Tunnelling and Underground Space Technology 35 (2013) 172–177

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Tunnelling and Underground Space Technology

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Study of pergolas for energy savings in road tunnels. Comparison withtension structures

A. Peña-García a,⇑, L.M. Gil-Martín b

a Department of Civil Engineering, ETSI Caminos, Canales y Puertos, University of Granada, 18071 Granada, Spainb Department of Structural Mechanics, ETSI Caminos, Canales y Puertos, University of Granada, 18071 Granada, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 October 2011Received in revised form 16 November 2012Accepted 15 January 2013Available online 24 February 2013

Keywords:Road tunnelLightingPergolasTension structuresEnergy savings

0886-7798/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.tust.2013.01.008

⇑ Corresponding author.E-mail address: pgarcia@ugr.es (A. Peña-García).

The huge consumption and environmental impact of electrical lighting in road tunnels in terms of energy,materials and maintenance, has evidenced the necessity of using solar light for tunnel lighting duringdaytime. One satisfactory solution has been to shift the threshold zone out of the tunnel by means of ten-sion structures. Although pergolas in the portal gate of road tunnels have been mainly used for structuralpurposes, they have been also claimed as a co-lateral solution to achieve this target. In this work, the the-oretical basis of the ad hoc use of pergolas for energy savings in road tunnels are developed, analyzed andcompared with tension structures. General expressions for the light distribution under any arbitrary per-gola, not reported in the reviewed literature for this study, are presented and the ESTS equation, used forenergetic evaluation of tension structures, is also generalized to the case of pergolas. Finally, the accuracyof pergolas for normative compliance in matter of illumination is discussed and several important con-clusions are presented.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In areas of heavy traffic, intersections of two highways at differ-ent levels are frequent. Some other times it is a railway whichpasses over the road. In these situations it is necessary to buildone structure to hold the upper superstructure. Sometimes, whenthe upper road or railway is in curve or crosses the road below withan oblique angle, some of the beams could be useful for the visualadaptation of drivers before they enter the underpass. Precast con-crete I-girders forming one pergola are generally used in order tomake the erection faster and easier. The dimensions of the girdersdepend on the length of the span, with depth between 0.60 and2.00 m and flange width between 0.80 and 1.50 m. Usually thesegirders are pin-connected in both ends and held by lateral retain-ing walls or piles as shown in Fig. 1a.

The light–dark succession under these pergolas has also beenconsidered to help the visual adaptation of drivers entering theunderpass under conditions of external sunlight without usingelectrical lighting and relying instead on reduced levels of naturallight before entering the tunnel itself. For this reason, concretevaults with openings have eventually been built in the portal gateof road tunnels (Fig. 1b) in order to start such visual adaptation be-fore the tunnel with the consequent saving of electrical lighting(road tunnels have a much more powerful lighting at their

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beginning, in the so called threshold zone (Adrian, 1982; CIE Publ.88, 2004), to achieve this adaptation).

This way of saving energy from the electrical lighting by shiftingthe threshold zone of tunnels has been also successfully performedby means of other kind of structures. One of these solutions are theso called ‘‘tension structures’’, that is, tensed translucent textilestructures allowing natural light to pass (Gil-Martín et al.,2011a,b). Optimization of tension structures in terms of light dis-tribution and energy saving is currently an active field of research(Peña-García et al., 2010; Peña-García et al., 2011; Peña-Garcíaet al., 2012).

In this work, the photometrical and energetic accuracy of pergo-las to shift the threshold zone of road tunnels is analyzed and someimportant conclusions are presented.

2. Results

2.1. Light distribution under one pergola

Let there be a pergola between two concrete walls (withoutopening) in arbitrary insulation conditions, that is, any locationin the world, any day in the year and time in the day. Given thatone pergola consists of the succession of several items (beam + freespace between two beams), the study of the light distribution onthe road under one the pergola can be reduced to one of these uni-tary components. In general, for such study, three well differenti-ated zones have to be considered: the shadow from the nearest

Fig. 1. Concrete pergola on roads. (a) Under superstructure. (b) At the portal gate ofa road tunnel in Lorca, Spain.

Fig. 2. Light distribution under one pergola.

Fig. 3. Insolation conditions on pergolas located in places with surface-solarazimuth angle u = 0�. where: h is the height of the tunnel or clearance, t is thethickness of the beams, w is the width of the beams, d is the distance betweenbeams, h is the solar altitude (angle between ray and the horizontal), Lbright is thelength of one illuminated zone, Ldark is the length of one beam shadow.

A. Peña-García, L.M. Gil-Martín / Tunnelling and Underground Space Technology 35 (2013) 172–177 173

wall to the sun, the shadow from the beam and the bright zone dueto the free space between beams. These zones are shown in Fig. 2below.

Since the calculation of the extension of both, illuminated anddark zones under the structure, may be somewhat involved, espe-cially in zones where the shadows of wall and columns overlap, thecase of one tunnel whose surface-solar azimuth angle is u = 0� hasbeen first considered and then these results have been extended tothe most general case corresponding to an arbitrary surface-solarazimuth angle u, that is any longitude, season and time in the day.

2.1.1. Particular case: parallel incidence to the road laneThe extension of both, bright and shadowed zones under the

pergola will be calculated when the surface-solar azimuth angleu = 0�. This particular result is extremely useful for incorporationinto the general case. Note that in this case, the wall makes no

shadow on the road under the structure so, we will only calculatethe shadow from the columns.

Fig. 3 below shows a longitudinal cross-section of the pergolaand the insolation conditions for a surface-solar azimuth angle, uequal to zero:

From Fig. 3, the following expressions can be easily deduced:

Lbright ¼h

tan hþ d� hþ t

tan h¼ d� t

tan hð1Þ

Ldark ¼hþ ttan h

þw� htan h

¼ wþ ttan h

ð2Þ

The sum of (1) and (2) makes the trivial relationship:

Lbright þ Ldark ¼ wþ d ð3Þ

Eqs. (1) and (2) show that, for surface-solar azimuth angles u = 0�,the length of the illuminated and dark zones do not depend onthe clearance of the tunnel but on the dimensions of beams, w,and the separation between two consecutive ones, d.

174 A. Peña-García, L.M. Gil-Martín / Tunnelling and Underground Space Technology 35 (2013) 172–177

Note that, for road tunnels with East–West orientation, this twodimensional case can be a good approach.

2.1.2. General case: arbitrary insulation conditionsNow let us consider the general situation corresponding to a

tunnel with arbitrary geographical longitude and latitude at anyseason and time in the day. In this case, it is necessary to considerthe shadow of the walls holding the beams (height h + d for thestructural configuration represented in Fig. 1a).

Concerning the shadow of the lateral wall, it is important to re-mark that the thickness of the walls have no influence on their sha-dow because, geometrically, it is the inner side of each wall whichlimits the penetration of rays within the pergola.

To calculate the shadow due to the wall on the side of the sun(the other side makes no shadow on the item), the sketch repre-sented in Fig. 4 must be considered. In this Figure, a longitudinalsection of the wall and the relative orientation of the tunnel havebeen represented:

From this figure the extension of the wall shadow on theground, PW, is given by:

PW ¼sin /tan h

ðhþ tÞ ð4Þ

Thus, the shadow due to the wall on one item (beam + space be-tween two beams) is one rectangle whose surface, SW, is given by:

SW ¼sin /tan h

ðhþ tÞðwþ dÞ ð5Þ

The shadow of the horizontal beam can be easily obtained rotatingthe wall orientation 90�.

Fig. 4. Shadow from the lateral wall for any arbitrary surface-solar azimuth angle.where: u is the surface-solar azimuth angle (horizontal angle between the roadlane and one line comming from one point directly beneath the sun). PW is theextension of the shadow of the wall in the space between beams.

From Figs. 3 and 4 the areas of shadow from the beam, SSB, andthe bright zone, SBR, can be obtained as:

SSB ¼ LdarkðLB � PWÞ ¼cos /tan h

t þw� �

ðLB � PW Þ ð6Þ

SBR ¼ LbrightðLB � PWÞ ¼ d� cos /tan ht

� �ðLB � PWÞ ð7Þ

LB is the length of the beam, i.e. the distance between axes of thelateral walls and the factor (LB � PW) corrects the overlap of both,beam and wall shadows, by resting the overlapping zone, whoselength is PW.

The final expression of the light distribution under one item ofthe pergola, can be obtained from expressions ()()()(5)–(7) above.

The total shadowed surface, SST, can be obtained by summationof expressions (5) and (6):

SST ¼ SW þ SSB

¼ sin /tan h

ðhþ tÞðwþ dÞ þ cos /tan h

t þw� �

ðLB � PWÞ ð8Þ

Introducing Eq. (4) in (8) and rearranging terms, a more intuitive,expression is obtained:

SST ¼sin /tan h

ðhþ tÞ d� cos /tan h

t� �

þ LBcos /tan h

t þw� �

¼ PW Lbright þ LBLdark ð9Þ

Whereas the surface of the illuminated zone, SBR, is given by expres-sion (7).

Expressions (7)–(9) are completely general and the sum of both,shadowed and bright areas, give the total surface:SST + SBR = (w + d)LB.

2.1.3. Analysis of results2.1.3.1. Surface-solar azimuth angle u = 0�. Although this trivial casewas used to derive the general expressions, due to its importance itwill be analyzed now within the general framework:

SW ¼ 0

SSB ¼t

tan hþw

� �LB ð10Þ

SST ¼ SW þ SSB ¼ SSB

SBR ¼ d� ttan h

� �LB

If we take some typical values for the parameters in (10), we cananalyze the results above. In particular, a shell concrete structurewith thickness, t = 0.35 m, clearance, h = 5.5 m, length of beams,LB = 13 m and clear distance between beams, d = 1 m will be consid-ered (in Fig. 1.b the clear distance between beams is around1.35 m). In Fig. 5 the total shadow surface (m2) has been repre-sented for several values of the solar altitude angle, h, in functionof the width of the beam. Fig. 5 shows that, for u = 0�, the shadowsurface increases linearly with the width of the beam, for smaller wor larger solar altitude, the shadow surface becomes smaller. InFig. 5 all the lines have the same slope.

This case corresponds to the maximum extension of the brightzone, SBR because there is no shadow from the lateral walls. Eq. (10)show that the surface SBR is independent of w, so, it is constant foreach value of h.

2.1.3.2. Surface-solar azimuth angle u = 0�. In this case, Eqs. (5)–(8)can be expressed as:

Fig. 5. Evolution of the total shadow surface with the width of the beam for u = 0�,t = 0.35 m, h = 5.5 m, LB = 13 m and d = 1 m (see Figs. 2 and 3 for nomenclature).

A. Peña-García, L.M. Gil-Martín / Tunnelling and Underground Space Technology 35 (2013) 172–177 175

SW ¼hþ ttan h

ðwþ dÞ

SSB ¼ wLB ð11ÞSST ¼ SW þ SSB

SBR ¼ d LB �hþ ttan h

� �

Values of bright surface, SBR, for both trivial cases u = 0� and u = 90�have been represented in Fig. 6 in function of w for several values ofh. Values of constants: t, h, LB and d are the same as in the previousexample.

Fig. 6 shows that the bright surface for u = 90� is smaller thanfor u = 0�. This is due to the shadow of the lateral wall whenu – 0�. The difference between both cases decreases as the valueof the solar altitude angle, h, increases.

Obviously, for low values of the solar altitude, that is, for anglesh 6 arctan hþt

LB

� �Eqs. (5), (7), and (8), become SW = SST = LB(w + d)

and SBR = 0. That is, the shadow of the wall occupies the wholespace between beams. In this situation, the shadow of the beam,SSB = wLB, would lay beyond this surface. So, the extension of theshadow is maximum. This limiting value of h for the typical param-eters considered, t = 0.35 m, h = 5.5 m, LB = 13 m, is h = 24�, whichcan be easily reached even during the middle hours of the day dur-ing winter. For example, in Granada (South of Spain), h = 28� at14:00 on December 21st.

Fig. 6. Evolution of the illuminated surface with the width, w of the beam fort = 0.35 m, h = 5.5 m, LB = 13 m and d = 1 m with u = 0� and u = 0�.

2.1.4. Arbitrary surface-solar azimuth angle, u, and solar altitude, hFor t = 0.35 m, h = 5.5 m, LB = 13 m and d = 1 m, the total shadow

surface has been analyzed. In Figs. 7a and b, values of the shadowarea in function of h and u have been represented respectively. Gi-ven that SST + SBR = (w + d)LB, the bright area can also be obtainedfrom this Figure.

Fig. 7 shows that the shadow area under the pergola is mostinfluenced by the solar altitude angle, h, than by the surface-solarazimuth angle, u .

2.2. Mean illuminance and energy savings

Once the distribution of shadow and bright zones under onearbitrary pergola is known, it is possible to check whether the lightdistribution fulfills the relevant light transition requirements andhow much energy the extension of the tunnel threshold zone withpergolas can save.

The achievement of both targets must be expressed in terms ofone photometrical quantity, the illuminance E, which is the lumi-nous flux, /, (power emitted, transported or received by a lightwave) received by one surface, S, coming from every direction:

E ¼ /S

ð12Þ

The illuminance unit is the lux and the illuminance on a horizontalsurface is called horizontal illuminance.

The illuminance on the road surface has two components: a di-rect component (light coming from the sun directly) and a diffusecomponent (light coming from the scattering in the atmosphere,

Fig. 7. Shadow surface in function of, (a) the surface-solar azimuth, u and (b) solaraltitude, h, for t = 0.35 m, h = 5.5 m, LB = 13 m, w = 1 m and d = 1 m.

Fig. 8. Compromise between w and d for three different mean illuminances.

Table 1Comparison of the relative energy savings obtained with pergola and tensionstructures in the tunnel under consideration (Pegálajar–Jaén).

d (m) w (m) N lS = N(w + d) (m) Qt�SQt

(%)

Pergolas Tension structures

1 5.40 3 19.2 70 801 8.60 2 19.2 70 801 11.80 2 25.6 60 73

176 A. Peña-García, L.M. Gil-Martín / Tunnelling and Underground Space Technology 35 (2013) 172–177

which is responsible for the blue of the sky). In a sunny day with-out clouds, the direct and the diffuse components contribute to theglobal illuminance with around 80% and 20% respectively. In thiswork we will just consider the direct component because of theexistence of lateral walls and upper beams makes the diffuse com-ponent negligible.

Let there be a horizontal illuminance E on the bright zone of theroad under one pergola. According to the definition of illuminanceabove, the luminous flux on the illuminated part of the road is gi-ven by / = ESBR. Nevertheless, given that we are not considering thediffuse light that might arrive in the shadowed zones, this lumi-nous flux will be also the luminous flux on the whole stretch,whose area is ST = (w + d)LB .

So the mean illuminance on the road under one stretch of thepergola, Em, is given by:

Em ¼ ESBR

ST¼ Eðd tan h� t cos uÞðLB tan h� ðhþ tÞ sinuÞ

ðwþ dÞLB tan2 hð13Þ

The expression of Em will be the input in the ESTS equation (Peña-García et al., 2011), which allows the comparison of different struc-tures shifting the threshold zone of one road tunnel in terms of en-ergy savings from the electrical lighting. This equation is given by:

Q t�S

Q t¼ 1� S

lSlt

ð14Þ

where Qt�S is the energy consumed by the electrical lighting in thethreshold zone when shifted by any kind of structure. Qt is the elec-trical energy consumed by the electrical lighting in the samethreshold zone without shifting structure. S ¼ Em

ETh, is the average en-

ergy savings under the structure, that is, the ratio between themean illuminance on the road under the structure and the theoret-ical illuminance in the threshold zone. lS is the length of the struc-ture (the pergola in this case). lt is the length of the threshold zone.

It is important to remark that, although the ESTS equation wasfirst derived to evaluate tension strustures (Peña-García et al.,2011), it is completely general and can take account of any kindof structure shifting the threshold zone of one road tunnel what-ever its material, length, shape and orientation. In particular, it isused in this work to evaluate pergolas.

Thus, introducing Eq. (13) in the ESTS equation and consideringthat the length of a pergola is given by lS = N(w + d), where N is thenumber of items, the energy saving in the threshold zone is:

Q t�S

Q t¼ 1� E

ETh

ðd tan h� t cos uÞðLB tan h� ðhþ tÞ sin uÞLB tan2 h

Nlt

ð15Þ

Being ETh the required illuminance calculated for this tunnel usingthe L20 method (CIE Publ. 88, 2nd Ed., 2004; Blaser and Dudli, 1993).

Note that, for surface-solar azimuth angles u = 90� and solaraltitudes below h ¼ arctan hþt

LB

� �, then Qt�S

Qt¼ 1, that is, given that

the whole road is shadowed by the wall, no solar light reachesthe road and, thus, the energy consumed by the electrical lightingin the threshold zone when shifted by any kind of structure (per-gola in this case), is the same as if there were no pergola.

Besides the parameters concerning the amount of luminous fluxon one given surface, there are other issues related with the lightdistribution on such road. The main parameter taking account ofthe light distribution is the mean uniformity, defined as

Um ¼Emin

Emedð16Þ

If we consider that only the direct component of illuminance hasinfluence on the light distribution under one pergola, then, in theshadowed zone, Emin = 0 and hence, in pergolas, Um = 0. In road tun-nels, the mean uniformity must be above 0.4 (CIE Publ. 88, 2004) so,pergolas do not fulfill this important requirement.

2.2.1. Application to a real road tunnelLet there be a pergola with lS = 15 m shifting the threshold zone

of a road tunnel with an almost perfect South–North orientation(37�11́ N, 3�35́ W) located in Jaén (South of Spain) at the mostunfavourable solar conditions, that is June 21th at 14:00 h. Thechoice of this particular tunnel is due to the necessity of comparingthe results of pergolas with these of tension structures obtained(Peña-García et al., 2011).

The maximum allowed speed in this tunnel is 80 km/h. So, thelength of the threshold zone, lt, is 64 m and the value of the re-quired illuminance level in the first half of the threshold zone ob-tained using the L20 method (CIE Publ. 88, 2nd Ed., 2004) isETh = 8222 lux. The solar coordinates in the chosen date and timeare h = 75� 490 4800 � 76� and u = 164� 440 5200 � 165�.

Typical values of illuminance at the place where the tunnel islocated at 14:00 h in June 21st vary between 50,000 and100,000 lux. In this paper these extreme values and an intermedi-ate one, 75,000 lux, will be considered.

To obtain the optimal dimensions of the pergola from Eq. (13),the fixed parameters are t = 0.35 m, h = 5.5 m, LB = 13 m,ETh = Em = 8222 lux and E = 50,000, 75,000 and 100,000 lux. Thevalues of w and d that verify Eq. (13) have been represented inFig. 8.

Fig. 8 shows that to achieve the required illuminance level, ETh

required by the L20 method, for a fixed value of the distancebetween beams d = 1 m, the width of the shell of concrete, w, in-creases from 5.40 to 11.80 m if the iluminance on the bright zonegoes from 50,000 to 100,000 lux.

If the values of w represented in Fig. 8 are introduced in Eq. (15),the energy savings corresponding to one given pergola can be ob-tained. In order to compare with the other way to shift the thresh-old zone of a road tunnel studied by the authors in previous works(tension structures), a value as near as possible to lS = 15 m for thelength of the tension structure, which was proved to be reasonablein terms of mechanical stability (Peña-García et al., 2011), will beconsidered here.

A. Peña-García, L.M. Gil-Martín / Tunnelling and Underground Space Technology 35 (2013) 172–177 177

Given that one pergola cannot have any arbitrary length butonly lengths allowed by the sequence of its items, the smallest va-lue above 15 m has been considered. In order to make comparisonwith pergolas, feasible values of energy savings obtained in(Peña-García et al., 2011), by means of the ESTS equation, havebeen extrapolated. Table 1 shows a comparative of the results.

3. Conclusions

After consideration of the results above, several conclusions canbe deduced.

1. General expressions for the light distribution under pergolaswhich have not been reported in the literature up to now, havebeen presented. They are valid irrespective of solar position andtunnel orientation.

2. This light distribution depends on geometric factors such as thedimensions of the pergola and solar position.

3. For low solar angles, for which there is no direct light from thesun under the pergolas, any attempt of saving energy with thesestructures is useless.

4. The requirement of mean uniformity on the road is never ful-filled when pergolas are used because there is no significantlight in the shadowed zones relative to the sunlit zones.

5. Given that concrete is a suitable material, pergolas are a robustsolution and their maintenance is much more easier than themaintenance of other classical methods to extend the thresholdzone of road tunnels such as tension structures.

6. Pergolas are more effective than tension structures in terms ofenergy savings, but not in terms of uniformity when shiftingthe threshold zone of the road tunnel.

7. Intermediate solutions mixing the robustness of pergolas andthe uniformity of tension structures must be studied and con-sidered as serious candidates to achieve remarkable energy sav-ings in the electrical lighting of road tunnels.

Acknowledgement

This research work was carried out under the financial supportprovided by Spanish Ministry of Education and Science as part ofthe Research Project BIA 2007-62595.

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