Analytical methods to reduce uncertainty in tunnelconstruction projects

J.Y. Ruwanpura, S.M. AbouRizk, and M. Allouche

Abstract: This paper presents a method to quantify uncertainty using simulation techniques and approximategeotechnical methods. Unknown soil conditions are major contributors to uncertainty in any underground constructionproject. Soil conditions are unknown because generally soil samples taken from vertical boreholes show only the soilspresent in the discrete borehole locations. The soil profiles between the boreholes therefore contribute to project uncer-tainty, and construction practitioners must make assumptions about these soil profiles for construction planning andscheduling purposes. Analytical and simulation methods are presented to accurately predict soil profiles between bore-holes and reduce uncertainty in a rough and ready fashion. These methods use existing borehole data to create an an-alytical model for soil prediction, which is then incorporated with a process interaction simulation model of theconstruction project using special purpose simulation concepts and advanced geotechnical characterization techniques.The application of these methods to an Edmonton tunnel construction project is also detailed. Construction engineers ormanagers can use these simulation methods to strengthen the geological data obtained for the construction project.

Key words: borehole data, construction, risk, soil families, soil profiles, soil transitions, special purpose simulation, tun-nelling, uncertainty.

Rsum : Cet article prsente une mthode pour quantifier lincertitude lors de lutilisation de techniques de simulationet de mthodes gotechniques approximatives. Des conditions de sol inconnues sont le principal facteur dincertitude detout projet de construction souterrain, Les conditions de sols sont inconnues parce que les chantillons de sol, pris deforages verticaux, ne montrent gnralement que les sols prsents aux endroits spcifiques du forage. Les profils desols entre les forages contribuent donc lincertitude du projet et les constructeurs doivent poser des hypothses sur lesprofils de sols lors de la planification et de ltablissement de lchancier de construction. On prsente des mthodesanalytiques et de simulation afin de prdire prcisment les profils de sols entre les forages et ainsi rduirelincertitude un niveau gnral et acceptable . Ces mthodes utilisent les donnes de forage existantes pour crerun modle analytique de prdiction des sols, lequel est ensuite incorpor dans un modle de simulation de processusdinteraction du projet de construction utilisant des concepts de simulation spciale et des techniques de caractrisationgotechniques avances. Lutilisation de ces mthodes lors dun projet de percement dun tunnel Edmonton est expli-qu en dtail. Les ingnieurs ou les gestionnaires de construction peuvent utiliser ces mthodes de simulation pour sou-tenir les donnes gotechniques obtenues pour le projet de construction.

Mots cls : donnes de forage, construction, risque, familles de sols, profils de sols, transitions de sols, simulation sp-ciale, percement de tunnels, incertitude.

[Traduit par la Rdaction] AbouRizk et al. 360

Introduction

Tunnel construction projects are considered to be high-risk projects. Identifying and quantifying uncertainty factorsin tunnel construction helps the project planners, engineers,and constructors to mitigate risks during construction. Soil

conditions are major contributors to uncertainty in any un-derground construction projects. For typical utility tunnelconstruction, soil samples from vertical boreholes spacedabout 300500 m apart show only the soil types that arepresent in the borehole locations. The soil profiles betweenthe boreholes are therefore uncertain. Practitioners must

Can. J. Civ. Eng. 31: 345360 (2004) doi: 10.1139/L03-105 2004 NRC Canada

345

Received 3 July 2003. Revision accepted 20 November 2003. Published on the NRC Research Press Web site at http://cjce@nrc.caon 6 April 2004.

J.Y. Ruwanpura. Department of Civil Engineering, ENF 232, The University of Calgary, 2500 University Drive NW, Calgary, ABT2N 1N4, Canada.S.M. AbouRizk.1 Department of Civil and Environmental Engineering, 220 Civil Engineering Building, University of Alberta,Edmonton, AB T6G 2G7, Canada.M. Allouche. Research Associate, Hole School of Construction, 220 Civil Engineering Building, University of Alberta, Edmonton,AB T6G 2G7, Canada.

Written discussion of this article is welcomed and will be received by the Editor until 31 August 2004.

1Corresponding author (e-mail: abourizk@ualberta.ca).

make assumptions about the soil profiles between the bore-holes for construction purposes. There are various factorsconsidered in predicting soil conditions in an area. Theavailability of a particular soil type, the start and end eleva-tions of the soil layers, the thicknesses of the soil layers, andthe distribution of the soil layers between the boreholes andwater table are some of the major factors that can affect tun-nel construction productivity.

This paper describes analytical methods to quantify andreduce uncertainty in tunnel construction projects. This anal-ysis helped the Asset Management and Public Works De-partment of the City of Edmonton to reanalyze the soilprofiles for a major tunnelling project in Edmonton, Alberta.The soil profiles predicted using the analytical methods ex-plained in the following sections were found to be accurateduring soil exploration and tunnel construction. Althoughthese methods are not a replacement for comprehensivegeotechnical investigation, construction engineers or manag-ers can use them to confirm, validate, or complement suchinvestigations.

Risks and uncertainty in tunnelconstruction

Risk can be defined as the possibility of suffering loss orharm (Concise Oxford Dictionary 1991). AbouRizk (2000)clarifies that the event and (or) its outcome must be associ-ated with a certain degree of uncertainty (the possibility) forrisk to be an issue. Therefore, risk and uncertainty go handin hand and must be assessed concurrently. Palisade Corpo-ration (1999) suggests that Risk derives from our inabilityto see into the future, and indicates a degree of uncertaintythat is significant enough to make us notice it. Lifson(1972) goes further in tying the two concepts together by in-dicating that Risk is the measure of uncertainty concerningoutcomes; it is the explicit, quantitative representation of theuncertainty associated with the estimates of outcomes.

The most effective way to deal with uncertainty is to col-lect more information and knowledge. When that is expen-sive or infeasible, various researchers have tried to quantifyuncertainty using analytical or simulation techniques. Theremaining paper details how applying analytical and simula-tion techniques can reduce uncertainty in tunnel constructionprojects.

To address uncertainty in tunnel construction, researchersrequire an approach that provides better characterization ofsoil conditions underground. Such approaches are oftentime-consuming and laborious. The method described in thispaper provides such soil characterization in a rough-and-ready manner that maximizes the certainty while minimiz-ing involvement of the practitioner by making use of exist-ing knowledge and simple probability concepts. The soilprofiles are then predicted based on these probabilities usingsimulation techniques. To carry out this characterizationmethod, the following must already be in place:1. a database of data from borehole logs within the area of

the tunnel2. an analytical model to predict soil conditions within the

tunnel alignment3. a process interaction simulation model for the tunnel to

be constructed using special purpose simulation concepts

equipped with advanced geotechnical characterizationtechniques.

This paper discusses an approach that uses the above-mentioned requirements in quantifying uncertainty in tunnelconstruction.

State-of-the-art in special purposetunnelling simulation

A special purpose simulation (SPS) template for utilitytunnel construction operations was designed in collaborationwith the Asset Management and Public Works Departmentof the City of Edmonton. AbouRizk and Hajjar (1998) de-fine SPS as a computer-based environment built to enable apractitioner who is knowledgeable in a given domain, butnot necessarily in simulation, to model a project within thatdomain in a manner where symbolic representations, naviga-tion schemes within the environment, creation of modelspecifications, and reporting are completed in a format na-tive to the domain itself. These SPS tunnel constructiontemplates developed with simphony (Hajjar and AbouRizk2000), enabled the City of Edmonton to evaluate varioustunnelling options expeditiously, primarily allowing the en-gineers to test the validity of their construction planningstrategies. A complete design, development, and implemen-tation of this tool can be found in Ruwanpura et al. (2001a)and Er et al. (2000).

Figure 1 depicts the modeling layout of the tunnel tem-plate including some of its input parameters, statistics, andcost planning outputs. Particular attention should be directedto the input parameters of the soil segment modeling ele-ment at the right side of the figure. The user could add manytunnel segments to the model depending on the soil prop-erties. In this example of the simulation template, there aretwo soil segments in the figure for illustration purposes: thefirst is excavated in bedrock (100%) and the second sectionis excavated in a combination of bedrock (80%) and glacialclay till (20%). The composition of the soils is subjectivelyset by the modeller and is therefore approximate in this tem-plate.

The following are sample applications of the tunnel simu-lation template that were implemented with the City of Ed-monton:1. testing the template for tunnel construction projects by

changing different resources and setting up options forundercut and shaft (see AbouRizk et al. 1999)

2. evaluating various alternatives at the project planningstage of an Edmonton tunnel construction project (Er etal. 1999, 2000)

3. evaluating two bidding scenarios and determining thebetter of the two based on the outputs of the simulationmodel (Ruwanpura et al. 2000)

However, the simulation results documented byRuwanpura (1999) demonstrated that uncertainty factorscould not be predicted using the current state-of-the-art de-scribed in Ruwanpura et al. (2001a). In this particular pro-ject, the adverse soil conditions along with several otherfactors had caused very low productivity in terms of tunnelprogress. This identified other factors that affect tunnellingproductivity, such as soil conditions, human productivity,tunnel boring machine (TBM) efficiency, and method of

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346 Can. J. Civ. Eng. Vol. 31, 2004

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AbouRizk et al. 347

Fig

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construction operation, and the need for a methodology topredict soil types and their transitions throughout the tunneltrajectory for the purpose of accurately predicting produc-tion rates.

Establishing a database of borehole data inthe tunnel area

This section describes a method to reduce the uncertaintybetween boreholes by dividing the distance separating theboreholes into segments to identify the soil transitions. Forexample, if there are two boreholes spaced at 250 m, the dis-tance may be divided into a few sections based on the soiltypes observed in the two boreholes and the surroundingarea of the tunnel. The construction manager could decidewhether he (she) needs to drill additional boreholes to fur-ther justify the existence of soil types other than those foundin the boreholes or to take extra measures to handle that por-tion of the tunnel. The overall process of this method in-volved five steps: gathering and characterizing the data,analyzing and dividing the data into unique groups, cluster-ing the soil families, developing algorithms to predict thesoil families, and applying the concepts to a real tunnel con-struction project.

Gathering and characterizing the dataBoreholes driven by the department of Asset Management

and Public Works of the City of Edmonton in the past30 years and the boreholes selected by the Alberta ResearchCouncil (ARC) to draw the graphical existence of the Ed-monton geology (McPherson and Kathal 1972) were col-lected. The geology of the Edmonton area is categorized into11 major soils: bedrock (soil 1), ice-shoved bedrock (soil 2),disturbed Saskatchewan gravels and sands (soil 3), Saskatch-ewan gravels and sands (soil 4), glacial till (soil 5), glacialsand and gravel (soil 6), lacustro-till (soil 7), glaciolacus-trine deposits 1 and 2 (soils 8 and 9), aeolian deposits (soil10), and alluvium (soil 11). The detailed description of thesesoil types and general observations can be found inRuwanpura et al. (2001b).

Analyzing and dividing the data into unique groupsThere are different soil types that exist vertically at dis-

crete elevations between the surficial soil and the bottom-most layer at a given point within an area. During the analy-sis of the Edmonton soil data, the following observationswere made: only unique surficial soil types exist in the area certain soils exist as the bedding layer to some other soils soils exist as pockets within another soil layer some soils co-exist with other soils

These observations suggest that there could be many verti-cal soil profile variations from the surface to the bedrocklayer from one point to another in the area. That means thereare several unique types of soils that interact with other soiltypes in the area. To identify these interactions, the conceptof a soil family (Fig. 2) was introduced. A soil family rep-resents the order of the different soil types that exist verti-cally at discrete elevations commencing from the surficialsoil to the bottom-most layer at a given point within an area.

According to ARC data, there are 59 soil families in the Ed-monton study area. The most common families are given inTable 1. The most common family in the Edmonton area is851, which consists of soil type 8 (Lake Edmonton) thesurficial soil type, followed by soil type 5 (glacial clay till)and soil type 1 (bedrock 1). This step provided a sound data-base of soil data in the Edmonton area.

Clustering the soil familiesAny area can be divided into various soil clusters (groups)

depending on different dependant variables (Isaaks andSrivastava 1989). In this study, the area was divided into var-ious clusters based on the surficial soil type, irrespective ofthe soil types under the surficial soil layer. However, therecould be several families of soils under one surficial soil; Ta-ble 2, for example, lists all the soil families where soil 8 isthe surficial soil. In Edmonton, there are 7 different soilclusters: cluster 5 (CL5), cluster 6 (CL6), cluster 7 (CL7),cluster 8 (CL8), cluster 9 (CL9), cluster 10 (CL10), and clus-ter 11 (CL11). There are 9 different soil families under CL5,4 soil families under CL6, 10 soil families under CL7, 30 soilfamilies under CL8, and 1 soil family each under CL9, CL10,and CL11 for the Edmonton study area. This clustering al-lows researchers to identify the coexistence of some soilfamilies with others.

Developing algorithms to predict the soilfamilies in the tunnel path

Using the steps explained above, it could be inferred thata particular soil exists in the neighbourhood of a particularborehole, although the borehole does not show any sign ofthis soil. Algorithms were developed that are documented inRuwanpura et al. (2001b) to calculate the probability of thecoexistence of a particular soil family in the neighbourhood,as shown in the boreholes, with respect to the other soil fam-ilies within the tunnel area. The notation used to describe asoil family is a list of numbers describing the soil layers in aborehole from surface to bottom. For example, a boreholewith soil family 85651 has soil type 8 as its surficial soil,with a layer of soil type 5 underneath, then a layer of soiltype 6, another layer of soil type 5, and a bottom layer ofsoil type 1. The following equations explain the specific al-gorithms used in this calculation.

An example will serve to better illustrate the calculations.Figure 3 shows several soil families in the boreholes in prox-imity to the tunnel that is 3440 m long. The families are 851,751, 51, 75651, 7561, 85651, and 651 in the respective bore-holes. The coexistence probability (PCEBase) of a particularsoil family (FamilyBase) in the neighbourhood of a boreholein the tunnel area is dependent on the other families (Fam-ily1 to Familyn) in the boreholes (BH1 to BHn) and can becalculated using eq. [1]. If FamilyBase is the same as the soilfamily in the borehole, the PCEBase value is equal to 1 irre-spective of eq. [1].

[1] PCEF(Base)

F(Base) F(Base, BH

soil family A

soil familyi = + Base)soil family

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348 Can. J. Civ. Eng. Vol. 31, 2004

where F(Base)soil family A is the number of occurrences of thebase soil family A in the database within a given area, andF(BHi)soil family is the number of soil family occurrences inborehole i that exist within a given area.

The following example illustrates the PCE for soil family51 with respect to a borehole in a typical tunnel path, BH2,which contains soil family 751:

F(Base)51 = 18 (see Table 1, line 3)

F(BH2)751 = 14 (see Table 1, line 4)

PCE 51,BH2 = 18/32

= 0.5625

The next step is to calculate a weighted factor (WF) for aparticular soil family at a target point within the tunnel tra-jectory using the distance of the boreholes to the target pointand the calculated PCE values for a particular soil family inthe respective boreholes. The weighted factor at target pointT (WFT) for soil family A in the tunnel direction could becalculated as per eq. [2] where dBH is the distance fromborehole (BH) to the target point T and PCEBH, soil family A isthe PCE value for soil family A at borehole BH. The use ofdistances gives a higher weighted value if the target point iscloser to the borehole. The weighted factors at the target

points along the tunnel path provide a distribution of a par-ticular soil family from the start of the tunnel to the end ofthe tunnel.

[2] WF

PCE

T, soil familyBH =1

BH BH, soil family A

BH =1

=

1

1

n

n

d/

/dBH

The final step is to calculate the weighted coexistencevalue (WCEV) for all soil families at each target point in thetunnel trajectory using eq. [3]. The minimum (WFMinimum)and maximum (WFMaximum) values for all WF values calcu-lated using eq. [2] for each soil family are taken into consid-eration in calculating the WCEV for each soil family at eachtarget point. The WCEV for soil family A at target point Tcan be calculated as per eq. [3]. The maximum value ofWCEV for soil families becomes the predicted soil family ateach target point. Equation [3] is a transformation formula tonormalize weighted factors calculated using eq. [2] and toidentify the optimum existence of the soil families along thetunnel path.

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AbouRizk et al. 349

Fig. 2. Soil families.

Total No. ofobservations Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Layer 6

79 8 5 1 76 8 5 3 1 18 5 1 14 7 5 1 8 8 5 6 5 1 6 8 7 5 1 6 8 5 2 5 1 5 8 5 6 5 3 15 7 5 6 5 1

Table 1. Most common soil combinations (families) stratigraphy of Edmonton.

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350 Can. J. Civ. Eng. Vol. 31, 2004

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WFT, soil family A Minimum, soil family A

Maximum, soi

l family A Minimum, soil family AWF

Returning to our example, there are several soil familiesin the boreholes in proximity to the 3440 m tunnel, as illus-trated in Fig. 3. Figure 4 shows the predicted soil familiesalong the length of the tunnel based on WCEV values. Theresults from Fig. 4 indicate the following soil family se-quence for the tunnel: 751 (0 to 220 m), 51 (221 to 479 m),7561 (480 to 719 m), 51 (720 to 823 m), 75651 (824 to998 m), 85651 (999 to 1794 m), 651 (1795 to 2420 m),85651 (2421 to 2761 m), and 851 (2762 to 3443 m). At thisstage, results are reevaluated using knowledge based on thearea by looking at previous, present, and following families(e.g., 751, 51, 7561) in the area to determine the probabilityof the sequence. For example, it is improbable that soil fam-ily 85651 would exist between soil family 851 and soil fam-ily 651 according to the knowledge base. These observationsamend the predicted results and are used to determine thenext best alternatives. The amended and final sequence is751 (0 to 220 m), 51 (221 to 823 m), 75651 (824 to 998 m),651 (999 to 2420 m) and 85651 (2421 to 3440 m) in the tun-nel trajectory.

Applying the concept to a tunnel construction projectThis section details the application of the modeling con-

cepts to the North Edmonton sanitary trunk (NEST) tunnelproject in Edmonton. The NEST tunnel project initially hadfew boreholes driven along the 1650 m-long tunnel path.Figure 5a shows the location of the initial boreholes drivenfor the project and the additional borehole data obtainedfrom the database created using ARC data close to the tun-nel path. The boreholes driven by the City of Edmonton aredenoted with TH and the ARC boreholes are denoted withBH.

The methodology presented in this paper was applied todetermine the existence of noncontinuous soil types in thelast 708 m of the tunnel. The main soil types available in thetunnel path are glacial clay till (soil type 5), reworked clayshale (soil type 2), and sand pockets (soil type 6). BoreholesTH99-1 and TH99-2 contain soil family 8565251, boreholesTH99-3 and BH287 contain soil family 85251, and bore-holes TH99-4, TH6-2, and BH2115 contain soil family 851.The last 708 m, as shown in Fig. 5a, contain several noncon-tinuous soil types including soil 6 and 2 in boreholes TH99-1to TH99-3. The elevation of both soil types 2 and 6 arewithin the dimensions of the tunnel or just below the bottomelevation of the tunnel. Based on the borehole data, it couldbe assumed that soil type 6 exists continuously from somepoint left of borehole TH99-2 to the right of borehole TH99-1(Fig. 5b). The borehole data also suggest that soil type 2does not exist in the tunnel path. Figure 5b shows one of themost likely profiles of soil types 2 and 6 between the bore-holes using linear approximations or interpolations a typ-ical industry practice.

Only soil family 851 was present in both the City of Ed-monton and the ARC boreholes for the first portion of thetunnel. However, the ARC borehole BH287 containing soilfamily 85251 is about 370 m away from the tunnel. SinceBH287 has no evidence of the existence of soil type 6, andthe distance between TH99-1 and TH99-2 is approximately400 m, the prediction of soil families was performed to dis-cover the following:1. the extent of soil type 6 between TH99-1 and TH99-22. the extent of soil type 2 between TH99-1 and TH99-3

An analysis was performed for the last portion of the tun-nel using the methodology described above and submitted tothe design and construction department of the City of Ed-monton. The conclusions are represented visually in Fig. 5c.There was no need to analyze the rest of the tunnel, as therewas no evidence to show that there could be noncontinuoussoil types except in the last 708 m.1. soil family 8565251 exists only about 54 m from bore-

hole TH99-1 to borehole TH99-2 and for only 67 m inthe area of borehole TH99-2. This confirms that soiltype 6 is not a continuous soil layer between TH99-1and TH99-2

2. soil family 85251 is the most likely soil family for264 m from borehole TH99-3 to the end of the tunneland for 321 m between boreholes TH99-2 and TH99-1

The analysis also recommended that the City of Edmon-ton consider exploring the soil conditions further, especiallybetween boreholes TH99-1 and TH99-2. This is motivatedby the demand to deal with the fundamentals of uncertainty,i.e., to collect more information but based on predictivemodeling outputs.

The City of Edmonton further explored the soil conditionsalong the tunnel path by driving four additional boreholes(TH00-1 to TH00-4), as shown in Fig. 6a. Borehole TH00-3contains soil family 851, whereas all other boreholes havesoil family 85251. The borehole TH00-2 confirmed the pre-diction that soil type 6 does not exist continuously fromTH99-2 to TH99-1, although both TH99-1 and TH99-2 con-tain soil type 6. Further, the existence of soil family 85251in boreholes TH00-4 and TH00-2 confirmed that soil type 2 iscontinuous from left of TH99-3 to TH99-1. This prediction

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AbouRizk et al. 351

Fig. 3. Sample tunnel and borehole locations (ARC data).

and analysis is a clear indication of the validity of the meth-odology proposed for tunnel construction projects. Engineerscan use this method to explore the soil types along the tun-nel path in addition to the usual geological explorations per-formed.

Ruwanpura and AbouRizk (2001) briefly discuss the soiltransitions along the tunnel trajectory, which is explained inthe next section. Another method to handle uncertainty ex-plains how the prediction of soil families could assist in de-ducing the soil profiles between the boreholes logically todetermine the soil transitions along the tunnel path. Basedon the prediction and the two new boreholes, the tunnellength between boreholes TH99-3 and TH99-1 can be dividedinto seven sections. These seven sections are shown inFig. 6b and are listed below: (i) section 1 165 m in soilfamily 85651, (ii) section 2 99 m in soil family 85251,(iii) section 3 30 m in soil family 8565251, (iv) section4 37 m in soil family 8565251, (v) section 5 271 m ofsoil family 85251, (vi) section 6 52 m of soil family85251, and (vii) section 7 54 m of soil family 8565251.

Using the prediction analysis of the soil families, it is pos-sible to reduce the uncertainty of the soil conditions betweenthe boreholes by identifying the extent of each soil family.

The analysis proved that soil type 6 does not exist contin-uously. Because of the analysis and the availability of newboreholes, it is easy to determine the soil profiles betweenthe boreholes more accurately and logically. Figure 6bshows the most likely profiles of soil 2 and 6 within soiltype 5 along the tunnel path based on the soil family predic-tion methodology. Figure 6b can be divided into several seg-ments to determine the transition from one soil to anotherand the modeling algorithms for these soil transitions. Thesealgorithms can then be implemented using special purposesimulation, as explained in the next section. The resultsshown in this section further prove that this technique is very

useful in predicting the noncontinuous soil layers (soil pock-ets) along the tunnel path.

Predicting soil transitions along the tunnel pathPredicting soil transitions along a tunnel path is a chal-

lenging task. The boreholes driven for a tunnel constructionproject only provide a handful of deterministic data points atdiscrete locations in either the tunnel alignment itself or ad-jacent to the tunnel trajectory. The borehole data determinesoil types at discrete locations and produces deterministicestimates of the type of material and the elevations of eachof the soil layers in the boreholes. Predicting soil composi-tions between the boreholes are generally achieved using ap-proximate methods, as demonstrated by Ruwanpura et al.(2001a).

A major deficiency of approximate methods is the deter-mination of transition points from one soil type to anotherwhen soil composition is mixed (e.g., clay material andsand). This section describes an approach for modeling thetransition of soils between the boreholes for simulation pur-poses, and the hightlights of this approach are as follows:1. develop an approach for calculating the transitional

probabilities to determine the transition from one soiltype to another in the tunnel trajectory

2. develop modeling algorithms based on the soil transitionpatterns included in the database of soil transition sce-narios

3. design of a tunnel construction simulation tool to incor-porate the modeling algorithms

4. apply the tunnel simulation tool to an actual project tovalidate its accuracy

Modeling transitional probabilitiesFigure 7 shows a typical scenario of soil type transitions

among three borehole locations along the path of a hypothet-

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352 Can. J. Civ. Eng. Vol. 31, 2004

Fig. 4. Weighted coexistence value (WCEV) of the soil families for sample tunnel.

ical tunnel. A simple two-state (soil type A, soil type B)Markov chain can be used to determine the occurrence ofsoil type A or B. Figure 7 shows that the transition from soiltype B to A at both the top elevation (elevationTop) and bot-tom elevation (elevationBottom) of the tunnel between bore-holes BH1 and BH2. This two-state Markov chain is definedby transitional probabilities of moving from one soil state toanother soil state. Transitional probabilities are dependanton the location of the tunnel, diameter of the tunnel, startand end elevations of the soil types, and the soil types in thevicinity. Equation [5] defines the transitional probability oftransiting from state b (soil type B) at one known point(BH1) in the tunnel to state a (soil type A) at a known point(BH2) at the top elevation of the tunnel (elevationTop).

The probability of observing soil type A (state a) in thetunnel path at elevationTop can be calculated using eq. [4]

[4] P AN A

TTop

Top

Top

( )( )

=

where NTop(A) is the number of observed transitions in soiltype A at elevationTop and TTop is the total number of all soiltypes observed along the tunnel path at elevationTop.

There are two overall probabilities that define the modelin detail for one elevation, which are listed below: PTop (A): overall probability of having soil type A at ele-

vationTop PTop (B): overall probability of having soil type B at ele-

vationTop

[5] P B ANn

BA

BTop( / ) =

where NBA is the number of observed transitions generatedfrom soil type B to A at elevationTop along the tunnel path.

The number of observed transitions generated from soiltype B to all states including soil type A and B at eleva-tionTop is denoted by nB. When two types of soil interactwithin the tunnel alignment, four transitional probabilitiesmust be defined:

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AbouRizk et al. 353

Fig. 5. (a) Preliminary boreholes; (b) approximate estimate of the soil types between the boreholes; and (c) analytical estimate of thesoil types between the boreholes.

PTop, BH2 (A/A): Probability of soil type A at location BH2in the tunnel path at elevationTop given that soil type A canbe observed at location BH1 at elevationTop

PTop, BH2 (A/B): Probability of soil type B at location BH2in the tunnel path at elevationTop given that soil type A canbe observed at location BH1 at elevationTop

PTop, BH2 (B/A): Probability of soil type A at location BH2in the tunnel path at elevationTop given that soil type B canbe observed at location BH1 at elevationTop

PTop, BH2 (B/B): Probability of soil type B at location BH2in the tunnel path at elevationTop given that soil type B canbe observed at location BH1 at elevationTop

Rules in transitional probability matrices for soilprediction (two continuous soils)

Figure 8 is used to explain the modified transitional prob-abilities rules using a hypothetical example of a tunnel witheight boreholes. There are only two soil types in the vicinityof the tunnel. The transitions are enumerated separately inseven elevation levels. The elevation level considers any gra-dients (if any) in the tunnel from its start to the end. The fol-lowing are the elevation levels, which reflect the soilcombinations in the tunnel vicinity: (i) top of the tunnel ele-vation (T), (ii) bottom of the tunnel elevation (B), (iii) centerof the tunnel elevation (C), (iv) mid-point between top andcenter of the tunnel elevation (T), (v) mid-point betweencenter and bottom of the tunnel elevation (B+), (vi) one point(user-determined) above the top of the tunnel elevation (T+),and (vii) one point (user determined) below the bottom ofthe tunnel elevation (B).

Requirements (vi) and (vii) are user inputs and could bedetermined based on the distribution of the soil profiles be-tween the start and end of the tunnel. In this example, it islimited to 1 m just below and above the tunnel to verify that

the transitions may consider the possible occurrence of soiltypes closer to the top and bottom elevations of the tunnel.Table 3 represents the transitional probabilities of the fol-lowing combinations for the tunnel depicted in Fig. 8, basedon eq. [4]: T+ = AAAABAAA, T = BAAABBAA, T =BBAABBAA, C = BAABBBAA, B+ = BABBBBAA, B =BABBBBAA, and B = BBBBBBAB.

The transitional probabilities in the matrix are stationary(or homogeneous) for the tunnel as the prediction analysisuses these probabilities throughout the entire tunnel. It repre-sents the probability of moving from one soil type to anotheror remaining in the same soil type.

For example, elevation T generates all four transitionalprobabilities. There are three transitions from A to A andone transition from A to B with a total of four transitionsgenerated from A. This prompts the calculation of the transi-tional probability of A to A as 0.75 (3 of 4 transitions) andtransitional probability of A to B as 0.25 (1 of 4 transitions).The transition probability of B to A is then 0.67 (2 of 3 tran-sitions) and B to B is 0.33 (1 of 3 transitions).

Three transition probability matrices are created from thedata in Table 4: top matrix to calculate the transition point atthe top elevation; center matrix to calculate the transition ofsoils in the middle of the tunnel, if any; and bottom matrixto calculate the transition point at the bottom elevation. Thetop matrix is made up of the transitions at elevations T+, T,and T; the center matrix is made up of the transitions at ele-vations T, C, and B+; and the bottom matrix is made up ofthe transitions at elevations B+, B, and B.

Modeling algorithms based on the transition scenariosof the soils

There are several soil combinations that make up the stra-tigraphy of any area. The method explained above intro-

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Fig. 6. (a) Location of all boreholes for NEST tunnel and (b) as-sumed soil profiles between the boreholes.

Fig. 7. Transition of soil type A and soil type B between bore-holes.

P(A/A) P(A/B) P(B/A) P(B/B)

T+ 0.83 0.17 1.00 0.00T 0.75 0.25 0.67 0.33T 0.75 0.25 0.67 0.33C 0.67 0.33 0.50 0.50B+ 0.50 0.50 0.40 0.60B 0.50 0.50 0.40 0.60B 0.00 1.00 0.17 0.83

Table 3. Transitional probabilities for the tunnel inFig. 8.

duced the various families of soils in stratigraphy ofEdmonton. The modeling algorithms for identifying soiltransitions vary according to the following factors:(i) num-ber of soils in the area, (ii) start and end elevations of thesoils, (iii) direction of the soil profiles, (iv) status of the soiltypes (continuous or pockets), and (v) start and end elevationof the tunnel between boreholes.

A sample database of the various combinations of twocontinuous layer soils, which is used for simulation model-ing, is shown in Fig. 9. Five soil-transition-modeling combi-nations can be derived from Fig. 9 based on the soiltransitions for the sample tunnel, as shown in Fig. 8:

1. Transition of one soil to another (soil type B to soil typeA) at both the top and bottom of the tunnel (for exam-ple, BH1 to BH2 and BH6 to BH7). This involves pre-dicting the transition points at both the top and bottomelevations of the tunnel.

2. Transition of soil type A to soil type B only occurs atthe top elevation (BH4 and BH5), requiring the predic-tion of the top transition point.

3. Transition of soil type A to soil type B only occurs atthe bottom (BH2 and BH3), requiring the prediction ofthe bottom transition point.

4. There are no soil type transitions either at the top orbottom of the tunnel. Transitions only occur betweenthe top and bottom elevations of the tunnel (BH3 andBH4), requiring no transition point predictions at the topand bottom of the tunnel.

5. There are no soil type transitions at the top, bottom, orinside the tunnel elevations. Transitions only occurabove or below the tunnel (BH5 to BH6 and BH7 andBH8) requiring no transition point predictions at the topand bottom of the tunnel.

Although some of the scenarios in Fig. 9 are very similarin terms of the transitions at top and bottom, the location ofthe transition points could make a difference in determiningthe productive boring rate. A complete list of all scenariosincluding the soils that are not continuous (e.g., pockets ofsand within clay) can be obtained from the database of sce-narios included in Ruwanpura (2001). Algorithms to calcu-late the transition points for two continuous soil layers varyaccording to many factors in addition to transitional proba-bility values, including the direction of the soil transitionprofile, number of top transitions, and number of bottom

transitions. Figure 10 shows the module for scenario 1 ofFig. 9.

Special purpose simulation tool based onsoil transition algorithms for tunnelling

The modeling algorithms documented above are imple-mented within a tunnel simulation tool described inRuwanpura et al. (2001a). The simphony simulation enginedocumented in Hajjar and AbouRizk (2000) provides a flexi-ble and easy-to-use modeling environment to implement thesoil transition concepts. The existing tunnel simulation tem-plate in simphony was embellished with additional modelingelements and algorithms without losing its originality. Themajor highlights of the embellishments are given below:1. The ability to input the soil types based on the present

observation point and the next immediate observationpoint along the tunnel path, and the ability to add dataabout the appropriate transitional probability values be-tween the two soil types to determine the transitionpoint at the top or bottom elevation of the tunnel.

2. The ability to input a user-defined method of calculatingthe boring rate for soils. Based on the data survey andinterviews with tunnelling experts, the final tunnel con-struction boring rate may be calculated using one of thethree methods mentioned below, if boring is performedin two soils:(i) Percentage weighting based on the composition ofthe soils. If soil type A represents 30% of the soil andsoil type B represents 70%, the boring rate is adjusted tobe 30% of the boring rate of A plus 70% of the boringrate of B.(ii) The lowest boring rate of the two soils.(iii) Worse than the minimum boring rate of the twosoils. Tunnel personnel identified this as the most com-mon situation, although the City of Edmonton cannotjustify it with supporting data.

3. The ability to model different transition combinationsinvolving two continuous soils, three continuous soils,and continuous soils with soil pockets.

4. The ability to add the data, such as soil type and eleva-tion of the soils, from the actual boreholes driven for aparticular project.

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Fig. 8. Transitions of soils in the tunnel.

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Top Center Bottom

Soil type A Soil type B Soil type A Soil type B Soil type A Soil type B

Transitional probabilitiesSoil type A 0.786 0.214 0.667 0.333 0.400 0.600Soil type B 0.714 0.286 0.500 0.500 0.313 0.688TransitionsSoil type A 11 3 6 3 2 3Soil type B 5 2 6 6 5 11

Table 4. Transitional probability matrices top, center, and bottom.

Fig. 9. Some combinations of two continuous soil layers in the database.

Application of the tunnel simulationtemplate to an actual project

This section presents a case study to validate the de-scribed modeling algorithms. The case study uses actual pro-ductivity data from a tunnelling project that was completedin 19941995. The data were obtained from the daily reportlogs and through consultation with the site supervisor andthe site engineer. The tunnel length used for validation pur-poses is 1651 m and the elevation varies from 675.79 m atthe tunnel start to 671.31 m at the tunnel end. This particulartunnel was excavated in bedrock comprising two soil types:shale and sandstone. The tunnel employed two separate con-struction methods. The first portion used for validation was a2.9-m finished diameter tunnel excavated using an M-126Lovat TBM lined with precast concrete segments. The sec-ond portion, which was 700 m long, was a 3.48-m finisheddiameter tunnel lined with shortcrete. The first portion hasbeen selected for analysis as the tunnel simulation templatehas been designed to simulate tunnels lined with precastliner segments. The tunnel is about 2025 m below groundlevel and has a gradient of 0.077% from the entry shaft tothe removal shaft. There are roughly 203 m of curved sec-tion starting at the 687th m of the tunnel. Although therewere 24 boreholes in the tunnel trajectory, only 17 boreholeswere driven in the first portion of the tunnel. Two of theseboreholes were very shallow and did not represent the soiltypes in the tunnel elevation. Figure 11 illustrates the lengthbetween the boreholes and the estimated soil combinationscenarios.

Several alternative models were created using the model-ing approach presented in this paper with different calcula-tion methods to determine the boring rate. Six models werecreated, of which three used the approximate soil composi-

tions as per the method outlined in Ruwanpura et al. (2001a,2001b). The best approximation is the linear interpolation ofthe soil conditions between the boreholes, which uses fifteenseparate soil modeling elements with approximate values.The other three models were created using the new modelingapproach with different calculation methods to determine theboring rate, as explained in the previous section of this pa-per. The results of all six models were tested against the ac-tual tunnel productivity. Since the final productivity of thesixth model, which is based on the assumption that the bor-ing rate is worse than the minimum boring rate of the twosoils (sandstone in this case), is very close to the actual pro-ductivity, Fig. 12 compares the results of the actual tunneladvance rates to those predicted based on the model pre-sented. The overall project productivity is very close to thepredicted productivity rates of this model. Up to about thefirst 300 m, the actual tunnel advance rate is far below thepredicted-tunnel advance rate of the simulation model be-cause of the learning curve typical of any project. For the re-mainder of the tunnel, the actual-tunnel advance rateremains close to the simulated-tunnel advance rates. Thiscomparison indicates that the proper selection of boring rateinputs could provide a more accurate prediction of tunnelconstruction productivity.

Conclusions

The methods to reduce uncertainty explained in this paperprovide some logical input for the industry practitioners toplan future tunnel construction projects. These methods notonly provided a database of borehole information collectedfrom two sources but also a logical method to assess uncer-tainty about soil types between the boreholes. Users can im-plement these methods using simulation to predict the

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Fig. 10. Algorithm module for scenario 1 in Fig. 9.

various possible transitions between the boreholes, which re-duce the uncertainty in assuming the soil content betweenthe boreholes.

The prediction of soil types has been identified during theimplementation of the special purpose simulation templateas a major factor in reducing uncertainty and improving tun-nel construction operations productivity. The soil predictionmethodology uses an analytical approach in predicting soiltypes that are beneficial to the project planners and engi-neers. The analysis is presented with the goal of demonstrat-ing how this analysis could be useful for constructionpurposes. This analysis also compliments the geotechnicalexplorations conducted for tunnel construction projects astested in the NEST project. After the preliminary soil char-acterization, the concept of soil families was introducedalong with soil clusters commencing from the surficial soiltype in any given area. The probability analysis predicted thecombination of soil families and their distribution, andthereby identified the existence of soil families along thetunnel path. This prediction method provides insight intotwo areas. First, since the prediction of the soil families is

established using an analytical method, it will provide fur-ther research to developing an analytical method to predictthe elevation of the soils using the concept of soil families.An accurate prediction of soil elevations could further allowthe end users to determine the distribution of the soil pro-files between the boreholes. Second, this method enables theproject engineers to further analyze the geological explora-tions for construction purposes.

The NEST tunnel analysis also proved how the predictionof soil families could aid in accurately assessing the soilprofiles to determine the soil transitions along the tunnelpath for simulation purposes. The use of this analysis for ac-tual tunnel construction will reduce the uncertainty of theproject by logically investigating the soil types in the tunnelpath before beginning actual construction. It also providesan opportunity for the construction engineers and managersto get acquainted with possible soil type occurrences alongthe tunnel path that can be useful for applications in projectscheduling and estimating for tunnel construction opera-tions. Although the application of this method was limited toEdmonton geology, the method can be used for any other

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Fig. 11. Profiles of the actual tunnel and its transition scenarios.

Fig. 12. Tunnel advance rate actual versus new modeling approach.

city or area provided that the city or area has adequate pub-lished data or borehole data from past tunnel constructionprojects.

This paper also presented the development of algorithmsto predict the soil transition points along a tunnel path usingtransitional probabilities. This new approach predicts thetransition points along the tunnel using an analytical methodrather than using approximations or assuming arbitrary tran-sition points. The soil composition and boring rates are cal-culated, based on the transition points, to arrive at the tunnelconstruction productivity. Several soil transition combina-tions, which are implemented within a special purpose tun-nelling simulation template for many scenarios, have beenpresented. With this new approach, the end users can specifythe borehole data rather than approximating soil data for aspecific tunnel section. Based on the soil data input and theuser inputs, the template determines the best modeling sce-nario between the two boreholes and predicts soil transitionpoints and productivity values. This method also enables theend users to specify the boring rate calculation method forproduction purposes. The tunnel construction productivity isdetermined through an analytical method based on the soiltransition points along the tunnel. The validated case studyproved that these modeling algorithms not only provide alogical approach to predicting productivity based on thetransition of soils but also provide an accurate predictiongiven the fact that the end user inputs the actual data. Thesuccessful development and application of the soil transitionmodeling algorithms, thus, reduce the risk and uncertainty inpredicting the tunnel advance rate and productivity. The ap-plication of these algorithms within special purpose simula-tion to future tunnel construction projects will provide betterproject planning and decision-making for engineers beforeactual construction begins.

The prediction of soil families and soil transitions couldalso be extended to more advanced levels. The analysisshown in this paper limits the prediction to major soil types.However, there are various minor soil types within a majorsoil category. For example, shale, clayshale, sandstone, ben-tonite, and siltstone are within the bedrock major category.The prediction of these individual soil types along a tunnelpath could provide better inputs for the simulation model.Further, a soil has various properties such as plasticity, mois-ture content, compressive strength, and granularity, and theboring rate would differ based on the soil properties. Thefollowing are recommended for further research:1. Extend this soil prediction study to minor soil types to

predict the probability of their existence and their eleva-tions.

2. Study the properties of the soils and develop an analyti-cal model that could be added to the SPS tunnel tem-plate to derive boring rates.

3. All the soil transition scenarios depicted in paper showsomewhat smooth transition curves from one boreholeto another. It is possible to assume that there are manytransitions between the two boreholes rather than asmooth transition from one soil to another. As there isan uncertainty in predicting the shape of the profile be-tween the boreholes, further analysis is required to de-termine the exact nature of the soil profile between theboreholes, as a future embellishment.

Hence, it is recommended that further analysis in this areaprovides an opportunity to improve the assessment of thesoil families and transition patterns between two boreholesthat can be modeled using special purpose simulation. Thesuccessful development and implementation of these toolswill reduce the uncertainty in predicting soil conditionsalong the tunnel path and will thereby provide a more com-prehensive tunnel simulation template that could be verybeneficial to academia and the industry.

Acknowledgements

This research was conducted under the Natural Sciencesand Engineering Research Council of Canada (NSERC)/Al-berta Construction Industry Research Chair in ConstructionEngineering and Management. This work was funded by anumber of Alberta construction companies and by theNSERC under project CRDPJ 249188-01, Production-based framework for construction planning and execution.

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