Probabilistic Cost Analysis for the High Speed Rail between Porto and Lisbon. Alignments A & B close to Leira.

Transcription

1 Probabilistic Cost Analysis for the High Speed Rail between Porto and Lisbon. by Y. Moret, R. L. Sousa and H. H. Einstein February 2008

2 1. Introduction The aim of this report is to present the progress on the cost analysis of the Porto-Lisbon high speed rail line for the two 50km long alignments close to the city of Leira. In the previous work we estimated the total cost of two different alignments and compared them with the cost estimation of RAVE. The approach was deterministic, i.e. no uncertainties in the geology and the construction method were included. The main conclusion from the previous work was to extend the work by including the uncertainties on the costs of the construction method. The results of this step are presented in the report. In the first part of this report, a brief introduction to the DAT structure, the background information on the project and the results from the previous work are presented. Then, the assumptions made to simulate probabilistically the total costs are explained and the results shown. Finally, next steps are suggested. 2. The DAT in brief Geology Input / Module Normally along the tunnel (or alignment) the geology is subdivided into Areas and Zones. An Area is a set of continuous and sequential regions that may consist of only one Zone or many Zones. The term "Zone" is used to express what can be described as a geologically homogeneous Zone, namely, a stretch of ground in which a particular set of parameters and parameter states may occur. Construction Simulation / Input The Construction Simulation simulates the construction process through the generated profiles. This involves relating the different geologic conditions (Ground Classes) to the construction methods (Construction Classes) through an interface that allows one to convert Ground Classes into Construction Classes, taking into account the excavation method chosen. Construction Classes define tunnel cross sections (or other structures), as well as the excavation method that best suits a particular Ground Class. This information and the relationship between construction methods, costs and advance rates must be prescribed by the user. 2/20

3 Figure 1 shows an example the relationships between Geologies, Geometries and Methods for a network of a tunnel. Figure 1 Relationships between Geologies, Geometries and Methods [1] The simulation of the construction process is based on the Monte Carlo method (probabilistic case). Each possible generated profile is simulated and related to a corresponding constructive sequence, which is simulated by the Construction Simulation, through that profile producing a total cost and a total time. This process is repeated for the many probabilistic profiles, producing at the end a Time-Cost scattergram. Figure 2 illustrates this process. 3/20

4 Figure 2 DAT Schema [2] In the present analysis for RAVE only cost uncertainties were considered, and therefore the final result consists of points aligned vertically on the t=0 line, instead of the typical scattergram presented in Figure Background information on the project Initially (July 2007), the total costs of the 50km section close to the city of Leira were estimated deterministically using the program DAT [3]. This was followed by a probabilistic evaluation of costs with the DAT, which is reported here. In order to produce a cost estimate in the DAT the following input data are necessary: areas, zones, ground parameter sets, ground classes, geometries, methods and the network. Since the only new information available is the minimum, mean and maximum costs, the input data have not been changed from the previous work with exception of the cost distributions. The input data are summarized in the next paragraphs. For more details we refer to the previous report [3]. 4/20

5 Areas Alignment A was divided into 6 areas, whereas alignment B was divided into 5 areas. These areas correspond to the different sections of the RAVE project (see Table 1 and 2). Table 1 Alignment A Area Section Length ST. ST Table 2 Alignment B Area Section Length ST. ST Zones and ground parameter sets Each area was divided into zones, which are defined by assigning a ground parameter set. A ground parameter set is defined by a combination of ground parameters. Each ground parameter has its own state. Ground classes Ground classes describe the ground conditions along the alignments and are a particular combination of ground parameter states. Ground classes are used to determine the construction method used. 5/20

6 Geometries After defining the ground classes it is necessary to define the geometries, which will then lead to the methods. Each area has a different geometry for viaduct, normal and special embankment, cut or tunnel. The reason is that the costs provided by RAVE are in euro/m 2 (for viaducts) and euro/m 3 (for the embankments and cuts). In order to be used in the DAT, these costs were then transformed into linear costs. This was done by dividing the total cost of each type of structure by their total length (in a particular area). Thus each area has a different linear cost for the different structures. More details can be found in report [3]. Methods Once the geometries have been defined it is necessary to define the methods that will then be related to the geometries and the ground classes. Table 3 presents the (possible) different methods and their description. Table 3 Possible methods Method Nor-Embank Spe-Embank Cut-A Cut-B Cut-C Cut-D Tunnel-Type1 Tunnel-Type2 Tunnel-Type3 Viaduct Nor-Embank-a Nor-Embank-A Spe-Embank-a Spe-Embank-A Description Normal Embankment construction method. Special Embankment construction method. Cutting construction method A Cutting construction method B Cutting construction method C Cutting construction method D Tunnel section type 1 construction method Tunnel section type 2 construction method Tunnel section type 3 construction method Viaduct construction method Normal Embankment construction method with replacement of soil (alluvium) Normal Embankment construction method with replacement of soil (terra rossa) Special Embankment construction method with replacement of soil (alluvium) Special Embankment construction method with replacement of soil (terra rossa) 6/20

7 Network The tunnel network for the simulation is normally constructed considering the construction sequence, project layout and different geometries (cut, normal embankment, special embankment, viaduct and tunnel). In this initial phase we have considered that the construction will start in area 1 and will progress linearly until the end of the alignment (area 6 in alignment A, area 5 in alignment B). This does not correspond to reality but since we are doing a cost analysis and not considering the time of construction this will not constitute a problem. For the future we will have to consider the different planning and sequencing of construction. Deterministic results The results obtained in the deterministic simulation for both alignments are presented in Table 4. See report [3] for more details on this simulation. Table 4 DAT simulation and RAVE results Alignment Cost - DAT simulation (euro) Cost RAVE (euro) A 265,245, ,245,719 B 446,018, ,018, Probabilistic estimation of costs 4.1. Comparison of previous [4] and new [5] data sources on costs In the previous work, based on information from [4], we transformed the total costs of a structure, e.g. a cut, into linear costs by dividing the total cost by the structure length. Thus a cut in an area has a different linear cost from a cut in another area. As explained previously, this was necessary because the DAT work with cost per linear meter. Costs of structures like the superior passages were introduced in the DAT as fixed costs. As an example, the cost for cleaning and for a superior passage (in section 2.1.3, alignment A) are given in Table 5. For the probabilistic estimation the new source of information [5] provides minimum, mean and maximum costs of single activities, e.g. cleaning, and of structures, e.g. 7/20

8 superior passages. These new data relate to the entire alignment Lisbon Porto and are given in cost per cubic meter in the case of cleaning, and in cost per square meter in the case of the superior passages. The minimum, mean and maximum cost from [5] for cleaning and for a superior passage in the Lisbon Porto alignment are given in Table 5. A comparison between the data from the two sources in Table 5 shows that the value used for the deterministic analysis (from previous source [4]) does not coincide with the mean value from the new source. The differences in values between the previous [4] and the new [5] source occur also for other cost items. Therefore, a direct comparison of the two sources of data is not possible. As the previous source [4] does not give any information on cost distribution, the two data sources needed to be related in order to 1) run a probabilistic analysis and 2) compare the results from the deterministic and the probabilistic analyses. How the data sources are related is explained in the next paragraph. Table 5 Cost data used in the deterministic analysis (from previous data source [4]) and cost data from new data source [5] used in the deterministic analysis (from [4]) New data source [5] unit - unit mínimo médio máximo Earthwork: cleaning cost/m cost/m Superior passage cost/m cost/m Derivation of minimum and maximum values In order to relate the data from the two sources and obtain results which could be compared to the results from the deterministic analysis, we first calculated the percentage increase from the mean to the maximum value, and the percentage decrease from the mean to the minimum value of the cost from the new data source [5]. Then, we multiplied these percentages with the cost from the previous source [4] in order to have estimates of the minimum and maximum cost to input in the DAT. A more detailed example of this calculation procedure is presented below. The minimum, mean, maximum cost per cubic meter for cleaning, and the cost per square meter of a superior passage are given in Table 6. These data are available from the new source [5]. 8/20

9 Table 6 Cost data from the new information source [5] unit minimum mean maximum Earthwork: cleaning cost/m Superior passage cost/m The values from Table 6 were used to calculate the percentage decrease from the mean to minimum value, and the percentage increase from the mean to the maximum value. These percentages are reported in Table 7. In the case of cleaning the minimum cost is 0.30 euro/m 3, which corresponds to a decrease of 40% from the mean value of 0.50 euro/m 3. The maximum cost is 1.0 euro/ m 3, which corresponds to an increase of 100% from the mean value. Table 7 Example of calculate percentage using the new information source [5] unit minimum mean maximum Earthwork: cleaning cost/m % % 1.0 Superior passage cost/m % % 750 These percentage values were used to calculate the increase in cost of activities and structures currently used in the DAT. The costs of cleaning and of a superior passage, from the previous data source [4] and currently used in the DAT, are given in Table 8 for section of alignment A. Table 8 Cost data from the previous information source [4] unit cost Earthwork: cleaning cost/m Superior passage cost/m The percentages calculated in Table 7 were applied to the cost data in Table 8. For example, the minimum cost of cleaning is the mean cost of 0.70 euro/m 3 decreased by 40%, resulting in 0.42 euro/m 3 (see Table 9). 9/20

10 Table 9 Example of calculated minimum and maximum costs to input in the DAT unit minimum mean maximum Earthwork: cleaning cost/m % % 1.40 Superior passage cost/m % % 625 The calculation procedure explained above has been carried out for all activities and structures in all sections of both Alignments A and B. The construction of an embankment requires more than one activity, namely removing, cleaning, constructing the embankment, and placing the ballast layer. The minimum, mean and maximum costs of these activities were summed up to give the minimum, mean and maximum cost for the construction of the embankment. This same procedure was followed to calculate the minimum, mean and maximum value for the cuts, the tunnels and the viaducts. The values were then input in the DAT. Table 10 summarizes the values for section for normal and special embankments; cuts A/B/C and D; tunnel types 2 and 3; viaduct; inferior (PI) and superior (PS) passages Probability distribution of costs Minimum, mean and maximum values for all the constructions methods and structures were used to calculate the variation in total cost of alignments A and B. This is done with probability distributions. 10/20

11 Table 10 Minimum, mean and maximum cost in section Nor-Embank Cost Variables (cost/m) Activities min mean max Remove Clean Embankment Ballast Nor-Embank Spe-Embank Cost Variables (cost/m) Activities min mean max Remove Clean Embankment Ballast Spe-Embank Cut-A/B/C Cost Variables (cost/m) Activities min mean max Cut-A Ballast Cut-A/B/C Cut-D Cost Variables (cost/m) Activities min mean max Cut-D Ballast Cut-D Tunnel-Type2 Cost Variables (cost/m) Activities min mean max Exca-support Drain-waterproof-lining Equip-security TA Tunnel-Type Tunnel-Type3 Cost Variables (cost/m) Activities min mean max Exca-support Drain-waterproof-lining Equip-security TA Tunnel-Type Viaduct Cost Variables (cost/m) Activities min mean max Viaduct PI - Small viaduct Cost Variables (cost) Activities min mean max PI - Small viaduct PS - Small viaduct Cost Variables (cost) Activities min mean max PS - Small viaduct /20

12 SimJava works with three distributions: uniform, triangular and bounded triangular [1]. In the case of the uniform distribution, the variable has the same probability of taking on any value between the minimum and maximum value (see Figure 3 (a)). For the triangular distribution, a minimum value, a most likely value, called mode, and a maximum value need to be provided (see Figure 3 (b)). The area under the triangle must sum up to the total probability of one. In the case of the bounded triangular distribution, probabilities greater than zero can be attributed to the minimum and maximum boundaries of the triangle. These probabilities are shown in Figure 3 (c) in form of spikes at the outer apices of the triangle. The area of the minimum value, the maximum value and the area under the triangle must sum up to the total probability of one. For the probabilistic analysis of alignments A and B we worked with the triangular distribution. The required input is the minimum, mode and maximum value. Given the minimum, the mean and the maximum value, the mode can easily be calculated. If the minimum, mean and maximum values could not be fitted into a triangular distribution, the bounded triangular distribution was used. The mode and the bounds were calculated for all cost variables in both alignments A and B. The minimum, the mean, the maximum, the mode and the bounds of the cost variables in section of alignment A are listed in Table 11. Table 11 Minimum, mode, mean and maximum cost values of section 2.1.3, alignment A min. bound Cost Variables minimum mode mean maximum max. bound Nor-Embank , , Spe-Embank , , , , Cut-A/B/C , , , , Cut-D , , , , Tunnel-Type , , , , Tunnel-Type , , , , Viaduct , , , , PI - Small viaduct , , , , PS - Small viaduct , , , , /20

13 (a) (b) (c) Figure 3 Uniform (a), triangular (b) and bounded triangular (c) distributions 13/20

14 4.4. Simulation results One thousand simulations were run for each alignment. In every simulation for every cost variable a value between the minimum and maximum is picked according to the probability distribution. Therefore every simulation provides a different total cost. The results of the simulations are shown in Figure 4 for alignment A and in Figure 5 for alignment B. For alignment A the mean total cost is approximately million with a standard deviation of 6.7 million, whereas for alignment B the mean value is approximately million with a standard deviation of 10.3 million. In Table 12 the mean values are compared with the deterministic value and the total costs provided by RAVE. Table 12 - Comparison of total costs Total costs (euro) Alignment RAVE Deterministic simulation Probabilistic simulation (mean value) A 265,245, ,245, ,312,005 B 446,018, ,018, ,319,193 The differences are small with the mean value from the probabilistic data slightly higher for alignment A and lower for alignment B. 14/20

15 [mio. euro] [of 1,000 simulations] Figure 4 Total cost distribution for alignment A; mean = 265,312,005 euro [mio. euro] [of 1,000 simulations] Figure 5 Total cost distribution for alignment B; mean = 445,319,193 euro 15/20

16 4.5. Alternative probability distribution of costs The new data source [5] reports mínimo, médio, and máximo cost. An example was already given in Table 5. In the analyses so far, we interpreted the médio value, as the statistical mean value. In the report [5] on page 43, thought, the mean is considered equivalent to the mode ( médio ou mais provável). For this reason, we run another set of simulations assuming that all the médio values in report [5] are mode values, rather than statistical mean values. As an example, the minimum, the mode and the maximum values in section of alignment A are listed in Table 13. Table 13 Minimum, mode and maximum cost values of section 2.1.3, alignment A Cost Variables minimum mode (=médio) maximum Nor-Embank , , Spe-Embank , , , Cut-A/B/C , , , Cut-D , , , Tunnel-Type2 24, , , Tunnel-Type3 33, , , Viaduct , , , PI - Small viaduct 137, , , PS - Small viaduct 375, , , A comparison between Table 13 and Table 11 shows that the mode values of Table 13 are equal to the mean values of Table 11. As explained above, in this case we are assuming that the data given in [5] as médio are mode values. Again 1000 simulations were run for each alignment. The results of this set of simulations are shown in Figure 6 for alignment A and in Figure 7 for alignment B. For alignment A the mean total cost is approximately million with a standard deviation of 6.2 million, whereas for alignment B the mean value is approximately million with a standard deviation of 9.9 million. In Table 14 the results from this set of simulations are compared with the total costs provided by RAVE, the deterministic values, and the probabilistic values from the first set of simulations. 16/20

17 [mio. euro] [of 1,000 simulations] Figure 6 Total cost distribution for alignment A, using médio as mode. Average total cost = 287,910,820 [mio. euro] [of 1,000 simulations] Figure 7 Total cost distribution for alignment B, using médio as mode. Average total cost = 467,992,279 17/20

18 Table 14 Comparison of total costs Alignment RAVE Total costs (euro) Mean total costs (euro) Deterministic Probabilistic simulation simulation médio = mean médio = mode A 265,245, ,245, ,312, ,910,820 B 446,018, ,018, ,319, ,992,279 The comparison of the mean values of the simulations, using first the médio as mean and then the médio as mode, shows that in the latter case the average total costs increase by approximately 10%. 18/20

19 5. Conclusion and future work This second study attempted a probabilistic approach to a high speed railway line using the DAT. It is unclear at this point whether the médio values in report [5] should be interpreted as mean or as mode values. Simulations for both scenarios were run, and it is possible to conclude that interpreting the médio values as mode values, i.e. most probable values, causes the average total costs to increase by 10%. Below are some suggestions of possible future work regarding the RAVE high speed lines: Main Suggestions: 1. Include time uncertainties 2. Include uncertainties in the geology Additional suggestions: 3. Extend the analysis to the entire line Lisbon-Porto (Question: deterministic first and then probabilistic?) 4. Extension of the DAT to include life cycle costs 5. Include uncertainty on the location of karst caverns (to study where to reinforce the structures or apply mitigation methods) 6. Include environmental issues/ costs 7. More detailed studies on a particular (long) tunnel construction method, time and cost of construction, section type (one tube, double tube), location of shafts 8. Resource managing (probably only in an more advanced stage of the project) Note that the suggestions mentioned above can be combined. 19/20

20 7. References [1] SimJava (2007). Decision Aids for Tunneling (DAT), User s Manual. Massachusetts Institute of Technology, Cambridge. [2] Einstein, H.H. (2002). Risk assessment and management in geotechnical engineering. 8th Portuguese Geotechnical Congress, Lisbon, pp [3] Sousa, R. L., Min, S., Einstein, H. H. (2007). Deterministic Cost Analysis for the High Speed Rail between Porto and Lisbon. Alignments A & B close to Leira. Report to RAVE, June [4] Ligação Ferroviária de Alta Velocidade entre Lisboa e Porto. Lote C1. Troco Alenquer (Ota) Pombal. Estudo previo. Volume 3, [5] Relatório de Custos. Eixos Lisboa-Porto e Lisboa-Madrid, Revisão A, /20