Conrete, Materiales de Construión, V. 17, No. 1, 1984, pp doi: /BF Mehan- Engineering Frature Mehanis, V. 55, No. 2, 1996, pp doi: Fatigue Damage Model for Conrete in Tension, International Journal of Damage Mehanis, V. 4, No. 4, 1995, pp doi: / Magazine of Conrete Researh, V. 48, No. 176, 1996, pp doi: / mar Loading,, V. 9, No. 2, 2005, pp doi: /s , V. 6, No. 5, 2014, pp doi: /mla , 148 pp. ACI Journal Proeedings, V. 55, No. 2, 1955, pp ACI Journal Proeedings, V. 63, No. 10, Ot. 1966, pp Loads, Civil Engineering Studies, Strutural Researh Series No. 372, - ACI Materials Journal, V. 88, No. 2, ACI Journal Proeedings, V. 63, No. 1, tane of Conrete under often Repeated Compressive Loads 2, Magazine of Conrete Researh, V. 25, No. 83, 1973, pp doi: /mar Fatigue of Conrete pp tude Loading, Institute, Farmington Hills, MI, 1982, pp sin-milwaukee, Milwaukee, WI, Magazine of Conrete Researh, V. 48, No. 177, 1996, pp doi: / mar Fatigue of Conrete Conrete Institute, Farmington Hills, MI, 1974, pp Loading of Conrete Strutures,, V. 17, 1984, pp Materiales de Construión, V. 17, No. 1, 1984, pp doi: /BF Conrete, Magazine of Conrete Researh, V. 52, No. 1, 2000, pp doi: /mar ACI Materials Journal/Marh-April 2017

11 Cement and Conrete Composites Response of Craked Conrete Interfae, Journal of Advaned Conrete Magazine of Conrete Researh, V. 32, No. 111, 1980, pp doi: /mar Magazine of Conrete Researh, V. 33, No. 116, 1981, pp doi: /mar , Cement and Conrete Researh, V. 27,, International Federation for Strutural Conrete ( Lausanne, Switzerland, 1988, 312 pp. Model Code for Conrete Strutures, Strength Conrete,, V. 13, No. 3, 2012, pp doi: /suo Fatigue, Journal of Composite Materials, V. 31, No. 2, 1997, pp doi: / Advaned Materials Researh, V , 2010, pp doi: Residual Stiffness and Strength for Fatigue of Fibre-Reinfored Composites, International Journal of Fatigue, V. 24, No. 7, 2002, pp doi: ACI Journal Proeedings, V. 67, No. 10, Ot. 1970, pp ACI Materials Journal, V. 95, No. 5, Sept.-Ot. 1998, pp Magazine of Conrete Researh, V. 50, No. 3, 1998, pp doi: /mar Interna-, V. 110, No. 5, Sept.-Ot. 2013, pp Journal of Applied Mehanis Zeitshrift des Vereines Deuther Ingenieure Fatigue of Conrete in Tension,, V. 12, No. 3, 2011, pp doi: /suo ACI Materials Journal/Marh-April

Mechanical Properties of High-Strength Concrete Manish Kumar 1, A.M. ASCE; Zhaoyu Ma 2 ; Moses Matovu 2

Mechanical Properties of High-Strength Concrete Manish Kumar 1, A.M. ASCE; Zhaoyu Ma 2 ; Moses Matovu 2 1.1 Introdution Mehanial Properties of High-Strength Conrete Manish Kumar 1, A.M. ASCE; Zhaoyu Ma 2 ; Moses Matovu 2 Mehanial properties of High-Strength Conrete (HSC) an be divided in two groups as shortterm