- Email: [email protected]
Evaluating risks using simulated annealing and Building Information Modeling
Applied Mathematical Modelling xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm
Evaluating risks using simulated annealing and Building Information Modeling q Dong-Woo Ryu a, Jung In Kim b,⇑, Sunduck Suh c, Wonho Suh c a
Korea Institute of Geoscience and Mineral Resources, Deajeon 305-350, South Korea Center for Integrated Facility Engineering (CIFE), Department of Civil and Environmental Engineering, Stanford University, Y2E2 Building, 473 Via Ortega, Room 292, Stanford, CA 94305, USA c Department of Transportation and Logistics Engineering, Hanyang University, 55 Hanyangdaehak-Ro, Sangnok-Gu, Ansan 426-791, South Korea b
a r t i c l e
i n f o
Article history: Received 12 January 2015 Received in revised form 1 March 2015 Accepted 24 April 2015 Available online xxxx Keywords: Risk analysis Tunnel construction Simulated annealing Building Information Modeling
a b s t r a c t Tunnel construction involves significant uncertainties in ground conditions, often causing cost overruns and schedule delays. To mitigate these risks, general contractors (GCs) should predict varying ground conditions based on information regarding ground conditions acquired before construction (i.e., borehole and geophysical investigations). Subsequently, GCs should also evaluate excavation costs and durations of their schedule based on predicted ground conditions; however, this is challenging because in current practice, GCs lack a method to incorporate these required processes into their existing evaluation process in a structured manner. To overcome this limitation, we developed a methodology to predict multiple sets of ground conditions by using simulated annealing (SA), which is a geo-statistical method, and then evaluate excavation costs and durations of a tunneling schedule via Building Information Modeling (BIM). For integration of SA and BIM, we extended existing BIM to accept multiple sets of ground conditions. To validate the effectiveness of our methodology, we applied it to a tunnel in Korea. Based on the application, we highlight that our methodology enables GCs to formally evaluate risks in excavation costs and durations of tunnel construction with complete information about ground conditions acquired before construction. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction Tunnel construction involves significant uncertainties in ground conditions that affect both tunnel design (e.g., support systems) and excavation productivity. Although various geotechnical (e.g., borehole and geophysical) investigations are performed before actual construction, there is often a certain degree of deviation between predicted and actual ground conditions. Panthi et al. [1] compared the predicted and actual rock mass conditions for four recently-constructed hydro-tunnels in Nepal Himalaya: the Khimti 1, the Kaligandaki ‘‘A’’, the Modi Khola, and the Middle Marsyangdi headrace tunnels [1]. They found that considerable differences existed between predicted and actual rock mass conditions for all four tunnels. In particular, although Class 3 (i.e., middle ground condition) was dominant in the predicted condition for the Kaligandaki
q
2013 International Applied Science and Precision Engineering Conference, October 2013 NanTou, Taiwan.
⇑ Corresponding author. Tel.: +1 650 723 4945; fax: +1 650 723 4806.
E-mail addresses: [email protected] (D.-W. Ryu), [email protected] (J.I. Kim), [email protected] (S. Suh), [email protected] (W. Suh). http://dx.doi.org/10.1016/j.apm.2015.04.024 0307-904X/Ó 2015 Elsevier Inc. All rights reserved.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
2
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
‘‘A’’ tunnels, Class 6 (i.e., poor ground condition) was dominant in the actual conditions. Due to these uncertainties in ground conditions, general contractors (GCs) often encounter difficulty completing their projects on time and within budget. To mitigate the risks caused by these uncertainties, GCs should conduct two required processes in preconstruction. First, GCs should predict varying ground conditions with complete information about ground conditions (i.e., borehole and geophysical investigations) acquired before construction. In addition, when predicting ground conditions, GCs should take into account spatial relationships among ground conditions because the ground conditions are spatially correlated with each other. Next, GCs should also evaluate the excavation costs and durations of their schedules based on the varying ground conditions predicted. Recently, ground conditions such as Rock Mass Rating (RMR), which was developed in 1973 requiring only a few basic parameters relating to the geometry relating to the geometry and mechanical conditions of the rock mass to improve the quality of site investigations by calling for the minimum input data as classification parameters, provide quantitative information for design purposes and enable better engineering judgment and more effective communication on a project, and Rock Quality Designation (RQD) have been estimated in unsampled areas based on the given data using geostatistical methods such as kriging and conditional simulation, which take into account geospatial relationships among sampled and unsampled areas [2–4]. Although kriging methods have been regarded as a good predictor from the viewpoint of specific statistical criteria such as minimum variance and unbiasedness, kriging methods have a serious shortcoming in that their resulting maps cannot reproduce a predefined spatial variability or other statistical models [5]. Thus conditional simulation methods can be considered as a remedy for the shortcomings of kriging and have been used in the prediction of geotechnical attributes that are spatially distributed; however, existing studies about conditional simulation methods cannot provide a formal reasoning mechanism appropriate for tunnel construction to reduce the uncertainty that is due to deficiency of borehole data and to exploit other types of information regarding ground conditions (e.g., geophysical investigation). Building Information Modeling (BIM) supports decisions about construction plans (e.g., schedules) by utilizing digital representations of the building process [6]. Because BIM allows GCs to facilitate the exchange and interoperability of information in digital format, it allows GCs to rapidly and formally evaluate direct costs and durations of construction schedules; however, existing studies on BIM are limited in cost and duration evaluation of excavation schedules for tunnel construction with varying ground conditions because each component in product models (i.e., designs) accepts only one material. Furthermore, the construction method models used in existing BIM are not specialized for tunnel construction. Consequently, GCs have difficulty evaluating risks in excavation costs and durations of tunneling schedules with complete information about ground conditions acquired before construction, because GCs lack a method to incorporate the two required processes into their existing evaluation process in a structured manner. To overcome these limitations, we developed a methodology by integrating geostatistical methods and BIM. We first specialized simulated annealing (SA), one of the conditional simulation methods, in the prediction of ground conditions for tunnel construction with complete information acquired before construction. We also specialized BIM-based evaluation processes of costs and durations for tunnel excavation. To integrate SA and BIM, we extended the existing BIM to accept multiple sets of ground conditions. After that, we applied the methodology to a tunnel in Korea to validate the effectiveness of our methodology.
2. Literature review This section describes the advantages and limitations of existing studies in facilitating the two required processes explained in the previous section. This section first introduces geostatistical methods for predicting ground conditions and then presents BIM for evaluation of costs and durations for construction schedules.
2.1. Geostatistical methods Geostatistical methods have been widely applied to predict ground conditions in a way that takes into account spatial relationships among sampled and unsampled areas. Kriging has been used to sketch the trend of georeferenced variables, and conditional simulation adopts the theory of regionalized variables based on the idea of kriging. Since different kriging and conditional simulation methods have different objectives, we investigated the characteristics of kriging and conditional simulation methods in order to select appropriate methods to facilitate our first required process. Over the past several decades kriging, which was first introduced by Krige [7], has become a fundamental tool in the field of geostatistics [7]. Kriging is based on the assumption that the parameter being interpolated can be treated as a regionalized variable. A regionalized variable is an intermediate between a truly random variable and a completely deterministic variable in that it varies continuously from one location to the next. Therefore, points that are near each other have a certain degree of spatial correlation, whereas points that are widely separated are statistically independent. This kriging minimizes estimation variance from a predefined covariance model that takes into account functions of distance. Thus, the kriging makes locally optimal predictions about ground conditions. However, because the kriging variance does not fully measure spatial uncertainty, the smoothing effect is detrimental if kriging predictions are used as parameters in a non-linear multiple-cell model (e.g., cost and duration evaluation). Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
3
Conditional simulation methods, such as Sequential Gaussian Simulation (SGS), sequential indicator simulation (SIS), and simulated annealing (SA), fully measure spatial uncertainty by reproducing sample data, their histogram, and their spatial correlation (i.e., variogram); thus, they can be used as remedy for kriging. Among these methods, SA, originally a random-search algorithm, forms the basis of an optimization technique that takes into account the different types of information provided (e.g., borehole and geophysical investigations). This SA process involves following five steps: (1) An initial three-dimensional numerical model is created by assigning a random value at each grid node by drawing from the population distribution. (2) An objective function is defined as a measure of difference between desired spatial features and those of the realization. (3) The image is perturbed by drawing a new value for a randomly selected location. (4) The perturbation is always accepted if the objective is decreased, and accepted with a certain probability if the objective is increased; and (5) The perturbation procedure is continued while reducing the probability with which unfavorable swaps are accepted until a low objective function state is achieved. Existing studies about SA are, however, limited to tunnel construction projects because the processes in the studies are not specialized in the prediction of parameters (e.g., RMR) required for tunnel construction.
2.2. Building Information Modeling (BIM) To facilitate the second required process (i.e., evaluation of costs and durations for tunnel construction with varying ground conditions), we investigated existing studies about Building Information Modeling (BIM), which enables GCs to exchange and interoperate information with one another in digital format [6]. By using BIM, GCs can rapidly and formally evaluate construction costs and durations of multiple schedules [8]. To utilize BIM for the evaluation, product and process models (i.e., design and schedule) for specific projects should be explicitly described. Industry Foundation Classes (IFC) formally represent various types of information (e.g., classification, geometry, location, function, topology, material) about a product model in the construction industry and thus enable GCs to explicitly describe the product model by BIM [9]. However, the IFC cannot adequately consider varying materials for each component because the IFC can accept only one material for each. Our research team was thus required to extend the existing IFC to represent varying material properties for each component that take into account spatial relationships with different components. To evaluate the costs and durations of construction schedules by BIM, Darwiche et al. [10] represented construction methods as a tuple of hObjecti hActioni hResourcesi (e.g., hWalli hPainti hPaint, Ladder, and Painteri) [10]. Since this representation does not include sequential relationships among activities, Aalami et al. [11] represented the methods as a tuple of hComponenti hActioni hResourcesi hSequencing constrainti hElaborationi (i.e., CARSE) [11]. Based on the tuple of CARSE, GCs populate a construction method template (CMMT), and thus are able to formally and rapidly evaluate the costs and durations of their construction schedules. However, this CARSE is not specialized for tunnel construction with varying ground conditions (i.e., materials). Consequently, our research team was required to develop a methodology to formally incorporate the two processes into their existing evaluation process for tunnel construction by integrating SA and BIM. To do this, we specialized the SA process and CARSE and extended the IFC data model for tunnel construction with uncertain ground conditions. The next section describes the methodology that we developed for this research.
3. Methodology and calculation Simulated annealing (SA) is originally a random-search technique which exploits an analogy between the way in which a metal cools and freezes into a minimum energy crystalline structure (the annealing process) and the search for a minimum in a more general system; it forms the basis of an optimization technique for combinatorial and other problems.
Table 1 Analogy between physical annealing and simulated annealing. Physical annealing
Simulated annealing
Thermodynamic simulation States of system Energy of a state Change of state Temperature Quenching Minimum energy
Optimization with constraints Solutions Cost of a solution Neighbor solution Control parameter Local minimum Minimum cost
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
4
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
In this study, the principles of simulated annealing are now outlined. Consider the objective function O that we want to minimize with respect to parameters p1 ; p2 ; . . . ; pi . In SA technique, this is done analogously to the physical process of a molten metal solidifying as it is cooled (Table 1). In SA technique, the parameters of O are perturbed randomly. Over a time step, t ! t þ 1, a single change in a parameter occurs, resulting in a change, Ot ! Otþ1 . If Otþ1 6 Ot , then the change is accepted (minimization problems). If Otþ1 > Ot , then the decision whether or not to accept the change is made randomly with probability P a of acceptance, where
Pa ¼ e
Ot Otþ1 c
ð1Þ
:
This is the Metroplis criterion, central to simulated annealing. The probability of acceptance of a particular increase in O is also determined by the parameter c. In the annealing analogue, c is the temperature of the system. Increasing the temperature makes the acceptance of a particular transition more likely. A Markov chain is constituted by making a series of random adjustments to a set of parameters, either accepted or rejected according to Eq. (1), with a fixed value of c. A new Markov chain may be initiated by a ‘cooling’ system (reducing c). In the physical analogue of the molten metal, after cooling to a fixed temperature, the system will tend, over many transitions governed by the Metropolis criterion, to a thermal equilibrium, such that the probability of a particular energy state is governed by the Boltzmann distribution. Each Markov chain of SA will tend similarly to an equilibrium time (the number of transition) that is takes depending inversely on the temperature. 3.1. Algorithm The annealing process may be simulated through the following steps (Fig. 1): (a) An initial three dimensional numerical model is created by assigning a random value at each grid node by drawing from the population distribution. (b) An objective function is defined as a measure of difference between desired spatial features and those of the realization (c) The image is perturbed by drawing a new value for a randomly selected location.
Fig. 1. The structure of a basic SA algorithm.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
5
(d) The perturbation is always accepted if the objective is decreased; it is accepted with a certain probability if the objective is increased. (e) The perturbation procedure is continued while reducing the probability with which unfavorable swaps are accepted until a low objective function state is achieved. 3.2. Objective functions The objective function O for simulated annealing is made up of the weighted sum of C components as follows:
O¼
C X
-c Oc ;
ð2Þ
c¼1
where -c and Oc are the weights and component objective functions respectively, and C is the number of component objective functions. All decisions of whether to accept or reject a perturbation are based on the change to the objective function as follows:
DO ¼ Otþ1 Ot ; DO ¼
C X
ð3Þ
-c Octþ1 Oct ¼
C X
c¼1
-c DOc ;
ð4Þ
c¼1
where weights -c ; c ¼ 1; . . . C, are established so that, on an average, each component contributes equally to the change in the objective function DO. That is, each weight -c is made inversely proportional to the average change in absolute value of its component objective function:
1 ; DO c
-c ¼
c ¼ 1; . . . C:
ð5Þ
In practice, the average change of each component DOc may not be computed analytically. However it can be numerically approximated by evaluating the average change due to a certain number M of independent perturbations:
X ðmÞ DOc ¼ 1 Oc Oc ; M m¼1
c ¼ 1; . . . C;
ð6Þ
where DOc is the average change for component c, OðmÞ is the perturbed objective value and Oc is the initial objective value. c Table 2 summarizes the component objective functions which are used in this study. A primary variable is RMR and secondary variable is log-transformed specific resistivity. Detail information can be found in [12]. We developed a methodology to evaluate risks in excavation costs and durations for tunnel construction in preconstruction by integrating SA and BIM. This methodology consists of two main procedures: (1) prediction of RMR for tunnel construction by SA, and (2) evaluation of risks in excavation costs and durations of schedules for tunnel construction based on BIM (Fig. 2). The remainder of this section describes each procedure in detail. 3.3. SA-based prediction of RMR for tunnel construction The first procedure is intended to predict varying ground conditions for tunnel construction. In our methodology, we use RMR as an engineering parameter to provide information about ground conditions for GCs to estimate excavation costs and durations of schedules for tunnel construction. Fig. 3 shows the details of the application of the SA technique for the prediction, and its uncertainty evaluation of RMR in this study. This procedure can be understood as one whereby various types of given information are integrated and optimized with some constraints, such as a statistical model, spatial variability, and
Table 2 Summary of various objective functions for SA. Statistics
Component objective functions
Histogram
P
Variogram Indicator variogram Correlation coefficient Conditional distribution
2
z ½F ðzÞ FðzÞ , where F is a conditional cumulative distribution function of simulated realization P ½c ðhÞcðhÞ2 , where c is a variogram of simulated realization z
cðhÞ2
h
i2
cj ðhi Þcj ðhi Þ
Pnc P j¼1
h
2
cj ðhi Þ2
, where cj is a indicator variogram of simulated realization in class j
½q q , where q is a correlation coefficient between primary and secondary variable of simulated realization Pns Pnp i¼0
j¼0 ½f i ðjÞ
f i ðjÞ , where f i is a conditional distribution of the primary variable given that the collocated secondary
variable is in class j
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
6
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
Fig. 2. Two main procedures of the methodology developed in this study.
Exploratory data analysis : geophysical properties and RMR
Geostatistical data analysis : geophysical properties and RMR
Construction of 3D ref. image : specific resistivityor P-wave velocity
Histogram and correlation analysis Indicator variogram modeling
SIS : E-type map
No Model validation Yes 3D simulated annealing : data integration and optimization
Realizations : RMR maps
Fig. 3. Optimization procedure for prediction and evaluation of its uncertainty.
Table 3 Facet of the slot for a material attribute in tunnel product model. Property
Cardinality
Value type
Range
Material (i.e., RMR)
{1:N}
Integer
0–100
given reference images or data. We use sequential indicator simulation (SIS) to reconstruct a 3-D reference image from geophysical surveys. SIS is a simulation technique corresponding to indicator kriging, which exploits the information of a distribution in addition to given data. To utilize complete information (i.e., borehole and geophysical investigations) about ground conditions acquired before actual construction, statistical correlation analysis between RMR and log-transformed geophysical investigation results (e.g., specific resistivity and P-wave velocity) is performed with statistical and spatial variability modeling of RMR from boreholes, which are utilized as objective functions. Our methodology uses nested variogram models, which are weighted linear combinations of basic theoretical variogram models. To reconstruct 3-D reference image, statistical and spatial modeling is performed; next, 3-D SIS is applied with given transverse and longitudinal images of geophysical properties. Generally, it is very difficult to detect local weak zones with only RMR from boreholes. Conversely, though, images of geophysical exploration can provide exhaustive information and roughly detect weak zones, which are simply areas of indirect information. Furthermore, these two types of the information have inherent uncertainties from various sources and are given in different scales and with their own physical meanings. Through data integration and optimization of given RMR and images of geophysical properties by the SA technique, the above problems are overcome and a 3-D spatial map of RMR is constructed. A number of realizations acquired from the SA technique make it possible to evaluate the uncertainties of predictions. The probability of each rock mass at each station is used as a measure of uncertainties in ground conditions (e.g., RMR). 3.4. BIM-based evaluation of risks in excavation costs and durations for tunnel construction The second procedure is intended to evaluate risks in excavation costs and durations of tunneling schedules based on the RMR values predicted from the first procedure. Before explaining the procedure, we first describe two different data models because the second procedure requires those models as input: (1) a tunnel product model with varying ground conditions, and (2) a construction method specialized for tunnel construction. To develop both models, we followed methodologies introduced by existing studies on ontology development [13,14]. For the first data model, we used the Industry Foundation Classes (IFC) data model as a baseline because the IFC represent various types of information (e.g., classification, geometry, location, function, topology, material) required by the construction Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
7
Table 4 Some facets of the slots in a tunnel construction method model. Property
Cardinality
Value type
Range
Unit cost Productivity Sequential constraint Starting location
{1:NC} {1:NC} {1:1} {1:1}
Float Float Boolean Integer
Positive Positive N/A N/A
industry [9]. As explained in the previous section, the existing IFC cannot adequately consider varying materials for each component. Consequently, we extended the existing IFC to represent varying material properties (i.e., RMR values) for each component, taking into account spatial relationships with different components. To do so, we changed only the facet for a material attribute (i.e., slot). Specifically, we redefined the number of the values (i.e., cardinality) for the facet from {1:1} to {1:N} as shown in Table 3. Here, N represents the number of realizations that resulted from the first procedure. For the tunnel product model to take into account spatial relationships among different components, the RMR values should be sequentially provided by the first procedure. As a baseline or the second data model, we used a construction method template (CMMT) from a tuple of CARSE. Although GCs formally and rapidly evaluate construction costs and durations of construction schedules with a CMMT, this CMMT had to be specialized for tunnel construction with varying ground conditions. Consequently, we redefined facets of slots for unit cost and productivity as well as sequential constraints. Table 4 shows some facets in a tunnel construction method model developed in this study. Here, NC represents the number of classes based on RMR. This model requires one of two different values for the slot of sequential constraints (i.e., increasing (T) and decreasing (F) based on station information from a tunnel product model). Based on input values provided for two models, the second procedure in our methodology involves several steps. First, it computes costs and durations for each component in the tunnel product model. Second, costs and durations are accumulated component by component based on the information about the sequential constraint and starting location. Third, when all components have been considered, this accumulation process is terminated. Fourth, the second and third processes are repeated for each of the realizations resulting from the first procedure. The last process generates empirical cumulative density functions (CDFs) for excavation costs and durations. To validate the effectiveness of our methodology, we applied the methodology to a tunnel in Korea. 4. Results 4.1. Application of the methodology This section describes our application of these processes to a 300-m-long roadway tunnel in Korea. Fig. 4 shows a topography and mesh for spatial modeling, which has 101 51 51 nodes, and Fig. 4(a) is a digital terrain model of the study site. Based on the methodology, we first conducted exploratory data analysis with log-transformed specific resistivity (LN(SR)), which is the value from one of the geophysical investigations used in this study, and RMR. Fig. 5 shows results
Fig. 4. Topography including tunnel layout and 101 51 51 mesh for SA.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
8
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
Fig. 5. Results of statistical correlation analysis between RMR and LN(SR), and indicator variogram modeling of RMR in horizontal and vertical directions, respectively.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
9
Fig. 6. 3-D spatial distribution of LN(SR) for SA.
Fig. 7. 3-D spatial distribution of RMR computed by SA.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
10
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx Table 5 An example of values required for the instance of tunneling method 1. Ground class
Unit cost
Productivity
1 2 3 4 5 Sequential constraint Starting location (Sta.)
2.7 2.8 3.4 6.3 7.5
6.1 6.3 7.5 11.5 37.9 T (increasing) 50
Fig. 8. Two empirical cumulative density functions for excavation costs and durations evaluated in this study.
of the analysis and modeling. Based on the results, we conducted geostatistical data analysis with LN(SR) and RMR. The behavior of the indicator variogram in the horizontal direction was periodic, due to periodic geological structures of the site, such as fracture clustering and small faults. After that, we reconstructed a 3-D reference image of LN(SR) for SA. Fig. 6 shows the reconstructed 3-D spatial distribution of LN(SR). As the last part of the first procedure, we conducted data integration and optimization of given RMR and images of specific resistivity via the SA technique. From the 80 realizations by SA, we constructed a 3-D spatial map of RMR as shown in Fig. 7. To evaluate risks in excavation costs and durations of a schedule for this tunnel, we sequentially filled RMR values from the 80 realizations via SA in the slots of material for the tunnel product model developed in this study. Consequently, the tunnel product model (i.e., BIM for tunnel) allowed the GC to take into account varying ground conditions, their spatial relationships, and complete information about ground conditions acquired before actual construction. We also filled values in the slots for the tunnel construction method model developed in this study. Table 5 shows an example of values required for one specific tunneling method. This tunneling method model allowed the GC to formally take into account information about construction methods specialized for tunnel construction. In this application, we used only two tunneling methods, which utilize the same resources but different sequences. We used cost-unit for the slots of unit cost instead of US dollar or Korean won. In addition, we also used time-unit for the slots of productivity instead of days or months. Based on these two models, we computed excavation costs and durations for 80 sets of possible ground conditions. After that, we generated two empirical cumulative density functions for the costs and durations as shown in Fig. 8. These empirical cumulative density functions allowed the GC to evaluate risks in excavation costs and durations of the schedule for the tunnel in this study.
5. Discussions and conclusion Since tunnel construction involves significant uncertainties in ground conditions, GCs for tunnel construction often encounter difficulty completing their projects on time and within budget. To mitigate the risks caused by such uncertainties, Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
11
GCs should first predict varying ground conditions by using complete information about ground conditions acquired before construction. During the prediction process, GCs should also take into account spatial relationships among ground conditions. In addition, GCs should evaluate the excavation costs and durations of their schedules based on the varying ground conditions predicted. To incorporate these required processes into their existing evaluation process in a structured manner, we developed a methodology that integrates SA and BIM. Specifically, we specialized the SA technique for tunnel construction, extended the existing IFC to accept multiple values for the slots of material (i.e., ground conditions), and specialized CMMT for tunnel construction. This methodology contributes to the field of construction management for tunnel construction. Based on the results of our application of this methodology, we highlight that the methodology, developed in this study, enables GCs to evaluate risks in excavation costs and durations for tunnel construction in a structured manner, using complete information about ground conditions acquired before construction. Although our methodology supports GCs in evaluating risks in excavation costs and durations for tunnel construction, it still has a limitation. A tunneling method model in our methodology cannot adequately take into account comprehensive information (e.g., mobilization and learning curves) about the construction methods related to transitions among different construction methods. It is not expected that the proposed method would be an immediate solution for every case. However, this would reduce uncertainty and expected to be of practical value to the construction. The proposed methodology does not enable GCs to consistently evaluate risks in excavation costs and durations of schedules that have more than two different construction methods without consideration of sequential constraints. Risk management is not expected to remove all risks associated tunnel construction. The proposed application is suggested to provide explicit decisions to be made which would mitigate the potential effect of certain risk. This also makes it difficult for GCs to evaluate the risks during construction. For future research, a construction method model that takes into account comprehensive information related to transitions should be integrated with our methodology. Acknowledgment This research was supported by the Basic Research Project of the Korea Institute of Geoscience and Mineral Resources (KIGAM, GP2015-010), the Ministry of Science, ICT and Future Planning of Korea, and the research fund of Hanyang University (HY-2015). References [1] K. Panthi, B. Nilsen, Predicted versus actual rock mass conditions: a review of four tunnel projects in Nepal Himalaya, Tunnelling Underground Space Technol. 22 (2) (2007) 173–184. [2] M. Cromer, C. Rautman, W. Zelinski, Geostatistical Simulation of Rock Quality Designation to Support Facilities Design at Yucca Mountain, ASTM special technical publication, Nevada, 1996. 218 p. [3] C. Ozturk, Geostatistical assessment of rock zones for tunneling, Tunneling Underground Space Technol. 17 (3) (2002) 275–285. [4] C. Hong, S. Jeon, Optimal estimation of rock mass parameters using genetic algorithm and conditional simulation, in: EUROCK 2004 & 53rdGeomechanics Colloquium, Salzburg, Austria, 2004, pp. 483–486. [5] P. Goovaerts, Geostatistics for Natural Resources Evaluation, Oxford University Press, 1997. pp. 483. [6] C. Eastman, P. Teicholz, R. Sacks, K. Liston, BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers, and Contractors, second ed., Wiley, Hoboken, NJ, 2008. [7] D. Krige, A statistical approach to some basic mine valuation problems on the Witwatersrand, J. Chem. Metall. Mining Soc. South Africa 52 (1951) 119– 139. [8] J. Gao, M. Fischer, Framework and Case Studies Comparing Implementations and Impacts of 3D/4D Modeling Across Projects, Technical Rep. No. 172, Center for Integrated Facility Engineering (CIFE), Stanford University, Stanford, California, 2008. [9] BuildingSMART, ‘‘Industry Foundation Classes (IFC).’’
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
Contents lists available at ScienceDirect
Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm
Evaluating risks using simulated annealing and Building Information Modeling q Dong-Woo Ryu a, Jung In Kim b,⇑, Sunduck Suh c, Wonho Suh c a
Korea Institute of Geoscience and Mineral Resources, Deajeon 305-350, South Korea Center for Integrated Facility Engineering (CIFE), Department of Civil and Environmental Engineering, Stanford University, Y2E2 Building, 473 Via Ortega, Room 292, Stanford, CA 94305, USA c Department of Transportation and Logistics Engineering, Hanyang University, 55 Hanyangdaehak-Ro, Sangnok-Gu, Ansan 426-791, South Korea b
a r t i c l e
i n f o
Article history: Received 12 January 2015 Received in revised form 1 March 2015 Accepted 24 April 2015 Available online xxxx Keywords: Risk analysis Tunnel construction Simulated annealing Building Information Modeling
a b s t r a c t Tunnel construction involves significant uncertainties in ground conditions, often causing cost overruns and schedule delays. To mitigate these risks, general contractors (GCs) should predict varying ground conditions based on information regarding ground conditions acquired before construction (i.e., borehole and geophysical investigations). Subsequently, GCs should also evaluate excavation costs and durations of their schedule based on predicted ground conditions; however, this is challenging because in current practice, GCs lack a method to incorporate these required processes into their existing evaluation process in a structured manner. To overcome this limitation, we developed a methodology to predict multiple sets of ground conditions by using simulated annealing (SA), which is a geo-statistical method, and then evaluate excavation costs and durations of a tunneling schedule via Building Information Modeling (BIM). For integration of SA and BIM, we extended existing BIM to accept multiple sets of ground conditions. To validate the effectiveness of our methodology, we applied it to a tunnel in Korea. Based on the application, we highlight that our methodology enables GCs to formally evaluate risks in excavation costs and durations of tunnel construction with complete information about ground conditions acquired before construction. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction Tunnel construction involves significant uncertainties in ground conditions that affect both tunnel design (e.g., support systems) and excavation productivity. Although various geotechnical (e.g., borehole and geophysical) investigations are performed before actual construction, there is often a certain degree of deviation between predicted and actual ground conditions. Panthi et al. [1] compared the predicted and actual rock mass conditions for four recently-constructed hydro-tunnels in Nepal Himalaya: the Khimti 1, the Kaligandaki ‘‘A’’, the Modi Khola, and the Middle Marsyangdi headrace tunnels [1]. They found that considerable differences existed between predicted and actual rock mass conditions for all four tunnels. In particular, although Class 3 (i.e., middle ground condition) was dominant in the predicted condition for the Kaligandaki
q
2013 International Applied Science and Precision Engineering Conference, October 2013 NanTou, Taiwan.
⇑ Corresponding author. Tel.: +1 650 723 4945; fax: +1 650 723 4806.
E-mail addresses: [email protected] (D.-W. Ryu), [email protected] (J.I. Kim), [email protected] (S. Suh), [email protected] (W. Suh). http://dx.doi.org/10.1016/j.apm.2015.04.024 0307-904X/Ó 2015 Elsevier Inc. All rights reserved.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
2
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
‘‘A’’ tunnels, Class 6 (i.e., poor ground condition) was dominant in the actual conditions. Due to these uncertainties in ground conditions, general contractors (GCs) often encounter difficulty completing their projects on time and within budget. To mitigate the risks caused by these uncertainties, GCs should conduct two required processes in preconstruction. First, GCs should predict varying ground conditions with complete information about ground conditions (i.e., borehole and geophysical investigations) acquired before construction. In addition, when predicting ground conditions, GCs should take into account spatial relationships among ground conditions because the ground conditions are spatially correlated with each other. Next, GCs should also evaluate the excavation costs and durations of their schedules based on the varying ground conditions predicted. Recently, ground conditions such as Rock Mass Rating (RMR), which was developed in 1973 requiring only a few basic parameters relating to the geometry relating to the geometry and mechanical conditions of the rock mass to improve the quality of site investigations by calling for the minimum input data as classification parameters, provide quantitative information for design purposes and enable better engineering judgment and more effective communication on a project, and Rock Quality Designation (RQD) have been estimated in unsampled areas based on the given data using geostatistical methods such as kriging and conditional simulation, which take into account geospatial relationships among sampled and unsampled areas [2–4]. Although kriging methods have been regarded as a good predictor from the viewpoint of specific statistical criteria such as minimum variance and unbiasedness, kriging methods have a serious shortcoming in that their resulting maps cannot reproduce a predefined spatial variability or other statistical models [5]. Thus conditional simulation methods can be considered as a remedy for the shortcomings of kriging and have been used in the prediction of geotechnical attributes that are spatially distributed; however, existing studies about conditional simulation methods cannot provide a formal reasoning mechanism appropriate for tunnel construction to reduce the uncertainty that is due to deficiency of borehole data and to exploit other types of information regarding ground conditions (e.g., geophysical investigation). Building Information Modeling (BIM) supports decisions about construction plans (e.g., schedules) by utilizing digital representations of the building process [6]. Because BIM allows GCs to facilitate the exchange and interoperability of information in digital format, it allows GCs to rapidly and formally evaluate direct costs and durations of construction schedules; however, existing studies on BIM are limited in cost and duration evaluation of excavation schedules for tunnel construction with varying ground conditions because each component in product models (i.e., designs) accepts only one material. Furthermore, the construction method models used in existing BIM are not specialized for tunnel construction. Consequently, GCs have difficulty evaluating risks in excavation costs and durations of tunneling schedules with complete information about ground conditions acquired before construction, because GCs lack a method to incorporate the two required processes into their existing evaluation process in a structured manner. To overcome these limitations, we developed a methodology by integrating geostatistical methods and BIM. We first specialized simulated annealing (SA), one of the conditional simulation methods, in the prediction of ground conditions for tunnel construction with complete information acquired before construction. We also specialized BIM-based evaluation processes of costs and durations for tunnel excavation. To integrate SA and BIM, we extended the existing BIM to accept multiple sets of ground conditions. After that, we applied the methodology to a tunnel in Korea to validate the effectiveness of our methodology.
2. Literature review This section describes the advantages and limitations of existing studies in facilitating the two required processes explained in the previous section. This section first introduces geostatistical methods for predicting ground conditions and then presents BIM for evaluation of costs and durations for construction schedules.
2.1. Geostatistical methods Geostatistical methods have been widely applied to predict ground conditions in a way that takes into account spatial relationships among sampled and unsampled areas. Kriging has been used to sketch the trend of georeferenced variables, and conditional simulation adopts the theory of regionalized variables based on the idea of kriging. Since different kriging and conditional simulation methods have different objectives, we investigated the characteristics of kriging and conditional simulation methods in order to select appropriate methods to facilitate our first required process. Over the past several decades kriging, which was first introduced by Krige [7], has become a fundamental tool in the field of geostatistics [7]. Kriging is based on the assumption that the parameter being interpolated can be treated as a regionalized variable. A regionalized variable is an intermediate between a truly random variable and a completely deterministic variable in that it varies continuously from one location to the next. Therefore, points that are near each other have a certain degree of spatial correlation, whereas points that are widely separated are statistically independent. This kriging minimizes estimation variance from a predefined covariance model that takes into account functions of distance. Thus, the kriging makes locally optimal predictions about ground conditions. However, because the kriging variance does not fully measure spatial uncertainty, the smoothing effect is detrimental if kriging predictions are used as parameters in a non-linear multiple-cell model (e.g., cost and duration evaluation). Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
3
Conditional simulation methods, such as Sequential Gaussian Simulation (SGS), sequential indicator simulation (SIS), and simulated annealing (SA), fully measure spatial uncertainty by reproducing sample data, their histogram, and their spatial correlation (i.e., variogram); thus, they can be used as remedy for kriging. Among these methods, SA, originally a random-search algorithm, forms the basis of an optimization technique that takes into account the different types of information provided (e.g., borehole and geophysical investigations). This SA process involves following five steps: (1) An initial three-dimensional numerical model is created by assigning a random value at each grid node by drawing from the population distribution. (2) An objective function is defined as a measure of difference between desired spatial features and those of the realization. (3) The image is perturbed by drawing a new value for a randomly selected location. (4) The perturbation is always accepted if the objective is decreased, and accepted with a certain probability if the objective is increased; and (5) The perturbation procedure is continued while reducing the probability with which unfavorable swaps are accepted until a low objective function state is achieved. Existing studies about SA are, however, limited to tunnel construction projects because the processes in the studies are not specialized in the prediction of parameters (e.g., RMR) required for tunnel construction.
2.2. Building Information Modeling (BIM) To facilitate the second required process (i.e., evaluation of costs and durations for tunnel construction with varying ground conditions), we investigated existing studies about Building Information Modeling (BIM), which enables GCs to exchange and interoperate information with one another in digital format [6]. By using BIM, GCs can rapidly and formally evaluate construction costs and durations of multiple schedules [8]. To utilize BIM for the evaluation, product and process models (i.e., design and schedule) for specific projects should be explicitly described. Industry Foundation Classes (IFC) formally represent various types of information (e.g., classification, geometry, location, function, topology, material) about a product model in the construction industry and thus enable GCs to explicitly describe the product model by BIM [9]. However, the IFC cannot adequately consider varying materials for each component because the IFC can accept only one material for each. Our research team was thus required to extend the existing IFC to represent varying material properties for each component that take into account spatial relationships with different components. To evaluate the costs and durations of construction schedules by BIM, Darwiche et al. [10] represented construction methods as a tuple of hObjecti hActioni hResourcesi (e.g., hWalli hPainti hPaint, Ladder, and Painteri) [10]. Since this representation does not include sequential relationships among activities, Aalami et al. [11] represented the methods as a tuple of hComponenti hActioni hResourcesi hSequencing constrainti hElaborationi (i.e., CARSE) [11]. Based on the tuple of CARSE, GCs populate a construction method template (CMMT), and thus are able to formally and rapidly evaluate the costs and durations of their construction schedules. However, this CARSE is not specialized for tunnel construction with varying ground conditions (i.e., materials). Consequently, our research team was required to develop a methodology to formally incorporate the two processes into their existing evaluation process for tunnel construction by integrating SA and BIM. To do this, we specialized the SA process and CARSE and extended the IFC data model for tunnel construction with uncertain ground conditions. The next section describes the methodology that we developed for this research.
3. Methodology and calculation Simulated annealing (SA) is originally a random-search technique which exploits an analogy between the way in which a metal cools and freezes into a minimum energy crystalline structure (the annealing process) and the search for a minimum in a more general system; it forms the basis of an optimization technique for combinatorial and other problems.
Table 1 Analogy between physical annealing and simulated annealing. Physical annealing
Simulated annealing
Thermodynamic simulation States of system Energy of a state Change of state Temperature Quenching Minimum energy
Optimization with constraints Solutions Cost of a solution Neighbor solution Control parameter Local minimum Minimum cost
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
4
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
In this study, the principles of simulated annealing are now outlined. Consider the objective function O that we want to minimize with respect to parameters p1 ; p2 ; . . . ; pi . In SA technique, this is done analogously to the physical process of a molten metal solidifying as it is cooled (Table 1). In SA technique, the parameters of O are perturbed randomly. Over a time step, t ! t þ 1, a single change in a parameter occurs, resulting in a change, Ot ! Otþ1 . If Otþ1 6 Ot , then the change is accepted (minimization problems). If Otþ1 > Ot , then the decision whether or not to accept the change is made randomly with probability P a of acceptance, where
Pa ¼ e
Ot Otþ1 c
ð1Þ
:
This is the Metroplis criterion, central to simulated annealing. The probability of acceptance of a particular increase in O is also determined by the parameter c. In the annealing analogue, c is the temperature of the system. Increasing the temperature makes the acceptance of a particular transition more likely. A Markov chain is constituted by making a series of random adjustments to a set of parameters, either accepted or rejected according to Eq. (1), with a fixed value of c. A new Markov chain may be initiated by a ‘cooling’ system (reducing c). In the physical analogue of the molten metal, after cooling to a fixed temperature, the system will tend, over many transitions governed by the Metropolis criterion, to a thermal equilibrium, such that the probability of a particular energy state is governed by the Boltzmann distribution. Each Markov chain of SA will tend similarly to an equilibrium time (the number of transition) that is takes depending inversely on the temperature. 3.1. Algorithm The annealing process may be simulated through the following steps (Fig. 1): (a) An initial three dimensional numerical model is created by assigning a random value at each grid node by drawing from the population distribution. (b) An objective function is defined as a measure of difference between desired spatial features and those of the realization (c) The image is perturbed by drawing a new value for a randomly selected location.
Fig. 1. The structure of a basic SA algorithm.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
5
(d) The perturbation is always accepted if the objective is decreased; it is accepted with a certain probability if the objective is increased. (e) The perturbation procedure is continued while reducing the probability with which unfavorable swaps are accepted until a low objective function state is achieved. 3.2. Objective functions The objective function O for simulated annealing is made up of the weighted sum of C components as follows:
O¼
C X
-c Oc ;
ð2Þ
c¼1
where -c and Oc are the weights and component objective functions respectively, and C is the number of component objective functions. All decisions of whether to accept or reject a perturbation are based on the change to the objective function as follows:
DO ¼ Otþ1 Ot ; DO ¼
C X
ð3Þ
-c Octþ1 Oct ¼
C X
c¼1
-c DOc ;
ð4Þ
c¼1
where weights -c ; c ¼ 1; . . . C, are established so that, on an average, each component contributes equally to the change in the objective function DO. That is, each weight -c is made inversely proportional to the average change in absolute value of its component objective function:
1 ; DO c
-c ¼
c ¼ 1; . . . C:
ð5Þ
In practice, the average change of each component DOc may not be computed analytically. However it can be numerically approximated by evaluating the average change due to a certain number M of independent perturbations:
X ðmÞ DOc ¼ 1 Oc Oc ; M m¼1
c ¼ 1; . . . C;
ð6Þ
where DOc is the average change for component c, OðmÞ is the perturbed objective value and Oc is the initial objective value. c Table 2 summarizes the component objective functions which are used in this study. A primary variable is RMR and secondary variable is log-transformed specific resistivity. Detail information can be found in [12]. We developed a methodology to evaluate risks in excavation costs and durations for tunnel construction in preconstruction by integrating SA and BIM. This methodology consists of two main procedures: (1) prediction of RMR for tunnel construction by SA, and (2) evaluation of risks in excavation costs and durations of schedules for tunnel construction based on BIM (Fig. 2). The remainder of this section describes each procedure in detail. 3.3. SA-based prediction of RMR for tunnel construction The first procedure is intended to predict varying ground conditions for tunnel construction. In our methodology, we use RMR as an engineering parameter to provide information about ground conditions for GCs to estimate excavation costs and durations of schedules for tunnel construction. Fig. 3 shows the details of the application of the SA technique for the prediction, and its uncertainty evaluation of RMR in this study. This procedure can be understood as one whereby various types of given information are integrated and optimized with some constraints, such as a statistical model, spatial variability, and
Table 2 Summary of various objective functions for SA. Statistics
Component objective functions
Histogram
P
Variogram Indicator variogram Correlation coefficient Conditional distribution
2
z ½F ðzÞ FðzÞ , where F is a conditional cumulative distribution function of simulated realization P ½c ðhÞcðhÞ2 , where c is a variogram of simulated realization z
cðhÞ2
h
i2
cj ðhi Þcj ðhi Þ
Pnc P j¼1
h
2
cj ðhi Þ2
, where cj is a indicator variogram of simulated realization in class j
½q q , where q is a correlation coefficient between primary and secondary variable of simulated realization Pns Pnp i¼0
j¼0 ½f i ðjÞ
f i ðjÞ , where f i is a conditional distribution of the primary variable given that the collocated secondary
variable is in class j
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
6
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
Fig. 2. Two main procedures of the methodology developed in this study.
Exploratory data analysis : geophysical properties and RMR
Geostatistical data analysis : geophysical properties and RMR
Construction of 3D ref. image : specific resistivityor P-wave velocity
Histogram and correlation analysis Indicator variogram modeling
SIS : E-type map
No Model validation Yes 3D simulated annealing : data integration and optimization
Realizations : RMR maps
Fig. 3. Optimization procedure for prediction and evaluation of its uncertainty.
Table 3 Facet of the slot for a material attribute in tunnel product model. Property
Cardinality
Value type
Range
Material (i.e., RMR)
{1:N}
Integer
0–100
given reference images or data. We use sequential indicator simulation (SIS) to reconstruct a 3-D reference image from geophysical surveys. SIS is a simulation technique corresponding to indicator kriging, which exploits the information of a distribution in addition to given data. To utilize complete information (i.e., borehole and geophysical investigations) about ground conditions acquired before actual construction, statistical correlation analysis between RMR and log-transformed geophysical investigation results (e.g., specific resistivity and P-wave velocity) is performed with statistical and spatial variability modeling of RMR from boreholes, which are utilized as objective functions. Our methodology uses nested variogram models, which are weighted linear combinations of basic theoretical variogram models. To reconstruct 3-D reference image, statistical and spatial modeling is performed; next, 3-D SIS is applied with given transverse and longitudinal images of geophysical properties. Generally, it is very difficult to detect local weak zones with only RMR from boreholes. Conversely, though, images of geophysical exploration can provide exhaustive information and roughly detect weak zones, which are simply areas of indirect information. Furthermore, these two types of the information have inherent uncertainties from various sources and are given in different scales and with their own physical meanings. Through data integration and optimization of given RMR and images of geophysical properties by the SA technique, the above problems are overcome and a 3-D spatial map of RMR is constructed. A number of realizations acquired from the SA technique make it possible to evaluate the uncertainties of predictions. The probability of each rock mass at each station is used as a measure of uncertainties in ground conditions (e.g., RMR). 3.4. BIM-based evaluation of risks in excavation costs and durations for tunnel construction The second procedure is intended to evaluate risks in excavation costs and durations of tunneling schedules based on the RMR values predicted from the first procedure. Before explaining the procedure, we first describe two different data models because the second procedure requires those models as input: (1) a tunnel product model with varying ground conditions, and (2) a construction method specialized for tunnel construction. To develop both models, we followed methodologies introduced by existing studies on ontology development [13,14]. For the first data model, we used the Industry Foundation Classes (IFC) data model as a baseline because the IFC represent various types of information (e.g., classification, geometry, location, function, topology, material) required by the construction Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
7
Table 4 Some facets of the slots in a tunnel construction method model. Property
Cardinality
Value type
Range
Unit cost Productivity Sequential constraint Starting location
{1:NC} {1:NC} {1:1} {1:1}
Float Float Boolean Integer
Positive Positive N/A N/A
industry [9]. As explained in the previous section, the existing IFC cannot adequately consider varying materials for each component. Consequently, we extended the existing IFC to represent varying material properties (i.e., RMR values) for each component, taking into account spatial relationships with different components. To do so, we changed only the facet for a material attribute (i.e., slot). Specifically, we redefined the number of the values (i.e., cardinality) for the facet from {1:1} to {1:N} as shown in Table 3. Here, N represents the number of realizations that resulted from the first procedure. For the tunnel product model to take into account spatial relationships among different components, the RMR values should be sequentially provided by the first procedure. As a baseline or the second data model, we used a construction method template (CMMT) from a tuple of CARSE. Although GCs formally and rapidly evaluate construction costs and durations of construction schedules with a CMMT, this CMMT had to be specialized for tunnel construction with varying ground conditions. Consequently, we redefined facets of slots for unit cost and productivity as well as sequential constraints. Table 4 shows some facets in a tunnel construction method model developed in this study. Here, NC represents the number of classes based on RMR. This model requires one of two different values for the slot of sequential constraints (i.e., increasing (T) and decreasing (F) based on station information from a tunnel product model). Based on input values provided for two models, the second procedure in our methodology involves several steps. First, it computes costs and durations for each component in the tunnel product model. Second, costs and durations are accumulated component by component based on the information about the sequential constraint and starting location. Third, when all components have been considered, this accumulation process is terminated. Fourth, the second and third processes are repeated for each of the realizations resulting from the first procedure. The last process generates empirical cumulative density functions (CDFs) for excavation costs and durations. To validate the effectiveness of our methodology, we applied the methodology to a tunnel in Korea. 4. Results 4.1. Application of the methodology This section describes our application of these processes to a 300-m-long roadway tunnel in Korea. Fig. 4 shows a topography and mesh for spatial modeling, which has 101 51 51 nodes, and Fig. 4(a) is a digital terrain model of the study site. Based on the methodology, we first conducted exploratory data analysis with log-transformed specific resistivity (LN(SR)), which is the value from one of the geophysical investigations used in this study, and RMR. Fig. 5 shows results
Fig. 4. Topography including tunnel layout and 101 51 51 mesh for SA.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
8
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
Fig. 5. Results of statistical correlation analysis between RMR and LN(SR), and indicator variogram modeling of RMR in horizontal and vertical directions, respectively.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
9
Fig. 6. 3-D spatial distribution of LN(SR) for SA.
Fig. 7. 3-D spatial distribution of RMR computed by SA.
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
10
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx Table 5 An example of values required for the instance of tunneling method 1. Ground class
Unit cost
Productivity
1 2 3 4 5 Sequential constraint Starting location (Sta.)
2.7 2.8 3.4 6.3 7.5
6.1 6.3 7.5 11.5 37.9 T (increasing) 50
Fig. 8. Two empirical cumulative density functions for excavation costs and durations evaluated in this study.
of the analysis and modeling. Based on the results, we conducted geostatistical data analysis with LN(SR) and RMR. The behavior of the indicator variogram in the horizontal direction was periodic, due to periodic geological structures of the site, such as fracture clustering and small faults. After that, we reconstructed a 3-D reference image of LN(SR) for SA. Fig. 6 shows the reconstructed 3-D spatial distribution of LN(SR). As the last part of the first procedure, we conducted data integration and optimization of given RMR and images of specific resistivity via the SA technique. From the 80 realizations by SA, we constructed a 3-D spatial map of RMR as shown in Fig. 7. To evaluate risks in excavation costs and durations of a schedule for this tunnel, we sequentially filled RMR values from the 80 realizations via SA in the slots of material for the tunnel product model developed in this study. Consequently, the tunnel product model (i.e., BIM for tunnel) allowed the GC to take into account varying ground conditions, their spatial relationships, and complete information about ground conditions acquired before actual construction. We also filled values in the slots for the tunnel construction method model developed in this study. Table 5 shows an example of values required for one specific tunneling method. This tunneling method model allowed the GC to formally take into account information about construction methods specialized for tunnel construction. In this application, we used only two tunneling methods, which utilize the same resources but different sequences. We used cost-unit for the slots of unit cost instead of US dollar or Korean won. In addition, we also used time-unit for the slots of productivity instead of days or months. Based on these two models, we computed excavation costs and durations for 80 sets of possible ground conditions. After that, we generated two empirical cumulative density functions for the costs and durations as shown in Fig. 8. These empirical cumulative density functions allowed the GC to evaluate risks in excavation costs and durations of the schedule for the tunnel in this study.
5. Discussions and conclusion Since tunnel construction involves significant uncertainties in ground conditions, GCs for tunnel construction often encounter difficulty completing their projects on time and within budget. To mitigate the risks caused by such uncertainties, Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024
D.-W. Ryu et al. / Applied Mathematical Modelling xxx (2015) xxx–xxx
11
GCs should first predict varying ground conditions by using complete information about ground conditions acquired before construction. During the prediction process, GCs should also take into account spatial relationships among ground conditions. In addition, GCs should evaluate the excavation costs and durations of their schedules based on the varying ground conditions predicted. To incorporate these required processes into their existing evaluation process in a structured manner, we developed a methodology that integrates SA and BIM. Specifically, we specialized the SA technique for tunnel construction, extended the existing IFC to accept multiple values for the slots of material (i.e., ground conditions), and specialized CMMT for tunnel construction. This methodology contributes to the field of construction management for tunnel construction. Based on the results of our application of this methodology, we highlight that the methodology, developed in this study, enables GCs to evaluate risks in excavation costs and durations for tunnel construction in a structured manner, using complete information about ground conditions acquired before construction. Although our methodology supports GCs in evaluating risks in excavation costs and durations for tunnel construction, it still has a limitation. A tunneling method model in our methodology cannot adequately take into account comprehensive information (e.g., mobilization and learning curves) about the construction methods related to transitions among different construction methods. It is not expected that the proposed method would be an immediate solution for every case. However, this would reduce uncertainty and expected to be of practical value to the construction. The proposed methodology does not enable GCs to consistently evaluate risks in excavation costs and durations of schedules that have more than two different construction methods without consideration of sequential constraints. Risk management is not expected to remove all risks associated tunnel construction. The proposed application is suggested to provide explicit decisions to be made which would mitigate the potential effect of certain risk. This also makes it difficult for GCs to evaluate the risks during construction. For future research, a construction method model that takes into account comprehensive information related to transitions should be integrated with our methodology. Acknowledgment This research was supported by the Basic Research Project of the Korea Institute of Geoscience and Mineral Resources (KIGAM, GP2015-010), the Ministry of Science, ICT and Future Planning of Korea, and the research fund of Hanyang University (HY-2015). References [1] K. Panthi, B. Nilsen, Predicted versus actual rock mass conditions: a review of four tunnel projects in Nepal Himalaya, Tunnelling Underground Space Technol. 22 (2) (2007) 173–184. [2] M. Cromer, C. Rautman, W. Zelinski, Geostatistical Simulation of Rock Quality Designation to Support Facilities Design at Yucca Mountain, ASTM special technical publication, Nevada, 1996. 218 p. [3] C. Ozturk, Geostatistical assessment of rock zones for tunneling, Tunneling Underground Space Technol. 17 (3) (2002) 275–285. [4] C. Hong, S. Jeon, Optimal estimation of rock mass parameters using genetic algorithm and conditional simulation, in: EUROCK 2004 & 53rdGeomechanics Colloquium, Salzburg, Austria, 2004, pp. 483–486. [5] P. Goovaerts, Geostatistics for Natural Resources Evaluation, Oxford University Press, 1997. pp. 483. [6] C. Eastman, P. Teicholz, R. Sacks, K. Liston, BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers, and Contractors, second ed., Wiley, Hoboken, NJ, 2008. [7] D. Krige, A statistical approach to some basic mine valuation problems on the Witwatersrand, J. Chem. Metall. Mining Soc. South Africa 52 (1951) 119– 139. [8] J. Gao, M. Fischer, Framework and Case Studies Comparing Implementations and Impacts of 3D/4D Modeling Across Projects, Technical Rep. No. 172, Center for Integrated Facility Engineering (CIFE), Stanford University, Stanford, California, 2008. [9] BuildingSMART, ‘‘Industry Foundation Classes (IFC).’’
Please cite this article in press as: D.-W. Ryu et al., Evaluating risks using simulated annealing and Building Information Modeling, Appl. Math. Modell. (2015), http://dx.doi.org/10.1016/j.apm.2015.04.024