Deterministic models for assessing productivity andcost of bored piles

TAREK M. ZAYED1* and DANIEL W. HALPIN2

1Assistant Professor, Construction Engineering and Management Department, faculty of Engineering, Zagazig

University, Zagazig, Egypt; Presently Assistant Professor Department of Building, Civil and Environmental

Engineering, Concordia University, 1257 Guy Street, BE Building, Room 8779, Montreal, QC, H3G 1M7, Canada2Head of Division of Construction Engineering and Management, School of Civil Engineering, Purdue University, West

Lafayette, IN 47907-1294, USA

Received 20 May 2004; accepted 25 November 2004

The assessment process of productivity and cost of bored pile construction is dictated by unseen subsurface

obstacles, lack of contractor experience and site planning. These problems complicate the estimator’s role in

evaluating pile equipment productivity and cost. Current research discusses the assessment of piling process

productivity and cost using the deterministic technique. Data are collected through questionnaires, site

interviews and telephone calls to experts in various construction companies. Many variables have been

considered in the piling construction process, such as pile size, depth, pouring method, soil type and

construction method. Five deterministic models have been designated to assess productivity, cycle time and

cost. The developed models are validated whereas 79% of the outputs have been predicted with more than 75%

accuracy. Consequently, three sets of charts have been developed to provide the decision-maker with a solid

planning, scheduling and control tool for piling projects. If a pile has 609 depth with w-18 (180 diameter pile) in

clay soil using a 59 auger height, the cycle time is estimated as 56 and 65.5 minutes; however, productivity is 6

and 5 holes/day for dry and wet methods, respectively.

Keywords: Bored pile, cost, cycle time, deterministic models, productivity

Introduction

Several problems face the installation or construction of

pile foundations. Some of these problems are subsur-

face obstacles, lack of contractor experience, and site

planning difficulties. The site pre-investigation usually

consists of statistical samples around the foundation

area that do not cover the entire area. Soil types differ

from site to site due to cohesion or stiffness, natural

obstacles, and subsurface infrastructure construction

obstacles. Lack of experience in adjusting the pile axis,

length and size present a further complication. Piling

machine mechanical and drilling problems must be

considered. Problems due to site restrictions and

disposal of excavated spoil have great effect on

productivity. The rate of steel installation and pouring

concrete is impacted by the experience of the steel crew

and method of pouring. All these problems, no doubt,

greatly affect the production of concrete piles on site.

There is a lack of research in this field. Therefore, this

study analyzes the piling process productivity factors

and assesses productivity considering most of the above

factors. Due to the above-mentioned problems, it is

difficult for the estimator to evaluate piling produc-

tivity. Therefore, it is necessary to use sophisticated

techniques to analyze the problem and determine the

closest optimal solution. The objective of this study is

to provide the piling process decision-maker with a tool

for assessing piling process productivity, cycle times,

and cost of the piling process using the deterministic

analysis technique.

Attributes matrix of productivity variables

A large number of variables affect the piling process

productivity, which is impossible to consider all of them

in one study. Based on studies of the construction

process and literature, the variables that affect produc-

tivity were identified (Peurifoy et al., 1996): (1) soil*Author for correspondence. E-mail: zayed@bcee.concordia.ca

Construction Management and Economics (June 2005) 23, 531–543

Construction Management and EconomicsISSN 0144-6193 print/ISSN 1466-433X online # 2005 Taylor & Francis Group Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/01446190500039911

type (i.e. sand, clay, stiff clay, etc.); (2) drill type (e.g.

auger, bucket); (3) method of spoil removal, the size of

hauling units and space considerations at the construc-

tion site; (4) pile axis adjustment; (5) equipment driver

efficiency; (6) weather conditions; (7) concrete pouring

method and efficiency; (8) waiting time for other

operations (i.e. pile axis adjustment); (9) job and

management conditions; and (10) cycle time. Out of

these variables, current research only concentrates on

the variables: pile size; soil type; pile depth; pouring

system; and auger height as shown in Table 1. The pile

size (w) varies within 180, 300, 480 and 600. Therefore,

this study concentrates only on these four categories of

pile sizes. The soil types that are included in this study

are clay, middle and sand. Middle soil type represents

all the types that in between pure clay and sand.

Different depths were planned to be encountered in

this study but the collected data were available only for

the 309, 409, 509 and 609 depths. Two pouring systems

or techniques are used: tremie and funnel. Tremie

technique is used in the wet method; however, funnel is

used in the dry method. Various auger heights have

been involved in this study, such as 39, 49, 59 and 69.

This study considers only the above-mentioned five

variables, with seventeen attributes according to the

specified limits, when estimating piling process pro-

ductivity. Therefore, the collected data have been

divided into several data sets to cope with the selected

variables and their attributes.

Conventional (deterministic) model design

The piling process cycle time activities’ durations are

estimated as crisp numbers (statistical mean for the

collected data sample). To build the conventional

(deterministic) model for the piling process, construc-

tion steps have to be defined in detail. Figure 1 depicts

the detailed construction steps of the piling process

starting from the axis adjustment until pouring

concrete and finishing the pile. The construction steps

(algorithm) can be summarized as follows:

(1) Adjust the piling machine on the pile axis.

(2) Haul with the auger to the drilling place.

(3) Start drilling until the auger is filled.

(4) Return from the drilling place up to the top of

the pile hole.

(5) Swing to the unloading area.

(6) Unload the dirt in the unloading area.

(7) Swing back to the top of the hole.

(8) Repeat steps 2–7 until the pile is completely

drilled.

(9) Relocate the machine and start steps 1–8.

(10) Start erecting the rebar cage using a crane.

(11) Erect the concrete pouring tool, either funnel

or tremie, into the hole.

(12) Use funnel for dry method and tremie for wet

method.

(13) Start pouring the concrete and finish the pile.

Accordingly, the deterministic model is designated to

assess the productivity and cost of the piling process.

The time required to construct a pile has to be

determined before productivity assessment. Both piling

machine and crane activities’ times have to be assessed

so that the time required to construct the pile is

defined. Consequently, the piling machine is respon-

sible for performing the activities: axis adjustment,

drilling and machine relocation. The crane is respon-

sible for the rest of the activities. Drilling time is the key

activity in this process, which depends mainly upon soil

type. The following designated generic models will be

applied to different soil types as shown in the analysis.

Hence, the following steps are considered in designat-

ing the deterministic models.

1. Drilling machine cycle time determination

Drilling has six main activities: hauling to the drilling

place, loading the auger (drilling), returning to the top of

the hole, swinging to unload area, unload dirt, and swing

back to the top of the hole. The pile has to be divided into

equal small depth segments (d) to facilitate cycle time

calculation as shown in Figure 2. The cycle time at the

beginning of the depth segment is, of course, different

from that at the end of the depth segment. To consider

this concept, the segment depth (d) has to be so small that

the cycle time difference between the upper and lower

segment’s edges is small. Therefore, it is assumed that the

cycle time does not change inside each depth segment,

which is the center (average) point. Hence, the cycle time

at the center of each depth segment represents the cycle

time through the entire segment. Then, the cycle time for

one segment can be calculated using Equation 1 as

Table 1 Piling process productivity variables attributes

matrix

Pile size (w) 180 300 480 600

Soil type Clay Middle Sand

Pile depth 309 409 509 609

Pouring method Tremie (wet

method*)

Funnel (dry

method**)

Auger length

(height)

39 49 59 69

Notes: *Wet method is the pile construction method that usesbentonite slurry to prevent the drilled hole’s sides from caving. **Drymethod is the pile construction method that does not use any meansof soil support because the soil can stand alone depending on itscohesion.

532 Zayed and Halpin

Figure 1 Flow diagram for pile construction on steps

Assessing productivity and cost of bored piles 533

follows: Cycle time (CT)5summation of the six acti-

vities times. Then,

CTi~Xm

i~1

Xn

j~1

xij ð1Þ

Time to drill one segment (T) is calculated based on

Equation 1 as follows:

Ti~CTi� d=hkð Þ ð2Þ

Hence, the total drilling time (TDT) to drill the pile is

calculated based on Equation 2 as follows:

TDT~X

Ti

TDT~CT1� d=hkð ÞzCT2� d=hkð Þz

CT3� d=hkð Þz . . . . . . . . . zCTi� d=hkð Þ

Because the pile is divided into small equal depth

segments and the auger height is similar for all

segments, then,

TDT~

d=hkð Þ� CT1zCT2zCT3z . . . . . . . . . zCTið Þ

TDT~ d=hkð Þ�X

CTi

� �ð3Þ

From Equations 1 and 3, then,

TDT~ d=hkð ÞXm

i~1

Xn

j~1

xij ð4Þ

2. Other activities’ times determination

Several other activities have to be considered as well as

drilling time, such as cage erection, funnel or tremie

erection, concrete pouring, machine relocation, and the

pile axis adjustment times. These different activities’

times have to be considered in determining the total

time to construct a pile. Each activity is discussed in

detail as follows:

(a) rebar cage erection (Cr), funnel erection (Fr),

tremie erection (Tr) and concrete pouring (Pr)

determination:

Cr, Fr, Tr and Pr depend upon the pile depth. Four

different categories of depth have been considered in

this study: 309, 409, 509 and 609. The term r has been

added to the variables to represent the different depth

categories.

(a) Wet and dry methods representation:

The only difference between the piling process dry

and wet methods of construction is the concrete

pouring tool. In the case of the wet method, a tremie

has to be used whereas a funnel is used in the dry

method. The tremie always takes a longer time to be

erected than the funnel. To include both terms in the

deterministic model, a switch term has to be used to

alternate between the two different values. In other

words, a d term is multiplied by the funnel and tremie

expressions to enable the deterministic model to use

only one of them according to the suggested method of

construction. Therefore, if the method of construction

is wet, the term (d) will enable the tremie expression

(Rr) and disable the funnel expression (Fr) and vise

versa. The term d, a 0/1 gate term, can be represented

as:

d~

1 if the wet method is used

tremie has to be erectedð Þ0 if the dry method is used

funnel has to be erectedð Þ

8>>><

>>>:

9>>>=

>>>;

Then, in the deterministic productivity model,

the term (12d) will be multiplied by (Fr) and the term

(d) will be multiplied by (Tr). For example, in case of

the dry method d50, then (12d51) opens the gate for

the funnel erection time to be included in the

deterministic model, the tremie erection time is erased

and vise versa.

(a) Adjusting the pile axis (A) and machine reloca-

tion (M) times’ determination:

These two cycle time activities depend upon machine

power and the labor crew. Therefore, they will be used

as a single value for each.

Based on the discussion in the above points (a), (b)

and (c), the other activities’ times (OAT) can be

Figure 2 Pile depth segments

(b)

(c)

534 Zayed and Halpin

expressed in Equation 5 as follows:

OAT~Crz(1{d)�Frzd�TrzPrzAzM ð5Þ

3. Total pile duration (TD) determination

The total duration to install a pile is the sum of the total

drilling time (TDT) and the other activities’ times (OAT).

Hence, based on Equations 4 and 5, the total duration per

pile in minutes (TD) can be calculated as follows:

TD~TDTzOAT

TD~

d=hkð ÞPm

i~1

Pn

j~1

xij

" #z

Crz 1{dð Þ � Frz

d � TrzPrzAzM

" #( )

minutesð Þ

ð6Þ

4. Drilling equipment duration for each pile

There are two major options related to the determination

of drilling equipment duration (DED). First, drilling

equipment can work as the major machine that drill, help

in erecting the rebar cage, and help in pouring the pile.

Therefore, its DED equals TD (Equation 6). Secondly,

drilling equipment can drill and then move to another pile

location; however, another crane and/or excavator can

complete the rebar cage erection and pouring concrete

activities (this option is the most popular). Considering

the second option, the DED for each pile can be

determined using Equation 7 as follows:

DED~ d=hkð ÞXm

i~1

Xn

j~1

xij

" #(z AzM½ � minutesð Þ ð7Þ

5. Productivity model determination

Productivity can be determined after calculating the

total duration to construct a pile (TD) and/or (DED).

The working hours (WH) per day have to be defined to

determine how many pile holes can be performed per

day. The regular working hours per day are 8. In this

study, the term working hours (WH) is left as a variable

for the user to adjust according to company policy.

Because the TD model (Equation 6) and the DED model

(Equation 7) use minutes as a duration unit, the working

hours (WH) have to be converted to minutes; therefore,

the working time per day will be (60*WH) minutes.

Hence, to calculate the productivity, the total working

time per day (60*WH) has to be divided by the TD

(option 1) or by the DED (option 2). The outcome is the

number of pile holes that can be constructed per day. But

this result considers productive time of 60 minutes per

hour; however, this is not realistic. This result considers

only the effect of the quantitative factors on productivity

and neglects the qualitative factors, such as operator

efficiency, weather conditions, site conditions, job

management, site investigation, mechanical problems,

etc. Therefore, a term for the effect of these qualitative

variables has to be considered in the productivity model.

This term has been calculated using the Analytic

Hierarchy Process (AHP) and fuzzy logic (Zayed, 2001;

Zayed and Halpin, 2004a). The final outcome of this

qualitative evaluation is the Productivity Index (PI). The

PI is estimated as 0.7 (Zayed, 2001; Zayed and Halpin,

2004a). The productivity model considers PI as a

variable; however, it has an average value of 0.7 in

current study based upon (Zayed, 2001; Zayed and

Halpin, 2004a, b). Hence, productivity can be deter-

mined using equation (8a and b) as follows:

Productivity holes=dayð Þ~

60 �WH � PI=TD option 1ð Þð8aÞ

Productivity holes=dayð Þ~

60 �WH � PI=DED option 2ð Þð8bÞ

Then, based on models (8a&b),

Productivity~

60 �WH � PI option 1ð Þ

d=hkð ÞPm

i~1

Pn

j~1

xij

" #z

Crz 1{dð Þ � Frzd � TrzPrzAzM½ �

8>><

>>:

9>>=

>>;

ð9aÞ

Productivity~60 �WH � PI option 2ð Þ

m n

d=hkð ÞP P

xij

� �z AzM½ �

i~1 j~1

8><

>:

9>=

>;

ð9bÞ

The productivity models in Equations 9a and 9b

provide only the number of holes per day. Common

practice uses the productivity in cy/day or lf/day;

therefore, the models in Equations 10a and 10b and

11a and 11b have been developed. Productivity can be

determined in cy/day or lf/day by multiplying Equations

8a and 8b by the pile volume and cross-sectional

area, respectively. Equations 10a and 10b determine

Assessing productivity and cost of bored piles 535

productivity in terms of cy/day whereas Equations 11a

and 11b determine productivity in terms of linear foot

of depth per day. The equation nominator for pro-

ductivity model (10a and 10b) include the number 1.75

that result from units conversion: 60*(p/4)*(1/27 cf per

cy)51.75. Both equations can be depicted as follows:

Productivity cy=dayð Þ~

1:75 �WH � PI � w2 � i � d� ��

TD option 1ð Þð10aÞ

Productivity cy=dayð Þ~

1:75 �WH � PI � w2 � i � d� ��

DED option 2ð Þð10bÞ

Productivity lf=dayð Þ~

60 �WH � PI � i � dð Þ=TD option 1ð Þð11aÞ

Productivity lf=dayð Þ~

60 �WH � PI � i � dð Þ=DED option 2ð Þð11bÞ

Because the PI has a value of 0.7, regular working

hours are 8 hours/day, and segments’ depth (d) is 109,

Equations 9a and 9b, 10a and 10b and 11a and 11b

turn out to be:

Productivity holes=dayð Þ~

336ð Þ=TD option 1ð Þð12aÞ

Productivity holes=dayð Þ~336ð Þ=DED option 2ð Þ

Productivity cy=dayð Þ~98 � w2 � i� ��

TD option 1ð Þ ð13aÞ

Productivity cy=dayð Þ~98 � w2 � i� ��

DED option 2ð Þ ð13bÞ

Productivity lf=dayð Þ~3360 � ið Þ=TD option 1ð Þ ð14aÞ

Productivity lf=dayð Þ~3360 � ið Þ=DED option 2ð Þ ð14bÞ

Data collection

Two types of data collection techniques were used in

this study. The first technique was direct data collection,

such as site interviews, site visits to fill data forms

and telephone calls. The second technique utilized

a questionnaire. A questionnaire was designated to

collect data from contractors and consultants who are

specialists in concrete bored pile construction and

design. This questionnaire was used to collect the piling

process cycle time, productivity and soil characteristics.

Reviewers were asked to provide information based on

one of the most average projects that they have

conducted or are currently conducting. Accordingly,

each questionnaire represents a full set of information

about at least one project. The reply percentage for the

questionnaire is 35.42%. The collected data include

cycle time activities durations, productivity, expenses

breakdown and quantitative assessment for the quali-

tative factors that affect productivity using a unified

scale. For further details, the reader is referred to Zayed

(2001) and Zayed and Halpin (2004a).

Deterministic model application

The designed deterministic models have been applied

to the piling process collected data to calculate its

productivity and cycle time. The productivity has been

determined using Equations 12a and 12b, 13a and 13b

and 14a and 14b. Equations 12a and 12b calculate the

productivity in terms of holes per day and Equations

13a and 13b in terms of cubic yard per day. Equations

14a and 14b determine productivity in terms of linear

foot of depth per day. The cycle time is calculated using

models (4) and (5). The application of these models is

discussed in the following sections.

Drilling time model application to w-18

The deterministic model in Equation 4 calculates the

total excavation (drilling) time. It is used to develop the

chart in Figure 3 that draws the relationship of drilling

time against the drilling depth using different auger

heights for clay soil with the wet method. Hence, these

curves are used to assess the drilling time that is

extremely important in planning piling projects. For

instance, if a project has a 609 depth with w-18 (180

diameter pile) in clay soil using a 59 auger height, its

drilling time is 21 minutes.

Other activities times model application to

w-18

The drilling time is calculated using Equation 4 and the

remaining cycle time activities’ duration is calculated

536 Zayed and Halpin

using Equation 5. Figure 4 shows the outcome of the

model in Equation 5 applied to the w-18 data set. This

figure shows other cycle time activities against different

pile depths: 309, 409, 509, and 609. Two curves have

been developed to represent the activities times using

the wet and the dry construction methods. Figure 4 can

be used to assess all cycle time activities except drilling

time. For instance, if a project has a 609 depth with

w-18 (180 diameter pile) in clay soil using a 59 auger

height, its other activities time is 35 and 44.5 minutes

for dry and wet methods, respectively.

Productivity model application to w-18

One of the major goals of this study is to determine the

piling process productivity considering different vari-

ables, such as auger height, depth, pile size and soil

type. The deterministic productivity model is indicated

in Equations 12a and 12b, 13a and 13b and 14a and

14b. Productivity models in the three previous equa-

tions have been applied to the available model building

and validation data sets considering various soil types.

The outcome of model building data set application is

shown in Figure 5. It shows the productivity in terms of

holes per day for the wet and dry construction methods

in clay soil. It provides a set of productivity curves at

different depths with a maximum depth of 609, using

different auger heights, such as 39, 49, 59, and 69. The

continuous curves represent the productivity using the

dry method and the dotted curves represent productiv-

ity using the wet method. Hence, for a project in clay

soil with a known depth, in the range that is considered

in this chart, productivity can be assessed in holes per

day. Moreover, the construction method, the drilling

tool and the pouring tool must be defined prior to

starting the work. For instance, if a project has a 609

Figure 3 Drilling time for W-18 pile in clay soil

Figure 4 Other activities times for W-18 pile Figure 5 Productivity for W-18 pile in clay soil

Assessing productivity and cost of bored piles 537

depth with w-18 (180 diameter pile) in clay soil using a

59 auger height, its productivity is 6 and 5 holes/day for

dry and wet methods, respectively.

Productivity model validation for w-18

Validation is so important because a model cannot be

used in practice unless it is valid. The results of a

productivity model have to be validated so that it can be

used for productivity estimating. After validation, the

model will be proper to fit the problem and predict the

productivity of piling process. Therefore, the produc-

tivity model in Equations 12a and 12b is used to

estimate the productivity for the validation data set.

Being determined, the estimated productivity is com-

pared with the collected productivity from the reviewers.

If the model provides close numbers to the collected data;

hence, it is valid and can be used to represent this process

in real world practice and vice versa. The available

validation data set is divided into four different data sub-

sets: w-18, w-30, w-48 and w-60. Each data sub-set is

categorized into three categories according to soil type:

clay, middle and sand. The deterministic productivity

model is applied to each category. To exactly determine

how accurate the predicted results of the productivity

model, a validation factor (VF) has to be calculated using

equation (15) as follows:

Validation factor VFð Þ~EP=AP ð15Þ

The VF has been calculated for each validation data

point considering its corresponding productivity model

result. Table 2 shows the VF for clay, middle and sand

soils using wet and dry methods in w-18. It shows that

VF for w-18 in clay soil with 309 depth using 39 auger

height and wet method is 0.88 while it is 0.97 for 49

auger height. This indicates that the model fits the

productivity for 39 auger height with 88% fitness while

it is 97% for 49 auger height. Therefore, this table

shows productivity model behavior regarding different

piling process variables. The concept of validation

factor (VF) has been designed to check the fitness

degree of the designed models. The value of the VF for

more than 36 % of the models’ outputs is more than

90% fitness, which expresses its good fitness of the

available data sets because construction projects have

large number of variables that affect production and

cost. About 30% of the outputs have the VF in the

range of 80–90% fitness while 13% of them have the

VF in the range of 75–80% fitness. Consequently, 79%

of the models outputs have been predicted with more

than 75% fitness, which is fairly good and acceptable.

Piling process cost estimation

Prior to approaching the cost analysis, it is better to

address the factors that influence the piling process

costs. There are large number of factors that affect pile

construction and dictate its construction method. This

study mentioned the major cost factors based on Reese

and O’Neill (1988), as shown in Table 3.

Accordingly, the cost estimate procedure is compli-

cated and hard to achieve. The data collected by Reese

and O’Neill (1988) from ADSC contractors did not

consider the mobilization and demobilization costs

because they were project-specific costs. Current study

considers the average of Reese and O’Neill (1988) cost

Table 2 Validation factor (VF) for w-18

Construction method at various auger heights

Wet method Dry method

Pile Depth VF for clay soil

Auger 39 Auger 49 Auger 59 Auger 69 Auger 39 Auger 49 Auger 59 Auger 69

309 0.88 0.97 1.04 1.09 1.04 1.17 1.27 1.34

409 0.77 0.86 0.92 0.97 0.91 1.03 1.12 1.19

509 0.73 0.82 0.88 0.93 0.87 0.99 1.08 1.15

609 0.70 0.79 0.85 0.90 0.80 0.91 1.00 1.07

VF for middle soil

309 0.81 0.89 0.95 0.99 0.96 1.08 1.16 1.23

409 0.70 0.78 0.83 0.87 0.82 0.93 1.01 1.07

509 0.65 0.73 0.79 0.83 0.76 0.87 0.94 1.01

609 0.62 0.69 0.74 0.78 0.70 0.80 0.87 0.93

VF for sand soil

309 0.82 0.90 0.96 1.00 0.97 1.09 1.17 1.24

409 0.71 0.79 0.84 0.88 0.84 0.94 1.02 1.08

509 0.66 0.74 0.79 0.83 0.77 0.88 0.96 1.02

609 0.62 0.70 0.75 0.79 0.71 0.81 0.88 0.94

538 Zayed and Halpin

figures to be used as a general value. The important

outcome of this cost analysis is the relative construction

cost of major activities in the piling process. Table 4

shows the cost figures that have been indicated in Reese

and O’Neill (1988) and its conversion using the

RSMeans 2000 conversion factor. The outcome con-

version factor that converts cost figures from 1987

prices to 2000 prices is 1.3637. The resulted cost

figures as of 2000 have been calculated for current

study use. Most costs in Table 4 are estimated in $/cy,

except the rebar cage cost which is estimated in $/hole.

It shows the details of each cost figure and explains

each abbreviation. The cost per cy has been taken from

Table 4 and multiplied by the volume of each pile to get

the total cost per hole in equation (16) as follows:

TCl~2:02 � 10{4 DClzPCð Þ � w2 �D� �

zRC ð16Þ

The cost model in Equation 16 has been applied to

the four construction methods of piling process as

shown in Table 5. It is clear that the total cost per pile is

different from construction method to the other for

different pile sizes and depths. Cost curves have been

constructed to predict the cost value per hole in

different depths within different pile sizes. Each pile’s

construction method cost is represented by curves

covering different pile depths and sizes. Figure 6 shows

the total cost curves for pile of sizes: 180, 300, 480, and

600 with different depths: 309, 409, 509, and 609 using

two construction methods: Dry Method Soil Uncased

(DMSUC) and Wet Method Soil Slurry (WMSS). The

continuous curves represent DMSUC costs and the

dotted curves represent WMSS costs. Similarly,

Figure 7 shows the same information for the two other

construction methods: Dry Method Soil Cased

(DMSC) and Wet Method Soil Cased (WMSC). For

further details about the above-mentioned construction

methods, the reader is referred to Reese and O’Neill

(1988) and Zayed (2001). For instance, if a project has

Table 3 Factors that affect piling process cost

Factor Factor description

Sub-surface (soil) conditions It has a great effect on the cost because of drilling difficulties in different soil types

Site conditions It includes trafficability, under ground lines, trees, ground surface elevations,

overhead lines, and nearby structures. All these sub-factors affect cost greatly

Geometry of pile (depth) Cost varies for different pile depths and sizes

Specifications including inspection

procedure

The way specifications is written down is very important in cost estimation because

the contractor will determine his/her prices according to the inspection procedure in

the project

Expected weather conditions Weather conditions

Location of the project and its closest

means of travel and unions

Location to the closest means of travel and unions

Governmental environmental regulations This is important regarding the cost of spoil soil removal

Availability of proper equipment Number of pieces of equipment that can fit in the site is critical in productivity

estimation and hence cost estimation

Contractor experience and economic

conditions

Contractor financial status

Contract requirements It includes bonding and insurance capacities, terms of payment, and terms of

reference in the contract

Table 4 Cost of piling process activities

Cost item Average cost ($/cy) Conversion Average cost

1987 factor** 2000 ($/cy)

Drilling cost (DMSUC) $62.00 1.3637 $84.55

Drilling cost (DMSC) $96.00 1.3637 $130.92

Drilling cost (WMSS) $113.00 1.3637 $154.10

Drilling cost (WMSC) $139.00 1.3637 $189.56

Rebar cage cost* $57.00 1.3637 $77.73

Concrete pouring cost* $23.00 1.3637 $31.37

Notes: Drilling cost5machine cost+crew cost. Placing cage cost5crane cost+crew cost. Placing concrete cost5tremie/funnel cost+crewcost+pump cost. The available average costs cover typical diameter from 120 to 720. Typical depth ranges from 159 to more than 509.Abbreviations: DMSUC: dry method in soil uncased; DMSC: dry method in soil using case; WMSS: wet method in soil using slurry; WMSC:wet method in soil using case. *This cost is per hole. **This factor is based on RSMeans 2000.

Assessing productivity and cost of bored piles 539

a 609 depth with w-18 (180 diameter pile) in clay soil

using a 59 auger height, its drilling time is 21 minutes.

Illustrative example

(A) A project of 105 pile holes with w-18 and 409

depth in clay soil needs to be constructed. How

many working days does the contractor need

the piling machine in each project? Knowing

that dry method can only be used in the project

of clay soil but wet method can be used for all of

them, the contractor decided to use wet method

for 36 holes of the clay soil project and dry

method for the rest due to the water table. How

many holes/day, cy/day, and lf/day can the

contractor do in this project? How many days

the contractor will take to perform this project?

(B) Suppose that a drilling contractor has to

estimate the costs of two different drilled shaft

bids. The first bid is 67 piles (drilled shafts)

with 300 diameter and 559 depth in stiff clay soil

with low water table. The second bid is 49 piles

(drilled shafts) with 600 diameter and 609 depth

in clay soil and 159 sand layer on top with low

water table. What will be the optimum cost

associated with each bid?

Solution of Part A: based on the developed set of charts,

the drilling time for the machine is calculated. This

project has 105 holes with 409 depth in clay soil. The

first 36 holes use wet method while the other 69 holes

use dry method. Drilling time does not depend on the

construction method because it affects only the pouring

tool that can be used. Therefore, the drilling time will

be the same for both dry and wet methods. According

to Figure 2, drilling time is 22, 16.5, 13.2, or 11 min/

hole using 39, 49, 59 or 69 auger height, respectively.

Hence, this project needs the piling machine for 7, 5, 4,

or 3 days, respectively. Table 6 shows the calculation of

these values. Hence, the drilling time (day) is calculated

in equation (17) as follows:

Table 5 Cost of piling process construction methods

Construction Method Diameter (ft) Total cost ($/hole) (as 2000 prices) at depths:

309 409 509 609

DMSUC: 180 $305.29 $381.15 $457.00 $532.86

dry method in 300 $709.85 $920.55 $1 131.26 $1 341.96

soil uncased 480 $1 695.95 $2 235.35 $2 774.76 $3 314.16

600 $2 606.19 $3 449.01 $4 291.83 $5 134.65

DMSC: 180 $396.32 $502.51 $608.71 $714.90

dry method in 300 $962.69 $1 257.68 $1 552.67 $1 847.65

soil using case 480 $2 343.23 $3 098.40 $3 853.57 $4 608.73

600 $3 617.58 $4 797.52 $5 977.47 $7 157.42

WMSS: 180 $441.83 $563.20 $684.56 $805.93

wet method in 300 $1 089.12 $1 426.24 $1 763.37 $2 100.50

soil using slurry 480 $2 666.88 $3 529.92 $4 392.97 $5 256.02

600 $4 123.27 $5 471.78 $6 820.29 $8 168.80

WMSC: 180 $511.44 $656.01 $800.58 $945.14

wet method in 300 $1 282.47 $1 684.05 $2 085.63 $2 487.21

soil using case 480 $3 161.86 $4 189.90 $5 217.94 $6 245.98

600 $4 896.68 $6 502.99 $8 109.31 $9 715.62

Figure 6 Cost of DMSUC/WMSS construction methods

540 Zayed and Halpin

Project Drilling Time~N �TDT

60 �WH � PIdaysð Þ ð17Þ

Then,

Project Drilling Time~

105 holesð Þ � 22 min=holeð Þð Þ60 min=hrð Þ � 8 hours=dayð Þ � 0:7ð Þ~

7 days

Accordingly, the project manager has the flexibility

to select the convenient auger height and time that the

machine is required in the site. Furthermore, the

technical office of the company can plan its piling

machines time among different sites.

Based on productivity figures, the machine produc-

tivity in each project is calculated. For 105 holes, 409

depth, clay soil, the first 36 holes use wet method while

the other 69 holes use dry method. Figure 5 shows that

productivity of constructing piles of 180 diameter with

409 depth is 7.25, 8.23, 8.95, and 9.5 holes/day for dry

method and 6.18, 6.88, 7.38, and 7.75 holes/day for

wet method using 39, 49, 59, and 69 auger height,

respectively. Table 7 shows productivity and time

calculations for the three projects. Hence, this project

will be accomplished using wet method in 36 holes,

which take 6, 5, 5, or 5 days using 39, 49, 59, or 69 auger

height, respectively. Furthermore, the other 69 holes

that have to be accomplished using dry method will

take 9, 8, 8, or 7 days to complete 15, 13, 13, or, 12

days for the 105 holes. The total piling process time

value in days is calculated as follows:

Piling Process Time~N=Pr ð18Þ

The application of Equation 18 is indicated in

Table 7. This table shows the productivity correspond-

ing to the required depth using different auger heights

and construction methods. The total pile installation

duration (TD) consists of the drilling time using the

piling machine and the other activities’ times that are

accomplished using a crane. Therefore, this time

represents the total duration that the contractor needs

to spend in each project. It is a very good tool that can

be used to estimate the project duration from piling

contractor perspective.

Solution of Part B: based on the given information,

the first bid can use dry method soil uncased

(DMSUC) because the soil can stand-alone without

Table 6 Drilling time for the illustrative example

No. of holes Depth Drilling time per hole (minutes) Total drilling time (days)

Auger 39 Auger 49 Auger 59 Auger 69 Auger 39 Auger 49 Auger 59 Auger 69

105 409 22 16.5 13.2 11 7 5 4 3

Figure 7 Cost of DMSC/WMSC construction methods

Table 7 Productivity in holes/day

Wet method

No. of holes Depth Productivity (holes/day) in clay soil Total piling process time (days)

Auger 39 Auger 49 Auger 59 Auger 69 Auger 39 Auger 49 Auger 59 Auger 69

36 409 6.18 6.88 7.25 7.75 6 5 5 5

Dry method

No. of holes Depth productivity (holes/day) in clay soil Total piling process time (days)

Auger 39 Auger 49 Auger 59 Auger 69 Auger 39 Auger 49 Auger 59 Auger 69

69 409 7.38 8.23 8.95 9.5 9 8 8 7

Assessing productivity and cost of bored piles 541

caving and the water table is low. Therefore, using

Figure 6, at Dry-300 with 559 depth, the total cost is

$1250/hole. Hence, the bid cost for 67 piles will be

$83750. This cost does not include overheads. Then,

the contractor can add the overhead costs and markup

to this cost to get the bid price.

Similarly, the second bid can use either dry method

soil cased (DMSC) or wet method soil slurry (WMSS).

Figure 7 shows that the total cost for DMSC with 600

diameter and 609 depth is $7,150/hole. From Figure 6,

the WMSS total cost for 600 diameter and 609 depth is

$8,160/hole. Hence, the optimum cost method is to use

DMSC of $7,150/hole. Then, the total bid cost is

$350 350. The total bid price can be calculated by

adding this total cost to the overheads and markup.

Accordingly, these cost figures can be used to select

the optimal construction method for the piling project

in addition to its cost for bid use. Consequently,

Figures 6 and 7 are good tools for piling projects cost

estimate process.

Conclusions

Five models have been designated to assess piling

process productivity, cycle time, and cost using the

conventional (deterministic) technique. These models

have been validated to assure their appropriateness in

piling process analysis. The concept of validation factor

(VF) has been designated to check their accuracy of

fitting. The value of VF for more than 36 % of the

models outputs is more than 90% accuracy, which

expresses its extreme fit for the available data sets.

About 30% of the outputs have the VF in the range of

80–90% accuracy while 13% of them have the VF in

the range of 75–80% accuracy. Consequently, about

79% of the models outputs have been predicted with

more than 75% accuracy.

Several sets of charts that represent productivity,

cycle times and cost have been developed. Based upon

these charts, the cycle time is 56 and 65.5 minutes for

dry and wet methods, respectively, if the constructed

pile has a 609 depth with w-18 (180 diameter pile) in

clay soil using a 59 auger height. In addition, its

productivity is 6 and 5 holes/day for dry and wet

methods, respectively. Therefore, the developed charts

are very beneficial for the contractor and the client to

plan bid their jobs.

References

Peurifoy, R.L., Ledbetter, W.L. and Schexnayder, C.J.

(1996) Construction, Planning, Equipment, and Methods,

5th edition, The McGraw-Hill Companies, Inc., USA.

R.S. Means (2000) Building Construction cost data, 58th

Annual Edition, R.S. Means Company, Inc., Kingston,

MA.

Reese, L.C. and O’Neill, M.W. (1988) Drilled Shafts:

Construction Procedures and Design Methods, Publication

no. FHWA.HI-88-042 and ADSC-TL-4, Federal Highway

Administration, USA.

Zayed, T.M. (2001) Assessment of productivity for concrete

bored pile construction, PhD thesis submitted to School of

Civil Engineering, Purdue University, West Lafayette, IN,

USA, May.

Zayed, T.M. and Halpin, D.W. (2004a) Quantitative

assessment for piles productivity factors. Journal of

Construction Engineering and Management, ASCE, 130(3),

405–14.

Zayed, T.M. and Halpin, D.W. (2004b) Simulation as a tool

for piles productivity assessment. Journal of Construction

Engineering and Management, ASCE, 130(3), 394–404.

Appendix I.

Notation

CTi5Piling machine cycle time at segment i

xij5Cycle time’s activity j estimated time in segment i

(i51, 2, ...., m and j51, 2, ........, n)

n5Maximum number of cycle time activities, which

is 6 in this process

m5Number of chosen depth segments

Ti5Time to drill segment i

d5Depth of equal segments (ft)

hk5Auger height, k53, 4, 5, or 6 corresponding to

auger heights 39, 49, 59, or 69, respectively (ft)

TDT5Total drilling time per pile

OAT5Total other activities’ time per pile

Cr5Rebar cage time for depth r (r51, 2, ...., p)

Fr5Funnel erection time for depth r (r51, 2, ...., p)

Tr5Tremie erection time for depth r (r51, 2, ...., p)

Pr5Concrete pouring time for depth r (r51, 2, ...., p)

A5Adjusting the pile axis time

M5Machine relocation time

WH5Working hours per day

PI5Productivity index (qualitative variables effect)

TD5Total duration to construct a pile

w5Pile diameter (ft)

N5Number of pile holes

Pr5Productivity per day

VF5Validation factor

EP5Estimated productivity

AP5Actual (field) productivity

TCl5Total pile’s cost for different methods l

($/hole)

DCl5Drilling cost per cy for different methods l

($/cy)

PC5Pouring cost per cy for concrete ($/cy)

542 Zayed and Halpin

RC5Rebar cage placing cost ($/hole)

D5Total pile depth (ft)

Subscripts and superscripts

i5Number of segments. It has a range from 1 to m

j5Cycle time activities number. It has a range from 1

to n

l5Different construction methods (DMSUC, DMSC,

WMSS, and WMSC)

l51, 2, 3 and 4

r5No. of different depths. r51,2,3,4 for

309,409,509,609 depths, respectively

p5Max. number of chosen depths. p54 in this study

Assessing productivity and cost of bored piles 543