外文翻译-- 隧道施工风险敏感型决策支持系统.doc

Risk-sensitive decision support system for tunnel construction Comprehensive and realistic tunneling plans must strive for optimal decisions that minimize time and cost while addressing important factors such as geologic uncertainty and variability,uncertainty in tunneling productivity , and the contractors risk sensitivity . This paper presents a computerized decision support system that incorporates all important tunneling risks. It consists of three interrelated models: the probabilistic geologic prediction model , the probabilistic tunnel cost estimating model , and the risk-sensitive dynamic decision model. The probabilistic geologic prediction model uses all available geologic information to characterize geologic uncertainty and variability along the tunnel profile in the probabilistic from of ground class transitions. The probabilistic tunnel cost estimating model evaluates tunneling time and cost performances for applying different excavation and support methods to different prevailing ground conditions by using Monte Carlo simulation to actual tunneling operations . 概率隧道成本估算模型评估隧穿时间和成本，表现为在利用蒙特卡罗模拟实际施工操作下，把不同的开挖和支护方法应用到不同的地面条件。Both models provide the main input for the risk-sensitive dynamic decision model, the core of the system, to determine the optimal excavation and support sequence and the corresponding risk-adjusted tunneling costs for the project as functions of available project information and the contractors risk sensitivity. 这两个模型提供了对风险敏感的动态决策模型这一系统核心的主要输入，作为可用项目信息和承包商的风险敏感度职能，以此来确定最优开挖与支护顺序和相应的风险调整后的隧道项目成本。 The application of the system to an actual highway tunneling project illustrates both the modeling power of the approach to quantify and incorporate risk, and its effectiveness for making optimal decisions as functions of the contractors degree of risk sensitivity.1, Ph.D. ,Lecturer,Department of Civil Engineering, Chulalongkorn University, Bangkok 10330, Thailand , fcevlkeng.chula.ac.th2, Ph.D. , Professor, Department of Civil and Environmental Engineering, University of Michigan,Ann Arbor, MI 48109-2125, USA, Geotechnical engineering for transportation projectsIntroductionTunnels are vital options for modern transportation systems because they are the only transportation system that can solve problems of difficult terrains,limited surface space,and increased demand of transportation. At the same time, tunnels are expensive underground structures where a variety of risks are encountered in every phase of the project delivery process. Comprehensive and realistic tunneling plans must strive for optimal decisions that minimize time and cost while addressing important tunneling risks. To this end, a risk-sensitive decision support system has been developed to quantify all important tunneling risks and to determine optimal tunneling plans and risk-adjusted costs for a project(Likhitruangsilp 2003)Tunneling risks One of the most important decisions in tunneling is to determine the optimal sequence of excavation methods and support system along the tunnel profile. These decisions are characterized by four primary factors: geologic uncertainty, geologic variability, uncertainty in tunneling productivity,and risk sensitivity.Geologic uncertainty The selection of tunneling methods for a project depends primarily on the expected geologic conditions of the tunnel, which are the aggregation of states of important rock mass properties such as rock type and discontinuities. Regardless of the number and extent of subsurface exploration undertaken, the tunnel geology cannot be known perfectly before construction begins. Even though several tunneling practices(e.g.,the observational method) have been adopted to mitigate geologic uncertainty, they cannot entirely eliminate this uncertainty from tunnel construction planning.Geologic variability Most tunnels traverse a variety of geologic conditions, the locations and extents of which are impossible to define in advance with certainty. For most tunneling projects with significant geologic variability, the selected tunneling methods must be adaptable to all anticipated geologic conditions without seriously interrupting excavation progress. These adaptable tunneling methods encompass the modification of excavation methods(e.g.,heading and bench, and multiple drift), round length, drill patterns, and details of support. Thus, tunneling decisions are dynamic in nature.Uncertainty in tunneling productivityAnother risk in tunneling decisions results from uncertainty in the productivity of tunneling processes. This uncertainty stems from the variation of construction equipment performance, the variation of worker outputs, and unexpected events such as accidents during construction. This uncertainty exists even if geologic conditions are known. Thus, its impact on tunneling decisions must be addressed explicitly.Risk sensitivity Individual valuation of benefits and costs for decisions involving risk (e.g., tunneling decisions) is often nonlinear because these decisions are not based on the maximization of expected monetary value. In other words, when making decisions under uncertainty a decision maker is typically sensitive to risk, either risk averse or risk preferring. An individuals risk sensitivity (risk preference) is influenced by several factors, especially that persons current net asset position. Typically, as a persons net position increase, the less risk-averse their behavior toward the same risk.A contractors risk aversion and its degree of risk exposure can have a major influence on construction decisions and the necessary amount of risk premium or contingency embedded in a contractors price in order to undertake the work. A more risk-averse contractor adopts a more conservative plan and includes a higher allowance as contingencies in his bid than a less risk-averse contractor does (Ioannou 1988). Thus, it is necessary to incorporate risk sensitivity into tunneling decisions. By considering all above factors, tunneling decisions can be considered a risk-sensitive dynamic probabilistic decision process, which can be structures by the risk-sensitive decision support system (Likhitruangsilp 2003).Risk-sensitive decision support system The risk-sensitive decision support system consists of three interrelated models: the probabilistic geologic prediction model, the probabilistic tunnel cost estimating model, and the risk-sensitive dynamic decision model. Probabilistic geologic prediction modelThe probabilistic geologic prediction model uses all available geologic information to characterize geologic uncertainty and variability along the tunnel profile in the probabilistic form of ground class transitions. The model is based on discrete-state, continuous-space Markov processes of important geologic parameters (e.g., rock fracture). These geologic Markov models are created from regional data (e.g., geologic maps) and updated by location-specific data (e.g., borehole tests) using direct assessment or Bayesian updating (Ioannou 1984).The model has been programmed in MATLAB. Its input includes the length of tunnel, the extent of each stage (e.g., round length), geologic parameters and their states, and the definition of ground classes. Based on this input, the model calculates the posterior state probabilities of geologic parameters and ground classes at different locations along the tunnel. Both state probabilities are subsequently used to determine the ground class transition probability matrices of the tunnel geology by applying the concept of composite ground class transitions (Likhitruangsilp 2003). The resulting transition probability matrices become the input for the risk-sensitive dynamic decision model.Probabilistic tunnel cost model The probabilistic tunnel cost estimating model performs stochastic evaluation of tunneling time and cost performance for different combinations of excavation and support methods with different ground classes (tunneling alternatives). The model includes the cost estimating submodel and the probabilistic scheduling submodel.The cost estimating submodel, created in a computer spreadsheet, organizes tunneling cost items, performs quantify takeoff computations, and calculates fixed costs and variable costs associated with each alternative. In addition to normal tunneling costs,it also considers risks of selecting a wrong excavation method during construction. Its input includes a work breakdown structure (WBS) designed specifically for tunneling projects; specifications of excavation methods and support systems; crew compositions for all tunneling operations; and material, equipment, and labor cost data. The final outputs from the cost estimating submodel are fixed costs and variable costs for different alternatives. Variable costs, consisting of hourly costs (/hr) and material unit costs per tunnel length (/m), provide inputs for the probabilistic scheduling submodel.The probabilistic scheduling submodel is implemented in ProbSched, a probabilistic scheduling simulation program (Ioannou and Martinez 1998).It evaluates tunneling time and cost performances for different alternatives.In addition to the input from the cost estimating submodel, it requires precedence networks of tunneling activities for different alternatives; time equations for activities in the activity networks; parameters of the time equations, either defined deterministically or assessed subjectively; and formulas for calculating tunneling unit costs (/m).The probabilistic scheduling networks are analyzed using Monte Carlo simulation.The final outputs include tunneling unit cost distributions for different alternatives, which provide inputs for the risk-sensitive dynamic decision model. A detailed description of this model can be found in Likhitruangsilp and Ioannou (2003).Risk-sensitive dynamic decision modelThe risk-sensitive dynamic decision model, the core of the proposed system, is formulated as a risk-sensitive stochastic dynamic programming model. Its input includes the ground class transition probability matrix for each tunneling stage determined by the tunneling unit cost distributions for different alternatives simulated by the probabilistic tunnel cost estimating model. The model also requires the decision makers (e.g., contractors) risk aversion coefficient (), which is the parameter of the exponential utility function used to encode the decision makers degree of risk preference. A positive means that the decision maker is risk averse, whereas a negative means that the decision maker is risk preferring. The risk-sensitive dynamic decision model, programmed in MATLAB, performs decision and risk analysis to determine the optimal tunneling policies and risk-adjusted tunneling costs of the project, both of which are functions of available information and the decision makers degree of risk sensitivity.ApplicationThe Hanging Lake Tunnel, a highway tunneling project in Colorado, is used to demonstrate the application of the proposed system. This rock tunneling project involved the construction of a pair of two-lane highway tunnels: the eastbound and the westbound tunnels. Here, we focus on the part of the westbound tunnel excavated by multiple-drift and blast methods. Based on several rock mass classification systems, the geologic conditions were classified into three ground classes: GC1 (best), GC2(medium), and GC3(worst). Three excavation methods (EM1,EM2,EM3) AND initial support systems (SS1,SS2,SS3) were designed corresponding to the three ground classes. For example, EM2 and SS2 are the most economical and structurally adequate excavation of six headings (drifts) and rock reinforcement systems consisting of dowels,spiles,and shotcrete,as shown in Figure 1. Descriptions of the ground class classification and the specifications of excavation and support methods can be found in Scotese and Ackerman (1992), and Essex et al. (1993). Thus, there are nine possible tunneling alternatives (i.e., 3 excavation and support methods 3 ground classes). For example,alternative (EM2,GC3) represents the decision to use EM2 for a particular round, and the prevailing ground class after blasting is GC3(i.e., structurally inadequate).Probabilistic geologic prediction model The probabilistic geologic prediction model for the Hanging Lake Tunnel was developed based on three important geologic parameters: rock quality designation (RQD), fracture frequency, and weathering and alteration. The combination of these geologic parameter states are classified into three ground classes corresponding to the classification described by Essex et al.(1993).The parameters for each geologic Markov model were estimated by analyzing data from the logs of boreholes (Leeds,Hill and Jewett, Inc. 1981).The posterior state probabilities at the observation points were subjectively encoded based on a variety of assessments by geology experts, including Leeds,Hill and Jewett, Inc. (1981), and Scotese and Ackerman (1992). These probabilities were used to determine the posterior state probabilities for non-observation points at intervals of 3.7 m (12 ft) along the tunnel. The ground class transition probability matrix between any two stages was then determined based on the concept of composite ground class transitions. An example of the model output is the ground class transition probability matrix between locations 746.1 m(2,448 ft) and 749.8 m(2,460ft):For example, given that the tunnel geology class 1 at location 746.1 m, the probabilities that it will make a transition to ground class 1 (remain the same), ground class 2, and ground class 3 at location 749.8 m are 44.52, 46.79, and 8.96 percent, respectively (i.e., the first row of the above matrix).Probabilistic tunnel cost estimating modelAccording to available information of the construction resources used in this project, the cost estimating submodel organized and calculated the equipment, labor, and equipment costs for each alternative. These costs then categorized into fixed costs and variable costs. The variable costs were used as inputs for the probabilistic scheduling submodel, which performed the probabilistic scheduling analysis of tunneling operations.The output included tunneling unit cost distributions for the nine alternatives, as shown in Figure 2.The tunneling unit costs for applying an excavation method in a particular round depend upon the prevailing ground class after blasting. If the selected method is appropriate for the revealed geologic conditions, this decision will lead to the lowest unit cost for the geologic conditions in that round e.g., (EM1,GC1),(EM2,GC2),(EM3,GC3). In contrast, if the selected method is structurally inadequate e.g., (EM3,GC1) for the actual ground conditions, the tunneling unit costs will be higher than the right decision cases. Risk-sensitive dynamic decision model Based on the inputs from the previous models, the tunneling decision was solved by using decision and risk analysis to determine risk-adjusted costs and optimal tunneling policies, both of which are functions of the contractors risk sensitivity. Figure 3 shows the resulting risk-adjusted tunneling costs for different degrees of the contractors risk sensitivity. As can be seen, the expected tunneling cost for this project (=0) is approximately 30.3M. As the risk aversion coefficient increases (i.e., a contractor becomes more risk adverse), the risk-adjusted cost increases almost linearly. In contrast, as the risk aversion coefficient decreases (i.e., a contractor is more risk preferring), the risk-adjusted cost decreases almost linearly.Figure 4 shows the optimal tunneling policies for the west tunnel segment given that the contractor is risk averse with =5. Nine bars in the figure correspond to the nine possible combinations of ground classes and excavation methods during construction. For example, given that the tunnel geology encountered at location 40.2 m (132 ft) is GC1 and EM1 was used in the previous round, the optimal policy for the risk-averse contractor with =5 is to use the same method (i.e., the first bar). However, if the current geologic conditions are GC2 and EM1 is being used , the contractor should switch to EM2 at that tunneling stage (i.e., the fourth bar).ConclusionsThe proposed risk-sensitive decision support system is the first system that can both quantify and incorporate all important risks associated with tunneling work. The system can be used to determine dynamic optimal tunneling plans and risk-adjusted costs as functions of a contractors risk sensitivity. Thus, it can provide optimal decisions not only for planning and estimating tunnel construction prior to construction but also for choosing the optimal excavation and support method based on actual geologic and construction conditions during excavation.FIG.1. Tunnel cross section and support system type 3 (SS3)FIG.2. Cumulative distribution functions of tunneling unit costs for different alternatives Note: a-(EM1,GC1); b-(EM1,GC2); c-(EM1,GC3); d-(EM2,GC1); e-(EM2,GC2); f-(EM2,GC3); g-(EM3,GC1); h-(EM3,GC2); i-(EM3,GC3)FIG.3. Relationship between risk-adjusted tunneling costs and risk aversion coefficient()FIG.4. Optimal tunneling policies for the Hanging Lake Tunnel project (west segment)for =5 (risk-averse contractors)ReferencesEssex,R., Louis, D., Klein, S., and Trapani, R. (1993). “Geotechnical aspects of the Hanging Lake Tunnels, Glenwood Canyon,Colorado.” Proc. Rapid Excavation and Tunneling Conf.,v1, 907-926Ioannou,P.G.(1984). “the economic value of geologic exploration as a risk reduction strategy in