INFRASTRUCTURE CONS CEE 404
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This 20 page Class Notes was uploaded by Mason Hackett on Wednesday September 9, 2015. The Class Notes belongs to CEE 404 at University of Washington taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/191989/cee-404-university-of-washington in Civil and Environmental Engineering at University of Washington.
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Date Created: 09/09/15
1 Deterministic and Probabilistic Analysis CA4PRS estimates can be produced from two types of analysis methods deterministic and probabilistic Deterministic estimation treats all of the input parameters as constants during productivity calculation which does not capture the variations frequently seen during construction In contrast probabilistic analysis treats all input parameters as variables that change according to an assigned probability distribution function The probability distribution predicts the likely behavior of an input parameter over a range of potential input parameter values Probabilistic estimation is the preferred means of CA4PRS analysis because this type of estimation can define and incorporate the uncertainty associated with determining each scheduling or resource input parameter Probabilistic analysis also yields a more comprehensive estimate than deterministic analysis by providing a range of likely construction productivity but requires more information about expected variable behavior and the likely variable probability distributions Included in this documentation is a general description and guide on selecting and using appropriate distribution functions for the different CA4PRS input parameters Distribution and distribution parameter recommendations are based on data collected from rehabilitation projects on I 15 Devore and I10 Pomona in California and the I5 James to Olive Streets Pavement Rehabilitation project completed in Seattle Washington 2 Monte Carlo Simulation In a probabilistic analysis CA4PRS combines probability distribution functions with Monte Carlo simulation Monte Carlo simulations refer to a stochastic problemsolving process that is used for solving complex problems The process is referred to as stochastic because it is dependent upon the use of random numbers Modeling construction productivity is suited to Monte Carlo simulation because construction productivity is based upon input parameters that will likely vary within a range of values A Monte Carlo simulation consists of a series of iterations or individual simulations which are used to produce a most likely representation of contractor productivity During one simulation iteration random values are assigned to each input parameter according to their specified probability distribution function The random input parameters generated during one Monte Carlo simulation iteration are placed into a CA4PRS estimate This estimate generates a contractor productivity estimate in lanemiles for that speci c iteration By running up to as many as several thousand iterations during a Monte Carlo simulation CA4PRS produces an overall gure for the most likely production as well as a distribution of likely productivity 3 Probability Distribution Functions CA4PRS probabilistic estimation requires users to assign a probability distribution function to the input parameters in both the scheduling and resource pro les Probability distributions are statistical functions that describe the probable behavior of a variable In a CA4PRS analysis the variables are the input parameters Input parameters assigned a probabilistic function will not have one precise value but rather a range of possible or potential values The probability distribution function describes the probability of an input parameter being assigned a particular value in this range of potential values Probability distributions are commonly described using graphical representation Figure 1 depicts the behavior of an unknown input parameter over a range of possible values For this example a common distribution called a normal distribution is depicted Normal distributions are de ned through two statistical parameters the mean u and the standard deviation 6 The mean value is the most likely or probable value in the probability distribution being modeled The standard deviation describes the width of the distribution and how far values are likely to be from the mean Standard deviations can be used for assigning the probability of a value for being within a range For instance for a normal distribution 682 of the area under the curve is within one standard deviation whereas 954 of the area under the curve is within two standard deviations Other distributions will have different shapes and descriptive parameters but are used for describing the probability of an input parameter having different values within a speci ed range 341 34m Figum 1 r Amphim mmmu nn nleypicalpmhahi ty dierihminn dxsmbuuons m CA4PRS 31 Deterministic Distribution m mm 139 parametas for a project may not Vary and are best held as constants For msmnce 32 Uniform Distribution probable M t i any q r y mm This type Figure 2 e A unifurm dism39hu nn Wih39ped39n eonlrmulors mm 33 Normal Distribution Normal drsmbuuons are one of tlne most frequently used forms of drstmbutron and are eommonly known as bell curves Wersstern 2004 Anormal drstnbuuon rs a drstmbutron L l turn quotml vary Ifthe rnput parameterrs predretedto be falrly eonsrstent tlnen a smaller standard y unknown datars to assume the value oftlne standard devratron wlll be 1072onn ofthe errpeeted rnput parameter mean 4sttttae F39gun 7 Numzldisn39ihu nnwih39ped39n cunn39ihulust m 34 Log Normal Distribution Dw mw represented by ths type of dumbunon on the 140 project m Cahfomxaana1ysxs of dumbunons Lee ets12001 0 Figure L Lug numal d39sn39ihulinn VVikipediz cunn39ih Imus 2m 3 5 Triangular Distribution A triangular dumbunon 15 a eonunuous probabuuy dumbunon that can be used when contributors 2006 To use nus type of dumbunon only me nnsunnnunn and mlmmum values for arange of potential mputparameters values neeouo be known or approximated Txus type ofdumbuuon can be used wnn almost any construcuon mput as values n c u K Figure 5 e Tr39nnguhr d39sm39hulinn W39ikipediz comm Imus 2m 3 6 Beta Distribution M aandb o dAf39ferentshapes b A b normal lognormal and triangular dumbuuons do not apply 26 24 a 05 a5Bl 2 2 39 alB3 2 oc2 2 a2 5 18 16 14 lt 12 1 08 06 04 02 0 0 01 02 03 04 05 06 07 08 09 1 Figure 6 Beta distribution W ikipedia contributors 2006 37 Geometric Distribution A geometric distribution refers to a unique type of distribution that is modeled with the statistical equation PXn 1pquot391p This equation describes the probability of achieving a success or outcome p for a statistical event on the nth attempt The probability of a failure on the rst try would be 1 p The probability of a failure on nl trials would be lpquot391 Accordingly the probability of a success on the nth attempt would be p leading to the distribution described by the previously depicted equation This distribution is commonly described through a coin ip analogy The probability of ipping heads on any trial is 12 sop 05 A success P will be defined as ipping the coin with the head up The probability of a success P on the rst trial is 05 The probability of seeing a success on the second trial is P 1 052391 x 05 The probability of a success on the third trial would be P 1 05 x 05 The probability for achieving a success on trials one through six are displayed in Table 1 Input parameters that display this type of behavior can be graphically modeled with the distribution shape shown in Figure 7 None of the CA4PRS input parameters will likely be modeled by this type of distribution Table 1 For A Coin Toss Probability of a Probability of Success On nth Trial 1 2 3 4 5 6 Trial Number Figure 7 Graphical representation of a geometric distribution 38 Truncated Normal Distribution A truncated normal distribution is very similar to a normal distribution but is con ned between an upper and a lower limit To use this type of distribution CA4PRS requires inputting the mean standard deviation maximum and minimum values for an input parameter This type of distribution could be used to describe an input parameter such as truck arrival rates when a minimum or maximum number of truck arrivals is known 39 Truncated Log Normal Distribution A truncated log normal distributions is very similar to a log normal distribution but is con ned between an upper and a lower limit The value of a variable will change logar39 39 quotJ J39 to the r 39 39 quotquot function but input parameter values will be con ned to an upper and lower limit 4 Assigning Probability Distributions Functions Assigning a distribution to an input parameter is dependent upon how much information is known about the input parameter being modeled or how con dently a user can predict input parameter behavior In general the most commonly used distributions will likely be the triangular normal and log normal distributions If additional information such as a maximum and a minimum value are known for an input users can begin applying truncated normal truncated log normal and beta distributions The geometric and uniform distributions do not appear to have as much relevance for modeling input behavior as the previously mentioned distributions While developing an estimate for a new project most users will only have an expected mean rate or approximate input parameter value Assigning productivity rates distributions and distribution parameters can be a dif cult task without information from past construction projects This section provides input parameter distribution information collected from three construction projects 1 I 10 Pomona California 2 115 Devore California and 3 15 James to Olive Streets in Seattle Washington Distribution data presented from these projects can be applied with user assumptions to assign proper input parameter distributions and distribution parameters for new estimates Distribution information is rst presented for the input parameters found in the scheduling pro le window followed by data for the resource pro le input parameters 41 Scheduling Input Parameter Pro le The scheduling profile is the second tab or window that a program user is required to ll complete during development of a CA4PRS estimate The scheduling pro le window contains 5 input parameters that can be assigned probability distributions 1 Mobilization time 2 Demobilization time 3 Demolition to new base lag time 4 New base to PCCP installation lag time 5 Demolition to PCCP installation lag time The type of distribution and distribution parameters applied to the input parameters will be strongly in uenced by many factors including the type of construction closure and construction sequencing Readers should note that the data presented in the following sections is speci c to one project and is not necessarily applicable to a future projects with significantly different conditions 411 Mobilization The documentation reviewed on the Californian reconstruction projects in Devore and Pomona does not contain any information on the distribution of mobilization time requirements On the 15 James to Olive Streets Pavement Rehabilitation project WSDOT construction inspection personnel collected mobilization time requirements from four closure windows A data sample from four construction closures does not provide a large or comprehensive representation of input parameter variability and behavior The mobilization times observed on this project are depicted in Table 2 This limited data does not depict an easily recognizable distribution Mobilization times could be logically assumed to have either a triangular normal and lognormal distributions Table 2 Mobilization Times From The 15 James To Construction Mobilization Closure Time 412 Demobilization Minimal distribution data eXists for demobilization times similar to mobilization times Recorded demobilization times from the 15 James to Olive Streets Pavement Rehabilitation project are presented in Table 3 Demobilization times have been calculated as the time that elapsed between the conclusion of PCC paving and the completion of temporary barrier removal The four available demobilization times do not depict an easily recognizable distribution Dependent on available information demobilization times are suggested to be modeled with triangular normal and lognormal distributions Table 3 Demobilization Times From The 15 James To Construction Closure Time 413 Demolition to New Base Installation Conclusive distribution data has not been collected on demolition to new base installation lag times Users are recommended to apply either a triangular normal or lognormal distributions The lag times observed during the four closures on the 15 James to Olive Streets Rehabilitation project are presented in Table 4 to provide program users an indication of the magnitude and variability of this input parameter Table 4 Demolition To New Base Installation Lag Times Observed On The 0 Construction Start of HMA 414 New Base Installation to PCCP Installation Conclusive distribution data has not been collected on demolition to new base installation lag times Users are recommended to apply triangular normal and lognormal distributions The lag times observed during the four closures on the 15 James to Olive Streets Rehabilitation project are presented in Table 4 to provide program users an indication of the magnitude and variability of this input parameter Table 5 End Of Base Paving To Start OF PCCP Times Observed On The 415 Demolition to PCCP Installation Conclusive distribution data has not been collected on demolition to new base installation lag times Users are recommended to apply triangular normal and lognormal distributions 42 Resource Input Parameter Pro le The scheduling profile is the second tab or window that a program user is required to ll complete during development of a CA4PRS estimate The scheduling pro le window contains 10 input parameters that can be assigned probability distributions 1 Demolition trucks per team 2 Demolition packing ef ciency 3 Number of demolition teams 4 Demolition team ef ciency 5 Base delivery truck arrival rate 6 Base delivery ef ciency 7 Batch plant capacity 8 Concrete delivery truck arrival rate 9 Concrete packing efficiency 10 Paver speed The distribution information presented in the following sections has been collected from only three construction projects and represents only a small fraction of possible construction conditions and equipment This guide only presents distribution recommendations based on these projects Users of this guide should make certain that conditions construction operations equipment and other factors are similar between referenced projects and future projects when applying distribution recommendations 421 Demolition Hauling Trucks 4211 Trucks Per Huur Per Team mfurmanun based eh 455 trunk mp5 Analysxs quhe data shuwed that en avenge 9 demulmun trunks zmved perhuur pertezm wnh a z 3 trunk standard dsvxanun The behavmr Based eh these ehmhgs futurepmgam uses zerecummendedtu apply henna urlugrnur mal msmhuhehsm demulmun trunk amv my 11 Diuhm nnu zmul 39nnmkmird nuxnzulded dulingwmmuw39nn quotmun Punmu Cali xmizpmjeu 4212 Packing Efficiency r M m1 3 memctuns 3 Kuhn 4 an The ubserved decrease m capacity was due m Lhamef ment paekmg caused by large bulky pavement semuns eugh researchers cullemed ledm urmauun he dataxs pmvlded furthe hsmhuheh uth h eh demuhtmn truck paekmg ef uent Prng users are 5121 uu ameters assumated wnh data par recummmdedtu apply mangulzr henna andlugrnurmal dxsmbununs 113 Number Mm On mast canslnlctmn pmjects m number afdzmnlmnn hams w be hm represented as a dztznnmlsuc mummy In mde m e wlzn ymmge casts and resumes m number a demalman hams mu mast hkzlyxemam canslam 11 Team Efrmizncy AAPRS prawsz users wnh m aplmn afestahhshmg a tum ef cient and hem emmmymmnan 011th HEI Pamnm mm hum emcxencyms summed based mm 9 teame mgmycanucmmlybe quotpresenuabymgmmmmmn Ema n I may v3 mm mm ummth uhuuvd my unmnmmm camnu 422 Base Delivery Truck 4221 Trucks Per Hour A distribution of base delivery truck arrivals can be seen in the data collected from the 15 James to Olive Streets pavement rehabilitation project On this project base paving progressed relatively rapidly which limited the calculation of truck arrivals on an hourly basis Instead HMA truck arrival rates have been modeled using minutes between truck arrivals as opposed to truck arrivals per hour Truck arrivals should exhibit the same arrival distribution regardless if arrival rates are considered using either minutes or hours HMA truck arrival behavior depicts a distinctly lognormal distribution Figure 10 Frequency O 3 6 9 12 15 18 21 24 27 30 33 More Time Between Truck Arrivals In Minutes Figure 10 I1VA truck arrival rates for trucks carrying 265 to 335 tons of HlVIA The distribution seen in Figure 10 has a mean time of nine minutes between truck arrivals with a standard deviation of about eight minutes If the distribution could be accurately calculated on an hourly basis the standard deviation would not likely be as large On an hourly basis the extremes in fast or slow arrival times would probably be more balanced with one another The high deviation associated with truck arrivals in minutes should be ignored Because the distribution of HMA truck arrivals is similar to that of demolition trucks shown in 4211 HMA trucks arrivals should be assigned an arrival standard deviation similar in magnitude to that of the demolition truck arrival standard deviation 4222 Ef ciency The HMA truck ticket receipts from the 15 James to Olive Streets Pavement Rehabilitation project contain HMA truck load information that is widely distributed The tonnage of HMA hauled per truck load varies between fteen to thirtyfour tons The distribution of load size using 66 truck tickets data from construction stages 1 and 4 have been used to produce Figure 11 This distribution of data points shows that the contractor utilized three different types of trucks to haul HMA loads The three different truck sizes can be approximated by 15 ton 27 ton and 33 ton loads This distribution shows that a contractor used the equipment that was available and not necessarily one type of truck In order to use the largest data sample distribution analysis will use truck ticket information from the trucks that hauled loads of 3 19 tons or more of HMA 35 Ooooooooooooo 3U oooooooooooooooo A 900000000000 m C 25 g o E 3 x 20 u a 2 15 n I 10 5 l 0 1o 20 30 40 50 60 Truck Loads From Sampled Truck Tickets Figure 11 The HTVIA load size distribution taken from truck tickets Twentyfour truck tickets for the HMA trucks that carried between 319 tons and 334 tons of HMA have been used to produce Figure 12 There is no obvious distribution for load size and the differences in load size appear negligible The difference between the average load and the maximum load is 02 tons For HMA trucks ca1rying 319 to 335 tons of HMA truck load sizes are consistent and by correlation packing efficiencies should also be consistent The tight clustering of HMA loads can be explained by the fact that trucks are probably loaded close to the legal axle weight limit permissible on Washington State roads Because of the minimal variation HMA packing efficiency should be assigned a deterministic distribution with a mean value of 100 Number of Occurrences 319 321 323 325 327 More HMA Truck Load Size tons Figure 12 Distribution of HlVIA truck load size 423 Batch Plant Capacity For most rapid rehabilitation projects large stationary concrete plants will likely have a production capacity that exceeds the material handling capacity of the contractor Equipment availability access space restrictions and other factors will limit how much material a contractor can place The contractor who completed the paving work on the I 10 rehabilitation project only utilized half the hourly capacity of a plant capable of producing 170m3 of material per hour The tight specifications and high costs associated with rapid construction projects also decrease production variability Contractors will likely have backup production plants and access to sufficient material supplies to meet contract quantities Batch plant capacity should be treated as deterministic or a normal distribution with only small variation low standard deviation 424 PCC Delivery Trucks 4241 Trucks Per Hour Data collected dunng constructron ofthe L10 project completedrn Pomona Ca1lfornlals presented ln Flgure 13 The data deprcts an average truck amval rate of 10 mlxer trucks perhour wnh a standard devlatlon of2 1 n a1 M I39Iquot Tubs En r l E l l t r i L t E t M s funny m 1 Tum erl39uJ F39gm 11L D39slrhul39nnufPCC de vexylmkznivals on the 15 James to Ollve Streets Pavement Rehabrlrtatron project PCC pavmg took elarge Flgure 14 The dlstxlbutlon ln Flgure 14 shows a dstrnct normal dsmbunon The of2 7 trucks perhour Table 6 PCC Truck Arrival Rates Per Hour Based Upon Truck Tic et Information 100AM 200AM 300AM 400AM 500AM 6282005 I 200AM I 300AM 400AM I 500AM 600AM Trucks Per Hour I 12 I 13 I 15 I 17 I 15 700PM 800PM 900PM 6182005 800PM 900PM 1000PM I 9 ITrucks Per Hour I 10 800PM I 900PM I1000PM I1100PM I1200AM 100AM I 1 6252005 I 9200PM OZOOPM 11200PM 12200AM 1200AM 2200AM Trucks Per Hour I 14 14 11 12 I 13 I 13 6282005 I 7200PM BZOOPM 9200PM 10200AM 11200AM 12200PM 1200PM Trucks Per Hour I 8 14 9 11 16 11 15 I 600PM I 700PM I 800PM I 900PM I1000AM I1100AM I1200PM 7162005 I 600PM 5200PM BIOOPM 9200PM ITrucks Per Hour I 16 I 17 I 8 7 2 6 a 5 4 S 3 g 2 g 1 g El I I I I I I I E 0 I I I I I I I I 8 10 12 14 16 18 More Truck Arrivals Per Hour Figure 14 The distribution of hourly arrival rates for PCC delivery trucks Data collection from two different PCC paving projects depicts lognormal distribution for PCC truck arrival behavior Users developing estimates for future are recommended to apply lognormal distributions with arrival distributions that have a standard deviation approximately 20 of the mean value 4242 Packing Ef ciency CA4PRS includes a packing ef ciency to address material buildup issues with Fast Setting Hydraulic Cement FSHC The 110 project completed in California used a concrete pavement mix that had a four hour cure time Due to the rapid set time material would tend to set and adhere to the inside of the mixing drum As more material accumulated in the drum less space was available for material Because of the material buildup and expense of these materials future construction projects are not likely to use these types of materials exclusively For nonFSHC projects users are recommended to use a deterministic distribution and a packing efficiency of 1 For FSHC projects a value less than one with a 10 standard deviation is advised 425 Paver Speed For users developing future estimates on projects that contain hand and machine paving PCC paver speed should be represented by a deterministic rate or a probabilistic distribution with a small stande deviation Paving machines produces the best ride and pavement quality in terms of a roughness index when they maintain a consistent speed In effort to deliver a high quality project most contractors will try to maintain a constant paver speed
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