REQUIREMENTS FOR TEST RESULTS OF CONCRETE, ACTIONS ON

CONCRETE OF NONCOMPL YING TEST RESULTS AND THEIR INFLUENCE ON COST OF CONCRETE

Hua Zhou*, Concrete OEM Pte Ltd., Singapore

29th Conference on OUR WORLD IN CONCRETE & STRUCTURES: 25 - 26 August 2004,

Singapore

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29'hConference on OUR WORLD IN CONCRETE & STRUCTURES: 25 - 26 August 2004, Singapore

REQUIREMENTS FOR TEST RESULTS OF CONCRETE,

ACTIONS ON CONCRETE OF NONCOMPL YING TEST

RESULTS AND THEIR INFLUENCE ON COST OF CONCRETE

Hua Zhou*, Concrete OEM Pte Ltd , Singapore

Abstract: The Singapore standard SS 289: 2000 defines concrete strength grade as the

characteristic strength with 5% defective rate, and gives two requirements for assessing the compliance of test results with the specified strength grade. For any non-complying test result, certain action is usually taken, this incurs cost to concrete supplier. Mathematical models for t he total cost 0 f ingredient materials and n oncomplying test results are established under the four typical types of actions on the concrete 0 f non-complying t est results in Singapore, numerical results of the total cost are calculated. It is noticed that actions on the concrete of non-complying test results can have significant influence on the total cost, concrete suppliers need to select appropriate defective rate of test results so as to minimize the total cost.

Keywords: Characteristic strength, cost, defective rate, specified strength grade, test results .

INTRODUCTION One 0 f the most important objectives in concrete supply is to achieve the specified strength

grade. Concrete strength depends on water/cement ratio that can be determined as below. First, determine the target mean strength ( X ) from the specified strength grade (f: )by

X =f: + k * a --------------------------------- (1) where k is a coefficient corresponding to the selected defective rate of test results (denoted by Pl.k)) , a is the standard deviation of test results that can be achieved during supply. Second, determine the water/cement ratio (wlc) from the target mean strength (X) by an empirical formula:

(w / c) = 25 /(X + 8) ---------------------------- (2) In the Singapore Standard SS 289: Part 1: 2000', concrete strength grade is defined as the characteristic strength with 5% defective rate . This gives a value of 1.64 to the coefficient k. The standard deviation 0 f 2 8-day test results achieved inS ingapore is normally a t a level of 4 N/mm2. Thus, the term (k * a ) in Eq. (1) has a value of 6.6 N/mm 2 , it is usually taken as 7.0 N/mm 2 in mix design. For the concrete with water/cement ratio so determined, the defective rate of test results during supply can be up to 5%.

Two requirements are set in SS 289: Part 4: 2000' for assessing the compliance of test results with the specified strength grade. First, the mean strength determined from the first two, three consecutive test results , or from any group of four consecutive test results (referred to as "rolling strength" hereafter) exceeds the specified strength grade by at least 1, 2, or 3 N/mm 2 (only the concrete of grade 20 or above is considered in this paper) . Second, any individual test result (or the average cube strength of a sample, referred to as "sample strength" hereafter) is not less than the specified strength grade less 3 N/mm2.

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SS 289: 2000 1 is referred to as concrete specification in the specifications of most projects in Singapore, various actions on the concrete of non-complying test results are specified in these project specifications or are actually in practice. Since any action on the concrete of non-complying test results incurs cost to suppliers, the strategy to the suppliers is to select appropriate defective rate of test results so as to minimize the total cost of ingredient materials and non-complying test results . The target mean strength and water/cement ratio for the concrete need to be designed accordingly.

COST OF INGREDIENT MATERIALS OF CONCRETE

The cost of ingredient materials of concrete (Cm, in S$/m 3 ) consists of the cost of cement (Ce), the cost of fine and coarse aggregates (Ca), and the cost of chemical admixture (C ca ) (the cost of water is neglected) . Thus, Cm can be expressed by

Cm =Ce + Ca + Cea ----------------------------- (3) Cc can be calculated by

Ce =CC * CP ----------------------------------- (4) where CC (in kg/m3) is the cement content in concrete, CP (in S$/kg) is the cement price . CC can be expressed as

CC =WC I(w/c) ------------------------------- (5) where WC (in kg/m3) is the water content. Substitute Eqs . (2) and (1) into Eq . (5), then substitute Eq . (5) into Eq. (4), it becomes

Cc = [WC * ( f: + k * (j + 8) 125J * CP ------------------- (6) Similarly, Ca can be calculated by

Ca =AC * AP -------------------------------------- (7) where AC (in kg/m3) is the total content of fine and coarse aggregates in concrete, AP (in S$/kg) is the weighted average price of fine and coarse aggregates. In concrete mix design in Singapore, air content in fresh concrete is usually taken as 2.5%, the total volume of ingredient materials is thus designed as 975 liters. Calculate the volume of fine and coarse aggregates by subtracting the volumes of water and cement from the total volume, and substitute it into Eq . (7) , then , Ca can be calculated by

Ca =(975 - WC - [WC * ( f: + k * (j + 8) 125J13.15} * 2.63 *AP --------- (8) where the specific gravity of cement (OPC) is taken as 3.15, the weighted average specific gravity of fine and coarse aggregates in concrete is taken as 2.63.

Similarly, Cca can be calculated by Cca ={[WC * (f: + k * (j + 8) 125]/100}* CAD * CAP -------------------- (9)

where CAD (in liter/100 kg cement) is the dosage of chemical admixture in concrete, CAP (in S$/Iiter) is the price of the chemical admixture .

A typical mix design in Singapore for the concrete using OPC cement and a water-reducing 3retarder has water content (WC) of 180 kg /m and a dosage (CAD) of 0.6 litre/100 kg cement for the retarder. Take the prices of ingredient materials as of the beginning of 2003 in the market as: CP = S$ 0.06 / kg. AP =S$ 0.01 / kg , CAP = S$ 0.4 /Iiter. Substitute these figures into Eqs . (6), (8) and (9), and add the obtained Ce. Ca. and Cca in Eq. (3), it becomes

Cm =0.389 * (f: + k *(j + 8) + 20.91 -------------------------- (10)

COST DUE TO ACTIONS ON CONCRETE OF NON-COMPLYING TEST RESULTS

Four typical types of actions are taken in Singapore on the concrete of non-complying test results , the costs to suppliers due to these actions are expressed as a function of the defective rate of test results (P,(k)) .

Type-1 actions When any sample strength is less than the specified strength grade, prove structural safety by conducting insitu test or structural calculation on the concrete represented by the sample, or otherwise strengthen or remove and recast the concrete.

Experience indicates that for most non-complying test results , the structural safety of the concrete represented can be proven by insitu test or structural calculation, the cost per insitu test or

558

structural calculation to suppliers is around S$500. The cost of strengthening or removing and recasting concrete is not considered in this paper. 3Given a defective rate of test results P,(k) and a sampling rate SR (in m /sample) during supply, the cost due to the non-complying test results (Cr. in S$/m3 ) can be calculated by

Cr =P,(k) .. 500 I SR --------------------------------- (11)

Type-2 actions When any rolling strength does not exceed the specified strength grade by at least 1, 2, or 3 Nlmm2,

fine the supplier S$500.

When any sample strength is less than the specified strength grade less 3 Nlmm2, fine the supplier

S$500. In addition, prove structural safety by conducting insitu test or structural calculation on the

concrete represented, or otherwise strengthen or remove and recast the concrete.

For the series of rolling strengths. their mean value Xr is equal to X in Eq . (1). their standard deviation (J r may range from 60% to 90% of (J in Eq . (1). Take (J r =0.8 .. (J for analysis, and take (f; + 3.0) as the specified characteristic strength for the rolling strengths, then, the coefficient k r corresponding to the percentage of non-complying rolling strengths (denoted by Prik)) can be calculated from

Xr = (f; + 3.0) + kr " (0.8" (J) =f: + k * (J ----------------- - - (12) Thus,

kr = ( k * (J - 3.0) 1(0.8 * (J) ---------------------------------- - (13) The cost due to non-complying rolling strengths (Cr-r, in S$/m 3 ) can be calculated by

Cr-r =Pr-r (k) .. 500 I SR ------------------------------------ (14) For sample strengths, take (f; - 3.0) as the specified characteristic strength , the coefficient

ks corresponding to the percentage of non-complying sample strengths (denoted by Pr-s(k)) can be calculated by

ks =(k .. (J + 3.0) I (J ----------------------- - ------ (15) For a non-complying sample strength, the cost to the supplier can be taken as S$1 000 with S$500 for the fine and the other S$500 for in situ test or structural calculation. Thus , the cost due to noncomplying sample strengths (Ct-s in S$/m3) can be calculated by

Cr- =Pros (k) .. 1000 I SR -------------------------------------- (16) The total cost due to non-complying test results (Cr) can be calculated by

Cr = Cr-r + Cr-s = [(Prik)12 + Pr-s(k)] .. 1000 I SR ------------ (17) s

Type-3 actions When any rolling strength does not exceed the specified strength grade by at least 1, 2, or 3 Nlmm2,

fine the supplier S$201m3 for the quantity of the concrete represented by the samples included in the

calculation of the rolling strength.

When any sample strength is less than the specified strength grade less 3Nlmm2, fine the supplier

S$201m3 for the quantity of the concrete represented by the sample. In addition, prove structural

safety by conducting insitu test or structural calculation on the concrete, or otherwise strengthen or

remove and recast the concrete.

However, the quantity of any batch of concrete is considered for fine only once.

The average quantity of concrete fined for a non-complying rolling strength is taken as the quantity represented by two samples for analysis. Then, the cost due to non-complying rolling strengths (Ct-r ) can be calculated by

rCr- =(20 .. 2) .. Prik) =40 .. Prik) ----------------------------- (18) where Pr-,{k) is determined from the kr in Eq. (13) .

For a non-complying sample strength, the cost to suppliers consists of the fine for the quantity represented and S$500 for in situ test or structural calculation. Thus, the cost due to non-complying sample strengths (Cr-s ) can be calculated by

Ct-s =20 .. Pt_ik) + 500 .. Pr-s(k) I SR --------------------------- (19) where Pr-ik) is determined from the ks in Eq. (15).

The total cost due to non-complying test results (Cr) can be calculated by Cr = Cr-r + Cr-s =40 .. Ptik) + [20 + 500 I SRi .. Pr-s(k) ----------- (20)

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Type-4 actions One concrete sample is taken from each truckload of concrete supplied. Two cubes are made from each sample for testing at 7-days. When the strength of any cube is lower than 80% of the specified strength grade, fine the supplier S$500.

Take the 7-day concrete strength to be 75% of the 28-day strength, then, the requirement for 7 -day cube strength can be translated into "the strength of any cube at 28-days shall not be less than 1.0667 (= 0.8 I 0.75) times the specified strength grade". For individual cube strengths at 28-days, their mean value Xic is equal to X in Eq . (1), their standard deviation O"ic is slightly higher than (J' in Eq . (1) . Take (Y ic = 1.03 * (J' for analysis , and take (1.0667 *f ; ) as the specified characteristic strength for ind ividual cube strengths at 28-days, then , the coefficient kic corresponding to the percentage of non-complying cube strengths (denoted by P,.;c(k)) can be calculated from

X;c =1.0667 * f; + kic * (1 .03 * (J') =f: + k * (J' - - - - - - --------- (21) Thus,

k iC = ( k * (J' - 0.0667 * f: ) / (1.03 * (J' ) ----------------------- (22) The cost due to non-complying cube strengths (C,) can be calculated by

C, =P'-idk) * 500 / (SR / 2) ----------------------------- (23) where sampling rate S R can bet aken as 5 m 3 per sample, equivalent to an average of 5 m3 per truckload.

NUMERICAL RESULTS OF TOTAL COST OF INGREDIENT MATERIALS AND NON-COMPLYING TEST RESULTS

The total cost of ingredient materials and non-complying test results (C" in S$/m3 ) is calculated by

C, = Cm + C, ------------------------------------------- (24) where Cm is calculated by Eq. (10), c, is calculated by Eq . (11), (17), (20) or (23) for the respective actions on the concrete of non-complying test results .

Typical values for P,(k) ranging from 5% as allowable in SS 289: 2000 to 0.01 % are selected, as shown in Tables 1 to 4, the corresponding values of C, for grade 30 concrete are calculated under the four typical types of actions . Three values of 4.0, 3.0 and 2.0 N/mm2 for a, representing respectively normal, good and excellent level of concrete quality control in Singapore, are used in the calculation. For the actions of Types 1 and 2, two typical sampling rates (SR) of 40 and 10 m 3 per sample are used for the calculation . For the Type 4 action, sampling rate (SR) is taken as 5 m3 per sample.

Numerical results of C , under the four typical types 0 factions are shown in Tables 1 to 4 respectively, the lowest values of C, (denoted by C,.min) are highl ighted in bold fond. It can be seen that the values of C,-min and P,-m;n(k) (the P'(k) correspondin~ to C, .min ) under the four typ ical types of actions differ significantly. For example, when a =4 N/mm , C,-min under Type-4 action is S$2 .78/m 3 or 7.2% higher than under Type-1 actions with SR = 40 m3 per sample.

Given that P,(k) is allowable to be up to 5% in SS 289: 2000, the concrete with P,(k) =1% may be considered to be of reasonably good quality. The graphs of C'_1% (the C, when P,(k) =1 %) versus a are plotted in Figure 1. C'.1% at lower a can be much higher than at higher a under Type-2, Type-3 and Type-4 actions. Only under Type-1 actions does C'-1% reduce with reduction in a .

CONCLUDING REMARKS Mathematical models for the total cost of ingredient materials and non-complying test results

are established under the four typical types of actions on the concrete of non-complying test results, numerical results of the total cost are calculated at various defective rates of test results . Examples of actual concrete supply have shown good agreement with the analysis in this paper . It can be seen that actions on the concrete of non-complying test results can have significant influence on the tota l cost. Concrete suppliers need to select appropriate defective rate of test resu lts to minim ize their total cost, concrete purchasers need to understand the impact of the actions on non-complying est es lts on the suppliers .

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REFERENCES

1. Singapore Productivity and Standards Board, "Singapore Standard 289 2000 Specification for Concrete", Singapore, 2000.

Part 1. Guide to specifying concrete. Part 4: Specification for the procedures to be used in sampling, testing and assessing compliance of concrete.

58.00

55.00

52.00l' if} 49.00 ~

~ 46.00 -U 43.00

40.00

-1 -

1

-+-Type-1 SR = 40-- -- I

---.- Type-1 SR = 1)I I~ Type-2 SR = 40 l----fr-- Type-2 SR I= 1) ~Type-3 ----- Type-4 I

- i

37.00 t ! 2 3 4

Figure 1 - Ct-1% versus a for grade 30 concrete

56l

Table I - N. umenca resu ts 0 fC, ~or gra de 30 con ere e under Type- ac Ions

SR (J PJ (k) and corresponding k

5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.3% 0.10% 0.01% 1.64 1.69 1.75 1.81 1.88 1.96 2.05 2.17 2.33 2.57 2.75 3.09 3.72

40 4.0 38.87 38.88 38.92 38.95 38.99 39.05 39.13 39.26 39.44 39.75 40.01 40.51 41.48 3.0 38.23 38.23 38.23 38.24 38.26 38.29 38.33 38.41 38.54 38.75 38.94 39.31 40.03 2.0 37.59 37.57 37.55 37.54 37.53 37.53 37.54 37 .57 37.63 37.75 37.87 38.11 38.59

10 4.0 40.74 40.57 40.42 40.26 40.12 39.99 39.88 39.82 39.82 39.94 40.12 40.55 41.49 3.0 40.11 39.91 39.73 39 .55 39.39 39.23 39.08 38.97 38.91 38.94 39.05 39.35 40.04 2.0 39.47 39.26 39.05 38 .85 38.65 38.47 38.30 38 .13 38.00 37.94 37.98 38.15 38.59

_J - jm per sample. (J - N/mm , and C, - S$/m .

Table 2 - Numerical results of C, for !!fade 30 concrete under Type-2 actions

SR (J PJ (k) and corresponding k

50% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.3% 0.10% 0.01% 1.64 1.69 1.75 1.81 1.88 1.96 2.05 2.17 2.33 2.57 2.75 3.09 3.72

40 4.0 40.12 39.99 39.88 39.79 39.71 39.66 39.59 39.58 39.64 39.84 40.05 40.52 41.48 3.0 40.36 40.19 39.98 39 .82 39.64 39.45 39.30 39.14 39.03 39.01 39.08 39.35 40.04 2.0 42.34 42.09 41.79 41.46 41.11 40.74 40.35 40.01 39.37 3882 38.57 38.39 38.62

10 4.0 45.76 45.00 44.29 43.63 43.00 42.41 41.72 41.11 40.60 40.31 40.30 40.59 41.49 3.0 48.62 47.77 46.73 45.85 44.89 43.88 42.95 41.90 40.88 39.96 39 .63 39.53 40.05 2.0 58.45 57.33 56.01 54.55 52.99 51.29 49.56 47.91 44.96 42.19 40.78 39.26 38.72

Umts. SR -

PJ (k) and corresponding k I

(J 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.3% 0.10% 0.01% 1.64 1.69 1.75 1.81 1.88 1.96 2.05 2.17 2.33 2.57 2.75 3.09 3.72

4 43.96 43.41 42.89 42.42 41.97 41.56 41.08 40.65 40.32 40.17 40.23 40.57 41.48 3 46.27 45.63 44.83 44.16 43.42 42.65 41.94 41.14 40.37 39.70 39.48 39.48 40.05 2 54.13 53.24 52.20 51 .04 49.81 48.47 47.10 45.79 43.47 41.29 40.19 39.03 38.69

Table 3. - Numerical results of C, for grade 30 concrete under Type-3 actions

Table 4 - Numerical results of C, for grade 30 concrete under Type-4 actions

PJ (k) and corresponding k (J 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5 % 0.3 % 0.10% 001%

I 1.64 1.69 1.75 1.81 1.88 1.96 2.05 2.17 2.33 2.57 2.75 3.09 3.72 I 4 64.94 62.92 61.04 58.91 56.64 54.30 52.24 49.59 46.82 44.13 42.89 41.70 41.65

3 72. 33 69.88 67.11 64.50 61.69 58.74 56. 10 52.64 49.15 45.13 43.24 41.18 I40.33 2 90 ": 9 I 8-.29 83 .59 I8006 I76 .69 72.46 67.93 62. 80 57.22 50.55 46 .75 42. 34 3904 1

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