Concrete Mix Design : A Summary Citation Morse, Charles Adelbert (1938) Concrete Mix Design : A Summary. Master's thesis, California Institute of Technology. doi:10.7907/ab53-yv81. https://resolver.caltech.edu/CaltechTHESIS:11252024-185950309 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Converse, Frederick James Thesis Committee: Unknown, Unknown Defense Date: 1 January 1938 Record Number: CaltechTHESIS:11252024-185950309 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11252024-185950309 DOI: 10.7907/ab53-yv81 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16875 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 26 Nov 2024 18:50 Last Modified: 26 Nov 2024 19:11 Thesis Files PDF - Final Version See Usage Policy. 12MB Repository Staff Only: item control page

CONCRETE MIX DES I GN: A SUl\llM.ARY Thesis by Charles A. Morse In Partial Fulfillment of the Requirements for the Degree of Master of Science California Institute of Technology Pasadena, California 1938 CONTENTS Page Foreword 1 Section l Study of various design methods 2 Section 2 Selected methods of design 8 Section 3 Comparison of theory and practice l? Section 4 ."Particle Interference:" a trouble-shooter developed by Mr. W. H. Spear Curves - listing: Figure l - Fineness-modulus Figure 2 - Surface-area Figure · 3 - Trial-mix strength curves Figure 4 - W/C-Strength curves Figure 5 - Ideal curves Fuller's Walsh's M. W.D. Distribution Division Schedule 3P Average curve for good mixes Average curve for poor mixes Figure 6 - Strength-Fines curve Figure ? - Strength-Silt curve 21 CO NTENTS (continued) Tables A Aggre ga te gr a din gs, sc hedule 3P, M. W.D. B C Mix design c a lculations - ana l ysis D Mix design c a lcula tions - batch Quantities E Analysi's Conversions E Tabula ted c a lcula tions for pa rticle interference Ac knowledgment Bibliogr a phy 1. FOREWORD Designing concrete mixes is a subject which has been considered by everyone from the wheelbarrow-pushing laborer to the systematic engineer. Arising from this variety of studies is a host of different concepts of what constitutes "good concrete." In an effort to collect, evaluate, and extract from this assortment of opinions, a usable, fundamentally correct method for the design of concrete mixes this study was undertaken, and herewith are presented the results. This paper presumes the assuraption that the accepted end in concrete design is the obtaining of strong, watertight, homogeneous concrete at a minimum of expense. 2. SECTION l Maximum strength is developed by that concrete which is most dense. Countless tests have shown this to be a fact. Sanford E. Thompson, writing in 1906 (Ref. 2, p. 184), outlines seven methods of designing such concrete (i.e., concrete with a minimum of voids): (l') Arbitrary selection, examples of which are, (a) Use half as much sand as stone, as 1:2:4 or l:3:6. (b) Use volume of stone equivalent to the cement plus twice the volume of sand, as 1:2:5 or 1: 3: 7. (2) Determination of voids in the stone and in the sand, and proportioning of materials so that the volume of sand is equivalent to the volume of voids in the stone and the volume of the cement is slightly in excess of the voids in the sand. ( 3 ') Determination of the voids in the stone, and, after selecting the proportions of cement to sand by test or judgment, proportioning the mortar to the stone so that the volume of mortar will be slightly in excess of the voids in the stone. ( 4' ) Mixing the sand an d s t one and providing sue h a proportion of cement that the paste will slightly more 3. than fill the voids in the mixed aggregate. (5') Making trial mixtures of dry materials in different proportions to determine the mixture giving the smallest percentage of voids, and then adding an arbitrary percentage of cement, or else one based on the voids in the mixed aggregate. ( 6') Mixing the aggregate and cement according to a given mechanical analysis curve. ( ?') Making volumetric tests or trial mixtures of con- crete with a given percentage of cement and different aggregates, and selecting the mixture producing the smallest volume of concrete; then varying the proportions thus found, by inspection of the concrete in the field. Concerning these methods Thompson writes, 11 The most practical method .... is by mechanical analysis of the aggregates, .... " (method 6'). He continues, ''Volumetric synthesis (method '7•), or proportioning by trial mixtures, is another method which is sometimes useful, and produces fairly scientific results." To modernize this list there must be added two methods which were developed in an effort to simplify scientific design. These are: (8') The surface-area method. (9') The fineness modulus method. 4. These eight methods may be further summa rized as being (1) Arbitrary proportioning (includes l') (2) Proportioning by voids (includes 2', 3', 4', 5', 6', ?') (3) Proportioning by surface-area (8') (4) Proportioning by fineness modulus (9'). Of these four general methods it may be said as follows: Arbitrary proportioning is an art acquired only by experience. Rules of thumb are often entirely adequate, but satisfactory only when accompanied by trained supervision. It seems well to point out here, however, that much excellent concrete has been placed which has been "designed" only by this method, and for many jobs , especially small ones, this method may prove the most generally advant a geous. It should be noted, however, that complete proportioning designed on the basis of voids may be successfully applied in the field with the aid of only crude methods. Such operations are well described in the Portland Cement Company's booklet, Des~g~ and Control of Concrete Mixes. In an article (Ref. 4) Mr. I!'. S. Besson discusses the remaining three methods, voids, surface-area, and finenessmodulus, so concisely that it seems well to quote him directly. He states: " .... There have been several methods of aggre gate classification , includin g the surface-area and fineness-modulus 5. methods, advocated as substitutes for the stra ight mechanical analysis (wh ich pictures the granulomet ric compos ition o f an aggre gate ) in attenrots t o obtain a me t hod ad a pted directly to the solution of engineering problems. But both the f i neness- modulus me thod and the surfa ce-a rea method are unsuitable modificat ions of the straight n~chani cal ana l ysi s. Fineness - modulus arbitrarily gives undue weight to the l arger particles making up the aggregate, while, on the other hand, the surfacea rea metho d gives exa ggerated weight to the finer particles. The fineness-modulus method i gnore s the finest of a ll. These methods do not give true pictures of the material analyzed . "Surfece a rea was brought .... to the fore by L. N. Edwards in 1918 .... The method does not weight the particles in any logical manner, so that it may be st a ted that the value of an aggregate for concrete va ries as an inverse function of the surface area, while (as used in ce ment specifications) the v a lue of a cement va ries as a direct function. "Fineness-modulus dates back to Duff A. Abrams' 1919 report .... Th is report states that t wo aggregates havi ng the same fineness-modulus will require the s ame quantity of water to produce a mix of the s ame plasticity, and will give concrete of the s ame strength, so long as the aggregates are not too coa rse for the quantity of cement. 11 Fineness-modulus is an attempt to meesure t he extent to which gradation and the coarser particles in an aggregate 6. affect the concrete strength. A satisfactory way to (do this is as follows):" For each cement to aggregate ratio make a series of samples (1) keeping the consistency constant (Note: use Burmister flow trough - most consistent method - detailed in M. W.D. Manual for Concrete Inspectors, p. 36 - see Ref. 6) (2) and varying proportions of each aggregate as indicated on figure 3. Plot strength tests of these samples against mix proportions, and obtain curves, as in figure 3, which indicate the desired relationships. Mr. Besson makes an analysis of these curves which holds in the general case (Ref. 4). "These curves may be analyzed as follows: (a) The highest curve (maximum strength) represents combinations of coarse gravel and coarse sand. (b) The lowest curve (minimum strength) represents combinations of fine gravel and fine sand. (o) The gravel has more influence upon strength than the sand .... 7. (d) Substituting coarse sand for fine moves the peak of the strength curve toward larger proportions of sand. (e) Mixes represented by the peaks of the curves are the best proportions for each of the four combined aggregates. "An analysi s such as (this) shows the exact influence of gradation and the importance of the coarser part icles. These results cannot be obtained by the surface-area and finenessmodulus methods, which weigh the particles in accordance with arbitrary assumptions." The justifiable conclusion seems to be that the voids method of design is preferable above all others. In view of this fact, the sucaeeding section outlines a design procedure on this bas is. 8. SECTION 2 Procedure for the design of a concrete mix on the basis of minimum voids, with the aid of mechanical analysis of the aggregate may be outlined as follows. It is necessary to determine: (1) .Amount of cement per cubic yard of finished concrete. (2) Water-cement ratio. (3) Aggregate sizes and grading desired. (4) Specific gravities (solid volume) of the several aggregates. (5) Absorption of the several aggregates. (6) Per cent of moisture in each of the several aggregates. From these above data the following may be obtained, which three statements are the design quantities of the mix: (1) Weight of cement per cubic yard. (2) Weight of each aggregate per cubic yard. (3) Amount of mixing water per cubic yard. This method contemplates a finished product consisting of one cubic yard, twenty-seven cubic feet, of finished concrete. This yard of concrete has the three constituents named in the last paragraph, viz.: cement, water, and aggregate. The relative quantities of each are determined by subtracting from twenty-seven cubic feet, first, the volume of cement used, and, second, the volume of water used. The remainder is the volume of aggregate used. But it is to be noted that this volume of aggregate is not the bulk volume, for in the mixed concrete the aggregate is completely surrounded (ideally) by (1) The larger aggregate by the smaller ( 2) The smaller aggregate by the cement (3) The cement by the (unabsorbed) water. Rather, this volume is the sum of the volumes of each individual particle. This g_uantity is known as the "solid volume." Considering, one at a time, the quantities to be determined, there are: (1) Cement vatte~ Information" on the amount of cement to use under any particular circumstances. Current literature seems to assume one of three things: (a) That the job foreman will strike a happy balance between the amount of cement used and the workability (an all-important item: For, of what virtue is dense concrete when filled with rock pockets and honeycombing?) (b) That this proportion will have been determined experimentally beforehand, aggregate characteristics and water-cement ratio having been held constant, and 10. the cement varied in trial batches. (c) That the amount of cement to be used per yard will have been specified by someone higher in authority than the mix designer. Published papers seem either to deal with specific special cases, or to be so complete and varied as to permit of no generalization. Reference 2 has a very . complete set of tables dealing with this matter. The amount of cement varies (a) wi th the particular aggregate (due to shape and maximwn size) (b) with strength desired. _Simply as an illustration the following table is included (Ref. 6) : 28 Day Strength Approx. bbl./ou.yd. Max. 4000#/sq_.in. 1.75 1.50 1.3?5 1.375 1.25 0.80 3000#/sq.in. 2500#/sq.in. W/0 0.90 1.00 0.95 2000#/sq.in. 1.125 1.05 1500#/sq.in. 1.00 1.10 The extent to which job conditions may vary from these figures may be seen by noting that the 4000-pound concrete 11. was placed with 1.60 bbl./cu.yd. with about the same W/C, a nd tha t the 1500 was run at the specified cement content, but with W/C equal to a bout 1.40. (2) Water-cement ratio Although subject to the specific conditions found on the job, this may be estimated from several curves available, one of which is reproduced here (figure 4) from Reference 3. On the job the apparent ratio will be found to va ry with the temperature and humidity of the atmosphere, among other things. (3 ) Aggregate sizes Aggregate size (maximum) may be determined by the material available. In any case, it must be small enough to pass between any reinforcing steel in the structure so as to allow reasonable workability of the concrete in placing. The aggregate should be of good quality, strong and non-friable (see A.S.T. M. specifications for details). The desirable proportioning of the various sizes of aggregate may be definitely determined, within small tolerances, from curves which have been established by experiment. in figure 5 . Several of these "ideal" curves are given 12. The a ggregate should be screened into as many different sizes as is necessary to obtain the desired ide al curve. The proportions necessary to duplicate this grading curve may be found readily by choosing arbitrary percent a ges ( known as "bin percentage") of each aggregate size, calculating the resulting curve, estimating a correction to the trial bin percentages, and repeating until the desired results are obtained. It may be convenient to determine from the ideal curve the ideal per cents of each aggregate size which will be present in the final aggregate mixture (or "ideal mix"). This allows the explicit calculation of bin percentages, directly, by solving a set of simultaneous e quations, or by successive approximations (which last is very rapidly done by experienced men). For sake of completeness: the grading analysis, showing the percentage of each sieve size contained in each bin of aggregate, is obt a ined by shaking a sample of the material from each bin through a set of screens having known openings which vary uniformly in clearance. The aggregate size and proportioning, then, has now been determined. It is now necess a ry to obt a in t he 13. (3) Specific gravities The quantity referred to here is the "solid volume" specific gravity, which may be defined as the ratio of the weight of any single, solid particle of the aggregate to the weight of an equal quantity of water. This may be obtained by (a) Filling container of known volume, v1 , with dry aggregate of known weight, W. (b) A known weight, W3 , and, hence, volume, of water is then added, taking time to let water Subtract {Nm displace all air . ..t Add to w3 the absorption (see (4), following) and call W2. (c) Calculation then gives d, the solid volume specific gravity: v1 is first converted to the weight, w1 , of an equal volume of water. Then: This quantity must be obtained for each aggregate, but once accurately obtained, it may be considered constant for that aggregate and need only be checked occasionally. (4) Absorption This is determined by evaporating damp aggrega te to 14. surface dryness, weighing, to const ant weight ( W1 ), then evaporating w ). 100 • W1 - W = Absorption%, G. w (5) Moisture in aggregates This is determined for each aggregate, at whatever intervals necessary by weighing moist sample, ( evaporating to dryness, ( 100 • W1 - W w W). W1 ) then Then: = total moisture, F. The necessary unknowns are now determined, and the mix may be calculated on the principles outlined previously. This example will illustrate, and indic a te a convenient form for computations. The figures are those for a day's run on the M. W.D. Distribution System. Given: Cement/ou.yd. == 1.69 bbl. Water-cement r atio - 0.78 Solid volume density of cement - 196#/ou. f t. Loose volume density of cement - l bbl. -- 94#/cu. f t. 4 Ou.ft. = 3?6# of cement From which is obtained: Volume of cement: 1.69 • ~z~ ~ 3.24 cu.ft. Volume of water: (l.69 • 3?6 94 )(0.?8) Sum, volume wa ter plus volume cement: ::: 5.28 ou.f t . 8.52 cu.ft. 15. Since remainder of yard must be aggregate: 27.00 - 8.52 or solid volume of aggregate := === 18.48 18.48 cu.ft. By sieving each of the three aggregates in use we get the "screen analysis" shown in table at left on sheet C. Experience suggests "ideal mix" percentages of 34.5% sand, 15.0% pea gravel, and 50.5% rock. Successive estimates, trials, and corrections indicate tha t the ideal 11 bin" percentages are 44.1% from the sand bin, 6.6% from the pea gravel bin, and 49.3% from the rook bin. It may be noted that these perce nta ges are determined by weight. But these same figures ma y be taken as per cents of solid volurae because the small differences in density may be neglected here. Knowing already the total solid volume of aggregate, and knowing now the individual per cents of solid volume for each aggre ga te, the remaining c a lculations are readily carried out as indic a ted on sheet D. Additional dat a , obt a ined by met hods outlined: Note: Sand Pea Rock Specific gravities: 2.62 2.68 2 .68 Today's moistures (total): 6.4% 1.5% 2.2% Absorptions: 0.6% 0.2% In seeking to obtain any pa rticular strength with co ncre te it must be observed, and may we ll be noted here, tha t 16. curing has a very great e ffect upon this item. Moist curing for a minimum of seven days is essential, and twentyei ght days is desira ble. C COMPUTATION OF SCREEN ANALYS IS OF MI XED .AGGREGATE Screen analysis o/; each size "Bin"% e a ch size in mix Reta ined on sieve size -1/8 0 1.4 0.6 200 2.6 1.1 100 11.7 5.2 -1/2 3.0 -1 1. 0 -1/8 -1/2 44.1 6.6 d Total 70 Total% -1 each re49 . 3 size tained 0.6 100 0.1 1.2 99.4 0.1 5.3 98.2 Agg. Grading re qu ired 34.5 48 21 .2 9 o4 28 22.5 9.9 14 17.4 7.7 8 18.6 8.2 3.0 0.4 0.1 9.5 92.9 0.1 10.0 83.4 0.1 0.1 7.9 73. 4 0.2 0.2 8.6 65.5 15.0 4 3/8 4.6 60.7 0.8 33.3 46 . 9 2 .0 0.4 6.4 56.9 2 . 2 23 .2 25 . 4 50.5 4.0 50 . 5 3/ 4 46.5 22.9 22.9 25.1 1 4.4 2. 2 2. 2 2. 2 Totals 100 .0 100.0 100.0 44 . 1 6 .6 49.3 100.0 D co:MPUTATION OF CONCRETE BATC H Q,UANTITIES Aggregate - 1/8" -1/2 11 - 1 11 Mixed Aggregate B - "B in" % e a ch size by solid volum.e 44.1 6.6 49 .3 100.0 C - Solid volume pe r conc rete batch, cu.fto 8.14 lo22 9.12 18.48 D - Specific gr avity, solid volume 2.62 2068 2068 204 1526 E - Wt.of dry a gg ./bat ch 3062 F - Tot a l moisture,% 6.4 1.5 2.2 G - Absorption,% 0.6 0.2 0.2 F - G 5.8 1.3 2.0 J - Surface mo isture wt.in batch E• H lb 100 s. 77 3 31 111 85 3' 34 122 1417 207 1560 3184 H - Surface moisture,% K - Total moisture wt. in batch 7 EoF lb 100 s. L - Gross wt. of agg. for batch E K Now deduct surface moisture on aggregate from mixing water to get water to be a dded: 5.28 - ti".14 = 3.50 cu.ft. Mixing time (spe c ified) not less than 1 1/2 minutes . is now designed. The mix Inforraa tion sheet for mixer opera tor reads (for one yard batch): Cement Sand Pea Rock Water 635# 1417# 207# • 1560# 3.50 cu.ft. 17. SECTION 3 Last year it was the author's good fortune to be in the employ of the betropoli tan Water District of Southern California as a concrete inspector. In this capacity time was spent both in the Rochester precast concrete pipe plant and in the field on some line structures. Through the kindness and cooperation of M:r. R. B. Diemer , Engineer of the Distribution System, of li':r. Hugh Jones, Assistant Engineer, Metropolitan Water District , and of Mr . W. H. Spear, Assistant Engineer, Nietropolitan Water District, the author has been permitted to make use of results obtained by the District on its pipe lines, as well as of results of a study, conducted by Mr . Spear, which will be treated in Section 4 of this paper. At present it is the purpose to compare with ttstandard," or ti idealn curves, two curves of aggregate analyses used by the District in the manufacture of its pipe. These two curves are average curves, the data being compiled from mixes used for pipe from January 26, 1937 through April 20, 193?, for one curve, and from April 21, 193? to July 24, 1937, for the other curve. ( For da.ta, see· sheets A and B. ) Throughout the former period considerable difficulty was had with the mix. Despite all efforts made to improve it by mixture changing, it remained harsh. The second period marks a series of smooth mixes brought about by the use of blending sand to increase the fines. From A MIX DESIGH DATA - SCHEDULE 3P - ROCHESTER PLJ.J.lf'I' - M. W.D. pate of Design %each size retained on Tyler Standard Sieves 1937 Ideal Mix Pan #200 #100 #48 #28 #14 #8 #4 3/8 11 3/4 11 l" 1-26 35-11-54 0.6 1.0 3.7 9.3 11.4 9.0 7.6 3.4 22.5 27.4 4.1 2-17 35-11-54 o.6 1.0 3.5 9.4 11.5 9.0 7.1 J.9 2~2.J 27.2 4.5 2-26 35-11-54 o.6 1.1 3.6 9.3 11.5 8.9 7.1 3.9 21.7 28.1 4.2 3- 2 35-12-53 o.6 1.1 3.6 9.3 11.6 8.8 7.3 4.7 22.7 27.0 3.3 3- 3 35-11-54 o.6 1.1 3.6 9.3 11.6 8.3 7.3 3.7 22.9 27.8 3.3 J- 5 35-15-50 0.5 0.9 3.6 9.4 11.8 8.8 7.6 7.4 20.7 25.4 3.9 3- 8 35-15-50 0.5 0.9 3.6 9.7 11.8 8.5 7.4 7.6 22.1 24.7 3.2 J- 9 35-14-51 o.6 0.9 3.4 9.4 11.7 9.0 7.J 6.7 24.6 23.6 2.8 3-11 36-12-52 0.5 0.9 3.7 9.8 12.0 9.1 7.5 4.5 25.5 23.9 2.6 3-15 35-15.5-49-5 0.5 0.7 3.7 9.2 11.7 9.1 s.4 7.1 17.0 27.5 5.1 3-17 35-15.5-49-5 0.4 1.0 4.0 9.4 11.9 8.3 7.2 8.3 21.8 25.2 2.5 3-20 35-15.5-49-5 o.6 0.9 4.0 9.6 11.5 8.4 8.0 7.5 21.8 23.9 3.8 3-25 35-15.5-49.5 o.6 1.0 3.9 9.7 11.3 8.5 8.1 7.4 24.s 22.5 2.2 4- 1 35-15.5-49-5 0.4 1.1 J.8 9.6 11.7 8.4 8.2 7.3 25.1 21.9 2.5 4- 9 35-15.5-49.5 0.5 1.1 3.9 9.7 11..3 8.5 7.S 7.7 25.2 21.7 2.6 * 4-J.6 35-15.5-49-5 0.5 1.1 3.9 9.8 11.4 8.3 7.7 7.8 25.8 21.2 .2. 5 4-19 35-15.5-49-5 0.5 1.1 4.6 11.0 9.9 7.9 7.9 7.6 23.1 22.9 3.5 4-20 35-14-51 0.3 o.s 4.4 11.0 10.5 8.0 9.:J_ 4.9 23.2 24.1 3.7 Totals 9.4 17.7 68.5 173.9 206.1155.3 138.6 111.4 417.8 446.0 60.3 Average 0.5 Total % ) Retained) 6.2 23.1 24.7 3.3 100.0 99.5 98.5 94.7 85.0 73.6 65.0 57.3 51.1 28.0 3.3 1.0 3.8 9.7 11.4 8.6 7.7 * Changed from 1.69 to 1.60 bbl./yd. of cement (strength higher than needed). B %each size retained on Tyler Standard Sieves Date of Design Ideal 1937 Mix ~ 4-21 35-14-51 o.6 4-27 35-14-51 5- 1 Pan #200 #48 #28 #14 #8 #4 3/8" 3/4" 111 1.7 6.5 11.5 8.2 6.5 7.2 6.8 23.7 3.6 0.5 1.5 5.8 10.8 9 •.3 7.1 8.1 5.9 24.2 23.4 3.4 35-14-51 0.8 1.7 5.1 10.0 10.3 7.1 6.9 7.0 25.9 2:2.3 2.9 5- 4 35-14-51 o.8 2.0 6.1 9.9 9.6 6.6 6.3 7.7 25.9 22.1 3.0 5-10 35-14-51 0.9 2.2 6.1 9.6 9.5 6.7 6.,3 7.7 26.3 21.8 2.9 5-12 35-14-51 1.0 ? r, _;,, • I 6.9 9.3 7.9 6.2 5.5 8.5 26.5 21.6 2.9 5-13 35-13-52 0.9 2.7 7.4 9.5 8.4 6.1 7.1 4.0 5-18 35-13-52 0.8 2.7 6.6 9.3 8.9 6.7 6.1 5.9 23.8 24.2 6.9 24 • ,.I, 24.5 5-21 .35-12-53 0.9 2.7 6.5 9.2 9.2 6.5 5.7 6.3 27. 2 22.2 J.6 5-28 35-12-53 o.8 2.3 5.9 9.5 9.0 7.5 6.7 5•.3 .29.8 20.4 2.8 6-10 35-13-52 1.1 2.7 6.3 9.2 8.4 7 .;,,? . 5.9 7.1 27.7 22.6 1.7 6-14 35-12-53 1.2 ,.... ;c:: ..,, r:. 6.3 8.7 8.5 7.8 6.2 5.8 26.9 ,..., ,.... r:. . ., 3.6 6-24 35-12-53 1.0 .,<.. ::> t'. 5.8 9.1 9.2 7.4 6.4 5.6 25.5 2.3.9 3.6 ,.... #100 t,r\ N ,::.,)• I ,::,,::, 2.8 Totals 11..3 .30.9 81.3 125.6 116.4 89.5 8/4.. 4 86.5 338.1 295.2 L10.8 Average 0.9 Total % ) Retained) 11-::- Started 6.6 26.0 22.7 J.l 100.0 99.1 96.7 90.5 80.8 71.8 64.9 58.4 51.8 25.8 3.1 2.4 6.2 9.7 using blending sa11d to raise fines. 9.0 6.9 6.5 Workability improved greatly. 18. 15% to 20% of the s and was this blend, of which a typical analysis is: Retained on % 0 7.0 200 23.1 100 46.3 48 19.2 28 4.4 100.0 While on this point of fines in the sand, it is of interest to note the curves of figures 6 and 7, contr:i.buted by Mr. Bert J. Soderblom. These curves ~re among the observations made by Mr. Soderblom during his residence at the Fan Hill Plant, Thousand Palms Tunnel No. 1, M.W.D. One curve shows a very critical point for strength with respect to the per cent of aggregate passing the 100 mesh screen. The other curve shows how the strength continues to drop, as the very fine particles, silt, increase in percentage. Returning to the distribution pipe, it is worthy of note that, with the control established, and with reasonably uniform rock plant output, it was possible to hold the strengths developed at a very steady figure. In addition, the mixing water remai ned a practically constant quantity over a day's run. Where aggregate moistures and grading were erratic, these two items were very jumpy. 19. Before leaving the pipe plants, a notation of the control methods and equipment used seems in order. A description of the concrete equipment at the Rochester pipe plant, owned and opera ted by the American Concrete and Steel Pipe Company, under contract to M. 'N .D., is a typical installation. Aggregate is delivered to the plant by trucks, dumped in a pit, and c arried to elevated storage bins by a bucket chain. fre1,'qhf Cement is unloaded from Ast ~raga cars by one man operating a small motor-driven scraper. It is stored in a large silo, and elevated to the mixer supply tank as needed. Materials are batched consecutively into a single weighing hopper, a F~irbanks-Morse scale. Each aggregate can be weighed automatically within five to ten pounds, plus or minus, depending upon circumstances, by the automatic photocell equipment. The aggregates can also be delivered by operating manually controlled air valves. Feed from the aggregate bunkers is through open gates onto short conveyor belts. The belts are motor driven, and each is equipped with a jog for close final weighing. by use of a screw. Cement feed is accomplished Water is measured into a one-batch storage t ank by an automatic shut-off meter reading to one-hundredths of a cubic foot. A release valve is provided for excess water. 2 0. Mixer capacity is about 3 1/2 yards. W ell water is used in mixing. The same plant is used for mixing dry batch for hauling to ditch. 21. SECTION 4 In preparj_ng this paper, two methods of mix design have been encountered which deal with calculations based on the aggregate particles themselves. One of these is a method of proportioning described by }[r. Archie A. Smith in Concrete for May, 1936. Its purpose is the calculation of a mix, having given the screen analysis, and water-cement ratio. given in detail. The procedure is After becoming accustomed to the method, one would probably find it as rapid as any other. It should be noted, however, that, because of assumptions of symmetrical size distribution in the method, some aggregates can throw the results into appreciable error. The other method of using the aggregate particles, is the method, already referred to, developed by Ivir. Spear for the calculation of particle interference. This affords a mathematical device, based upon screen analysis, for showing up immediately any flaws in the design. It is based upon the space between particles of any given size available to receive the particles smaller. Mr. Spear's work is reproduced, on the follo wing pages, verbatim, save for one or two explanatory lines. The curve of this aggregate is plotted on figure 5, and the mis-matchings indicated by the table on the 200 mesh, the 16, the 3/8, and the 3/4 are apparent. The exoess in the 3/8 size will be particularly apparent, for this central part 22. of the ideal curve seems most sensitive to variations. Movements which will make a mix impossible here, are only permissible variations at either end. 23. CONCRETE DESIGN CALCULATION OF PARTICLE I NTERFERENCE By W. H. Spear Given: a particular screen analysis of combined aggregates. Consider the solid volurne of the tot a l mixed concrete as 100%, and compute the percenta ges of each size of aggregate according to screen analysis on the design sheet. ','/hen mixing has taken place the average cle a r distance apart of two adjacent particles of any size "n" may be ca lled "t", and should be large enough so tl:1at the space will accomod a te the next smaller size. The solid volume "S" of the size "n", divided by its natural volume "V", in a dry rodded state may be c a lled "do", i.e., "de," would be 60% of a material having 40% voids. The solid volume "S" of the size "n", divided by its expanded volume "E", when the particles have been pushed apart by smaller particles, cement and water (forgetting these as though not present to affect density) will be called "da", or RELATIVE DENSITY. The average diameter of that size "n" will be c a lled "Dn", and is the average distance between centers of particles before mixing. The average distance between centers of particles in the s ame group size after mixing will be called "Dm", and "Dm" eq_uals ttDn" + "t". 24. The followin g derivation determines the formula to be used in calculating particle interference in a ny mix design: The natura l volume "V" of the size "n" will be: V = NxgxD 3 n Where N number particles in the unit of volume Where g function of the shape of the particles. The expanded volume 11 E" of the size "ntt when this size is added to a smaller size "m", plus cement and water will be: 3 E = N x g X Dm Where N and g are identical with above, in both cases the same solid volume being considered. It will be noted that these factors cancel in the following analysis: do XV :::: s or d da x E == s or d 0 a :::::. s V ::::: S E 3 3 E N X g X Dm do Dm ::::: - == - =3 == S/ E V N X g X Dn d~ n S/ V n5 or Dm Dn - 3~ - do d or e. or t Dn - + D = Dn n Dn + t Dn 3 ~ a 3 ~ a 25. Solving this fort: Where: d 0 = determined experimentally and is according to natura l voids. da = computed from design quantities ( item 7 on sample calculation sheet). Data assumed in following sample calculation: l. Assume water-cement ratio = 0.78. 2. Assume 6 3/ 4 sacks of cement per yard, or 6.75 c.f. {loose volume) for concrete yielding 4,400 to 5,000 lbs. per square inch strength. Therefore Wa ter~ 6.75 x 0.78 = 5.28 c.f. per cubic yard. Water Cement Ratio=.78 Water=5.28 c.f. .012 45.8 3.58 d = Item (5) + Item (6) Exper. d0 = Item (8) + Item (7 ) = 3 Item (9) = Item (10) - 1 = Item (11) x Item (,4.) = (7) (8) (9) (10) (11) (12) (lJ) .320 Subtract Item (5) from unity; begin at right (6) .096 2.58 .037 .212 1.93 2.93 25.0 .600 .008 .110 .llO .194 . 88 1.88 6.6 .630 .099 .364 .OJ6 .221 .147 5.3 100 .221 .442 .596 .88 1.550 .88 .68 .63 . 278 1.88 1.68 6.6 .650 .098 .552 .051,. 1.765 1.168 7.9 16 1.63 4.7 .650 .650 ,4.• 3 .139 .498 .069 .878 .589 10.0 30 .150 .429 .065 -41+2 .295 9.5 50 22.4 3/4" 9.423 18.85 25.4 3/8" 3.53 7.78 1.10 2.10 9.1 .650 .072 .658 .047 .62 1.62 4.2 .650 .156 .985 .153 7.06 14.18 6.52 14.12 .46 1.46 3.1 .650 .209 .832 .174 7.061 14.181 22.76 4.699 6.9 4 The amount greater depends on richness of cement, varying from 2 x .051 m.m. to 2 x .025, i.e., t wice t he thickness of cement film. 1.76 3.14 .89 1.89 6.7 .650 .097 .611 .059 3.530 2.J62 8.6 8 Total Aggregate=l8.48 c.f., or 68.4% of Total Unit * 11 t 11 must be greater than Average 11 D11 of next smaller size. column to right = Item (4): - Set 1 t 11 * .004 Solid Vol. = Item (2) x % of Total .Aggregate (5) 11 .024 .037 Avg.Diam. m.m. = Dn (4) .550 .,328 0 Max.Diam. m.m.(screen) (3) a 1.2 .6 Analyses% (2) .074 200 0 c,creen Cement=J.24 c.f. (1) Item F In applying the formula to pr actical use set up in tabular form as follows: (Actual test run on Distribution System) 22.8 73.2 2.51 3.51 43.2 .650 .015 1.000 .015 29.14 26.67 2.2 l" NOTES ON FIGURE 5 All analyses given in this paper, with the exception of the following table, E, are be.sed on the total aggregate as one hundred per cent. However, to present the curves on the same basis as Fuller's, the screen analysis must be computed on the basis of 2.ggrega te plus cement (weights) equal 100 per cent. The results of this conversion are given in table E for: (1) M. V~ .D. ideal curve (2) M.W.D. average-field-conditions curves curve A being for satisfactory mix curve B being for unsatisfactory mix. (J) Curve of aggregate used in particle interference calculation • .Also tabulated there are the coordinates, under the smue conditions, for: (4) Fuller's curve of maximmn density - practical mix. To moke the conversion, it is observed that (1) Analysis curves are plotted on coordinates of sieve size, and proportion of the total by weight. (2) From table D: Weight of total aggregate per cu.yd. 3062# Weight of cement per cu.yd.= 635# 3687 Hence the aggregate is ~ or 83.2% of the total solids, by 3687 weight. (3) Multiplying the aggregate previously recorded by 83.2% v1ill give the percentage of total solids, the desired basis for plotting for direct comparison with Fuller. NOTES ON FIGURE 5 (continued) (.4-) 635 The cement is-------, or 17.2% of the total solids. 3687 It will be assumed that all of the cement passes the 200 mesh sieve. TABLE E Retained on Tyler Sieves: 3/8 3/4 111 A 82.8 82.4 82.0 78.9 70.6 61.3 54.1 47.6 42.5 23.3 2.7 B 82.S 82.5 80.5 75.J 67.2 59.7 54.0 48.5 43.1 21.4 2.5 C 82.8 82.2 81.1 76.5 68.6 60.8 54.1 49.5 45.0 26.2 2.1 82.8 82.6 81.3 77.2 69.8 61.0 54.5 47.4 41.6 20.5 1.8 93.0 89.0 85.0 81.8 76.8 72.2 66.1 60.0 47.4 25.0 8.9 Curve (M. W.D.ideal) D Pan 200 100 48 28 14 8 4 (particle interference) E (Fuller) ACKNOWLEDGI\IEFTS Acknowledgment is gratefully made for their kindness, coopera tion, and services, to: Mr. F. J. Converse, Assistant Professor of Civil Engineering, California Institute of Technology, Mr. R. B. Diemer, Distribution Engineer, M. W.D., Mr. Hugh Jones, Assistant Engineer, M. W.D., Mr. W. H. Spe ar, Assistant Engineer, M. W.D., Mr. Bert J. Soderblom, Inspector, M. W.D., as well as others. B IBL IO GRAPHY Useful references employed are: 1. Reinforced Concrete Construction, Vol. 1, George A. Hool. 2. Concrete - Plain and Reinforced, Frederick w. Taylor and Sanford E . Thompson. 3. Simplified Concrete Mix Design, H. N. Walsh, in Vol. 5, American Concrete Institute. 4. The Case aga inst Surface .Are a and Fineness Modulus, F. S . Besson, in Engineering News Record, Vol. 114, p. 298. 5. Also: discussion, P. Dekker, Vol. 114, p. 853. Proportioning - Its Fundament al Principles, Archie A. Smith, in Concrete, Vol. 44, No. 5. 6. Manual for Concrete Inspectors, published by the Metropolitan Water District of Southern California ( M. W.D.).