Derivation of a traffic load model for the structural design of highway bridges in South Africa

Van der Spuy, Pierre Francois (2020-03)

Thesis (PhD)--Stellenbosch University, 2020.


ENGLISH ABSTRACT: This study sets out to derive a new traffic load model for the design of highway bridges in South Africa, with novel contributions to the field of bridge traffic loading. The current code for bridge design in South Africa, Technical Methods for Highways 7 (TMH7), was published in 1981 and was shown by previous studies, and by this study, to be deficient at characteristic level. This is especially true for shorter spans. TMH7 does not give any indication of the levels of safety used to calibrate the code and it is therefore not clear whether the code is still providing the necessary safety margins. Several studies, outlined in this document, show that the Uniformly Distributed Load (UDL) and knife edge loads for type NA loading should be increased. NA is referred to in TMH7 as normal loading. Further to this, the legal limit for Gross Vehicle Weight (GVW) was increased to 56 t and the vehicle characteristics on our roads have changed significantly since 1981. TMH7 loading is widely regarded in industry as too complex to apply and engineers have called for a simplified load model. A study of this nature is therefore well motivated to ensure safety of road users and to increase design efficiency for bridge engineers. Derivation of traffic load models requires measured traffic data. Previous studies showed that at least one year of Weigh in Motion (WIM) data is required to make accurate predictions of load effects at long return periods. Most WIM sensors in South Africa are located on National Route 3 (N3) and National Route 4 (N4) which are the major import and export routes in the country and which also carry the heaviest traffic. Stations along these routes are considered to be well calibrated. A WIM station along the N3 at Roosboom is chosen for this study, as seven years of traffic from 2010 to 2016 are available and the station is considered one of the heaviest loaded in the country. A comparison with other stations confirms this. In contrast with TMH7, it is typical in international codes to provide a load model for the slow, or heavy, lane which is reduced transversely by Multiple Lane Factors (MLFs). To align with international norms, a slow lane model is derived in this study based on the seven years of data at the Roosboom station as discussed previously. This measurement record includes the identification of 12.5 million heavy vehicles. The slow lane in the direction from Durban to Johannesburg is studied as vehicles in this direction are heavier than vehicles travelling from Johannesburg to Durban. Span lengths that are investigated range from 5 m to 50 m in increments of 5 m. The model derived herein is not valid for span lengths outside these bounds. The load effects (LEs) that are investigated are hogging on two span structures and sagging and shear on single span structures. For characteristic loads a 5 % probability of exceedance in a 50 year reference period is selected, similar to the Eurocode and the South African building design codes. This leads to a characteristic return period of 975 years. A censored GEV distribution is introduced to model the LEs. The shape factor is almost always negative, indicating an underlying Weibull distribution. This confirms the finding of other researchers that traffic LEs are bounded. The characteristic axle load amounts to 160 kN, which is used to calculate a UDL to replicate the characteristic load effects, resulting in a slow lane load model with a UDL of 13 kPa and a triple axle of 160 kN, spaced at 1.2 m. To distribute the slow lane model transversely, it is necessary to derive MLFs which take into account the reduced probability of simultaneous heavy vehicles in adjacent lanes. A novel method is presented in this work in which multiple lane WIM data is used to calculate MLF factors. A WIM station in Pretoria at Kilner Park measures four lanes of traffic at 0.01 s accuracy. This is the only station in South Africa measuring more than two lanes. By studying concurrent characteristic LEs in adjacent lanes it is possible to determine MLFs, first for two lanes loaded, then three lanes loaded and finally for four lanes loaded. The resulting MLFs are 1.0; 0.78; 0.07; 0.00. This implies that traffic from the fourth lane does not contribute to the characteristic global LEs. Vehicles that travel at speed, referred to as free flowing traffic, cause additional forces on bridge decks due to dynamic interaction between the vehicles and a bridge (Vehicle Bridge Interaction - VBI). To account for these increased loads, it is typical to multiply the static loads by a dynamic amplification factor (DAF) which is defined as the ratio between the total load effect to the static load effect. It is not the aim of this study to do an in depth investigation of dynamic amplification for South African bridges and it is therefore decided to adopt the values given in the ARCHES report D10, which are based on European traffic. It is reasonable to assume that South African roads conform to at least class B road profiles, implying a DAF of 1.4 up to 5 m span length and reducing linearly tot 1.2 at a 15 m span length. Seeing that South African vehicles are heavier than in Europe and have more axles, it is reasonable to assume that the DAF for South African traffic would be lower than for Europe. The ARCHES values can therefore be considered to be conservative in the absence of a comprehensive VBI study and measurements. To derive a design load model, it is necessary to establish Partial Factors (PFs) in accordance with structural reliability theory. Target 50 year β values are taken in accordance with the South African building design codes, which are based on extensive studies of historical practise in South Africa. For Ultimate Limit State (ULS), the 50 year β value is taken as 3.5 for a high consequence of failure and for Serviceability Limit State (SLS) as 1.5. The SLS value is in accordance with international standards. The reliability index is directly related to the probability of failure and hence it is possible to determine return periods of 435 years for SLS and 5040 years for ULS. For traffic loads, where the return periods for static loads are long, the probabilities of non-exceedance are close to 1.0 for characteristic, SLS and ULS. This leads to very small differences in load effects between characteristic and ULS return periods, especially when a censored GEV distribution is fitted which tends towards the Weibull distribution. When the LEs are near the bound of the fitted underlying Weibull distributions then there is hardly any uncertainty in the loading and all the uncertainty is located in the resistance. A new approach is introduced to address statistical uncertainty in fitting parameters. As seven years of data is used it is not surprising to find very small statistical uncertainty. Final partial factors are a function of reliability based partial factors, model uncertainty and statistical uncertainty. These amount to 1.18 for SLS and 1.33 for ULS. Chapter 8 presents a worked example for a typical bridge configuration for various widths and span lengths and considers both characteristic loads and ULS. The findings from this section are that the new model with DAF is always critical for all deck widths, for all span lengths and load effects when compared to normal loading in TMH7. The new model also exceeds LM1 in the Eurocode at characteristic and ULS levels. Although TMH7 abnormal and super loading is compared to the new model, it should be compared to a separate new model for abnormal loading which is outside the scope of this study.

AFRIKAANSE OPSOMMING: Hierdie studie beoog om 'n nuwe verkeersbelastingmodel vir die ontwerp van snelweg brûe in Suid-Afrika af te lei, met nuwe bydraes tot die veld van brugverkeersbelasting. Die huidige kode vir brugontwerp in Suid-Afrika, Technical Methods for Highways 7 (TMH7), is in 1981 gepubliseer en volgens vorige studies, en deur hierdie studie, skiet dit tekort op karakteristieke vlak. Dit geld veral vir korter spanlengtes. TMH7 gee geen aanduiding van die veiligheidsvlakke wat gebruik is om die kode te kalibreer nie en dit is dus nie duidelik of die kode steeds die nodige veiligheidsmarges bied nie. Verskeie studies, wat in hierdie dokument uiteengesit word, toon dat die verspreide belasting en mesrandlaste vir tipe NA belasting verhoog moet word. NA word in TMH7 verwys na as normale belasting. Verder is die wettige perk vir die bruto voertuiggewig (GVW) tot 56 ton verhoog en die voertuigkenmerke op ons paaie het sedert 1981 aansienlik verander. TMH7 belasting word in die industrie as te kompleks beskou en ingenieurs het 'n beroep gemaak op vereenvoudigde lasmodel. 'n Studie van hierdie aard is dus goed gemotiveer om die veiligheid van padgebruikers te verseker en om die ontwerpdoeltreffendheid vir brugingenieurs te verhoog. Afleiding van verkeersbelastingmodelle vereis gemete verkeersdata. Vorige studies het getoon dat ten minste een jaar data benodig word om akkurate voorspellings te maak van laseffekte by lang herhaalperiodes. Die meeste meetstasies in Suid-Afrika is op Nasionale Roete 3 (N3) en Nasionale Roete 4 (N4) geleë, wat die belangrikste invoer- en uitvoerroetes in die land is en wat ook die swaarste verkeer dra. Stasies langs hierdie roetes word as goed gekalibreer beskou. 'n Meetstasie langs die N3 by Roosboom word vir hierdie studie gekies, aangesien sewe jaar se verkeer van 2010 tot 2016 beskikbaar is en die stasie beskou word as een van die swaarste in die land. 'n Vergelyking met ander stasies bevestig dit. In teenstelling met TMH7, is dit in internasionale kodes tipies om 'n lasmodel te bied vir die stadige of swaar baan wat dwars verminder word deur Multiple Lane Factors (MLF's). Om in lyn te kom met internasionale norme, word 'n stadige baanmodel afgelei in hierdie studie gebaseer op die sewe jaar data van die Roosboom stasie, soos vroeër bespreek. Hierdie meetrekord bevat die identifisering van 12.5 miljoen swaar voertuie. Die stadige baan in die rigting van Durban na Johannesburg word bestudeer omdat voertuie in hierdie rigting swaarder is as voertuie wat van Johannesburg na Durban ry. Spanlengtes wat ondersoek word, strek van 5 m tot 50 m in stappe van 5 m. Die model wat hierin afgelei is, is nie geldig vir spanlengtes buite hierdie grense nie. Die laseffekte (LE's) wat ondersoek word, is negatiewe buiging op twee spanstrukture en positiewe buiging en skuif op enkelspanstrukture. Vir karakteristieke laste word 'n waarskynlikheid van oorskryding van 5% in 'n verwysingsperiode van 50 jaar gekies, soortgelyk aan die Eurocode en die Suid-Afrikaanse gebouontwerpkodes. Dit lei tot 'n karakteristieke herhaalperiode van 975 jaar. 'n Gesensureerde GEV-verspreiding word ingestel om die LEs te modelleer. Die vormfaktor is byna altyd negatief, wat 'n onderliggende Weibull verdeling aandui. Dit bevestig die bevindinge van ander navorsers dat LEs ‘n eindige bogrens het. Die karakteristieke aslas beloop 160 kN, wat gebruik word om 'n verspreide las te bereken om die kenmerkende laseffekte te produseer, wat lei tot 'n verwysingsmodel met 'n verspreide las van 13 kPa en 'n drievoudige as konfigurasie van 160 kN elk, met 'n afstand van 1.2 m tussenin. Om die stadige baanmodel dwars te versprei, is dit nodig om MLFs af te lei wat die verminderde waarskynlikheid van gelyktydige swaar voertuie in aangrensende bane in ag neem. In hierdie werk word 'n nuwe metode aangebied waarin gemete data in veelvuldige lane gebruik word om MLF faktore te bereken. ‘n Meetstasie in Pretoria by Kilner Park meet vier bane van die verkeer met 'n akkuraatheid van 0,01 s. Dit is die enigste stasie in Suid-Afrika wat meer as twee bane meet. Deur gelyktydige karakteristieke LE's in aangrensende bane te bestudeer, is dit moontlik om MLF's te bepaal, eerstens vir twee bane belaai, dan drie bane belaai en laastens vir vier bane belaai. Die resulterende MLFs is 1.0; 0.78; 0.07; 0.00. Dit impliseer dat verkeer vanaf die vierde baan nie bydra tot die karakteristieke globale LEs nie. Voertuie wat vinnig ry, ook vry vloeiende verkeer genoem, veroorsaak ekstra kragte op brugdekke as gevolg van dinamiese interaksie tussen die voertuie en 'n brug. Om rekenskap te gee van hierdie verhoogde kragte, is dit tipies om die statiese laste te vermenigvuldig met 'n dinamiese versterkingsfaktor (DAF) wat gedefinieer word as die verhouding tussen die totale laseffek en die statiese laseffek. Dit is nie die doel van hierdie studie om 'n diepgaande ondersoek na dinamiese versterking vir Suid-Afrikaanse brûe te doen nie, en daarom is dit besluit om die waardes in die ARCHES-verslag D10, gebaseer op Europese verkeer, aan te neem. Dit is redelik om aan te neem dat Suid-Afrikaanse paaie aan ten minste klas B ISO profiel voldoen, wat 'n DAF van 1.4 op ‘n 5 m spanlengte impliseer en lineêr verminder tot 1.2 op 'n spanlengte van 15 m. Aangesien Suid-Afrikaanse voertuie swaarder is as in Europa en meer asse het, is dit redelik om te aanvaar dat die DAF vir Suid-Afrikaanse verkeer laer sou wees as vir Europa. Die ARCHES-waardes kan dus beskou word as konserwatief in die afwesigheid van 'n uitgebreide studie en metings. Om 'n ontwerpbelastingsmodel af te lei, is dit noodsaaklik om parsiële faktore (PFs) af te lei in ooreenstemming met die betroubaarheidsteorie. Teikenwaardes vir 50 jaar β word geneem volgens die Suid-Afrikaanse bouontwerpkodes, wat gebaseer is op uitgebreide studies van historiese praktyk in Suid-Afrika. Vir Uiterste Limietstaat (ULS) word die 50 jaar β waarde as 3.5 beskou vir 'n hoë gevolg van faling en vir Dienslimietstaat (SLS) as 1.5. Die SLS waarde is in ooreenstemming met internasionale standaarde. Die betroubaarheidsindeks hou direk verband met die waarskynlikheid van faling en daarom is dit moontlik om herhaalperiodes van 435 jaar vir SLS en 5040 jaar vir ULS te bepaal. Vir verkeerslading, waar die herhaalperiodes vir belastings lank is, is die waarskynlikheid dat dit nie oorskry word nie, naby 1.0 vir karakteristiek, SLS en ULS. Dit lei tot baie klein verskille in LEs tussen karakteristiek, SLS en ULS herhaalperiodes, veral as 'n gesensureerde GEV-verdeling gebruik word wat neig na die Weibull verdeling. As die LEs naby die bogrens van die onderliggende Weibull verdeling is, is daar amper geen onsekerheid in die belasting nie, en is die onsekerheid is meestal in die weerstand geleë. ‘n Nuwe benadering word voorgestel om statistiese onsekerheid in verdelingsparameters aan te spreek. Aangesien daar sewe jaar data gebruik word, is dit nie verbasend om baie klein statistiese onsekerheid te vind nie. Finale parsiële faktore is 'n funksie van betroubaarheidsgebaseerde parsiële faktore, modelonsekerheid en statistiese onsekerheid. Dit beloop 1,18 vir SLS en 1,33 vir ULS. Hoofstuk 8 bied 'n uitgewerkte voorbeeld vir 'n tipiese brugkonfigurasie vir verskillende wydtes en spanlengtes en neem beide karakteristieke laste en ULS in ag. Die bevindinge uit hierdie afdeling is dat die nuwe model met DAF altyd oorheers vir alle dekwydtes, vir alle spanlengtes en LEs in vergelyking met normale belasting in TMH7. Die nuwe model oorskry ook LM1 in die Eurocode op karakteristieke en ULS vlakke. Alhoewel abnormale en superbelasting met die nuwe model vergelyk word, moet dit vergelyk word met 'n aparte nuwe model vir abnormale belasting wat buite die bestek van hierdie studie val.

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