Establishment of cost functions for construction of various types of public water services assets in Portugal

Transcription

1 Establishment of cost functions for construction of various types of public water services assets in Portugal Abstract This paper describes research on the establishment, validation and testing of construction cost functions of various types of public water services assets in Portugal: ground-level and elevated water storage tanks, water pumping or booster stations, water transmission mains and wastewater pumping stations. It also involves the validation of the parameters used to describe these assets, such as physical characteristics (e.g., total volume; tank height; pipe material, nominal pressure, nominal diameter and length) or hydraulic variables (e.g., flow capacity; installed electrical power; pumping head). To this end, a methodology including four steps and 15 tasks was established and were analysed 415 price lists. The sample derived from 221 construction contracts from 16 Portuguese water utilities managed by the Águas de Portugal Group. Data concerning 754 assets were collected and organized in databases according to type of asset. Construction cost functions (civil engineering construction, equipment, electrical facilities and total) were derived by statistical regression analysis. The analysis and discussion of the functions included the comparison with cost functions previously published by three Portuguese authors and between the estimated construction costs and the real ones, as well as the estimation of construction costs by the developed functions for ground-level water storage tanks associated with pumping stations, some design examples and some assets already constructed by other Portuguese water utilities. This research is relevant to the speciality of Urban Hydraulics, insofar as it consolidates the knowledge of design engineers and water utilities on the assessment of construction costs of the analysed types of water services assets. Keywords: cost function, ground-level water storage tank, elevated water storage tank, water pumping or booster station, water transmission main, wastewater pumping station. INTRODUCTION Since 1993, 7,5 billion Euros have been invested in water supply systems, wastewater systems and solid waste management in Portugal, of which more than two thirds were European Union funds. As a result the extent ad quality of these services has significantly improved, in compliance European Union regulations and national demand for environmental and public health (Alegre and Covas, 21). There is now a general awareness among the international community that decision-making relative to infrastructure of public water services should be transversal. According to Alegre and Covas (21), it should be based on three dimensions of analysis (including cost, performance and risk), be interdisciplinary (involving engineering, financial management and information management) and be developed at three decision levels (strategic, tactical and operational). The current paper focuses on costs, which play an important role in an effective decision-making during the design stage, tender evaluation and construction phases (Life Cycle Costing (LCC), unknown author, 29; Grigg, 23). According to Alegre and Covas (21) and the ISO : 28 standard, life-cycle cost analysis is a methodology for the economic evaluation of the cost of a particular asset over its life cycle. In the case of water services assets, it can be subdivided into investment costs (including consultancy and construction costs), maintenance costs (including charges relating to the conservation of infrastructures, manual labor, materials, equipment, accessories and transport), operating costs (including staff costs, energy and reagents, as well as occupancy costs) and decommissioning costs (including charges related to the deactivation of the asset at the end of the useful life). The assessment of these costs should be easy to accomplish. However, engineers often have to take decisions based on vague, incomplete, scattered and/or outdated data, so it becomes a challenging task. 1

2 In this context, it is of the upmost importance to have reliable cost functions that predict the costs of various types of assets. This paper reports on construction cost functions for brand new water services assets in continental Portugal, using key parameters of each asset. The estimated costs include neither VAT nor extra works. A review of the state-of-the-art in Portugal concluded that the national bibliography on the assessment of construction costs are the publication of Lencastre et al. (1995), the study of Águas de Portugal Serviços, S.A. (25) and the study of AdP Águas de Portugal, SGPS, S.A. (28). These references are more temporally distant from each other than desirable, their methodologies are based on different principles and the scopes of the functions are not identical. Table 1 presents a summary of previous construction cost functions obtained by these authors and the dates of publication. Table 1 Previous cost functions for construction of water services assets in Portugal Author Asset Cost function Key parameter Applicable scope of key parameter Monetary unit (1) Ground-level 242,91, (R 2 = 99,6%) V = [5; 2 ] 1994 (2) water V: total 16541, (r =,92) storage volume (m 3 V = [1; 7 ] /m 3 23 ) (3) tanks 5941,7, (R 2 = 97,8%) V = [1; 1 ] /m 3 28 (1) Elevated water storage (3) tanks (1) (2) (3) (1) (2) (3) Water pumping stations Water transmission mains 158, (R 2 = 99,5%), ,3 14 (R 2 = not known) 2578,79,, (R 2 = 95,%) 174,8,, (R 2 = 97,%) 348, (r =,96) 25176, (r =,95) ,15 (R 2 = not known) ,, , (R 2 = not known) V: total volume (m 3 ) Q: flow capacity (L/s) H: pumping head (w.c. m) P: installed electrical power (kw) Q: flow capacity (L/s) H: pumping head (w.c. m) V = [5; 5], for a 2, m tank height V = not known, for a 2, m tank height Q = [5,; 3,] H = [25,; 75,] Year P= [,; 595,] /kw 23 Q 2, H not known ,15 (R 2 = not known) Q > 2, (upper limit not known) H not known 1317,, 292, (R 2 = not known),8, ,22 (R 2 = 98,%),13,736 13,9 (R 2 = 1,%) D: nominal diameter (mm) D = [6; 15] D = [14; 5] 1,1956, (r =,91) D = [6; 7],1855 2,9114 (r =,83),171 2,3592 (r =,85),6, ,867 (R 2 = 99,7%),9,564 43,897 (R 2 = 99,8%),15,171 46,218 (R 2 = 99,9%),8, ,697 (R 2 = 99,9%) D = [63; 4] D = [63; 45] D = [6; 6] D = [63; 25] D = [63; 25] D = [6; 6] 28 /m 1994 /m 23 /m 28 2

3 Author Asset Cost function (1) (2) (3) Wastewater pumping stations 5317,19, (R 2 = 99,1%) 2987,8,, (R 2 = 97,%) 13446, (r =,98) Key parameter Q: flow capacity (L/s) H: pumping head (w.c. m) Applicable scope of key parameter Q = [5,; 2,] H = [5,; 5,] P = [,; 1,[ 1675, (r =,71) P: installed P = [1,; 3,[ electrical ,17, (r =,91) power (kw) P = [3,; 155,] 224, (r =,9) P = [,; 155,] 42313,6 396,9,226 1,23 (R 2 = not known) 1564,4,, 2485,2, 1,23 (R 2 = not known) Q: flow capacity (L/s) H: pumping head (w.c. m) Q = [6,; 1,] H not known Monetary unit Year 1994 /kw Notes: Authors: (1) Lencastre et al. (1995); (2) Águas de Portugal Serviços, S.A. (25); (3) AdP Águas de Portugal, SGPS, S.A. (28). Cost functions: C T: total cost; C CE: civil engineering construction cost; C EQ+EF: equipment and electrical facilities cost; C EQ: equipment cost; C i: total cost per pipe material (i = DI: ductile iron; HDPE PN1: high-density polyethylene with a nominal pressure of 1; HDPE PN16: high-density polyethylene with a nominal pressure of 16; ST: steel). Given this situation, Águas de Portugal Serviços, S.A. is promoting the upgrade and improvement of such construction cost functions. To this end, data from real water and wastewater systems, from various Portuguese water utilities, were gathered by AdP Águas de Portugal Group. These data were collected and treated, applying a methodology which includes four distinct steps and a total of 15 tasks. So, the current paper describes research on the establishment, validation and testing of construction cost functions of various types of public water services assets in Portugal: ground-level and elevated water storage tanks, water pumping or booster stations, water transmission mains and wastewater pumping stations. It also involves the validation of the parameters used to describe these assets, such as physical characteristics (e.g., total volume; tank height; pipe material, nominal pressure, nominal diameter and length) or hydraulic variables (e.g., flow capacity; installed electrical power; pumping head). To this end, a methodology including four steps and 15 tasks was established and were analysed 415 price lists. The sample derived from 221 construction contracts from 16 Portuguese water utilities managed by the Águas de Portugal Group. Data concerning 754 assets were collected and organized in databases according to type of asset. Construction cost functions (civil engineering construction, equipment, electrical facilities and total) were derived by statistical regression analysis. The analysis and discussion of the functions included the comparison with cost functions previously published by three Portuguese authors and between the estimated construction costs and the real ones, as well as the estimation of construction costs by the developed functions for groundlevel water storage tanks associated with pumping stations, some design examples and some assets already constructed by other Portuguese water utilities. CASE STUDY In Portugal, AdP Águas de Portugal Group is responsible for the provision of essential public services in the fields of water supply, wastewater collection and treatment and solid waste management. AdP - Águas de Portugal, SGPS, S.A. is a state-owned holding company that has invested more than 7,5 billion Euros in works since It is a leading business group operating in the environmental sector in Portugal, whose mission is to contribute to the pursuit of public policy and national objectives in the above areas within a framework of economic, financial, technical, social and environmental sustainability. 3

4 The 2 regional water utilities of the AdP Águas de Portugal Group, in partnership with municipalities, serve about 8% of the Portuguese population (more than 23 municipalities from a total of 38) and operate 247 water treatment plants and 899 wastewater treatment plants and all associated infrastructures. The sample of the case study derived from 221 construction contracts from 16 Portuguese water utilities, resulting in a total of 754 assets analysed (635 excluding the found outliers of water transmission mains). Figure 1 shows the location of the AdP Águas de Portugal Group s water utilities in continental Portugal whose real data have been used. Table 2 presents a summary of the sample, which permits the conclusion that the case study is representative of the Portuguese situation. Water supply systems Wastewater systems Water supply and wastewater systems Figure 1 Location of the AdP Águas de Portugal Group s water utilities in continental Portugal whose real data have been used (in pink, North region; in green, Central region; in blue, South region) Table 2 Sample characterization of the case study Asset Ground-level water storage tanks Ground-level water storage tanks associated with pumping stations Elevated water storage tanks Number of water utilities per region North: 5 Central: 3 South: 3 (Total = 11) North: 3 Central: 3 South: 1 (Total = 7) Central: 1 South: 2 (Total = 3) Number of construction contracts Construction contracts date 25 to 211, , 26, 28, 29 25, 28, 211, 213 Number of assets per region North: 64 Central: 13 South: 6 (Total = 83) North: 11 Central: 6 South: 4 (Total = 21) Central: 2 South: 4 (Total = 6) General characteristics of the asset Total volume: 4 to 15 m 3 Total volume: 5 to 6 m 3 Flow capacity: 1,3 to 224, L/s Pumping head: 15, to 229, w.c. m Installed electrical power:,94 to 175,18 kw Total volume: 1 to 5 m 3 Tank height: 14,1 to 27, m 4

5 Asset Water pumping or booster stations Ductile iron Number of water utilities per region North: 3 Central: 1 South: 1 (Total = 5) North: 4 Central: 4 South: 1 (Total = 9) Number of construction contracts Construction contracts date to to 211 Number of assets per region North: 18 Central: 1 South: 1 (Total = 2) North: 144 Central: 21 South: 2 (Total = 167) General characteristics of the asset Flow capacity:,59 to 496, L/s Pumping head: 3, to 174, w.c. m Installed electrical power:,28 to 941,18 kw Nominal diameter: 6 to 7 mm Length: 85, to 17 32,33 m Water transmission mains (outliers not included) HDPE NP1 HDPE NP16 Steel Wastewater pumping stations North: 2 Central: 2 South:1 (Total = 5) North: 3 (Total = 3) North: 1 Central: 1 (Total = 2) North: 4 Central: 6 South: 2 (Total = 12) to 26, 28 to to 27, and to 211 North: 22 Central: 3 South: 2 (Total = 27) North: 18 (Total = 18) North: 2 Central: 4 (Total = 6) North: 164 Central: 15 South: 18 (Total = 287) Nominal diameter: 63 to 2 mm Length: 86,1 to 6 198, m Nominal diameter: 63 to 2 mm Length: 61,3 to 4 995,6 m Nominal diameter: 6 to 9 mm Length: 53,3 to 17 26,98 m Flow capacity: 3, to 1 329, L/s Pumping head: 4,1 to 83, w.c. m Installed electrical power:,61 to 7,41 kw METHODOLOGY All the data of the case study were collected and treated, applying a methodology which includes four distinct steps and a total of 15 tasks, as follows. Step 1: Collection and data processing The first task of step 1 was the selection of construction contracts. AdP Águas de Portugal Group stores all its construction contracts in a SAP application (an Enterprise Resource Planning system), as price lists. With the help of Águas de Portugal Serviços, S.A., the main requirements for construction contracts to be analysed were established: (i) the construction contracts should belong only to the AdP Águas de Portugal Group; (ii) the construction contracts should be located across continental Portugal (divided into North, Central and South regions); (iii) the works should have been awarded as public sector contracts; (iv) the construction contracts should comprise a single asset or several types of assets with separate and detailed construction costs to each asset; (v) the construction contracts should refer to the construction of brand new assets, not refurbishment or improvement of existing assets; (vi) the construction contracts date should have been between 25 and 212 (after this decision, one construction contract from 213 was also included); (vii) the chosen price list is that from the construction firm to whom the contract was awarded; (viii) the construction costs taken from the price lists are the contract award costs and do not include VAT. This method led to 415 preliminary price lists available in Microsoft Excel format. In order to develop databases for each asset, and through a carefully analysis, the number of price lists was reduced to 221. The second task referred to development of a database for each type of asset, recorded in files in Microsoft Excel format containing the components summarized in Table 3. When the necessary components weren t described in the price lists, clarifications were requested from the water utilities, equipment suppliers or catalogs were consulted, or hydraulics or regulatory formulas were applied. 5

6 Information source Construction contract characterization Water utility name and file name Table 3 Components of the database General items Contracting water utility name, order number, name of construction contract, construction contract date, country region, construction contract value, cost of construction site Specific items Asset Asset characterization Construction cost item Ground-level water storage tanks Ground-level water storage tanks associated with pumping stations Elevated water storage tanks Water pumping or booster stations Water transmission mains Wastewater pumping stations Storage tank: total volume, number of cells, tank height (only for elevated water storage tanks), foundation soil and water treatment type Pumping station: flow capacity, pumping head, pumps hydraulic power, pumps efficiency, pumps motor s efficiency, installed electrical power, number of pumps (includes the reserve pump), pumps installation (series or parallel), existence of variable speed motors and foundation soil Flow regime (gravity or pressure), pipe material, nominal pressure, nominal diameter and outside diameter, length, pavement type, pavement area, pavement width, foundation soil, volume of excavation, trench width, mean excavation depth, mean earth cover and groundwater level As for water pumping or booster stations Earthworks Foundation works and structural works Architectural and building works and finishes Landscaping Equipment Water treatment facilities (only for storage tanks) Electrical facilities Total Pavement removal and replacement Earthworks Pipe works Pipe fittings, control and safety devices and thrust blocks Special works Electrical facilities and remote control systems Total As for water pumping or booster stations The compiled databases comprised a total of items, divided into general items and specific items. It is believed that databases are very complete, reliable, flexible, innovative and adequately represent the variables that influence the construction cost of each asset. As such, in the future, through the introduction of new records, these databases can be expanded and promote various types of analysis in order to refine the construction cost functions now developed. The last task of step 1 was sample characterization as presented in Table 2. Step 2: Analysis of construction cost for each asset type The first task of step 2 was the calculation of factors to update costs for inflation, namely the cumulative inflation factors. The inflation rate for the costs of construction of assets in the public sector varies every year. PORDATA, a contemporary Portuguese database, provides statistical data on various sectors (e.g., social, economics, environmental, etc.) for the Portuguese regions and municipalities, Portugal and the 27 countries of the European Union expressed as indicators. Figure 2 presents the evolution of the inflation rate and cumulative inflation factor between 199 and 214, considering the public consumption deflator values indicated on the PORDATA website 1. 1 See website 6

7 Cumulative inflation factor 4% 35% 3% 25% 2% 15% 1% 5% % % 1% % -1% -2% -3% -4% -5% -6% Inflation rate Year Figure 2 Evolution of the inflation rate and cumulative inflation factor between 199 and 214, considering the public consumption deflator values indicated on the PORDATA website The second task was the calculation of the present cost (year 214) for each construction cost item presented in Table 3 (construction contracts referred to the years 25 to 213) using the cumulative inflation factors. Before this, the costs of construction site (usually considered to be 5% of the total works cost) were distributed proportionally between the cost items. The present cost (year 214) was calculated using the following equation (ISO : 28): 1 in which PC present cost (year 214); IC - cost in the year of opening the works to tender; t i inflation rate in the year of opening the works to tender; n number of years between the year of opening the works to tender and 214 and IF -n cumulative inflation factor in the year of opening the works to tender. The third task was the evaluation of generic cost indicators (for each speciality or category: construction cost, percentage of total cost and unit construction cost). Step 3: Derivation of construction cost functions for each asset type The first task of step 3 was the analysis and adjustment of the key parameters for each type of asset, which was an iterative process, based on the key parameters of the previous cost functions for construction of water services assets in Portugal (Table 1) and on the sample construction costs analysis. The second task was statistical analysis with regression models (using Microsoft Excel regression tools), whose selection depended on the type of variables to be analysed. The dependent variable is the construction cost for each category, while the independent variables are the key parameters of each asset. In order to measure the quality of fit of the mathematical equation to the sample, a few correlation factors were calculated: Pearson correlation coefficient, coefficient of determination, adjusted coefficient of determination and p-value. For water transmission mains, a simplified outlier analysis was carried out. The third task was the construction cost function formulation. The fourth task was sensitivity analysis, including: (i) the effect of varying the construction cost in a given category on the total cost (for all assets); (ii) the number of cells as a key parameter in the cost of ground-level water storage tanks; (iii) the derivation of construction cost functions considering the country divided into three regions (for ground-level storage water tanks and wastewater pumping stations). Step 4: Analysis and discussion of the developed construction cost functions The developed construction cost functions were analysed and discussed using five distinct analyses. The first task was to compare the developed construction cost functions for each type of asset with the previous cost functions for construction of water services assets in Portugal. Note that these cost functions were updated to the year 214 using the cumulative inflation factors previously calculated in step 2. 7

8 The second task was the comparison of the construction costs estimated by the developed functions with the real costs in terms of the percentage difference between them. In the third task, it was checked how to estimate construction costs for ground-level water storage tanks associated with pumping stations by combining the developed functions for ground-level water storage tanks with the functions of water pumping or booster stations. The fourth task was the estimation of construction costs by the developed cost functions for some design examples. The last task comprised the estimation of construction costs by the developed cost functions for some assets already constructed by other Portuguese water utilities. DEVELOPED CONSTRUCTION COST FUNCTIONS Ground-level water storage tanks The construction cost items for ground-level water storage tanks listed in Table 3 were grouped in three main categories: civil engineering construction cost (including earthworks, foundation works and structural works, architectural and building works and finishes, and landscaping), equipment and electrical facilities cost (including equipment, water treatment facilities and electrical facilities) and total construction cost (civil engineering construction plus equipment and electrical facilities costs). The problem was approached using the total volume as a key parameter and a power regression model for all cost categories. The developed construction cost functions for ground-level water storage tanks are depicted in Figure 3. Cost, C ( /m 3 ) (214) C CE = 437,6 V -,49 R² =,6568 C T = V -,51 R² =,7447 Civil engineering construction -CE Equipment and electrical facilities - EQ+EF Total - T C EQ+EF = V -,728 R² =, Total volume, V (m 3 ) Figure 3 Developed construction cost functions for ground-level water storage tanks (civil engineering construction cost, equipment and electrical facilities cost and total construction cost) The first sensitivity analysis showed that, on average, civil engineering construction and equipment and electrical facilities represent about 68% and 32% of the total construction cost for a total volume in the interval [4; 3 [ m 3. For a total volume in the interval [3 ; 15 ] m 3, civil engineering construction is about 81% of the total construction cost and equipment and electrical facilities constitute the remaining 19%. By the second sensitivity analysis it was concluded that for the same total volume (15 to 2 m 3 ), a groundlevel water storage tank with two cells is more expensive than one with only one cell. A third sensitivity analysis allowed concluding that a ground-level water storage is more expensive if located in the North region and is cheaper if in the South for a total volume in the interval [15; 1 [ m 3. For a total volume in the interval [1 ; 2 ] m 3, a ground-level water storage is more expensive if located in the South and is cheaper if in the Central region. 8

9 Elevated water storage tanks The construction cost items for elevated water storage tanks listed in Table 3 were grouped in the same three main cost categories as ground-level water storage tanks. The problem was first approached considering the total volume as a key parameter. However, an elevated water storage tank with 15 m 3 and a tank height of 22, m is more expensive than one with 2 m 3 and 15,5 m, so the tank height is also a key parameter and the first approach was abandoned. For the second approach, it was considered that the total volume and the tank height have influence on the civil engineering construction cost (because it requires special construction techniques), but the equipment and electrical facilities cost are only influenced by the total volume (because the equipment design does not depend on the tank height). Multiple linear and a simple linear regression models were applied for civil engineering construction and equipment and electrical facilities costs. The developed construction cost functions for elevated water storage tanks are depicted in Figure 4. Cost, C ( ) (214) (a) Sample h = 25, m Civil engineering construction - CE C CE = 36,8 V h = 14,1 m h = 22, m h = 15,5 m h = 15, m h = 2, m C CE = 36,8 V C CE = 36,8 V ,44 h ,27 h = 14,1 m R 2 =,9695 h = 15, m C CE = 36,8 V Total volume, V (m 3 ) h = 27, m Cost, C ( ) (214) (b) C EQ+EF = 195,84 V R² =, Total volume, V (m 3 ) Equipment and electrical facilities - EQ+EF Figure 4 Developed construction cost functions for elevated water storage tanks: (a) civil engineering construction cost; (b) equipment and electrical facilities cost Sensitivity analysis showed that, on average, the civil engineering construction represents about 78% of the total construction cost for a total volume x tank height equal or lower than 13 5 m 3 x m. The equipment and electrical facilities represent about 22% of the total construction cost for a total volume in the interval [1; 5] m 3. Water pumping or booster stations Water pumping and booster stations were analysed together because the nature of the construction costs is the same. Both are installed in independent buildings, all the pumps have the same characteristics (flow capacity, pumping head, hydraulic power, efficiency in a parallel installation) and the installed electrical power does not include the reserve pump. The construction cost items for water pumping or booster stations listed in Table 3 were grouped in three main cost categories: civil engineering construction cost (including earthworks, foundation works and structural works, architectural and building works and finishes, and landscaping), equipment and electrical facilities and total construction cost (civil engineering construction plus equipment and electrical facilities costs). The key parameters of water pumping and booster stations are the flow capacity, the pumping head and the installed electrical power, so it is important to determine the best combination of these parameters in order to derive the appropriate construction cost functions. The problem was first approached considering the installed electrical power as a key parameter and using a power regression model for all categories. Notice that the flow capacity and the pumping head affect the installed electrical power value. However, it is well known that the size of the pumps, the nominal diameter of the pipes, accessories, valves, measure equipments and the size of the building depend more on flow capacity than on pumping head, and do not depend on efficiency (Marchionni et al., 214b). As such, Marchionni et al. (214b) studied the following 9

10 hypothesis: the key parameters for costs of civil engineering construction and equipment are the flow capacity and the pumping head while the installed electrical power is the only key parameter for the cost of electrical facilities. Results of the statistical analysis have shown that the pumping head is not statistically significant. Therefore, the second approach considered that the flow capacity is the only key parameter for costs of civil engineering construction and equipment, while the installed electrical power alone determines the cost of electrical facilities. Once again, note that the flow capacity and the pumping head affect the installed electrical power value. In this approach the construction cost items were regrouped in three categories: civil engineering construction cost (including earthworks, foundation works and structural works, architectural and building works and finishes, and landscaping), equipment and electrical facilities. A power regression model was selected for each category. The construction cost functions for water pumping or booster stations are depicted in Figure 5. Cost, C ( /L/s) (214) (a) C CE = 1457 Q -,528 R² =,7631 C EQ = 9886,5 Q -,394 R² =,6339 Civil engineering construction - CE Equipment - EQ Flow capacity, Q (L/s) Cost, C ( /kw) (214) C EF = P -,7 R² =,7927 (b) Installed electrical power, P (kw) Electrical facilities - EF Figure 5 Construction cost functions for water pumping or booster stations: (a) civil engineering construction cost and equipment cost; (b) electrical facilities cost Sensitivity analysis showed that, on average, civil engineering construction and equipment represent, respectively, about 34% and 3% of the total construction cost for a flow capacity in the interval [,59; 496,] L/s. Electrical facilities represent about 36% of the total construction cost for an installed electrical power in the interval [,28; 941,48] kw. Water transmission mains The construction cost items for water transmission mains listed in Table 3 were grouped together in a single category named total construction cost (including pavement removal and replacement; earthworks; pipe works; pipe fittings, control and safety devices and thrust blocks; special works; electrical facilities and remote control systems). Note that the pipe material of the water transmission mains is an intrinsic key parameter, as is the length, since it is needed to calculate the total construction cost from the unit construction cost per meter. The problem was first approached using the nominal diameter as a key parameter and a polynomial regression model for ductile iron, a simple linear regression model for HDPE (NP1 and NP16) and a power regression model for steel. The total construction cost varied greatly for the same nominal diameter, leading to weak correlations. Three further approaches were then attempted, using a multiple linear regression model for all pipe materials and considering the following key parameters: nominal diameter and length in the second approach, nominal diameter and mean earth cover in the third approach and nominal diameter, length and mean earth cover in the fourth. It was concluded that there were no standard key parameters for all pipe materials, and the correlation factors were not good. 1

11 The fifth approach to the problem used a simplified outlier analysis, per nominal diameter of each pipe material, assuming an outlier if one or more of the following criteria were met: (i) construction contract under 5 ; (ii) the unit cost per meter of a construction cost item or category greater than five times the mean cost per meter of the same; (iii) pipe fittings, control and safety devices and thrust blocks and/or special works cost greater than 4% of the total construction cost; (iv) total construction cost per meter negatively influenced the overall statistical behavior of the phenomenon under analysis. The outliers were excluded from the original sample (45 from ductile iron, 46 from HDPE NP1, 25 from HDPE NP16 and three from steel). In this approach, a polynomial regression model was used for ductile iron, HDPE NP1 and HDPE NP16, while a power regression model was used for steel pipes. Although the correlations are good for ductile iron and steel, and quite acceptable for HDPE NP1 and HDPE NP16, careful use of the developed cost functions is recommended. The developed construction cost functions for water transmission mains are depicted in Figure 6. Cost, C ( /m) (214) Total - T (a) C T =,11 ND 2 -,1687 ND + 72,343 R² =,8324 DI Cost, C ( /m) (214) Total - T (b) C T =,15 ND 2 -,172 ND + 33,382 R² =,5141 HDPE NP ND (mm) ND (mm) Cost, C ( /m) (214) Total - T (c) C T = -,1 ND 2 +,2613 ND + 12,86 R² =,634 HDPE NP16 Cost, C ( /m) (214) Total - T (d) C T = 2 x 1-5 ND 2,4897 R² =,7935 ST ND (mm) ND (mm) Figure 6 Developed construction cost functions for water transmission mains (total construction cost): (a) DI - ductile iron; (b) HDPE NP1; (c) HDPE NP16; (d) ST - steel An additional trial was then carried out using the nominal diameter and length as key parameters and a multiple linear regression model for all the pipe materials, but its results did not show significant improvements in correlation factors. Sensitivity analysis showed that, generally: (i) the fraction of total construction cost due to pavement removal and replacement, earthworks or pipe works is very variable; (ii) pipe fittings, control and safety devices and thrust blocks make up about 2% of the total construction cost; (iii) although special works sometimes contribute significantly to the total construction cost, on average it corresponds to about 3%; (iv) electrical facilities and remote control systems contribute little to the total construction cost. Wastewater pumping stations The construction cost items for wastewater pumping stations listed in Table 3 were grouped in the same three main cost categories as water pumping or booster stations. Note that all the pumps have the same characteristics (flow capacity, pumping head, hydraulic power, efficiency in a parallel installation) and the installed electrical power does not include the reserve pump. 11

12 The key parameters of wastewater pumping stations are also are the flow capacity, the pumping head and the installed electrical power, so it is important to determine the best combination of these parameters in order to derive the appropriate construction cost functions. At first, the problem was approached considering the installed electrical power as a key parameter and using a power regression model for all categories. Notice that the flow capacity and the pumping head affect the installed electrical power value. Similarly to water pumping or booster stations, it is well known that the size of the pumps, the nominal diameter of the pipes, accessories, valves, floodgates, measure equipments, pre-treatment equipments and the size of the building depend more on flow capacity than on pumping head, and do not depend on efficiency. As such, it was extrapolated the conclusion of Marchionni et al. (214b) that the pumping head is not statistically significant also for wastewater pumping stations. Therefore, the second approach considered that the flow capacity is the only key parameter for costs of civil engineering construction and equipment, while the installed electrical power alone determines the cost of electrical facilities. Once again, note that the flow capacity and the pumping head affect the installed electrical power value. In this approach the construction cost items were regrouped in three categories: civil engineering construction cost (including earthworks, foundation works and structural works, architectural and building works and finishes, and landscaping), equipment and electrical facilities. A power regression model was selected for each category. The developed construction cost functions for wastewater pumping stations are depicted in Figure 7. Cost, C ( /L/s) C CE = 9664,4 Q -,39 R² =,4864 (a) C EQ = 8169,7 Q -,359 R² =, Flow capacity, Q(L/s) Civil engineering construction - CE Equipment - EQ Cost, C ( /kw) (b) C EF = P -,55 R² =,548 Electrical facilities - EF Installed electrical power, P (kw) Figure 7 Developed construction cost functions for wastewater pumping stations: (a) civil engineering construction cost and equipment cost; (b) electrical facilities cost The first sensitivity analysis showed that, on average, civil engineering construction and equipment represent, respectively, about 39% and 37% of the total construction cost for a flow capacity in the interval [3,; 1 329,] L/s. Electrical facilities represent about 24% of the total construction cost for an installed electrical power in the interval [,61; 7,41] kw. A second sensitivity analysis concluded that the civil engineering construction is more expensive than the equipment in the North region, while the opposite case holds in the other regions. The civil engineering construction is most expensive in the Central region and the cheapest in the North for a flow capacity in the interval [3,48; 81,] L/s. The equipment cost is highest in the Central region and cheapest in the North for a flow capacity in the interval [3,48; 3,] L/s. In the flow capacity interval [3,; 81,] L/s, the equipment is most expensive in the Central region and the cheapest in the South. Finally, the electrical facilities are most expensive in the South region and the cheapest in the North for the installed electrical power interval [,74; 329,23] kw. 12

13 Summary of the developed construction cost functions Table 4 presents a summary of the developed construction cost functions for each asset. Asset Cost function (in 214) Ground-level water storage tanks Elevated water storage tanks Water pumping or booster stations Water transmission mains Wastewater pumping stations Table 4 Developed construction cost functions for each asset 437,6, (R 2 =,6568) 13698, (R 2 =,7416) 11448, (R 2 =,7447) 36, , ,27 (R 2 =,9695) 195, (R 2 =,8827) 1457, (R 2 =,7631) 9886,5, (R 2 =,6339) 22777, (R 2 =,7927),11, ,343 (R 2 =,8324),15,172 33,382 (R 2 =,5141),1, ,86 (R 2 =,634) 2 1, (R 2 =,7935) 9664,4, (R 2 =,4864) 8169,7, (R 2 =,5135) 11574, (R 2 =,548) Key parameter V: total volume (m 3 ) V: total volume (m 3 ) h: tank height (m) Q: flow capacity (L/s) H: pumping head (w.c. m) P: installed electrical power (kw) ND: nominal diameter (mm) L: length (m) Q: flow capacity (L/s) H: pumping head (w.c. m) P: installed electrical power (kw) Applicable scope of key parameter Monetary unit V = [4; 15 ] /m 3 V = [1; 5] h = [14,1; 27,] Q = [,59; 496,] H = [3,; 174,] P= [,28; 941,18] D = [6; 9] L = [53,3; 17 26,98] D = [6; 7] L = [85,; 17 32,33] D = [63; 2] L = [86,1; 6 198,] D = [63; 2] L = [61,3; 4 995,6] Q = [3,; 1 329,] H = [4,1; 83,] P= [,61; 7,41] Note: Cost functions: C CE: civil engineering construction cost; C EQ+EF: equipment and electrical facilities cost; C T: total cost; C EQ: equipment cost; C EF: electrical facilities cost; C i: total cost per pipe material (i = DI: ductile iron; HDPE PN1: high-density polyethylene with a nominal pressure of 1; HDPE PN16: high-density polyethylene with a nominal pressure of 16; ST: steel). ANALYSIS AND DISCUSSION OF THE DEVELOPED CONSTRUCTION COST FUNCTIONS Comparison of developed construction cost functions with previous cost functions for construction of water services assets in Portugal Figure 8a presents a graphical comparison of the function derived for total construction cost of ground-level water storage tanks with previously published cost functions for construction of water services assets in Portugal. Figure 8b presents the graphical comparison of total construction costs of a few examples of elevated water storage tanks (total volume from 1 to 5 m 3 for a tank height of 2, m) estimated using three different cost functions, since the cost functions themselves were not graphically comparable. /L/s /kw /m /L/s /kw 13

14 Cost, C ( /m 3 ) (214) Águas de Portugal Serviços, S.A. (25) C T = 1889 V -,6 r =,92 (a) AdP - Águas de Portugal, SGPS, S.A. (28) C T = 5939,3 V -,389 R² =,978 Developed function (214) C T = V -,51 R² =,7447 Lencastre et al. (1995) C T = 428,56 V -,197 R² =, Total volume, V (m 3 ) Sample Cost ( ) (214) (b) Developed function (214) Lencastre et al. (1995) AdP - Águas de Portugal, SGPS, S.A. (28) Total volume (m 3 ) Figure 8 (a) Comparison of the function derived for total construction cost of ground-level water storage tanks with previously published cost functions for construction of water services assets in Portugal; (b) Comparison of total construction costs of a few examples of elevated water storage tanks estimated using three different cost functions In the case of ground-level water storage tanks, it can be observed that the developed construction cost function: (i) is far superior to that of Lencastre et al. (1995), because those authors did not include the landscaping and electrical facilities and nowadays water utilities tend to install much more equipment than in the past; (ii) is quite similar to those from both AdP studies (25 and 28), although the temporal universe of data and the range of the samples are different, and Águas de Portugal Serviços, S.A. (25) study did not considerer any updated process costs. For elevated water storage tanks it can be observed that the total construction costs estimated by the developed function (214): (i) are far superior to those obtained by Lencastre et al. (1995), for same reasons as above; (ii) are also far superior to those obtained by AdP Águas de Portugal, SGPS, S.A. (28), although this study did not explain the costs methodology. Table 5 compares total construction costs for water pumping or booster stations and wastewater pumping stations estimated for design examples using four different cost functions (since the cost functions themselves were not graphically comparable), and the total construction cost estimated at the design phase. Table 5 Comparison between total construction costs for water pumping or booster stations and wastewater pumping stations estimated for design examples using four different cost functions and those estimated at the design phase Total construction cost estimated by formulae Asset Water pumping or booster stations Wastewater pumping stations Characteristics of the asset Flow capacity: 1,44 L/s Pumping head: 64,1 w.c. m Installed electrical power: 33,12 kw Flow capacity: 78, L/s Pumping head: 11,9 w.c. m Installed electrical power: 47,65 kw Total construction cost estimated at the design phase Developed function (214) Lencastre et al. (1995) Águas de Portugal Serviços, S.A. (25) AdP Águas de Portugal, SGPS, S.A. (28) 124 9, , , , , , , , ,88 Not applicable In the case of water pumping and booster stations, it can be observed that the total construction cost estimated by the developed function (214): (i) is far superior to that estimated according to Lencastre et al. (1995), because the latter authors did not include the landscaping and electrical facilities and nowadays water utilities tend to install much more equipment than in the past; (ii) is inferior to that estimated by Águas de Portugal Serviços, S.A. (25) for unknown reasons; (iii) is far superior to that estimated by AdP Águas de Portugal, SGPS, S.A. 14

15 (28), probably due to the very specific costs methodology used in this study, or because the pumping head of the design example is outside the applicable scope of the key parameter (note that pumping head is unknown). For wastewater pumping stations it can be observed that the total construction cost estimated by the developed function (214): (i) the total construction cost estimated by the developed function (214) is far superior to that by Lencastre et al. (1995), for same reasons as above; (ii) is superior to that estimated by Águas de Portugal Serviços, S.A. (25) for unknown reasons; (iii) is not comparable with that from AdP Águas de Portugal, SGPS, S.A. (28), because the latter cost function is not applicable to the characteristics of this design example. Figure 9 compares the function derived for total construction cost of water transmission mains with previously published cost functions for construction of water services assets in Portugal (Figure 9a for ductile iron, Figure 9b for HDPE NP1, Figure 9c for HDPE NP16 and Figure 9d for steel). Cost, C ( /m) (214) Cost, C ( /m) (214) Sample Lencastre et al. (1995) (a) C T =,14 ND 2 -,2195 ND + 113,3 R² =,98 AdP - Águas de Portugal, SGPS, S.A. (28) Developed function (214) C T =,11 ND 2 -,1687 ND + 72,343 R² =, C T =,6 ND 2 +,1522 ND + 75,837 R² =,997 Águas de Portugal Serviços, S.A. (25) 2 1 C T = 1,3654 ND,7495 r =, Sample AdP - Águas de Portugal, SGPS, S.A. (28) C T =,15 ND 2 -,17 ND + 46,2 R² =,9993 (c) ND (mm) Águas de Portugal Serviços, S.A. (25) C T =,1953 ND + 2,6942 r =,85 Developed function (214) C T = -,1 ND 2 +,2613 ND + 12,86 R² =,634 DI HDPE NP ND (mm) Cost, C ( /m) (214) Cost, C ( /m) (214) Sample (b) 5 Developed function (214) C T =,15 ND 2 -,172 ND + 33,382 R² =, ND (mm) (d) HDPE NP1 Águas de Portugal Lencastre et al. (1995) Serviços, S.A. (25) C T =,24 ND 2 +,1299 ND + 22,95 R² = 1 AdP - Águas de Portugal, SGPS, C T =,2118 ND + 3,3248 r =,83 S.A. (28) C T =,9 ND 2 -,564 ND + 43,88 R² =,9983 Sample AdP - Águas de Portugal, SGPS, S.A. (28) C T =,8 ND 2 +,1497 ND + 73,668 R² =,9992 Developed function (214) C T = 2 x 1-5 ND 2,4897 R² =, ND (mm) ST Figure 9 Comparison of the function derived for total construction cost of water transmission mains with previously published cost functions for construction of water services assets in Portugal: (a) DI - ductile iron; (b) HDPE NP1; (c) HDPE NP16; (d) ST - steel In the case of water transmission mains, it can be observed that: (i) the developed construction cost functions for ductile iron and HDPE NP1 are inferior to those of Lencastre et al. (1995), due to the very specific costs methodology used by those authors; (ii) the developed construction cost functions for ductile iron, HDPE NP1 and HDPE NP16 give higher results than those of Águas de Portugal Serviços, S.A. (25), probably because the latter study did not consider any updated process costs; (iii) the developed construction cost functions for ductile iron, HDPE NP1, HDPE NP16 and steel are inferior to those of AdP Águas de Portugal, SGPS, S.A. (28), probably due to the very specific costs methodology used by the latter study. Comparison of the construction costs estimated by the developed functions with real construction costs For each asset of the sample, the total construction costs were estimated through the developed cost functions presented in Table 4. These costs were then compared with real total construction costs through the percentage difference between them (Table 6). 15

16 Table 6 Comparison of the total construction costs estimated by the developed functions with real total construction costs Asset Percentage difference Maximum Minimum Average Ground-level water storage tanks 13% -62% 4% Elevated water storage tanks 22% -21% 5% Water pumping or booster stations 2% -68% 7% Water transmission mains Ductile iron 159% -59% 11% HDPE NP1 111% -37% 1% HDPE NP16 61% -37% 6% Steel 38% -25% -5% Wastewater pumping stations 266% 12% 156% On average, the total construction costs estimated by the developed functions are similar to real total construction costs, except for wastewater pumping stations, which had a weak coefficient of determination. However, in certain cases the maximum or minimum deviations are very significant. Estimation of construction costs by the developed functions for ground-level water storage tanks associated with pumping stations The problem of how to estimate the total construction cost of ground-level water storage tanks associated with pumping stations was approached in two ways: (i) approach A as a sum of the developed construction cost functions of the ground-level water storage tanks (civil engineering construction cost, equipment and electrical facilities cost) and of water pumping or booster stations (civil engineering construction cost, equipment cost, electrical facilities cost); (ii) approach B as the civil engineering construction cost function developed for groundlevel water storage tanks plus the equipment and electrical facilities construction cost functions developed for water pumping or booster stations. Results are shown in Figure 1 and Table 7. Cost ( ) (214) Real total construction cost Total construction cost estimated by approach A Total construction cost estimated by approach B ID Ground-level Ground-level Water pumping station Water pumping station water storage tank water storage tank Installed Installed ID Total Flow Pumping ID Total Flow Pumping electrical electrical volume capacity head volume capacity head power power (m 3 ) (L/s) (w.c. m) (kw) (m 3 ) (L/s) (w.c. m) (kw) 1 5 1,3 88, 1, ,2 31,3 1, ,7 13, 12, ,8 4, 4, ,5 27, 1, ,9 22, 3, ,78 93, 11, ,2 19, 27, ,78 212,8 25, ,3 88, 5, ,33 229, 133, , 5,4 37, ,56 19, 26, ,48 74, 1, ,2 77,77 5, ,5 21, 6, ,6 48,85 6, , 15, 45, ,65 51, 6, ,88 115,6 11, , 55, 25,3 Figure 1 Comparison of two approaches for estimating the total construction costs by the developed functions for ground-level water storage tanks associated with pumping stations Table 7 Comparison of the total construction costs estimated by the developed functions with real total construction costs for ground-level water storage tanks associated with pumping stations Percentage difference Approach Maximum Minimum Average A 19% -21% 51% B 37% -43% 1% On average, results from approach A exceed the real total construction costs, which is logical because the separate construction cost functions consider duplicate works. This does not correspond to the reality in which the equipment of a water pumping station is installed in the pump house of the tank. The total construction costs estimated by approach B are similar to real total construction costs, so this method should be adopted in future for new assets. 16