Calculation of Actual Magnitude By: Emilio M. Morale, MSCE - Mater of Science in Civil Engineering major in Geotechnic and Structure, Carnegie Mellon Univerity, Pittburgh Pa. Chairman PICE Geotechnical Diviion, Former Senior Lecturer Graduate School, Dept of Civil Engineering, UP Diliman. Mark K. Morale, M.Sc - Mater of Engineering Major in Geoengineering, Univerity of California - Berkeley, CA. Former Member of the faculty, Mapua Intitute of Technology CE Department., Member of the Faculty, Graduate School, Dept. of Civil Engineering, UP Diliman. 1.0 INTRODUCTION Mot often, the quantification of hrinkage train and magnitude are not neceary requirement, a proviion of adequate number and pacing of hrinkage and contruction joint normally would enure a trouble free concrete lab contruction. It i only when trouble arie like eriou cracking and curling i there a need to look into actual magnitude particularly if liability or litigation threat are in the offing. The actual magnitude of hrinkage train are quantifiable baed on well etablihed procedure publihed by the American Intitute (ACI 209R-92). 1] Particularly, thi calculation would be needed in order to determine whether a member would crack or not due to hrinkage or if the problem of cracking i due to ome other caue. In uch cae, it i neceary that the actual magnitude of hrinkage train be determined to enure that thee train do not exceed the permiible limit. 1.1 Prediction of Actual Value baed on ACI 209R-92 hrink due to moiture lo. However, the actual magnitude of ultimate hrinkage i dependent on a lot of factor a contained in ACI 209R-92. Thee factor are: Relative Humidity Minimum Thickne Water Cement Ratio W/C Slump Air Content Fine Content In order to predict the actual hrinkage, it i neceary to perform actual calculation taking into account the foregoing factor. Totally neglecting thee procedure render any concluion invalid and at bet highly peculative. The ue of a real contruction problem would bet illutrate the need for and importance of Calculation procedure baed on univerally accepted State of Practice. Thi wa what happened in a real world project of our, 2] where major cracking ha occurred; blame i being placed quarely on the Engineer of Record with variou claim that are unubtantiated. One of thee i a claim by the contractor hired foreign conultant that hrinkage tree even with the high W/C ratio i not the caue of cracking. The conultant even provided overimplified calculation jut to jutify that crack were not due to hrinkage ince by not being able to do o, the very high and non compliant W/C ratio a placed will urely point to the main reaon for the cracking. In order to diprove the elf erving and highly erroneou calculation preented, we proceeded with the appropriate Calculation baed on a rational procedure a recommended in ACI Committee 29 1]. Thi i the main topic of thi article and by outlining the procedure taken, the reader/ will be guided in how actual hrinkage i calculated which even if complicated i required particularly when the problem blow into a litigation headache. 1] ACI Committee 209. Prediction of Creep, and Temperature Effect in Structure. ACI 209F-92 contained in ACI Manual of Practice, 1996, Part 1. 2] For Obviou Reaon the Project and peronage involved cannot be named.
1.1.1 Calculation of the Ultimate Value The ultimate hrinkage value can be predicted for condition other than tandard 3] uing: Where: x K x K x K x K x K x K H D F B AC = i the train at tandard or other condition = Ultimate Strain K = Correction Factor for Relative Humidity H D K = Correction Factor for Minimum Member Thickne K = Correction Factor for Conitency K = Correction Factor for Fine Aggregate Content F B AC K = Correction Factor for Cement Content K = Correction Factor for Air Content The attached chart in Appendix B give the correponding value ued on our calculation for the variou condition baed on ACI 209R-92. Baed on the foregoing equation and quantification of actual condition for the pecific project (ee Appendix A for a complete detail of the above.) The following value for the correction factor for ambient Project condition have been ued. The foregoing value need to be applied on the Ultimate Value to yield the hrinkage train at actual condition. It i not correct to ue aumed Standard Value a wa done by the contractor Foreign Conultant for the concrete in quetion becaue the condition were not tandard for thi project. In addition, the concrete a poured by the contractor exceively violate the pecified maximum Water Cement Ratio W/C (Specified 0.42 v. Actual 0.8333) by 98.4% baed on tet of Water Content and Water Cement Ratio W/C conducted by a New Zealand Laboratory and a cited in the contractor Conultant Final Report. However, the effect on the reulting train i non linear and i greater at higher water content. The Portland Cement Aociation 4] ha a widely accepted and well documented procedure for prediction of what hrinkage train could be under variou Water Cement Ratio and under other equally important conideration for the ambient project condition exiting during the pour. (thu, it i important for the conultant and the PM to record thee condition at every pour). The chart below i taken from Reference 2.0 and how how the hrinkage contribution from variou Water Cement Ratio could be quantified: From: Ref. 2.0 PCA Handbook Deign of Mixture, 13 th Ed. Page 155. Factor Ambient Relative Humidity Minimum Thickne Cement Content Actual Condition at Time of Pour A] Correction Factor 85% K 0.48 100mm K 1.0642 285 kg/cu.m. K 0.81099 Slump 2 inche K 0.97 Air Content 2% K 0.97 Fine Content 50% K 1.0 H D B AC F Product 0.3654 A] Aumed Value applied to both condition uniformly. 5] 3] The tandard condition are baed on US condition. 4] Steven H. Komatka and William C. Panaree. Deign and Control of Mixture. Thirteenth Edition. Portland Cement Aociation, Old Orchard Road, Skokie, Illinoi. 5] Kong. Handbook of Structural. ACI Method 209 Correction Factor. Fig. 2-7- Chapter 11, -age 12, Pitman Publihing, Inc., Ma. 1983.
Baed on thee chart, and with the following actual data: W/C Ratio A Specified 0.42 25.9 Reulting Water Content i gallon/cy W/C Ratio actually poured Determined from average of Lab tet W/C=0.8333 The reulting Water Content i 47.9 (Computed from ubmittal gallon/cy of Mix Deign From thee value, the Upper Band of the curve i entered to yield the following hrinkage magnitude: Value In millionth A pecified W/C = 0.42 290 A poured and determined By New Zealand Lab W/C Ave = 0.8333 1,020 There i ignificantly, a leer hrinkage value baed on the pecified W/C of 0.42 over normal concrete and a very large increae in the cae of exceive W/C a provided (W/C=0.833 provided v. W/C=0.42 pecified). The value obtained, 290 microtrain or 0.29 and 1.020 microtrain or 1.02 are ued a bae or reference figure in predicting quantitatively the actual hrinkage magnitude in thi pecific cae uing ACI 209 procedure. The effect of variou other factor can be introduced further. It can be een from the above that the actual Ultimate Strain ( ) produced by the a poured concrete (W/C=0.8333) i 251.7% greater than for the pecified concrete (0.290 v. 1.020 ). If the hrinkage correction factor a precribed by ACI 209 are applied, the reulting Actual would be: A Specified W/C=0.42 A Poured W/C=0.8333 (Contractor) 0.290 1.020 Product of Correction Factor 0.3654 0.3654 Ultimate Value 0.1060 0.3727 1.2 Prediction of at any Time Baed on ACI 209R-92 prediction at any time after age 7 day for moit cured concrete i given by equation 2-9 ACI 209R-92 a follow: where: t 35 t t t = at any time (t) t = Time in day after the end of initial Wet curing u = Ultimate hrinkage value Thi equation i a very powerful tool in quantifying the actual magnitude of hrinkage at any time but more importantly during the moit critical tage of trength development when the concrete ha not yet fully attained it deign trength. Uing the above Equation 2-9 with a curing period of 14 day a pecified, the following hrinkage train factor are generated for variou time beyond the 14 day initial wet curing period. Period Time Day Correction Value 1 0 0 2 5 0.125 3 15 0.3 4 25 0.416667 5 35 0.5 6 45 0.5625 7 85 0.708333 8 105 0.75 9 125 0.78125 10 165 0.825 11 205 0.854167 12 215 0.86 13 365 0.9125 14 8000 0.995644 What the foregoing data portray i that the hrinkage value attained at approximately one year (365 day) i 0.91 of the ultimate hrinkage value. More importantly it how that hrinkage train development i gradual and doe not reach peak value until a coniderable period of time ha elaped. Thi i very crucial in determining and quantifying what actually happened to the lab when thee were reported to have cracked after approximately one month after pouring. u
2.0 SIGNIFICANCE OF CALCULATION RESULTS Baed on calculation conitent with ACI 209R, the following concluion can be made: 1) The a pecified concrete with W/C=0.42 will not exceed the Allowable Tenile Strain Capacity of unreinforced concrete at any time. ( =0.1060 v. Allowable =0.150 to 0.200). 2) The a poured concrete exceeded the Allowable Tenile Strain Capacity even initially at approximately 30 day after wet curing (almot exactly at the ame time the firt crack were oberved). ( =0.3727 v. Allowable =0.150 to 0.200). The reult undercore the effectivene of the hrinkage control meaure that have been pecified by thi Engineer of Record to limit the train to tolerable value have the correct W/C been followed. It i not correct to ue any other data uch a Approximately 0.35 a the actual train ince thi i not repreentative of the actual condition and remain merely a baele aumption. In truth, the actual magnitude i very much le than thi prediction, due to the effect of very low W/C pecified and other meaure ued to control hrinkage. The reult of the calculation for predicting the actual magnitude of the Ultimate baed on ACI 209R- 92 (Section 3.0) and the prediction of the rate of development of hrinkage with time (Section 2.0) alo from ACI 209R-92 where graphically preented in order to preent a clearer picture of what actually happened and what wa the real caue of hrinkage. Note: Thi i conitent with the Field obervation that the cracking occurred approximately one month after pouring. 2.1 Platic Stage At the critical tage when platic hrinkage wa happening (1-3 day) the correponding trength are a follow: Thu, it can be een that trength development at the critical Platic Development would have been adequate for the pecified W/C Ratio and i more than 2.5 time that of the a poured concrete. Thu, the a poured concrete had very low available trength becaue of the very high W/C Ratio and i inadequate to reit platic hrinkage cracking. 2.2 Curing Stage For the pecified 14 day curing period, drying hrinkage i not yet developing, for thi reaon the time cale for train development i offet by 14 day. What thi mean in imple language i that the drying hrinkage i potponed until after the wet curing period of 14 day. During thi time, and becaue the area i fully encloed, humidity built up, becaue of the wet curing procedure and due to the abence of air movement. 2.3 Drying Period Beyond the 14 day Wet Curing pecified, hrinkage train from drying tarted to et in and the development i predicted by Equation 2-9 of ACI 209R. Depite the high relative humidity inide the pouring area, it wa not enough to arret cracking of the a poured lab due to the very high hrinkage potential from the exceive water content of the a poured lab, omething clearly illutrated by CHART A which i a graphical preentation of the calculation reult. 3.0 Cloure The foregoing calculation for an actual problem have hown that hrinkage tree can be calculated and that the hrinkage i exceive and beyond that have occurred tolerable limit due to the high water cement ratio W/C of the a laid concrete in violation of the pec. The rational formula a precribed by ACI Committee 209 i an invaluable tool in determining the magnitude of hrinkage train in the concrete which are indiputable if the actual condition are ued. A poured (W/C = 0.8333) (W/C = 0.42 a pecified) (f c=3,000 pi min. floor pec.) 980 pi 2,450 pi 1,470 pi
STRUCTURAL, GEOTECHNICAL CIVIL and FORENSIC ENGINEERS