ORIGINAL PAPER Ju¨rg Andreas Stu¨ckelberger Hans Rudolf Heinimann Edouard Charles Burlet Modeling spatial variability in the life-cycle costs of low-volume forest roads Received: 22 July 2005 / Accepted: 12 December 2005 / Published online: 6 May 2006 Ó Springer-Verlag 2006 Abstract Cost estimation is probably the most decisive factor in the process of computer-aided, preliminary planning for low-volume road networks. However, the cost of construction is normally assumed to be route- independent for a specific project area, resulting in sub- optimal layouts. This is especially true for mountainous terrain and in areas with unstable subsoil. Here, we present a model for more accurately estimating spatial variability in road life-cycle costs, based on terrain sur- face properties as well as geological properties of the subsoil. This parametric model incorporates four struc- tural components: embankment, retaining structures, pavement, and drainage and stream-crossing structures. It is linked to a geo-database that allows users to derive location-specific parameter values as input. In applying this model, we have demonstrated that variability in costs ranges widely for mountainous areas, with the most expensive construction being approximately five times greater there than on more favorable sites. This variability strongly affects the optimal layout of a road network. First, when location-specific slope gradients are considered, costs are reduced by about 17% from those calculated via currently available engineering practices; when both slope gradient and geotechnical formations are included, those costs are decreased by about 20%. Second, the length of the road network is increased by about 4% and 10% respectively, compared with current practices. Keywords Low-volume forest roads Route-dependent construction cost Spatial variability of life-cycle cost Route location Optimal road network Introduction Computer-aided engineering approaches for the layout of low-volume forest road networks have been in development since 1970s (Kirby 1973; Mandt 1973; Dykstra 1976), resulting in software packages, such as PLANS (Twito et al. 1987), PLANEX (Epstein et al. 2001), or NETWORK 2001 (Chung and Sessions 2001). Each formulates the problem in terms of combinatorial optimization, which comprises three main components: (1) a finite set of possible road segments for a specific project area, (2) an objective function, and (3) an opti- mization mechanism. The objective function represents both construction and transportation costs, which must be minimized by considering specific constraints. Accu- racy of this cost information is a decisive factor in identifying an optimal or at least near-optimal solution. However, construction-cost estimates very often rely on expert judgments, and are assumed to be route-inde- pendent. Because high costs are increasingly becoming a major concern when building low-volume roads, engi- neers urgently need to develop an effective, more highly accurate procedure for estimating route-dependent costs. Three methodological streams of cost estimating are available: (1) direct rule-of-thumb estimating, (2) esti- mating relationships, and (3) bottom-up parametric modeling. The first method employs a judgmental esti- mate by an expert familiar with the current task. Such direct estimations rely more or less on data from past Communicated by Walter Warkotsch J. A. Stu¨ckelberger (&) Forest Engineering Group, Swiss Federal Institute of Technology ETH, 8092, Zurich, Switzerland E-mail: [email protected]Tel.: +41-44-6323242 Fax: +41-44-6321146 H. R. Heinimann Forest Engineering Group, Swiss Federal Institute of Technology ETH, 8092, Zurich, Switzerland E-mail: [email protected]E. C. Burlet Forest Engineering Group, Swiss Federal Institute of Technology ETH, 8092, Zurich, Switzerland E-mail: [email protected]Eur J Forest Res (2006) 125: 377–390 DOI 10.1007/s10342-006-0123-9 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by RERO DOC Digital Library
Transcript
ORIGINAL PAPER
Jurg Andreas Stuckelberger Æ Hans Rudolf Heinimann
Edouard Charles Burlet
Modeling spatial variability in the life-cycle costs of low-volumeforest roads
Received: 22 July 2005 / Accepted: 12 December 2005 / Published online: 6 May 2006� Springer-Verlag 2006
Abstract Cost estimation is probably the most decisivefactor in the process of computer-aided, preliminaryplanning for low-volume road networks. However, thecost of construction is normally assumed to be route-independent for a specific project area, resulting in sub-optimal layouts. This is especially true for mountainousterrain and in areas with unstable subsoil. Here, wepresent a model for more accurately estimating spatialvariability in road life-cycle costs, based on terrain sur-face properties as well as geological properties of thesubsoil. This parametric model incorporates four struc-tural components: embankment, retaining structures,pavement, and drainage and stream-crossing structures.It is linked to a geo-database that allows users to derivelocation-specific parameter values as input. In applyingthis model, we have demonstrated that variability incosts ranges widely for mountainous areas, with themost expensive construction being approximately fivetimes greater there than on more favorable sites. Thisvariability strongly affects the optimal layout of a roadnetwork. First, when location-specific slope gradientsare considered, costs are reduced by about 17% fromthose calculated via currently available engineering
practices; when both slope gradient and geotechnicalformations are included, those costs are decreased byabout 20%. Second, the length of the road network isincreased by about 4% and 10% respectively, comparedwith current practices.
Computer-aided engineering approaches for the layoutof low-volume forest road networks have been indevelopment since 1970s (Kirby 1973; Mandt 1973;Dykstra 1976), resulting in software packages, such asPLANS (Twito et al. 1987), PLANEX (Epstein et al.2001), or NETWORK 2001 (Chung and Sessions 2001).Each formulates the problem in terms of combinatorialoptimization, which comprises three main components:(1) a finite set of possible road segments for a specificproject area, (2) an objective function, and (3) an opti-mization mechanism. The objective function representsboth construction and transportation costs, which mustbe minimized by considering specific constraints. Accu-racy of this cost information is a decisive factor inidentifying an optimal or at least near-optimal solution.However, construction-cost estimates very often rely onexpert judgments, and are assumed to be route-inde-pendent. Because high costs are increasingly becoming amajor concern when building low-volume roads, engi-neers urgently need to develop an effective, more highlyaccurate procedure for estimating route-dependentcosts.
Three methodological streams of cost estimating areavailable: (1) direct rule-of-thumb estimating, (2) esti-mating relationships, and (3) bottom-up parametricmodeling. The first method employs a judgmental esti-mate by an expert familiar with the current task. Suchdirect estimations rely more or less on data from past
Communicated by Walter Warkotsch
J. A. Stuckelberger (&)Forest Engineering Group,Swiss Federal Institute of Technology ETH,8092, Zurich, SwitzerlandE-mail: [email protected].: +41-44-6323242Fax: +41-44-6321146
H. R. HeinimannForest Engineering Group,Swiss Federal Institute of Technology ETH,8092, Zurich, SwitzerlandE-mail: [email protected]
E. C. BurletForest Engineering Group,Swiss Federal Institute of Technology ETH,8092, Zurich, SwitzerlandE-mail: [email protected]
Eur J Forest Res (2006) 125: 377–390DOI 10.1007/s10342-006-0123-9
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projects or programs, with readily available data. Thisapproach has historically been dominant in preliminaryroad-network planning, serving as the basis for softwarepackages, such as PLANEX or NETWORK 2001.
The second approach, using estimating relationshipsand formulae, calculates the cost of either individualcomponents or the entire system, and is based on cost-driving technical parameters. Markow and Aw (1983)have identified relationships to predict the volume ofearthwork needed, as well as the numbers of culvertsand bridges per unit length. Those relationships esti-mate physical construction quantities, which are thenmultiplied by respective unit prices and summed todetermine the total cost of construction. In contrast,Anderson and Nelson (2004) have devised an estimat-ing relationship that uses only road gradient as an in-put parameter.
The third method—bottom-up parametric model-ing—starts with a work-breakdown structure (WBS)that represents the subsystems, components, or elementsof a whole project. Here, similar deliverables aregrouped into classes and a physical measure is then usedas an indicator for cost within each class. Durston andOu (1983) have developed an approach that considersthe following subsystems: earthwork, clearing area,grubbing area, seeding area, ditch relief culverts, drain-age crossings, and the aggregate volume for surfacing.This particular model, run on a hand-held computer, hasbeen demonstrated to be more effective and accuratethan previously used techniques. Heinimann (1998) hasdeveloped a similar approach that has been provenuseful for cost-modeling under steep-slope conditions.
Here, we report the development and analysis of amodel for estimating the life-cycle costs of forest roads,using location-specific parameters within a given projectarea. Our emphasis is on low-volume routes throughmountainous regions. In addition, we present validationresults, and discuss the influence of different cost-mod-eling options on both construction cost estimations androad network layouts.
Methods
Model development
Cost estimation framework
Understanding how the design elements of road andterrain features can influence life-cycle costs is a chal-lenging task. A cost-estimating procedure for predictingspatial variability must be able to automatically derivethe cost-driving characteristics of road components forany specific location within a project area, and to ana-lyze cost per unit of road length based on their unit–costinformation.
Identification of the building components for low-volume roads follows a standardized WBS (Westney1997) within the construction industry, i.e., the cost
classification by elements (CCE) approach (CCE 1991).This method consists of three hierarchical levels: (1) themacro element, (2) the element group, and (3) the ele-ment level. For preliminary planning, Level 2 is anappropriate decomposition that accommodates fourelement groups: embankment structure, supporting andretaining structures, pavement structure, and drainageand stream-crossing structures. A standard design cross-section defines the structural dimensions in terms ofcrown, surface, ditch, and shoulder width, cut-and-fillslope angles, and retaining wall specifications (Fig. 1).To verify how those element groups affect constructioncosts, we assessed five low-volume projects carried outunder different slope conditions in Switzerland (Fig. 2).There, the cost for the embankment structure (A) de-pended heavily on the slope gradient, whereas the costfor supporting and retaining structures (B) seemed to berelevant for slope gradients >50%. The costs forpavement (C) and drainage structure (D) were some-what variable, as explained by the bearing capacity ofthe subsoil and by the design standard. For example, oursecond study site, ‘‘Prabe Sud’’, is situated in limestonein the central Swiss Alps with heavy rainfalls, where itsasphalt concrete surface course incurred high construc-tion costs. This preliminary, approximate analysisclearly indicated that slope gradient is the leverage factorfor an analytical cost model. Additionally, the shearstrength of the subsoil is critical to the design of cut-and-fill slopes (Coulomb 1776; Terzaghi 1944), as well as forthe design of the pavement structure (AASHTO 1993).Therefore, spatial information about geotechnical soilproperties must be included if road engineers are toimprove the accuracy of cost modeling.
Embankment model
Design engineers can choose among full-bench, self-balanced, or retaining-wall cross sections. Therefore, ourcurrent analysis combined the element groups‘‘embankment’’ and ‘‘retaining’’ structures. Theembankment model was aimed at calculating the exca-vation volume of a standard cross section at any loca-tion within a project area (Fig. 3). This model assumed(1) the slope angle of the terrain (g) to be constant forthe whole cross section, (2) the cut-and-fill volume to beself-balanced, (3) the angles for cut-and-fill slopes to bedetermined by the geotechnical properties of the subsoil,(4) consolidation of cut-and-fill slope material to differ,and (5) the bedrock surface to be parallel to the terrainsurface. Loosening and loss of fill-slope material wasassessed with a shrinking factor (fshr) that depended onsubsoil geotechnical properties.
Because the cut-slope angle (/cut) is most often higherthan that of the fill slope (/fill), the self-balanced designrequired the axis to be shifted horizontally in uphilldirection (Fig. 3). However, if the slope angle had be-come equal to or larger than the fill-slope angle, the roadwould then have needed to be built according to a full-
378
Fig. 1 Standard design cross-section with four element groups: (A)embankment structure, (B) retaining structures, (C) pavementstructure, and (D) drainage and stream-crossing structures. hw
height of retaining wall, hg depth of foundation of retaining wall, wcrown width (surface + shoulder + ditch). Figure is not drawn toscale, especially in shoulder and ditch dimensions
00% 10% 20% 30% 40% 50% 60% 70% 80% 90%
100
200
300
400
500
600
700
800
900
1000
B
A
AA
A
A
B
C
B
B
D
C
C
C
C
D
D
D
D
1. Hellikon
5. Gadmen
4. Griden
3. Les Mélèzes
2. Prabé Sud
cost
[CH
F20
00/m
']
slope gradient [%]
Fig. 2 Cost of element groupsin relation to slope gradient. Allvalues are in Swiss francs(CHF), adjusted to price levelfor Year 2000
379
bench design. Heinimann (1998) has devised Eqs. 1, 2,and 3 to calculate excavation volumes for the conditionsand constraints mentioned above; these equations arevalid only for positive slope angles. Nevertheless, on adigital elevation model (DEM), values for slope gradientmay also be negative. Therefore, our algorithmicimplementation had to be robust, which required a moredetailed model formulation as follows:
To make the analytical explanation easily understand-able, only positive slope gradients were considered in
Eqs. 1, 2, 3, 4, 5, 6, 7, 8, and 9. Cut-slope and fill-slopeangles (/cut and /fill) had to be greater than groundslope (g) because of geometrical constraints. Here, weexamined three different cases in terms of variable a(Eqs. 5, 6): (1) fill-slope angles larger than cut-slopeangles, (2) cut-slope angles greater than fill-slope angles,and (3) fill-slope angles equal to cut-slope angles. In thefirst case, the resulting value was less than zero (a<0).Therefore, the root term of Eq. 5 was the limiting factor,and the discriminate d had to be positive (Eq. 6), therebyresulting in Eq. 7.
All factors in the numerator of Eq. 7 were positive, andboth /cut and /fill were always greater than g. Hence, theformulation was correct for any possible case. Likewise,because the negative branch of the root term in Eq. 5 ledto values greater than w, only the positive branch of theroot term was feasible.
The second case dealt with fill angles smaller than cutangles (a>0). In most case, however, geotechnical sta-bility required the latter to exceed the former. Assumingthat, in some cases, the fill angles were smaller, the rootterm in Eq. 5 become smaller than b. As a consequence,only the positive branch of the root term resulted infeasible solutions.
downhill side; g slope angle, depending on terrain surface; /cut cutangle, depending on geotechnical properties; and /fill fill angle,depending on geotechnical properties
380
The third case considered fill angles equal to cut an-gles (a=0). The conditions for this case follow fromEq. 8. Furthermore, for a self-balanced design the cut-road width was equal to the fill-road width (Eq. 9).
fshr � tanð/cutÞ�tanð/fillÞ � tanðgÞ
�
� tanð/fillÞ�tanð/cutÞ � tanðgÞ
�
¼ 0 ð8Þwcut ¼ wfill ¼ �
cb¼ w
2ð9Þ
Equations 1, 2, 3, 4, 5, 6, 7, 8, and 9 are analogouslyapplicable for negative slope gradients (g<0). However,in these cases cut-slope and fill-slope angles (/cut and/fill) had to be more negative than ground slope angle (g)because of geometrical constraints.
When one knows the relation of wcut to wfill, one canthen calculate self-balanced cut-and-fill volumes for eachlocation in the project area. However, such a cross-sec-tion design is not always the most appropriate. Fullbench is a second option for cross-section design,increasing embankment stability in steep terrain orunstable subsoil conditions by shifting the road structurehorizontally in the uphill direction. As the third optionfor cross section, the retaining-wall design locates thosestructures on either the uphill or downhill side of theroad. We used a lookup table to define the critical ter-rain slope figures for each geotechnical unit as well as todiscriminate among these three cross-section designsolutions (c.f., geotechnical parameters).
In difficult terrain conditions, part of the excavationvolume may be of rock. Practical experience in Swit-zerland has shown that the unit cost for its excavation isapproximately four to five times greater than for theremoval of soil alone. Inaba et al. (2001) have developedan empirical model to estimate the share rock excavationas a function of slope, a coefficient for each geologicalunit (coefrock), and crown width for low-volume roads(Eq. 10). For the current study, we determined the share
of rock for cut-slope areas in three groups of geologicalformations, all with crown widths of 4.10 m (Fig. 4).The first group comprised mesozoic and tertiary sedi-ment formations, typical of the northern slopes of theAlps, and included conglomerate, sandstone, limestone,and flysch. The second group consisted of intrusive andthe metamorphic rock formations—granite and gneiss—that are typical for the central and southern slopes of theAlps. The third group consisted of quaternary formationsuch as moraine and alluvial deposit. For slope gradientsof up to approximately 40%, the necessary volume ofrock excavation was of minor importance and could beeasily neglected. At gradients of 70%, about one-third ofthe volume was rock; at gradients of about 90%, two-thirds consisted of rock. In general, the rock excavationvolume was calculated as the product of the cut-slopevolume multiplied by the rock share factor (Fig. 4).
wherecoefrock geological parameter for rock ratio estimation
(c.f., Table 1)g slope gradiente the Euler numberlogit interim result for logit-functionprock share of rock in total cut area [0...1]~w the dimensionless numerical value of the road
crown width in meter.
The total costs for earthwork and embankmentpreparation for a road segment depended on both theearth excavation volume (Vcut) and rock excavationvolume (Vrock). Volume was approximated by the frus-tum of a pyramid (Eq. 11), whereas the total embank-ment cost was determined with Eq. 12.
whereA0 area (either fill or cut) of the initial cross-sectionA1 area (either fill or cut) of the following cross-
sectionl middle length of the arc of the segmentV volume (either fill or cut)
Cemb ¼ Vfill � ccomp þ Vcut
�cexe þ prock � crock
�ð12Þ
whereccomp cost for compaction per volume unitCemb embankment costcexc excavation cost per volume unitcrock extra cost for rock excavation per volume unitprock share of rock in total cut area [0...1]Vcut cut volumeVfill fill volume.
Retaining structure model
In difficult terrain conditions (e.g., steep slopes, unstablesoil conditions), retaining structures are necessary toprovide safe embankments. Assuming that the slopegradient could be extracted automatically from a DEM,and that preference rules indicated a retaining-wallcross-section design, we then calculated the height (hw)(Fig. 1) and length of the retaining wall. Additionalheight (hg) used for the foundation was presumed to beconstant. The cost for a retaining wall was assumed tobe proportional to its height times length (Eq. 13), a rulethat seems appropriate for heights of up to 3 m.
Cwall ¼ ðhw1 þ hw2 þ 2� hgÞ � l� cwall ð13Þ
wherecwall cost for retaining wall per unit areaCwall cost for retaining wallhw1,hw2
height of retaining walls (uphill and downhillsides)
hg constant value for foundation and clearance ofretaining wall (in the present model=1 m)
l length of road segment
Pavement structure model
The cost of pavement structures is assumed to be pro-portional to numerous variables, including the surfacedroad area for specific soil-bearing conditions, expectedtraffic volume, and the aggregate materials used for thesub-base, the base course, and the surface course. Todesign the pavement structure, we adapted AASHTOprocedures to the special requirements for low-volumeroads in Switzerland (Burlet 1980). In Eq. 14, both aT
able
1Engineeringandcost
parametersforeach
geotechnicalunit.Thedata
werecalibratedfortheareaofWagital(Switzerland)
Geotechnicalunit
Road
type
Engineeringparameters
Cost
parameter
Flatcost
IDName
tan
(/cut)
tan
(/fill)tan
(/wall)f shr
coef
rockc e
xc
(CHF/m
3)c c
omp
(CHF/m
3)c rock
(CHF/m
3)c p
av
(CHF/m
2)c w
all
(CHF/m
2)c d
rain
(CHF/m
)c0
ann
(CHF/m
/a)c1
ann
(CHF/m
/a)Link
(CHF)Length
(CHF/m
)
10
Standard
subsoil
11.00
0.80
10
0.80
1.0
6.80
412.00
28
80
18
1.20
20
021
Moraine
11.00
0.80
10
0.80
0.68
6.80
412.00
28
80
18
1.20
20
022
Alluvialdeposit
11.00
0.80
10
0.80
0.11
6.80
412.00
28
100
18
1.20
20
031
Conglomerate
11.00
0.80
10
0.80
1.07
6.80
412.00
28
80
18
1.20
20
032
Sandstone
11.00
0.80
10
0.80
0.95
6.80
412.00
28
100
20
1.20
20
033
Flysch
20.80
0.67
10
0.80
0.54
6.80
10
5.00
52
200
85
2.50
50
034
Lim
estone
11.25
0.80
10
0.80
1.43
6.80
415.00
28
80
15
1.00
00
041
Granite
11.25
0.80
10
0.80
1.73
6.80
415.00
28
80
18
1.00
00
042
Gneiss
11.25
0.80
10
0.80
1.69
6.80
415.00
28
80
18
1.00
00
051
Landslide
20.80
0.67
10
0.80
06.80
10
080
200
85
4.50
50
12
52
Landslide,
active
20.80
0.67
10
0.80
06.80
10
080
200
85
7.50
50
12
53
Landslide,
veryactive
20.80
0.67
10
0.80
06.80
10
080
200
85
10.00
50
12
61
Stream,stable
subsoil
11.00
0.80
10
0.80
1.0
6.80
412.00
41
200
20
3.00
51,000
062
Stream,instable
subsoil
10.80
0.67
10
0.80
0.54
6.80
10
5.00
64
200
85
4.00
55,000
081
Existingroad,good
31.00
0.80
10
0.80
1.0
0.00
00.00
00
01.20
20
082
Existingroad,poor
11.00
0.80
10
0.80
1.0
0.00
00.00
00
01.20
20
45
91
Marshland
�1
�1
�1�1
�1�1
�1
�1
�1
�1
�1
�1
�1
�1
�1
�1
92
Lake
�1
�1
�1�1
�1�1
�1
�1
�1
�1
�1
�1
�1
�1
�1
�1
382
standard road width and widening at curves andswitchbacks were considered.
Cpav ¼�
ws0 þkcwr
�� l� cpav ð14Þ
wherecpav cost for pavement per unit areaCpav cost for pavement structurekcw constant value for road widening in curves (in
the present model, = 26 m)l length of road segmentr curve radiusws0 standard road surface width
Drainage and stream-crossing structures
The cost for drainage structures, such as ditches orculverts, was assumed to be proportional to road length(l) (Eq. 15). Ditch relief culverts ideally are arranged atconstant 50-m intervals, but would be unnecessary onflat terrain (<12%). Three principal types of stream-crossing structures are available: bridge, culvert, andford, the last type being the only one automaticallyconsidered in the present model. Its construction in-curred a higher cost due to the hardening measures ofthe surface, extra drainage (e.g., a culvert at the vertexlocation in the channel), and additional retainingstructures. The unit cost for a ford presumably dependson geology and size of the area defined by its location.
Cdrain ¼0 if tanðgÞ\12%Cculvert
d � l else
ð15Þ
whereCculvert cost for single culvertCdrain cost for drainage structured distance between ditch relief culverts (in the
present model=50 m)l length of road segment
Life-cycle cost model
Life-cycle costs entail those for construction, routineand periodic maintenance, rehabilitation, and decom-missioning. The model analyzed here did not considerthe last two factors, and assumed the maintenance costto be dependent only on road gradient and geology. Thisassumption, however, differs from practices in USA andin Canada, where thresholds for total traffic volumetrigger periodic maintenance.
To make these cost components comparable, theymust be normalized in time. Net present value (NPV),annual equivalent rate (AER), and internal rate of re-turn (IRR) are measures commonly used for obtainingthe time value of money. Our model followed the NPV
approach, assuming a project life cycle of 50 years, aninterest rate of 2%, and a constant share in maintenancecosts per year. Equations 16 and 17 are widely applied inengineering economics (Heinimann 1998; Park andSharp-Bette 1990).
Cann ¼ Creg þCperi
nð16Þ
Ctot ¼ Ccon þ Cann �1� ð1þ iÞ�N
i
!
ð17Þ
whereCann average annual maintenance costCcon construction costCper periodical maintenance costCreg regular maintenance costCtot total cost for a single road segmenti annual interest rate (in the present model=2%)n periodical-maintenance interval (in the present
model=5 years)N amortization period of the road (in the present
model=50 years)
Curve and switchback model
Detailed road engineering defines the horizontal layoutof a road as a consecutive set of straight lines and curves,whereas computer-aided preliminary planning toolsusually use a traverse representation, consisting of acontinuous series of lines. The latter approach has twoshortcomings (see Heinimann et al. 2003). First, theroad length for curves is shorter than the tangent dis-tance, and the road does not widen (c.f., Eq. 14). Sec-ond, a change in direction of >135� requires a ‘‘hairpinbend’’ embankment structure, called a switchback.Constructing a switchback always involves considerableadditional earthwork and surfacing, resulting in signifi-cantly higher total cost. The balancing of cut-and-fillvolumes is not possible for a single cross-section of aswitchback, but must be achieved between the beginningand the end of the switchback curve. Figure 5 showsthat, depending on the central angle (c), our procedurefor calculating switchback costs required several inter-mediate cross-sections. The best possible volume balancewas then identified by shifting the switchback centerorthogonally to the contour lines, at a step width of0.5 m and within an interval of �5 m to +5 m. Thisprocedure was similar to one proposed by Aruga et al.(2004).
Organization of input data
Data model
One purpose of the present model was to derive cost-driving features automatically from a geographicaldatabase. This database, represented by 10·10-m cells,
383
had two layers: (1) a DEM of the terrain surface, and (2)a geotechnical classification of the subsoil. A first lookuptable specified the engineering and cost properties foreach geotechnical unit. A second lookup table definedthe design elements of a standard cross-section for eachgeotechnical unit. Figure 6 shows an entity-relationshipmodel of the data. This data structure makes it possibleto adapt the model to any area specific conditions in theworld as long as the road can be modeled by the fourelement groups explained in section cost estimationframework.
Geotechnical parameters
Engineering and cost properties are specific for eachgeotechnical unit. Site specific parameters are stored as a
record in a data base table consisting of five engineeringproperties [cut-slope inclination (tan(/cut)), fill-slopeinclination (tan(/fill)), inclination of retaining wall(tan(/wall)), shrinking factor (fshr), and a coefficient forrock ratio estimation (coefrock), c.f., Eq. 10], sixparameters for construction costs [excavation cost (cexc),cost for emplacement and compaction of the fillingmaterial (ccomp), additional cost for rock excavation(crock), cost for pavement structures (cpav), cost forretaining walls (cwall), and cost for drainage structures(cdrain)], and two parameters for maintenance [constantcost per road length (c0ann), and variable cost propor-tional to the road gradient (c1ann) and road length].
Special terrain types (e.g. landslides, stream crossings,rehabilitation of existing roads) may require additionalcost parameters. These parameters can be defined by flat
a) b)Fig. 5 Road segments ofswitchbacks, a c centralangle=180�), b c centralangle=220�. Each switchbackstarts and ends at regular nodes(bold point symbols). Thecenterline is subdivided into 6(a) or 10 (b), respectively,intermediate sections (slim pointsymbols). Regular nodes arefixed whereas locations ofintermediate nodes depend onthe location of the center as wellas c
parameters for the geo- technical unit
digital elevation model (DEM) layer of the geological, geo- technical subsoil (Geotype)
mc
1
geor
efer
ence
d da
tasc
alar
dat
a
Geotype (ID) Roadtype (ID)
parameters for the road- type
Roadtypemc
1
... ......
Fig. 6 Entity-relationshipmodel for the input data
384
cost per link or flat cost per length. Sites where con-struction is impossible (e.g. lake, marshland) are repre-sented by negative values.
Construction processes (full mechanized, low mech-anized, labor intensive) are represented by cost valuesonly that may be obtained by analyses of contractorbids, engineering estimation, or final costing analysis.Table 1 shows all geological parameters used in the areaof Wagital (c.f., model evaluation).
Road parameters
The model assumes one predominant road type for aspecific project area. However, the designer may specifydifferent design parameters, e.g. a smaller road width inrocky terrain are, or a less maximum, road gradient ininstable subsoil. The road type is linked to the geo-technical unit and defined by the parameters maximalallowable road gradient (mmax), minimal radius in curves(rmin) and switchbacks (rSB), standard road surfacewidth (ws0), width for ditch and shoulders (wd+s), roadwidening in curves (kcw), and minimal excavation depthfor pavement structures (zmin). Table 2 shows all roaddesign parameters used in the area of Wagital (c.f.,model evaluation).
Model implementation
Our procedures were implemented via Borland Delphi7.0 software (Object Pascal language), which producedapproximately 3,700 lines of code. Input and outputdata consisted entirely of text files that could be easilyimported from or exported to commercial geographicalinformation systems, such as ESRI ArcGIS. At present,this implementation can handle areas of up to 100 km2,with 10·10 m raster cells. The model split the road routeinto 10-m segments for straight lines and curves, and 2-m sections for switchbacks. Procedures for optimizingthe road network were implemented in a separate pro-gram unit, which was previously described by Stuckel-berger et al. (2004).
Validation and evaluation
Model validation
Validation was aimed at demonstrating that our modelreasonably represented the cost of low-volume road
projects. It required high-quality cost data normallyavailable only after a project is completed. However, afull validation that investigates assumptions, inputparameters, and output values is difficult to achieve.Therefore, compromises were necessary, resulting in apreliminary validation approach.
In this current study, validation was performed forprojects on two different geological formations. The firstcovered an area in the molasse zone; the second, inlimestone. Both were located on the northern slopes ofthe Swiss Alps. The first part of the validation comparedthe excavation volumes produced by the model withthose values obtained from actual, detailed road pro-jects, as engineered by students in the molasse zone. Thesecond part occurred in the limestone zone, and wasmainly focused on investigating rock excavation vol-umes and costs. Decisive figures from real-world caseswere extracted from engineering documentation, espe-cially technical reports and cost estimates. Applicationof the model required us to specify the design elementand the unit-cost parameters, both of which were storedin a lookup table linked to the geology layer of thespatial database (Fig. 6).
The first part of the validation demonstrated thatour model accurately estimated the excavation volume.However, it also showed that a 10·10-m representationresulted in inaccurate estimates for stream channel orterrain edge locations. For the second part, data ob-tained from the engineering documentation were com-pared with the model output (Table 3). Here, themodel overestimated the total embankment volume byabout 16%, seemingly favoring a full-bench cross-sec-tion design. In contrast, the road engineers preferred aretaining-wall cross-section design, which was repre-sented by a much higher cut-slope volume predicted bythe model. Cost figures showed that the model estimatefor the embankment structure was within the range ofaccuracy (±10%), while the engineer’s estimate for thepavement structure was about 20% higher. Althoughthe road engineer planned for additional turnouts andother areas to be surfaced with aggregate material, ifthose factors were neglected, costs for the pavementstructure were more or less identical. The usefulness ofour validation results was limited because they werebased on a comparison of estimates from an engineerversus a model. A more reliable validation would haverequired accurate post-construction information ondesign-element unit quantities and unit cost, which isusually not available.
Table 2 Design parameters for each road type used in the area of Wagital (Switzerland)
�1 No go �1 �1 �1 �1 �1 �1 �11 Standard road 0.12 20 10 3.4 0.6 26 0.302 Road in instable 0.10 20 10 3.4 0.6 26 0.503 Existing road 0.20 10 5 3.4 0.6 13 0.30
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Table 3 Comparison of excavation and cost figures for two alternatives: (1) results of engineering project design and contractor bid versus(2) model results
Costs, in Swiss francs (CHF), are adjusted to price level for Year 1997
Fig. 7 Spatial variability inroad life cycle costs for ScenarioIII, based on slope gradient andgeotechnical soil properties.The lake ‘‘Wagital’’ (35 km2) isat eastern boundary andwatershed is at westernboundary
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Model evaluation
The objectives of our model evaluation were (1) toinvestigate the influence of terrain parameters, e.g., slopeand geology, on the spatial variability in constructioncosts; and (2) to assess the effect of cost-estimatingstrategies on optimal road network layout.
Evaluation of road network layout
The ‘‘Wagital’’ project site is located on the northernslopes of the Swiss Alps, in flysch and limestone zones.This area is characterized by extremely difficult geo-technical conditions, such as low soil-bearing capacity(CBR values <3%), unstable terrain with many land-slides, and a dense channel network. Evaluation wasbased on three cost-estimating scenarios:
1. Scenario I, which assumed construction costs to beroute-independent (240 CHF/m) and constant for theentire project area. The design parameters (minimumcurve radius (rmin), maximal allowable road gradient(mmax), etc.) correspond to road type#1 ‘‘standardroad’’ of Table 2
2. Scenario II, in which slope gradient was consideredthe only parameter affecting the spatial variability ofconstruction costs. The geotechnical parameterscorrespond to geotechnical unit#10 ‘‘standard sub-soil’’ of Table 1.
3. Scenario III, which considered both slope gradientand geotechnical information as decisive parametersas well as different road types for cost variability. Alldesign and cost parameters are shown in Tables 1and 2.
Scenario I served as a reference for the engineeringpractices currently used to estimate costs at a pre-liminary planning stage.
Results and discussion
Spatial variability of construction costs
The 35-km2 project area included the lake ‘‘Wagital’’ atthe eastern boundary and a watershed at the westernboundary. For each of these three scenarios we calcu-lated in each grid cell the potential road life-cycle costfor a unit length of 1 m, assuming a straight alignmentof the road parallel to the contour line. Figure 7 illus-trates the spatial variability in road life-cycle costs forScenario III, which considered both slope gradient andgeotechnical soil properties. Figure 8 presents the vari-ability of life-cycle cost per unit for the three modelscenarios as cumulated frequency curves.
Scenario I assumed a route independent cost of240 CHF/m. Therefore the variability is zero, resultingin a vertical straight line of cumulated frequency curve.
Fig. 8 Variability of life-cyclecost per unit for Scenario I, II,and III. The curves show thecumulated frequency of theproject area to the constructionand maintenance costs for eachscenario
Table 4 Quantiles of costestimation after scenariosI, II, III
10%-quantile(Q0.1)
Median (50%) 90%-quantile(Q0.9)
Difference(Q0.9�Q0.1)
CHF EUR CHF EUR CHF EUR CHF EUR
Scenario I 240.0 155.8 240.0 155.8 240.0 155.8 0.0 0.0Scenario II 160.1 104.0 179.0 116.2 234.2 152.1 74.1 48.1Scenario III 139.5 90.6 238.0 154.5 441.6 286.8 302.1 196.2
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Fig. 9 Model-designed roadnetwork for Scenarios I, II, andIII, based on cost-estimatingstrategies defined in evaluationlayout. Background: hill shadeof relief, streams, and lake
Table 5 Key values calculatedfor road network, based onthree different cost-estimationscenarios
Criterion Unit Scenario I Scenario II Scenario III
Network length m 17,406 18,176 19,001Embankment and retaining structures 1,000 CHF 3,098 1,972 1,847Pavement structure 1,000 CHF 3,337 3,062 2,871Drainage and stream-crossing structures 1,000 CHF 207 298 167Total construction cost 1,000 CHF 6,642 5,332 4,885Avg. construction cost CHF/m 382 293 257Maintenance cost/year 1,000 CHF/a 50.1 67.7 50.9Net present value (50 years) 1,000 CHF 8,196 7,430 6,464Relative difference Reference �17% �21%
+27% +15% Reference
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Scenario II, which considers terrain slope gradient asthe only factor influencing construction cost resulted in amedian cost of about 180 CHF/m with a range of about75 CHF/m between the 10%-quantile (Q0.1) and 90%-quantile (Q0.9) (Table 4). The cumulated frequencycurve represents more or less the distribution of theslope gradients in the project area.
Scenario III represents a cost estimating procedurethat considers terrain, slope, and different road typesresulted in a cumulative frequency curve with mediancost of about 240 CHF/m and a variability range ofabout 300 CHF/m. The huge cost variability is a resultof different subsoil that was represented by three classes:(a) stable subsoil in limestone and moraine, (b) instablesubsoil in flysch formation and high landslide activity,and (c) stream crossing sites with laborious constructionwork.
The cumulative frequency curves of Scenario II andIII asymptotically converge to the 100% line. However,values above the 98%-quantile should be excluded fromanalysis due to model limitation for very steep terrainconditions.
Assuming that Scenario III is closest to reality andthe most accurate procedure, the results depicted inFig. 8 clearly demonstrate that conventional cost-esti-mation practices (which are route- and location inde-pendent) are inappropriate for difficult terrainconditions.
Influence of cost-estimating procedures on road networklocation
A minimum spanning tree problem was used to evaluatehow various cost-estimating strategies affect the optimallayout of road networks. In this study, ten mandatoryaccess points were linked by a minimum-cost network(Fig. 9). Access points 000, BRH, and AU are at lakelevel (about 900 mNN), ROW, SBU, ALP, and OBOhave a intermediate elevation between 1,000 mNN and1,200 mNN, and EGS, TAS, and STO have a high ele-vation of about 1,300 mNN. We first devised a finite setof vertices that corresponded to the centers of all 10·10-m grid cells. Second, a set of road links was defined fromeach vertex to its adjacent vertices. Third, we formulateda set of design constraints, e.g., minimum curve radius,maximum road gradient, and turning constraints for thecombination of incoming and outgoing road links (Ta-bles 1, 2). We then calculated the first- and second-orderSteiner points (Promel and Steger 2002). Finally, weidentified the minimum cost spanning tree by combiningDijkstra’s (1959) shortest path (SP) and Prim’s (1957)minimum spanning tree (MST) algorithms (see alsoStuckelberger et al. 2004).
Figure 9 presents the evaluation results for the threescenarios. A visual assessment of the map demonstratesthat the three strategies greatly affected the spatial lay-out of the road network. Scenario I has two connectionsfrom lake level to high level (BRH-SBU-ROW-EGS and
AU-ALP-STO). Because the costs are route indepen-dent, the model tried to keep the road network at min-imal length. Both effects resulted in a lot of switchbacksand therefore high life-cycle cost. Scenarios II and IIIshows nearly identical road routes in 000-BRH-SBU-AU and EGS-ROW-TAS. However, Scenario II con-nects the high level via access points AU-SBU-STO inless stable subsoil where as Scenario III made a con-nection via AU-OBO-ALP-STO in limestone layer,which is stable and therefore favorable.
Table 5 contains key data for the scenarios. Again,Scenario I depicted current engineering practices, whichassumed route-independent costs. Optimization for thisscenario resulted in the shortest road length (17.4 km),but the highest life-cycle cost (+27%) compared withthe minimum cost alternative. Scenario II (slope gradi-ent only) produced a total network length of 18.2 km.Compared to the minimum cost alternative, this sce-nario resulted in life-cycle costs of 15% above the min-imum but 17% below the conventional practice. Finally,Scenario III, with both slope gradient and geotechnicalinformation as major decisive parameters, was mostcost-effective, with a minimum road network tree andlife-cycle costs 21% lower than those incurred by stan-dard, current practices.
Conclusions
We have developed a model for estimating forest roadconstruction costs. This system considers location-spe-cific terrain and subsoil parameters, and can be used toevaluate how various cost-estimating strategies affect theoptimal layout of road networks. Our model consists offour element groups—embankment, retaining, pave-ment, and drainage structures—their dimensions andquantities being defined in terms of topographic, subsoil,and cross-sectional parameters. A spatial database thatcomprises a digital elevation model (10·10-m resolution)and specifications for geotechnical formations is a pre-requisite if one is to derive location-specific terrainparameters. Our validation and evaluation of this modeldemonstrated that: (1) under difficult terrain conditions,construction costs can range from 140 (10%-quantile) to440 CHF (90%-quantile) per unit of length, therebytypically requiring a factor of about 3 between minimumand maximum costs; (2) a cost-estimating procedure thatincorporates both slope gradient and geotechnicalproperties of the subsoil results in an optimal roadnetwork in which, compared with current engineeringpractices, construction costs are reduced by about 25%and life-cycle costs by about 20%, all while road lengthsincrease about 10%; and (3) a cost-estimating procedurethat considers only slope gradient can still produce anoptimal road network with 20% lower constructioncosts and 17% lower life-cycle costs. Therefore, based onthese results, we believe that spatial variability in con-struction costs decisively affects the identification of anoptimal road network, and that an improved strategy
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for cost estimations should become a matter of coursefor engineering practices.
Our approach may be used in any case for which sitespecific life-cycle cost information is available for ele-ment groups (1) embankment, (2) supporting andretaining, (3) pavement, and (4) drainage structures.However, the model is restricted to terrain conditionswith slope gradient below 150%, where height ofretaining structures is less than 3 m, and where nobridges and tunnels are required. Nonetheless, our val-idation also revealed some uncertainty that requiresfurther investigation. A first problem consists of streamcrossings for which we implemented only the ford-case.In some sites bridges may be more appropriate. A sec-ond problem is the road location near sharp terrainedges and small channels for which a 10·10-m gridresolution is inappropriate to map these small-scaleterrain features. Finally protective structures againstnatural hazards (rock fall, mudflow, avalanches) whichresult in additional cost, is a third problem to be inves-tigated for extreme area conditions.
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