A Preliminary Cost Estimation for Short Tunnels Construction Using Parametric Method

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1 A Preliminary Cost Estimation for Short Tunnels Construction Using Parametric Method 88 Ahmad Reza Sayadi, Jafar Khademi Hamidi, Masoud Monjezi and Meysam Najafzadeh Abstract Cost estimation is one of the most critical tasks in pre-feasibility studies and planning of tunnel construction projects. This paper presented a cost estimation model for excavation and support of short tunnels using uni-variate (UVR) and multi-variate regression (MVR) techniques. Hence, a database consisting of two explanatory variables including RMR and tunnel depth along with tunnel support and excavation costs was compiled from 12 tunnel sections in the North-West of Iran. Mean absolute error rates of 13 and 11 %, respectively obtained from UVR and MVR analyses provide promising initial results of relation between rock mass characterization and construction costs in the phase of pre-feasibility study. However, an extended database is required to extend the finding of this study to develop a universal model. Keywords Short tunnels Cost estimation Regression analysis Drilling and blasting 88.1 Introduction Rock tunnels as the most appropriate underground structures for traffic works in mountainous areas are generally constructed by using two conventional (drilling and blasting) and mechanized excavation methods. Feasibility studies, design and selection of tunneling method and finally project completion are a function of several factors but above all, of construction costs. Several models have been developed in this field. One of the first systematic studies is that of California department of water resources in which the diameter and geological conditions of the tunnel are used as cost effective parameters (Lamb 1971). This model presented in A.R. Sayadi (&) J.K. Hamidi M. Monjezi Academic Member, Tarbiat Modares University, Tehran, Iran sayadi@modares.ac.ir M. Najafzadeh Msc Student, Tarbiat Modares University, Tehran, Iran 1961 is only applicable to limited areas of the United States and only for water transfer tunnels which are constructed by conventional method. In 1971, a computer model was developed based on previous models (Bledsoe 1970). In 1976, a tunnel cost model (TCM), as a computer simulation system for estimating the cost and time of building stone tunnels was proposed (Moavenzadeh and Markow 1976). In 1999, a time and cost estimation model was developed for both mechanized and conventional methods on the basis of construction data of 250 km of road tunnels in Norway and some other countries (Bruland 2000). In another study in 2006, a model was presented on the basis of 149 cases of 23 sections of 42 km of dug tunnels in Greece between 1988 and 2004 (Petroutsatou et al. 2006). Another cost estimation model of urban subway system in Turkey was presented in 2009 (Sonmez and Ontepeli 2009). Gunduz et al. (2011) estimated the costs of light rail transport systems (LRT) and metro using parametric method. Most recently, Rostami et al. (2013) estimated the costs of tunneling based on multivariate G. Lollino et al. (eds.), Engineering Geology for Society and Territory Volume 1, DOI: / _88, Ó Springer International Publishing Switzerland

2 462 A.R. Sayadi et al. Table 88.1 Descriptive statistics of gathered data Overburden height (m) Length (m) RMR Excavation unit cost Rock support unit cost Total unit costs Minimum Mean Maximum Standard deviation statistical analysis of data from 272 tunneling projects in the U.S. and Canada. The effective factors on tunnel cost depending on the type of tunnel and circumstances may be classified as follows: 1. Geomechanical parameters, geology and geological hazards within the tunnel path: compressive and tensile strength of rock material, the height of overburden, rock mass classification systems such as the rock quality index (RQD), rock mass rating (RMR), rock mass quality (Q) and geological strength index (GSI), weathering of rocks, fault areas, groundwater, the percent of abrasive minerals such as quartz, the in situ stress, wall strain and tunnel roof (Bledsoe 1970; Bruland 2000; Petroutsatou et al. 2006); 2. Technical parameters of tunnel: tunnel shape, length and size, cross-section, slope and curve (Lamb, 1971; Moavenzadeh and Markow 1976; Rostami et al. 2013); 3. Economic parameters: methods of financing, exchange rate, inflation rate (Bledsoe, 1970; Rostami et al. 2013); 4. Management parameters: executive experience of managers, human resource skills, support and logistics. In this research, the main purpose is to provide a reliable early cost estimating model for short tunnels which are constructed by drilling and blasting method. This model is developed by using univariate (UVR) and multivariate regression (MVR) techniques Data Structure The dataset consists of 12 records from 12 tunnel sections along the main path of Shahriar dam in Eastern Azerbaijan province of Iran, including tunnel length and depth, RMR value for each section, excavation and support costs. These tunnels have been constructed using conventional drill and blast method. The cross section of each tunnel is horseshoeshaped. The tunnels vary in length from 111 to 540 m. This range of tunnel length is mainly associated with short tunnels. Costs are based on prices of fourth quarter of 2009 in Iranian Rial (IRR) currency. At this period, one US dollar equal to about IRR 10,000. Descriptive statistics of variables in the database and input parameters for generated models is summarized in Table As seen in the Table, the RMR changes from 35 to 61, indicating that the tunnels are mostly excavated in fair rock masses. The height of overburden has a range from 24 to 92 m, showing that the tunnels are shallow Methodology Various methods have been proposed for cost estimation models in construction practices in mining and civil engineering. In the pre-feasibility and feasibility levels, parametric methods are commonly used. In this method, the correlation between actual costs and other system variables which have technical or economic nature have been studied, and one or more cost estimation relationship (CER) has been presented (Evans et al. 2006). Various approaches can be used in this context, but preceding research shows that the regression technique because of strong mathematical basis and ease of use of the obtained cost function, is very common (Mason and Smith 1997; Sayadi et al. 2011, 2012). The structure of the proposed model is dependent on previous experiences in cost modeling as well as statistical considerations of data and the results of validation functions. In this study, a variety of cost functions as indicated in Eq. (88.1), because of its widespread use in the other models of cost estimate, have been evaluated. Here, Y represents the cost and x is the explanatory variable. Y ¼ ax b Y ¼ ae bx Y ¼ ax þ b ð88:1þ The general form of the multivariable regression function is linear polynomial as shown in Eq. (88.2). In this equation, Y and x denote the cost and independent variable, respectively, c 0 is intercept, c 1 to c n are coefficients of each independent variable, and e 0 is residual error. However, other functions including logarithmic and exponential ones used for modeling resulted in unacceptable estimates compared to linear polynomial equation. The statistical software package Statistica Release was used for making multivariate models. Y i ¼ c 0 þ c 1 x 1 þ c 2 x 2 þc n x n þ e i ð88:2þ

3 88 A Preliminary Cost Estimation for Short Tunnels Construction 463 Table 88.2 Specification of univariate regression results Function Y = ax + b Function Y = ax b Function Y = ae bx Support Excavation Support Excavation Support Excavation R RMSE a b To evaluate the overall significance of the model, F-test method, t and p values are applied. In the F-test, the hypothesis of being zero of all regression coefficients is evaluated. Accordingly, significance of each explanatory variable is analyzed with t-test. In the t and F tests, basis is numerical comparisons which are defined in the significance level and considering degrees of freedom, desire regression is obtained from relevant table. But the simplest and fastest way to accept or reject the premise of the studied hypothesis is the p value. For validation of the developed models, two methods have been applied. In first step, each function s performance is measured by the mean absolute error rate (MAER) [18]. In this method, the mean difference between actual and estimated costs is assessed based on a percentage of the actual costs. This value can be calculated using Eq. (88.3) (Kim et al. 2004), in which Ce is the estimated tunnel costs, C a is the actual tunnel costs (from the database) and n is the number of data used in regression model. MAER ¼ P Ce Ca Ca 100 n ð88:3þ In the second method, the suitability of MVR is evaluated using the residual analysis Regression Analysis for Unit Cost Estimation Explanatory Variables Since in planning phase of a tunneling project, access to all parameters affecting the costs is very difficult and sometimes impossible, the parameters with the most influence and easily accessible are selected. These parameters include RMR classification system and the height of overburden. Since all the tunnel sections have similar cross section, the parameter of tunnel diameter was excluded from the independent variables set Univariate Regression Different mathematical functions, as indicated in Eq. (88.1), have been examined by using RMR as the explanatory variable for unit cost estimation of support installation and excavation (Table 88.2). Among all the functions tested, the function in the form of cost = (ae bx ) showed more consistency with the data, given to the high R 2 and low RMSE. Here, constants a and b are obtained by regression analysis. Finally, the relation of tunnel excavation (C EXC ) and support unit costs (C SUP ) with RMR are obtained as given in Eqs. (88.4) and (88.5). Costs are in million IRR per meter of the tunnel length. C EXC ¼ 20:7 e ð0:002rmrþ C SUP ¼ 24:6 e ð 0:006RMRÞ Multivariate Regression ð88:4þ ð88:5þ Tables 88.3 and 88.4 show the results obtained from the MVR in which two independent variables including RMR and overburden height (H) were used for unit cost estimation of tunnel excavation and wall support. Tables include coefficients for each independent variable, intercepts, t- and F-test and p values. As seen in the Tables, in generated equations, low p values and high t- and F-test values under the hypothesis H 0 validate the regression results. Finally, multivariate unit cost functions for tunnel excavation (C EXC ) and wall support (C SUP ) using RMR and overburden height (H) are obtained as Eqs. (88.6) and (88.7), respectively. Costs are in million IRR per meter of the tunnel length. C EXC ¼ 20:577 þ 0:0584RMR 0:0005H C SUP ¼ 32:707 0:119RMR 0:0008H ð88:6þ ð88:7þ

4 464 A.R. Sayadi et al. Table 88.3 Obtained results for tunnel excavation unit cost Coefficient B t-test p-level Total F-test Total p-level Intercept RMR Height of overburden Table 88.4 Results for tunnel support unit cost Coefficient B t-test p-level Total F-test Total p-level Intercept RMR Height of overburden Table 88.5 Mean absolute error rate (in percent) Function Excavation cost Support cost Total costs Y = ax b Y = ae bx Y = ax + b Y = ax 1 + bx Fig Residual analysis for cost model of excavation Model Validation The accuracy of the results obtained from the developed equations were evaluated by the mean absolute error rate (MAER) values as shown in Table It can be noted that this rate for the selected cost function (Y = ae bx (is less than 14 %, meaning that the newly developed formulas have the required estimation validity and capability for tunneling costs. In this study, the model adequacy is also checked through analyzing the residual. The analysis is made to check the distribution of residuals using histogram and normal probability plot as illustrated in Figs and As can be followed from the figures, the residuals have nearly a normal distribution with zero mean, indicating that the developed estimation model is almost unbiased Discussion In previous researches on cost estimation models, the parameter of diameter has been used. However, the tunnels studied in this research have similar cross section and the same diameter, and hence this parameter can be excluded. The tunnel length parameter is another effective parameter. The length of tunnels varied from 111 to 540 m showed a negligible effect on tunnel excavation and support costs. On the contrary, the RMR and overburden height demonstrated strong correlations to tunneling costs, consequently were

5 88 A Preliminary Cost Estimation for Short Tunnels Construction 465 Fig Residual analysis for cost model of support taken into account as explanatory variables. Based on the obtained results, among the three possible univariate functions, the form of Y = ae bx, with a mean absolute error rate of 13 % is better than others for estimation of the tunneling cost. The results showed that the costs of excavation increase with RMR. Also, the cost of tunnel excavation showed a reverse relation with RMR. The reason for this is that, with increasing rock mass quality, the less and lighter support system with less installation expenditure is required. Linear, logarithmic and exponential regression techniques were applied for multivariate modeling and it was concluded that only the linear regression model is significant. Validation of the model using MAER method indicated that the error changed in % provides an acceptable range in pre-feasibility study phase Conclusion The aim of this paper was to provide a reliable cost estimation model for short tunnels which are constructed using conventional method in Iran. For this, both uni- and multivariable regression techniques were implemented because of their mathematical background and their wide applications in cost estimation using RMR and tunnel depth. Low error of provided models which have been tested with respect to mean criteria of absolute error rate and other statistical tools, confirms the adequacy of the results. This model provides the possibility of a fast and acceptable estimation of the excavation as well as support cost of tunnels at the phase of pre-feasibility study in tunnel projects. References Bledsoe JD (1970) The development of a tunnel system model. Massachusetts Institute of Technology, Massachusetts Bruland A (2000) Hard rock tunnel boring advance rate and cutter wear, doctoral thesis. Norwegian institute of technology, Trondheim Evans D, Lanham J, Marsh R (2006) Cost estimation method selection: matching user requirements and knowledge availability to methods. University of the West of England, Bristol Gunduz M, Ugur LO, Ozturk E (2011) Parametric cost estimation system for light rail transit and metro trackworks. Expert Syst Appl 38(3): Kim GH, An SH, Kang KI (2004) Comparison of construction cost estimating models based on regression analysis, neural networks, and case-based reasoning. Build Environ 39: Lamb TJ (1971) A computer model for tunneling costs. Massachusetts Institute of Technology, Massachusetts Mason AK, Smith AE (1997) Cost estimation predictive modeling: regression versus neural network. Eng Eco 42(2): Moavenzadeh F, Markow MJ (1976) Simulation model for tunnel construction costs. J Constr Div ASCE (CO1):51 66 Petroutsatou C, Lambropoulos S, Pantouvakis JP (2006) Road tunnel early cost estimates using multiple regression analysis. Oper Res Int J 6(3): Rostami J, Sepehrmanesh M, Alavi E, Mojtabai N (2013) Planning level tunnel cost estimation based on statistical analysis of historical data. Tunn Undergr Space Technol 33:22 33 Sayadi AR, Lashgari A, Paraszczak JJ (2011) Hard-rock LHD cost estimation using single and multiple regressions based on principal component analysis. Tunn Undergr Space Technol 27: Sayadi AR, Lashgari A, Fouladgar MM, Skibniewski MJ (2012) Estimating capital and operational costs of backhoe shovels. J Civil Eng Manag 18(3): Sonmez R, Ontepeli B (2009) Predesign cost estimation of urban railway projects with parametric modeling. J Civil Eng Manag 15(4):