Probabilistic prediction of expected ground condition and construction time and costs in road tunnels

Probabilistic prediction of expected ground condition and construction time and costs in road tunnels

Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745 Contents lists available at ScienceDirect Journal of Rock Mechanics and Geot...

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Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

Contents lists available at ScienceDirect

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Probabilistic prediction of expected ground condition and construction time and costs in road tunnels A. Mahmoodzadeh, S. Zare* School of Mining, Petroleum and Geophysics Engineering, Shahrood University of Technology, Shahrood, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 December 2015 Received in revised form 29 April 2016 Accepted 8 July 2016 Available online 4 September 2016

Ground condition and construction (excavation and support) time and costs are the key factors in decision-making during planning and design phases of a tunnel project. An innovative methodology for probabilistic estimation of ground condition and construction time and costs is proposed, which is an integration of the ground prediction approach based on Markov process, and the time and cost variance analysis based on Monte-Carlo (MC) simulation. The former provides the probabilistic description of ground classification along tunnel alignment according to the geological information revealed from geological profile and boreholes. The latter provides the probabilistic description of the expected construction time and costs for each operation according to the survey feedbacks from experts. Then an engineering application to Hamro tunnel is presented to demonstrate how the ground condition and the construction time and costs are estimated in a probabilistic way. In most items, in order to estimate the data needed for this methodology, a number of questionnaires are distributed among the tunneling experts and finally the mean values of the respondents are applied. These facilitate both the owners and the contractors to be aware of the risk that they should carry before construction, and are useful for both tendering and bidding. Ó 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Keywords: Markov process Geological condition Monte-Carlo (MC) simulation Construction time and costs Hamro tunnel

1. Introduction Minimizing uncertainties is one of the important issues during project design and planning. Ground condition and construction time and costs can be considered as the most important uncertainties. The construction time and costs are directly connected with the description of ground condition. Accordingly, in subsurface projects, the actual ground condition and construction time and costs are not ascertainable, and hence the probability methods should be used to assess such factors. At present, construction time and costs are commonly assessed on a deterministic basis. The deterministic approach, however, does not appropriately reflect the uncertain reality. Systematic underestimation of construction costs related to infrastructure projects has been documented (e.g. Flyvbjerg, 2004). Major losses and delays in tunnel construction projects have been reported by insurers (e.g. Landrin et al., 2006). The need for analyzing the uncertainty

* Corresponding author. Fax: þ98 233 239 2205. E-mail address: [email protected] (S. Zare). Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.

and risks of tunnel construction has been recognized by the tunneling community (e.g. Lombardi, 2001; Eskesen et al., 2004; Reilly, 2005; ITIG, 2006). The uncertainty in estimations of construction time and costs results from the common variability of construction performance and occurrence of extraordinary events (also denoted here as failure of construction process) such as tunnel collapses (Isaksson and Stille, 2005). Risks resulting from construction failure are commonly analyzed separately using techniques such as fault tree or event tree analysis, decision trees or risk matrices (Benardos and Kaliampakos, 2004; Shahriar et al., 2008; Hong et al., 2009;   Aliahmadi et al., 2011; Jurado et al., 2012). Spa cková (2012) modeled tunnel construction failure by means of a Poisson process. Sousa and Einstein (2012) presented a dynamic Bayesian network (DBN) model, which estimates the expected utility as a sum of expected costs and the risk of tunnel collapse. The full probability distribution of the construction costs, however, was not assessed. Some models allow one to probabilistically estimate the time or costs without taking into account the occurrence of extraordinary events. Typically, Monte-Carlo (MC) simulation was adopted in these models (Chung et al., 2006; Ruwanpura and Ariaratnam, 2007; Min et al., 2008).

http://dx.doi.org/10.1016/j.jrmge.2016.07.001 1674-7755 Ó 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

Full probabilistic estimates of tunnel construction time or costs, taking into account both the common variability and the risk of extraordinary events, were presented in Isaksson and Stille (2005),   Grasso et al. (2006), and Spa cková and Straub (2013). The probabilistic model inputs are mostly based on expert assessments. The description of geotechnical conditions is based on geological investigations, and the estimations of average advance rates and construction costs can be supported by simulations of construction processes and collected data (Burbaum et al., 2006; Kim and Bruland, 2009). However, little information is available on the random variability of construction performance and failure rate. Available studies such as the analysis of tunnel boring machine (TBM) penetration rate (Alvarez Grima et al., 2000; Sapigni et al., 2002; Chung et al., 2006) only capture a part of the uncertainty. Flyvbjerg (2004) presented the first study that quantifies the overall uncertainty in construction cost estimates based on an analysis of data from previous projects. Since only the cost overrun was assessed, the study is helpful for describing the present practice, but the results are not suitable for a probabilistic prediction of construction costs of future projects. The present study was undertaken at Hamro road tunnel with the length of 1310 m and cross-sectional area of 97 m2 as part of SanandajeMarivan road under construction in Iran. In order to estimate the geological conditions, the total tunnel alignment is first divided into several equal parts (cells), each of which is 10 m in length. In order to specify the occurrence probability of parameters (i.e. rock type, rock quality designation (RQD), and groundwater), six cells related to the locations of 4 boreholes and 2 portals (entry and exit), called as “observational cells” were considered. However, in this study, due to the inaccessibility to the data related to the exact locations of boreholes and also because that a length of 200 m relevant to the entry and exit portals of the tunnel has not been excavated initially, all the observations are considered to be nondeterministic. Afterwards, in order to find the occurrence probability of the parameters states in other cells (unknown cells), programming of Markov process was performed with MATLAB (MathWorks, 2013), and other cells were also predicted using observational cells, consequently specifying a profile titled parameter, profile for each parameter which could determine the occurrence probability of each state of parameters inside each cell. Ultimately, by combining different states of parameters, different geological settings for the tunnel alignment were obtained, for which several ground classes (each including the special excavation method and support system) were introduced by 10 experts so that each one of the classes was responsible for a specific number of ground conditions obtained as described above. In the following stage, a profile was obtained by combining parameter profiles which could determine the probability of each ground class inside each cell, nominated as the “ground class”. Because each ground class has different construction time and costs, there is a possibility for the occurrence of different construction time and costs within each section. In the next stage, the construction time and costs of all the cells were added up using MC simulation method in the Primavera risk analysis program. Finally, with the aid of cumulative graph, column graph and scatter diagram, different construction time and costs with specific occurrence probability (uncertainties) were obtained.

735

available, the predictions shall be based on the uncertainty. The PEGC predicts the expected ground condition along the tunnel alignment using primary data including geological maps, geophysical studies, geotechnical studies, etc. Usually the expected conditions along the tunnel cannot be deterministically expressed and thus the statistical methods should be used for probabilistic description of such conditions (Chan, 1981). One of the most important statistical methods used for PEGC is the Markov process which approximates each parameter state considering the previous state. Different stages of PEGC have been briefly introduced as follows: (1) Estimations of transition probability from the state i to the state j (pij) and transition intensity coefficient of the state i (CXi ) of the desired geological parameter using statistical methods according to the following equation (Chan, 1981):

Tij pij ¼ Pn

(1)

k¼1 Tik

where Tij is the number of transitions from the state i to the state j, Pn k¼1 Tik is the total sum of transitions from the state i to the other states of the related parameter, and n is the total number of parameter states. Transition intensity coefficient of the state i (CXi ) is the reciprocal of the expected extent (length) of the state i (HXi ) along the tunnel length. (2) Calculation of transition intensity matrix of parameter X (AX) using the transition probability and transition intensity coefficient according to the following equation (Chan, 1981; Ioannou, 1984):

2

AX

CX1 6 CX pX 2 21 ¼ 6 4 « CXn pXn1

CX1 pX12 CX2 « CXn pXn2

/ / 1 /

3 CX1 pX1n CX2 pX2n 7 7 5 « CXn

(2)

(3) Calculation of the interval probability matrix. Based on the Markov process, the occurrence probability of a certain state of geological parameter X can be calculated in the next location. Considering Fig. 1, estimation of the occurrence probability of state j (j ¼ 1, 2, ., n) from the parameter X at the given location (L) in relation to the initial location (O0) with the distance u ¼ L  O0 is required (L > O0). Thus there should be a location at which the occurrence probability of states for a certain parameter is known. Using this state, the Markov process can predict such probabilities in the next location (Chan, 1981; Ioannou, 1984, 1987). In order to calculate the occurrence probability of parameter (X) states in a cell with the distance of u in relation to the initial cell, a matrix called interval probability matrix (VX(u)) should be used and is defined as (Ioannou, 1984):

State

X(O0)



X(L)

Cell

i



j

2. Methodology 2.1. Probabilistic estimation of ground condition (PEGC) Ground condition is considered as one of the main factors in selecting excavation method and support system. Since very few or no data on geological conditions of the tunnel alignment are

Fig. 1. Predicting the occurrence probability of each parameter (X) state.

V X ðuÞ ¼

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

n

vXij ðuÞ

o

where vXij ðuÞ is the occurrence probability of the parameter (X) state j with the distance u from the cell O0. Also Eq. (3) can be expressed as follows:

V X ðuÞ ¼ expðuAX Þ ¼ I þ uAX þ

Triangle (Min, Moderate, Max)

(3)

1 2 2 1 u AX þ / þ um Am X 2! m!

(4)

where I is the unit matrix in the sizes of n  n, and m is a large number which can be indefinite (Ioannou, 1987). A closed-form expression for VX(u) can be constructed by using the spectral resolution of A (Cox and Miller, 1965) or exponential transforms (Howard, 1960, 1971).

SXj ðuÞ ¼

n X

SXi ð0ÞvXij ðuÞ

Min

Max

Cost (a)

Construction time

(4) Calculating the occurrence probability of parameter states in a situation where the parameter state is not known deterministically but only a probability mass function (PMF) has been given for it in the location O0. In this state, considering SXj ðuÞ as the occurrence probability of the state j of the parameter X at the location O0 þ u, it can then be calculated according to the following equation (Chan, 1981):

Moderate

Probability

736

(5)

i¼1

where SXj ðuÞ is the occurrence probability of the state i of the parameter X in the location O0. Using the results of all calculated occurrence probabilities related to all the desired parameter states along the tunnel length, it would be possible to obtain each parameter profile and ultimately the ground class profile from the combination of the obtained profiles. The goal of geological model is the formation of ground class profile so that it would be possible to use it in the model established to estimate the construction time and costs of each class in any location of the tunnel alignment.

Construction cost (b) Fig. 2. (a) Triangular probability density function for cost; (b) Cost-time scatter diagram (Primavara, 2009).

the tunnel. The entire geological and construction uncertainties for a tunnel are thus represented by a number of cost-time pairs, which can be shown in a so-called cost-time scatter diagram (see Fig. 2b) where each point represents a simulated cost-time pair for constructing the tunnel (Haas and Einstein, 2002; Primavara, 2009). 3. Results and discussion

2.2. Probabilistic estimation of construction time and costs (PECTC) 3.1. PEGC in Hamro road tunnel The PECTC simulates the construction process through each of the ground class profiles. This involves relating geological/ geotechnical conditions (ground classes) to construction classes or “tunneling methods”, which define tunnel cross-sections and initial and permanent supports, as well as the excavation method best suited for a particular ground class. Each method is associated with construction cost and time, which are usually given in the form of cost and advance-rate distribution expressing cost and time uncertainties for each tunneling method. In the PECTC, probabilistic input and also construction cost or time for a particular ground class are usually defined by a triangular probability density function (PDF, see Fig. 2a). The triangular PDFs are often used to estimate uncertainties because the three parameters (minimum, moderate, maximum) of the triangular PDF are more easily estimated than other functions, for which more abstract parameters such as standard deviation or skewness are required. Nevertheless, other distribution forms can also be used. The construction of a tunnel is simulated by advancing round by round (cycle by cycle) through one of the geological profiles. Each round is associated with the construction cost and time corresponding to the particular ground class encountered along the geological profile. The cost and time are taken from a triangular distribution as shown in Fig. 2a. The construction simulation is repeated for the entire set of simulated geological profiles, each simulation resulting in a different cost-time pair for constructing

Design and construction decisions in tunneling depend on geological parameters such as rock type, joint density, faulting, joint appearance, degree of weathering and groundwater characteristics (Ioannou, 1984). Considering the initial information, three parameters, i.e. rock type, RQD and groundwater, have been examined in this study and the states relevant to each parameter have been presented. (1) Rock type parameter with four states: limestone (Li), shale (Sh), sand shales and shale limestones sequence (ShL), and limestone and shale sequence (LSh), which are numbered states 1e4, respectively. (2) RQD parameter with three states: <5, 5e25, and 25e50, which are numbered states 1e3, respectively. (3) Groundwater parameter with three states: low, moderate, and high, which are numbered states 1e3, respectively. According to Table 1, for each state of the three parameters mentioned above, the average length was estimated according to the views of tunneling experts considering the tunnel longitudinal profile before construction. Finally, by reversing the average length of the states, the transition intensity coefficient of each state of the parameters was obtained. Also using the questionnaires of the experts, the transition probability matrixes for each parameter were obtained.

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745 Table 1 Average length and transition intensity coefficient related to each state of parameters. State

Rock type

Li Sh ShL LSh <5 5e25 25e50 Low Moderate High

RQD

Groundwater

Average length of the states (m)

Transition intensity coefficient (m1)

320 120 780 90 280 650 380 620 260 430

0.0031 0.0083 0.0012 0.0111 0.0035 0.0015 0.0026 0.0016 0.0038 0.0023

2

Pw

Aw

(1) For rock type parameter:

0 6 0:48 6 Pr ¼ 6 4 0:28

0:24 0

3 0:02 0:04 7 7 7 0:44 5

0:74 0:48

0:28 0 0:01 0:01 0:98 0 2 0:0031 0:0007 0:0022 6 0:0039 0:0083 0:0039 6 Ar ¼ 6 4 0:0003 0:0003 0:0012 0:00015 0:00015 0:0108

0 6 ¼ 4 0:50

0:72 0

0:28

0:72

2

For the purpose of this study, in order to obtain more accurate data, the views from 10 experts have been used. All the experts were university graduate and postgraduate people from civil engineering, rock mechanics engineering and geology engineering fields with at least 5 years of experience in road tunneling. The expert views were collected and used to obtain the data. Afterwards, using the above-mentioned transition intensity matrix (Eq. (2)) as well as the transition intensity coefficient and transition probability matrix, the transition intensity matrix for each parameter was obtained:

2

(3) For groundwater parameter:

3 0:0002 0:0005 7 7 7 0:0006 5

0:0016

6 ¼ 4 0:0019 0:0006

3 0:28 7 0:50 5 0 0:00115

0:0038 0:0017

0:00045

3

7 0:0019 5 0:0023

In order to estimate the geological condition along the Hamro road tunnel alignment using the Markov process, first the total tunnel alignment was divided into several equal parts (cells), each with the length of 10 m. Six cells related to the locations of 4 boreholes (BH1eBH4) and 2 portals (entry and exit), called as “observational cells”, were used to specify the occurrence probability of different parameters (rock type, RQD and groundwater) states considered in this study (Fig. 3). As can be seen from Fig. 3, the observational cells are shown in color and a length of 10 m has been considered for each observational location. However, in this study, due to the inaccessibility to the data related to the exact location of boreholes and portals, all the observations were considered to be non-deterministic. Hence, the occurrence probability of different states of the parameters was estimated using the experts views, geological profile and the data obtained from the boreholes. Finally, considering the experts views (10 experts), the occurrence possibility of each state inside observational cells was obtained (Table 2). To obtain the parameter profile, since the occurrence probability of the states in the observational cells locations was expressed as non-deterministic, the following equation can be used (Chan, 1981):

0:0111

n n X 8 X P½XðOt1 Þ ¼ m P½XðOt Þ ¼ w, > > > > m¼1 w¼1 > > > > > < v Xz0 w ðOt  L0 ÞvXmz0 ðL0  Ot1 Þ ns vXmz ðL0  Ot1 Þ ¼ ðOt1 < L0 < Ot ; t ¼ 1; 2; 3; /; sÞ 0 > vXmw ðOt  Ot1 Þ > > > > > > n  > > : X P½XðO Þ ¼ wv ðL  O Þ ðL > O Þ s

w¼1

0:0018

Fig. 3. Quantity and location of observational cells.

8 Cells (80 m)

6

5

Borehole 4 (10 m) O

15 Cells (150 m)

Borehole 3 (10 m) O 4

42 Cells (420 m)

3

Borehole 2 (10 m) O

2

24 Cells (240 m)

3 0:0032 7 0:0014 5 0:0026

Borehole 1 (10 m) O

3

6 7 P d ¼ 4 0:05 0 0:95 5 0:33 0:67 0 2 0:0035 0:0003 6 Ad ¼ 4 0:0001 0:0015 0:0008

s

36 Cells (360 m)

0:90

0

1

0:10

s

Entry portal (10 m) O

0

0

where m and w are the occurrence probabilities of a given parameter state in the observational cells Ot1 and Ot, respectively. According to Eq. (6), several non-deterministic observations are shown in Fig. 4.

(2) For RQD parameter:

2

Xwz0

(6)

Exit portal (10 m) O

Parameter

737

738

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

tunnel alignment. Obviously, it would not be possible to consider a separate excavation method and support system for each geological condition; however, five different excavation methods and support system suitable for a number of these geological conditions were considered. Such geological conditions were identified in 5 classes (Table 3) using the questionnaire as per the experts views. Table 4 represents the geological class specifications. For the formation of ground class profile, the geological conditions related to each parameter (Table 3) and the data of the occurrence probability for the parameters were used. For this purpose, first the obtained data for parameter profile were input into Excel 2013. Next, considering Table 3, the occurrence probability of each ground class inside each cell was obtained using Excel 2013 software. To describe the methodology to obtain the occurrence probability of each ground class in each cell, the ground class 3 (GC 3) is taken for example which includes 8 geological conditions as shown in Table 3: g31 ¼ (1, 2, 1), g32 ¼ (1, 2, 2), g33 ¼ (1, 2, 3), g34 ¼ (4, 2, 1), g35 ¼ (4, 2, 2), g36 ¼ (4, 2, 3), g37 ¼ (1, 3, 3), g38 ¼ (3, 3, 3). In this study, if each geological condition is considered as (i, j, k), where i, j and k are the indicatives of rock type, RQD and groundwater, respectively, for a certain ground class, it means that for each cell, the state i from the rock type parameter (i.e. one of the four states of rock type parameter), the state j from the parameter RQD (i.e. one of the three states of RQD parameter), and the state k from the groundwater parameter (i.e. one of the three states of the groundwater parameter) occur with a certain probability. Accordingly, to identify the occurrence probability of each ground class in a given cell, the occurrence probability of states i, j and k inside the cell must be identified and then the obtained probabilities for each geological condition must be multiplied by each other. If the ground class includes several geological conditions, such calculations must be performed for each individual geological condition inside the related cell and finally added up to obtain the occurrence probability of that class inside the relevant cell. In the following section, considering the above discussion, the procedure for obtaining the ground class 3 inside the cell l is presented as follows:

Table 2 Occurrence probability of each state of parameters in the observational cell location. Parameter

State

Rock type

RQD

Ground water

Cell State

BH4

Exit

3 2 10 85 1 90 9 3 7 90

1 3 95 1 5 15 80 80 15 5

5 54 40 1 15 80 5 85 10 5

5 9 85 1 95 4 1 4 95 1

80 10 6 4 9 90 1 2 8 90

90 5 4 1 3 95 2 2 8 90

X(L35)

z1

z 35

X(O2) w

X(O2) m

X(L37)

X(L38)

...

X(L60)

X(O3)

z 37

z 38

...

z 60

w

X(O3) m

X(L62)

X(L63)

...

X(L103)

z 62

z 63

...

z103

X(O4) m

X(L105)

X(O5) m

z121

Cell

State

BH3

z0

State

Cell

BH2

...

m

Cell

BH1

...

X(O1)

State

1 2 3 4 1 2 3 1 2 3

Entry

X(L1)

Cell

State

State State State State State State State State State State

Occurrence probability (%)

X(L0)

X(L106)

...

z105

z106

...

z119

X(L121)

X(L122)

...

X(L128)

z122

...

z128

X(O4) w X(O5)

X(L119)

w X(O6) w

Fig. 4. Prediction method of the occurrence probability of the parameter states between two observational cells.

Eq. (6) is related to the unknown cells between the two observational cells O1 and O2, predicting the occurrence probability of each state of groundwater, RQD and rock type in the unknown cell L0. After determining the occurrence probability of each parameter state in the unknown cell L0, the next cell L1 is considered. By using L1 and z1 to replace L0 and z0 in Eq. (6), the occurrence probability of parameter states in L1 can be determined. This process is repeated until the last unknown cell (z35) between the two observational cells (O1 and O2). In order to determine the occurrence probability of each parameter state, coding was made for Eq. (6) in MATLAB (MathWorks, 2013). The obtained results from MATLAB for the occurrence probability of the individual states of the parameters inside the relevant cell along the tunnel length are shown in Figs. 5e7. For the parameters and states considered in this study, a total of 3  3  4 ¼ 36 different geological conditions could occur along the Li

1

P½gð1Þ belongs to GC 3 ¼ P½gð1Þ ¼ g3i  ði ¼ 1; 2; /; 8Þ ¼ P½gð1Þ ¼ g31  þP½gð1Þ ¼ g32  þ/ þP½gð1Þ ¼ g38  ¼ P½rð1Þ ¼ 1; dð1Þ ¼ 2; wð1Þ ¼ 1þP½rð1Þ ¼ 1; dð1Þ ¼ 2; wð1Þ ¼ 2þ P½rð1Þ ¼ 1; dð1Þ ¼ 2; wð1Þ ¼ 3 þP½rð1Þ ¼ 4; dð1Þ ¼ 2; wð1Þ ¼ 1þ P½rð1Þ ¼ 4; dð1Þ ¼ 2; wð1Þ ¼ 2 þP½rð1Þ ¼ 4; dð1Þ ¼ 2; wð1Þ ¼ 3þ P½rð1Þ ¼ 1; dð1Þ ¼ 3; wð1Þ ¼ 3 þP½rð1Þ ¼ 3; dð1Þ ¼ 3; wð1Þ ¼ 3

Sh

ShL

LSh

0.9 0.8

Probability

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

Cell number Fig. 5. The rock type parameter profile.

86

91

96 101 106 111 116 121 126 131

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

below 5

1

5 to 25

739

25 to 50

0.9 0.8

Probability

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96 101 106 111 116 121 126 131

Cell number Fig. 6. The RQD parameter profile.

low

1

medium

high

0.9 0.8 0.7

Probability

0.6 0.5 0.4 0.3 0.2 0.1 0 1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96 101 106 111 116 121 126 131

Cell number Fig. 7. The groundwater parameter profile.

3.2. PECTC in Hamro road tunnel

P½gð1Þbelongs to GC 3¼P½rð1Þ¼1P½dð1Þ¼2P½wð1Þ¼1þ P½rð1Þ¼1P½dð1Þ¼2P½wð1Þ¼2þP½rð1Þ¼1P½dð1Þ¼2P½wð1Þ¼3þ P½rð1Þ¼4P½dð1Þ¼2P½wð1Þ¼1þP½rð1Þ¼4P½dð1Þ¼2P½wð1Þ¼2þ P½rð1Þ¼4P½dð1Þ¼2P½wð1Þ¼3þP½rð1Þ¼1P½dð1Þ¼3P½wð1Þ¼3þ P½rð1Þ¼3P½dð1Þ¼3P½wð1Þ¼3

The PECTC determines the construction time and costs of each cell of the individual ground classes. In order to estimate the Table 4 Ground class specifications and construction methods.

Similar procedure is performed for the other ground classes, and ultimately using the results gained for each ground class, a profile can be obtained, as shown in Fig. 8. This profile gives the occurrence probability of each ground class inside all the cells and is called the ground class profile. The aim of the PEGC is to attain the ground class profile so that it can be used as the input for the PECTC.

Ground class

Specifications

GC 1 (very weak)

Table 3 Identification of geological conditions related to individual ground classes.

GC 3 (weak to medium)

Sidewall drift method. Support: IPE 180, with the spacing of 0.5e0.75 m; Shotcrete: 20 cm thick, reinforced by 2 layers of meshes in sizes of f8 mm@100 mm  100 mm Central diaphragm method. Support: IPE 180, with the spacing of 0.75e1 m; Shotcrete: 20 cm thick, reinforced by 2 layers of meshes in sizes of f6 mm@100 mm  100 mm Top heading & benching method. Support: IPE 180, with the spacing of 1e1.2 m; Shotcrete: 20 cm thick, reinforced by 2 layers of meshes in sizes of f6 mm@100 mm  100 mm Top heading & benching method. Support: fully grouted rock bolts with the diameter of 25 mm, the length of 4e6 m, and the spacing of 2 m  2 m; Shotcrete: 15 cm thick, reinforced by 2 layers of meshes in sizes of f6 mm@100 mm  100 mm Top heading & benching method. Support: fully grouted rock bolts, with the diameter of 25 mm, length of 4e6 m, and the spacing of 2 m  2 m; Shotcrete: 10 cm thick, reinforced by one layer of mesh in sizes of f6 mm@100 mm  100 mm

Ground class

Rock type parameter state

RQD parameter state

Groundwater parameter state

GC 1

1, 2 2 1, 1, 1, 2, 3 1, 4

1 2 2 2 3 3 3 2 3 3

1, 2, 1 1, 3 2 3 1, 1 2

GC 2 GC 3 GC 4

GC 5

2, 3, 4

4 3 2, 3 4 2, 3, 4

GC 2 (weak)

GC 4 (medium)

2, 3 3 2, 3 GC 5 (medium to good) 2, 3

740

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

GC 1

1

GC 2

GC 3

GC 4

GC 5

0.9 0.8

Probability

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96 101 106 111 116 121 126 131

Cell number Fig. 8. The ground class profile.

construction time and costs for each cell (10 m) in Hamro tunnel, a specific questionnaire was designed and distributed among the experts. The experts should consider an activity network for each of the ground classes in a way that the considered activity network could complete a construction cycle (excavation and support system) of the related ground class. Afterwards, the required construction time and costs (for the year 2015) related to each activity as well as those required between the end of each activity and the start of new activity, delays, machinery malfunction, etc. could be approximated using the experience from the previously accomplished projects in the similar geological conditions. Ultimately the experts were supposed to add up such time and costs to obtain the total time and costs required for each construction cycle of the ground classes. Afterwards, by averaging the presented views of various experts for each ground class, the time and costs for each cell were obtained (Table 5). Also because the construction costs of each cycle were increasing year by year, the annual increasing percentage of costs was estimated by the experts and ultimately by conversion of this increase in costs for each cell of the ground classes (Table 5). It is notable that the construction time and costs relate to the state where the tunnel is excavated from only one end (entry or exit). In the case of tunneling from both ends, the total construction time is reduced by half compared to that in the case of excavation from one end, and the construction costs are also reduced. Also in estimating the construction time and costs, the tunnel benching was not considered. After determining the construction time and costs of each cell (10 m) for a ground class, the total construction time and costs of the whole tunnel can be approximated by adding up the construction time and costs of all 131 cells. As each ground class occurs with a certain probability (the ground class profile) within each cell, to estimate the total construction time and costs, the MC simulation method was used.

Primavera risk analysis (PRA) program was used to perform MC simulations. After data input and during simulation, the prepared program was repeated for specified times. In each repetition, the non-deterministic values of construction time and costs were determined randomly based on the distributions and the input data. The PRA software stores the estimated total construction time and costs at the end of each repetition. After all the repetitions were finished, the stored values were used for plotting the desired graphs and preparing the probabilistic function related to the implementation of the above items. In order to illustrate the final time and costs of project on the graphs obtained from PRA software, various levels of assurances from 0 to 100% can be used. For example, the graph with 50% level of assurance gives the maximum time and costs that could happen with 50% probability. It must be noted that the maximum time and costs obtained for the project are equal to the calculated ones considering the assigned level of assurance. Meanwhile, the minimum time and costs for the project are the same as those obtained at zero level of assurance. Therefore, if suitable ranges for time and costs are to be determined in the scatter diagram, it would be the same dots between the maximum and minimum time and costs (a range of dots with the probability between zero and the considered one (50% here)). In the following section, the graphs obtained from PRA software will be explained. Figs. 9 and 10 illustrate the column graphs of the total construction time and costs of Hamro road tunnel. These graphs describe the normal distribution of construction time and costs. Different results of construction time and costs have been obtained for different levels of assurances from 0 to 100%. The probability percentage closer to 100% means higher level of assurance for the project to be accomplished with the estimated construction time and costs, consequently reducing the uncertainties. When the level of assurance is more close to 0, the inverse should be expected, causing higher uncertainties. As an optimum state, it would be

Table 5 The construction time and costs of each individual cell (10 m) of the desired ground class. Ground class

GC GC GC GC GC

1 2 3 4 5

Construction time per cell (d)

Construction cost per cell (US $)

Percentage of annual increasing construction costs (%)

Minimum

Moderate

Maximum

Minimum

Moderate

Maximum

Minimum

Moderate

Maximum

13.4 11.7 10 8.4 6.3

16.7 14.2 11.7 10 8.4

20 16.7 14.2 11.7 10

116,667 106,117 92,260 78,734 57,654

119,543 116,667 106,117 92,260 78,734

141,484 119,543 116,667 106,117 92,260

5e10 5e10 5e10 5e10 5e10

15e20 15e20 15e20 15e20 15e20

25e30 25e30 25e30 25e30 25e30

Hits

100

50 5

0

2208

2250

Time (d)

2291

2334

100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%

741

2360 d 2309 d 2300 d 2295 d 2290 d 2286 d 2283 d 2279 d 2277 d 2274 d 2271 d 2267 d 2264 d 2261 d 2258 d 2254 d 2250 d 2245 d 2240 d 2231 d 2182 d

Cumulative frequency

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

Fig. 9. The column graph of construction time.

Fig. 10. The column graph of construction cost.

possible to assume the occurrence level of assurance of either total construction time or total construction cost to be equal to 50%. However, depending on the economic conditions and the type of project, the level of assurance could be above or lower than 50%. In the present study, if a level of assurance of 50% is assumed, as can be seen from Figs. 9 and 10, the project can be accomplished with the total construction costs of about US $25,423,334 and the total construction time of 2271 days.

Time (d)

Time

2300

2350 100%

Cost 50%

25000000

25333334 Cost (US $)

25666667

Fig. 11. The cumulative graph of construction time and cost.

0%

Cumulative probability

2250

2200

Fig. 11 represents the cumulative graph of total construction time and costs of Hamro road tunnel. Using this graph, it could be possible to determine the probability of accessibility to different values of total construction time and costs of the project. In this graph, the accessibility level of assurance to the two different values (50% and 80%) of total construction time and costs has been illustrated. To show the relationship between the total construction time and costs, the scatter diagram is also used. For a specified level of assurance, the construction time and costs for a given project can be determined using this diagram. Fig. 12 illustrates the total construction time and costs with 50% level of assurance. For 50% level of assurance of the total construction costs, it means that half of the simulation dots lie above the horizontal line and the other half lie below it. Also 50% level of assurance for total construction time means that half of the simulation dots are located on the left side of the vertical line and the other half on the right side. The green dots represent the points that lie below the horizontal line (cost) and left of the vertical line (time). The green dots indicate that the probability of total construction time and costs falls below the specified level of assurance

742

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

Fig. 12. Scatter diagram of construction time and costs with the 50% level of assurance.

Outside both limits

Inside both limits

80%

16%

4%

Cost (US $)

26000000

25666667 80%

US $25557941 25333334

25000000

64% 24666667 2166

2290 d 2208

2250

16% 2291

2333

Time (d) Fig. 13. Scatter diagram of construction time and costs with the 80% level of assurance.

shown by the vertical and horizontal lines respectively, meaning that for higher level of assurance specified by the horizontal and vertical lines, there will be a greater number of green dots, and hence lower uncertainty is induced. The red dots indicate the reversal state so that with the increase in the level of assurance value specified by the horizontal and vertical lines, the number of red dots decreases, meaning that the uncertainty is decreased. When the level of assurance specified by the horizontal and vertical lines is higher, there will be a less number of black dots, and hence a lower uncertainty (Fig. 13). Sometimes the conditions dictate that the uncertainty of one of the variables (construction time and cost) can be lower or higher than that of the other one. For example, when a lower uncertainty for the construction time is required (i.e. the construction time is more important), the level of assurance value considered by the vertical line (for time) should be greater than that determined by

the horizontal line (for cost), in other words, the number of green dots for the vertical line should be more than the horizontal line (Figs. 14 and 15). Therefore, depending on the economic conditions, the project type and other factors, different uncertainties can be considered during the initial planning concerning the total construction time and costs of tunneling. In the scatter diagrams, the percentage of the black dots will vary only when the levels of assurance for both the time and cost are changed. For example, in Fig. 12 where the 50% level of assurance is adopted for the time and cost, the black dots constitute 50% of all the dots in the diagram; and when the level of assurance concerning the time and cost reaches 80% (Fig. 13), the black dots encompass 32% of all the dots. Whereas in the case that the level of assurance is assumed to be constant for time (cost) and variable for cost (time), it can be observed in Fig. 14, where the level of

A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745

Inside both limits

80%

743

Outside both limits

40%

10%

Cost (US $)

26000000

25666667

50%

US $25423334

25333334

25000000

2290 d

40% 24666667 2166

2250

2208

10% 2333

2291

Time (d) Fig. 14. Time-cost scatter diagram when lower uncertainty is considered for construction time.

Inside both limits

26000000

Outside both limits

27%

8%

21%

Cost (US $)

25666667 72%

US $25520293 25333334

25000000

2256 d

20% 24666667 2166

2208

52%

2250

2291

2333

Time (d) Fig. 15. Occurrence probability of the exact construction time and costs on the scatter diagram estimated by the innovative method.

assurance is fixed for the cost and has attained 50% for the time, that the black dots comprise 50% of all the dots. But in the case where the level of assurance increases concerning each of the two parameters (time and costs) or both, the number of green dots increases, more than that of the red dots, and vice versa. 4. Validation of the results obtained from innovative methodology Since the construction of Hamro road tunnel was completed during this study, and due to the accessibility to more accurate data after construction, the authors decided to validate the results obtained from the innovative method against the post-construction data, so that the method proposed in this paper could be employed for the estimation of construction time and costs in the future projects with lower uncertainty. The construction time and costs of Hamro road tunnel obtained using the post-construction data and the views of the experts responsible for the tunneling

project were equal to 2256 days and US $25,520,293, respectively. It must be mentioned that the Hamro tunneling project was considered to start in 2015 in this study, accordingly the actual costs were updated in accordance with the building code of the mentioned year; also considering the actual time of tunnel construction, the estimated costs have been increased by 25% in accordance with the annual increase in expenses, so that the estimated total costs of the project could be calculated with the highest accuracy possibly. Since the time and costs in the scatter diagram obtained from the innovative method occur with 27% and 72% levels of assurance, respectively, it can be concluded that the 50% level of assurance in this paper could be the optimum state, because 50% level of assurance lies almost in the middle of 27% and 72% levels of assurance. Accordingly, if we consider 50% level of assurance as an optimal state, it means that about 15 days more for the time and US $86,000 less for the costs have been allocated compared to those for the actual state, and this would prove the lower uncertainties with respect to employing the innovative method. This is true that

744

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the closer the level of assurance to 100% is, the lower the uncertainty about the maximum time and costs will be. In this case, however, they may be greatly different from the actual time and costs. Hence, the main aim of the simulations is to decrease the uncertainties related to construction time and costs obtained by the simulations in comparison to the actual time and costs. The 100% level of assurance therefore is not indicative of the actual time and cost obtained by simulations. As a result, 27% and 72% levels of assurance are not measured against 100%, whereas they must be measured against the optimal state considered. Hence, it can be said that the pre-construction innovative method can be used in estimating the construction time and costs of future tunneling projects to considerably reduce the uncertainties and thereby decrease the decision-making risks concerning construction time and costs estimation in initial planning stages. 5. Conclusions Minimizing uncertainties related to project design and planning is a significant issue. Usually the uncertainties in subsurface projects arise from the unknown ground conditions which may cause the designer to fail to consider all the potential issues prone to occur during the construction process. Construction time and cost uncertainties can be considered as the most important uncertainties, for they are directly connected with thorough recognition of the subsurface conditions. Accordingly, in subsurface projects, the actual time and costs are not ascertainable, and hence the probability methods should be used to assess such factors. In this study, an innovative method for the probabilistic estimation of ground condition and construction time and costs for Hamro road tunnel was proposed. As an optimum state, it would be possible to assume the occurrence probability of either construction time or costs to be equal to 50%. However, depending on the economic conditions and the type of project, the level of assurance could be above or lower than 50%. In the present study, if a level of assurance of 50% is assumed, the project can be accomplished with the total construction cost of about US $25,423,334 and the total construction time of 2271 days. It is notable that these total construction time and costs are related to the state where the tunnel is excavated from only one end (entry or exit). In the case of tunneling from both sides, the total construction time is reduced by half compared to that in the case of excavation from one end, and the construction costs are also reduced. In the following study, the findings for construction time and costs of tunnel were compared with the actual ones. Finally, considering the proximity of the results obtained by the innovative methodology and the actual data, it was concluded that the preconstruction innovative method could be used for estimating the required construction time and costs of tunnels for the future projects to considerably reduce the uncertainties and decisionmaking risks on construction time and costs estimations during the initial planning stages. Conflict of interest The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. Acknowledgment The authors are grateful to M. Mohammadi, H. Nikoogoftar and F. Rezaei for their assistance and guidance.

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A. Mahmoodzadeh, S. Zare / Journal of Rock Mechanics and Geotechnical Engineering 8 (2016) 734e745 Dr. S. Zare is currently an Associate Professor at School of Mining, Petroleum and Geophysics Engineering in Shahrood University of Technology, Iran. He received his BSc degree in Mining Engineering-Exploitation from Amir-Kabir University of Technology and his MSc degree in Mining EngineeringRock Mechanics from Tarbiat-Modares University, Iran in 1995 and 1999, respectively. After completing his MSc studies, He worked in consulting in the tunnelling industry on many tunnelling projects. He obtained his PhD degree in Civil Engineering from Department of Civil and Transport Engineering in Construction Engineering-Tunnelling, Norwegian University of Science and Technology (NTNU) in 2007. His research interests cover tunnelling in rock and soft ground, rock mechanics, stability analysis and support design.

745

A. Mahmoodzadeh is currently a rock mechanics engineer. He obtained his BSc degree in the Mining Engineering-Exploration from Department of Engineering at University of Kurdestan, Iran in 2013, and his MSc degree in the Mining Engineering-Rock Mechanics from Depa rt ment o f Scho ol o f Mi ning , Pet rol e um a nd Geophysics Engineering at Shahrood University of Technology, Iran in 2016. His BSc and MSc works focused on designing of towny tunnels and reducing the time and costs uncertainty of tunneling projects using DAT method in the road tunnels, respectively. Currently his research focuses on rock mechanics, geotechnical engineering, support design, and risk management.