A WATER RESOURCES TECHNICAL PUBLICATION ENGINEERING MONOGRAPH No. 34
Control of Crackingin Mass Concrete Structures UNITED STATES DEPARTMENT REVISED REPRINT - 1981 OF THE INTERIOR BUREAU OF RECLAMATION A WATER RESOURCESTECHNICAL PUBLICATION
EngineeringMonograph No. 34
Control of Cracking in Mass Concrete Structures
bY C. L. TOWNSEND
DamsBranch Division of Design Engineeringand ResearchCenter
UNITED STATES DEPARTMENT OF THE INTERIOR Bureau of Reclamation As the Nation’s principal conservation agency, the Department of the Interior has responsibility for most of our nationally owned public lands and natural resources. This includes fostering the wisest use of our land and water resources, protecting our fish and wildlife, pre- serving the environmental and cultural values of our national parks and historical places, and providing for the enjoyment of life through outdoor recreation. The Department assessesour energy and mineral resources and works to assure that their development is in the best interests of all our people. The Department also has a major responsi- bility for American Indian reservation communities and for people who live in Island Territories under U.S. administration.
ENGINEERING MONOGRAPHS are published in limited editions for the technical staff of the Bureau of Reclamation and interested technical circles in Government and private agencies. Their purpose is to record developments, innovations, and progress in the engineering and scientific techniques and practices that are employed in the planning, design, construction, and operation of Reclamation struc- tures and equipment.
First Printing: October 1965
Revised Reprint: May 1981
UNITED STATES GOVERNMENT PRINTING OFFICE
DENVER: 1981 -
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC., 20402, and the Bureau of Reclamation, Engineering and Research Center, Denver Federal Center, P 0 Box 25007, Denver CO 80225, Attn D-922. Pre Face
VARIOUS BUREAU OF RECLAMATION papers and artificial cooling and the results obtained. Be- memoranda on heat flow and temperature control cause of the limited availability of these &t,a and of mass concrete have been written during the past memoranda and because *additional experiences in 25 years. Several of these writings were con-. cooling of mass concrete structures have modified, cerned only with the mathematical relationships in some instances, the application of temperature of heat flow. Others either gave general consid- control measures, this Engineering Monograph eratdons TV be taken into account in design and was written to summarize studies and procedures construction, or described a particular instance of as they relate to present day practice.
iii
Contents
Pap2 . . . 111
Introductbn------______----___---_--__---_-- ____------_--_ Volumetric Changes in Mass Concrete- ______The Temperature Control Problem- __ _ - - - ______- - ______Applications-______-_____------_-----____------____ Costs_--_---______--______------
Temperaturecontrol Studies------9 General___-_-______------9 Range of Mean Concrete Temperatures------....------9 Diffusivityof concrete----- ______-_-___-_-__ 10 Amplitudes of air temperatures------10 Amplitudes of concrete temperatures- - - - - _- - - - - ______15 Reservoir water temperatures- ______- ______----_---_-- 19 Solarradiation effect ______---___--_----_- ______22 ClosureTemperature_--- ______-_--_--_-_--__---- ______23 Temperatures in Mass Concrete-- _____ -__----__-__--__-_-_____ 39 Heat of hydration----....--- ______--_---__-- 40 Schmidt’sMethod__---______-______----- 41 Carlson’sMethod------______---- ______-_--- ____-_____- 48 Temperature distributions_ - __ _ _ _- - ______- - - _- ______- 49 Removal of heat by cooling pipe- - - ______- - _ - - - ______- __ 49
57 Length of Construction Block_------______57 Width of Construction Block_------____ ---_------__-___- _____ 58 Control of Temperature Drop------______-__- ___.______- 60 Rate of Cooling ______. -- ______---_---~~~----~---- ______- 63 Joints-______-______------65 Temperature Reinforcement-General- - _ __ -.- _ - - _ -______- 65 Temperature Reinforcement-Frames Attached to Mass Concrete- 66
V vi CONTENTS
Page Construction Requirements _____ ._...... - - -..-. _ - ______._. ______67 SurfaceTreatments__------_-___-.__-._--.------___._____ 67 SurfaceGradients------_____. -_.--__------____ 68 Foundation Irregularities___--_----______-_---_-_------_ 69 Relaxation of Initial Cooling--- _ __ - - ______. ______- _ 69 FinalCooling---_---- ____ --_---_-- _._____ -_- _._____ ------70 Height Differerltial-__---_--_-_--- ____. -___-___-- __._ ------70 Openings in Dam------_____ -- _.__ -_-__-_-_---__------71 Extended Exposure of Horizontal Construction Joints- ______7 1
FIGURES
NUTObt7 1 Glen Canyon Dam-cooling pipe layout------_---- ______5 2 Glen Canyon Dam-concrete cooling details------_ __ - __ _ - _ _ __ 6 3 MonticelloDam-coolingpipelayout--- ______-_-_-___----__ 7 4 Hungry Horse Dam-location and general layout_- __ __ - ______11 5 Hungry Horse Dam-climatic and mean concrete temperatures- __ _ 12 6 Monticello Dam-general layout-. __ _ _- _ __ _-_ - _ _ __ _ - ______13 7 Monticello Dam-climatic and mean concrete temperatures- ______14 8 Computation form (Sheet 1 of 2)-range of mean concrete tempera- tures_---_--_-___--______------15 9 Computation form (Sheet 2 of 2)-range of mean concrete tempera- tures____--______-___-_------_-_-_-_------16 10 Glen Canyon Dam-air and water temperatures- __ _ - _ _ - - - _ _ _- _ _- 17 11 Temperature variations of flat slabs exposed to sinusoidal tempera- ture variation on both faces------_------______20 12 Range of actual reservoir temperatures under operating conditions (Sheet 1 of 2)---- ______-- _____ -__-- ______--_-__-__ 21 13 Range of actual reservoir temperatures under operating conditions (Sheet2of2) _____ -_- ____ -__-----_--_- ______--__-___--_- 22 14 Range of actual reservoir temperatures under operating conditions- Salt River Project dams--- ____ -___-___-__- ______-___-__ 23 15 Reservoir temperatures-Grand Coulee Dam_---_-----_-___-_--- 24 16 Reservoir temperatures- HooverDam _____ ---_-__-_----_-__-_- 25 17 Reservoir temperatures-Shasta Dam_____------_-_------26 18 Reservoir temperatures-Owyhee Dam- - _ _ __ _ - _ _ - ______27 19 Reservoir temperatures-Hungry Horse Dam _ _ - - _- - _ _- - - _ - - - _ _ 28 20 Reservoir temperatures-Hiwassee Dam-_---_----____-_------29 21 Reservoir temperatures-Fontana Darrl------_-_---__-_--___ 30 22 Reservoir temperatures-Elephant Butte Dam - ______31 23 Reservoir temperatures-Grand Lake, Colorado ______32 24 River water temperatures-Sacramento River- - - - __ - - _ - - _ - _ - _- _ - 33 25 Increase in temperature due to solar radiation-Latitudes 30°-35’- 34 26 Increase in temperature due to solar radiation-Latitudes 35’-40’- 35 27 Increase in temperature due to solar radiation-Latitudes 40’-45’- 36 28 Increase in temperature due to solar radiation-Latitudes 45’-50°- 37 CONTENTS vii
NW7lbU Page 29 Variation of solar radiation during year------_____ --_-___-----_ 38 30 Temperat$ure history of artificially cooled concrete- __ . - - - ______- - 40 3 1 Temperature rise in mass concrete-type of cement - _ - _- _ _- _ - - _ _- 42 32 Effect of initial temperature on heat of hydration-- - - ______- _- 43 33 Ross Dam-Schmidt’s Method of temperature computation- - - - _- - 46 34 Ross Dam-Temperature distribution by Schmidt’s Method-- _ - _ - _ 47 35 Temperature variations with depth in semi-infinite solid _ _ - - - - - __ _ 50 36 Pipe cooling of concrete-values of “X”- _ - - _ - - ______- - ______51 37 Pipe cooling of concrete-values of “Y”- _ _ - - _ _ - _ - _ - _ _ _ _- _ _ _- - - _ 52 38 Pipe cooling of concrete-values of “Z” ______- _ - - - - _ _ __ - - _ - - - - 53 39 Foundation restraint factors ____------___-_-- _____ - ______-- 59 40 Typical temperaturerisecurves----- .______---_-___-- ______62 41 Tensions versus concrete strength-early age- _ _ _ _ _- _ _- - __ - ______64
TABLES
I Thermal Properties of Concrete for Various Dams- - - - - ______- _ 18 II Amplitudesof Air Temperatures------..-- ______19 III Related Values of Ax and At for Schmidt’s Method- - - _- _ - _ _- - _ 44 IV Computation of Temperatures in 5-foot.-thick Concrete Wall- _ - _ 49 V ValuesofD,02,andh2,forPipeCooling-----_---- _____ ----___ 54 VI Effect of ArtificialCooling Pipe _____---_- ____ ---- _____ -_- ____ 55 VII Temperature Treatment Versus Block Length- ______- - _ __ - _ __ _ 60 VIII Computation for Temperature of Concrete Mix------_ _ __ _ - - _ __ 63 IX Computationof TemperatureStress_-- ______-----_-__-_--___ 69
Introduction
CRACKING in mass concrete structures is undesir- regular structural cracks of varying width which able as it affects the water-tightness, durability, completely cross construction blocks, to the regular appearance, and internal stresses of t,he structures. contraction joint with a relat.ively uniform open- Cracking in mass concrete will normally occur ing which separates the construction blocks in a when tensile stresses are developed which exceed concrete monolith. the tensile strength of the concrete. These tensile Trial-load analysesare used to shape and propor- stresses may occur because of imposed loads on tion the dam properly to the site for the prescribed the structure, but more often occur because of loading conditions. Temperature control studies restraint against volumetric change. The largest furnish data for these trial-load analyses. Basi- volumet,ric change in mass concrete results from cally, to function in the manner designed, an arch change in temperature. Owing to the heat of dam must be a continuous structure from abut- hydration of the cementing materials in mass con- ment to abutment. Similarly, a gravity dam with crete, this change in temperature may be relatively longitudinal joints must have a monolithic section large. Cont.rol of #the subsequent temperature in an upstream-downstream direction. Provision drop may be necessary if cracking is to be pre- for the construction of these structures must in- vented or minimized. clude measures by which the concrete is cooled and Temperature control measures are adopted, as measures by which the transverse and longitudinal necessary, to minimize cracking and/or to cont,rol contraction joints are permanently closed by grout- t,he size and spacing of cracks. As referred to ing before the reservoir loads are applied. The here, cracks include the controlled crack, which is more widely-used temperature control measures to more commonly referred to as a contraction joint. These cracks occur when various parts of the mass assure continuity within a structure are precooling concrete are subjected to volumetric changes due of the concrete, artificial cooling of the concrete to temperat.ure drop, drying shrinkage, and/or by means of embedded pipe systems, use of a con- autogenous shrinkage. Such cracks vary from ex- struction slot, or a combination of these methods. tremely small or hairline surface cracks which The most commonly used of these measures for penetrate ‘only a few inches into the mass, to ir- dams designed by the Bureau of Reclamation is the 1 2 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES pipe-cooling method, supplemented where neces- though the final state of temperature equilibrium sary by the precooling method. depends on site conditions, a degree of control over Early studies are based on existing data and on these volume changes can be effected by limiting a possible construction schedule. Actual exposure the amount of temperature rise which occurs im- conditions, water temperatures, and construction mediately after placement and/or by controlling progress may vary widely from the conditions as- the placing temperature of the concrete. The sumed, and adjustments are made during the con- temperature rise may be controlled by embedded struction period. Construction procedures and pipe cooling systems, placement in shallow lifts, practices are anticipated during the design and or by the use of a concrete mix designed to limit specifications stage. Revisions and amendments the heat of hydration. The last procedure is nor- are made during construction, when necessary, to mally accomplished through a reduction in the obtain the best structure possible consistent with amount of cement, use of a low-heat cement, use of economy and good construction practices. a pozzolan to replace part of the cement, use of admixtures, or a combination of these factors. Volumetric Changes in Mass Concrete The placing temperature can also be varied, within limits, by precooling measures which lower the Volume change, as referred to herein, applies temperatures of one or more of the ingredients of to expansion and contraction of hardened concrete. the mix before batching. This will proportion- Wetting, drying, and temperature variations are ately reduce the overall volume change. the principal causes of these expansions and con- Drying shrinkage can cause, as a skin effect, tractions, although the chemical interaction be- hairline cracks on the surface of a massive struc- tween certain minerals and the alkalies inherent ture. This occurs because of the restraint the in- in cement may also contribute to volume change. terior mass exerts on the surface layers. It is, In the past, relatively large volumetric changes however, negligible as a causeof volumetric change in several structures have resulted from the inter- in mass concrete. The primary objection to these action between the aggregates and the alkalies random hairline cracks of limited depth is that in cement. Volume change in concrete due to they may provide the entry for further and more alkali-aggregate reaction has been reduced in pres- extensive cracking and spalling under adverse ex- ent day structures as a result of laboratory investi- posure conditions. Proper curing applied during gations of the concrete aggregates. Selection of the early age of the concrete should therefore be nonreactive aggregates and/or the use of low- used and thought of as a crack prevention alkali cements now controls this type of volume measure. change. Autogenous volume change is usually a shrink- age and is entirely a result of chemical reaction The Temperature Control Problem within the concrete itself. Autogenous shrinkage The method and extent of temperature control is highly dependent upon the characteristics and amount of the cementing materials. The magni- is governed by site conditions and the structure tude of the shrinkage varies widely. At Norris itself. The ideal condition would be to place the Dam, for example, measurements showed up to concrete at such a temperature that the subsequent 90 millionths of an inch per inch autogenous hydration of the cement combined with exposure shrinkage. At Grand Coulee Dam, about 60 mil- temperatures would cause a rise in temperature as lionths of an inch per inch was noted. Although the structure assumes its final stable temperature.’ of unknown magnitude, the autogenous shrinkage *Numerous references are made, as above, to the flnal stable at Friant Dam was of sufficient magnitude and temperature of a concrete structure. Such a condition does not exist a8 a single, definable temperature. A final state of tem- continued over such a period of time as to require perature equilibrium will eventually exist in which the tempera- regrouting of the contraction joints, ture at any given point in the structure, or the mean temperature across a glveu aeettou, will fluctuate between certain limits. The volumetric change due to temperature can Because of these varying temperatures and ever-changing tem- be controlled within reasonable limits and can be perature distributions, the term “5nal atable temperature” should be thought of 88 an approximate or average eondltiou of made a part of the design of a structure. Al- temperature. INTRODUCTION 3 This would result in no volumetric temperature duced cement content, and pozzolans will normally shrinkage, and any subsequent cracking would be be used for gravity-type dams containing no associated with foundation settlements, loadings, longitudinal joints. The degree of precooling or localized stresses. This condition was closely and/or the design of the concrete mix is generally approximated by precooling measures at Vaitarna based on the size of the block. Normally, a 25” Dam in India and Klang Gates Dam in Malaya to 30” temperature drop can be allowed to take where relatively high final stable temperature con- place in the size of block now being used in gravity ditions exist. Temperature conditions in the dams before tensile stresses great enough to cause United States, however, are not conducive to such cracking across the block will develop. This a temperature treatment. Most of the sites in this allowable drop should be less if severe exposure country have a final stable temperature in the temperatures can be expected while the interior order of 40’ F. to 60” F. To allow for a moderate concrete temperatures are relatively high. temperature rise in these instances would require below-freezing placing temperatures. Since the Applications ideal condition cannot be realized, maximum con- crete temperatures will be above the final stable The need for controlling concrete temperatures temperature and a drop in temperature must be undoubtedly was recognized by the Bureau of Ret- considered. Unless otherwise noted, all statements lam&ion soon after the first large concrete struc- made herein will be directed toward structures tures were built. In subsequent large structures, which cannot be placed or constructed under the the fact that the temperature of concrete rises an ideal condition. appreciable amount above its placing temperature In practically all mass c0ncret.e structures, con- was either ignvred, which led to unfavorable traction joints are provided to allow for volume cracking in many instances, or a construction pro- changes caused by temperature drops. If the gram was adopted which mini,mized the effects of structure is an arch dam, contraction joint grout- the temperature changes. The latter was usually ing will be required if the arches are to be mono- accomplished either by placing the concrete at a lit,hic and are to transfer the reservoir load to the reduced rate, by placing in shallow lifts, or by the abutments by arch action without excessive de- use of closure slots. flection. An arch dam, therefore, will normally During the construction of Gibson (1929-30) require that an embedded pipe system be used to and Ariel (1930) Dams, actual concrete tempera- cool the concrete artificially, either during the tures were obtained which provided data on heat construction of the dam or immediately after- generation and the subsequent rise of concrete ward, so that the contraction joints will be open temperatures during the early age of concrete. and can be grouted before the reservoir is filled. An experimental artificial cooling installation was In some instances, as wit,h extremely thin arch used in Ariel Dam where closure blocks were dams, natural cooling over a winter period will cooled by circulating water through vertical cored accomplish the same effect. holes, 5 to 12 inches in diameter. At about the The gravity-type st’ructure with no longitudinal same time, early designs for Hoover Dam indi- contraction joints requires only that degree of tem- cated that a definite control of concrete tempera- perature control necessary to prevent structural tures would be required because of the unprece- cracking circumferentially across the block as the dented size of that structure, and studies were block cools and approaches its final stable tem- made as to how this could best be accomplished. perature. Since open longitudinal joints would These studies included the air-cooled slot method, use of precooled aggregates, use of precast con- prevent a gravit)y block carrying it.s load as a crete blocks, and the embedded pipe method. monolith, gravity-type dams with longitudinal As a part of the Hoover Dam studies, an experi- contraction joints must be cooled by an embedded mental installation using l-inch pipes at 4-foot 8- pipe system and the longitudinal contraction joints inch horizontal spacing on the tops of 4-foot lifts grouted before the full reservoir load is applied was made in a small se&ion of Owyhee Dam, then to the dam. The precooling method of temper- under construction. The results of this artificial ature control and the use of low-heat cements, re- cooling teet checked the mathematical theory and 4 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES
proved the embedded cooling coils to be a prac- embedded in the concrete, or by thermocouples. tical means of controlling concrete t,emperatures. Enibedded resistance thermometers should be em- As a result of the mathema’tical studies and the bedded at midlift and the electrical cable extended Owyhee teds, the pipe cooling method was to a terminal board where readings can be taken adopted for the temperature control of Hoover whenever desired. Thermometer tubes are nor- Dam. mally lengths of cooling tubing with the embedded Temperature control through artificial cooling end crimped shut and which extend from near the proved so successful at Hoover Dam, the Bureau center of a block at midlift t’o the downstream face. of Reclamation has used essentially the same sys- Insert-type resistance thermometers are inserted tem on succeeding dams. In addition to reducing into these tubes to obtain the concrete tempera- the maximum concrete temperatures, these em- tures. Thermocouples are placed in the fresh con- bedded pipe cooling systems provided the means crete near the center of a block at midlift height, of cooling so that the t,ransverse and longitudinal and the lead wires from tihe thermocouples are car- contraction joints could be grouted during or im- ried to readily accessible points on the downstream mediately after the construction period. fa.03. The layout of the concret’e cooling system as Aside from the embedded pipe cooling system, used at Hoover Dam is basically t:he same as that the most widely used method of temperature con- used today. It consists of pipe or tubing placed trol is that *hich reduces the placing temperature in grid-like coils over the ent.ire top surface of of the concrete. This has varied from the simplest each 5- or V/&foot lift. of concrete. Coils are of expedients, such as at Bartlett Dam in Arizona formed by joining together lengths of l-inch out- where concrete placement was restricted to night- side diameter, thin-wa.11 ‘metal pipe or tubing; the time placement during the hdt summer months, maximum length of coil is normally between 800 to a complete precooling treatment where a maxi- and 1,200 feet in length. The number of coils in mum temperature has been specified for the con- a Mock depends on the size of the block and the crete as it is placed in the forms. The usual horizontal spacing. The horizontal spacing of maximum temperature specified has been 50° F., the pipe or tubing varies between 21/, feet and 6 but this has varied from a 65’ F. maximum tem- feet, depending on exposure condit.ions, length of perature limitation at Monti&lo Dam to a 45” F. blook, height of lift, and proximity of foundation temperature limitation at Donnells Dam. These or abutment. Figures 1 and 2 show cooling de- temperature control limitations sh:ould not be con- tails for Glen Ca’nyon Dam, and Figure 3 shows fused wit,h the 80” to 90” F. limitations on the similar details for Monticello Dam. placing temperature of concrete for some of the The velocity of flow of the cooling water through t,he embedded coils is normally required older dams. The 80” to 90” F. limit,ations were to be not less t.han 2 feet per second (about 4 put in specifications for controlling the quality of gallons per minute). Cooling water is usually the concrete rather than as a crack prevention pumped through the coils, although a gravity sys- measure. t.em may sometimes be used to advantage. When Ot.her measures have been in between that de- river water is used, the warmed water is usually gree of control obtained by restricted time of wasted after passing t’hrough the coils. However, placement and that obt,ained by a complete pre- there have been instances where to avoid use of cooling of the materia1.s making up the concrete river water having a high percentage of solids, t,he mix. Placing temperatures at Davis Dam were warmed water was cooled and recirculated. When reduced by the addition of up to 90 pounds of ice using refrigerated water, the warmed water is per cubic yard COO/in9 has been completed and IuJ9 tubing has been gmuted, the fipple ihO thin IS to be removed and the hole filled wall tubmg---.. h drypock. DETAIL .? COP when not connected Adopter coupbng--- . - Std p!pe thrend .’ . , ~----~--J-./:----jl. A>- -__.._ W,opn,pp,e w;+hpaperto prevent bonding to concrete NIPPY exponwon EXPLANATION EL. 3195.0 EL. 5375.0 LAYOUT OF COOLING COILS FIGURE I.---Glen Canym. Dam-cooling pipe layout. 6 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES ,,-Wrap exposed header or tubmg wth ,I paper to prevent bonding to concrete Extend header or tubmg 6*mm thru h!gh block Thermocouple we to be temporon/ co/led and sus- pended on heo d er or tubmg for pro- tectmn unhl embedment-. ____ we to downstream :-Contractionpnt INITIAL INSTALLATION FINAL INSTALL A T/ON TYPICAL EXPANSION COUPLING SHOWlNG CON~RACnoN JOlNT CROSSlNo L--d ,A- LL’Ld r&o” trocttoion ” ” ,, Mets, and o@/ets to joint* _ _ _ __ + y+,‘/ COO//W CO//S L--A Number dep6zdent on .. -7..r+ , area and required ...... ) /oyoutottopofmch A . 7’b’lift : -+,:+--I L--d . . : : . . 1 ,,,a”--’ 1, --+-- 1 Af?RAIK;EMENT OF INLETS AND OUTLETS AT THE DOWNSTREAM FACE Actual req uired foundations moy ditter widely from assumed ez- covotion lines shown TYPICAL SECTION TiVRU DAM Cwlmg m/s shall be okxedr~~~. M top of each 7Xconcrete lift Place tobli mg on o/l rock surfaces to within pl’of the top of the lift btsing placed c**/ipg Jy’ ‘in9 to be pbced to clew opevmgs in dam o min of ~4’07 _d Coohog tubmg loid over reinforcement. Expons~on couplings shall be used at contraction joint crossings. Cwling cods my extend over top of Where tubing is instolled fff thermelsr we//s, NM emb6dded end of the gallery (I coils moy be terminated on tubing 6 to be flo/tened ondcrimped to sev/ cgoinst @ad leokoge each side with limited number of pipes Arrangement of tubmg moy vary from thot shown The octuol crossmg over top, at optmn of contractor. orron ement of the toting in the strvctule shoU be os directed. Where o b! ock 1s bounded by the downstream tote and requires two or more coils, the contractor may elect tp terminate a// corls at downstream face m lieu of using R headers &treom blocks requiring two or more cods will reqwre headers Tubmg placed on rock to be spaced at 2!6”, tubmg ot top of 6och 7!6’bft to be spaced according to zones os shown in tub/e. Coils placed m Zone / shall be approxhnotely BW’in length with no cod longer than 900’ in /en /hi all other cods rho/lb+ opprox- in&e/y 1200’a length wt % no cod longer than 13W’in length Adjocen t coils served by the some header shall be os nearly the some length ,os powble. Thermometer we/s WI// be used to determine concrete ten&wotwes ot locutions dwected to s&ament or replace thermocouple wire CO@ tubmg p/aced wrthm 23 to M feet of the fwndot!m nxk ~T&i&g 1* ’ -rJt&q to be embedded m pkwement lift Ts all, where pmct~ccoble. be p/aced (IS separate coils LX wdh below gallery. Make complete coils on each side of seoomte heoden to fahlok swcml cm/m ,n the oreo gallery and cross under gallery os few times ospos~% Each block Shall hove on indep6i&nt cce/mg &tern at each cmcrete Ilft TYPICAL SECTION THRU GALLERY FIGTJEE Z.-Glen Ca%uon Darn-concrete cooling detail& INTRODUCTION Top of poropet-Ei 460. -_ --Assumea me of er~ovo+~on &on9 oovns’ieom foe e’mometer ‘ubmg placed oifwoy be’reen scooi,n9 ifts at Z5’interuols DOWNSTREAM ELEVATION Pro,ected .-Vermomew ?ubmg Lo appronmo+e : centers of b.‘ocks-- ._.._ ,-Downstream ‘ace oc dam ,8” AL ‘, ‘. PLAN AT EL. 400 T”P,CIlL LI”O”F FOR BLOCKS WHERE WIDTH EXCEEDS LENGTH Upstream face of dam PLAN AT EL. 200 TlPlClL LI”O”T FOR BLOCKS WHERE LENGTH EXCEEDS WlDTH FIQIJBJE 3.-Monticello Dam-cooling pipe layout. 8 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES summer months to cool the tops of the newly inst.alling cooling systems and circulating river placed lifts. and refrigerated water through the coils was $0.21 Complete temperat,ure treatments, over and per cubic yard. At Hungry Horse Dam (1948)) above the use of embedded pipe cooling ,and pre- the contractor was paid $0.49 per cubic yard for cooling, have been used in some structures. In installing the embedded pipe systems and circulat- these instances, reductions were made in the ing river water through the embedded coils, and amount of cement used, low-heat cements were the cooling materials cost about $0.22 per cubic specified, or effective use was made of a pozzolan yard, for a total cooling cost to the Government of to replace part of the cement to lower the ,tempera- $0.71 per cubic yard of concrete. Costs at. Flam- t.ure rise. Special cements, low-cement contents, ing Gorge Dam (1963) totaled $0.85 per cubic precooling measures, and embedded pipe cooling yard for furnishing, installing, operat,ing, and systems were used in the base blocks of Detroit grouting ,the cooling systems. An additional $0.11 Dam, constructed by the Corps of Engineers. per cubic yard was paid to the contractor for Glen Canyon Dam, because of the size of t,he sprinkling the aggregates for about 200,000 cubic blocks in the dam and the relatively low grouting yards of concrete placed during the 1961 summer ‘temperature, was constructed wit,h a 50” F. maxi- period. Aside from cooling, the cost of furnish- mum placing temperature, embedded cooling coils, ing and installing the grouting systems and grout- a Type II cement, and mix containing two sacks ing ‘the contraction joints at Flaming Gorge Dam of cement and one sack of pozzolan. was almost $0.19 per cubic yard. Because the cost of precooling is usually in- costs cluded in the cost per cubic yard of concrete, no summary can ,be made as to the actual cost per Unit costs per cubic yard of concrete vary con- cubic yard for ,this method of temperature control. siderably depending on the size of the structure The degree of precooling necessary, of course, and the method or degree of control. Each of the would cause t.he cost to vary considerably. At pipe-cooling and precooling met’hods is costly, Detroit D,am, oompleted in 1953, the cost of pre- but the precooling will ordinarily cost slightly less cooling measures to obtain a placing temperature than artificially cooling the concrete by use of of 50” F. was $0.56 per cubic yard. Additional emfbed,ded pipes. cooling through an embedded pipe system at the The cost of all labor and materials chargeable base of the dam amounted to $0.74 per cubic yard to cooling at Hoover Dam (1931) was about $0.25 f,or the concrete cooled in ‘that. region. The total per cubic yard of concrete for an embedded pipe cost of ‘temperature control, dist,ributed over the cooling system with refrigera.tion plant. At total volume in Detroit Dam, was $0.63 per cubic Shasta Dam (193’7), the cost. of furnishing and yard of concrete. Temperature Control Studies General and construction problems are gradually assem- bled and decisions made on the nature and extent HE measures required to obt,ain a monolithic of the concrete temperature control, closure or structure and the measures necessary to re- grouting temperature, reduction of temperature T duce cracking tendencies to a ,minimum are gradients near exposed faces, insulation, and other determined by temperature control studies. crack prevention measures. Topographic condi,tions, accessibility of t,he site, length of construction period, and the size and Range of Mean Concrete Temperatures type of dam will influence the size of ‘blocks, rate of placement, and the temperature control and The temperature and temperature distributions related crack prevention measures. Temperature which exist at any given time are of interest in control studies begin early in the design stage several design problems, but are not normally used when programs are laid out to collect essential air as such in the trial-load analysis to determine tem- and water temperature d&a. Such programs perature stresses in arch dams. Of primary inter- should obt.ain maximum and minimum daily air est in the trial-load analysis is the range or ampli- temperatures, maximum and minimum daily river tude of the mean concrete temperature for each of water temperatures, and representative wet- and the arc.hes or voussoirs used in the analysis. This dry-bulb temperatures during the year. mean concrete temperature will be sufficient to In addition to the climatic conditions at the site, determine temperature stresses for most arch the period of flood runoff and reservoir operation dams. Temperature gradients which exist between requirements are studied to see what methods of t.he up&ream and downstream faces may also be temperature control would be adaptable to the taken into consideration in some instances. c.onditions during the c,onstruction period. The The average arch thickness from abutment to ever-growing collection of data on t,he site, dam, abutment. is used in computing the range of mean 9 10 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES concrete temperature where the arch does not heat in B.t.u./lb /” F., and p is the density in appreciably change thickness. For variable thick- lb /cu ft. Values of the diffusivity for a given ness arches, temperature ranges at the quarter- concrete are determined from laboratory tests, points should be computed. The number of arches although they will normally be estimated for the for which these ranges of temperature are deter- earlier studies. As the thermal characteristics of mined should be the same as the arches used in the the coarse aggregate govern to a large extent the trial-load analysis. The range of mean concrete thermal characteristics of the concrete, the earliest temperature with reservoir full is the normal con- of these estimates can be based upon the probable dition. When stage construction is taken into con- type of coarse aggregate for preliminary studies. siderat,ion, when the reservoir is to be filled or Table I gives thermal properties of concrete for partially filled before concrete temperatures have various dams and for several coarse aggregates. reached their final state of temperature equilib- Empirical factors of the contribution of each per- rium, or when the operation of the reservoir is cant by weight of the various concrete materials such that maximum and minimum reservoir levels on the thermal properties of concrete can also be occur at times other than extremes of temperature, used to estimate the thermal properties. These further studies are prepared to determine mean factors are presented in “Thermal Properties of concrete temperatures existing for the particular Concrete,” Bulletin No. 1, Part VII, of the condition. Each study is numbered according to Boulder Canyon Project Final Reports. the trial-load study number to differentiate be- Amplitudes of Air Temperatures.-Any estima- tween later studies. tion of air temperatures which will occur in the The range of mean concrete temperature for future at a given site must be based on air tem- each theoretical arch or voussoir is determined peratures which have occurred in the past, either from the air and water temperatures which are at that location or in the near vicinity. The assumed to exist at the site, as modified by the Weather Bureau has collected weather data at a effects of solar radiation. Thermal properties of great number of locations, and records from one or the concrete establish the ability of the concrete more of these locations may be selected and ad- to undergo temperature change. justed to the site. For this adjustment, an increase Figures 4 to 7, inclusive, show the general fea- of 250 feet in elevation is assumed to decrease the tures, climatic conditions, and actual ranges of air temperature lo F. Similarly, an increase of reservoir water temperatures and mean concrete 1.4“ in latitude is assumed to decrease the temper- temperatures at Hungry Horse Dam in Mont,nna ature 1” F. A program for obtaining actual air and Monticello Dam in California. temperatures at the site should be instituted as Figures 8 and 9 show the computations for the soon as possible to verify the above data. Figure range of mean concrete temperature at Hungry 10 shows the data assembled for the start of the Horse Dam using assumed reservoir water and air temperature studies on Glen Canyon Dam, along temperatures. Explanations for the computations with actual data obtained at the site during the are given in the following discussions. 3-year period immediately prior to construction. Difueivity of Concrete.-The diffusivity of con- Mean daily and mean annual air temperatures crete, hZ, is an index of the facility with which con- are used, as it would be physically impossible to crete will undergo temperature change. Although apply theoretical day-to-day temperatures to the desirable from the heat standpoint, it is not practi- cable to select aggregate, sand, and cement for a concrete. The theory developed applies these daily concrete on the basis of heat characteristics. The and annual air t,emperature cycles as sinusoidal thermal properties of the concrete must therefore variations of temperature, although the cycles are be accepted for what they are. not true sine waves. The amplitudes of these two The value of the diffusivity of concrete is usu- sine waves, with periods of 1 day (24 hours) and ally expressed in ft =/hr., and can be determined 365 days (8,760 hours), are obtained from the mean annual, the mean monthly, and the mean from the relationship h2=$ where K is the con- monthly maximum and mean minimum air tem- ductivity in B.t.u./ft /hr /” F., 0 is the specific peratures. In the computation, the annual and TEMPERATURE CONTROL STUDIES 11 12 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES ‘R3”“+Maximum recorded - Mean daily maximum- --Mean annual ,---Minimum recorded o- - -3& JAN. 1 FEB. 1 MAR.! APR.~ MAY 1 JUNE I JULY AUG. SEPT.] OCT.] NOV. DEC. HUNGRY HORSE DAM I I I I I I 3550 3500 3450 n A c W I I/ I w 3400 IA I 2 3350 0 ,- Q 3300 RANGE OF > RANGE OF W RESERVOIR- -I 3250 MEAN WATER W CONCRETE TEMPERATURES EMPERATURES 3200 3150 t 3100 t- 30 40 50 60 70 35 40 45 50 55 60 TEMPER ATURE --DEGREES ‘I,F. ,I FIGURE 5.-Hungry Horse Dam-olimatio and mean concrete temperatures. TEMPERATURE CONTROL STUDIES 13 14 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES 1150 4 ‘--Maximum recorded - 30 - minimum Mini mum recorded-; 20 - 6, AIR TEMPERATURES JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. 1 NOV.1 DEC. MONTICELLO DAM I I I I I I I I I I I I 450 -I I- c ii 400 l.L I z 350 0 - RESERVOIR 2 300 > TEMPERATURES y 250 W 200 L I I I I I 40 50 60 70 80 90 45 50 55 60 65 70 75 00 TEMPERATURE-DEGREES F. FIWJRE 7.-Monticello Dam-climatic and mean concrete temperatures. TEMPERATURE CONTROL STUDIES 15 TEMPERATURE RANGE OF Humase DAM (Effect of solar rodiotion not included) For yeorbchange fly&=-=& = U%!d?z I For 365-h change l?, &m{- q . e* -o.n7* For doily change &= #.).)fz4. = 0.w E. Thickness of dam, ft. Curve referred to is “Tamperoture Voriotions of Flat Slobs Exposed to Sinusoidal Temperature Variations on Both Faces: FIGURE &-Computation form (sheet 1 or R)-rarcge of mean concrete temperaturea. daily amplitudes are assumed to be the same for which, when added to the amplitudes of the daily extreme and usual weather conditions. and annual cycles, will account for the actual To account for the maximum and minimum maximum and minimum recorded air tempera- recorded air ‘temperatures, a ,third and somewhat tures at the site. For usual weather conditions, fictitious temperature cycle must ‘be assumed. these amplitudes are assigned values which ac- This third temperature variation is associated count for temperatures halfway betKeen the mean with the movements of barometric pressures across monthly maximum (minimum) and the maximum the country. Plots of mean daily air temperatures (minimum) recorded. Table II summarizes the for stations in the vicinity of Hoover Dam in- above discussion and shows how t,he amplitudes of dicated that about two cycles per month could be the above three temperature cycles are found. expected. Similar plots throughout the western Amplitudes of Concrete Temperatures.--The part of the United States show from one to three range or amplitude of concrete temperatures which cycles per month. Arbitrarily, therefore, the third result from air and water exposurq are deter- temperature variation is set up as ‘a sine wave with mined by applying assumed external sinusoidal a 15-day (365-hour) period. By adding the three temperature variations to the edges of a theoreti- sine waves together, any and all recorded tempera- cal flat slab. The problem is idealized by assum- tures can be accounted for. ing that the width of the slab is the same as the For extreme weather conditions, the amplitudes thickness of the dam at the elevation under consid- of the 15-day cycle are assigned numerical values eration, and that no heat flows in a direction nor- 16 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES MEAN CONCRETE TEMPERATURES TEMPERATURE RANGE Thick Effect Exposed to olr Air on D.S. Face Elev- ness of on both faces Water on US. Face OF Hungry Horse DAM “,i,.C. of Solor Ext Weo Usual Wea. Ext Wea (Usual Wea Effect of Solar Radiation included Latitude 48’ TJ Remarks: SOLAR RADIATION VALUES 131* Point I 49” I 106” Point 2 74” 1 810 Point 3 99 E lev- *::- Upstream 1 Downstream 1 Upstream 1 Dawnstreom 1 Upstream I Dawnstriam Average “... .r_-_lamp. #a:--n,ss Normal angle Normal angle Normal angle Normal angle Normal angle Normal angle atIon Factor- Temp. Rise % Slope Slope ,E:ril$ Slope ~o~~~~, Slope ~~,“$~i Slope ~~i~~~ Slop ,z;lz, US. D.S. Ft 100% Actual ~65 100 o 7.3 7 . 3 0 2.7 2.7 0 6.3 6.3 0 4.3 4.3 o 4.8 4.8 o 6.0 6.0 6.1 3550 97 o 7.3 7.1 0.25 3.4 3 3 o 6.3 6.1 0.2: 5.1 it.2 o 4.8 4.7 0.5 7.1 6.9 6.0 3500 94 o 7.) 6.9 .S 4.0 318 o 6.3 5.9 .5 6.0 5.6 o 4.0 4.5 .5 7.3 7.4 5.8 .345c 91 0 7.; 6.6 .6 4.2 3.8 0 6.3 5.7 .6 6.2 5.6 0 4.5 4.4 .6 8.1 7.4 5.6 3400 88 0 7.3 6.4 .6 4.2 i.7 0 6.3 5.6 .6 6.2 5.5 0 4.8 4.2 .6 6.1 7.~fi md 85 o 7.3 6.2 27 4.9 4.2 0 6.3 5.4 .6 6.2 5.3 0 4.8 4.1 .G 8.1 6.9 5.2 FIGURE 9.-Ccwnputation fom (sheet 2 of 2)-ralzge of mean concrete temperaturee. ma1 to the slab. The law of superposition is used of the external temperature. Figure 11 shows the in that the final amplitude in the concrete sltib is relationships thus derived for temperature varia- the sum of the amplitudes obtained from the tions in flat slabs exposed to sinusoidal tempera- external temperature variations. For a slab ex- ture variat,ions for h2= 1.00 ft 2/day, a period of 1 posed to air on both faces, three amplitudes repre- day, and a thiclmess of slab of II. To use this senting daily, X-day, and annual cycles are ap- figure, a correlation equation is given by which I, plied to the s1a.b. Although not strictly true at can be computed for any other combination of the reservoir surface, the amplitude of the reser- actual thickness of dam, diffusivity constant, and voir water temperature is assumed to have an an- period. nual cycle. The computation shown in Figure 8 follows the To apply the results of theoretical heat-flow above theory. From the actual thickness of dam, studies in a practical and usable form, unit. values I,, a value of I, is obtained from the correlation were assumed for the several variables and a curve equation for each of the a.ir temperature cycles. was dbtained showing the ratio of the variation of For each value of Z,, a ratio of the variation of tihe mean temperature of the slab to the variation mean concrete temperature to the variation of ex- TEMPERATURE CONTROL STUDIES FIIQURE IO.-Glen Canyon Dam-air and water temperatures. CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES TABLE I.-Thermal properties of concrete for various dams - - Conductivity K Specific heat C Diffusfvity h2 Density B.t.u./ft /hr IOF. B.t.u./lb /OF. ft l/hr Dam t:ssturated \ - I lb /cu It -- - 700 900 700 900 w 700 900 --_------ Norris____._____-_.___-_-_____ 160.6 2.120 2.105 2.087 0.234 0.239 0.247 0.056 0.055 0.053 Glen Canyoti ______---__- 148.4 2.02 2.01 2.01 .211 216 222 065 .063 .061 Seminoe _____.______.___ ---__- 155.3 1.994 1.972 1.951 204 :213 :222 :063 .060 .057 Wheeler _____ ---- _____ -- ____ -_ 14.5. 5 1.815 1.800 1.785 :223 .229 236 .056 054 .052 Flaming Gorge------___.. -_ 150.4 1.78 1.77 1. 76 ,221 .226 :232 .054 :052 .050 Kortes mixes: 1 bbl cement/cu yd and O.O-percent air--_-- ___. -- 157.6 1.736 1.724 1.711 .210 .215 .221 ,052 .051 .049 0.85 bbl cement cu yd and O.O-percent air- ____ - - _ _ _ - 158.1 1.715 1.710 1.705 209 .215 220 052 .050 049 Hungry Horse_--- _._____ --__-- 150.1 1. 72 1.72 1.71 1217 .223 : 229 :053 051 :050 Hoover______---____~------156.0 1.699 1.688 1.677 212 .216 221 .051 :050 .049 Gibson- _ _ _ _ _. _. ______155.2 1.676 1.667 1.657 :218 222 : 229 050 048 .047 Canyon Ferry- ______. _ _. _ - - _ _ 151.3 1.63 1.62 1.61 214 :218 222 :050 : 049 048 Altus-___.______-----.--~--- 149.7 1.578 1.579 1.580 :225 * 229 :234 .047 046 :045 Monticello------______-___-- 153.1 1.57 1.56 1.55 .225 .230 .235 .046 :044 .043 Yellowtail------______-__-__- 152.8 1. 57 1. 56 1. 55 .219 .223 .227 .047 .046 .045 Angostura mixes: 0.9 bbl cement/cu yd and 3.0-percent air-- _ _ _ _. _ _ _ _ 151.2 1.491 1.484 1.478 .221 .228 .234 .045 .043 .042 1.04 bbl cement/cu yd and O.O-percent air------.._ 152.6 1.571 1.554 1.537 227 .234 240 045 .044 ,042 Hiwassee----_-_- ____._ -----__ 155.7 1.505 1.491 1.478 :218 .225 :233 :044 .042 .041 Parker_--_---_-__------~-- 155.1 1.409 1.402 1.395 213 216 .221 043 .042 .041 Owyhee.. . _ . ______. . _. ______152.1 1.376 1.373 1.369 :208 :214 .222 :044 042 041 O’Shaughnessy---- ___.._ -._--... 152.8 1.316 1.338 1.354 .217 .218 .223 .040 :040 :040 Friant mixes: Portland cement_- _. ______. 153.6 1.312 1.312 1.312 .214 .214 217 040 .040 .039 20-percent pumicite _._____.. 153.8 1. 229 1.232 1.234 ,216 221 :227 :037 ,036 035 Shasta------__.._.___ -_.. 157.0 1.299 1.309 1.319 222 : 229 .235 .037 037 :036 Bartlett---.-.----- _.__.._.____. 1.56. 3 1.293 1.291 1.289 :216 .222 .230 .038 :037 .036 Ilorris-.. .-. . _ __- ___._. . . . .__. 156. 9 1. 290 1.291 1.293 .214 .216 .222 039 .038 .037 Chickamauga-.---- _._.___ ---_.. 156.5 1. 287 1.277 1.266 225 . 229 .233 :037 .036 .035 Grand Coulcc----- _...... ~--_.. 158.1 1.075 1.077 1.079 : 219 .222 .227 031 031 030 Ariel____. -__----- .._...... -__. 146.2 D.842 0.884 (I.915 .228 .235 .244 :025 :026 :026 Bull Run-.._-_---- ...... __ --_.. 159.1 3.835 0.847 (I.860 .215 ,225 .234 .024 .024 .023 - - - Thermal Properties of Coarse Aggregate --. - Quartsite-~~------_..._.___ -__. 151.7 2.052 2.040 2.028 .209 ,217 .226 .065 .062 .059 1)olomite ____ --__- __....______. 156.2 1. 948 1.925 1.903 .225 .231 238 .055 .053 .051 Limestone ____ -__-_~ . . .._.____. 152.8 1.871 1.842 1. 815 .221 ,224 :230 ,055 .054 ,052 Granite __._ ----._- _....._.____. 150.9 1.515 1.511 1.588 .220 .220 .224 .046 .045 045 Basalt ____ ----_-_- _.__ -__----_ 157.5 1.213 1.212 1.211 226 .226 .230 .034 .034 :033 Rhyolitt:.----- _____ -__------_.. 146.3 1. 197 1.203 1.207 :220 .226 .232 .037 .036 .036 - -. -.-__ - TEMPERATURE CONTROL STUDIES 19 TABLE II.-Ampliludes of air temperatures taken reservoir water temperatures over a period of several years in a number of reservoirs. From Extreme weather Usual weather conditions conditions t,hese data, maximum ranges of temperature for Period - -- - the operating conditions encountered during the Above Below Above Below mean mean mean mean data period were obtained as shown in Figures _- -___ -- 12 and 13. Reservoir water temperatures were Annual __.__----___-______(I) also determined for periods of about 11/z years at 18day- __ _-- ______(4) Mormon Flat, Horse Mesa, Roosevelt, and Stewart Daily- ______(3) iMountain Dams. These data are shown in Figure - 14. Figures 15 through 19 show temperature vari- 1 The difference between the higheat&-an monthly and the meon annual. 1 The difference between the Zmoeatmt-an monthly and the mean annual. ations with depth throughout t,he year at various 8 One-half the minimum difference between any mean monthly matimum and the corresponding mean monihly minimum. dams in the western I’nited States. Figures 20 4 The difference between [‘+a] and [the htghurt maximum recordedminus the mean annual]. and 21 show similar data obtained by the Tennes- 1 The difference between P+a] and [the Zourest minimum recordeddifference from mean annual]. see Valley Authority for 5- and g-year periods at 6 The difference between [I+ and [the difference between the mean annual and the overage of the higx eat m&mum recordedand the highestm&m Fontana and Hiwassee Dams. Figures 22 and 23 monthly m&mum 7 The difference b etwecn [*+$I and [the difference between the mean annual not’ only provide data at Elephant Butte Dam and and the average of the minimum recorded and the Zowcstmean monlhly minimum]. at Grand Lake (Colorado), but also illustrate two methods of plotting data on reservoir tempera- ternal temperature is obtained. The products of tures. these ratios and their respective amplitudes are When no data are available at nearby reservoirs, algebraically added to and subtracted from the t’he next best estimate of t,he reservoir tempera- mean annual air temperature to obtain mean con- tures would be obtained by the principle of heat crete temperatures for the condition of air on both continuity. This method takes into consideration faces. Mean concrete temperatures which would the amount and temperature of the water entering result from a fictitious condition of water on both and leaving the reservoir, and the heat transfer faces are then obtained, and the two conditions are across the reservoir surface. These heat budget simply averaged together to obtain the condition computations, though accurate in themselves, are of air on one face and water on the other. based on estimates of evaporation, conduction, ab- Reservoir Water Temperatures.-The stabilized sorption and reflection of solar radiation, and re- temperature distributions in a concrete dam are radiation, u-hich are in turn based on cloud cover, dependent, to a large extent, upon the reservoir air temperatures, wind, and relative humidity. water temperatures. These reservoir water tem- Variable as these factors are, any forecast of tem- peratures vary with depth, and for all practical perature conditions in a reservoir based on the purposes can be considered to have only an an- principle of heat continuity must be considered nual cycle. There will also be a time lag between only as an estimate. tihe air and water tmperatures, the greatest lag In the absence of data from nearby reservoirs occurring in the lower part of the reservoir. Nor- and data on the flow and temperature of the river, mally this time lag need not be taken into consid- a rough estimate of the reservoir temperatures can eration. There are circumstances, however, as be prepared based on the monthly mean air tem- with extremely thin arch dams, when the effects of peratures at the site, the operation and capacity this time lag should be investigated. The reser- of the reservoir, and the general characteristics of voir water temperatures normally used in deter- the river flow. The amplitude of the water tem- mining the range of mean concrete temperatures perature variation at the surface will be nearly for a proposed dam are those temperatures which equal to that of the mean monthly air temperature, will occur after the reservoir is in operation. except that it will not go below 32” F. Below the The best, estimate of the expected reservoir water surface, the operation of the reservoir contributes temperatures would be one based on water tem- to a wide range of temperatures experienced at the peratures recorded at nearby lakes and reservoirs different elevations on the upstream face of the of similar depth and with similar inflow and out- da,m. Flood control reservoirs vary between wide flow conditions. The Bureau of Reclamation has limits depending upon the operating criteria of CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES Temperature Variations of Flat Slabs Exposed to Sinusoidal Temperature Variation on Both Faces W lx 2 Conditions: a IY h2= 1.00 ft2/day ‘W Period of temperature variation = J = I day : W Thickness of slab as shown = J!, II’ For other conditions: THICKNESS OF SLAB - FEET (8,) FIMJRE Il.-Temperature variation.8 of pat slabs exposed to 8Znusoidal temperature variation olt both faces. the reservoir. The water surface of a storage res- temperature of the incoming water will be very ervoir will fluctuate through a wide range as it is low in the winter and early spring months. The filled and then drawn upon for irrigation water; distance from the source will affect the *stream% the reservoir water surface for a power dam will temperature considerably by the time it enters normally remain at a relatively uniform level. the reservoir. A large part of the water for Lake The flow of the river determines, to a large ex- Mead starts as snowmelt, but ‘by the time it reaches tent, the reservoir water temperatures. Snowmelt t,he reservoir, hundreds of miles downstream, it and proximity to the source may mean that the has warmed up considerably. Colorado River TEMPERATURE CONTROL STUDIES water temperatures vary during ‘the year from 32” Mathematical Model of Stream Temperature” by to about 60” F. in the river below Grand Lake, David W. Duttweiler (Thesis, The John Hopkins Colorado, ‘and from 40” to 82” F. at. Hoover Dam. University, 1963) gives methods for estimating Water temperatures on the Sacramento River in stream temperatures, both in natural flow and California were obtained at eight locations. downstre YELLOWTAIL DAM OWYHEE DAM MONTICELLO DAM -__- FOLSOM DAM GRAND LAKE, COLO. FRIANT DAM 38 40 45 50 55 60 65 70. ,5*‘lo 45 50 55 60 65 70 71 BQ 45-50 55 60 65 70 75 80. 35-40 45 50 55 60 65. 35.40 41 50 55 60 65 70 IS 80. FIGURE 13.-Range of actual reeervoir temperatures under operating conditions (eheet 2 of 8). such, the reservoir temperatures would, for all States. These data were then correlated with the- depths, approach those of the incoming river oretical studies which take into consideration water temperatures. Other reservoirs may take varying slopes, orientation of the exposed faces, several years to fill with the full flow of the river. and latitudes. Lake Mead, for example, would require about 2l/, The results of these studies are presented in an years of the mean river discharge to fill the reser- unpublished Bureau of Reclamation memoran- voir. The water moves into the reservoir and stays dum, “The Average Temperature Rise of the Sur- for a relatively long period of time, during which face of a Concrete Dam Due to Solar R.adiation,” t,ime it is ,affect.ed by the climatic conditions of the by W. A. Trimble. Figures 25 through 28 sum- site. marize the results obtained by the Trimble mem- Solar Radiation Effect.-The mean concrete orandum and give values of the temperature temperatures obtained from air and water temper- increase for various lati,tudes, slopes, and orienta- atures require adjustments due to the effect of solar tions. It should be noted that the curves give a radiation on the surface of the dam. The down- value for the mean annual increase in temperature st.ream face, and the upstream face when not cov- and not for any particular hour, day, or month. ered by reservoir water, receive an appreciable Examples of how this solar radiation varies amount of radiant heat from the sun and this has throughout the year are given in Figure 29. the effect of warming the concrete surface above If a straight gravity dam is being considered, the surrounding air temperature. The amount of the orientaton will be the same for all points on this temperature rise above the surrounding air the dam, and only one value for each of the up- temperatures has been recorded at the faces of stream and downstream faces will be required. several dams in the western portion of the United For an arch dam, values at the quarter points TEMPERATURE CONTROL STUDIES 23 :-----ROOSEVELTDAM I’ Nor W S. El. 2136.-” -HORSE MESA DAY -- \ Nor WS. El. 1914.-- LAKE ROOSEVELT =3c(Arizona) RIVER / Ii HORSE MESA RESERVOIR 1932 IS33 FIGURE 14.-Range of actual reseruoir temperatures under operating conditions-8aZt Riwer project dams. should be obtained as the sun’s rays will strike tensile stresses in arch dams tend to occur in the different parts of the dam at varying angles. The lower part of the dam, at the intrados in the cen- temperature rises shown on the graph should be tral part, and at the extrados near the abutments. corrected by a terrain factor which is expressed as With the same loading conditions, vertical tensile the rat,io of actual exposure to the sun’s rays to the stresses tend to occur on the upstream face near theoretical exposure. This is required because the the base of the dam and on the downstream face theoret,ical computations assumed a horizontal near the top of tihe dam. With minimum reser- plane at the base of t.he structure and the effect of voir load and maximum or near-maximum con- the surrounding terrain is to block out certain crete temperatures, tensile stresses tend to occur hours of sunshine. Although this terrain factor along the intrados near the abutments, and ver- will actually vary for different points on the dam, tical tensile stresses tend to occur on the down- an east-west profile of the area terrain, which stream face near the base of the dam. The tensile passes through the crown cantilever of the dam, stresses on the upstream face occurring with res- will give a single factor which can be used for all ervoir load and near-minimum concrete tempera- points and remain within the limits of accuracy of tures can be reduced by additional cooling of the the method itself. Figure 9 shows the computa- concrete prior to grouting the contraction joints. tion of the solar radiation values and how they are Such additional cooling, however, will increase applied to the previously obtained mean concrete the tensile stresses for the minimum reservoir- temperatures. maximum Mnperature condition. The actual closure temperature for an arch dam is, therefore, Closure Temperature a compromise arrived at to minimize the tensile In general, with normal reservoir load and mini- stresses, with additional weight being given to re- mum or near-minimum concrete temperatures, duce the tensile stresses at the upstream face. CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES h az IIIIII IIlI~llllll IIIIII 111111111111 II\ lll~lllllll;lllllllll IIIIII III-1 11l1111~ IZiCkFEB. MAR.TAPR.T MAY IJUNE~JULY I AUG. ISEPT.~ OCT. 1 NOV.~ DEC. 1 FIGURE Xi-Reservoir temperatures-Grand Coulee Dam. TEMPERATURE CONTROL STUDIES W liiiiiiiiiiiiikiii iiiiibFWtYi iiiiifliiiii iIi!lI I, iY/iil1i111! IitttFWt1fIII cr 11III I II/II APR.) MAY IJUNE JULY 1 AUG. ISEPT OCT. NOV. DEC. FIGURE K-Reservoir temperature+-Hoover Dam. 26 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES 0 I W oz I> c 60 h z % W l- 50 30 FIQURE 17.-Reservoir tempcratrcres-Shasta Dam. -. -.---_- .-_ TEMPERATURE CONTROL STUDIES 28 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES Ii, /1 ,,),I, I I, I I!,,, I,,, I, I,, 1 I,,,, , I III’ IllI II I II III1 III III I I,,,III ,I 90, 1 IIll tr I-II n-l-r: 77 III I I I ‘4 t I I --I I FIQWE B-Reservoir temperatures-Hungr$i Horse Dam. TEMPERATURE CONTROL STUDIES PIQURE Z&-Reservoir temperaturea-Hizoaesee Dam. CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES 80 60 FIGURE PI.-Reservoir temperatures-Montana Dam. TEMPERATURE CONTROL STUDIES 31 c AUGUST 30.1941 30 40 50 30 40 50 60 TEMPERATURE IN DEGREES FAHRENHEIT NOTES Observotlons started February 1940 T=Air temperature in degrees Fahrenheit. No observations mode from Feb28 to May 31 due to unsafe ,ce conditions FICXJBE 23.-Reservoir temperatures--Grand Lake, Colorado. rEMPERATURE -OF. TEMPERATURE- “F. TEIv~PERATURE-~F: s : g 0” z $ g 0” 2 0” -T MILE O.O-SHASTA DAM MILE 34.9-BALLS FERRY MILE 92.9-VINA MILE l28.6-ORD FERRY MILE 179.5-MERIDIAN IILE 225.4-KNl6HTS LANDING , hk z MILE 258.6-SACRAMENTO WATER WORKS MILE-299.5 RIO VISTA (U.S.E.D. DOCK) 34 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES .35O \ I \ \ \ I io”l I I 0.6 - \I \ I\ \I \ I I\ I .30° -I \ go \ 9 \ i= II: ,25’ >W - % ,20° IL= w 0.0 0' 20’ 40° SO” loo0 120° 140° 160° 180° ANGLE OF NORMAL TO SURFACE MEASURED FROM NORTH LATITUDES 3o”- 35O FIGUBE Zi.-Increase in temperature due to solar radiation-latitudes 30”-35”. TEMPERATURE CONTROL STUDIES 35 0.7 0.6 0.5 ow 3 0.4 5 m g 0.3 w 8 0.2 s: 0. I 0.0 -0.1 \ \ \ \ .-k5O) -0.2 -0.3 \ ,0.36” -0.4 I ( 20O 40O 60° loo0 120° 140° 160° 180° ANGLE OF NORMAL TO SURFACE MEASURED FROM NORTH LATITUDES 35O- 4o” FIGURE 26.-Zncrease in temperature due to solar radiation-Latitudes S5’-40’. 36 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES tY I \I\ Y Ill II II \I If 25’ ‘f! w 15O o w I e 5 IO0 * 0. I 0.0 -0. I - 0.2 -0.3 - 0.4 O” 20° 40° 60’ 80° loo0 120° 140° 160° I 80° ANGLE OF NORMAL TO SURFACE MEASURED FROM NORTH LATITUDES 4o”-45O FIGUBE n .-Znweaee in temperature due to 8okw radiation--Latitude8 40°-450. TEMPERATURE CONTROL STUDIES 37 0.9 0.8 0.6 0.5 \I ( U-O i ow > e 0.4 5 2o" g LL 0.1 let-1 0.0 -0.1 -0.2 -0.3 0.3c -0.4 0 o" i 40° 60° E ANGLE OF NORMAL TO SURFACE MEASURED FROM NORTH LATITUDES 4 5O- 5o” J?mm~ !B.-Increase in temperature due to 8olar radiatiwn-Latitude8 45’-50’. CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES I Hug.I--’ 1 / July I i 1 Seplt.Sept I---. I pr. I ,*’ I I / I[ I’ 1 / /O ‘ct.I ,--Upstream face of No !Feb. I t / -Downstream face of /* YO over Darn I / I / /’ / -I-/ L -*,July I I ) G-Y / A-- !Aug. I i Y ’ iept 1T. / I j&r. I I --Upstream face of !g - Hoover Dam _ or. I /I eb. I Dee 0 I 2 3 4 5 6 7 8 9 IO II 12 13 14 I5 16 17 TEMPERATURE DIFFERENCE -CONCRETE SURFACE AND AIR -“F. FIOURE 29.-Variation of solar radiatiola during year. TEMPERATURE CONTROL STUDIES 39 The degree of subcooling, that is, t.he actual reach the grouting temperature at different times amount of cooling below the final stable tempera- in the several grout lifts. This requires close con- ture, is normally based upon what the trial-load trol over the contraction joint grouting program, analyses show to be desirable from a stress stand- and may require that lower portions of the dam be point; but the degree of s&cooling may be influ- artifically warmed to permit an orderly grouting enced by practical or economic considerations. program which can be accomplished before the top The designer often has to make a design decision of the dam becomes too warm. whet,her to lose 2” to 5’ of temperature benefit in the arches ‘by using the river water available to Temperatures in Mass Concrete cool artificially the concrete in the dam, or whether to obtain the desired temperature benefit by re- Before reaching any final stable state of tem- quiring mechanically refrigerated water to per- perature equilibrium, the temperature history of form t.he cooling. the concrete is associated with many factors. The From the practical standpoint, it is possible to placing temperature and the rate of placing the cool the concrete by means of an ~mbedaedpipe concrete; exposure conditions during placement ; cooling system to within 4” to 5’ of the mean tem- the amount and types of cement, pozzolan, and perature of the cooling water available. Concrete admixtures; and whether any additional tempera- temperatures as low as 35” F. have been obtained ture control measures such as embedded cooling with a refrigerating plant using brine as the cool- pipes were used are the most important of these factors. A schematic temperature history of con- ant. Where cooling is accomplished with river crets placed in an artificially cooled concrete dam water, concrete temperatures depend on the mean is shown in Figure 30. river water temperature. At Hungry Horse Dam, At any time during the early age of the con- 32’ to 34” F. river water was available during the crete, concrete ,temperatures can ,be obtained by colder months of the year, and final cooling was taking into consideration the flow of heat across accomplished to 38” F. with this river water. A an exposed face, the flow of heat through an single closure temperature of 38” F. was deter- internal boundary such as the rock foundation mined satisfactory for the particular layout and ‘or a previously placed lift, the heat of hydration section of Hungry Horse Dam. At Monticello of the freshly placed concrete, the diffusivity of Dam, river water was both limited in quantity and t,he concrete, and the removal of heat by an em- was relatively warm since the stream primarily bedded cooling system. Afterward, t.he tempera- carries a surface runoff during periods of rainfall. tures existing at any specific point in a mass Refrigeration of the cooling water was required in concrete structure are dependent upon a number this instance to obtain t,he desired closure tempera- of other factors. These include the air and water tures. Two closure temperatures were used at temperat,ures adjacent to the structure boundaries, Mont.icello Dam, 45O F. in the lower part of the ground temperature, wind, precipitation, relative dam and 55O F. in the upper part of the dam. humidity, solar radiation, and canyon wall re- This was done so that more load could be carried radiation. The fluctuation or range of tempera- by the lower portion of the dam. tures experienced at a specific point is also related In relatively thin arch dams, pipe cooling may to the distance to the boundaries of the structure. be omitted and the concrete permitted to cool nat- In regard ,to the longtime hydration of cement, urally over t:he winter. Depending on the sever- t,he rate of heat generation is related to the type of it.y of the exposure conditions, it may then be nec- cement. Standard cement generates the majority essary to wait unt,il the concrete temperatures rise of its heat in the first 3 or 4 days after place- to above 32O F. before grouting the contraction ment.; a low-heat cement generates perhaps half joints. Closure temperatures of 35” to 36” F. can of its heat during the same period of time. After be obtained in these struct,ures. Because of the a period of a year or two, however, all types of varying thicknesses, concrete temperatures in thin cement have either stopped generating heat or are arch dams which are left to cool naturally will generating heat at such a low rate that the heat is 40 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES p------*------_- >k------*------*------A I Initial cooling I I NO pipe cooling. Periodvaries 1 Intermediate and 1 Requires from 2 or3 1 Finolonnuol I I period 1 from I or2 monthsto obout I final cooling I yearsto20years I temperature I I I I yeor,dependingongrouting i periods. I dependinganamount I cycle I I I program. I of subcooling. I I I I I I I 0 Placing temperature varies from 40°F.to 60°F. unless restricted to on intermediatetemperoture because of length of block. 0 Temperature history between cooling periods dependent an exposuretemperatures,thickness of section,diffusivity of concrete,ondtype and amount of cement. 0 Rangeofmean concrete temperature. FIOIJRE 30.-Temperature history of artificially cooled concrete. dissipated to the surfaces of the structure and lost assumed. Since the validity of any heat-flow com- before it can increase the internal concrete tem- putation is dependent on the correctness of the perat.ure. Based on actual temperature observa- assumed exposure conditions and concrete proper- tions at Hoover, Shasta, Seminoe, and Hungry ties, experience and good judgment are essential. Horse Dams, the temperature rises in the concrete To combine the effects of natural and artificial subsequent to secondary cooling are almost en- cooling, the solutions of the separate idealized t.irely related to ,the ,amount of subcooling accom- problems are superimposed to obtain final concrete plished bc low the final stable temperature and to temperatures. the exposure conditions existing from the time of He& of Hydration.-Newly placed concrete such subcooling to the eskablishment of the final undergoes a rise in temperature due to the exo- &a010 temperature. thermic reaction of the cementing materials. The Average temperatures which occur during oper- amount of this heat generation is dependent upon ation of a structure, after equilibrium has been the chemical composition, fineness, and amount of established between the concrete temperatures and cement; the amount and type of pozzolanic ma- the ex’ternal boundary conditions, have been dis- terial used, if any; the water-reducing agent or cussed earlier as the range of mean concrete tem- retarder used, if any; and the temperature of the perature. Often, however, temperature distribu- concrete during the early period of hydration. tions or temperatures at a specific point are Some of these factors may be controlled and used as desired, and these can be t,heoretically obtained by temperature control measures, others are employed several methods, both during the early age of the for quality or economy; others must be accepted concret,e and in the final state of temperature and used as agiven condition. equilibrium. Portland cement may be considered as being The following discussions cover the more com- composed of four principal chemical compounds. mon temperature investigations and studies. In These are tricalcium silicate, dicalcium silicate, most of these studies, certain conditions must be tricalcium aluminate, and tetracalcium alumino- TEMPERATURE CONTROL STUDIES 41 ferrite, or, as they are more commonly known, by laboratory test, using the actual cement, con- Cd, C&, C,A, and C4AF. The relative propor- crete mix proportions, and diffusivity for the con- tions of these chemical compounds determine the crete under consideration. different types of cement. Table 5 of the Seventh Pozzolans are used as a replacement for part of Edition of the Bureau of Reclamation’s Concrete the portland cement to improve workability, to Manual gives typical compound composition for effect economy, to better the quality of the con- the several types of cement. Type I cement is the crete, or to reduce the t.emperat.ure rise resulting standard cement and the most commonly used in from the hydration of the cementing materials. general construction. Type III cement is a high For early studies, the thermal properties of the early-strength cement used primarily in emer- different types of pozzolans (fly ash, ground slag, gency construction and repairs, and in the labora- clays, shales, diatomaceous earth, etc.) can be as- tory where early results are required. Type V sumed to generate about 50 percent as much heat cement is a sulfate-resistant cement developed for as the cement it replaced. use where soils or ground water containing rela- Placing concrete at lower temperatures will tively high concentrations of sulfates exist. lower the early rate of heat generation in the con- Because the heat of hydration of cement is crete. This benefit will be relatively small, as largely dependent upon the relative percentages shown in Figure 32. Adiabatic tests in the labora- of the chemical compounds in the cement, Types tory normally take this effect into consideration by II and IV cement were developed for use in mass using the placement temperature and mass cure concrete construction. Type 11 cement is com- temperature cycle anticipated for the structure. monli referred to as modified cement. It is used where a relatively low-heat generation is desirable Schmidt’s Method.-Temperature distribut.ions and is characterized by low C,A and high C,AF in a mass where boundary conditions are variable contents. Type IV cement is a low-heat cement are easily determined by the Schmidt or Schmidt- characterized by its low rate of heat generat.ion Binder Method.” This method is most frequently during early age. Type IV cement has high per- used in connection with temperature studies for centages of C;S and C4AF, and low percentages mass concrete structures in which the temperature of 0,s and C,A. Very often, the run-of-the-mill distribution is to be estimated. The approximate cement from a plant will meet the requirements of date for grout.ing a relatively thin arch dam after a Type II cement, and the benefits of using this a winter’s exposure, the depth of freezing, and t.ype of cement can be obtained at little or no extra temperature distributions after placement are cost. Type IV cement, because of its composition, typical of the solutions which can be obtained by is obtained at premium prices. t.his step-by-step method. Different exposure tem- Figure 31 shows typical temperature rise curves peratures on the two faces of the theoretical slab for the various types of cement. The temperature and heat of hydration can be taken into considera- rise curves are based on one barrel (four sacks) of tion. cement per cubic yard of concrete and no em- In its simplest form, Schmidt’s Method assumes bedded pipe cooling. These curves should only no heat flow normal to the slab and is adapted to a be used for preliminary studies because there is slab of any thickness with any initial temperature a wide variation of heat generation within each distribution. Schmidt’s Method states that the type of cement. For final ‘temperature control temperature, tP, of an elemental volume at any studies, the heat generation 2 should be obtained subsequent time is dependent not only upon its own temperature but also upon the temperatures, 2 Conversion of calories/gram hydration rise to degree F. temperature rise is made by : aScha&, Alired, 1933, Industrtal Heat Transfer, JOho Wiley Temp. rise (OF.1 = 1.8(cal/g. hydration) and Sons. c(“,“,i;,“ho;f’) Jakob, Max, 1949. Heat Transfer, Volume I, Pages 373-375, John Wiley and Sons. where C=spectdc beat of concrete and weight Is ia pounds per Qrinter, L. E., 1949, Numerical bfethods of Analysis in Enoi- cubic yard. neWnO, page 86. Macmillan Co. CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES -----Adiabatic temperature rise of stondard cement 6C ,,---Modified cement 50 , c --Low-heat cement Ii 0 ’ 40 % iE w 5 2 30 6 f-standard cement ii w l- . \ . I’ -1 I ‘1 20 I PAveroge temperature - 1 rise for 5-foot lifts J exposed on top. IO 0 2 4 6 8 IO I2 I414 I616 I8 20 22 24 AGE -DAYS Cement content- I bbl per cu yd Diffusivity - 0.050 ft2/ hr FIQURE 31.-Temperature rise in mas8 concrete-type of cement. TEMPERATURE CONTROL STUDIES 43 FIOUBE 32.-Efect of initial temperature on heact of hydratim. 44 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES TABLE III.-Related values of AZ and At for Schmidt's Method - Ax-f& (ft Yr 1 At-hours At-days - - - 1 2 3 4 6 3 10 12 1 2 3 4 6 10 16 -- -_ -_ -_-----__- 0.031 (). 249 1. 352 I.431 ). 498 ). 610 (1. 704 (). 787 (I.863 1. 220 1. 725 2. 113 2.440 2. 728 3. 857 4. 724 . 032 . 253 . 358 .438 . 506 . 620 . 716 . 800 . 876 1.239 1. 753 2. 147 2.479 2. 771 3. 919 4.800 . 033 .257 363 445 . 514 . 639 . 727 .812 .890 1. 259 1. 780 2. 180 2. 517 2. 814 3. 980 4.874 .034 .261 : 369 : 451 . 521 .639 . 738 . 825 . 903 1. 278 1.807 2.213 2. 555 2. 857 4. 040 4.948 . 035 . 265 . 375 .458 . 529 . 648 . 748 . 837 .917 1.296 1.833 2. 245 2. 592 2. 898 4. 099 5. 020 . 036 . 268 .380 465 . 537 . 657 . 759 .849 . 930 1. 315 1. 859 2. 277 2. 629 2.939 4. 157 5. 091 .037 .272 . 385 : 471 . 544 . 666 . 769 . 860 5. 161 . 038 . 276 .390 .478 . 551 . 675 . 780 1872 :955942 1. 351330 1.9101. 885 2. 308339 2.6652. 701 3.2. 020980 4.4 214271 5.231 . 039 . 279 .395 . 484 . 559 . 684 . 790 .883 : 967980 1. 368386 1.9601.935 2.2.400 370 2. 736771 3.3.059 098 4.4.382 327 5.299 040 . 283 . 400 .490 . 566 693 800 . 894 5.367 :041 .287 .405 .497 .573 : 702 : 811 .906 .993 1.404 1.986 2.432 2.809 3.140 4.441 5.439 . 042 .290 410 . 502 . 580 . 71'0 .820 .917 I 5. 499 .043 . 293 : 415 . 508 . 587 .718 829 .927 Ii: 016004 1.1.437 420 ,2.0322. 008 2.4882. 459 2.2.840 873 3. 212175 4 490543 5. 564 .044 .297 .420 .514 .593 .727 : 839 1938 1.. 028 1.453 2.055 2.517 2.907 3.250 4. 596 5.629 . 045 . 300 .424 . 520 . 600 . 735 . 849 .949 I 5. 692 . 046 .303 .429 . 525 . 607 .743 .858 . 959 1::051 039 1.4701.486 2. 078101 2. 574546 2.9722. 939 3.3.286 323 44.648 699 5.755 . 047 .307 .434 . 531 .613 .751 .867 .970 1.. 062 1. 502 2. 124 2.602 3.004 3.359 4 750 5.817 . 048 .310 . 438 . 537 . 620 . 759 . 876 .980 1. 073 1.518 2. 147 2.629 3. 036 3. 394 4.800 5. 879 . 049 . 313 .443 . 542 .626 . 767 . 885 . 990 1. 084 1. 534 2. 169 2. 656 3.067 3.429 4 850 5.940 * 050 . 316 . 447 . 548 .632 .774 .894 1.. 000 1.. 095 1. 549 2.191 2.683 3.098 3.464 4.899 6.000 . 051 . 319 .452 . 553 . 639 . 782 . 903 1. 010 1. 106 1. 565 2.213 2.710 3. 129 3.499 4 948 6. 060 . 052 1322 .456 . 559 . 645 .790 . 912 1.020 1. 117 1. 580 2. 234 2. 736 3. 160 3. 533 4.996 6. 119 . 053 326 .460 . 564 . 651 .797 .921 1. 030 1. 128 1.595 2.256 2.763 3. 190 3. 567 5.044 6. 177 . 054 : 329 . 465 .569 .657 . 805 .930 1. 039 1. 138 1. 610 2. 277 2. 789 3. 220 3. 600 5.091 6.235 . 055 .332 .469 . 574 .663 . 812 .938 1.049 1. 149 1.625 2.298 2.814 3. 250 3. 633 5. 138 6. 293 .056 . 335 473 .580 . 669 .820 .947 1. 058 1,. 159 1. 640 2.319 2.840 3.279 3.666 5.185 6.350 .057 .338 : 477 . 585 .675 1827 . 955 1. 068 1. 170 1. 654 2. 339 2.865 3.308 3. 699 5. 231 6. 406 . 058 . 341 .482 . 590 . 681 . 834 .963 1.077 1. 180 1.669 2.360 2. 890 3.337 3. 731 5.276 6.462 . 059 .344 . 486 . 595 .687 841 .972 1. 086 1. 190 1.683 2.380 2.915 3.366 3. 763 5.322 6. 518 .060 .346 .490 .600 . 693 : 849 .980 1.095 1.200 1. 697 2. 400 2. 939 3. 394 3. 795 5.367 6. 573 .061 . 349 .494 .605 . 699 .856 .988 1. 105 11210 1.711 2.420 2.964 3.422 3.826 5.411 6. 627 . 062 . 352 . 498 .610 . 704 863 .996 1. 114 1.220 1. 725 2.440 2.988 3.450 3.857 5. 455 6.681 .063 .355 . 502 . 615 .710 : 869 1. 004 1. 123 1. 230 1. 739 2.459 3. 012 3.478 3.888 5.499 6. 735 .064 .358 . 506 .620 .716 .876 1.012 1. 131 1. 239 1.753 2.479 3. 036 3. 505 3.919 5. 543 6. 788 . 065 .361 . 510 .625 . 721 .883 1.020 1. 140 1. 249 1. 766 2.498 3. 059 3.533 31950 5. 586 6.841 .066 . 363 . 514 . 629 . 727 .890 1, 028 1. 149 1. 259 1. 780 2.517 3. 083 3.560 3.980 5.628 6. 893 . 067 . 366 . 518 .634 . 732 .897 1.035 1. 158 1. 268 1.793 2. 536 3. 106 3. 587 4.010 5.671 6. 946 . 068 . 369 . 522 .639 . 738 .903 1.043 1. 166 1. 277 1. 807 2. 555 3. lb9 3. 613 4. 040 5. 713 6.997 .069 .371 . 525 . 643 . 743 . 910 1.051 1. 175 1.287 1.820 2. 574 3. 152 3.640 4.069 5. 755 7.048 * 070 .374 .529 .648 .748 .917 1.058 1. 183 I .296 1.833 2. 592 3. 175 3. 666 4.099 5. 797 7. 099 - - TEMPERATURE CONTROL STUDIES 45 t1 and &, of the adjacent elemental volumes. At sired to know the temperature distribution on the time At, this can be expressed as: following April 1. The diffusivity of Ross Dam concrete was 0.042 ft.‘/hr., and a time interval of tl+w--2)tz+tz 10 days was selected as being a reasonable time in- t 2. AI= M crement. For these values, a space interval of 4.49 would be required to meet the simple form of where M= Cp(Ax’2=(az>‘, since the diffusivity of KAt h2At Schmidt’s Method. Since the diffusivity varies K slightly with temperature, the space interval was concrete, h2, is given as -a By choosing M= 2, CP used as 4.5 feet. For the 126-foot section of the temperature, t2, at a time At, becomes t2, A$= dam under consideration, this required 28 space 4+t3__ * In this case, by selecting the time and space intervals. The temperature at the center of each space in- inzervals such that At=%, the subsequent tem- terval was obtained from the initial temperature distribution across the section, as given by em- perature of an elemental volume is simply the bedded strain meter groups and thermometers. An average of the two adjacent elemental tempera- estimate of the exposure conditions on the up- tures. For M=2, Table III gives values of At and stream and downstream faces of the dam between Ax for various values of h*. An example of the use of Schmidt’s Method was August 1 and April 1 was also required. These the determination of concrete temperatures for dais were obtained from the curves of the mean contraction joint grouting at Ross Dam. At this mbnthly air temperatures and measured reservoir dam, the temperature distribution at a given eleva- water temperatures. The computations form was tion was known on ,4ugust 1, 1945, and it was de- then outlined as follows : Space intervals (AZ) =4.5 feet - - Exp. 1 2 3 ------26 27 28 Exp. temp. temp. -- (0) 54 49.0 47.9 47.4 --______49.9 50.5 52.0 66 (1) 55 51. 0 48.2 66 (2) 55 65 (3) 55 63 The computation for the temperature of any the Ross Study and the results of these studies are space interval at a succeeding time interval then shown in Figures 33 and 34. proceeds by simply averaging the two adjacent The principal objection to the Schmidt Met.hod temperatures in the preceding time interval. For of ,temperature comput:ation is the time required example, the temperature of Space Interval NO. to complete *he step-by-step computation. This 54+47.9=51 o. has been overcome by the use of electronic dat,a 1 at Time Interval No. 1 would be 2 * , processing machines which save many man-hours the temperature of Space Ihterval No. 2 at Time of work. Programs have been prepared which will take into consider,ation different varying ex- In Interval No. 1 would be 4g*oz47*4 = 48.2, etc. posures on ,the two faces of the slab, a varying heat this manner, the temperature distribution for Time of hydration with time, and ,the increasing of the Interval No. 1 is determined before progressing slab th,ickness at regul,ar intervals such as would to Time Interval No. 2, etc. The computations for occur when additional lifts are placed. 46 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES -7 Time UP Space intervals interva h!aI ------face 1 2 3 4 5 6 7 8 9 10 ; 11 12 -_ -_ 13 14 -_ ------0 54 49. c 47. 9 I 47. 4 47. 1 47. c1 47. 4 49. 2 50. 7 51. 4 51. 7 51. 8 51. 8 51. 8 51. 8 1 1 55 51. a 48. 2 47. 51 47. 2 47. 2 48. 1 49. 0 50. 3 51. 2 51. 6 51. 8 51. 8 51. 8 51. 8 2 55 51. 6 49. 2 47. 7 47. 4 47. 6 , 48. 1 49. 2 50. 1 51. 0 51. 5 51. 7 51. 8 51. 8 51. 8 3 55 52. 1 49. 6 48. 3 47. 6 47. 8 48. 4 49. 1 50. 1 50. 8 51. 4 51. 6 51. 8 51. 8 51. 8 4 54 52. 3 50. 2 48. 6 48. 0 , 48. 0 / 48. 4 49. 2 50. 0 50. 8 51. 2 51. 6 51. 7 51. 7 51. 8 5 53 52. 1 50. 4 49. 1 48. 3 48. 2 48. 6 49. 2 50. 0 50. 8 51. 2 51. 4 51. 7 51. 7 51. 8 6 52 51. 7 50. 6 49. 4 48. 6 48. 4 48. 7 49. 3 49. 9 50. 6 51. 0 51. 4 51. 6 51. 8 51. 8 7 51 51. 3 50. 6 49. 6 48. 9 48. 6 48. 8 49. 3 50. 0 50. 4 51. 0 51. 3 51. 6 51. 7 51. 8 8 50 50. 8 50. 4 49. 8 49. 1 48. 8 49. 0 49. 4 49. 8 50. 5 50, 8 51. 3 51. 5 51. 7 51. 8 9 48 50. 2 50. 3 49. 8 49. 3 49. 0 49. 1 49. 4 50. 0 50. 3 50. 9 51. 2 51. 5 51. 6 51. 8 10 46 49. 2 50. 0 49. 8 49. 4 49. 2 49. 2 49. 6 49. 8 50. 4 50. 8 51. 2 51. 4 51. 6 51. 8 11 44 48. 0 49. 5 49. 7 49. 5 49. 3 49. 4 49. 5 50. 0 50. 3 50. 8 51. 1 51. 4 51. 6 51. 8 12 42 46. 8 48. 8 49. 5 49. 5 49. 4 49. 4 49. 7 49. 9 50. 4 50. 7 51. 1 51. 4 51. 6 51. 8 13 41 45. 4 48. 2 49. 2 49. 4 49. 4 49. 6 49. 6 50. 0 50. 3 50. 8 51. 0 51. 4 51. 6 51. 8 14 40 44. 6 47. 3 48. 8 49. 3 49. 5 49. 5 49. 8 50. 0 50. 4 50. 6 51. 1 51. 3 51. 6 51. 8 15 40 43. 6 46. 7 48. 3 49. I. 49. 4 49. 6 49. 8 50. 1 50. 3 50. 8 51. 0 51. 4 51. 6 51. 8 16 40 43. 4 46. 0 47. 9 48. 8 49. 4 , 19. 6 19. 8 50. 2 50. 4 50. 6 51. 1 51. 3 51. 6 51. 8 17 40 43. 0 45. 6 47. 4 48. 6 49. 2 19. 6 $9. 9 50. 1 50. 4 50. 8 51. 0 51. 4 51. 6 51. 8 18 40 42. 8 45. 2 47. 1 48. 3 49. 1 $9. 6 19. 8 50. 2 50. 4 150. 7 51. 1 51. 3 El. 6 51. 8 19 40 42. 6 45. 0 46. 8 48. 1 49. 0 ! i9. 4 i9. 9 50. 1 50. 4 ,50. 8 51. 0 51. 4 /51. 6 51. 8 20 40 42. 5 44. 7 46. 6 47. 9 48. 8 ! L9. 4 t9. 8 50. 2 50. 4 I50. 7 51. 1 51. 3 I51. 6 51. 8 I 21 40 42. 4 44. 6 46. 3 47. 7 48. 6 ! L9. 3 L9. 8 50. 1 50. 4 50. 8 !51. 0 51. 4 ,51. 6 51. 8 22 40 42. 3 44. 4 46. 2 47. 4 48. 5 L9. 2 L9. 7 50. 1 SO.4 ISO. 7 !il. 1 51. 3 I51. 6 51. 8 I 1 23 40 42. 2 44. 2 45. 9 47. 4 48. 3 19. 1 19. 6 50. 0 50. 4 ! 50. 8 il. 0 il. 4 il. 6 51. 8 24 40 42. 1 44. 0 45. 8 47. 1 48. 2 ,: 19. 0 19. 6 io. 0 50. 4 ! 50. 7 til. 1 il. 3 t il. 6 51. 8 I - = = ZZI = = = = Down- Time Space intervals - - - I 3tream intervah 3- 15 16 17 18 19 20 / 21 i 22 23 24 25 26 27 28 face _- _------!- 0 51. 8 51. 9 52. 1 52. 3 52. 3 52. 0 51. 7 51. 0 50. 1 49. 7 49. 5 49. 9 50. 5 52. 0 66 1 il. 8 52. 0 52. 1 52. 2 52. 2 52. 0 51. 5 50. 9 50. 4 49. 8 49. 8 50. 0 51. 0 58. 2 66 2 il. 9 52. 0 52. 1 52. 2 52. 1 51. 8 51. 4 51. 0 50. 4 50. 1 49. 9 50. 4 54. 1 58. 5 65 3 il. 9 52. 0 52. 1 52. 1 52. 0 51. 8 51. 4 50. 9 50. 6 50. 2 50. 2 52. 0 54. 4 59. 6 63 4 51. 9 52. 0 52. 0 52. 0 52. 0 51. 7 51. 4 51. 0 50. 6 50. 4 51. 1 52. 3 55. 8 58. 7 61 5 51. 9 52. 0 52. 0 52. 0 51. 8 51. 7 51. 4 51. 0 50. 7 50. 8 51. 4 53. 4 55. 5 68. 4 59 6 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51. 4 51. 0 50. 9 51. 0 52. 1 53. 4 55. 9 57. 2 56 7 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51:3 51. 2 51. 0 51. 5 52. 2 54. 0 55. 3 56. 0 53 8 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51. 4 51. 2 51. 4 51. 6 52. 8 53. 8 55. 0 54. 2 50 9 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51. 4 51. 4 51. 4 52. 1 52. 7 53. 9 54. 0 52. 5 48 10 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51. 5 51. 4 51. 8 52. 0 53. 0 53. 4 53. 2 51. 0 43 11 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51. 5 51. 6 51. 7 52. 4 52. 7 53. 1 52. 2 48. 1 40 12 51. 9 52. 0 52. 0 51. 9 51. 8 51. 6 51. 6 51. 6 52. 0 52. 2 52. 8 52. 4 50. 6 46. 1 37 13 51. 9 52. 0 52. 0 51. 9 51. 8 51. 7 51. 6 51. 8 51. 9 52. 4 52. 3 51. 7 49. 2 43. 8 35 14 51. 9 52. 0 52. 0 51. 9 51. 8 51. 7 51. 8 51. 8 52. 1 52. 1 52. 0 50. 8 47. 8 42. 1 33 15 51. 9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 8 52. 0 52. 0 52. 0 51. 4 49. 9 46. 4 40. 4 31 16 51. 9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 9 51. 9 52. 0 51. 7 51. 0 48. 9 45. 2 38. 7 30 17 51. 9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 8 52. 0 51. 8 51. 5 50. 3 48. 1 43. 8 37. 6 31 18 51.9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 9 51. 8 51. 8 51. 0 49. 8 47. 0 42. 8 37. 4 33 19 51.9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 8 51. 8 51. 4 50. 8 49. 0 46. 3 42. 2 37. 9 34 20 51.9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 8 51. 6 51. 3 50. 2 48. 6 45. 6 42. 1 38. 1 35 21 51.9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 7 51. 6 50. 9 50. 0 48. 4 45. 4 41. 8 38. 6 37 22 ; 51.9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 7 51. 3 50. 8 49. 6 47. 7 45. I 42. 0 39. 4 39 23 51. 9 52. 0 52. 0 51. 9 51. 8 51. 8 51. 6 51. 2 50. 4 49. 2 47. 4 44. 8 42. 2 40. 5 42 24 1 51.9 52. 0 52. 0 51. 9 51. 8 51. 7 51. 5 51. 0 50. 2 48. 9 47. 0 44. 8 42. 6 42. 1 45 - -j - - - FIGURE 33.-Ross Dam-Schmidt’s Method of temperature computation. TEMPERATURE CONTROL STUDIES 48 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES Carlson’s Method.-A method of temperature sulating forms. Select X=0.5 feet, T=1/ day, computation in mass concrete which is partic- and h*= 1.00 ft.?/day. Therefore, S= 1. Assume ularly adaptable to temperat.ures occurring in A0 as 6.2’ F. for the first l/ day and 8.5” F. for thick walls and placement lifts near the rock the second I/ day. Assume both the initial and foundation was devised by Roy W. Carlson. exposure temperature of the concrete as ‘70” F. This method, like the Schmidt Method, is essen- from time zero to the end of the first time interval, tially ,a step-by-step integration which can be with the exposure temperature rising to 74O F. simplified by selection of certain variables. Con- 6 hours later. Using a relative temperature of dit.ions such TABLE IV.-Computation of temperatures in &foot-thick concrete wall (1) (2) (3) (4) (5) (6) (7) I 1st time interval 2d time interval sta. Depth below Z A+&20 A8=8.6’ (n) sllrtace (feet) 4. - - Cl Lt &l Cl LT 4.1 .- -- 0 0 0 0.0 4.0 1 0.5 0 0.268 12.4 4.54 4.5 22.7 8.83 9.9 2 1.0 0 .268 12.4 4.54 5. 7 27.6 10.23 12.9 3 1. 5 0 .269 12.4 4.53 6. 1 28.9 10.59 14.1 4 2.0 0 .286 12.4 4.43 6.2 29.3 10.48 14.5 5 2. 5 0 .500 12.4 3. 10 6.2 29.4 7.35 14.6 - - be the ca.sewhere insulated or partially insulated Dam cooling studies. From these studies, a num- forms are used, or where concrete lifts are placed ber of curves and nomographs were prepared for a on the rock foundations. In these instances, the vertical spacing (height of placement lift) of 5 given equations cannot be simplified to the extent feet for application at Hoover Dam. Given con- desired, and the thermal oonductivities, specific crete properties and a single rate of flow of water heats, and space intervals must be taken into con- were also used as constants. Later, the theory was sideration. Changing the space intervals in one developed using dimensionless parameters. The material so as to maintain a fixed S is not permis- comptitations and results of these later studies are sible. To t,h.e above list of equations must be presented iA the Bureau of Reclamation’s Tech- added n.dditional values of Zj, cj, and Lj when nical Memorandum No. 630, “Cooling of Mass pasqing from one material to another. Examples Concrete by Water Flowing in Embedded Pipes,” of these computations are presented in Carlson’s by V. M. Kingston, and in “Cooling of Concrete paper on pages 96-98. Dams,” Bulletin 3, Part VII-Cement and Con- Temperature Distribution&-Problems involv- crete Investigations of the Boulder Canyon Proj- ing temperature distributions near exposed faces ect’ Final Reports. For the more general applica- may be solved in several ways. Schmidt’s Method tion, Figures 36, 3’7, and 38 are master curves for may be used, for example, when it is desired to the computation of temperatures resulting from know the depth of freezing so that piping systems artificial cooling. Figure 36 shows values of “X” within the mass concrete will not freeze. The same for various conditions of concrete properties, flow method is used advantageously to determine when of cooling water, length of cooling coil, horizontal a concrete section completely thaws out after it has and vertical spacings, and time. In this case, “X” been exposed over a winter and frozen throughout represents the final mean temperature difference its thickness. This was the situation at Seminoe in degrees per degree initial temperature differ- Dam where the top portion of the dam was to be ence, or grouted as early in the spring as possible. Mean temp. of entire length of The variation in temperature at any particular cylinder-initial temp. of water. x= point can also be estimated by the use of Figure 35. Initial temp. of concrete-initial This figure gives the ratio of the temperature temp. of water. range in the concrete at any given depth to the temperature range at the surface for the daily, 15- For the same variables, curves of “Y” and “Z” day, and annual cycles of temperature. are given in Figures 37 and 38. The “Y” curve is Rem,oval of Heat by Cooling Pipe.-The theory used to compute the temperature rise in the cooling for the removal of heat from concrete by embedded water and the “Z” curve is used to compute the cooling pipes was first developed for use in Hoover mean temperature of concrete at a given length 50 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES IOC 9( 8( 7c 6C 5c 4c /// I I’ ,i’/ r h2z 0.060 ft2/hr-c-, I LO50---.,, , . I I I ,-A-/ Ii i //’ I / “.’ 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 TEMPERATURE RANGE IN CONCRETE RATIO TEMPERATURE RANGE AT SURFACE FIQVRE 35.-Temperature variatbns with depth in semi-infinite solid. TEMPERATURE CONTROL STUDIES 51 Id CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES TEMPERATURE CONTROL STUDIES 53 54 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES from the inlet, The latter curve is not normally lying lift or to the foundation. Such a study may used because the normal field practice is to reverse be done by Schmidt’s Method, or by the method the flow of the cooling water each day. outlined in Chapter V of the Boulder Canyon In Figures 36,37, and 38, the following nomen- report “Cooling of Concrete Dams.” clature is followed : K=conductivity of the concrete to be cooled in TABLE V .-Values of D, Da, and ho1 for pipecooling B.t.u./ft /hr /“F. Bpacing L=length of the cooled cylinder measured along -- D D2 h% the cooling pipe in feet vergal Horizontal (few c,=specific heat of the cooling water in B.t.u./ -~ lb /“I;“. 2% 2. 82 7. 95 1. 31h2 pco=density of the cooling water in lb /ft 3 pul= volume o f water flowing through the cooling 2% 3. 99 15.92 1. 19h* pipe in ft 3/hr 3 4. 35 18.92 1. 16 D=diameter of the cooled cylinder in feet 4 5. 02 25. 20 1. 12 5 5. 64 31.81 1. 09 h*=diffusivity of the concrete in ft 2/hr 6 6. 18 38. 19 1. 07 t=total elapsed time the cooling has been in operation in hours. 7% 2% 4. 88 23.81 1. 13h* 7% 4 6. 15 37.82 1. 07 The curves were computed for a ratio of b/a of 7% 5 6. 86 47.06 1.04 100, where b is the radius of the cooled cylinder 7% 6 7. 54 56.85 1. 02 and a is the radius of the cooling pipe. Actual 7% 7% 8. 46 71.57 1. 00 9 9. 26 85.75 0. 98 cooling pipe spacings are nominal spacings and 7% will seldom if ever be spaced so as to obtain a b/a 10 10 11.284 127.33 0. 94h2 ratio of 100. In order to take the actual horizontal I and vertical spacings into consideration, a ficti- tious diffusivity constant should be used. This is Several difficulties are encountered in this latter acceptable between certain limits as the cooling method when attempting to use the formulas for rate is proportional to t.he diffusion constant. heat losses or gains from a heat-generating lift, Table V gives the values of D, D2, and h2t for var- from an inert lift, and from an inert semi-infinite ious spacings of cooling pipe. The b/a ratios of solid. For example, the theoretical equation for the spacings shown vary from about 34 to 135. the adiabatic temperature rise is given as Within these limits, the values of h2, may be used T= T, ( l-e-‘“t) and T, and m are selected to with sufficient. accuracy. make the theoretical curve fit the actual laboratory The curves given in Figures 36, 37, and 38 are data. This is not easily done at times, and can used in a straight-forward manner as long as no result in some error in the theoretical heat loss in appreciable heat of hydration is occurring in the the heat-generating lift. The loss from the inert concrete during the period of time under consider- lift cannot take into consideration a varying sur- ation. When the effect of artificial cooling is de- face temperature which also introduces an error. sired during the early age of the concrete, that is, The third error is introduced when a new lift is when a high rate of heat generat.ion is occurring, placed on an older lift which is still generating ii step-by-step computation is required which takes heat. Unless the older lift is quitA: old, the heat into consideration heat increments added at uni- being generated may be enough to be taken into form time intervals during the period. These heat consideration. Table VI gives an example of the increments are obtained from the results of a sep- computation using Fignre 36. In this case, the arate study which takes into consideration the average temperature during the interval and the adiabatic temperature rise, the loss or gain of heat temperature at the end of the interval, both wit.h- to the surface of the lift due to exposure condi- out. cooling water, were obtained by a Schmidt’s t.ions, and the loss or gain of heat from an under- Method computation. _.-._ . ..^ TEMPERATURE CONTROL STUDIES 55 TABLE VI.-EJect of arti$cicil cooling pipe GWEN CONDITIONB 7%root llfte 40” F. lnitkd cooling water temp. Moot horizontal spacing hk1.248 It s/day W-foot coil K=1.7 B.t.u./ft /hr /F. M)” F. placing temperature eaPuPe=2,Guo Temp. at end of Temp. at end of X interval w/o intervel with &YS) cooling water c0011ngwater - _- -- -- 0 -_------_- __--- --_- ---_------_____--______.-.._-e_- ---- 50.0 0. 5 0.011 0.99 0.01 62.0 '22.0 0.2 65.5 65. 3 1.0 0.022 0.98 0.02 68.5 6.5 0.5 70.3 69.8 1.5 0.034 0.96 0.04 71.6 3. 1 1.0 72.8 71.8 2.0 0.045 0.94 0.06 73.8 2.2 1.7 74.7 73.0 2.5 0.056 0.93 0.07 75.2 1.4 2. 1 76.0 73.9 3.0 0.067 0.91 0.09 76.5 1.3 2.8 77. 1 74.3 3.5 0.078 0.90 0. 10 77.4 0.9 3.3 77.9 74.6 4.0 0.090 0.89 0.11 78.3 0.9 3.7 78.7 75.0 4.5 0.101 0.88 0.12 79.0 0.7 4. 1 79.3 75.2 5.0 0.112 0.86 0. 14 79.6 0.6 4.7 79.9 75.2 1 Avg. temperature of concrete minus initial temperature of cooling water (Arst interval anly). D esign Considerations length of Construction Block concrete temperature to the closure temperature, the rate of temperature drop, and the age of the OR given site and loading conditions, the over- concrete when the concrete is subjected to the tem- all thickness of a dam is determined by gravity perature change. For arch analyses. Thickness, therefore, is a Beyond the control of the designer are other given condition at the time the length of construc- factors, such as the thermal coefficient of expan- tion block is considered. Where this thickness is sion, the effective modulus of elasticity,5 the elastic large, a decision must be made whether to con- and inelastic properties of the concrete, and the struct the section by means of one or more con- restraint factor. The actual stresses will further struction blocks separated by longitudinal joints, vary between quite wide limits because of condi- or to apply rigid temperature control requirements tions occurring during the ~construction period and const,ruct it as a single block. which introduce localized stress conditions. Ten- With modern construction equipment capable sile stresses and resulting cracks may occur be- of continuous concrete placement around-the- cause the larger blocks cover a greater area of the clock, the length of a construction block is not nor- foundation and are thereby subjected to a greater mally related to the size or capacity of the con- number of stress concentrations due to the physical struction plant. More generally, the length of con- irregularities and variable composition of the struction block is governed by the stresses which develop within the block. These tensile stresses 6 The effective modulus of elasticity is often given as : occur between the time the block is first placed and i EOII= - E. the time when it has cooled to its minimum tem- 1+0.4 g perature and are related to many factors. Factors where EC is the modulus of elasticity of concrete and Er Is the subject, to at least some degree of control include modulus of elasticity of the foundation rock. By inspection, it is evident that lower concrete stresses will result on a founda- the overall temperature drop from the maximum tion of low elasticity. 57 58 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES foundation. Also, cracks may occur becauseof de- 28 days from 3.3 X l@ to 5.7X 10s, and at age 1 lays in the construction schedule and construction year from 3.3 X lo6 to 6.8 X 106. The coefficient of operations. thermal expansion, while not varying appreciably Longer blocks are more likely to have cold joints with age, has had values ranging from 4.3 x 1O-6to occurring during placement of the concrete, and 5.7 X 10W6.Because of these variations and because t,hesecold joints form definite planes of weakness. the other stress-producing factors are either un- The longer blocks may also be exposed for longer known or susceptible to change during construc- periods of time, allowing extreme temperature tion, it is difficult in the design stages to determine gradients to form near the surfaces. The stresses the actual stresses which will occur in a given size caused by these steep temperature gradients may block. t’hen cause cracks to form along any planes of The strength of the concrete and the creep prop- weakness which exist as a result of construction erties of the concrete both vary with age and make operations. it all the more difficult to determine whether or not The size of block does not affect the stress in the the stresses will be acceptable at the time they are normal equation for temperature stress, S=Ee imposed upon the structure. For example, studies ( T2 - T,) , where S is the unit stress, E is the effec- of the creep properties of concrete used in five tive modulus of elasticity, e is the thermal co&- dams showed that stresses varied to such an extent cient of expansion, and ( TZ- T,) is the tempera- that, for a temperature drop of 1” per day st’arting ture drop. This equation is valid only where there at age 4 days, the theoretical temperature stresses is a direct restraint against movement, such as were 12, 20. 65, and 75 percent higher in Flaming would exist along the rock-concrete contact sur- Gorge, Ross, Hungry Horse, and Glen Canyon face. The equation for temperature st,ress in a Dams, respectively, than those in Monticello Dam. large concrete block is better expressed as S= REe Similarly, for a temperature drop of lo per day (Ts-T,), where R is a restraint factor. The starting at age 180 days, t,he stresses were 2, 10,33, restraint factor is a function of the length of block and 75 percent higher, in the same order! as com- and the height above the foundation. pared to Monticello Dam. The most commonly used values of the restraint Lacking data to comptite stresses, field experi- factor are given in Figure 39.6 Stresses obtained ences on other jobs should guide the designer in by the above are uniaxial stresses. Higher stresses determining the degree of temperature control for than t,hese can occur under biaxial or triaxial re- a new structure. Such experiences are reflected straint conditions. Bringing into consideration in Table VII, which can be used as a guide during these addit,ional restraints, the maximum stresses the early stages ‘of ‘design to determine the pri- can be estimated by multiplying the above results mary means of temperature cotitrol. by $& for biaxial restraint and &p for triaxial Width of Construction Block restraint,. Values of Poisson’s rat,io; p, for con- Contraction joints are normally spaced about 50 crete vary with age and with different concretes, feet apart, but may be controlled by the spacing with most values ranging from 0.15 to 0.20 at age and location of penstocks and river outlets, or by 28 days and from 0.16 to 0.27 at age 1 year. definite breaks and irregul,arities of the founda- Although subject to theoretical determination tion. A uniform spacing is ,desirable so t,hat the by means of the above stress relat,ion, the varia- cont.raction joints will have uniform openings for tions in the values of E and e ma.ke such a deter- mination of questionable value. For example, contraction joint grouting. Spacings have varied in dams designed by the Bureau of Reclamation values of the modulus of elasticity of concrete at from 30 feet to 80 feet as measured along the axis age 2 days have varied from 1.4 X lo6 to 2.8 X 106, of the dam. When the blocks are 30 feet or less at age ‘7 days from 2.1 X lo6 to 4.2X 106, at age in width, a problem arises in regard to obtaining a good groutable opening of the contraction joint. ODerived from test data reported in 1940 by R. W. Carlson and T. J. Reading to the Portland Cement Association. These In these cases, it may become necessary to cause ‘a data were plotted in the TVA Technical Monograph No. 67, larger temperature drop to take place than would “Measurements of the Structural Behavior of Norris and H1- wassee Dams.” otherwise be desiraible. This temperature drop is DESIGN CONSIDERATIONS 59 I .OOH .90 .80 .70 .60 W v) .!50H w > .30 iz .20 a .I0 AT CENTER SECTION I .OOH a .90 z .80 .70 .60 .5OH .40 .30 .20 .I0 n 700 90 80 70 60 50 40 30 20 IO 0 I10 10090 8070 6050 4030 20 IO 0 PERCENTAGE REST RAINT-TENSION AT $ POINT SECTION AT $ POINT SECTION E\Ioum 39.-Foundation restraint factore. not without limit, however, it must be compatible It is theoret,ically possible to compute t.he re- with the drop allowed for the longer dimension quired temperature drop for a given size of con- of ,the block. A furt.her consideration is the maxi- st.ruction block to obtain a desired joint opening. mum length-t,o-width ratio of the block which will This theoretical temperature drop from maximum exist ,at the top of the dam. If the ratio of the temperature to grouting temperature must be longer dimension to the shorter dimension is much modified because some compression is built up in over 2.5, cracking at approximate third points of the block as the temperature increasers during the the block can be expected. Ratios of 2.0 to 1 or first few days after placement. A 2” to 4” tem- lessare desirable, if practicable. perature drop from the maximum temperature, 60 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES TABLE VII.-Temperature treatment versus block length between layers of 1 hour, and 5-foot lifts, the maximum width of block would be : Block length Treatment Over 200 feet Use longitudinal joint. Stagger longitudinal joints w= 0.21(4.600)(l) =66 feet * in adjoining blocks by minimum of 30 feet dS>WV)(3+1) Temperature drop from maximum concrete tem- perature to grouting temperature--OF. Control of Temperature Drop ff=0.2Lto 0.5L 1 OverN=0.5L 1 Control of the temperature drop from the maxi- mum concrete temperature to t,he grouting tem- 150 to 200 feet- _ 25 35 40 perature is the one factor relating to stress 120 to 150 feet_- 30 40 45 development over which a measure of control can 90 to 120 feet- _ _ 35 45 No restriction be achieved. A reduction in the total temperature 60to90feet---- 40 No restriction No restriction Up t,o 60 feet- - - 45 No restriction No restriction drop may be accomplished by controlling the tem- perature rise which occurs immediately after 1H=height above foundation; L=block length. placement. of concrete, by reducing the placing temperature of the concrete, or by both measures. depending on the creep properties of the concrete, The temperature rise is normally controlled by may be required to relieve this compression before the selection of the type and amount of cement any contraction joint opening Frill occur. It must used in the concrete, the replacement of part be furt.her modified with time, due to the weight of t.he cement, by a pozzolan, and the artificial cool- of the c.oncrete in the block and t.he creep prop- ing of the concrete through an embedded pipe sys- ert.iesof the concrete. tem during the first few days after placement. Measured joint, openings in Hungry Horse Dam Minor benefits may also accrue due to evaporative averaged ‘75 percent of the theoret.ical. Other ex- cooling when the concrete is water cured. In most periences with arch da.ms having ‘block widths of instances, Type II cement will produce concrete approximately 50 feet. have indicated that a mini- temperatures which are acceptable. Id the sma.ller lnum temperature drop of 25’ from the maximum structures, Type I cement will usually be satisfac- temperat.ure to t.he grouting temperature is desir- tory. Other factors being equal, Type II is usually able, and will result, in groutable contraction joint selected because of its better resistance to sulfate openings of 0.06 ,to 0.10 inch. For the wider blocks attack, better workability, and lower permeability. wit.h ‘70 feet. or more between contraction joints, Type IV cement, although originally developed a 20° temperature drop will be sufficient. for use in mass concrete to reduce the temperature For planning purposes, the maximum widt.1~of rise, is now used only when other methods of con- block permitted by plant, capacity is given by trol will not accomplish the desired result. For example, it may be used near the base of long W=o.21 dapot+l, blocks where a high degree of restraint exists. Concrete with Type IV cement requires more cur- where ing than concrete with other types of cement, and U’=width of block in feet extra care is required at early ages to prevent. dam- P=plant capacity in cubic yards per day age to the concrete from freezing or from too early t=maximum time (in hours) allowed between a form removal. layers to prevent cold joints (1 to 3 hours Concrete technology has reached the point where normally, depending on mix) the old standard of four or more sacks of cement b= bucket capacity in cubic yards per cubic yard for mass concrete is no longer the tl=depth of layer in feet, criterion. Present-day mix designs can usually n=number of layers placed to reach full obtain the required concrete strengths with about. height, of lift. three sacks of cementing materials per cubic yard For example, given n plant capacity of 4,600 of concrete for the interior mass of the dam. The cubic yards per day, ‘bucket. capacity of 8 cubic cementing materials may be entirely cement or yards, depth of la.yer of 20 inches, time allowable may be a mixture of cement and a pozzolanic ma- .-. _..-- _-. .._._ DESIGN CONSIDERATIONS 61 terial. As the temperature rise in concrete is di- gregate has also been obtained by forcing refrig- rectly related to the amount of cement and to the erated air through the aggregate, while the amount of pozzolan, and as the heat generation of aggregate is draining in a storage bin after being the pozzolanic replacement is roughly 50 percent immersed, while it. is draining on a conveyor belt that of cement, the subsequent temperature rise in after being sprayed with cold water, or while it is present-day concrete has been reduced by as much passing through the bins of the batching plant. as 40 percent over that obtained in the p&t. Fig- The sand is usually cooled by passing it t,hrough ure 40 shows t,ypical temperature rise curves for vertical, tubular heat exchangers. Cold air jets concrete placed in Monticello and Hungry Horse in conjunction with conveyor belts have also been Dams. used. Immersion of sand in cold water has not Maximum concrete temperatures can be lowered been successful because of the difficulty in remov- by reducing the placing temperature of the con- ing the free water from the sand after cooling. crete. In addition to the direct reduction in tem- Cooling of the cement is a definite problem. perature, this also results in a slower rate of hydra- Bulk cement is almost always obtained at rela- tion of the cement. When no special provisions tively high temperatures, and the be& that can be are employed, concrete placing temperatures will hoped for, in some cases, is that it will cool natu- be very close to the mean monthly air temperature, rally and lose a portion of the excess heat before it ranging from 4” to 6’ higher than the mean air is used. In some instances, the vertical tubular temperature in the winter time and this same heat exchangers may ‘be used for cement cooling. amount lower than the mean air temperat.ure in the Mix water has been cmled to varying degrees, summer time. The actual concrete mix tempera- the more common temperatures being from 32” ture depends upon the ba.tch weights, specific heats, to 40” F. Adding slush or crushed ice to the mix and the temperatures of the individual materials is an effective method because it takes advantage going into the concrete mix. of the latent heat of fusion of ice. The addition Table VIII shows a sample computat,ion for of large amounts of ice, however, may not be too estimating the concrete placing temperature of an practicable in some instances. First, the batching assumed mix. By dividing the total B.t.u.‘s in the hopper must be designed in such a way as to prs- mix by the total B.t.u.‘s required to vary the tem- vent the ice from adhering to the sloping sides of perature of the material 1” F., the temperature the batcher. In part, this may be overcome by of the concrete as mixed can be estimated. In the batching the ice with the sand. Second, if the 89 060 coarse aggregate and sand ‘both contain appreci- sample computation, this would be ) 1 074 or 82.9” able amounts of free water, the additional water to F. To estimate how much any ‘o;e ingredient be added to the mix may be so small that replace- would have to be changed to lower ‘the mix tem- ment of part of the free water by ice would not perature 1” F., the tjotal B.t.u.‘s required to vary be of apprecia’ble value. the temperature of the material 1’ F. would be An embedded pipe cooling syst,em has two pri- divided by the B.t..u.‘s required for the individual mary functions : To reduce the maximum tempera- mix ingredient. For example, the mix water to ture of the concrete, and to reduce the temperature 1074 of the concrete to t,he required grouting tempera- be added would have to be cooled & or 7.67” F. ture during the const.ruction period. An embed- to lower the concrete temperature 1” F. ded pipe cooling system erribedded on the top of Various methods have been used to reduce con- each 5- or 71/&foot lift of concrete cannot remove crete placing temperatures, and the method or the heat as fast as it is generated in t,he concrete oombination of methods will vary with ‘the degree during the first 2 to 5 days, but can remove t.he of cooling required and the construction contrac- tor’s previous experience. Cooling of the coarse heat faster than it is generated after that time. aggregate has varied from shading and sprinkling The maximum temperature of concrete cooled by the aggregate in t.he stockpiles to chilling the ag- an embedded pipe cooling system will, therefore, gregate in large tanks where the aggregate is im- be reached during this period and subsequent tem- mersed in refrigerated water for a given period of peratures can the maintained below this initial max- time. Rel,atively complete cooling of coarse ag- imum temperature. Without an embedded pipe 62 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES EL.262.5 E L.3437.5 BLOCK 14 BLOCK 25 60- MAY JUNE 1 1 1 1 1 , 1 , , 2 3 4 5 6 I8 9 IO AUGUST v-l W r; W 5 t.z eo- : 2 - (3 I 60 w - m 0 _ W I a EL.41 2.5 E L.3362.5 3 m + BLOCK 4 ; 70- BLOCK IO Q a 3 w 50 t P 2 if 5 W 60 I I I t 1 I I I 1 DECEMBER I- 6 7 8 9 IO II 12 I3 14 SEPTEMBER 70 70 8 60 i I 60.5 6 7 8 9 IO II 12 13 JULY NOVEMBER MONTICELLO DAM HUNGRY HORSE DAM FIGURE 40.-Typical temperatwc rise curvea. DESIGN CONSIDERATIONS 63 TABLE VIII.-Computafion for temperature of concrete mix Batch weight, B.t.u. to vary ( Total B.t.u. Material pound Specificheat tmlperature of in materir\l material lo F. _- .- _- --- Watertobeadded ______-- ____ ---_--_. 140 1. 0 140 60 8,400 Cement ______-_-__--_- _._____.__. 240 0. 23 55 150 8,250 Sand-----__------_------~~~.~~~.~~~-~- 900 0. 22 198 85 16, 830 No. 4to Kin. aggregate---__--_------~~---~ 650 0. 22 143 80 11,440 gin.to6in.aggregate ___.______-__-__---_ 2, 220 0. 22 488 80 39,040 Free moisture: 20 20 85 1,700 8 8 80 640 22 22 80 1,760 1,000 _- 89.060 -- 1Estimated heat gain due to motors, friction, etc. system, concrete temperatures in a &foot place- Rate of Cooling ment lift would reach a peak temperature at 3 to 5 days and would then drop slowly until t,hat lift Artificial cooling is accomplished by circulating was covered by the next placement lift. Another cold water through l-inch outside diameter pipe temperat,ure rise would then mur and, depending or t,ubing laid grid-like over the top surface of on the length of exposure period, a new and higher each 5- or Q/z-foot lift of concrete. The rate of maximum t.emperature than before could be ob- cooling is controlled so that the tensions set up in tained. In 7$foot lifts, the same pattern would the concrete by the drop in temperature will not occur except that the peak temperature would be exceed the tensile strength of the concrete. Cool- reached in 5 to 8 days. ing of the concrete for 3 to 4 weeks at a rate of tem- The typical temperature history of artificially perature drop of about lo per day can create ten- cooled concrete is shown in Figure 30. The nor- sions which are equal to or exceed the tensile mal use of the embedded pipe cooling system con- st,rength of the concrete. As shown in Figure 41, sists of an initial cooling period from 10 to 15 a temperature drop of about 2” per day can cause days. During this initial cooling period, the con- cracking in about 11 days. To prevent the artifi- crete temperatures are reduced from the maximum cial cooling from causing cracks, an initial cooling concrete temperature to such a temperature that, period of not more than 2 weeks is usually speci- upon stopping the flow of water through the cool- fied, and the cooling systems are so operated that ing system, the continued heat of hydration of the the temperature drop is not more than 1” per day. c,ement will not result in maximum temperatures Figure 41 shows a t,ypical increase in tensile higher than thnt previously obtained. Subsequent strength of concrete with age, together with the to this initial cooling period, an intermediate and tensions created in the concrete for different rates :L final cooling period are utilized to lower the of temperature drop. These tensions vary with concrete temperature to the desired grouting tem- the creep properties of the concrete. After the perature. Depending on the temperature drop and initial cooling period is completed, a variable pe- final temperature to be obtained, the season of the riod of time elapses before the intermediate and year when this cooling is accomplished, and the final cooling periods are scarted during which the temperature of the cooling water, the intermediate concrete gains tensile strength. Since the modulus and final cooling periods will require a total of of elasticity of the concrete at this time is higher, f ram 30 to 60 days. the rate of temperature drop should again be held 64 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES ,‘I 1/2O-7-, I \ \ \ \-Stresses due to indicated OF. drop per day I 00 / \ \ ’ I’,1! \’ \\ \ \\\\.\ \\\ +d1 \\\ 2oc ,--Tensile strength of concrete 25( 30 50 LO 20 30 40 AGE---DAYS FICWRE 41.-!l’ensim versus concrete strength-early age. DESIGN CONSIDERATIONS 65 to not more than 1” per day, and a rate of lh” to ment. Expansion joints are provided in a unit- Sk0 per day would be preferable. structure to allow for the expansion of the unit in The rate of temperature drop forced upon the such a manner as not to change the stresses in, or concrete by an embedded pipe cooling system can the position of, an adjacent unit or structure. be controlled by varying the length of coil, the hor- Contraction joints are provided in a structure to izont:~! spacing of the tubing, the velocity of the prevent the formation of tensile cracks in the cooling water, and the temperature of the cooling structure as the structure contracts. In this re- water in the cooling systems. The length of coil spect, the contraction joint may be defined as a and the horizontal spacing are determined by the designed crack. Contraction joints should be so size of the blocks and the purpose of the cooling constructed that no ‘bond exists between the con- systems; that is, whether the cooling systems are cretes separated by the joint. Except for dowels, primarily for lowering the temperature of the con- reinforcement should not extend across a contr:lc- crete prior to contraction joint grouting, for con- tion joint. t,rolling the maximum concrete temperature, for The location of contraction joints is largely a reducing temperature gradients near exposed sur- matter of past experience. Accurate analyses are faces, or any combination of these. difficult ‘because of the many variables, the largest The efl’ects of changes during the construction of which in mass concrete are the degree of re- period such as the type or amount of cement used straint and the temperature distributions and var- in the concrete, curing methods employed, expo- iations. In relatively thin walls and slabs, drying sure t,emperatures varying from those assumed, or shrinkage also is of concern sinus its effect could any other factors which influence concrete tem- be equivalent to that of a 60” to 100” temperature peratures, are normally taken care of by varying drop. Any spacing of joints should, therefore, be the periods of flow and the rate of flow of the cool- based upon experimental data and systematic ob- ing water. If these changes become major changes servation. Spacing of joint8 in mass concrete and vary greatly from those assumed, the tem- structures is given in Table VII. Knowing where perature effects can be taken care of by varying cracks are likely to occur, the designer and the the horizontal spacing of the tubing and/or length constructor can alleviate many of the problems of cooling coil in those portions of the dam t.hen arising from random cracking. being constructecl. Temperature Reinforcement-General Joints If a concrete structure is free to expand or con- A construction joint in concrete is defined as a tract with variations in temperature, no stresses concrete surface, upon or against which new con- of any significance will be developed. This is crete is t.o be phaced and to which the new concrete true even in reinforced concrete, as the coefficients is to adhere, that hm become so rigid Vhat new of thermal expansion of steel and concrete are concrete cannot, be made monolithic by vibration essentially the same. When, however, the move- with that previously placed. Construction joints ment of any part of the structure is restrained, are placed in concrete structures to fa.cilitate con- either by external restraints or by the restraint struction, t,o reduce initial shrinkage stresses and exerted by one part of the structure upon an cracks, to permit installation of embedded metal- adjacent part,, a drop in temperature will cause work, or to allow for t,he subsequent placing of tensile stresses. Cracks caused by these tensile &her concrete, backfill concrete, or second-stage stresses not only will ‘be unsightly, but could also concrete. Construction joints also occur as a re- serve to accelerate ,the deterioration of t.he struc- sult of inadvertent delays in concrete placing op- ture to perform its purpose. erations. Construct.ion joints are, therefore, con- Temperature reinforcement does not prevent struct.ion expedients required to obtain t.he desired cracking, but it can distribute cracks and control concrete structure. their width so that the usefulness of the structure Expansion and contraction joints are provided will not be seriously affected. Since cruk widths in concret.e structures to accommodate volumetric and spacings tend to be greater for widely spaced changes which occur in the structure after place- reinforcement bars, smaller bars at closer spacing 66 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES should be used for temperature reinforcement in the difference, D, between the mean annual and preference to large bars at wide spacing. Rein- the loTest mean monthly. forcement bars should be placed as close as pram- 3. Determine the average daily variation, r, ticable to the surface. Steel having a high elastic in the warmest month, and the average daily limit is also advantageous. variation, d, in the coldest month. 4. For a known or assumed h’ (diffusivity constant), use Figure 11 to determine the ratio Temperature Reinforcement-Frames of the variation of the mean temperature in the Attached to Mass Concrete slab or beam under consideration to the varia- tion of the daily external air temperat,ure. This Temperature reinforcement in frame- and box- assumes a sinusoidal variation in temperature type structures Surface Treatments daily cycle of air temperature and little, if any, stress benefit will be obtained at the surface. With INCE the large majority of all cracks start at wood forms which prevent heat from being lost an exposed surface, several provisions for rea’dily to the surface, the temperature near the S surface treatment can be utilized which will surface will be close to that obtained in the interior reduce the cracking tendencies at such surfaces. of the mass, and no stress benefit will occur at the These include surface cooling, time of form re- surf ace. moval, and water curing. The time of form removal from mass concrete If the concrete near the surface of a mass con- structures is important in reducing the tendency crete structure can be made to set at a relatively to crack at the surface when wood forms or in- low temperature a.nd can be maintained at this sulated steel forms are used. If exposure temper- temperature during the early age of the concrete, atures are low and if the forms are left in place say, for the first 2 weeks, cracking at the surface for several days, the temperature of the concrete can be minimized. Under this condition, tensions adjacent to the form will be relatively high when at the surface are reduced, or the surface is put the forms are stripped, and the concrete will be into compression, when the inte+or mass of con- subjected to a thermal shock which will cause crete subsequently drdps in temperature. The use cracking. Prom the temperature standpoint, of noninsulating steel form which are kept cool forms should either be removed as early as prac- by continuous water sprays will tend to accom- ticable or should remain in place until the temper- plish this desirable condition. If, however, water ature of the mass has stabilized. In the latter case, sprays are not used to modify the temperature of a uniform temperature gradient would have been the steel forms, the early-age temperature history established between the interior mass and the sur- of the face concrete will be even greater than the face of the concrete, and removal of the forms, 67 CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES except in adverse exposure conditions, would have cooling, would lower the temperature of the mass no harmful results. in a uniform manner. Following the removal of forms, proper curing If extreme exposure temperatures exist soon is important if drying shrinkage and resulting after placement of the concrete, insulation of the surface cracks are to be avoided. Curing com- faces may be employed to prevent steep gradients pounds which prevent the loss of moisture to the near the exposed surfaces. Suoh insulation may air are effective in this respect, but lack the cooling be obtained by measures varying from simply benefit which can be obtained by water curing, leaving wood or insulated forms in place to the In effect, water curing obtains a surface exposure use of commercial-type insulation applied to the condition more beneficial than the fluctuating daily forms or to the surfaces of the exposed concrete. air temperature. With water curing, the daily ex- Tops of blocks can be pro&ted with sand or saw- posure cycle is dampened because the daily varia- dust when an extended exposure period is tion in the water is leas than that of the daily air anticipated. temperature. A benefit also occurs from the evap- Whatever the type of insulation, measures orative cooling effect of the water on the surface. should be taken to exclude as much moisture from The actual effective exposure temperature is diffi- the insulation as practicable. The insulation cult to compute becauseit varies considerably with should also be as airtight as possible. For a short the rate and amount at which the water is applied period of exposure, small space heatirs may be to the surface. Intermittent sprays which main- used, either by themselves or in conjunction with tain the surface of the concrete in a wet to damp canvas coverings which enclose the work. Care condition with some free water always available should *be taken, however, when using space is the most desirable condition. heaters in enclosed areas to avoid drying out of the concrete surfaces. Surface Gradients Stresses due to temperature gradients may be of concern not only during the construdtion period During periods of cold weather, steep tempera- discussed above but during the life of the struc- ture gradients between the relatively warm in- ture. Stresses ‘across a section due to temperature terior of a mass and its surface will cause high gradients can be obtained from the expression tentile stresses to form at the surface. The sur- 3 face treatments previously described can reduce -eE =u=ba(l b2 o T(z)dz+3(2x-b) these temperature gradients, particularly when [S used in conjunction with artificial cooling, but the l (2r--b)T(z)&-baT(z)] use of insulat.ion or insulat,ing-forms will give greater protection. Although steel forms are where e is the thermal coefficient of expansion, E beneficial from the standpoint of avoiding thermal is modulus of elasticity, p is Poisson’s ratio, and shock upon the removal of forms, there are times b is the thickness of section with a temperature when wooden forms would be preferable. During distribution, T( 8). Where the temperature the fall of the year ,when placing temperatures are variation, T(o), cannot be expressed analytically, still relatively high, the tendency of the surface the indicated integrat,ions can be performed nu- of the concrete is to drop rapidly to the exposing merically by the use Iof Simpson’s Rule. For ex- temperature. This may occur while the interior ample, using b = 30 feet, e= 6.0 X HY, E= 2,500,OOO concrete is still rising in temperature. In this in- pounds per square inch, p=O.20, and an assumed stance, wooden forms would prevent the rapid T(z) as shown in Table IX, the stresses would be drop at the surface and, combined with artificial computed as follows : CONSTRUCTION REQUIREMENTS 69 TABLE IX.-Computation of temperature stress - - fi lb:& 3 -- .- -- 0 0. 0 0 For the given conditions: 10,584 74 - 199 4, 125 29 3 8. 3 eE 6 15. 8 - 284 -=O.l -174 -1 baa -4 9 22. 7 - 272 - 2,853 -20 12 29. 1 - 175 u,=O.1[(900)(1003.8) -4, 182 -29 15 35. 1 0 + 3(22- 30) (8862) -4,431 -31 18 40. 7 244 - (30)aT(dl -3,600 -25 21 46. 0 552 - 1,959 -14 24 50. 9 916 762 5 27 55. 6 1334 Simplifying: 4,023 28 30 60. 0 1800 a,=5317z-2700T(z) 8,094 56 -- -- I + 10,584 b 1003. 8 8862 s0 - - Similar stress computations made for sudden and concrete held in place by previously placed temperature drops at the surface of a mass con- concrete which has not undergone its full volu- crete structure show that tensile stresses as high as metric shrinkage. 16 to 18 pounds per square inch per degree temper- A forced cooling of the concrete adjacent to and ature drop can be expected to occur. As can also below the break in slope, and a delay in placement be found from the stress relationship in Table IX? of concrete over the bre.ak in slope, can be em- any linear distribution of temperature acrOSs a ployed to minimize cracking of the concrete at section will result in no temperature stress in the these locations. Although uneconomical to re- section. move sound rock at tibrupt foundation irregular- ities and replace it with concrete, the elimination Foundation Irregularities of these points of high strecrs concentration is worthwhile. Such cracks in lifts near the &but- Although the trial-load analyses assume, and the ments very often are the source of leaks which design drawings show, relatively uniform founda- lead to spalling and deterioration of the concrete. tion and abutment excavations, the final excava- tion may vary widely from that assumed. Faults Relaxation of Initial Cooling or crush zones are often uncovered during excava- tion, and the excavation of the unsound rock leaves In the early spring and late fall months when definite depressions or holes which must be filled exposure conditions are severe, the length of the with concrete. Unless this backfill concrete has initial cooling period and the r&e of temperature undergone most of its volumetric shrinkage at the drop can be critical in thin concrete sections where time overlying concrete is placed, cracks can occur pipe cooling, cotibined with low exposure temper- in the overlying concrete near the boundaries of atures, can cause ihe concrete temperature to drop the backfill concrete as loss of support occurs too fast. During these periods, artificial cooling within the area of backfill concrete. Where these should be stopped 4 to 5 days ,after placement and areas are extensive, the backfill concrete should be the concrete should be allowed to cool in a natural placed and -led before additional concrete is manner. In structures with thicker sections, the placed over the area. Similar conditions exist exposure temperatures have less effect on the im- where the foundation undergoes abrupt changes mediate temperature drop, and t’he initial cooling in slope. At the break of the slope, cracks often period can be continued with the primary purpose occur because of the differential movement which of controlling the temperature difference between takes place between concrete held in place by rock the exposed faces and the interior. A Schmidt’s CONTROL OF CRACKING IN MASS CONCRETE STRUCTURES Method of comput.ation, using e&.mated exposure ture distribution throughout the structure will be conditions, will usually su5ce to determine the obt,ained when all blocks in the dam are placed in conditions existing for intermediate sections. cdnformance with a uniform and continuous place- ment program. This even temperature distribu- Final Cooling tion is desirable, not only becauseof the subsequent uniform system of contraction joint openings, but Cooling and contraction joint grouting of the also because the overall stress distribution will be mass concrete in concrete dams is performed by nearer that assumed in the design. Extreme tem- grout lifts starting in the lowest part of the dam perature gradients on the exposed sides of blocks and progressing upward. These grout lifts are can also cause the start of circumferential crackg normally 50 to 60 feet in height and extend from across the blocks. The chances of such cracks abutment to abutment across the full length of the forming will be lessened when each lift is exposed dam. Each contraction joint in each grout lift for a minimum length of time. has its own vertical and horizontal seals so that the Secondly, a uniform placement will result in a grout lift can be grouted as a unit. Cooling is com- more uniform loading of the foundation. During pleted in each grout lift just prior to grouting the that period of construction when the contraction contraction joints, the program of cooling being joints are open, the individual blocks react on the dictated by construction progress, method of cool- foundation as individual columns. If extreme ing, season of the year, and any reservoir filling height differentials exist between blocks, unequal criteria. settlements in the foundation may result. A third As indicated in Figure 21, cooling prior to reason for the height differential is that it will grouting the contraction joi’nts is normally accom- cause construction of the dam to progress uni- plished from 1 or 2 months to about 1 year after formly up from the bottom of the canyon. Con- t~heconcrete is placed. In the smaller construction t.raction joints can then be grouted in advance of blocks, final cooling may be accomplished in a a rising reservoir, thus permitting storage at ear- single continuous cooling period. In the larger lier times than would occur if construction progress blocks, however, the final cooling should be per- was concentrated in selected sections of the dam. formed in two steps to reduce the vertical temper- An additional maximum height differential, that ature gradient which occurs at. the boundary of ,a occurring between the highest and lowest blocks grout. lift due to the grout lift pattern of cooling. in the dam, should be required if the early storage The first of these steps is commonly referred to as is desirable. the intek-mediate cooling period and the second W-here one or two blocks are left low for diver- step then becomesthe final cooling period. sion or as a construction expedient, several adverse In practice, the intermediate cooling period for conditions may occur as const’ruction progresses. a grout lift lowers the temperature of the concrete One’ of these conditions occurs when a large height in that lift to approximately halfway between the differential exists during a long period of cold temperature existing at the start of the cooling pe- weather. Under such a situation, a definition OF riod and the desired final temperature. Each grout tilting of the high block out, into the area of the lift, in succession, undergoes this intermediate low block occurs because of the temperature dif- cooling period before proceeding with the final ferential between the cold face adjacent to the low cooling of the next lower grout lift. Such a pat- block and the opposite face which remains rela- tern of cooling, once underway, will require little, tively warm. This deflection could damage the if any, additional cooling. metal seals installed for construction joint grout- ing on the opposite face of the block if the de- Height Differential flection becomes too great. The deflection could also prevent continued placement of concrete in For several reasons, a maximum height differ- the block adjoining the opposite face of the high ential between adjacent. blocks is specified in con- block. Continued placement in that block, while struction specifications for an arch dam. First, the high block is deflected out into the opening of from a temperature standpoint, an even tempera- the low block, would progressively wedge the high CONSTRUCTION REQUIREMENTS block out. During the following warm season, Extended Exposure of Horizontal when the cold exposed face warms up, the high Construction Joints block would tend to return to its original position, causing a shearing movement upward with the pas- Whenever irregular placement occurs and tops sibility of horizonal cracks being formed in the of construction blocks are left exposed for more adjoining block. These problems peculiar to a than 2 weeks, several crack-producing factors are considerable height differential can be met and at work which can start cracks or break bond be- corrected by the timely use of the embedded pipe tween lifts. The edges of horizontal construction cooling systems. joints occurring at the tops of lifts left exposed The actual height differential is a compromise over a winter’s season are particularly vulnerable between arriving at the uniform temperature con- to surface tensions during the annual temperature ditions and construction progress desired, and the cycles which occur during and after the construc- contractor’s placement program. In Bureau of tion period. These construction joints are cold Reclamation practice, the maximum differential joints and require special treatment to obtain an between adjacent blocks is usually stipulated as effective bond between the old concrete and the 25 feet where 5foot lifts are used or 30 feet where new concrete. Horizontal cracks often occur at 74/,-foot lifts are used. The maximum differential the location of these cold joints during subse- between the highest block in the dam and the low- quent winter exposures, surface tensions causing est block in the dam is usually limited to 40 feet the crack to extend into the concrete along the con- where B-foot lifts are used and to 52.5 feet where struction joint plane as much as 10 or 12 feet. Q&foot lifts are used. Preventive measures used are those directed to- ward obtaining the best possible bond between the Openings in Dam old and new concrete. In the early sprihg, in addi- tion to preparing the surface for placement of Where possible, galleries and large openings in fresh concrete, considerable benefit is obtained by the dam should be located in regions of low stress circulating warm water through embedded tubing or where cracks would not be detrimental to struc- in the top 2 or 3 placement lifts of the previously tural stability. Because openings concentrate placed concrete before new concrete is placed. In conjunction with warming the old concrete, sev- stresses at their edges, all possible means should be eral shallow lifts may be placed initially on the used to prevent the beginning of cracks from the old concrete or the horizontal spacing of the cool- Proper curing methods surfaces of such openings. ing coils in the first 2 or 3 lifts of new concrete The entrances to such should be used at all times. may be reduced. Both of these measures will hold openings should be bulkheaded and kept closed, down the temperature rise in the new concrete and, with self-closing doors where traffic demands, to combined with the lower placing temperatures prevent the circulation of air currents through the normally occurring in the early spring months, openings. Such air currents not only tend to dry will create a temperature differential in the con- out the surfaces but also can cause the formation crete which will reduce the tendency to shear or of extreme temperature gradients. break bond on the horizontal joint plane. - - - . . SELECTED ENGINEERING MONOGRAPHS Monograph No. Title 1 Petrography and Engineering Properties of Igneous Rock (microfiche only) 3 Welded Steel Penstocks Design and Construction 6 Stress Analysis of Concrete Pipe 7 Friction Factors for Large Conduits Flowing Full 8 Theory and Problems of Water Percolation 9 Discharge Coefficients for Irregular Overfall Spillways 13 Estimating Foundation Settlement by One-Dimensional Consolidation Tests 14 Beggs Deformeter Stress Analysis of Single-Barrel Conduits 16 Spillway Tests Confirm Model-Prototype Conformance 19 Design Criteria for Concrete Arch and Gravity Dams 20 Selecting Hydraulic Reaction Turbines 21 Crustal Disturbances in the Lake Meade Area 23 Photoelastic and Experimental Analog Procedures 25 Hydraulic Design of Stilling Basins and Energy Dissipators 26 Rapid Method of Construction Control for Embankments of Cohesive Soil 27 Moments and Reactions for Rectangular Plates 28 Petrographic and Engineering Properties of Loess (mircrotiche only) 29 Calculation of Stress From Stain in Concrete (microfiche only) 30 Stress Analysis of Hydraulic Turbine Parts 31 Ground-Water Movement 32 Stress Analysis of Wye Branches 33 Hydraulic Design of Transitions for Small Canals (microfiche only) 34 Control of Cracking in Mass Concrete Structures 35 Effect of Snow Compaction on Runoff from Rain or Snow 36 Guide for Preliminary Design of Arch Dams 37 Hydraulic Model Studies for Morrow Point Dam 38 Potential Economic Benefits from the Use of Radioisotopes in Flow Measurements through High-Head Turbines and Pumps 39 Estimating Reversible Pump-Turbine Characteristics 40 Selecting Large Pumping Units 41 Air-Water Flow in Hydraulic Structures A free pamphlet is available from the Bureau of Reclamation entitled, “Publications for Sale. ” It describes some of the technical publications currently available, their cost, and how to order them. The pamphlet can be obtained upon request to the Bureau of Reclamation, Engineering and Research Center, P 0 Box 25007, Denver Federal Center, Bldg. 67, Denver CO 80225,