SUPPLEMENT 1127 PAY FACTORS DETERMINATION FOR PAVEMENT AND STRUCTURE CONCRETE

Transcription

1 State of Ohio Department of Transportation SUPPLEMENT 1127 PAY FACTORS DETERMINATION FOR PAVEMENT AND STRUCTURE CONCRETE July 17, Scope Structures Pavements Tables Scope. The purpose of this Supplement is to provide direction for determining the appropriate procedure to apply pay factors due to strength results for Structure and Pavement Concrete with QC/QA requirements according to A and and respectively Structures. Use the following procedure to determine the random number for the sublots, analyze the strength test results, and apply the appropriate pay factor according to item A: A. Random Number Determination. The random number for determining the load from which a quality control (QC) sample in a sublot is to be taken may be found using a random number generator or using Table Use the following procedure if using the table: 1. Arbitrarily select a number from Table to apply to the first sublot in the lot. 2. Random numbers for subsequent sublots are determined by proceeding to the next number down the column and moving to the next column when the end of the column is reached. 3. Proceed, in order, until random numbers for all of the sublots are selected. 4. The quantity of the sublot is multiplied by the random number to determine the yardage to be sampled. Since it is not feasible to sample the exact cubic yard, the load in which the cubic yard is contained is to be sampled. Do this by dividing the yardage determined by the random number by the size of the loads, then round up to the next integer. This is the load to be sampled and tested. The load to be sampled for Quality Assurance (QA) is determined by the following method: 1. Group the sublots in multiples of 10, or fraction thereof. 2. The Random number selected for the first QC sublot in the group determines from which sublot the QA sample will be taken for that group of sublots. Multiply the random number by the number of sublots and round to the nearest whole number. B. Analysis of Test Data. Once the samples are taken, cylinders are tested, all test results are received, and results are validated by the QA sample, the Engineer will analyze the data as follows: Determine arithmetic mean (x ) for QC compressive strength results using the following formula: 1

2 x = (Σ x) n * x = The average of the set test specimens for the sublot. n = Total number of test results in each lot * The Arithmetic mean can also be determined using software (i.e. MS Excel AVERAGE) Determine, for each lot, the sample Standard Deviation (δ) for compressive strength. Use the following formula: δ = (x x ) 2 /(n 1) ** The Standard Deviation can also be determined using software (i.e. MS Excel STDEVA). Determine the compressive strength Quality Index (QI) for each lot. Use the following formula: Q I = (x - f c) / δ f c = the Design Strength for the lot of concrete Round the QI value to the nearest Using the QI value, enter the Table for the number of samples in the lot; go down the column to the QI value determined above. The value in the left column is the Percent Within Limits (PWL) for the Lot. When the exact QI value is not in the table, interpolate between the next higher (QH) and next lower (QL) values in the column and corresponding PWL, (PWLH) and (PWLL), to determine the exact PWL (PWLI): PWL I = Q I Q L Q H Q L + PWL L C. Pay Factor. From the values determined by the analysis of the test data, use Table to determine the pay factor for the lot. Apply that pay factor to each pay item in the lot except for quantities of unacceptable material. D. Example. A bridge deck, approach slabs and parapets that require Contractor sampling. The Bridge deck has 588 yd 3 ; two approach slabs have a combined quantity of 78 yd 3 ; and two parapets have 84 yd 3 of concrete. There are 750 yd 3 of concrete total on the 3 items. However, the Contractor is slipforming the parapets. Therefore the concrete producer is using a different JMF and the slipformed concrete is being considered a different Lot than the concrete for the deck and approach slabs. The minimum number of sublots in a lot is 3. In the Quality Control Plan, the contractor divided the sublots as follows: - Bridge Deck 588 yd 3 11sublots of 50 yd 3 & 1 sublot of 38 yd 3 LOT 1 - Approach Slabs*** 78 yd 3 2 sublots of 39 yd 3 LOT 1 - Parapets 84 yd 3 3 sublots of 28 yd 3 LOT 2 *** The bridge deck and approach slab concrete could have also been combined for 666 yd 3. The last 38 yd 3 of the deck and first 12 yd 3 of the first approach slab placed could have been combined and the random number would determine when/where the sample would be taken for that sublot. This would have left 66 yd 3 of concrete (2 sublots) to be sample during the placement of the approach slabs. The bridge deck could have also been divided into 12 equal sublots of exactly 49 yd 3. ** 2

3 Once the Engineer receives the breakdown of the sublots and determines that the concrete will be delivered in 10 yd 3 loads, the EXAMPLE TABLE 1 can be started by: 1. Determining the random numbers from the Random Number Table Select an arbitrary number, shown below as 0.673, from the fourth column in the example random number table below. Proceed down the column in the random number table until all of the random numbers for the lot are determined. RANDOM NUMBERS Knowing the sublot size, the yardage to be sampled is determined by multiplying the random number by the sublot size. 3. The load to sample is calculated by dividing the yardage by the batch size and rounding up. SUBLOT RANDOM NUMBER SUBLOT SIZE EXAMPLE TABLE 1 LOT 1 - BRIDGE DECK AND APPROACH SLABS YARDAGE LOAD REF. DESCRIPTION STRENGTH 1 STRENGTH 2 STRENGTH 3 AVERAGE STRENGTH BRIDGE DECK BRIDGE DECK BRIDGE DECK BRIDGE DECK BRIDGE DECK BRIDGE DECK * BRIDGE DECK

4 BRIDGE DECK BRIDGE DECK BRIDGE DECK BRIDGE DECK BRIDGE DECK APPROACH SLAB * APPROACH SLAB Average Strength To determine the sublots to be sampled by the Department for QA, first group the sublots into multiples of 10 or fraction thereof. In EXAMPLE TABLE 1 sublots 1-1 thru 1-10 are one group; and sublots 1-11 thru 1-14 are another. There are two QA samples for this lot. a. To determine which sublot to sample from the first group, again pick an arbitrary random number in the table shown above as.648 in the sixth column. Multiple the random number times the number of sublots in the group x 10 sublots = 6.48, round up to 7. Perform the QA sampling from sublot 1-7, denoted with an asterisk (*). b. For the second group the number in the random is x 4 sublots = round up to 4. Perform the QA sampling from sublot 1-14, also denoted with an asterisk (*). 5. In this example for Lot 2 (slipformed parapet concrete) start with a new arbitrarily selected random number from the example random number table above. a. EXAMPLE TABLE 2 shows the QC samples. Use the random number from the table.128 multiple the first sublot yardage and round the yardage up to next yard x 28 = round up to 4 b. Divide the yard selected (4 in the example) by the batch size (10 yd3,) and round up to determine what load in the first sublot will be sampled. 4/10 =.4 so sample from load 1. c. Repeat a and b for each sublot. 6. To determine the sublot to be sampled for Lot 2 by the Department for QA in EXAMPLE TABLE 2, group the sublots into multiples of 10 or fraction thereof. Is this case there are only 3 sublots. a. Arbitrarily pick another random number,.058 from the fifth column in the random number table above and multiple it times the number of sublots x 3 =.174. b. Round up to the next integer or one (1). The QA sample comes from the 1 st sublot marked in the table below with an asterisk (*). SUBLOT RANDOM NUMBER SUBLOT SIZE EXAMPLE TABLE 2 LOT 2 - SLIPFORMED PARAPET WALLS YARDAGE LOAD REF. DESCRIPTION STRENGTH 1 STRENGTH 2 STRENGTH 3 AVERAGE STRENGTH 2-1* PARAPET (EAST) PARAPET (WEST) PARAPET (WEST) Average Strength

5 7. Once the samples are taken; specimens tested; and test results received, the PWL and pay factors can be calculated. a. Determine the average strength of the lot. i. For lot1, the Average Strength (x ) is 5,233 psi ii. For lot 2, the Average Strength (x ) is 4,797 psi. b. Determine the standard deviation of the lot. This can be accomplished using the formula above, or it can be done more simply by using STDEVA in Excel. Ref i. For lot 1, the Standard Deviation ( δ ) is 547 psi. ii. For lot 2, the Standard Deviation ( δ ) is 337 psi. c. Determine the Percent Within Limits and Pay Factor: i. Lot 1: Design Strength (f c) = 4,500 psi 1) QI = (x f c)/ δ = (5,233 4,500) / 547 = ) PWL Table n= >10; QI = 1.34 PWL = between 91 and 92%. 3) PWL = [( )/( )] + 91= 91.4, 4) Round to the nearest whole number = 91 5) Pay Factor for 91 PWL (Table ) = 1.00 ii. Lot 2: Design Strength (f c) = 4,500 psi 1) QI = (x f c)/ δ = (4,797 4,500) / 337 = ) PWL Table n=3; QI = 0.88 PWL between 77 and 78% 3) PWL= [( )/( )] + 77= ) Round the PWL to the nearest whole number = 78 5) Pay Factor for 78 PWL (Table ) = d. Applying Pay Factors. Payments for items placed are provided upon completion of the placement. Pay adjustments are made by change order. The bid prices for the items in this example are as follows in EXAMPLE TABLE 3: i. Determine the bid cost for each item and apply the appropriate pay factor by multiplying the total bid cost for the item by the pay factor. Subtract the total bid cost from the factored cost to determine the pay adjustment. Item Description Bridge Deck, Class QC 2 Approach Slab, Class QC 2 Parapets, Class QC 2 Quantity EXAMPLE TABLE 3 Bid Unit Price Total Bid Cost 5 Pay Factor Factored Cost Pay Adjustment 588 yd 3 $500/yd 3 $294, $294, yd 3 375/yd 3 $29, $29, yd 3 325/yd 3 $27, $26,208 - $ Pavements. After accepting the Contractor s lot and sublot divisions according to Supplement 1064 and the Engineer will determine the core locations. Analyze the data and establish pay factors as follows: A. Analysis of Test Data. Once the samples are taken, cores are tested, all test results are received, and results are validated by the QA sample, the Engineer will analyze the data as follows:

6 1. Record the compressive strength data for each sublot of concrete. 2. Determine arithmetic mean (x ) for QC compressive strength core results using the following formula: x = (Σx) n x = the core strength result for the sublot. n = the total number of cores in the lot * The Arithmetic mean can also be determined using software (i.e. MS Excel AVERAGE) 3. Determine, for each lot, the Standard Deviation (δ) for core strengths using the following formula: δ = (x x ) 2 /(n 1) ** **The Standard Deviation can also be determined using software (i.e. MS Excel STDEVA) 4. Calculate the required design strength (f cr) by multiplying the lot standard deviation (δ) by 1.65 and then adding the design strength (f c), typically 4000 psi (27.5MPa). f cr = f c δ B. Pay Factor. From the values determined by the analysis of the test data, calculate the strength pay factor (PFS) for each pay item in the lot as follows: PF S = x / f cr When the x is greater than f cr the pay factor for the pavement items is Consider high-early strength concrete as a separate lot and calculate the pay factor for each sublot, according to Table , based on the sublot s strength and design strength (f c). PF S = x/ f c When the x is greater than f c the pay factor for the high early strength pavement sublots is 1.00 C. Example. There is a total replacement of 3 miles of 11 inch Item 452 concrete pavement on the route (STA 0+00 to ) along with eight 10 inch ramps (A G) of 300 yards in length each. The pavement is three (3) 12 ft. lanes with a 12 ft. outside shoulder and a 12 ft. inside shoulder in each direction. The ramps are all 16 ft. wide. The paver has a maximum paving width of 24 ft., so the plan is to place two lanes at one time, then the third lane and the inside and outside shoulders separately. The Contractor has decided to use high-early strength concrete on all ramps in order to open them in 3 days. There is no need for QC MS or QC FS on this job. In the second construction season, the Contractor changes coarse aggregate and mix design, requiring a new JMF; and separate lots. 1. Determine how many lots will be needed. Since the ramps are using high-early strength (HES) concrete and the pavement is using regular QC 1 concrete, there are two lots. Lot 1 is the 3-lane pavement, and inside and outside shoulders; and Lot 2 is the ramps. 2. Split up of the sublots for the pavement should be every 2,000 yd 2 as follows: a. 24 ft (8 yd) width pavement 2000/8= every 250 yd 250 yd; 30 yd b. 12 ft (4 yd) width pavement 2000/4= every 500 yd 500 yd; 280 yd * 6

7 c. 12 ft (4 yd) inside shoulder 2000/4 = every 500 yd 500 yd; 280 yd d. 12 ft (4 yd) outside shoulder 2000/4 = every 500 yd 500 yd; 280 yd e. 16 ft (5.33 yd) ramp 2000/5.33= at least every 375 yd The Contractor choses to consider each 300 yard ramp as a sublot. 3. Random numbers are determined for each sublot using Supplement 1064 and strength cores are taken at the same location as the thickness cores. For illustrative purposes, the random number table in will be used. a. In this example, the 3 rd number in the 2 nd column of Table is chosen (0.216) as the beginning random number for sublot 1-1. EXAMPLE TABLE 4 is set up with the sublot identification and beginning and ending stations for the first season s paving. b. The random numbers are determined from the random number table and core locations determined by multiplying the sublot length by the random number and adding to the beginning station of the sublot. 7.5 *.216 = 1.62 = c. Using the next random number in the column of the table, determine the location of the core by repeating b for each sublot of pavement. 4. To determine the sublots to be sampled by the Department for QA, first group the sublots into multiples of 10 or fraction thereof. In EXAMPLE TABLE 4 sublots 1-1 thru 1-10 are one group; and sublots 1-11 thru 1-20 are another, and so on. a. To determine which sublot to sample from the first group, again pick an arbitrary random number in the Table In this case the fourth number in the fourth column,.652. Multiple the random number times the number of sublots in the group x 10 sublots = 6.52, round up to 7. Perform the QA sampling from sublot 1-7, denoted with an asterisk (*). b. For the second group the number in the random table order is x 10 sublots = round up to 4. Perform the QA sampling from sublot 1-14, also denoted with an asterisk (*). c. Continue to repeat the procedure for the QA samples. EXAMPLE TABLE 4 SUBLOT BEGIN STA END STA RANDOM NO LOCATION QC TEST QA TEST LOT 1 24 WIDE PAVING 750 SUBLOTS *

8 * * * WIDE PAVEMENT 1500 SUBLOTS * INSIDE SHOULDER 1500 SUBLOTS * ' OUTSIDE SHOULDER 1500 SUBLOTS

9 * LOT 2 - HIGH EARLY STRENGTH CONCRETE RAMPS 1 CORE / RAMP 900 / RAMP 2-1 RAMP A 900' * 437' RAMP B 900' ' RAMP C 900' ' RAMP D 900' ' The Contractor takes possession of the QC cores for testing by an AMRL accredited lab and the Department takes possession of the QA core for curing and testing. Once the cores are tested, the results are submitted to the Engineer for analysis. The average strength, standard deviation and required strength for each lot are determined. The results for this season s paving in this example were calculated using and Excel spreadsheet and are as follow: EXAMPLE TABLE 5 LOT 1 DESIGN STRENGTH (f c) QC 1 = ,000 psi ARITHMETIC MEAN (AVERAGE) ( x ) STANDARD DEVIATION (δ) 4,738 psi 396 psi REQUIRED STRENGTH (f cr) (396) 4,654 psi PAY FACTOR (PFs) 4738 / 4654 = Because the ramps are made with high-early strength concrete they are analyzed according to Table with the design strength (f c). EXAMPLE TABLE 6 shows the calculation for sublot 2-1. Repeat the examples below for each sublot when using high-early strength concrete. EXAMPLE TABLE 6 SUBLOT 2-1 DESIGN STRENGTH (f c) QC FS = ,000 psi CORE STRENGTH ( x ) PAY FACTOR (PFs) 5890 / 4000 = ,890 psi 6. The pay factors are applied to the unit bid price as follows: Ref Item Description Pavement (Mainline & Shoulders) Pavement (Ramps) EXAMPLE TABLE 7 Quantity (Sq. yd.) Bid Unit Price Total Bid Cost Pay Factors Pay Factor Factored Cost Pay Adjustment 105,600 $72/yd 2 $7,603, $7,603, /yd 3 $435, $435,

10 Tables. Use the following tables for determining the random number and calculating the Percent within Limits for structures: TABLE RANDOM NUMBERS

11 TABLE PERCENT WITHIN LIMITS (PWL) QI Values for Number (n) of Sublots PWL \ n For negative Q I values Use the absolute value of the Q I and subtract the PWL from 100 to determine the correct PWL. Ex: n=5; Q I = PWL = = 38 11